{"http:\/\/dx.doi.org\/10.14288\/1.0072138":{"http:\/\/vivoweb.org\/ontology\/core#departmentOrSchool":[{"value":"Applied Science, Faculty of","type":"literal","lang":"en"}],"http:\/\/www.europeana.eu\/schemas\/edm\/dataProvider":[{"value":"DSpace","type":"literal","lang":"en"}],"https:\/\/open.library.ubc.ca\/terms#degreeCampus":[{"value":"UBCV","type":"literal","lang":"en"}],"http:\/\/purl.org\/dc\/terms\/creator":[{"value":"McIvor, Jacob Donald","type":"literal","lang":"en"}],"http:\/\/purl.org\/dc\/terms\/issued":[{"value":"2014-01-02T18:03:09Z","type":"literal","lang":"en"},{"value":"2013","type":"literal","lang":"en"}],"http:\/\/vivoweb.org\/ontology\/core#relatedDegree":[{"value":"Master of Applied Science - MASc","type":"literal","lang":"en"}],"https:\/\/open.library.ubc.ca\/terms#degreeGrantor":[{"value":"University of British Columbia","type":"literal","lang":"en"}],"http:\/\/purl.org\/dc\/terms\/description":[{"value":"The success of many orthopaedic procedures relies on the accurate and timely machining of bone, which can be difficult to achieve. Errors during machining can negatively affect implant placement or cause neurovascular injury. Bracing can improve the performance of both humans and machines during a variety of interactive tasks such as writing and grinding. The purpose of this thesis was to assess the feasibility of braced computer assisted orthopaedic surgery by testing the influence of bracing on the\nperformance of a surgically relevant task.\n\nWe developed a computer assisted orthopaedic surgery research system and experimental bracing devices for two surgical drilling tasks: navigated targeting and cortical drilling. The performance of each device was tested in a user study with 25 (13 male, 12 female) non-expert subjects.\n\nIn the navigated targeting task, subjects aligned a drill bit with a randomly generated trajectory while using a rigid brace to support the forearm and two different versions of guidance displays to provide visual feedback: a 2D axial display and a 3D-perspective display. Bracing reduced variation within- and between-trials, but did not affect final accuracy or targeting speed. There was a significant increase in final radial (170 %, 95% CI: 140\u2013210 %) and angular error (350 %, 95% CI: 300\u2013400 %) with the 3D-perspective display.\n\nIn the cortical drilling task, subjects attempted to minimize plunge of the drill bit after breakthrough. An experimental damper-based bracing device was designed by developing a numerical model to predict drill plunge, extending the model to predict the behaviour with bracing, and estimating an optimal brace damping range. Subjects drilled through oak workpieces using a standard high speed steel drill bit and a brad point drill bit at 4 damping levels. At a level of 10Ns\/mm, there was a significant decrease in plunge depth of 74% (95% CI: 71\u201376 %) and no significant difference in drilling duration.\n\nThis thesis provides experimental evidence that a simple bracing strategy can improve the performance of a clinically relevant task; Applying bracing to computer assisted orthopaedic surgery may be an effective way to improve performance and warrants further investigation.","type":"literal","lang":"en"}],"http:\/\/www.europeana.eu\/schemas\/edm\/aggregatedCHO":[{"value":"https:\/\/circle.library.ubc.ca\/rest\/handle\/2429\/45698?expand=metadata","type":"literal","lang":"en"}],"http:\/\/www.w3.org\/2009\/08\/skos-reference\/skos.html#note":[{"value":"Effect of Bracing and Navigation Display Design on Targeting Accuracyand Plunge Depth During Surgical DrillingbyJacob Donald McIvorB.Sc., Mechanical Engineering, The University of Alberta, 2007A THESIS SUBMITTED IN PARTIAL FULFILLMENTOF THE REQUIREMENTS FOR THE DEGREE OFMASTER OF APPLIED SCIENCEinTHE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES(Biomedical Engineering)The University Of British Columbia(Vancouver)December 2013? Jacob Donald McIvor, 2013AbstractThe success of many orthopaedic procedures relies on the accurate and timely machining of bone, whichcan be difficult to achieve. Errors during machining can negatively affect implant placement or causeneurovascular injury. Bracing can improve the performance of both humans and machines during avariety of interactive tasks such as writing and grinding. The purpose of this thesis was to assess thefeasibility of braced computer assisted orthopaedic surgery by testing the influence of bracing on theperformance of a surgically relevant task.We developed a computer assisted orthopaedic surgery research system and experimental bracingdevices for two surgical drilling tasks: navigated targeting and cortical drilling. The performance ofeach device was tested in a user study with 25 (13 male, 12 female) non-expert subjects.In the navigated targeting task, subjects aligned a drill bit with a randomly generated trajectorywhile using a rigid brace to support the forearm and two different versions of guidance displays toprovide visual feedback: a 2D axial display and a 3D-perspective display. Bracing reduced variationwithin- and between-trials, but did not affect final accuracy or targeting speed. There was a significantincrease in final radial (170 %, 95 % CI: 140?210 %) and angular error (350 %, 95 % CI: 300?400 %)with the 3D-perspective display.In the cortical drilling task, subjects attempted to minimize plunge of the drill bit after breakthrough.An experimental damper-based bracing device was designed by developing a numerical model to predictdrill plunge, extending the model to predict the behaviour with bracing, and estimating an optimal bracedamping range. Subjects drilled through oak workpieces using a standard high speed steel drill bit anda brad point drill bit at 4 damping levels. At a level of 10 N s\/mm, there was a significant decrease inplunge depth of 74 % (95 % CI: 71?76 %) and no significant difference in drilling duration.This thesis provides experimental evidence that a simple bracing strategy can improve the perfor-mance of a clinically relevant task; Applying bracing to computer assisted orthopaedic surgery may bean effective way to improve performance and warrants further investigation.iiPrefaceThis thesis is an original intellectual product of the author, J. McIvor. Antony Hodgson provided guid-ance on methodology and provided revisions for the writing of this thesis. James Boak also assistedwith proofreading.The user studies described in Chapter 3 and Chapter 5 were approved by the University of BritishColumbia Behavioural Research Ethics Board (Certificate H09-01080).Camila Casquihilo provided advice on the statistical analysis employed to analyse the data in Chap-ter 3 and Chapter 5 as part of STAT 551: Statistical Consulting. Ms. Casquihilo supported our selectionof a Linear Mixed Effects model and provided guidance on how to create an appropriate model, performmodel diagnostics, and interpret the results.The calibration algorithm used to determine the primary axis of the drill bit was developed by theauthor as part of APSC 530 (Appendix F). This work was based on a similar algorithm developed byAmber Simpson Simpson [2010: Chapter 4].Sean Gillen created two original illustrations (Figure 1.4) based on images from Hoffman [2008]and Jones [2011].iiiTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiiList of Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xixList of Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxiiDedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxiii1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1.1 Challenges in Orthopaedic Surgery . . . . . . . . . . . . . . . . . . . . . . 31.1.2 Limitations to Human Performance . . . . . . . . . . . . . . . . . . . . . . 61.1.3 Humans Use Bracing to Improve Performance . . . . . . . . . . . . . . . . 71.1.4 Applying Bracing To Robotics . . . . . . . . . . . . . . . . . . . . . . . . . 101.1.5 Clinical Bracing Research . . . . . . . . . . . . . . . . . . . . . . . . . . . 131.1.6 Applying Bracing to CAOS . . . . . . . . . . . . . . . . . . . . . . . . . . 171.2 Research Goals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181.3 Selection of Surgically Relevant Task . . . . . . . . . . . . . . . . . . . . . . . . . 181.3.1 Surgical Drilling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181.3.2 Navigated Drill Targeting . . . . . . . . . . . . . . . . . . . . . . . . . . . 201.3.3 Cortical Drilling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231.4 Hypotheses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261.5 Thesis Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27iv2 Experimental Computer Assisted Surgery System Design . . . . . . . . . . . . . . . . 282.1 Braced Computer Assisted Orthopaedic Surgery (CAOS) Research System . . . . . . 282.2 System Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292.3 Tracked Drill . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292.4 Workpiece Holder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302.5 Tool, Anatomy, and Target Tracking . . . . . . . . . . . . . . . . . . . . . . . . . . 312.5.1 Rigid Body Tracking Notation . . . . . . . . . . . . . . . . . . . . . . . . . 312.5.2 Transform: Drill to tip, T DRILLT IP . . . . . . . . . . . . . . . . . . . . . . . . . 332.5.3 Transform: Anatomy to Target, T DRFGOAL . . . . . . . . . . . . . . . . . . . . . 342.5.4 Transform: Goal to Tip, T GOALT IP . . . . . . . . . . . . . . . . . . . . . . . . . 352.5.5 Transform: View to Goal, T GOALV IEW . . . . . . . . . . . . . . . . . . . . . . . 352.6 Graphical User Interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352.6.1 Guidance Display . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352.6.2 2D Axial Guidance Display . . . . . . . . . . . . . . . . . . . . . . . . . . 362.6.3 3D Box Guidance Display . . . . . . . . . . . . . . . . . . . . . . . . . . . 362.6.4 Effective Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362.6.5 User Input . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392.7 Measuring Drill Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 402.8 Measuring Drill Current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 402.9 User Study Management . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 422.10 System Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 422.11 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433 Navigated Targeting User Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473.1 Hypotheses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473.2 Materials and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483.2.1 Study Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483.2.2 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483.2.3 Experimental Task . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 513.2.4 Subjects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 513.2.5 Conducting the Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . 523.2.6 Acquiring and Processing the Data . . . . . . . . . . . . . . . . . . . . . . . 533.2.7 Statistical Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 573.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 593.3.1 Typical Trial . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 593.3.2 Typical Block . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 603.3.3 Typical Subject . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 613.3.4 All Subjects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 713.3.5 Statistical Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 843.3.6 Observations and Subject Feedback . . . . . . . . . . . . . . . . . . . . . . 91v3.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 933.4.1 Influence of Static Forearm Brace . . . . . . . . . . . . . . . . . . . . . . . 933.4.2 Influence of Guidance Display Type . . . . . . . . . . . . . . . . . . . . . . 953.4.3 Participant Feedback . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 973.4.4 Sources of Uncertainty and Variation . . . . . . . . . . . . . . . . . . . . . 973.4.5 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 993.4.6 Clinical Relevance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1003.4.7 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1023.4.8 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1033.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1034 Damper-Based Brace Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1044.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1044.2 Materials and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1054.2.1 Design Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1064.2.2 Pilot Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1064.2.3 Model Development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1074.2.4 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1204.2.5 Experimental Brace Implementation . . . . . . . . . . . . . . . . . . . . . . 1214.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1234.3.1 Pilot Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1234.3.2 Freehand Plunge Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . 1264.3.3 Braced Cortical Drilling Simulation . . . . . . . . . . . . . . . . . . . . . . 1324.3.4 Optimal Brace Damping . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1354.3.5 Brace Damping Level Calibration . . . . . . . . . . . . . . . . . . . . . . . 1354.3.6 Simulated Experimental Brace Performance . . . . . . . . . . . . . . . . . . 1394.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1424.4.1 Modelling Assumptions and Limitations . . . . . . . . . . . . . . . . . . . . 1424.4.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1464.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1475 Plunge Depth User Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1495.1 Hypotheses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1495.2 Materials and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1505.2.1 Study Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1505.2.2 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1505.2.3 Experimental Drilling Task . . . . . . . . . . . . . . . . . . . . . . . . . . . 1535.2.4 Subjects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1535.2.5 Conducting the Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . 1545.2.6 Acquiring and Processing the Data . . . . . . . . . . . . . . . . . . . . . . . 155vi5.2.7 Model Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1575.2.8 Statistical Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1575.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1615.3.1 Typical Trial . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1615.3.2 Typical Condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1625.3.3 Typical Subject . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1625.3.4 All Subjects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1685.3.5 Comparison to Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . 1685.3.6 Atypical and Notable Trials . . . . . . . . . . . . . . . . . . . . . . . . . . 1725.3.7 Statistical Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1805.3.8 Observations and Subject Feedback . . . . . . . . . . . . . . . . . . . . . . 1835.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1845.4.1 Influence of Brace Damping Level . . . . . . . . . . . . . . . . . . . . . . . 1855.4.2 Influence of Drill Bit Type . . . . . . . . . . . . . . . . . . . . . . . . . . . 1885.4.3 Comparison to Cortical Drilling Model . . . . . . . . . . . . . . . . . . . . 1885.4.4 Comparison to Other Work . . . . . . . . . . . . . . . . . . . . . . . . . . . 1895.4.5 Sources of Variation and Uncertainty . . . . . . . . . . . . . . . . . . . . . 1935.4.6 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1945.4.7 Clinical Relevance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1965.4.8 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1985.4.9 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1995.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2006 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2016.1 Research Goals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2016.2 Experimental Computer Assisted Surgery System . . . . . . . . . . . . . . . . . . . 2016.2.1 Contributions and Key Findings . . . . . . . . . . . . . . . . . . . . . . . . 2026.2.2 Strengths and Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . 2026.2.3 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2036.3 Navigated Drill Targeting User Study . . . . . . . . . . . . . . . . . . . . . . . . . 2036.3.1 Hypotheses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2036.3.2 Contributions and Findings . . . . . . . . . . . . . . . . . . . . . . . . . . . 2046.3.3 Strengths and Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . 2056.3.4 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2056.3.5 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2056.4 Modelling Manual Cortical Drilling . . . . . . . . . . . . . . . . . . . . . . . . . . 2066.4.1 Contributions and Key Findings . . . . . . . . . . . . . . . . . . . . . . . . 2066.4.2 Strengths and Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . 2066.4.3 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2076.4.4 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207vii6.5 Cortical Drilling User Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2076.5.1 Hypotheses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2076.5.2 Contributions and Key Findings . . . . . . . . . . . . . . . . . . . . . . . . 2076.5.3 Strengths and Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . 2086.5.4 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2096.5.5 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2096.6 Overall Implications and Significance . . . . . . . . . . . . . . . . . . . . . . . . . 2096.6.1 Recommendations for Practice . . . . . . . . . . . . . . . . . . . . . . . . . 2106.6.2 Recommendations for Future Research . . . . . . . . . . . . . . . . . . . . 2106.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212A Detailed Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222A.1 Radial Axis Error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222A.2 Angular Targeting Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223A.3 Empirical Drilling Parameter Estimation . . . . . . . . . . . . . . . . . . . . . . . . 224A.4 Effective Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224B Ethics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229B.1 Ethics Consent Form . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229B.2 Debrief Questionnaire . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233C Equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235C.1 Optical Tracker . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235C.1.1 Working Volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235C.2 Marker Coordinate Frames . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237C.3 Targeting Display Box . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237C.4 Experimental Damper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237C.5 Workpiece Holder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238C.5.1 Flexure Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238C.5.2 Flexure Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240D Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246D.1 Subjects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246D.2 Missing\/Problem Trials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246D.2.1 Problem Targeting Trials . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246D.2.2 Problem Plunge Trials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246D.3 Plunge Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246D.4 Targeting Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255viiiE Statistical Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266E.1 Modelling Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266E.2 Plunge Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269E.2.1 Drilling Duration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269E.2.2 Drill Plunge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272E.2.3 Mean Drilling Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276E.2.4 Prebreakthrough Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280E.2.5 Estimated Human Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285E.3 Targeting Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292E.3.1 Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292E.3.2 Accuracy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303E.3.3 Variability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313F UKF Drill Axis Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 330F.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 330F.1.1 Project Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332F.1.2 Drill Calibration Requirements . . . . . . . . . . . . . . . . . . . . . . . . . 332F.1.3 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333F.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333F.2.1 Computer-Assisted Surgery . . . . . . . . . . . . . . . . . . . . . . . . . . 333F.2.2 Computer Assisted Drilling . . . . . . . . . . . . . . . . . . . . . . . . . . 340F.2.3 Kalman Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345F.2.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 346F.3 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 346F.3.1 Calibration Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 346F.3.2 UKF Axis Calibration Algorithm . . . . . . . . . . . . . . . . . . . . . . . 348F.3.3 Testing, Validation and Comparison . . . . . . . . . . . . . . . . . . . . . . 353F.3.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354F.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354F.4.1 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354F.4.2 Filter Tuning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355F.4.3 Testing and Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . 356F.4.4 Experimental Calibration Data . . . . . . . . . . . . . . . . . . . . . . . . . 358F.4.5 Least-Squared Circle Fitting Comparison . . . . . . . . . . . . . . . . . . . 364F.4.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364F.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364F.5.1 Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364F.5.2 Comparison to Other Methods . . . . . . . . . . . . . . . . . . . . . . . . . 366F.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367F.6.1 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367ixF.6.2 Strengths and Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . 368F.6.3 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 368F.6.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 369F.7 Supporting Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 370F.7.1 Experimental Drill . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 370F.8 Code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 371F.8.1 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 371F.8.2 UKF Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 372xList of TablesTable 1.1 Goals for Optimal Surgical Outcome . . . . . . . . . . . . . . . . . . . . . . . . 5Table 1.2 Examples of Tasks Where Bracing is Used . . . . . . . . . . . . . . . . . . . . . 7Table 1.3 Tools Commonly Used in Orthopaedics . . . . . . . . . . . . . . . . . . . . . . . 19Table 1.4 Surgical Drilling Tasks That May Benefit From Bracing . . . . . . . . . . . . . . 20Table 2.1 Effective Guidance Display Targeting Resolution . . . . . . . . . . . . . . . . . . 39Table 2.2 Goal to Tip Tracking Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45Table 3.1 Example Targeting Testing Schedule . . . . . . . . . . . . . . . . . . . . . . . . 52Table 3.2 Navigated Targeting Data Structure . . . . . . . . . . . . . . . . . . . . . . . . . 59Table 3.3 Uncertainty of the fixed effects conditional on the estimates of the random-effectvariances and empirical best linear unbiased prediction (EBLUP) modes . . . . . . 89Table 3.4 Debrief Questionnaire Display Preference . . . . . . . . . . . . . . . . . . . . . 92Table 4.1 Braced Cortical Drilling Design . . . . . . . . . . . . . . . . . . . . . . . . . . . 106Table 4.2 Experimental Brace Design Requirements . . . . . . . . . . . . . . . . . . . . . 107Table 4.3 Human Arm Anthropometric Data . . . . . . . . . . . . . . . . . . . . . . . . . 112Table 4.4 Empirical Drilling Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117Table 4.5 Drilling Model Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120Table 4.6 Pilot Testing Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124Table 4.7 Airpot? Damping Levels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138Table 5.1 Approximate Workpiece Material Properties . . . . . . . . . . . . . . . . . . . . 153Table 5.2 Example Testing Schedule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154Table 5.3 Drill Plunge Data Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160Table 5.4 Debrief Questionnaire Bracing Summary . . . . . . . . . . . . . . . . . . . . . . 184Table 5.5 Drill Plunge Study Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . 192Table 5.6 Comparison Between Simulated and Clinical Cortical Drilling Task . . . . . . . . 196Table B.1 Debrief Questionnaire Summary . . . . . . . . . . . . . . . . . . . . . . . . . . 234Table C.1 Definition of Optical Marker Local Coordinate Systems . . . . . . . . . . . . . . 237Table C.2 Flexure Properties: 17-7 PH Stainless Steel . . . . . . . . . . . . . . . . . . . . . 240xiTable D.1 Subject Info and Task Schedule . . . . . . . . . . . . . . . . . . . . . . . . . . . 247Table D.2 Problem Targeting Trials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248Table D.3 Removed Plunge Trials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249Table D.4 Problem Trials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250Table F.1 Example Computer Assisted Surgery Procedures . . . . . . . . . . . . . . . . . . 334Table F.2 Commercially Available CAOS Systems . . . . . . . . . . . . . . . . . . . . . . . 335Table F.3 3D Sphere Fitting Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344Table F.4 3D Circle Fitting Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344Table F.5 Filter Tuning Parameter Bounds . . . . . . . . . . . . . . . . . . . . . . . . . . . 353Table F.6 Optimized Tuning Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 360Table F.7 Simulated Data Ground Truth Difference . . . . . . . . . . . . . . . . . . . . . . 360Table F.8 Experimental Calibration Algorithm Comparison . . . . . . . . . . . . . . . . . . 364Table F.9 Drill Marker Positions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 370xiiList of FiguresFigure 1.1 Braced and Unbraced Writing . . . . . . . . . . . . . . . . . . . . . . . . . . . 3Figure 1.2 Time-Error Tradeoff . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4Figure 1.3 Human Bracing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7Figure 1.4 Internal and External Bracing . . . . . . . . . . . . . . . . . . . . . . . . . . . 8Figure 1.5 Human Bracing Study Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9Figure 1.6 Active Handrest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10Figure 1.7 Tool Guide on Robotic Arm . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11Figure 1.8 Braced Automated Drilling System . . . . . . . . . . . . . . . . . . . . . . . . 12Figure 1.9 Real and Virtual Bracing for a Coarse-Fine Manipulator . . . . . . . . . . . . . 13Figure 1.10 Position Repeatability of Braced Robot and Human . . . . . . . . . . . . . . . . 14Figure 1.11 Arm Rests for Microsurgery . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15Figure 1.12 Automatically Adjusting Arm Rest . . . . . . . . . . . . . . . . . . . . . . . . . 16Figure 1.13 Braced Dentistry: Introral Fulcrum During Scaling . . . . . . . . . . . . . . . . 17Figure 1.14 Targeting Error Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21Figure 1.15 BrainLab? Navigation Display . . . . . . . . . . . . . . . . . . . . . . . . . . . 22Figure 1.16 Fracture Repair . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23Figure 1.17 Cortical Drill Plunge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24Figure 1.18 Alajmo Drill Plunge Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25Figure 1.19 Clement Drill Plunge Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26Figure 2.1 CAOS Research System Overview . . . . . . . . . . . . . . . . . . . . . . . . . 30Figure 2.2 Optically Tracked Drill . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31Figure 2.3 Workpiece Holder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32Figure 2.4 CAOS Research System Scene Graph . . . . . . . . . . . . . . . . . . . . . . . 33Figure 2.5 Drill Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34Figure 2.6 2D Axial Perspective Guidance Display . . . . . . . . . . . . . . . . . . . . . . 37Figure 2.7 3D Perspective Box Guidance Display . . . . . . . . . . . . . . . . . . . . . . . 38Figure 2.8 Guidance Display Magnification . . . . . . . . . . . . . . . . . . . . . . . . . . 39Figure 2.9 Force Sensor Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40Figure 2.10 Raw and Filtered Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41Figure 2.11 Raw and Filtered Current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41xiiiFigure 2.12 Drill Current Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42Figure 2.13 Raw and Filtered Tip Position . . . . . . . . . . . . . . . . . . . . . . . . . . . 44Figure 2.14 Breakthrough Plane Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . 45Figure 3.1 Targeting User Study Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48Figure 3.2 Drill Targeting Task Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49Figure 3.3 Forearm Brace . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50Figure 3.4 Goal Trajectory Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51Figure 3.5 Subject Posture for Drill Targeting Study . . . . . . . . . . . . . . . . . . . . . 52Figure 3.6 Tip and Tail Error Metrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55Figure 3.7 Combined Error Metric . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56Figure 3.8 Targeting Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58Figure 3.9 Typical Targeting Trial . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60Figure 3.10 Final Error - Typical Trial . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61Figure 3.11 Typical Block . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62Figure 3.12 Targeting Time - Typical Block . . . . . . . . . . . . . . . . . . . . . . . . . . 63Figure 3.13 Final Targeting - Typical Block . . . . . . . . . . . . . . . . . . . . . . . . . . . 63Figure 3.14 Final Error - Typical Block . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64Figure 3.15 Tip Error - Typical Subject . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65Figure 3.16 Tail Error - Typical Subject . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66Figure 3.17 Tip and Tail Error - Typical Subject . . . . . . . . . . . . . . . . . . . . . . . . 67Figure 3.18 Targeting Time - Typical Subject by Test . . . . . . . . . . . . . . . . . . . . . 68Figure 3.19 Targeting Error - Typical Subject by Test . . . . . . . . . . . . . . . . . . . . . 69Figure 3.20 Target Stability - Typical Subject . . . . . . . . . . . . . . . . . . . . . . . . . . 69Figure 3.21 Speed-accuracy Trade-off - Typical Subject . . . . . . . . . . . . . . . . . . . . 70Figure 3.22 Tip Error - Study Time-Average . . . . . . . . . . . . . . . . . . . . . . . . . . 72Figure 3.23 Tail Error - Study Time-Average . . . . . . . . . . . . . . . . . . . . . . . . . . 73Figure 3.24 Targeting Error - Study Time-average . . . . . . . . . . . . . . . . . . . . . . . 74Figure 3.25 Gross Positioning Time - All Trials by Block . . . . . . . . . . . . . . . . . . . 75Figure 3.26 Gross Positioning Time - By Subject . . . . . . . . . . . . . . . . . . . . . . . . 75Figure 3.27 Fine Positioning Time - All Trials by Block . . . . . . . . . . . . . . . . . . . . 76Figure 3.28 Tip and Tail Targeting Time - All Trials by Block . . . . . . . . . . . . . . . . . 77Figure 3.29 Tip Targeting Error Components - All Trials by Block . . . . . . . . . . . . . . 78Figure 3.30 Tail Targeting Error Components - All Trials by Block . . . . . . . . . . . . . . 79Figure 3.31 Tip and Tail Targeting Error - All Trials by Block . . . . . . . . . . . . . . . . . 80Figure 3.32 Total Targeting Error - All Trials by Block . . . . . . . . . . . . . . . . . . . . . 81Figure 3.33 Tip Targeting Variability - All Trials . . . . . . . . . . . . . . . . . . . . . . . . 82Figure 3.34 Tail Targeting Variability - All Trials . . . . . . . . . . . . . . . . . . . . . . . . 83Figure 3.35 Targeting Time - Expected Value . . . . . . . . . . . . . . . . . . . . . . . . . . 85Figure 3.36 Targeting Error - Expected Value . . . . . . . . . . . . . . . . . . . . . . . . . . 87xivFigure 3.37 Final Targeting Error - Expected Value . . . . . . . . . . . . . . . . . . . . . . . 89Figure 3.38 Final Targeting Variability - Fixed Effects . . . . . . . . . . . . . . . . . . . . . 91Figure 4.1 Cortical Drilling Modelling Approach . . . . . . . . . . . . . . . . . . . . . . . 109Figure 4.2 Human Kinematic Chain Model . . . . . . . . . . . . . . . . . . . . . . . . . . 111Figure 4.3 Two-link Arm Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111Figure 4.4 Effective 1 DOF Arm-Drill Impedance . . . . . . . . . . . . . . . . . . . . . . . 112Figure 4.5 Effective Human Impedance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115Figure 4.6 Human Reaction Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116Figure 4.7 Experimental Damper-based Brace . . . . . . . . . . . . . . . . . . . . . . . . . 122Figure 4.8 Bovine Femur Drill Plunge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124Figure 4.9 Typical Plunge Trial . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125Figure 4.10 Pilot Plunge Trials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125Figure 4.11 Typical Freehand Plunge Simulation . . . . . . . . . . . . . . . . . . . . . . . . 126Figure 4.12 Simulated Freehand Drilling Trajectory With Increasing Force . . . . . . . . . . 127Figure 4.13 Predicted Drilling Duration With Increasing Force . . . . . . . . . . . . . . . . 127Figure 4.14 Simulated Freehand Drill Plunge Trajectory With Increasing Force . . . . . . . . 128Figure 4.15 Predicted Freehand Drill Plunge With Increasing Force . . . . . . . . . . . . . . 128Figure 4.16 Predicted Freehand Drilling Duration and Drill Plunge . . . . . . . . . . . . . . 129Figure 4.17 Comparison of Simulated and Experimental Drilling . . . . . . . . . . . . . . . 130Figure 4.18 Comparison of Simulated and Experimental Drilling Duration . . . . . . . . . . 130Figure 4.19 Model Drill Plunge Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . 131Figure 4.20 Typical Braced Plunge Simulation . . . . . . . . . . . . . . . . . . . . . . . . . 132Figure 4.21 Simulated Drilling Duration with Increased Brace Damping . . . . . . . . . . . 133Figure 4.22 Simulated Braced Drilling Duration . . . . . . . . . . . . . . . . . . . . . . . . 133Figure 4.23 Simulated Drill Plunge with Increased Brace Damping . . . . . . . . . . . . . . 134Figure 4.24 Simulated Braced Drill Plunge . . . . . . . . . . . . . . . . . . . . . . . . . . . 134Figure 4.25 Simulated Braced Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135Figure 4.26 Optimal Damping at 30 N . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136Figure 4.27 Optimal Brace Damping Levels . . . . . . . . . . . . . . . . . . . . . . . . . . 137Figure 4.28 Airpot? Drop Trials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137Figure 4.29 Simulated Brace Performance in Oak . . . . . . . . . . . . . . . . . . . . . . . 139Figure 4.30 Simulated Brace Performance in Human Femur . . . . . . . . . . . . . . . . . . 141Figure 4.31 Example of Corkscrew Behaviour . . . . . . . . . . . . . . . . . . . . . . . . . 144Figure 4.32 Pilot Corkscrew . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145Figure 4.33 Model Freehand Learned Stiffness . . . . . . . . . . . . . . . . . . . . . . . . . 147Figure 5.1 Simulated Cortical Drilling Study Design . . . . . . . . . . . . . . . . . . . . . 150Figure 5.2 Plunge Study Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . 151Figure 5.3 Drill Bits Used in Plunge Study . . . . . . . . . . . . . . . . . . . . . . . . . . 152xvFigure 5.4 Plunge Study Workpiece . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154Figure 5.5 Subject Posture for Cortical Drilling Study . . . . . . . . . . . . . . . . . . . . 155Figure 5.6 Drill Plunge Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157Figure 5.7 Drill Duration Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158Figure 5.8 Secondary Drill Plunge Metric Processing . . . . . . . . . . . . . . . . . . . . . 159Figure 5.9 Typical Drilling Trial . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161Figure 5.10 Drilling Trial Set Variation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162Figure 5.11 Typical Set of Drilling Trials . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163Figure 5.12 Typical Subject Test Set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164Figure 5.13 Typical Subject Box Plot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165Figure 5.14 Typical Subject - Drilling Duration and Plunge . . . . . . . . . . . . . . . . . . 166Figure 5.15 Typical Subject - Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167Figure 5.16 Drill Plunge Performance Metrics . . . . . . . . . . . . . . . . . . . . . . . . . 169Figure 5.17 Plunge Study Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170Figure 5.18 Drilling Velocity and Estimated Human Force . . . . . . . . . . . . . . . . . . . 171Figure 5.19 Study Drill Plunge Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172Figure 5.20 Drilling Duration Model Comparison . . . . . . . . . . . . . . . . . . . . . . . 173Figure 5.21 Drill Plunge Model Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . 174Figure 5.22 Drill Plunge Modelling Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . 175Figure 5.23 Atypical Trial - Incomplete . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176Figure 5.24 Atypical Trial - Re-drill . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177Figure 5.25 Atypical Trial - Delayed Breakthrough Detection . . . . . . . . . . . . . . . . . 177Figure 5.26 Atypical Trial - Excessive Plunge . . . . . . . . . . . . . . . . . . . . . . . . . 178Figure 5.27 Atypical Trial - Drill bit-Workpiece Interaction . . . . . . . . . . . . . . . . . . 179Figure 5.28 Drilling Duration - Conditional Expectation . . . . . . . . . . . . . . . . . . . . 180Figure 5.29 Drill Plunge Depth - Conditional Expectation . . . . . . . . . . . . . . . . . . . 181Figure 5.30 Mean Drilling Force - Conditional Expectation . . . . . . . . . . . . . . . . . . 182Figure 5.31 Prebreakthrough Force - Conditional Expectation . . . . . . . . . . . . . . . . . 183Figure 5.32 Experimental Drill Plunge - Praamsma 2008 . . . . . . . . . . . . . . . . . . . 185Figure 5.33 Free Body Diagram of Drill During Approach . . . . . . . . . . . . . . . . . . . 188Figure 5.34 Experimental Drill Plunge - Khokhotva 2009 . . . . . . . . . . . . . . . . . . . 190Figure A.1 Shortest Line Between Two Lines in 3D . . . . . . . . . . . . . . . . . . . . . . 222Figure A.2 Angular Targeting Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225Figure A.3 Typical Drilling Rate Trial . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226Figure A.4 Experimental Drilling Resistance . . . . . . . . . . . . . . . . . . . . . . . . . 226Figure A.5 Experimental Drilling Resistance . . . . . . . . . . . . . . . . . . . . . . . . . 227Figure A.6 OpenGL Perspective Viewing Frustum . . . . . . . . . . . . . . . . . . . . . . . 227Figure C.1 NDI Hybrid Polaris? Working Volume . . . . . . . . . . . . . . . . . . . . . . 236xviFigure C.2 Drill Marker Coordinate System . . . . . . . . . . . . . . . . . . . . . . . . . . 241Figure C.3 DRF Coordinate System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241Figure C.4 SRF Coordinate System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242Figure C.5 SRF Coordinate System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242Figure C.6 Guidance Display Targeting Box . . . . . . . . . . . . . . . . . . . . . . . . . . 243Figure C.7 Airpot? Schematic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244Figure C.8 Cantilever Beam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244Figure C.9 Workpiece Holder Flexure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245Figure D.1 Problem Targeting Trials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248Figure D.2 Problem Plunge Trials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249Figure D.3 Drilling Duration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251Figure D.4 Drill Plunge Depth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252Figure D.5 Mean Drilling Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253Figure D.6 Estimated Human Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254Figure D.7 Gross Targeting Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255Figure D.8 Fine Targeting Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256Figure D.9 Tip Targeting Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257Figure D.10 Angular Targeting Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258Figure D.11 Tip Targeting Error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259Figure D.12 Angular Targeting Error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260Figure D.13 Total Targeting Error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261Figure D.14 Horizontal Tip Variation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262Figure D.15 Vertical Tip Variation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263Figure D.16 Horizontal Tail Variation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264Figure D.17 Vertical Tail Variation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265Figure E.1 LME Model Diagnostics - Drilling Force . . . . . . . . . . . . . . . . . . . . . 273Figure E.2 LME Model Diagnostics - Drill Plunge Depth . . . . . . . . . . . . . . . . . . . 277Figure E.3 LME Model Diagnostics - Mean Drilling Force. . . . . . . . . . . . . . . . . . . 281Figure E.4 LME Model Diagnostics - Prebreakthrough Force . . . . . . . . . . . . . . . . . 284Figure E.5 LME Model Diagnostics - Estimated Human Force . . . . . . . . . . . . . . . . 293Figure E.6 LME Model Diagnostics - Gross Targeting Time . . . . . . . . . . . . . . . . . 299Figure E.7 LME Model Diagnostics - Fine Targeting Time . . . . . . . . . . . . . . . . . . 300Figure E.8 LME Model Diagnostics - Tip Targeting Time . . . . . . . . . . . . . . . . . . . 301Figure E.9 LME Model Diagnostics - Tail Targeting Time . . . . . . . . . . . . . . . . . . 302Figure E.10 LME Model Diagnostics - Final Horizontal Tip Error . . . . . . . . . . . . . . . 319Figure E.11 LME Model Diagnostics - Final Vertical Tip Error . . . . . . . . . . . . . . . . 320Figure E.12 LME Model Diagnostics - Final Horizontal Tail Error . . . . . . . . . . . . . . . 321Figure E.13 LME Model Diagnostics - Final Vertical Tail Error . . . . . . . . . . . . . . . . 322xviiFigure E.14 LME Model Diagnostics - Final Tip Targeting Error . . . . . . . . . . . . . . . 323Figure E.15 LME Model Diagnostics - Final Angular Targeting Error . . . . . . . . . . . . . 324Figure E.16 LME Model Diagnostics - Final Total Targeting Error . . . . . . . . . . . . . . . 325Figure E.17 LME Model Diagnostics - Final Horizontal Tip Variability . . . . . . . . . . . . 326Figure E.18 LME Model Diagnostics - Final Vertical Tip Variability . . . . . . . . . . . . . . 327Figure E.19 LME Model Diagnostics - Final Horizontal Tail Variability . . . . . . . . . . . . 328Figure E.20 LME Model Diagnostics - Final Vertical Tail Variability . . . . . . . . . . . . . 329Figure F.1 Example CAS Coordinate Systems . . . . . . . . . . . . . . . . . . . . . . . . . 331Figure F.2 Example Navigation Display . . . . . . . . . . . . . . . . . . . . . . . . . . . . 331Figure F.3 Mechanical Linkage Example: K-Link . . . . . . . . . . . . . . . . . . . . . . . 337Figure F.4 Optical Tracking System Example . . . . . . . . . . . . . . . . . . . . . . . . . 338Figure F.5 Electromagnetic Tracking System Example . . . . . . . . . . . . . . . . . . . . 338Figure F.6 CAS-d Scene Graph . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 340Figure F.7 Drill Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342Figure F.8 Special Calibration Tool Example . . . . . . . . . . . . . . . . . . . . . . . . . 343Figure F.9 Pivot Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343Figure F.10 Rotation Calibration Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . 344Figure F.11 Optically tracked drill . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 348Figure F.12 Pierce Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 349Figure F.13 Observation Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352Figure F.14 Example Simulated Calibration Data . . . . . . . . . . . . . . . . . . . . . . . . 355Figure F.15 Example Ground Truth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 356Figure F.16 Example Pierce Point Convergence . . . . . . . . . . . . . . . . . . . . . . . . 357Figure F.17 Example Ground Truth Difference . . . . . . . . . . . . . . . . . . . . . . . . . 358Figure F.18 Example Covariance Matrix Norm . . . . . . . . . . . . . . . . . . . . . . . . . 358Figure F.19 Simulated Ground Truth Difference Comparison . . . . . . . . . . . . . . . . . 359Figure F.20 Empirical CDF Ground Truth Difference . . . . . . . . . . . . . . . . . . . . . 359Figure F.21 Typical Experimental Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 360Figure F.22 Typical Experimental Convergence . . . . . . . . . . . . . . . . . . . . . . . . 361Figure F.23 Experimental Covariance Norm Convergence . . . . . . . . . . . . . . . . . . . 362Figure F.24 Experimental Pierce Point Repeatability . . . . . . . . . . . . . . . . . . . . . . 362Figure F.25 Experimental Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363Figure F.26 Experimental UKF vs 3D-Circle Error Comparison . . . . . . . . . . . . . . . . 365Figure F.27 Drill Marker Coordinate System . . . . . . . . . . . . . . . . . . . . . . . . . . 370Figure F.28 Standard UKF Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373xviiiList of Symbolsu - specific cutting energy (J\/mm3)?e - elbow torque (N m)?s - shoulder torque (N m)?e - elbow angle (rad)?s - shoulder angle (rad)a1 - upper arm length (m)a2 - forearm length (m)B - empirical drilling parameter (1\/mm)bB - brace damping coefficient (N s\/m)dw - workpiece depth (mm)D - drill bit diameter (mm)f - drill feed (mm\/rev)FB - brace force (N)FD - drilling force (N)FH - human drilling force (N)p - pressure (N\/mm2)tD - drilling duration (s)vD - drill velocity (mm\/s)x - empirical drilling parameter (-)xixList of Abbreviations2D two-dimensional3D three-dimensionalAIC Akaike Information Criterion, [Sakamoto 1986]ANOVA analysis of variance, a set of statistical techniques to identify sources of vari-ability between groupsBP brad point drill bitBIC Bayesian Information Criterion, [Schwarz 1978]CAS Computer Assisted SurgeryCAOS Computer Assisted Orthopaedic SurgeryCI confidence intervalCT computed tomographyDOF degrees of freedomDRF dynamic reference frame, a marker frame attached to the anatomyEBLUP empirical best linear unbiased predictionEMG electromyographyEMTS Electromagnetic Tracking SystemENT Ear Nose and ThroatFLE fiducial localization errorFRE fiducial registration errorGUI graphical user interfacexxHSS high speed steel drill bitICC intraclass correlation coefficientIGSTK Image Guided Surgery Toolkit, an open-source C++ toolkit.IQR inter-quartile rangeLED light emitting diodeLMM linear mixed modelLS3DCF least-squares 3D circle fittingML maximum-likelihood, method for statistical parameter estimation.MRI magnetic resonance imagingMVC maximum voluntary contractionOTS Optical Tracking SystemPBF pre-breakthrough force (N)PD plunge depthREML restricted maximum-likelihood, method for statistical parameter estimation.RMS root mean squareRPM rotations per minuteSRF static reference frame, a marker frame fixed to the environmentSAT speed-accuracy tradeoffTCF tracker coordinate frame, the coordinate system of the optical tracking system.TKA total knee arthroplasty, total knee replacement surgeryTRE target registration errorUKA uni-compartmental knee arthroplasty, partial knee replacement surgeryUKF unscented Kalman filterVI virtual instrumentxxiAcknowledgementsThis thesis has been a challenging journey, and there are many people whose contributions I would liketo recognize.This journey began as a result of the introduction I received to research during my undergraduatedegree from Dr. Jason Carey and the encouragement to pursue postgraduate studies from Curt Stout. Iam grateful to both of them for recognizing my potential and starting me on this path.I would like to thank my supervisor , Dr. Antony Hodgson, for providing valuable technical guidanceand sharing his expertise along the way.Drs. Pierre Guy, Bassam Masri and Nelson Greidanus provided initial consultations and facilitatedvisits to the operating room. I am grateful for what was a tremendous learning opportunity.Thanks to the members of my examination committee, Dr. Elizabeth Croft and Dr. Tom Oxland forreviewing what turned into a fairly large document and providing suggestions for improvement.I would like to acknowledge the funding support provided by the National Science and Engineer-ing Research Council (NSERC) and the Institute For Computing, Information and Cognitive Systems(ICICS). During the last portion of my degree I was based at the Centre for Hip Health and Mobility(CHHM) and I benefited both personally and professionally from the collaborative, multidisciplinarywork environment. I am grateful to the funding agencies, researchers, and staff that made the centre areality.I would like to thank the subjects who volunteered to participate in my user study.I would like to acknowledge the community of users and developers of several open-source softwarepackages that were key to my work, including LATEX for the creation of this document and R for thestatistical analysis.I am also grateful that I had the opportunity to work with numerous talented and knowledgeablecolleagues both within the Neuromotor Control Lab and the Orthopaedics and Injury BiomechanicsGroup, including Robyn Newell, Claire Jones, Seth Gilchrist, Arian Amyrkevan, and Jeremy Kooyman.The assistance ? and more importantly, the welcome distractions ? were much appreciated.Finally, I simply would not have made it without the tremendous amount of support I received fromfriends and family. Thank you to Jenna Gyurkovits, Emma Horsley, Jean Gallagher, James Boak, ChrisBibby, and numerous others. I am especially grateful to my parents. From the bottom of my heart:thank you.xxiiFor my family.xxiiiChapter 1IntroductionTo err is human, but to really foul things up requires a computer.? Paul Ehrlich1.1 Motivation for Investigating Influence of Physical Support andDisplay Design on Performance of Orthopaedic SurgeryThe success of many procedures in orthopaedic surgery relies on the accurate and timely machining ofbone. Planning and performing these machining tasks accurately is challenging due to difficulties inadequately visualizing the complicated geometry [Langlotz 2003], and coping with the high requiredcutting forces [Carter 1978], and heat sensitivity [Karmani 2006] of bone. As a result, the technicaldemand of performing these machining tasks manually often exceeds the capabilities of the human sen-sorimotor system. Although training and practise can improve performance, many motor tasks exhibitan inverse relationship between accuracy and speed [Bogacz 2010] and there are also absolute limits toperformance due to uncertainty, noise, and delays in our motor control system [Franklin 2011].To address these physiological limitations, surgeons have conventionally used jigs and guides thatare complicated, time-consuming, invasively fixated, and rely on experience to use accurately [Plaskos2002]. More recently, a group of technologies referred to as Computer Assisted Orthopaedic Surgery(CAOS) have been introduced to improve performance by providing some combination of enhanced vi-sualization and physical support [Jaramaz 2006]. While some of these CAOS systems have demonstratedimproved accuracy, they also incur significant capital and operating costs, which, together with severalother factors, have limited widespread adoption [Chauhan 2004]. There is a need in orthopaedic surgeryfor an approach that offers the accuracy of more sophisticated navigation and robotic techniques withthe speed and flexibility of direct, handheld tool use. When faced with other challenging tasks, humansoften brace part of their body against the work surface to increase stability and improve performance.We believe that applying a similar bracing strategy to CAOS may be a cost effective way to improveperformance.For example, partial knee resurfacing, or uni-compartmental knee arthroplasty (UKA), is a procedurefor reducing pain and improving function for patients suffering from osteoarthritis. Revision rates of1CHAPTER 1. INTRODUCTION10 % to 20 % have been reported [Eickmann 2006], and the correct alignment of the implants hasbeen identified as a key factor [Kasodekar 2006]. CAOS technologies have been introduced to improveaccuracy, but these systems have considerable capital costs ($150,000-$300,000 for navigation, up to$800,000 for robotics), per-case disposable costs, and maintenance costs [Mathias 2007].The RIO? (Mako Surgical Corp., FL, USA) is one such system for UKA. The RIO? is a semi-activerobotic system; the surgeon and the robot both hold the tool. The surgeon actively controls cuttingwhile the robot limits motion to the resection area, defined with virtual cutting boundaries that arebased on preoperative computed tomography (CT) imaging. In a study of 10 patients, the system wasable to achieve differences between planned and achieved tibiofemoral angle of (0.3?0.4)?, with anaverage total operating time of 132 min [Pearle 2010]. The conventional UKA procedure typically haslarger differences and variability of tibiofemoral angle ((?0.84?2.75)?) but a shorter operating time((88?16)min) [Cobb 2006].While the RIO? system can increase accuracy, the procedure takes longer than the conventionalmethod and there are additional limitations. Besides operating time, one of the biggest limitations iscost: as of August 2010, the platform cost $793,000 and the software for UKA surgery cost $148,000[Lang 2011]. In addition to these capital costs, per-case disposable costs and maintenance costs, addi-tional staff are required; the system requires an average of 41 min setup time by a specialized technician[Pearle 2010]. The system itself is bulky, and takes up valuable space in the operating room. Finally,the preoperative CT scans are expensive and expose the patient to additional radiation.These same concerns are echoed across other surgical procedures and may explain why CAOS sys-tems have not seen widespread adoption. Several other studies, (e.g. Chauhan [2004]) have also demon-strated that accuracy improvements have come at the expense of increased operating time and highercapital and per-procedure costs. Craven [2005] analysed a number of factors influencing the acceptanceof CAOS technologies and concluded that there was?poor validation of accuracy, lack of standardization, inappropriate clinical outcomes mea-sures for assessing and comparing technologies, unresolved debate about the effectivenessof minimally invasive surgery, and issues of medical device regulations, cost, autonomy ofsurgeons to choose equipment, ergonomics and training.?To be successful, CAOS systems must have improved accuracy, visualisation, and verification of thesurgical goal while being demonstratively cost-effective, reducing or at least not extending operationtime, and, if possible, not requiring expensive and irradiating imaging. We believe that a bracing strategycould potentially meet these requirements.Humans naturally employ bracing strategies to improve the performance of a variety of motor tasks.For example, bracing is often used during writing (Figure 1.1b). By resting the forearm, wrist, and littlefinger against the writing surface, a secondary, parallel load path is formed. Forming this secondarypath reduces the number of joints that must be controlled, which increases stability and precision anddecreases fatigue. Bracing can also be used to enhance force exertion; one recent study found a 43 %increase in one-hand isometric force exertion capability [Jones 2013]. Further, this strategy is oftenemployed intuitively, requiring minimal instruction.2CHAPTER 1. INTRODUCTION(a) Unbraced writing (b) Braced writingFigure 1.1 Instead of writing with the arm in the air, bracing the little finger, wrist, and forearmagainst the work surface is easier and produces better results.A bracing strategy could improve the performance of orthopaedic tasks with a better tradeoff ofaccuracy, speed, and cost than more complicated robotic solutions (Figure 1.2). The following sectionsexpand these issues in enough detail to motivate our specific research goals.1.1.1 Challenges in Orthopaedic SurgeryIn the previous section we used the example of UKA to illustrate one procedure that may benefit frombracing. In this section, we begin with a broader discussion of orthopaedics and the underlying need forinnovation in this field.Orthopaedics focuses on the diagnosis, treatment, rehabilitation and prevention of diseases of themusculoskeletal system. This system enables a person to bear weight and move, and is comprised of theskeleton, joints, muscles, ligaments, cartilage, tendons, nerves, and other connective tissue. A variety ofafflictions such as trauma, congenital disorders, and degenerative diseases such as arthritis, infections,and tumours, can cause pain, physical disability, loss of personal and economic independence, andsometimes death. These conditions collectively affect hundreds of millions of people worldwide, span-ning age, gender, socio-economic status and nationality, and are the second greatest cause of disabilitybehind mental and behavioural disorders [Murray 2012]. Disability due to musculoskeletal disorders isestimated to have increased 45 % from 1990-2010 compared to a 33 % average across all other diseaseareas [Murray 2012]. This trend is expected to continue as the number of older people increases andmore people adopt a sedentary lifestyle with reduced physical activity and increased obesity [Woolf2010].The economic burden on society due to direct costs to the health care system and indirect losses toproductivity is substantial. For example, the sum of direct health care costs and indirect lost wages inthe United States for the years 2004-2006 was estimated to be $950 billion dollars annually, or 7.4 % ofthe national gross domestic product [United States Bone and Joint Initiative 2011]. Managing this largeand increasing burden will require improvements in both prevention and treatment. The focus of thisthesis is on the latter: improving the effectiveness of orthopaedic surgery.3CHAPTER 1. INTRODUCTIONFigure 1.2 Potential opportunity of applying a bracing strategy to Computer Assisted OrthopaedicSurgery (CAOS) using uni-compartmental knee arthroplasty (UKA) as an example. Pro-cedure time and coronal implant alignment error tradeoff for different approaches to uni-compartmental knee arthroplasty (UKA). More desirable solutions lie closer to the origin.The dashed blue ellipse indicates that bracing could potentially offer a better time-error per-formance than current solutions. (Source: Conventional and Acrobot: Cobb [2006], Mako:[Pearle 2010])Although orthopaedic treatments are generally quite effective at reducing pain and improving func-tion, there is still a need for continuous improvement and the development of novel techniques. Forexample, total knee arthroplasty (TKA) is widely used to relieve pain and improve function for patientssuffering from knee osteoarthritis. The procedure is generally successful, with over 85 % of patientsreporting improvements in symptoms [Weinstein 2013]. However, failures can and do occur and some-times necessitate costly (upwards of $20,000 dollars) revision surgery [Slover 2008]. In the UnitedStates, the number of TKA procedures has doubled in the past decade The financial burden of a 5-10%revision rate for this many cases is a significant incentive for improvement.In addition to the primary goals of improving function and reducing pain, there are a number ofadditional factors that influence the outcome of an orthopaedic treatment (Table 1.1). To expedite thepatient?s recovery, blood loss should be kept to a minimum, and all attempts should be made to reducethe chance of infection. Operating room time should also be minimized, both for the patient?s health andbecause it is expensive. Other financial considerations include minimizing procedure costs and hospitalstay. These factors are interrelated and sometimes conflict with one another. For example, minimally4CHAPTER 1. INTRODUCTIONinvasive techniques aim to use smaller incisions to help reduce blood loss and disruption of soft tissue,which is linked to shorter recovery periods. However, smaller incisions make it harder to see, potentiallyincreasing operating time and decreasing accuracy. Balancing accuracy, speed, and cost is challenging.Table 1.1 Goals for Optimal Surgical Outcomemaximize post operative function minimize post operative painminimize hospital stay minimize recovery periodminimize blood loss minimize chance of infectionminimize operating time minimize procedure costsSource: summarized from Hodgson [2008].Depending on the procedure, accuracy is often a key factor. This may be to ensure fractured bonesheal properly, limb length is maintained, function is restored to a joint, or all parts of a bone tumour areremoved. Achieving high levels of accuracy can be challenging due to difficulties in locating the correctposition, and difficulties in actually performing the task: visualization and machining.Locating the correct position and adequately visualizing the surgical field is often difficult. Thestructures being operated on are often located deep within the body and it is difficult to see withoutcreating large incisions or disrupting large amounts of soft tissue. There is also anatomical variationbetween different patients. Medical imaging can be used to enhance visualization, although in additionto the capital cost of the hardware, they introduce additional challenges depending on the modality.For example, radiological methods like CT or fluoroscopy lead to undesirable radiation exposure tothe patient and the operating room team [Rampersaud 2001]. A radiation free alternative is magneticresonance imaging (MRI) , but this modality is sensitive to metallic objects. When performed beforethe surgery, i.e., pre-operatively, differences in patient position might cause discrepancy between theimage and the reality during the operation. It is also possible to perform imaging during the surgery,i.e., intra-operatively, though these typically require specialized equipment and operating suites. Thereare also image-free systems that use statistical models to approximate the anatomy geometry. All thesefactors make locating the correct position challenging.Once the proper structure has been located, accurately machining the bone itself is a second chal-lenge. Bone is a complex living tissue that is non-homogeneous both in material properties and ge-ometry and it is possible to damage bone surrounding the area being cut. The density and hardness ofbone requires significant cutting forces. If too much heat is generated during cutting, osteonecrosis (i.e.,bone tissue death) can occur, which can lead to screw loosening and implant failure [Augustin 2008].It is also possible to damage surrounding tissue. Bone is always surrounded by soft tissue, so exposureis required for access, and since one of bone?s functions is to protect other structures, there are oftendelicate neurovascular structures in close proximity.The difficulty in handling these challenges is partially reflected by the amount of training that sur-geons require. In Canada, an orthopaedic surgeon typically complete 4 years of undergraduate educa-tion, 4 years of medical school, 5 years of residency, and often 1-2 years of fellowship if they wish to5CHAPTER 1. INTRODUCTIONspecialize [Canadian Medical Association 2012]. Even with this extensive training, it can be difficult forsurgeons to attain the required accuracy. The retirement of a growing number of older surgeons will putadditional strain on our medical system, providing further motivation for developing effective trainingtools, and developing techniques that enable less experienced surgeons to take on more cases withoutsacrificing performance.The next section describes several factors that limit human motor task performance.1.1.2 Limitations to Human PerformanceAlthough humans are able to perform a wide variety of motor tasks, some tasks are so demanding thatperformance is limited by the sensorimotor system?s ability to find solutions to inherent physiologicalchallenges and other factors related to the task and the environment. In this section, we present anoverview of these challenges that limit human motor task performance.Complicated human motor tasks are enabled by the sensorimotor system. This system is part of thehuman motor control system and includes the sensory, motor, and central integration and processingcomponents involved in bodily movements [Riemann 2002]. Franklin [2011] provide a detailed reviewof six inherent challenges that limit performance of the sensorimotor control system, summarized below:Redundancy: The human body has over 200 joints controlled by around 600 muscles. Since thereare many more muscles than degrees of freedom, the motor system is redundant: there are multiple waysof achieving the same task. For example, for joints that are controlled by multiple muscles, such as theelbow, the same motion can be produced by different combinations of muscles and with different levelsof co-contraction.Noise: Accurate perception and precise action is limited by noise in the nervous system. Further-more, noise levels increase with fatigue and the level of the motor command [Selen 2007].Delay: Delays are present in the sensing, processing, and execution stages of the sensorimotorsystem. These delays also vary depending on sensory modality, processing complexity, and musclelocation.Uncertainty: Control decision must often be made based on incomplete information of the envi-ronment and the results of the task. Humans must also cope with unstable and unpredictable systems.Nonstationarity: Motor system properties can change over time due to growth, development,ageing, and fatigue, which makes adaptation important.Nonlinearity: The motor system is highly nonlinear, so responses to multiple inputs can not simplybe summed together to predict the response to a novel input.In addition to these physiological limitations, human factors can also lead to errors. The InternationalErgonomics Association [2010] defines human factors as?[t]he scientific discipline concerned with the understanding of the interactions among hu-mans and other elements of a system, and the profession that applies theoretical principles,data and methods to design in order to optimize human well being and overall system per-formance.?6CHAPTER 1. INTRODUCTIONModern operating rooms are technologically complex, high-stress environments which require multi-disciplinary teams to work together in a coordinated fashion [Shouhed 2012]. Surgeon performance isaffected by acute stress which can be brought on by technical complications, time pressure, distraction,interruptions and increased workload [Arora 2010].1.1.3 Humans Use Bracing to Improve PerformanceAs mentioned earlier, people employ a bracing strategy to improve their performance during a varietyof interactive motor tasks, often without the person being consciously aware of what they are doing.Bracing is often used during precision manipulation (Figure 1.3). In this case, the increased stabilityprovided by the close contact helps reduce fatigue and increase precision. Bracing is used in a varietyof tasks (Table 1.2) to reduce fatigue, increase precision and generate higher forces.Figure 1.3 A railroad watch finisher makes an adjustment on a railroad movement. Note how hebraces his hands and face against the table to increase dexterity and precision. (Source: ElginNational Watch Company, modifications by Wayne Schlitt (Watch Word magazine) [GFDL(http:\/\/www.gnu.org\/copyleft\/fdl.html)], Wikimedia Commons.)Table 1.2 Examples of Tasks Where Bracing is Usedwriting welding painting (maulstick)soldering sculpting mousingtyping carving shootingThe bracing strategy involves forming a secondary, parallel load path, which can be accomplishedin several ways. This secondary path can be created by adjusting the posture so that the limb is pressedagainst the body (internal bracing) (Figure 1.4a), by positioning the limb against the environment orsome sort of auxiliary bracing device i.e., a brace (external bracing) (Figure 1.4b).Literature on bracing is limited and is largely divided between two areas: investigating human brac-ing in the context of ergonomics and applying the behaviour to improve the performance of roboticarms. There are also a few clinical examples.7CHAPTER 1. INTRODUCTIONHuman Bracing ResearchAlthough there are a variety of examples of humans using a bracing strategy to improve performance,we have only been able to identify a few formal studies.Bracing may be a natural extension of how humans often approach manipulation tasks. Many bi-manual manipulation tasks exhibit asymmetry, where each hand plays a slightly different role. Guiard[1987] proposed a descriptive model of bimanual control that treats the two hands as a pair of abstractmotors that humans tend to assemble in series, forming a kinematic chain. For example, during hand-writing a right hand dominant person will use the left hand to control the position of the page relative tothe table while the right hand controls the position of the pen relative to the page. This divides the timeand spatial scales between the two hands: infrequent, gross postural corrections are handled by the lefthand, while frequent, fine manipulations are handled by the right. Further, the right hand operates in thecoordinate system formed by the left. Guiard theorizes that?the outstanding manipulative efficiency of humans results not only from role differenti-ation between the two hands but also, and perhaps more significantly, from the fact thatbetween-hand division of labour is typically hierarchical, with the two hands working in acoordinated fashion at two contiguous levels of resolution.?We believe that employing a bracing strategy may facilitate this division of labour by making it easierto operate in the coordinate system of the workpiece and by dividing the degrees of freedom (DOF) ofthe task to the appropriate temporal-spatial scale.Ergonomics is one field where the effects of bracing has been quantified in some scenarios. Duringa series of studies to develop a 3D whole body model to predict posture for standing hand force exer-tion, Hoffman [2008] noticed that subjects would sometimes tuck their arm against their body during a(a) (b)Figure 1.4 Illustration of (a) internal bracing, and (b) external bracing in a pushing task. Internalbracing involves a change in posture to brace the limb against the body. External bracing usesan auxillary device or structure. (Source: Sean Gillen ?2013, based on images from Hoffman[2008] and Jones [2011].8CHAPTER 1. INTRODUCTIONpushing task. Hoffman [2008] hypothesized that this internal bracing strategy was used to reduce themoment generated in the shoulder. Jones continued this work and addressed external bracing explicitly(Figure 1.5). She demonstrated that the availability of surfaces to brace against can increase one-handisometric force exertion capability by 43 % [Jones 2013].Figure 1.5 Research apparatus for assessing effect of bracing availability on one-hand isometricforce exertion capability. (Source: reprinted from Jones [2013] ?2013 Taylor & Francis, withpermission.)There are a handful of studies that have evaluated the effect of using armrests on muscle activity. Lee[2006] evaluated muscle activity of a static and dynamic mousing task with the use of a forearm supportusing surface electromyography (EMG) and found that the activity of trapezius, deltoid, biceps brachii,extensor carpi radialis longus, and extensor digito- rum, decreased by 43 % to 67 %. Murphy [2011]developed a dynamic armrest that passively supports the arm throughout movement of a hydraulic-actuation joystick, like those commonly used to operate heavy mobile machines such as excavators andskidders. Their study reported statistically detectable decreases in the mean and peak muscle activationsof the upper trapezius and anterior deltoid when the dynamic armrest was used compared to a staticarmrest. There was also a statistically detectable decrease in mean and peak anterior deltoid activationcompared to when no armrest was used. Unfortunately, the study did not report the magnitudes of thesereductions, or standardize the results to maximum voluntary contractions. Presumably, reduced muscleactivation will result in decreased fatigue. While there is evidence to support muscle activity reductionsduring static bracing, it is important to note that these tasks involved minimal interaction forces.Fehlberg [2012] developed and tested an ?Active Handrest? that enabled continuous dexterous ma-nipulation over a larger workspace than what is possible with the arm alone (Figure 1.6). Although thedevice was not developed for a specific purpose, the authors suggest that it could be of use in ?surgeryand medical tasks, upper limb rehabiliation, artistry, machining, pick-and-place tasks, or any task re-quiring dextrous control of tools.? Static bracing strategies typically tradeoff improved stiffness and9CHAPTER 1. INTRODUCTIONprecision for a reduced workspace. For example, the finger of an outreached arm can cover a planar,hemispherical area of approximately 1 m2. If the hand is braced against a static rest, the finger can covera circle with a diameter of roughly 0.1 m, an area of approximately 0.01 m2. This represents a change inarea of two orders of magnitude. The Active Handrest automatically adjusts position as the user moves,providing support over a large area. In the study, the accuracy and time of a circle tracing task weretested under a variety of support conditions: no support, fixed elbow rest, fixed hand rest, passive handrest, and active handrest. Fehlberg found that the active handrest significantly improved accuracy com-pared to the unsupported and fixed rests, reducing error by 26 %. Their results suggest that the gains inperformance were a result of not only gravity support but also the damping provided by the device.Figure 1.6 Concept and prototype of Active Handrest. (Source: reprinted from Fehlberg [2012]?2012 SAGE Publications, with permission.)The studies above collectively demonstrate that depending on the nature of the task, a bracing strat-egy can be used to reduce fatigue, improve precision, generate higher forces, or some combination ofthe three.1.1.4 Applying Bracing To RoboticsOver the past 30 years, several researchers have investigated applying the bracing strategy employedby humans to improve the performance of robotic manipulators. This idea was first proposed by Book[1984] as a means to increase the precision of lightweight, flexible arms. Typically, ensuring high preci-sion over a large workspace requires large, heavy manipulators to achieve high stiffness, but movementspeed suffers. Lightweight arms are much faster to move, but are less accurate because of their lowstiffness. Book proposed increasing the precision of these lightweight arms by first grossly positioning10CHAPTER 1. INTRODUCTIONthe arm in the general vicinity of the task, and then bracing the arm against the workpiece or a nearbysurface using secondary links to allow fine motion. The primary goal is to optimize the balance betweenstiffness and mobility.Book proposed a variety of methods for establishing a connection to support the bracing forcesincluding a simple normal force, mechanical clamping, vacuum attachment, and magnetic attachment.People typically use a simple contact with a frictional force created through gravity or muscle activationproducing a bias force. Asada [1985a] utilized the normal force strategy to developed the concept of a?tool guide? or ?jig hand?. By bracing the tool guide against the workpiece, high dynamic interactionloads are handled by the increased stiffness or bias force that prevents lift-off, which improves accuracy.This concept was applied to a grinding robot. The grinding wheel is attached to the tool guide whichis held against the workpiece using a preload exerted by the robotic arm (Figure 1.7a). Any reactionforces generated by the grinding process, as a result of uncertainties in the workpiece, are shielded fromthe arm by a spring (Figure 1.7b). Experimental results showed that the stiffness of the grinding tool inthe direction normal to the grinding surface increased by a factor of 50.(a) (b)Figure 1.7 Adaptable tool guide for a grinding robot: (a) model and (b) schematic. The springsuspension mechanism protects the robot arm from vibration and impulsive loads generatedby the grinding tool. (Source: reprinted from Asada [1985b], ?1985, with permission fromElsevier.)Fields [1989] used a similar design for a robotic system to automate the fixturing and drilling ofaerospace sheet metal parts. Like grinding, drilling involves significant axial interaction forces that canaffect accuracy. In order to stabilize the tool and reduce high dynamic loading to the end of the compliantrobotic arm, the drill is mounted to the tool guide and actuated by a pneumatic cylinder (Figure 1.8). Therobotic arm applies a preload to the tool guide to brace it against the workpiece. Experimental resultsshowed that positional accuracy improved from?2.80mm to?0.25mm. This system demonstrates oneof the key concepts of implementing a bracing strategy: allocating degrees of freedom to independentmotions.In addition to the mechanical design of the bracing mechanism, implementing a bracing strategy fora robot involves developing an appropriate control strategy to control the manipulator before, during,11CHAPTER 1. INTRODUCTIONFigure 1.8 The positional accuracy of automated drilling of sheet metal parts can be improvedthrough bracing by separating the positioning and drilling. The end effector assembly is at-tached to a robotic arm through the mounting hub and is pressed into the workpiece generatinga normal force. This normal force helps maintain position while the pneumatic cylinder inde-pendently actuates the drill. (Source: reprinted from Fields [1989], ?1989, with permissionfrom Elsevier.)and after bracing is established. Book [1984] identified control issues during each phase:? Gross Motion1. Choosing a trajectory that balances speed without exciting vibration;2. Following the trajectory chosen with a controller that is accurate and stable over largechanges in parameters; and3. Selecting a destination to allow best use of other degrees of freedom.? Rendezvous and Inactive phases1. An accurate, gentle collision with the bracing structure;2. Passive damping of the high frequency dynamics; and3. Appropriate control of the statically indeterminate braced structure.? Fine Motion1. Sensing the position relative to target; and2. Fast, probably conventional control of fine motion degrees of freedom.Researchers have developed the necessary control strategies to apply bracing to a variety of appli-cations [Chung 1987; Kwon 1988; Book 1989; Fields 1989; Hollis 1992; Delson 1993; Book 1994;Zupanc?ic? 1996; Schimmels 1996; Schimmels 2001a; Schimmels 2001b; Greenfield 2005; Itoshima12CHAPTER 1. INTRODUCTION(a) (b) (c)Figure 1.9 Bracing strategies for a coarse-fine manipulator: (a) real, (b) virtual (workpiece refer-enced), and (c) virtual (enviroment referenced). (Source: reprinted from Hollis, ?1992 IEEE,with permission.)2011]. Although reviewing all of the control algorithms is beyond the scope of this thesis, there are sev-eral key concepts worth mentioning. Hollis describe two types of bracing for a coarse-fine robot. Theyrefer to ?real bracing? when the coarse manipulator is mechanically braced against a bracing structure(Figure 1.9a) and ?virtual bracing? when the position of the fine manipulator is controlled through a feed-back loop by sensing the position of the workpiece (Figure 1.9b) or environment (Figure 1.9c). In thiscase, a virtual brace is similar to the concept of a virtual fixture used in haptics. Hollis experimentallyimplemented a ?real? bracing solution for precise assembly of electronics and demonstrated that 98 % ofalignments were within 1 ?m, an order of magnitude better than unbraced coarse-fine manipulation andtwo orders of magnitude better than coarse manipulation alone.Zupanc?ic? [1998] tested an Asea Irb 6 industrial manipulating robot and three human operators usinga standard repeatability positioning task for industrial robots (ISO 9283)(Figure 1.10). Zupanc?ic? foundthat static bracing improved positional repeatability. In this study, an Optotrak? optical motion capturesystem was used to measure position. The task was to move to each of five points defined within theworkspace a total of 30 times. The robot was programmed to move to the defined points while the humanoperator used a wire frame with five rings for reference. The repeatability of the robot was on the orderof 0.2 mm, with about 50 % improvement in the braced case. The human operators? repeatability wasaround 30 mm, two orders of magnitude larger than the robot. When their forearms were braced, thehuman operators experienced a 25 % improvement in repeatability. This study showed that both humansand robots can obtain significant precision improvements from bracing.The research described above has established that applying a bracing strategy to robots can improvestiffness and accuracy. Implementing the necessary control schemes, however, is not trivial, and is anarea of ongoing research.1.1.5 Clinical Bracing ResearchThere are only a few clinical examples where specific devices have been designed to facilitate bracingor where performance has been evaluated. These applications include reducing hand tremor and fatiguein microsurgery, especially neurosurgery, and stabilizing tools using finger rests in dentistry.13CHAPTER 1. INTRODUCTIONMicrosurgeryIn microsurgery, minimizing hand tremor is a challenge. Anatomical constraints sometimes force sur-geons to maintain unnatural postures which causes fatigue that may exacerbate hand tremor. Surgeonsoften try to reduce fatigue and increase stability by placing their arms or hands or both on the patient?shead, or various types of arm and hand rests attached to the head frame (Figure 1.11a), operating ta-ble, or surgeon?s chair. A variety of such systems have been developed [Sugita 1978; Greenberg 1981;Kobayashi 1984; Gilsbach 1984; Klein 1984]. Since fixed rests only offer support in one location andadjustment can be difficult, time consuming, or both, several groups have also developed systems thatare easier to reposition.One example of a system that is easier to reposition is the freely movable armrest [Ohta 2000].When a button is pushed, compressed air releases the friction joints, allowing the armrest to movefreely; when the button is released, the arms lock into place. Although they were unable to quantitativelymeasure surgeon stability or fatigue, when the freely movable armrest was used clinically the authorsobserved ?substantial difference in performance?, ?markedly improved? stability, and ?greatly reduced?fatigue. Ohta also reported that supporting the wrist was better for higher stability and finer movements,whereas supporting the forearm was better when greater movement was required. One limitation ofthis system is the need to let go of the surgical tool to activate the button, potentially interrupting thesurgeon?s concentration.Figure 1.10 Experimental setup of study to compare positional repeatability of braced and un-braced human and robot. (Source: reprinted from Zupanc?ic? [1998] ?1998, with permissionfrom Elsevier.)14CHAPTER 1. INTRODUCTIONA similar freely movable armrest was developed and evaluated during a simulated microsurgerysuturing task [Yako 2009]. In a study of 6 subjects, Yako found a decrease in task duration from an av-erage of 873 s to 790 s, a statistically detectable decrease of approximately 10 % (p = .039). Fatigue andmaneuverability were assessed on a subjective scale from 1 to 10. There was a statistically detectabledecrease in fatigue (6.2 versus 4.3, p = .031) and statistically detectable increase in maneuverability(4.0 versus 6.3, p = .031). This system measurably improved performance, although it still relied onmanual intervention to adjust position.To address this limitation, the authors developed a passive robotic system called EXPERT [Okamoto2011; Louis 2012; Goto 2013]. This system adjusts the armrest position automatically in responseto the surgeon?s movements (Figure 1.12). The authors tested the system in a study similar to theone described above [Goto 2013]. All of the subjects reported decreased fatigue scores and increasedmaneuverability scores on a visual analogue scale when using the system versus without (p < .05). Tasktime decreased for 4 of the 6 subjects, while 2 subjects showed increases. EXPERT has also been usedwithout complications during 13 surgeries, although in order to be commercially viable, the authors feelthe system needs to smaller and lighter [Louis 2012]. Another likely advantage for widespread adoptionis cost-effectiveness: since the system simply supports the surgeon and does not touch the patient, thereis no need for clinical trials before commercial production [Goto 2013].There are several remaining questions regarding armrests. Unfortunately, it is difficult to directlycompare the results of the freely movable arm [Yako 2009] to the EXPERT [Goto 2013] since theexperimental task differs; it is therefore difficult to assess whether the additional cost and complexityassociated with the EXPERT system is justified. The studies to date have all been performed with expert(a) (b)Figure 1.11 Two types of support systems used for neurosurgery: (a) headframe-mounted hand restsystem and (b) chair-mounted freely movable armrest. (Source: (a) reprinted from Gilsbach[1984] Figure 4, ?1984 Springer-Verlag, with kind permission from Springer Science andBusiness Media; (b) reprinted from Ohta [2000] Figure 5, ?2000 Wolters Kluwer Health,with permission.)15CHAPTER 1. INTRODUCTIONsurgeons, so it is unclear whether more junior surgeons would see similar or greater improvements inperformance.DentistryDentists and dental hygienists are explicitly trained to ?fulcrum?, or use finger rests, to improve perfor-mance while performing dental scaling and other procedures. The basic intraoral fulcrum is formed byresting the ring finger on a tooth near the tooth being instrumented (Figure 1.13). This fulcrum providesa stable support for the hand, a pivot point for rotation, and a source for leverage which enables preciseinstrument control, decreases the likelihood of injury to the patient or clinician if the patient suddenlymoves, and reduces muscle stress in the clinician [Darby 2006].There are several alternative to the basis intraoral fulcrum. An extraoral fulcrum is formed by restingagainst the patient?s chin or cheek. Advanced fulcrum techniques vary where the finger rest is in relationto the treatment area, or involve the use of more than one finger. The middle finger can be stacked againstthe ring finger, of a finger from the non-dominant hand can be used as a finger rest, or to stabilize andprovide additional force to the instrument.The use of finger rests has been advocated for nearly a century, and while the benefits of usingthis technique to improve precision and prevent injuries caused by sudden movements are generallyaccepted, only two studies have investigated whether using finger rests reduces muscles stress. Dong[2005] tested 12 predental students and concluded that thumb pinch force and muscle activity decreasedwhen using one and two finger intraoral finger rests compared to no finger rest in a simulated dentalscaling task. Cosaboom-FitzSimons [2008] performed a similar study with 32 senior dental hygieniststudents and concluded that similar levels of muscle activity were produced across five different typesof fulcrum. Although the Cosaboom-FitzSimons study attempted to address limitations they identifiedwithin the Dong study, it is difficult to directly compare the results. Cosaboom-FitzSimons claim thatthe extraoral fulcrum condition (i.e., bracing outside the patient?s mouth, typically against chin or cheek)in their study is equivalent to the no finger rest condition in the Dong study. Unfortunately, neither study(a) (b)Figure 1.12 Automatically adjusting arm rest: (a) EXPERT system and (b) schematic. (Source:reprinted from Okamoto [2011], ?2011 Springer, with kind permission from Springer Sci-ence and Business Media.)16CHAPTER 1. INTRODUCTIONFigure 1.13 A clinician utilizing an introral fulcrum during dental scaling. Their ring finger isrested against an adjacent tooth to provide support, help stablize the instrument, increaseprecision, and minimize the risk of injury. (Source: Sgt. Brian J. Griffin, public domain,Wikimedia Commons.)explicitly measured performance in terms of scaling efficiency or time.Robotically Assisted ProceduresIntuitive Surgical (Sunnyvale, California, US) has recently been granted a couple patents related tobracing during robotically assisted procedures. The primary patent, titled ?Bracing of bundled medicaldevices for single port entry, robotically assisted medical procedures? describes a method for stabilizingthe movement of a teleoperated tool during minimally invasive surgery [Mohr 2011].SummaryClinically, bracing is used intuitively in some cases and taught explicitly in others; however, in general,it is understudied and appears to be underutilized as a design element in an engineered system. The nextsection describes why we believe a bracing strategy may be an effective way to improve the performanceof orthopaedic surgery, especially CAOS procedures that already rely on computer assistance to enhanceprecision.1.1.6 Applying Bracing to CAOSWe believe that a bracing strategy may offer significant performance gains without suffering from manyof the limitations of current CAOS techniques. Specifically, we believe that bracing can enable a surgeonto perform many motor tasks quickly and accurately, without the need for expensive robotic hardware.The potential improvement in the tradeoffs between accuracy, time, and cost is a result of several factors:Augmented Stability: Forming a closed kinematic chain can lead to increased stiffness, reducedfatigue, increased precision and more efficient force application. With the appropriate impedance, a17CHAPTER 1. INTRODUCTIONbrace can potentially decrease the response to perturbations in the environment.Less Invasive Fixation: A bracing connection can be formed by simply apposing the hand or toolagainst an appropriate bracing structure or surface without the need for invasive, rigidly affixed pins orscrews. This could in principle save time.Intuitive: Since humans employ bracing strategies naturally, a properly designed bracing strategycould likely require minimal training.Simple and Cost Effective: A bracing strategy does not necessarily require expensive actuators,sensors, or control hardware, which would reduce costs and setup time compared to existing roboticdevices.Surgeon Control: The surgeon would remain in control of the cutting process.1.2 Research GoalsThe goal of this thesis was to assess the feasibility of applying a bracing strategy to CAOS by:G1. Developing a bracing strategy for a surgically relevant task; andG2. Experimentally assessing whether the bracing strategy improved task performance.The next section describes how a surgically relevant task was chosen.1.3 Selection of Surgically Relevant TaskWe chose to assess the effects of bracing on two aspects of surgical drilling: navigated targeting andcortical drilling. In this section, we provide the rationale for selecting these tasks.The primary motivation was simplicity. During a drilling task, there is a natural separation betweenthe alignment and machining phases. Once a hole has been started, there is limited opportunity tochange the orientation and it is primarily a single DOF task.Orthopaedics primarily involves bone-machining tasks as opposed to manipulation or positioningtasks. A variety of tools are capable of machining different surfaces, and there are differences in thenumber of degrees of freedom of the cutting and alignment. Table 1.3 lists tools commonly used inorthopaedics and their associated machining shapes and degrees of freedom.1.3.1 Surgical DrillingIn this section we provide an overview of surgical drilling and discuss some of the limitations and com-plications that make it a likely candidate for improvement through a bracing strategy. A comprehensivereview of bone drilling can be found in a recent review by Pandey [2013].Drilling is a machining method to produce a cylindrical hole. Material is removed by cutting surfaceson a rotating drill bit. The cutting force depends on the axial thrust force (N) and torque (N m) appliedto the rotating (rotations per minute (RPM)) drill bit. In a freehand drilling task, a drill motor suppliesthe torque while the user exerts and controls the thrust force. In general, the goal of a drilling task is to18CHAPTER 1. INTRODUCTIONTable 1.3 Tools Commonly Used in OrthopaedicsDegrees of FreedomTool Machining Shape Constraintsa Cuttingb RelativecBroach Linear 5 1 0Drill Cylinder 4 1 1Saw Plane 3 3 1Mill Surface 1 5 1a Constraints required to align tool in preparation for cut.b Cutting motionsc Movement of cutting surface relative to handle.create a hole in the correct location, in the correct orientation, and to the correct depth while maintainingan appropriate thrust force for efficient drilling.A typical drilling task can be divided into four phases: planning, targeting, drilling, and withdrawal.The goal of the targeting phase is to align the drill bit to the desired start point and trajectory. Thedrilling phase begins when a torque is applied to the drill bit through the application of an axial thrustforce and the rotation of the drill motor. When the desired depth is reached, the drill bit is withdrawn.Drilling is commonly performed in orthopaedics since there are a variety of situations that requirea hole in bone. Holes are often drilled in preparation for a screw or other threaded device for rigidfixation, to form a bony tunnel to route other tissue (e.g., tendons during anterior cruciate ligamentreconstruction), or to relieve pressure (e.g., core decompression for osteonecrosis). Accuracy is oftenquite important; an improperly placed hole can have significant consequences in terms of neurovascularinjury (e.g., pedicle screws) or improperly aligned implants.Surgical Drilling ChallengesThere are several challenges to achieving accurate and timely surgical drilling:? bone density? bone geometry? bit walking \/ skiving? bit breakage? bit bending? heat generationIn general, freehand (i.e., manual) drilling is an unstable task [Rancourt 2001b]. Small perturbationscan cause the thrust force to be applied off axis, generating large moments that lead to undesirablemovement unless the necessary lateral stability can be maintained. This instability increases for longerdrill bits and greater thrust forces, both of which are relevant in bone drilling. Drill bits are reportedto be one of the most frequently broken surgical instruments [Bertollo 2011]. Long, narrow bits, suchas those commonly used in orthopaedics, are especially susceptible to bending and breaking. In manycases, it is extremely difficult to remove a broken drill bit, so they are often left in situ; since the bits are19CHAPTER 1. INTRODUCTIONmade of biologically inert material, this generally does not result in any biological reaction, but it cancomplicate completion of the procedure.Through consultation with a clinical collaborator, we identified a number of different surgicaldrilling tasks that could potentially benefit from bracing (Table 1.4). For each task, we assigned therelative importance of alignment accuracy, depth control, bit bending, and whether the task relied onfluoroscopic guidance.Table 1.4 Surgical Drilling Tasks That May Benefit From BracingTask\/Procedure Alignment Depth Bit Bending FluoroscopyCore decompression H + + +Sacroiliac screw placement VH + + +Locking of intramedullary nails M - + +Pedicle screws VH + (b\/t) - +ACL reconstruction M + (b\/t) - -Hip resurfacing H - - -Maxillofacial implants H + a - -TKA tibial jig placement H - - -CAOS marker placement L + - -Open fracture reduction L + a - -a thin boneWith an emphasis on simplicity for this initial exploration, we selected two tasks: navigated targetingand cortical drilling. The justification is further expanded in the sections below.1.3.2 Navigated Drill TargetingNavigated targeting is one of the first steps in a typical CAOS drilling task. The goal of this task is toalign the drill with the pre-determined entry point and trajectory using the feedback provided by theguidance display of a CAOS system.We chose navigated targeting drilling as a likely task for improvement through bracing for severalreasons:1. It applies to a variety of CAOS procedures;2. It does not involve significant user interaction forces during the targeting phase;3. Passive rigid braces can improve positional repeatability [Zupanc?ic? 1998]; and,4. The construction of a complex bracing device is not required.The performance of this task can be measured by analysing the error between the goal trajectory andthe drill bit pose and the time taken to complete the task. The difference is represented using a distanceand an angle. The radial error is the perpendicular distance from the goal axis to the drill bit tip. Theangular error is the angle between the goal axis and the drill bit axis. The components of targeting20CHAPTER 1. INTRODUCTIONerror are illustrated in Figure 1.14.Drill BitGoal Axis?r?Figure 1.14 The error between the a goal axis and achieved axis is represented with an angularerror, ? , and a radial error, r. Coincident axes will have a radial error of 0. Parallel axes willhave an angular error of 0.A preliminary study with a single subject showed that an external guide stabilising device can de-crease navigated drilling time [Kendoff 2007]. In this study, a junior surgeon performed twenty drillingtrials freehand and twenty trials with a clamped alignment guide. Each hole was drilled to a target80 mm through a foam block that had a density similar to human cancellous bone. There was a statis-tically detectable difference (p = .009) in drilling time between trials drilled freehand, with an averageof 5.4 min (? : 1.3 min, Range: 3.0 min to 6.0 min), and trials drilled using the guide, with an averageof 5.8 min (? : 1.8 min, Range: 4.0 min to 10.0 min). However, there was no difference in accuracy.Freehand trials had an average error of 0.7 mm (? : 0.6 mm, Range: 0 mm to 2 mm), while trials withthe guide had an average error of 0.6 mm (? : 0.6 mm, Range: 0 mm to 2 mm). This study providesencouraging evidence that providing mechanical support can reduce time without affecting accuracy.Guidance DisplayAlthough it was not originally the primary focus of this study, during preliminary development of asimple CAOS system for testing braced performance it became clear that the design of the guidancedisplay used for visual feedback could have a significant impact on performance.A variety of medical procedures use visualizations based on medical imaging as an integral part ofplanning, execution, and verification. These procedures are collectively referred to as image-guidedsurgery or image-guided interventions. A cohesive overview of the technologies and challenges in-volved is provided by Peters, Terry; Cleary [2008], especially the chapter by Holmes III [2008]. Sincethe focus of this study was on the execution phase and it was a preliminary investigation into bracing,we wanted to avoid the complexity of having to image and register the anatomy and determine the ap-propriate surgical plan. We assumed that the planning had already been completed, and focussed onmore abstract representation of a particular execution task, which in this case was the alignment of thedrill axis.21CHAPTER 1. INTRODUCTIONMost commercially available CAOS systems combine a standard top-front-right orthographic viewand a special 2D view for aligning trajectory. For example, the BrainLab? system for femoral hipresurfacing uses two orthographic views and an axial view to help align the drill for proper pin placement(Figure 1.15). The two axes are aligned when the circles and cross-hairs in the axial view overlap oneanother.Figure 1.15 Navigation display of the BrainLab? Computer Assisted Surgery (CAS) system forfemoral hip resurfacing. The user needs to align the drill axis, shown in yellow, to theplanned pin axis, shown in blue. (Source: www.brainLab.com)Although most commercial systems are still based around a static 2D monitor, several researchershave investigated alternative ways to provide visual feedback. In his thesis work, Kassil [2007] de-veloped an LCD display that attached directly to a drill and compared targeting performance with astandard 2D monitor. The tool-mounted LCD display with an axial perspective had statistically lesspositional error (2.41 mm vs. 2.81 mm, p = 0.004) and angular error (1.86 mm vs. 2.32 mm, p = 0.001)but slightly longer completion times (32.5 s vs. 28.6 s, p = 0.02) than the monitor with a standard or-thographic viewpoint [Kassil 2009]. The study also looked at whether augmented video would improveperformance, but there was no statistical difference in error or completion time compared to the axialdisplay without video. Despite these promising results, we decided to use the conventional display sincethe focus of our study was on bracing.We developed and experimented with a number of novel guidance displays, but ultimately chose touse a simple axial perspective display similar to the ones found on several commercial and research sys-tems and a 3D perspective of the same display. The axial guidance display uses an exocentric viewpointaligned with target axis; the target remains centred while the cues attached to the drill move. The 3Ddisplay also uses an exocentric viewpoint, except the position of the camera relative to the target more22CHAPTER 1. INTRODUCTIONclosely represents the position of the subject?s eyes relative to the target. We hypothesized that the 3Dperspective guidance screen that provided better context to the alignment task would be more intuitiveand yield better targeting performance.1.3.3 Cortical DrillingCortical bone, or compact bone, is one of two types of osseous tissue that form bone. Cortical boneforms the cortex or outer shell of most bones and is much denser than cancellous bone [Carter 1978].Cortical drilling is a common task in long-bone fracture repair and is employed as a preparatory stepfor screw placement in both open and closed reductions (Figure 1.16). A hole is created through oneor both cortices so that a screw can be inserted to reduce and stabilize the fracture directly or with theuse of implants. The goal of cortical drilling is to create the hole in the correct location with minimaldamage to other tissue. This includes damaging surrounding bone through excessive generation of heat,and potentially damaging nerves, vasculature, and soft-tissue if the drill penetrates, or plunges, too farafter breaking through the far surface of the bone [Alajmo 2012].Figure 1.16 Cross-sectional view of indirect internal fixation using a plate. Cortical drilling is usedto prepare the holes for the screws in internal fixation of bone fractures. The cortical boneis shown in grey. (Source: reprinted from Wagner [2003], ?2003, with permission fromElsevier).We chose cortical drilling as a likely task for improvement through bracing for several reasons:1. Performance relies on the manual control of drilling thrust force in an unpredictable system;2. It is commonly performed;3. It is often completed under fluoroscopic guidance;4. The bone geometry is relatively simple; and,5. Related research by our group in distal locking of intramedullary nails [Beadon 2007].There are three main aspects of cortical drilling performance: positioning accurately, maintainingan appropriate thrust force to prevent osteonecrosis, and minimizing unwanted penetration of the drill,23CHAPTER 1. INTRODUCTIONor plunge depth. Other considerations include the total task time (as it influences operating room costs)and avoiding drill bit breakage.We are primarily focussed on the issue of force control. High forces are necessary to drill efficientlyand avoid excessive temperature build up that can cause osteonecrosis. Predicting when breakthroughwill occur is challenging because of anatomical variation in bone thickness and bone density. If break-through occurs when significant force is still being applied to the tool, the spring-like properties of thehuman arm result in rapid advancement of the drill before the user has an opportunity to react and thiscan lead to injury (Figure 1.17).Earlier work in our research group investigated applying computer-assistance to distal locking ofintramedullary nails [Beadon 2007]. Typically, this procedure is performed under fluoroscopic guidance.Beadon developed a radiation-free technique to determine the location and orientation of holes using anAurora Electromagnetic Tracking System (Northern Digitial Inc, Waterloo, ON).Figure 1.17 Drill plunge depth is the undesirable and uncontrolled penetration of the drill bit be-yond the far surface of the bone. This is illustrated using a coronal cross section of a distalfemur Sawbones model (Model 3303-3007, Sawbones, Vashon, Washington, USA).Research regarding surgeon performance in cortical drilling is limited. Dubrowski 2004 were oneof the first to study drill plunge, and did so in the context of surgical education. The main finding wasthat plunge was related to pre-breakthrough force (PBF), the thrust force exerted by the user immediatelybefore breakthrough. They found a statistically detectable increase in drill plunge between experiencedsurgeons and residents; practising surgeons plunged (3?2)mm on average. The difference was at-tributed to an anticipatory versus reactionary force control strategy: experienced surgeons anticipatedbreakthrough and reduced their thrust force, whereas less experienced residents drilled with the sameforce. The reactive control strategy translates to larger temporal delays between breakthrough and ter-mination of the drilling action. In a further study, they demonstrated that experienced surgeons use the24CHAPTER 1. INTRODUCTIONnoise produced by the drill as feedback for impending breakthrough [Praamsma 2008].Recently, Alajmo [2012] evaluated the effects of drill bit sharpness, bone quality, and surgeon ex-perience on plunge depth. In the study, surgeons drilled a series of holes in a generic and osteoporoticsynthetic bone model using sharp and blunt drill bits (Figure 1.18). The artificial bone was mounted ina foam bone holder. The authors found a statistically detectable difference of approximately 2.5 mm be-tween experienced and inexperienced surgeons when using the sharp drill bit. Using the blunt bit, therewas no effect of experience. On average, surgeons plunged over 20 mm in normal bone and 10 mm inosteoporotic bone. The mean plunge depth of several subjects was over 30 mm, which means that atleast one of their three trials was even higher. Both these factors can likely be attributed to thrust force;blunt bits require greater amounts of thrust force, while less-dense osteoporotic bone requires less thrustforce.(a)(b) (c)Figure 1.18 A previous study to assess the effect of drill bit sharpness, bone quality and surgeonexperience on drill plunge depth: (a) experimental setup, (a) typical participant, and (c)plunge depth measuring device. Note how the subject has their right arm braced closelyagainst their body as they hold the drill. (Source: reprinted from Alajmo [2012], ?2012Lippincott Williams & Wilkins, with permission.)The most comprehensive study of drill plunge to date was completed recently by Clement [2012].A total of 153 surgeons and physicians each performed three bicortical drillings on a generic artificialbone. The bone was mounted rigidly, with a polystyrene plate on the far side of the cortex to enable25CHAPTER 1. INTRODUCTIONthe measurement of plunge depth with a depth gauge (Figure 1.19). Average plunge depth was 6.3 mm(SD: 0.33?18.67 mm); the study found no statistically detectable difference based on surgical speciality(p > .05) or experience (p > .05).Figure 1.19 A previous study to quantify drill plunge depth. An artificial bone model was mountedrigidly against a polystyrene plate to measure plunge depth. (Source: reprinted from Clement[2012], ?2012, with permission from Elsevier.)Based on these past studies, we know that plunge depth is primarily related to how much force isapplied immediately before breakthrough. Novices tend to use higher forces and a reactionary controlscheme that result in greater amounts of plunge. More experienced users rely on an anticipatory controlscheme, using drilling sounds and knowledge of the anatomy to predict when breakthrough will occurand reduce their forces accordingly.Drill Bit GeometryOptimizing drill bit geometry is an ongoing area of research. It is well established that drill bit geometryhas a significant effect on drilling force [Jacob 1976; Wiggins 1976; Saha 1982; Powers 2006; Darvish2009]. Since plunge depth during cortical drilling has been related to applied drilling force [Dubrowski2004], we hypothesized that different drill bit geometries would result in different plunge depth. Inaddition, early pilot testing identified some bit-dependent interactions during breakthrough. Drill bitswith a negative rake angle, such as a standard twist drill geometry, can grab and pull themselves into thematerial. This behaviour is referred to as ?corkscrewing?, and could potentially lead to greater amountsof plunge depth. To ensure any potential benefits of bracing were not related to a specific drill bitgeometry, a second type was tested. We chose to use a brad point (BP) type drill bit that is unlikely toexperience corkscrewing.1.4 HypothesesFor the navigated drill targeting task:H1.1 A passive rigid forearm brace will enable markedly improved targeting performance compared tofreehand:26CHAPTER 1. INTRODUCTION(a) Smaller final radial error;(b) Smaller final angular error;(c) Smaller position variation; and,(d) Faster targeting.H1.2 A 3D perspective guidance display will enable markedly improved targeting performance com-pared to a 2D axial guidance display:(a) Smaller final radial error;(b) Smaller final angular error;(c) Smaller position variation; and,(d) Faster targeting.For the cortical drilling task:H2.1 Increased levels of brace damping will markedly reduce drill plunge depth compared to freehand.H2.2 Increased levels of brace damping, at a level that markedly reduces drill plunge depth, will notmarkedly increase drilling duration.H2.3 A brad point type drill bit will enable markedly reduced drill plunge depth compared to a HSSdrill bit.In this thesis, we test these hypotheses.1.5 Thesis OrganizationThe remainder of this thesis is organized as follows:In Chapter 2, we describe the development of a CAOS research system for the development and testingof experimental bracing devices for surgical drilling.In Chapter 3, we detail a user study with a cohort of 25 non-surgeons designed to test the effect ofa passive brace for forearm support and the CAOS system guidance display on targeting performance .In Chapter 4, we describe the development of an experimental damper-based bracing device to mini-mize cortical drill plunge, including pilot testing, modelling, and calibration of the damper.In Chapter 5, we detail a user study with a cohort of 25 non-surgeons designed to test the effect ofthe damper-based brace and drill bit type on drill plunge during a simulated cortical drilling task .In Chapter 6, we described the contributions of this research, discuss their strengths, limitations, andimplications, and present considerations for future work in the area of braced orthopaedic surgery.27Chapter 2Design of a Computer Assisted SurgerySystem to Support ExperimentationThe trouble with measurement is its seeming simplicity.? AnonymousIn order to assess the potential benefit of applying a bracing strategy to Computer Assisted Or-thopaedic Surgery (CAOS), we needed to develop a basic CAOS system to use in developing and testingexperimental bracing devices. This system needed to provide the basic planning and navigation func-tionalities of a clinical CAOS system as well as the ability to record other relevant information on taskperformance.This chapter describes the development of such a system to support research into braced CAOS pro-cedures. Our system is based on an NDI Polaris? optical tracker and custom software developed withLabVIEW. In addition to tracking the position of a drill relative to a workpiece, the system measuresdrilling force and drill current. This framework provides the necessary hardware and software for assess-ing the performance of a static rigid brace for improving targeting and a damping brace for minimizingcortical drill plunge.2.1 Braced CAOS Research SystemThe purpose of a computer assisted drilling system is to provide the surgeon with real-time feedbackon the position and trajectory of the drill bit relative to a planned trajectory. In our case, we are alsointerested in recording this information along with other measures of the surgeon?s performance underdifferent experimental conditions. In addition to measuring the tool pose relative to the anatomy, weneed to measure the force being applied to the workpiece to examine the drilling process, and to measurethe current driving the tool to determine when the user starts and stops drilling. We also extend thefunctionality of the system to partially automate the user studies described in Chapter 3 and Chapter 5.28CHAPTER 2. EXPERIMENTAL COMPUTER ASSISTED SURGERY SYSTEM DESIGN2.2 System OverviewThe CAOS Research System is composed of a computer running custom software and several pieces ofhardware: a drill, an optical tracker for measuring position, a force sensor for measuring drilling force,and a power supply for powering the drill and measuring current. A schematic overview of the systemis shown in Figure 2.1.The software is based on a custom LabVIEW (National Instruments, Austin, TX, USA) virtualinstrument (VI), which provides a graphical user interface and the means to interact with the varioushardware used for data acquisition. Our VI is based on the Data Acquisition Reference Application forLabVIEW1. An earlier attempt to use C++ and the Image Guided Surgery Toolkit (IGSTK) [Enquobahrie2007] was abandoned due to problems with inconsistent tracker data logging 2.The system operates on a PC compatible computer (Intel Core 2 Quad CPU 2.40 GHz, internalstorage 4GB, NVIDIA GeForce 9500GT 512MB Video Card), and communicates with an NDI HybridPolaris? Optical Tracking System (NDI, Waterloo, Ontario, Canada) to measure pose and a 50 lb (220 N)capacity S-type load cell (Intertechnology, INC. Don Mills, Ontario, Canada) to measure drilling force.The force data is acquired at 1000 samples per second. The position data is limited to an acquisitionrate of 60 samples per second by the tracking system. Three foot pedals (Programmable USB FootSwitch: StealthSwitch II, H-Mod, Inc., 1954 First Street #513, Highland Park, IL 60035, USA) areused to acquire input from the user. We modified a commercially available hand-held, battery-powereddrill (Model DW907, DeWalt, Baltimore MD, USA). We replaced the battery with a DC Power Supply(Sorenson XHR-40-25, AMETEK Programmable Power, San Diego, CA, USA) to supply consistentpower to the drill and provide current measurement. The current and force signals were digitized usinga 16 bit NI USB-9215 analog-to-digital converter (National Instruments, Austin, TX, USA).2.3 Tracked DrillSeveral modifications were made to the drill so that we could track its position, use a power supplyinstead of the batteries, and connect it to our experimental bracing device.Four retroreflective markers were attached to the drill to enable position tracking. Four of the screwsthat held the drill together were replaced with standoffs to accept the threaded marker mounting posts.Once the markers were attached, the tool was characterized using 6D Architect software (NDI, Waterloo,Ontario, Canada). The definition of the local coordinate frame of the drill is described in Appendix C.2.One of the power packs was modified to connect with a DC power supply. We removed the batterycell and connected leads. By using a power supply instead of the battery cells, the power supplied tothe drill could remain consistent over many trials instead of varying as the battery was depleted. Thismodification also helped reduce the weight of the drill from 1.66 kg to 1.38 kg, making it slightly easierto hold. The other advantage of using the power supply was the ability to externally monitor the current,which provided an indication of when the drill was turned on. Although not required in this study, the1Available from http:\/\/zone.ni.com\/devzone\/cda\/epd\/p\/id\/64382We were unable to consistently record data at 60 Hz and effectively limited to 30 Hz. Although this is sufficient fornavigation, it limited our ability to capture drill plunge events.29CHAPTER 2. EXPERIMENTAL COMPUTER ASSISTED SURGERY SYSTEM DESIGN3HrsoQal &oPSXtHr2StiFal 7raFNHr3oZHr 6XSSl\\6tatiF 5HIHrHQFH )raPH)orFH 6HQsorAPSliIiHrAQaloJ to DiJital &oQYHrtHrD\\QaPiF 5HIHrHQFH )raPH:orN 3iHFH +olGHr)orFH&XrrHQt7raQsIorPs\/&D DisSla\\DrillDrill 0arNHr )raPH\/aE9,(:+arGZarH ,QtHrIaFH3osH3osH3osH8sHr ,QSXt)oot 3HGals)orFH \t &XrrHQtFigure 2.1 Schematic overview of the CAOS Research System.current could also be used to estimate the drilling torque.2.4 Workpiece HolderWe needed a way to mount the workpiece that would satisfy the following requirements:? position the workpiece repeatably? install new workpieces quickly? accommodate drill plunge? measure axial force? track the position of the targetTo satisfy these design requirements, we designed and constructed a workpiece holder based on aflexure design (Figure 2.3). The flexural bearings provide five degrees of support for the holder whileallowing axial force to be transmitted unimpeded to the force sensor (Appendix C.5). The holder itselfis an open box with an opening to allow the drill bit to plunge freely. A raised lip provides an index toposition the workpiece in a repeatable position, and clamps are used to fix it in place. A marker frame (dynamic reference frame (DRF)) is attached to the workpiece holder to track its position.30CHAPTER 2. EXPERIMENTAL COMPUTER ASSISTED SURGERY SYSTEM DESIGNFigure 2.2 A modified DeWalt (Baltimore, MD, USA) Model DW907 cordless drill is fitted withretro-reflective markers to enable optical position tracking. A bracket was attached to connectto the experimental bracing device. The accelerometer shown attached to the drill body wasnot used in the present study.The base of the workpiece holder is rigidly attached to a frame to maintain its position with respectto the work table. The vertical position of the workpiece holder is adjustable to maintain a consistentposture for subjects of different heights. The workpiece used in each study is described in more detailin Section 3.2.2 and Section 5.2.2 and illustrated in Figure 5.4.2.5 Tool, Anatomy, and Target TrackingThe main function of the CAOS system is to track the motion of the tool relative to the patient anatomyand provide a real-time guidance display for the user. The optical tracker measures the pose of markersrigidly attached to the relevant bodies. In our study, we wish to measure the pose of the drill tip relativeto a virtual target referenced to the anatomy. In order to calculate the transforms we are interested in,we need to perform several calibrations and registrations.2.5.1 Rigid Body Tracking NotationIn order to track the motion of one rigid body with respect to another, we need to know both the trans-lation and rotation, hereto referred to as pose. We represent this measure as a right-handed trans-form, TBA, which represents the position and rotation of coordinate system A with respect to coordinatesystem B. Each transform consists of three components of translation (i.e. t = [tx, ty, tz]T ) and a rep-resentation of rotation. Although there are several different ways to represent rotation, we chose touse a quaternion, which is a four element representation of an axis vector and angle of rotation, i.e.q = qw +qxi+qy j+qzk = [qx,qy,qz,qw]T .Other transforms can be composed using the relation:TCA = TBA ?TCB.31CHAPTER 2. EXPERIMENTAL COMPUTER ASSISTED SURGERY SYSTEM DESIGNFigure 2.3 The workpiece holder provides a means to repeatably mount the workpiece, measure theforce applied by the tool, and measure any relative movement. A frame holds the workpieceholder stationary relative to the work table.The composed rotation is found using the quaternion multiplication operation:qCA = qBA?qCB.The composed translation is found by adding the translation components rotated into the base frameusing quaternion conjugation:tCA = tBA +qBA ? tCB ? (qBA)?= tBA + tB?CA .Figure 2.4 shows a scene graph of the CAOS research system. The optical tracker measures the poseof three bodies directly with respect to the tracker coordinate frame (TCF): the tool (T DRILLTCF ), the staticreference frame (SRF) (T SRFTCF ), and the DRF (TDRFTCF ). The SRF is rigidly attached to the environment, andacts as a global reference for the other markers in case the camera is accidentally moved. The DRF isrigidly attached to the workpiece(the simulated anatomy), and is used to track any relative motion of the?patient?.32CHAPTER 2. EXPERIMENTAL COMPUTER ASSISTED SURGERY SYSTEM DESIGN75A&.(5D5,\/\/7,3 G2A\/D5)65)9,(:Figure 2.4 This scene graph illustrates the hierarchical arrangement of the coordinate systems inour Computer Assisted Orthopaedic Surgery (CAOS) research system. A solid arrow betweenframe A and B indicates that the transform T AB was measured directly.2.5.2 Transform: Drill to tip, T DRILLT IPIt is not possible to track the pose of the drill bit directly, so we must calibrate the position of the drillbit tip and the orientation of the drill bit axis with respect to the local coordinate frame of the drill.Whenever the drill bit is changed, the tip position needs to be calibrated. The primary axis of the drillwill remain nominally the same.The goal of this calibration is create a new reference frame with the origin located at the tip, andthe z axis aligned along the drill axis. Figure 2.5 illustrates the drill bit coordinate system and thecalibration procedures that represents the calibration. The tip position translation is determined byperforming a pivot calibration procedure. The tip of the bit is placed in a small divot to fix its locationwhile the drill is pivoted. A least-squares sphere-fitting algorithm is applied to the data to estimate thetip translation, with an RMS error of 0.3 mm as determined in pilot studies. The tip axis is determinedby performing a rotation calibration procedure and applying a unscented Kalman filter (UKF) basedalgorithm (Appendix F). This method has an uncertainty of approximately 0.3? and 0.2 mm in radialtranslation. After the tip and primary axis calibrations are combined, there is still one ambiguous degreeof freedom: rotation around the primary axis, the definition of which is arbitrary. Since the drill markerslie in a vertical plane with respect to the drill, we use them to define the y rotation of the tip coordinateframe. This ?up? direction is used to orient a 3D model of the drill in the guidance display in an intuitivedirection.33CHAPTER 2. EXPERIMENTAL COMPUTER ASSISTED SURGERY SYSTEM DESIGN2.5.3 Transform: Anatomy to Target, T DRFGOALThis transform defines the position of the target anatomy relative to the attached DRF. In a clinicalsetting, preoperative images are typically registered to intraoperative measurements in order to alignthe preoperative plan with the anatomy. In this study we define the goal using the tracked drill andEquation 2.1. The drill calibration, T DRILLT IP , is known; TTCFSRF , TTCFDRF , and TTCFDRILL are measured by thetracker at the time of goal definition. The goal definition varies slightly depending on the experimentaltask.T DRFGOAL = TDRFT IP= T DRFTCF ?TTCFSRF ?TSRFTCF ?TTCFDRILL ?TDRILLT IP= (T TCFDRF )?1 ?T TCFSRF ? (TTCFSRF )?1 ?T TCFDRILL ?TDRILLT IP (2.1)For the plunge depth user study described in Chapter 5, we want to know how far the drill tip travelsafter breaking through the workpiece. The target is defined with respect to the breakthrough plane of theworkpiece: the origin is on the plane and the z-axis is aligned with the normal vector. The breakthroughplane was defined by recording the position of three small divots on the surface of the workpiece holderwith the drill bit tip and defining the plane that passes through these three points.For the targeting user study described in Chapter 3, the goal is a virtual trajectory that passes throughthe workpiece. This goal trajectory represents the desired entry point and orientation of a hole to whichthe user is trying to align the drill bit. The drill is used to define a reference trajectory approximatelycentred on and perpendicular to the surface of the workpiece. Goal trajectories are generated by applyingD5,\/\/77,3yxzxzy7iSDrill(a) Coordinate System (b) Pivot Procedure (c) Rotation ProcedureFigure 2.5 Illustration of the (a) drill bit tip coordinate system and the drill bit calibration. Theunknown transform from the local drill coordinate frame defined by the markers to the drillbit must be calibrated. A (b) pivot and (c) rotation calibration procedure are combined todetermine the location and orientation of the drill bit tip.34CHAPTER 2. EXPERIMENTAL COMPUTER ASSISTED SURGERY SYSTEM DESIGNrandom rotations and translations to this reference trajectory. We used horizontal distances of ? 25 mmand horizontal angles of ? 5?.2.5.4 Transform: Goal to Tip, T GOALT IPThe position of the tip frame in the target reference frame is the primary transform used by the guidancedisplay, and provides a direct indicator of the targeting error. It is calculated for each measurementusing:T GOALT IP = TGOALDRF ?TDRFTCF ?TTCFDRILL ?TDRILLT IP= (T DRFGOAL)?1 ? (T TCFDRF )?1 ?T TCFDRILL ?TDRILLT IP . (2.2)By choosing the coordinate systems appropriately, individual components of this transform canprovide meaningful error metrics. For example, the z-component represents the perpendicular distanceof the drill bit tip beyond the breakthrough plane during plunge trials, while the x- and y-componentsrepresent the horizontal and vertical components of the tip error during targeting trials.2.5.5 Transform: View to Goal, T GOALV IEWThe guidance display represents a view from a virtual camera. In our case, the camera is attached to thetarget in an exocentric arrangement, which means that the view remains fixed relative to the target, andthat the cues representing the tool move as the tool moves in space. These transforms are constant andare chosen differently depending on the perspective of the display. They are discussed in more detail inSection 2.6.2 and Section 2.6.3.2.6 Graphical User InterfaceThe graphical user interface (GUI) provides information to and receives information from the surgeon.Typical clinical CAOS systems are designed for a particular procedure, and are set up to guide the surgeonthrough each step of planning, navigation, and validation. The focus of our system is on navigation, sothe most important component is a Guidance Display.2.6.1 Guidance DisplayThe Guidance Display provides the surgeon with real-time visual feedback of the pose of the toolrelative to the target. For surgical drilling, the position and orientation of the drill bit relative to thetarget trajectory are displayed. We designed two different types of display, one with a 2D axial view ofthe target, and one with a 3D view of the target.The guidance display is displayed on a secondary monitor (BENQ FP951, 19 inch LCD SXGA, 1280x 1024 resolution, 0.294 mm pixel pitch) The monitor used in the study has a resolution of 86.3 pixelsper inch. A near full-screen viewport of 1276 x 895 pixels is used to display the guidance display.35CHAPTER 2. EXPERIMENTAL COMPUTER ASSISTED SURGERY SYSTEM DESIGNIn addition to the guidance display, a standard orthographic view was implemented with the camerasfixed to the TCF. These views are commonly used by commercial CAS systems for gross positioning.These views display 3D models of the drill, the SRF, the DRF and a semi-transparent representation ofthe working volume of the tracker. The models were created in 3D computer assisted design software,then imported into LabVIEW as stereolithographic files (.stl).2.6.2 2D Axial Guidance DisplayThe 2D Axial Display is based on a guidance display commonly found in current CAOS system. Theexocentric view is fixed along the goal trajectory. As shown in Figure 2.6, the display consists of a blackcrosshair attached to the target and two targeting cues. The red cue represents the position of the drillbit tip, while the yellow cue represent the position of the rear of the drill. To align the trajectory, boththe red and yellow cue should be aligned to the black cross hair. The frame is 200 mm wide, 150 mmtall and each of the lines are 2 mm wide (Appendix C.3). The conic or triangular cross hairs have a baseof 20 mm and a height of 30 mm.For the 2D display, the T GOALV IEW transform is calculated based on a camera position of [0, 0, ?300]T ,a camera target of [0, 0, 0]T , and an up direction of [0, 1, 0]T .2.6.3 3D Box Guidance DisplayThe motivation behind the 3D box display was to provide the user with a more intuitive view of thetargeting task. The exocentric view is fixed relative to the goal from a point offset vertically from thetrajectory to simulate the perspective of a user looking down on the scene. As shown in Figure 2.7, thedisplay is based on a rectangular prism that is centred on the target. The drill is displayed as a blackcylinder, with a blue line that projects the current trajectory. The red sphere represents the locationwhere the drill axis crosses the target plane. The blue sphere represents the location where the drill axiscrosses the offset plane which is parallel to the target plane and offset 300 mm. To align the trajectory,the red and blue spheres should be aligned to the front and back cross hairs, respectively. This displayalso makes is easier to determine how far the tip is from the goal plane. The target frame is 200 mmwide, 150 mm tall, and 300 mm deep. Each of the lines are 2 mm wide (Appendix C.3). The targetingspheres have a diameter of 10 mm.For the 3D display, the T GOALV IEW transform is calculated based on a camera position of [0, 300, ?300]T ,a camera target of [0, 0, 150]T , and an up direction of [0, 1, 0]T .2.6.4 Effective ResolutionTable 2.1 lists the resolution of the guidance displays in mm\/pixel. Figure 2.8 shows how the movementof the targeting cues on the guidance display compares to the real world movement of the tool for themonitor used in the study. Tip and tail motion is amplified in both directions using the 2D guidancedisplay. The 3D guidance display is more variable: horizontal tip movement is slightly amplified,whereas vertical tip and both tail movements are attenuated. Due to the separation of the front and reartargets in the 3D perspective, the 3D display cues move through a smaller range of the screen for a given36CHAPTER 2. EXPERIMENTAL COMPUTER ASSISTED SURGERY SYSTEM DESIGN(a)(b)Figure 2.6 2D axial perspective guidance display: (a) offset and (b) on target. The black frame is150 mm tall and 200 mm wide and centred on the target. The view is fixed at a distance of300 mm from the target (out of the page). The red cue represents the location of the tool tip.The yellow cue, for aligning the trajectory, is ?mounted? to the rear of the tool, 300 mm fromthe drill tip along the drill tip axis. These images are approximately 1?4 scale.37CHAPTER 2. EXPERIMENTAL COMPUTER ASSISTED SURGERY SYSTEM DESIGN(a)(b)Figure 2.7 3D Perspective Box Guidance Display: (a) offset (b) on-target. The red cue representswhere the drill axis crosses the target plane. The blue cue represents the drill angle, andspecifically where the projection of the drill axis crosses the xy plane 300 mm from the target.The location of the drill tip from the target plane is also indicated by a thick black cylinder,providing a cue for depth. The black frame is 150 mm tall, 200 mm wide, and 300 mm deep.These images are approximately 1?4 scale.38CHAPTER 2. EXPERIMENTAL COMPUTER ASSISTED SURGERY SYSTEM DESIGNdistance in real space than the 2D cues. This difference is on the order of 45?65 % or less.Table 2.1 Effective Guidance Display Targeting ResolutionDisplay Tip Cue Tail CueX (mm\/px) Y (mm\/px) U (mm\/px) V (mm\/px)2D 0.16 0.16 0.16 0.163D 0.27 0.53 0.43 0.67Minimum change in drill position per pixel movement of cue.Based on guidance display viewpoint and viewport size (1276 pxx 895 px).Figure 2.8 Corresponding movement of targeting cues on guidance display when drill is moved,based on the viewpoint, display viewport, monitor resolution (86.3 pixels\/inch) and monitorsize. Note that the 2D-perspective guidance display amplifies all motion, whereas the 3D-perspective guidance display attenuates all motion except horizontal tip movements.2.6.5 User InputIn addition to the keyboard and mouse, a set of three foot pedals can be used to acquire input from theuser (Programmable USB Foot Switch: StealthSwitch II, H-Mod Inc., Highland Park, IL, USA). Thisallows the user to interact with the system while their hands are occupied with the tool. For example,one foot pedal is used to set a target based on the current drill position, while another pedal is used tostart and stop data recording.39CHAPTER 2. EXPERIMENTAL COMPUTER ASSISTED SURGERY SYSTEM DESIGN2.7 Measuring Drill ForceA uniaxial force sensor was used to measure the axial force applied to the workpiece holder at 1000 Hz.The force sensor was calibrated by suspending masses of known weight to the workpiece holder viaa pulley. The results are shown in Figure 2.9. This sensor has a rated accuracy of 0.037 % full scaleor approximately 0.1 N. Figure 2.10 illustrates the raw and filtered force data for a static trial. Weapplied a low pass, fourth order, zero-lag Butterworth filter with a cutoff frequency of 60 Hz. Zero-phase filtering was implemented using the Matlab function filtfilt after the data were collected.The cutoff frequency was chosen to obtain a signal-to-noise ratio of approximately one at the cut-offfrequency. The raw and filtered standard deviations of the force signal are 0.04 N and 0.01 N.Figure 2.9 The force sensor was calibrated by suspending known masses from the workpieceholder via a pulley. The gain was determined by linear regression.2.8 Measuring Drill CurrentWe used the remote current monitoring on the power supply to measure the current from the drill at1000 Hz. This provided a simple way of determining when the drill was running. The output currentmonitor offset potentiometer and output current monitor range potentiometer were adjusted to ensurethe 0 V to 5 V output accurately represented the 0 A to 25 A current range as described in the OperatingManual. This calibration meant the current gain was simply 5 A\/V. We applied a low pass, fourth order,zero-lag Butterworth filter to the data with a cutoff frequency of 60 Hz. Zero-phase filtering was im-plemented using the Matlab function filtfilt after the data were collected. The cutoff frequencieswas chosen to obtain a signal-to-noise ratio of approximately one at the cutoff frequency. A thresholdof 0.2 A was selected to define when the drill was considered powered, below the experimentally deter-mined current draw required to barely start the drill turning (0.31 ? 0.08 A). The free-running, no-load40CHAPTER 2. EXPERIMENTAL COMPUTER ASSISTED SURGERY SYSTEM DESIGNFigure 2.10 Raw and filtered force during a static trial.current was also determined experimentally. Raw and filtered data from a static trial are illustrated inFigure 2.11. The raw and filtered standard deviations of the current signal are 0.07 A and 0.007 A.Figure 2.11 Raw and filtered current during a static trial. Note the noise present when the drill isnot powered.The current trace of a typical plunge trial is illustrated in Figure 2.12. The drill draws approximately0.31 A when beginning rotation under no load, and 3.6 A when rotating freely. A threshold of 0.2 A wasused to determine when the drill was powered.41CHAPTER 2. EXPERIMENTAL COMPUTER ASSISTED SURGERY SYSTEM DESIGNFigure 2.12 Plot of drill current during a typical simulated cortical drilling trial. Free runningcurrent of 3.6 A and and onset threshold of 0.2 A were determined through pilot testing.2.9 User Study ManagementIn addition to the real-time navigation and data logging of the CAOS research system, we also developedand integrated an automated experimental trial management system into our LabVIEW VI for the userstudy. For each subject, the task schedule (described in Section 3.2.3 and Section 5.2.3 was entered intothe system. The system automatically changed guidance display type and prompted the user to changeexternal conditions (e.g., bracing, drill bit type) for each trial.2.10 System PerformanceThere are several factors that influence the overall performance of our system. Since our experimentalCAOS research system is primarily a navigation-type application, the primary performance indicatorsare the latency and accuracy of the guidance display, i.e., how well does the information on the screenrepresent the current surgical state.To minimize latency, graphical processing was kept simple and there was no perceptible delay be-tween the motion of the tool and the motion of the cues on the guidance display. The limiting factor isthe maximum 60 Hz acquisition rate of the tracking hardware; however, most of the movements of thetool are slow enough that this is not an issue.The spatial uncertainty of a tracking system is typically characterized using target registration error(TRE), which represents the distance between corresponding points in two registered spaces. The TRE42CHAPTER 2. EXPERIMENTAL COMPUTER ASSISTED SURGERY SYSTEM DESIGNdepends on the uncertainty of measuring a single marker, (i.e. fiducial localization error (FLE)), thegeometry of the markers that define the rigid bodies (i.e. fiducial registration error (FRE)), and thespatial arrangement of rigid bodies. Fitzpatrick [1998] developed an expression to estimate the TREbased on the FLE, and the number of and configuration of fiducial markers,?TRE2(r))???FLE2?N(1+133?k=1d2kf 2k), (2.3)where N is the number of fiducial markers, fk is the root mean square (RMS) distance of the fiducialsfrom the principal axis k and dk is the distance of the target from principal axis k. West [2002] showedthat when a tool is measured relative to a secondary coordinate frame, the overall TRE can be found byapplying Equation 2.3 to each frame independently and adding the resulting values in quadrature:(TRE3)2 = (TRE1)2 +(TRE2)2 (2.4)The NDI Polaris? optical tracking system has a rated volumetric uncertainty (i.e. FLE) of 0.35 mmRMS within the silo-shaped working volume characterized between 1400 mm and 2400 mm from thecamera (Appendix C.1.1). For a typical tip calibration of [-31.86 -27.99 161.07], a target location of[-68.29 94.14 13.13], and the marker configurations as described in Appendix C, the TRE predicted fromEquation 2.3 is 1.57 mm. This equation assumes an isotropic FLE model, whereas the uncertainty in anoptical tracking system is know to be anisotropic with greater uncertainty parallel to the camera axis.We recorded a trial while the drill was stationary to experimentally quantify the noise and design anappropriate filter. Noise in the position data is a result of jitter in the optical tracking system. The signalnoise in each component of the transform is approximately normal. Figure 2.13 illustrates the processedand filtered pose data for a static trial and Table 2.2 lists the standard deviation for each component.As expected, the components approximately aligned with the camera axis (i.e., tx and tu) exhibit greateruncertainty than those in the camera plane (i.e., ty, tz, and tv).It is important to note that in order to maintain a responsive display, position filtering was only ap-plied in post-processing ? the guidance display for the targeting study was driven by the raw transforms.Noise in the tracked position ? primarily a result of jitter ? was directly displayed to the user.For the drill plunge trials, the primary metric of interest is how far the drill bit tip travels past theback surface of the workpiece, or the front surface of the workpiece holder. The uncertainty in thebreakthrough plane varies with position due to uncertainties arising from measuring the three planedefinition points. The uncertainty varies from 0.6 mm to 1.6 mm and increases significantly outside thearea bound by the plane definition points (Figure 2.14).2.11 ConclusionsIn this chapter we described the CAOS research system used in the development and testing of an exper-imental damping brace for minimizing drill plunge during cortical drilling and an experimental bracefor forearm support during navigated targeting.43CHAPTER 2. EXPERIMENTAL COMPUTER ASSISTED SURGERY SYSTEM DESIGN(a)(b)(c)Figure 2.13 Raw and filtered position data from a trial with a stationary drill: (a) horizontal, (b)vertical, and (c) depth.44CHAPTER 2. EXPERIMENTAL COMPUTER ASSISTED SURGERY SYSTEM DESIGNTable 2.2 Goal to Tip Tracking NoiseComponent Position Velocity(mm) (mm\/s)x 0.29 (0.11)a 23.4 (2.0)y 0.12 (0.05) 9.9 (0.8)z 0.19 (0.08) 15.8 (1.3)u 0.28 (0.13) 23.3 (2.4)v 0.12 (0.04) 9.8 (0.7)rb 0.31 (0.12) 25.4 (2.2)r2c 0.31 (0.14) 25.2 (2.5)a SD Raw (SD Filtered)b Tip error:?x2 + y2c Tail error:?u2 + v2Figure 2.14 Uncertainty in breakthrough plane. The rectangular box represents the surface of theworkpiece holder with the approximate locations of the three divots (P1,P2,P3) used to definethe breakthrough plane. The contour lines indicate the positional uncertainty of the drill bittip relative to the plane. The inner circle represents the hole in the workpiece holder to allowfor drill plunge. In this region, uncertainty increases from 0.6 mm to 1.6 mm towards theupper right.45CHAPTER 2. EXPERIMENTAL COMPUTER ASSISTED SURGERY SYSTEM DESIGNThe CAOS research system is capable of tracking the pose of the tool and the workpiece relative toa SRF at a rate of 60 Hz. We developed a unscented Kalman filter (UKF) based calibration algorithmand routine to determine the primary axis of the drill bit and combined that with a pivot calibration todetermine the tip location. The uncertainty of a single spatial measurement is approximately 1.6 mm,with approximately twice as much uncertainty along the axis aligned with the camera axis. The work-piece holder is capable of repeatably mounting a test workpiece and measuring a maximum axial forceof 200 N at 1000 Hz. The current supplied to the drill can be measured at 1000 Hz to determine whenthe drill is powered on.Based on these results, the CAOS research system should be acceptable for use in the targeting studydescribed in Chapter 3 to assess a static rigid brace for forearm support and the development and testingof a damping brace for minimizing drill plunge in cortical drilling described in Chapter 4 and Chapter 5,respectively.46Chapter 3User Study on Influence of Simple Bracingand Display Design on NavigatedTargetingBefore shooting, one must aim.? African ProverbTo assess the potential value of using passive rigid forearm bracing, we created a task to simulatenavigated targeting of a surgical drill. The goal of this task is to align the drill bit axis to a pre-determinedtrajectory using the visual feedback provided by a guidance display.We designed and conducted a user study in which subjects performed the drill targeting task whilethe drill bit pose and task duration were measured. We compared the effect of static arm brace use andfeedback display design on positional and angular targeting error.3.1 HypothesesIn Section 1.4, we hypothesized that:H1.1 A passive rigid forearm brace will enable markedly improved targeting performance compared tofreehand:(a) Smaller final radial error;(b) Smaller final angular error;(c) Smaller position variation; and,(d) Faster targeting.H1.2 A 3D perspective guidance display will enable markedly improved targeting performance com-pared to a 2D axial guidance display:(a) Smaller final radial error;47CHAPTER 3. NAVIGATED TARGETING USER STUDYParticipantUnbracedT012DT02 T10DisplaySubjectDaPSiQJTarget3DT01 T02 T10 T012DT02 T103DT01 T02 T10ForearmBraceFigure 3.1 Illustration of targeting study design. Each participant was assigned to a task schedulewith a randomized brace order and display order. A set of 10 targets were randomly generatedand repeated for each combination of brace and guidance display. The display order was thenrepeated for the second brace condition.(b) Smaller final angular error;(c) Smaller position variation; and,(d) Faster targeting.The first hypothesis is based on similar work that demonstrated bracing in the form of a static armrest could improve precision in a positioning task [Zupanc?ic? 1998] and reduce the task completion timeof a simulated micro-surgical task [Yako 2009].The second hypothesis is based on our belief that a guidance display that shows more details of taskcontext should be more intuitive and easier to use.3.2 Materials and Methods3.2.1 Study DesignWe designed a user study to test the effect of forearm bracing and guidance display design on targetingerror and targeting speed. Subjects participated in both this study and the simulated cortical drillingstudy described in Chapter 5 during a single session in a randomly assigned order.We adopted a within-subjects design. The conditions were nested instead of fully randomized be-cause changing the forearm bracing took time and manual intervention from the researcher, which wouldhave a significant effect on the total testing time. There were a total of 4 blocks, with two guidance dis-play levels (2D,3D) nested within two bracing levels (None, Forearm); the same 10 randomly generatedtargets were used for each block (Figure 3.1). This 2x2x10 design yielded a total of 40 navigated target-ing trials per subject. The number of targets was chosen so that subjects could complete both the drilltargeting task and the cortical drilling task in approximately one hour.3.2.2 Experimental SetupThe experiment was conducted in the Neuromotor Control lab, located at the Point Grey Campus ofthe University of British Columbia. Subjects stood in front of a work table, and positioned a drill sothe drill bit was in contact with a piece of wood clamped to the workpiece holder. A computer monitor48CHAPTER 3. NAVIGATED TARGETING USER STUDYprovided visual feedback through a guidance display to help the participant align the drill bit axis to apre-determined goal trajectory. The distance from the subject?s eyes to the centre of the monitor wasapproximately 1100 mm. A forearm brace was mounted to the rigid frame and used to support theforearm during certain trials. The overall setup is shown in Figure 3.2.MonitorDRFStart PositionSRFBraceDrillWorkpiece HolderForce SensorFigure 3.2 Experimental setup of drill targeting task. A real-time guidance display on the com-puter monitor showed the drill pose relative to the workpiece, which was measured with anoptical position tracker (not shown). A passive rigid brace supported the user?s forearm duringtargeting.Passive Rigid Brace For Navigated TargetingEarly work in braced robotics demonstrated an improvement in positional repeatability in both humansand robots with a passive rigid brace [Zupanc?ic? 1998]. We decided to test if a passive rigid brace couldproduce similar improvements in navigated targeting performance.We modified an arm chair rest to support the forearm of a user while they targeted the drill (Fig-ure 3.3). The length was extended by replacing the existing pad with a 30 mm x 30 mm x 400 mm pieceof sanded wood. The height of the brace was adjusted before the task so that the forearm would besupported when the drill was in the vicinity of the target.By carrying some of the weight of the drill, the brace should reduce muscle fatigue and limit ex-cursion of the arm in the region of contact, and therefore improve targeting accuracy and speed. Sincethe arm rest provides little lateral support, we predicted there will be less error in the more constrained49CHAPTER 3. NAVIGATED TARGETING USER STUDYvertical direction than in the less constrained horizontal direction.Figure 3.3 A modified arm chair rest provided a static rigid brace for the forearm.Drill BitSince no holes were actually drilled, the type of drill bit was not important. Each of the drill targetingtrials was completed using a 3\/16 inch (4.76 mm) brad point bit (Model 48-15-0185, Milwaukee ElectricTool Corp., Brookfield, WI 53005, U.S.A). This type of drill bit has a well defined tip so that subjects canfocus on alignment rather than worrying about the bit slipping. A new bit was used for approximatelyevery 5 subjects, which we deemed a good compromise between wear and cost-effectiveness.WorkpieceA test workpiece of 5 mm thick oak wood was attached to the workpiece holder described in Section 2.4with two clamps. The workpiece provided a rigid surface to target against. Oak was chosen as aconvenient and inexpensive alternative to bone.Goal TrajectoriesA set of 10 randomized trajectories were generated for each participant. A reference trajectory wasdefined perpendicular to the workpiece and at a height such that the participant?s forearm supported bythe brace. Each goal trajectory was then offset from the reference trajectory by a horizontal distanceand a horizontal angle generated from a uniform distribution of ? 25 mm and ? 5?, respectively. Thesevalues provided some targeting variation while ensuring that the trajectories were approximately centredon the workpiece holder. An example set of goal trajectories is illustrated in Figure 3.4.50CHAPTER 3. NAVIGATED TARGETING USER STUDYFigure 3.4 Example goal trajectories. Looking vertically down, this figure shows the workpieceat the top on edge and a set of goal trajectories generated with a random horizontal offset,?x ? U (?25mm,25mm), and random horizontal rotation, ??y ? U (?5?,5?). The height(into the page) of the reference trajectory was adjusted to match the height of each participant.Guidance DisplaysWe tested the 2D and 3D guidance displays illustrated in Section 2.6.2 and Section 2.6.3. The 3D displayprovides more context for the targeting task, so we predict that it should improve targeting performancecompared to the 2D axial display.3.2.3 Experimental TaskThe goal of the targeting task was to align the drill bit with the goal trajectory as quickly and as ac-curately as possible and maintain that orientation until the end of the fixed duration. Even though thetip was in contact with the workpiece, no hole was drilled. A trial duration of 15 seconds was selectedthrough pilot testing as a good balance between difficulty and fatigue.3.2.4 SubjectsTwenty-five subjects (thirteen males; twelve females; age range 25?44; mean age 30) were recruitedfrom the University of British Columbia Point Grey Campus. The inclusion criteria was an age of 19?65 years, normal or corrected-to-normal vision, and no history of neuromuscular injury to the upperextremities. Subjects reviewed the Subject Consent Form (Appendix B.1) and provided informed con-sent before participation. Each subject completed the drill targeting and cortical drilling studies in asingle session that lasted approximately one hour. A $10 gift card was provided as compensation for thesubject?s time. This study was approved by the UBC Behavioural Research Ethics Board (H09-01080).51CHAPTER 3. NAVIGATED TARGETING USER STUDYTable 3.1 Example Targeting Testing ScheduleSubject ID Task Brace Guidance Display1 Targeting, Drilling Unbraced, Forearm 2D, 3DEach subject was assigned to a predetermined task schedule which dictated the order in which thetask conditions were completed.3.2.5 Conducting the ExperimentAfter providing informed consent, subjects were asked to provide their age, gender, and dominant hand.In order to ensure their safety, subjects were required to wear safety glasses, roll up long sleeves, removeany jewellery from the hands, and tie back any long hair.Each subject was assigned a unique subject identification number to anonymise their data and acorresponding task schedule (Table 3.1). This task schedule dictated the order in which subjects wouldcomplete the two experimental tasks, and the corresponding order of damping levels and drill bit types.A complete list of testing schedules can be found in Appendix D.1.The height of the workpiece holder was adjusted in order to maintain similar posture between sub-jects. The workpiece holder was adjusted vertically so that the subject?s forearm was parallel to the floorand 90? relative to the upper arm (Figure 3.5). The height of the static arm brace was adjusted so thatthe forearm was supported in this position.Figure 3.5 The height of the workpiece holder was adjusted so the subject?s forearm was parallelto the floor and approximately 90? relative to the upper arm. The height of the forearm bracewas adjusted to support the forearm in this position.Subjects were instructed to perform several targeting trials to become comfortable with each guid-ance display type. Trials were completed according to the task schedule. The researcher installed theforearm brace, while the guidance display was changed automatically by the experimental CAOS system.The beginning and end of each trial were indicated with audible beeps. The trial began with thedrill at rest in the start position, with the tip in a small divot on the work table. The researcher manuallyinitiated the trial through the CAOS research system, which played a set of three audible beeps. On the52CHAPTER 3. NAVIGATED TARGETING USER STUDYthird beep, the guidance display would turn on and the participant moved the drill to align the drill bit tothe goal trajectory. After 15 seconds had elapsed, the CAOS research system would play a single beep toindicate the end of the trial. The guidance display would turn off, and the subject would return the drillto the starting position in preparation for the next trial. Subjects were told that if they felt fatigued aftercompleting a trial, they could take a break by returning the drill to the rest position.After each block, the research CAOS system automatically changed the guidance display type. Afterthe second block, the researcher changed the bracing condition. Subjects had an additional opportunityto rest while these changes were made.After completing all the targeting trials, subjects were asked to complete the targeting portion of theDebrief Questionnaire (Appendix B.2).3.2.6 Acquiring and Processing the DataData AcquisitionDuring each trial, data from the tracker and the force sensor were recorded. The tracker data consistedof the SRF, the DRF, and the tool measured at 60 Hz and the computed transforms of the drill bit tip inthe target coordinate frame, T GOALT IP . Each of these transforms consisted of three Cartesian coordinates,a quaternion and a measure of uncertainty. The axial force on the workpiece was recorded at 1000 Hz.Each type of measurement was saved to its own file and organized by a unique trial identification num-ber.Data ProcessingData from each trial were processed using custom routines written in MATLAB? (Version 7.14.0.739,The Mathworks, Natick, MA, USA). After interpolating any missing frames1, the transforms were fil-tered with a low pass, fourth order, zero-lag Butterworth filter with a cut-off frequency of 5 Hz. Theforce and current data were filtered with a low pass, fourth order, zero-lag Butterworth filter with acut-off frequency of 60 Hz. Cutoff frequencies were selected to achieve a signal-to-noise ratio of ap-proximately one at the cutoff frequency. Illustrative examples of the raw and filtered force, current, andposition data can be found in Section 2.7, Section 2.8, and Section 2.10, respectively.Performance MetricsIn order to quantify task performance and compare experimental conditions, we extracted several met-rics from the processed data. Accuracy is our primary interest, along with speed and variation withinand between trials.For accuracy we used the error between the drill bit and the goal trajectory. We chose to use a similarapproach to how the guidance displays were created, and represented the error using the distance fromthe goal trajectory to two points along the drill bit. We used the tip of the drill as one point, and defined1We used the MATLAB? function interp1 to replace missing frames and ensure the data was spaced uniformly in timeusing the piecewise cubic spline method. The median percentage of missing frames was 6 % (IQR: 5?10 %, Range: 2?29 %).53CHAPTER 3. NAVIGATED TARGETING USER STUDYthe tail as a point 300 mm along the drill axis towards the back of the drill. The horizontal and verticalerror of the tip were available directly as the x and y components of the composed transform T GOALT IP , i.e.,tx and ty. The horizontal and vertical error of the tail, tu and t f , were calculated from using the positionand rotation of T GOALT IP . If the drill bit was perfectly aligned with the goal trajectory, all four componentswould be zero. The mean and standard deviation of the last 0.5 s of the trial were calculated to determinethe final error (Figure 3.6b).Four additional accuracy metrics were calculated: tip radial error, tail radial error, angularerror, and targeting error (Figure 3.7a). The radial errors are simply combinations of the horizontaland vertical components and the targeting error is the sum of the two radial errors:eR =?t2x + t2y , (3.1)eR2 =?t2u + t2v . (3.2)eT = eR + eR2 (3.3)The angular error (?) is defined as the angle between the primary axis of the drill bit and thegoal trajectory and is ideally zero. The angle between two vectors can be found using the dot product.Since the z?axis of the GCF is aligned with the goal trajectory, the unit vector of the goal trajectory isugoal = [0,0,1]T . The drill bit axis is also aligned with the z?axis of the tip coordinate frame, so theunit vector of the drill bit axis in the GCF is found by rotating the z?axis with the quaternion of thecomposed transform Tgoaltip ,ubit = qgoaltip ? [0,0,1]T ?qtipgoal. (3.4)The angular error is then found using the dot product:eA = arccos(??ubit ?ugoal??)(3.5)We defined the final accuracy as the average error value over the final 0.5 s of each trial. The vari-ability or intra-trial precision represents how well a user maintained the final accuracy; we calculatedthis metric using the standard deviation of the error values over the same time period (Figure 3.7b). Therepeatability or inter-trial precision, or how consistent subjects were between trials, was calculated asthe standard deviation of the final errors for each block under a set of conditions.To assess targeting speed, we analysed how long it took for subjects to transition from the targetingphase to hold phase.A gross targeting time (s) was used to correct for any difference in initial target distance. In orderto maintain consistent posture between subjects, the height of the workpiece was adjusted to match the54CHAPTER 3. NAVIGATED TARGETING USER STUDY(a)(b)Figure 3.6 Tip and tail error metrics of a typical trial: (a) the horizontal and vertical distance fromdrill bit tip to the goal trajectory are represented by tx and ty. tz represents the normal distancefrom the goal plane to the drill bit tip, and tu and tv are the translation of a point projected300 mm from the tip along the drill axis. (b) the average over the last 0.5 s of the trial are usedto define the the final error metrics.55CHAPTER 3. NAVIGATED TARGETING USER STUDY(a)(b)Figure 3.7 Combined error metrics for typical targeting trial: (a) tip radial error, eR, tail radialerror, eR2, angular error, eA, and targeting error, eT ; (b) the average over the last 0.5 s of thetrial are used to define the the final combined error metrics.56CHAPTER 3. NAVIGATED TARGETING USER STUDYsubject?s height; however, since the start position was fixed relative to ground, the distance between thestart and goal varied slightly. In order to correct for any difference in targeting speed, we divided thetask into gross and fine positioning phases using the Euclidean distance of the tip from the trajectoryorigin:d =?t2x + t2y + t2z . (3.6)We chose a distance threshold of 100 mm to separate gross and fine positioning (Figure 3.6a).Radial targeting time (s) was defined as the time when the drill bit remained in contact with theworkpiece (Figure 3.8b). A contact force threshold of 1 N was determined through pilot testing as theminimum force when the drill tip was barely in contact with the workpiece.Angular targeting time (s) was defined as the time when the angular orientation was held relativelysteady (Figure 3.8c) We developed a method using the reverse time integral that is insensitive to the finalangular error (Appendix A.2).3.2.7 Statistical AnalysisStatistical analyses were conducted with R statistical software (Version 2.15.1, R Foundation for Statisti-cal Computing, R Development Core Team, 2012). Since our data involved repeated measures on blocksnested within subjects and the response variables are continuous, we used a linear mixed model (LMM)for analysis.Linear Mixed ModelsA mixed-effects model is a type of statistical model that contains both fixed effects and random effects.Fixed effects are parameters associated with an entire population or with certain repeatable levels ofexperimental factors, while random effects are associated with individual experimental units drawn atrandom from a population [Pinheiro 2000]. Mixed-effects models are particularly useful when datais grouped, such as longitudinal data, repeated measures, blocked designs, and multilevel data. Mea-surements grouped within a statistical unit are typically correlated, which violates the assumption ofindependent measurements in analyses like analysis of variance (ANOVA). Mixed-effects models arealso capable of handling both balanced and unbalanced data, which prevents the exclusion of subjectswith one or more missed data points.A LMM approach was used for several reasons:? We wish to generalize our results to a larger population, so SUBJECT should be treated as a randomeffect.? BRACE and DISPLAY were fixed effects.? We have a mixture of continuous and categorical covariates.? The study followed a nested design, so trials within a block could not be considered independent.? We expected and observed unequal variances between groups.57CHAPTER 3. NAVIGATED TARGETING USER STUDY(a)(b)(c)Figure 3.8 Targeting time for a typical trial: (a) gross targeting time, tG, is defined using a distancethreshold between drill bit tip and goal origin, (b) radial targeting time, tR, is defined using acontact force threshold of 1 N, and (c) angular targeting time, tA, is defined using the reverseintegral of angular error and the root mean square (RMS) of the angular error.58CHAPTER 3. NAVIGATED TARGETING USER STUDY? Some trials were missing or had to be removed, so the data were not balanced.We based our analysis on the ?top-down? modelling approach described in West [2006] for a three-level LMM and performed the modelling using the R package nlme [Pinherio 2013]. We chose betweenmodels by comparing the values of the Bayesian Information Criterion (BIC) and by calculating likeli-hood ratio statistics with a significance level of ? = .05. A detailed description of the analysis can befound in Appendix E.1.Analysis of the navigated targeting study data must consider three levels (Table 3.2). We includedfixed effects for all covariates under consideration (REP, DISPLAY, BRACE, AGE, and GENDER). HANDwas not included since there were only 3 left handed subjects in the study, and we did not expect anyeffect. Since we want to make inferences regarding the population that our subjects were drawn from,we used a random effect to model the SUBJECT factor. Based on our study design, we also included arandom intercept and slope for each block nested within a subject.Table 3.2 Navigated Targeting Data StructureLevel of Data VariableCluster of Units(Level 3)Cluster ID (Random) SubjectCovariates Age, dominant hand, genderAnalysis Unit(Level 2)Unit ID (Random) BlockCovariates Brace condition, display typeTime(Level 1)Time variable TargetDependent variables Final error, final variation, targeting timeTime-varying covariates Tip error, tail errorSource: adapted from Li [2012: p. 274].3.3 ResultsIn this section, we present the results of the targeting user study. We illustrate a typical trial, a typicalblock, and a typical subject before presenting descriptive and statistical results for the overall study.Since many of the metrics do not follow a normal distribution, descriptive statistics are reported hereas median and inter-quartile range (IQR), or as a 95 % confidence interval (CI).3.3.1 Typical TrialEach targeting trial is divided into three phases: gross positioning, fine positioning, and hold (Fig-ure 3.9). In this example, the subject took 1.6 s to move the drill tip within the 100 mm gross distancethreshold. After 8.5 s of positioning, the tip is held fixed and after 9.7 s the drill orientation is held rela-tively constant. This equates to a fine positioning time of 8.1 s and a hold time of 5.3 s. The final 0.5 s ofthe trial (indicated in grey in Figure 3.9) are used to compute the accuracy and variability (Figure 3.10).59CHAPTER 3. NAVIGATED TARGETING USER STUDYIn this example, the horizontal and vertical errors of the tip (mean ? 1 SD) were (1.3?0.1)mm and(?1.4?0.1)mm, respectively, for a combined radial tip error of 1.9 mm. The horizontal, vertical,and radial errors of the tail were (1.7?1.2)mm, (?0.1?0.7)mm, and 1.8 mm, respectively, which isequivalent to an angular error of 0.37?. The total targeting error is 3.8 mm. The variation in tail positionis much larger than the variation in the tip. This is to be expected since the tip?s movement is restrictedby being pressed into the workpiece. Note how the tail error is initially reduced but then increased andheld constant while the tip is aligned. This behaviour is specific to the 2D guidance display and wasobserved as a strategy for coping with the opaque tail targeting cue obstructing the tip targeting cue.Figure 3.9 Tip and tail error for a typical targeting trial. Gross positioning time (tG) is based on adistance threshold of 100 mm. Radial hold (tRh) and angular hold (tAh) indicate when the tipand tail position are stabilized.3.3.2 Typical BlockA block consisted of a set of 10 different targets under the same combination of guidance display andbracing condition. In this example of a 2D braced block, the tip positioning appears to be fairly con-sistent, while tail positioning shows more variation (Figure 3.11). Gross positioning time is consistentbetween trials with a median value of 1.1 s (IQR: 1.0?1.2 s). The time taken to stabilize the tip and tailare more variable (Figure 3.12). Median radial tip hold time was 5.5 s (IQR: 4.6?8.8 s), while medianangular hold time was 8.9 s (IQR: 6.2?10.6 s). There does not appear to be any change in targeting timesover the course of a block, suggesting negligible learning effects.For this block, the final tip and tail errors have similar magnitudes (Figure 3.13). The larger errorbars indicate there is more variation in the final tail position within a trial than the final tip position.It also clear that the between trial variation is greater than the within trial variation for both the tipand the tail, and the majority of trials show a negative vertical bias for both the tip and tail error (i.e.,60CHAPTER 3. NAVIGATED TARGETING USER STUDYFigure 3.10 Final errror is calculated using the final 0.5 s of the tip and tail targeting cue positions.The mean and standard deviation indicate final error and variability. The small gray dotindicates the final position.ty f < 0, tv f < 0). The final error also shows negligible learning effects (Figure 3.14).3.3.3 Typical SubjectEach subject performed 4 blocks with a short rest in between while conditions were changed. The samedisplay order was repeated under each bracing condition. The time-averaged tip error for a typical sub-ject is fairly consistent, although the final error varies more for 3D trials than 2D trials (Figure 3.15).The time-averaged tail error exhibits greater variation between trials, and there is noticeably more vari-ation in positioning for 3D trials (Figure 3.16). The tail error for 2D trials appears to take longer tostabilize than 3D trials, but the final magnitude and variation between trials is lower.Final horizontal and vertical tip error for typical subject are evenly distributed horizontally but ex-hibit a negative vertical bias (Figure 3.17a). The between-trial variation appears to be larger than thewithin-trial variation. There also appears to be a clear difference based on guidance display type. Tri-als completed with the 2D guidance display are generally closer to the origin whereas trials completedwith the 3D guidance display show larger magnitude and variation in error. The final horizontal andvertical tail error appear to have similar trends (Figure 3.17b). The between-trial variation appears to belarger than the within-trial variation. While the tip and tail errors appear to have similar magnitudes andvariability for the 2D display, the tail error appears to be larger and more variable for the 3D display,especially in the vertical direction.For a typical subject, gross targeting time appears consistent between blocks while fine targetingtime varies considerably (Figure 3.18). There does not appear to be any noticeable pattern with over ablock or over the course of trials that would indicate a systematic increase or decrease in time due to61CHAPTER 3. NAVIGATED TARGETING USER STUDY(a)(b)Figure 3.11 Variation in a typical block: (a) tip error and (b) tail error for a typical subject in the2D braced condition.62CHAPTER 3. NAVIGATED TARGETING USER STUDYFigure 3.12 Targeting time for a typical 2D braced block. Note how gross positioning time isrelatively constant, the tip is stabilized before the tail (e.g., tAh > tRh), and there does notappear to be any learning effect.Figure 3.13 Final tip and tail targeting error across trials of a typical 2D braced block. Note that tailposition is less stable than tip position. Also note that the majority of trials have a negativevertical bias.63CHAPTER 3. NAVIGATED TARGETING USER STUDYFigure 3.14 Final tip and tail targeting error across trials of a typical 2D braced block. Note thatthere appear to be negligible learning effects.learning or fatigue. For this subject, fine targeting time was as short as 1.6 s and as long as 13.1 s.There appears to be noticeably less targeting error for 2D trials compared to 3D trials (Figure 3.19).The tip and tail error for 2D trials have similar magnitudes, whereas the 3D trials appear to have largertail error.For this subject, braced 2D trials show slightly less variation in final tail position than unbraced 2Dtrials (Figure 3.20). There also appears to be less variation in tip position than tail position; less variationis expected since the tip of the drill bit is pressed against the workpiece, and the tip should move lessthan the measurement noise of the optical tracker (Section 2.10).There appears to be a trade-off between total targeting error and fine positioning time, especially forthe 2D display (Figure 3.21). When the subject spent more time positioning with the 2D display, theywere able to achieve smaller errors. It appears as though this trend was the same for both braced andunbraced 2D trials.64CHAPTER 3. NAVIGATED TARGETING USER STUDYFigure 3.15 Tip error by block for a typical subject. Each subplot illustrates the targeting trials aswell as the time-averaged mean and ?1 standard deviation. Note how the final error appearsto have greater magnitude and variation for the 3D trials compared to 2D trials.65CHAPTER 3. NAVIGATED TARGETING USER STUDYFigure 3.16 Tail error by block for a typical subject. Each subplot illustrates the targeting trials aswell as the time-averaged mean and ?1 standard deviation. Note the substantial variationbetween trials. Also note how 2D trials tend to have a final lower error, but take longer tostabilize, whereas 3D trials stabilize quicker but have a higher final error with more variationbetween trials.66CHAPTER 3. NAVIGATED TARGETING USER STUDY(a)(b)Figure 3.17 Final error for a typical subject: (a) tip and (b) tail. Note how 2D trials are clusteredmuch closer to the origin and how 3D tail error is larger and more variable than tip error.Braced 2D trials appear to have less tail error than unbraced 2D trials. Also note how all ofthe conditions appear to have a negative vertical bias.67CHAPTER 3. NAVIGATED TARGETING USER STUDYFigure 3.18 Targeting time for a typical subject in the order the blocks were presented from topto bottom. The gross targeting, fine targeting, and hold time are shown in light, mid, anddark grey, respectively. Note the amount of variation in fine targeting time and how grosstargeting time is a small, relatively consistent portion of each trial.68CHAPTER 3. NAVIGATED TARGETING USER STUDYFigure 3.19 Tip and tail targeting errors for a typical subject arranged in sequence by trial. Notethat errors tend to be higher for the 3D display compared to the 2D display, and that tailerrors are noticeably higher than tip errors, particularly when using the 3D display. Alsonote that the tail errors in the braced 2D trials appear to be slightly lower than in unbraced2D trials and that there do not appear to be any clear learning effects.Figure 3.20 Final tip and tail position variability for a typical subject. The dashed lines indicatethe deviation in tip and position expected from the measurement noise in the tracker for asingle measurement.69CHAPTER 3. NAVIGATED TARGETING USER STUDYFigure 3.21 The speed-accuracy tradeoff (SAT) for a typical subject. Note how 2D trials appear tohave longer fine positioning time, but smaller total targeting error.70CHAPTER 3. NAVIGATED TARGETING USER STUDY3.3.4 All SubjectsIn this section, we present descriptive data from all subjects. All 25 of the subjects were able to learnhow to use the experimental CAOS system to align the drill with the target after 2 or 3 practise trials.Of the 1000 trials that were recorded, 57 (6 %) were excluded (Appendix D.2), leaving 943 valid trialsfor analysis. Trials were removed for several reasons. One subject had an erroneous target that wasphysically unobtainable due to interference between the drill and the workpiece holder. Trials were alsoremoved when a subject started or finished the trial early, or when they attempted to align the targetingcues to the wrong location. And finally, several trials were removed because the subject blocked theoptical markers.There appear to be differences in the time-averaged tail error time series for both display type andbracing condition (Figure 3.22). The final tip error appears to be lower for 3D trials compared to 2Dtrials. There also appears to be less variation in final position for braced 3D trials compared to unbraced3D trials.The average tail error time series also appears to have display type and bracing condition dependentdifferences (Figure 3.23). Trials with the 3D display trial appear to reduce and stabilize tail error quicker,but to have larger final errors than the 2D display. Braced trials also appear to have less variation towardsthe end of a trial, especially with the 3D display.Comparing the average tip error across directly, the blocks appear to have similar trajectories exceptfor the final error as described above (Figure 3.24a). Comparing the average tail error directly illustratesdifferences in timing and final error (Figure 3.24b). Trials with the 2D display appear to have a shortdelay where the tail targeting error remains relatively constant. Braced 2D trials appear to stabilizesooner then unbraced 2D trials, but they reach the same final error.TimeGross targeting times exhibited a range of approximately 1 s between overall SUBJECT means, a small0.1 s increase for braced trials, and a negligible increase for 3D displays. Gross positioning times forma small proportion of the overall trial with a median value of 1.1 s (IQR: 0.9?3.2 s). There appears tobe a slight increase for braced trials, but no perceptible difference between displays (Figure 3.25). Theaverage gross positioning time also appears to vary between subjects (Figure 3.26).Fine positioning time varies considerably between trials and appears to be about 2.5 s less for 3Dtrials on average (Figure 3.27). The overall median was 6.5 s (IQR: 4.36?9.01; Range: 1.31?14.3).Braced 2D trials appear to have slightly less variation than unbraced 2D trials. Unbraced and braced 3Dtrials are both skewed to the right, which is to be expected; there is a physiological limit to how fast finetargeting can be completed with some trials and subjects taking longer. This skew also implies that themajority of trials are close to the finite limit.The radial targeting time is skewed to the right, with at least an 0.8 s delay after gross positioning(Figure 3.28a). There appears to be a trend of longer radial positioning with the 2D display comparedto trials with the 3D display. There also appears to be longer angular targeting times for the 2D display(Figure 3.28b). 3D trials appears to be more skewed to the right than the 2D trials. The braced 2D trials71CHAPTER 3. NAVIGATED TARGETING USER STUDYFigure 3.22 Tip error by block for all trials. Each subplot illustrates the time-averaged mean and?1 standard deviation. Note how the final error appears to have greater magnitude andvariation for the 3D trials compared to 2D trials. Also note how braced trials, especially 3Dbraced trials, appear to have smaller variation in error.72CHAPTER 3. NAVIGATED TARGETING USER STUDYFigure 3.23 Tail error by block for all trials. Each subplot illustrates the time-averaged mean and?1 standard deviation. Note the substantial variation between trials. Also note how 2Dtrials tend to have a final lower error, but take longer to stabilize, whereas 3D trials stabilizequicker but have a higher final error with more variation between trials.73CHAPTER 3. NAVIGATED TARGETING USER STUDY(a)(b)Figure 3.24 Time-averaged trial for all trials by block: (a) tip error and (b) tail error for all trials.74CHAPTER 3. NAVIGATED TARGETING USER STUDYFigure 3.25 Gross positioning time for all subjects by block. Random horizontal jitter has beenapplied to the data help illustrate distribution. Note how all blocks have comparable valuesand variation.Figure 3.26 Gross positioning time for all trials by subject. Note how average gross positioningtime varies between subjects.75CHAPTER 3. NAVIGATED TARGETING USER STUDYFigure 3.27 Fine positioning time for all trials by block. Note how 3D trials appear to have lowertimes. Also note how 2D braced trials appear to have less variation in fine targeting timethan unbraced 2D trials.also appear to have less variation than the unbraced 2D trials.AccuracyIn this section we present descriptive results for accuracy. We begin with the individual horizontal andvertical components before presenting the combined tip, tail, and total targeting error.Horizontal tip error appears to be symmetrical around zero, with no noticeable effect due to braceor display (Figure 3.29a). The overall median was ?0.01 mm (IQR: ?0.58?0.645; Range: ?3.07?2.91). Vertical tip error exhibits a negative bias, with greater error and greater variation during 3D trials(Figure 3.29b). The overall median was ?1.28 mm (IQR: ?3??0.45; Range: ?10?6.2).Horizontal tail error is symmetrical around zero, with 3D trials exhibiting noticeably larger variation(Figure 3.30a). The overall median was 0.05 mm (IQR: ?0.81?0.925; Range: ?7.21?6.95). Vertical tailerror exhibits a negative bias, with greater error and greater variation during 3D trials (Figure 3.30b).The overall median was ?1.64 mm (IQR:?5.52??0.575; Range: ?21.5?14.2).The horizontal and vertical components are combined together to give the radial tip and tail error.Tip error is larger for 3D trials than 2D trials and there appears to be no noticeable effect of bracing(Figure 3.31a). The overall median was 1.7 mm (IQR:1.02?3.24; Range: 0.1?10). Tail error is similar totip error, with 3D trials exhibiting large error and more variation than 2D trials (Figure 3.31b). Braced2D trials appear to have slightly less variation than unbraced 2D trials. The overall median was 2.58 mm(IQR: 1.35?6.28; Range: 0.17?21.5).The total targeting error is the sum of the tip and tail error. Total targeting error is larger and76CHAPTER 3. NAVIGATED TARGETING USER STUDY(a)(b)Figure 3.28 Targeting time for all subjects: (a) tip and (b) tail. Note how both radial and angularpositioning times are shorter for the 3D display.77CHAPTER 3. NAVIGATED TARGETING USER STUDY(a)(b)Figure 3.29 Tip targeting error components for all subjects: (a) horizontal and (b) vertical. Notehow the horizontal component of error is approximately zero for all conditions. Also notehow the vertical component has a negative bias and tends to be larger with the 3D display.78CHAPTER 3. NAVIGATED TARGETING USER STUDY(a)(b)Figure 3.30 Tail targeting error components for all subjects: (a) horizontal and (b) vertical. Notehow the vertical components tends to be larger, especially for the 3D trials. Also note thenegative bias in the vertical components and the greater variation in the 3D trials.79CHAPTER 3. NAVIGATED TARGETING USER STUDY(a)(b)Figure 3.31 Targeting error for all subjects: (a) tip and (b) tail. Note how the magnitude anddeviation of targeting error for the 3D trials are larger than the 2D trials. Also note how thetail errors appear larger than the tip errors.80CHAPTER 3. NAVIGATED TARGETING USER STUDYmore variable for 3D trials compared to 2D trials and there appears to be less variation in braced 2Dtrials compared to unbraced 2D trials (Figure 3.32). The overall median of the total targeting error was4.26 mm (IQR: 2.49?9.46; Range: 0.4?31.5). Total targeting error for 3D trials was approximately threetimes greater than 2D trials. Data from the 3D trials also exhibit about twice as much variation.Figure 3.32 Total targeting error for all trials by condition. Note the large difference betweendisplay types, and how there appears to be some improvement between braced and unbraced2D trials.VariabilityThe vast majority of trials exhibit a horizontal tip variability less than that which would be expectedfrom tracker noise alone (Figure 3.33a). The overall median was 0.076 mm (IQR: 0.059?0.099; Range:0.023?0.533).Similarly, the vast majority of trials also exhibit a vertical tip variability less than that which wouldbe expected from tracker noise alone (Figure 3.33b). The overall median was 0.017 mm (IQR: 0.012?0.024; Range: 0.003?0.135).The variability of the horizontal (Figure 3.34a) and vertical (Figure 3.34b) components of the tail aremuch larger than the tip, and larger than the measurement noise from the tracker. Braced trials appearto have lower vertical tail variation than unbraced trials. The overall median horizontal tail variabilitywas 0.27 mm (IQR: 0.198?0.38; Range: 0.061?6.14). The overall median vertical tail variability was0.136 mm (IQR: 0.085?0.237; Range: 0.016?3.14).81CHAPTER 3. NAVIGATED TARGETING USER STUDY(a)(b)Figure 3.33 Tip targeting variability for all subjects: (a) horizontal and (b) vertical. Note that tipvariability is consistent across all conditions.82CHAPTER 3. NAVIGATED TARGETING USER STUDY(a)(b)Figure 3.34 Tail targeting variability for all subjects: (a) horizontal and (b) vertical. Note that thereappears to be a slight decrease in vertical variability for braced trials.83CHAPTER 3. NAVIGATED TARGETING USER STUDY3.3.5 Statistical AnalysisIn this section, we describe the linear mixed effects analysis of the data. We fit a three-level LMM to eachmetric, with trials nested within blocks, and blocks nested within subjects. We fit each model with themaximal random effect structure justified by the data. Diagnostic plots can be found in Appendix E.3.Targeting TimeGross Targeting TimeWe found that gross targeting time was statistically dependent on REP, BRACE, and initial distance (D0).DISPLAY was not significant, but was retained in the model. There was insufficient evidence to includeAGE, GENDER, or any higher level interactions (?2(27) = 33, p = 0.19). We applied a log base-10transform to correct for heteroscedasticity in the residuals. There was insufficient evidence to rejectthe null hypothesis that the random slope for BLOCK should be removed (?2(2) = 14, p = 0.00075).There was also insufficient evidence to adopt a residual covariance structure that varied by BLOCK(?2(3) = 5.2, p = 0.16), DISPLAY (?2(1) = 1.5, p = 0.23), or BRACE (?2(1) = 3, p = 0.084), so weused the default homogeneous structure.The conditional expectation of gross targeting time was 0.93 s, 1.05 s, 0.95 s and 1.07 s for thebraced-2D, unbraced-2D, braced-3D and unbraced-3D trials, respectively. The intraclass correlationcoefficient (ICC) for SUBJECT and BLOCK were 55 % and 65 %, respectively. The SUBJECT randomintercepts ranged from 60 % to 170 %, the BLOCK random intercepts ranged from 84 % to 120 % andthe BLOCK random slope ranged from 96 % to 103 %.The effect of REP had a small but statistically detectable influence of 98.9 % ( 95 % CI: 98.4?99.5 %), which means that there was evidence for a small learning effect, and that gross targeting timeis expected to decrease approximately 10 %, or 0.1 s over the course of the 10 trials within a block. In-cluding TEST did not significantly improve the model (?2(1) = 3.7, p = 0.054), so there was insufficientevidence to suggest that any learning persisted between blocks.The influence of D0, or initial start position, was statistically detectable. Initial start position variedfrom 450 mm to 611 mm. At the lower height, the expected change in gross targeting time was 52 %(95 % CI: 46?58 %), and at the upper height the expected change in gross targeting time was 170 %(95 % CI: 156?189 %).Fine Targeting TimeWe found that fine targeting time was statistically dependent on DISPLAY. BRACE was not significant,but was retained in the model. There was insufficient evidence to include REP, D0, AGE, GENDER, orany higher level interactions (?2(29) = 29, p = 0.48). A log base-10 transform was applied to correctfor heteroscedasticity in the residuals. The random slope for BLOCK was removed in order to allow themodel to converge. There was sufficient evidence to adopt a residual covariance structure that varied byDISPLAY (?2(1) = 49, p = 2.2 ?10?12).84CHAPTER 3. NAVIGATED TARGETING USER STUDYThe conditional expectation of fine targeting time was 7.60 s, 7.49 s, 4.89 s and 4.82 s for the braced-2D, unbraced-2D, braced-3D and unbraced-3D trials, respectively. The ICC for SUBJECT was 7 % andthe ICC for BLOCK was 46 %. The SUBJECT random intercepts ranged from 79 % to 128 %, the BLOCKrandom intercepts ranged from 88 % to 115 %. The standard deviation of the residuals for blocks of 3Dtrials was 1.4 times greater than the residuals for 2D trials.The conditional expectation of the fixed effects for gross and fine targeting time show how grosstargeting time is relatively constant and how fine targeting time is expected to be smaller for 3D trials(Figure 3.35).Figure 3.35 Conditional expectations of targeting time fixed effects. Note the reduction in finetargeting time with the 3D display.AccuracyThe final horizontal and vertical error values, tx f , ty f , tu f , and tv f , are continuous outcome variableswith an approximately normal distribution. In the absence of any systemic error, we would expect themean of each component to be zero. However, the pooled data suggested that the vertical componentsmay have a negative bias. Based on visual analysis of the pooled data, we also expected difference inthe amount of variation within between conditions. We fit a LMM to each component to assess whetherthese differences were statistically detectable.The final tip, angular, and total targeting errors, eR f , eR2 f , and eA f , are continuous on the interval[0,?). Since they are formed by the square root of the sum of squares of independent random variableswith a normal distribution, these variables follow a chi distribution with two degrees of freedom.85CHAPTER 3. NAVIGATED TARGETING USER STUDYHorizontal Tip ErrorWe found that horizontal tip error was statistically dependent on DISPLAY and REP, and there was also asmall effect of the GENDER-REP interaction. BRACE was not significant, but was retained in the model,and GENDER was kept since the interaction with REP was significant. There was insufficient evidenceto include an intercept, AGE, D0, or other interactions (?2(26) = 37, p = 0.073). Using an restrictedmaximum-likelihood (REML)-based likelihood ratio test, there was insufficient evidence to reject thenull hypothesis that the random slope for BLOCK should be removed (?2(2) = 5.8 ?10?7, p = 1). Therewas sufficient evidence to adopt a residual covariance structure that varied by BLOCK (?2(3) = 73, p =7.8 ?10?16).The conditional expectation of horizontal tip error was 7.59 mm, 7.49 mm, 4.89 mm and 4.82 mmfor the braced-2D, unbraced-2D, braced-3D and unbraced-3D trials, respectively. The ICC for SUBJECTwas 2 % and the ICC for BLOCK was 12 %. The SUBJECT random intercepts ranged from ?0.2 mm to0.2 mm, and the BLOCK random intercepts ranged from ?0.3 mm to 0.3 mm.The standard deviation of horizontal tip error varied by block. The expected standard deviation var-ied, from highest to lowest: unbraced 3D, braced 3D, unbraced 2D, braced 2D. The standard deviationfor braced 2D trials was 15 % smaller than unbraced 2D trials, and there was a 4 % reduction for 3Dtrials. Unbraced 3D blocks had approximately 45 % greater standard deviation than unbraced 2D blocks.Vertical Tip ErrorWe found that vertical tip error was only statistically dependent on DISPLAY. The fixed effect of BRACEwas not significant, but was retained in the model. There was insufficient evidence to include REP, AGE,GENDER, D0 or any higher level interactions (?2(29) = 36, p = 0.18). There was sufficient evidence tokeep the random slope for block (?2(2) = 6.6, p = 0.04), and there was sufficient evidence to adopt aresidual covariance structure that varied by BLOCK (?2(3) = 500, p = 0).The conditional expectation of vertical tip error was ?0.9 mm, ?0.9 mm, ?3.0 mm and ?2.9 mmfor the braced-2D, unbraced-2D, braced-3D and unbraced-3D trials, respectively. The ICC for SUBJECTwas 7 % and the ICC for BLOCK was 82 %. The SUBJECT random intercepts ranged from ?1.1 mm to1.0 mm, the BLOCK random intercepts ranged from ?1.7 mm to 2.0 mm.Horizontal Tail ErrorWe found that horizontal tail error was only statistically dependent on DISPLAY. BRACE was not signif-icant, but was retained in the model. There was insufficient evidence to include REP, AGE, GENDER, D0or any higher level interactions (?2(29) = 41, p= 0.063). There was sufficient evidence to reject the nullhypothesis that the random slope for block should be removed (?2(2) = 8.8 ? 10?7, p = 1). There wassufficient evidence to adopt a residual covariance structure that varied by BLOCK (?2(3) = 300, p = 0).The conditional expectation of horizontal tail error was 0.2 mm, 0.2 mm, ?0.2 mm and ?0.2 mmfor the braced-2D, unbraced-2D, braced-3D and unbraced-3D trials, respectively. The ICC for SUBJECTwas 4 % and the ICC for BLOCK was 9 %. The SUBJECT random intercepts ranged from ?0.3 mm to0.5 mm, the BLOCK random intercepts ranged from ?0.2 mm to 0.2 mm.86CHAPTER 3. NAVIGATED TARGETING USER STUDYVertical Tail ErrorWe found that vertical tail error was only statistically dependent on DISPLAY. BRACE was not signifi-cant, but was retained in the model. There was insufficient evidence to include REP, AGE, GENDER, D0or any higher level interactions (?2(29) = 41, p = 0.064). Using an REML-based likelihood ratio test,there was insufficient evidence to reject the null hypothesis that the random slope for block should beremoved (?2(2) = 4.9, p = 0.09). There was sufficient evidence to adopt a residual covariance structurethat varied by BLOCK (?2(3) = 920, p = 0).The conditional expectation of vertical tail error was ?1.0 mm, ?1.0 mm, ?5.6 mm and ?5.6 mmfor the braced-2D, unbraced-2D, braced-3D and unbraced-3D trials, respectively. The ICC for SUBJECTwas 1 % and the ICC for BLOCK was 90 %. The SUBJECT random intercepts ranged from ?0.8 mm to0.8 mm, the BLOCK random intercepts ranged from ?0.4 mm to 0.4 mm.Component SummaryThe conditional expectation of the fixed effects for individual targeting error components illustrate theexpected improved accuracy of the 2D display (Figure 3.36). This figure also illustrates the expectednegative vertical bias for both displays.Figure 3.36 Expected value of linear mixed model of targeting error. Note how greater accuracy isexpected with the 2D display.Tip ErrorWe found that tail targeting time was only statistically dependent on DISPLAY. BRACE was not signifi-cant, but was retained in the model. There was insufficient evidence to include REP, AGE, GENDER, D087CHAPTER 3. NAVIGATED TARGETING USER STUDYor any higher level interactions (?2(29) = 30, p = 0.4). A log base-10 transform was applied to correctfor heteroscedasticity in the residuals. There was insufficient evidence to reject the null hypothesis thatthe random slope for block should be removed (?2(2) = 2.3, p = 0.3), and there was sufficient evidenceto adopt a residual covariance structure that varied by BLOCK (?2(3) = 18, p = 0.00041).The conditional expectation of tip targeting error was 1.1 mm, 1.0 mm, 2.9 mm and 2.8 mm for thebraced-2D, unbraced-2D, braced-3D and unbraced-3D trials, respectively. The ICC for SUBJECT was< 1 % and the ICC for BLOCK was 53 %. The SUBJECT random intercepts ranged from 63 % to 145 %and the BLOCK random intercepts ranged from 60 % to 147 %.Angular ErrorWe found that angular targeting error was only statistically dependent on DISPLAY. BRACE was not sig-nificant, but was retained in the model. There was insufficient evidence to include REP, AGE, GENDER,D0 or any higher level interactions (?2(29) = 34, p = 0.23). A log base-10 transform was applied tocorrect for heteroscedasticity in the residuals. There was insufficient evidence to reject the null hypoth-esis that the random slope for block should be removed (?2(2) = 1.7, p = 0.4). There was sufficientevidence to adopt a residual covariance structure that varied by BLOCK (?2(3) = 15, p = 0.0019).The conditional expectation of angular targeting error was 0.15?, 0.14?, 0.62? and 0.56? for thebraced-2D, unbraced-2D, braced-3D and unbraced-3D trials, respectively. The ICC for SUBJECT was< 1 % and the ICC for BLOCK was 66 %. The SUBJECT random intercepts ranged from 75 % to 130 %and the BLOCK random intercepts ranged from 58 % to 150 %.Total Targeting ErrorWe found that total targeting time was statistically dependent on DISPLAY. BRACE was not significant,but was retained in the model. There was insufficient evidence to include REP, AGE, GENDER, D0 orany higher level interactions (?2(29) = 27, p = 0.58). A log base-10 transform was applied to correctfor heteroscedasticity in the residuals. There was insufficient evidence to reject the null hypothesis thatthe random slope for block should be removed (?2(2) = 1.7, p = 0.4), and there was sufficient evidenceto adopt a residual covariance structure that varied by BLOCK (?2(3) = 29, p = 2.2 ?10?6).The conditional expectation of total targeting error was 2.5 mm, 2.3 mm, 9.1 mm and 8.5 mm for thebraced-2D, unbraced-2D, braced-3D and unbraced-3D trials, respectively. The ICC for SUBJECT was< 1 % and the ICC for BLOCK was 68 %. The SUBJECT random intercepts ranged from 66 % to 147 %and the BLOCK random intercepts ranged from 70 % to 142 %.Total targeting error was expected to be smaller when using the 2D display (Figure 3.37). Also notehow the tip and tail have similar magnitudes for the 2D display, while the tail error is larger than thetip error for the 3D display. The conditional expectation of the tip error and angular error are mainlydependent on display (Table 3.3).88CHAPTER 3. NAVIGATED TARGETING USER STUDYFigure 3.37 Conditional expectation of total targeting error fixed effects.Table 3.3 Uncertainty of the fixed effects conditional on the estimates of the random-effect vari-ances and empirical best linear unbiased prediction (EBLUP) modesDisplay Bracing Radial Targeting Error (mm) Angular Targeting Error (?)E[] 95 % CI E[] 95 % CI2DUnbraced 1.1 0.9 1.2 0.15 0.13 0.17Braced 1.0 0.8 1.4 0.14 0.10 0.183DUnbraced 2.9 2.2 3.8 0.62 0.48 0.80Braced 2.8 1.8 4.2 0.56 0.38 0.82VariabilitySince the components of variability are the standard deviations of a continuous variable, they shouldfollow a chi distribution. We expected that since the tip of the drill bit is held fixed in the workpiece, thatany variation in the position should be a result of tracker measurement noise, and should be independentof SUBJECT, BRACE, and display. If bracing improves a subject?s ability to hold the orientation of thedrill steady, BRACE should have a statistically detectable influence on the tail components.Horizontal Tip VariationWe found that horizontal tip variation was only statistically dependent on BRACE. DISPLAY was not sig-nificant, but was retained in the model. There was insufficient evidence to include REP, AGE, GENDER,D0 or any higher level interactions (?2(29) = 36, p = 0.17). A log base-10 transform was applied to89CHAPTER 3. NAVIGATED TARGETING USER STUDYcorrect for heteroscedasticity in the residuals. There was insufficient evidence to reject the null hypoth-esis that the random slope for block should be removed (?2(2) = 3.9 ?10?7, p = 1). There was sufficientevidence to adopt a residual covariance structure that varied by BRACE (?2(1) = 4, p = 0.045).The conditional expectation of horizontal tip variation was 0.080 mm, 0.074 mm, 0.080 mm and0.074 mm for the braced-2D, unbraced-2D, braced-3D and unbraced-3D trials, respectively. The ICCfor SUBJECT was 2 % and the ICC for BLOCK was 3 %. The SUBJECT random intercepts ranged from94 % to 108 % and the BLOCK random intercepts ranged from 99 % to 101 %. These results show thathorizontal tip variation was largely independent of subject and condition, which is what we expectedsince the tip of the drill bit is held fixed in the workpiece and the only variation expected is measurementnoise from the tracker.Vertical Tip VariationWe found that vertical tip variation was not statistically dependent on any of the fixed effects. Therewas insufficient evidence to include DISPLAY, BRACE, REP, AGE, GENDER, D0 or any higher levelinteractions (?2(29) = 39, p = 0.11). We retained DISPLAY and BRACE in the model for the rest of theanalysis. A log base-10 transform was applied to correct for heteroscedasticity in the residuals. Usingan REML-based likelihood ratio test, there was insufficient evidence to reject the null hypothesis that therandom slope for block should be removed (?2(2) = 3 ?10?7, p = 1). There was sufficient evidence toadopt a residual covariance structure that varied by BRACE (?2(1) = 1.7, p = 0.19).The conditional expectation of vertical tip variation was 0.019 mm, 0.015 mm, 0.015 mm and 0.013 mmfor the braced-2D, unbraced-2D, braced-3D and unbraced-3D trials, respectively. The ICC for SUBJECTwas 7 % and the ICC for BLOCK was 10 %. The SUBJECT random intercepts ranged from 71 % to 129 %and the BLOCK random intercepts ranged from 92 % to 111 %. These results show that vertical tip vari-ation was largely independent of subject and condition, which is what we expected since the tip of thedrill bit is held fixed in the workpiece and the only variation expected is measurement noise from thetracker.Horizontal Tail VariationWe found that horizontal tail variation was only statistically dependent on BRACE. DISPLAY was notsignificant, but was retained in the model. There was insufficient evidence to include REP, AGE, GEN-DER, D0 or any higher level interactions (?2(29) = 32, p = 0.3). A log base-10 transform was applied tocorrect for heteroscedasticity in the residuals. There was insufficient evidence to reject the null hypoth-esis that the random slope for block should be removed (?2(2) = 3 ?10?7, p = 1). There was sufficientevidence to adopt a residual covariance structure that varied by BRACE (?2(1) = 14, p = 0.00016).The conditional expectation of horizontal tail variation was 0.31 mm, 0.28 mm, 0.30 mm and 0.27 mmfor the braced-2D, unbraced-2D, braced-3D and unbraced-3D trials, respectively. The ICC for SUBJECTwas 10 % and the ICC for BLOCK was 13 %. The SUBJECT random intercepts ranged from 78 % to140 % and the BLOCK random intercepts ranged from 91 % to 115 %.90CHAPTER 3. NAVIGATED TARGETING USER STUDYVertical Tail VariationWe found that vertical tail variation was only statistically dependent on BRACE. DISPLAY was not sig-nificant, but was retained in the model. There was insufficient evidence to include REP, AGE, GENDER,D0 or any higher level interactions (?2(29) = 28, p = 0.52). A log base-10 transform was applied tocorrect for heteroscedasticity in the residuals. There was insufficient evidence to reject the null hypoth-esis that the random slope for block should be removed (?2(2) = 0.96, p = 0.6). There was sufficientevidence to adopt a residual covariance structure that varied by BRACE (?2(1) = 7.3, p = 0.0068).The conditional expectation of vertical tail variation was 0.17 mm, 0.12 mm, 0.17 mm and 0.12 mmfor the braced-2D, unbraced-2D, braced-3D and unbraced-3D trials, respectively. The ICC for SUBJECTwas 13 % and the ICC for BLOCK was 26 %. The SUBJECT random intercepts ranged from 67 % to177 % and the BLOCK random intercepts ranged from 83 % to 123 %.Component SummaryThe conditional expectations of the fixed effects of each variability component illustrates the reductionsin tail variation expected with bracing (Figure 3.38).Figure 3.38 Conditional expectations of targeting variability fixed effects. Note how the final ver-tical and horizontal variation of the tip (?x f and ?y f ) are constant across conditions, whilethe final vertical and horizontal variation of the tail (?x f and ?y f ) are reduced with bracing.3.3.6 Observations and Subject FeedbackEach participant completed the drill targeting section of the debrief questionnaire after completely thetargeting trials (Appendix B.2). The vast majority of participants found the two display types intuitive91CHAPTER 3. NAVIGATED TARGETING USER STUDY(92%-2D, 92%-3D) and the majority of participants reported that the forearm brace made it easier toposition the drill tip (88%) and easier to align the drill axis (84%).Table 3.4 summarizes a paired comparison of the participants responses to the two sets of displayquestions.Table 3.4 Debrief Questionnaire Display PreferenceQuestion 2D 3D No preferenceIntuitiveness 3 (12) 7 (28) 15 (60)Tip Positioning Ease 4 (16) 14 (56) 7 (28)Axis Positioning Ease 5 (20) 12 (48) 8 (32)Values are number of subjects (%).The following is a list of observations made during and after user testing:? Some subjects purposefully moved the drill back and forth to determine or confirm the visual-motor correspondence before beginning targeting.? When using the 2D guidance, the rear cue often obstructed the tip cue; to compensate, manysubjects purposely increased the angular error until they were satisfied with the tip position.? Subjects often spent a long time fine-tuning 2D position.? Almost all subjects preferred the 3D display over the 2D display and many reported that theybelieved their performance was better using the 3D display.? Several subjects mentioned that the depth indicator on the 3D display was helpful for gauging thedistance to the workpiece.? Subjects typically focused on the screen, and rarely looked at the tool or workpiece? Subjects generally positioned the tip against the workpiece first, then adjusted the angle.? Several subjects reported that jitter of the targeting cues was annoying, and that the 2D displaywas worse.? Several subjects reported that the arm rest was not long enough to properly support their arm forall of the targets.? A few subjects reported that the aggressive tip on the brad point drill bit made it difficult toreposition because it would get stuck in the workpiece.? Subjects often incorrectly positioned the targeting cues too low with the 3D screen.? Subjects often spent a long time fine-tuning 2D position.? Several subjects reported a need for more padding on the armrest.? One subject noted that ?[the] [a]rm rest was helpful - lets you focus on wrist instead of the wholearm.?? A few subjects used internal bracing to help stabilize the drill, for example, by tucking their elbowinto their hip\/waist (e.g., S3).92CHAPTER 3. NAVIGATED TARGETING USER STUDY3.4 DiscussionThe purpose of the user study presented in this chapter was to assess the influence of a static, rigidforearm brace and the design of visual feedback guidance display on navigated targeting performance.A simple armrest brace was constructed and tested with two different styles of guidance display on aposition-and-hold trajectory alignment task. We hypothesized that bracing the forearm would enablequicker, more accurate targeting with less variation than freehand, and that a 3D perspective guidancedisplay would enable quicker, more accurate targeting with less variation compared to a 2D axial per-spective display. In general, display type had a much larger impact on targeting performance thanbracing. Our data showed that the forearm brace decreased targeting variability slightly, but had nostatistically detectable effect on targeting time or final accuracy.3.4.1 Influence of Static Forearm BraceContrary to our hypothesis, the static forearm brace did not lead to faster or more accurate targeting.There was a small reduction in within-trial targeting variation; the vertical component of the tail was30 % more stable when bracing was used. There was also evidence of improved repeatability withina block. Bracing did lead to a statistically detectable increase in gross targeting time of an average of0.1 s, but this is unlikely to be clinically relevant.Decreased Angular Targeting VariabilityWe expected that bracing would decrease variability. Supporting the forearm should reduce neuromus-cular noise since fewer joints are involved, and reducing the gravity load should reduce muscle activityand the noise associated with larger motor recruitment and fatigue. In our data there was a small butstatistically detectable decrease in final vertical tail variability of about 30 % and a small but statisticallyundetectable decrease in final horizontal tail variability of about 10 %. Our results are consistent withprevious studies that have reported increases in perceived stability when using static arm and handrests[Ohta 2000], with the added benefit that we were able to quantify the results rather than just relying onsubjective feedback.As expected, there was no difference in radial targeting variability. As long as the tip of the drillbit remains in contact with the workpiece, the variation in the tip should be similar to the measurementnoise in the tracker, which is what our results showed (Figure 3.33).Increased Within-Block RepeatabilityAll of the targeting components except vertical targeting error had statistically detectable reductionsof within-block standard deviation. With the 2D display, bracing reduced the standard deviation ofhorizontal and vertical tip position by 15 %, horizontal tail position by 22 %, and vertical tail positionby 25 %. These results are consistent with the Zupanc?ic? [1998] study, which found a 25 % improvementin positional repeatability with bracing.93CHAPTER 3. NAVIGATED TARGETING USER STUDYSmall Increase in Gross Targeting TimeOn average, there was an approximately 0.1 s increase in gross targeting time when using the forearmbrace. This increase in time is unlikely to be clinically relevant, but it does illustrate the trade-offbetween mobility and stability. This increase in movement time is likely due to a decrease in movementvelocity, as a result of not using all of the muscles in the arm.Minimal Effect on Final ErrorAlthough the majority of participants reported that the forearm brace improved their ability to positionthe drill tip and align the drill axis, and on average, the 2D display did show a small 0.4 mm reductionin total targeting error, based on the data, we were unable to demonstrate that forearm bracing hadany statistically detectable influence on final error. The discrepancy between the data and the subjects?impressions may result from an unmeasured reduction in muscle exertion or fatigue that made the taskfeel easier, or there could also be bias because the forearm brace was the focus of the study. There areseveral other factors that may explain why no improvement was seen.First, navigated targeting error depends on the accuracy and resolution of the measurement systemand guidance display. If a user is unable to detect a discrepancy between the desired and measuredposition based on the feedback, they can not make the necessary correction. For the 2D display, theperceptible visual change was smaller than the tracker noise, so the limiting factor was likely the mea-surement noise, and not the ability of the subject to position the drill.Second, since the task involved targeting against a workpiece, minimal force was required to ma-nipulate the pose of the drill once the tip was placed. The brad point (BP) drill bit has a prominent tipand the workpiece is capable of supporting some lateral load. Since some of the gravity load wouldbe supported by the workpiece, the brace may not have reduced the load much further. The expectedreduction in neuromuscular noise with smaller force levels would likely be smaller than if the tip wasnot supported.Third, a few subjects were observed to utilize internal bracing [Hoffman 2008: 133], by tucking theirelbow into their hip or waist during unbraced trials. This strategy would have provided similar benefitsto the forearm brace by decreasing the number of joints and muscles involved and making it easier tosupport the mass of the drill.Lastly, placing the tip against the workpiece also forms a closed kinematic chain. We expected thata brace that steadies the arm during targeting may help reduce mental fatigue since there is evidence thatslow movements are ?controlled by attention-demanding mental processes? [Zelaznik 1981]. However,simultaneously maintaining contact with both the workpiece and the brace may have actually increasedthe difficulty of the task.The forearm brace we tested in our study is similar to the fixed armrest used as comparison in the ac-tive handrest study [Fehlberg 2012]. For the circle-tracing task in that study, the fixed handrest showeda slight improvement in time-error trade-off, but there were no statistically detectable differences inmedian error or completion time.Another study that looked at armrests in laparoscopic surgery found statistically detectable decrease94CHAPTER 3. NAVIGATED TARGETING USER STUDYin number of errors, maximum tissue damage rates and discomfort rates, but no change in task comple-tion time [Galleano 2006]. With an armrest, the median number of errors increased from 10 to 16 inan ideal, unstressed posture, and increased from 41 to 97 in an elevated, stressed posture. Their resultssuggest there is an interaction between using the armrest and posture. Since the posture of subjects inour study could be considered ideal, we can theorize based on their results that we may have seen agreater difference in our study under less ideal postures.3.4.2 Influence of Guidance Display TypeGreater Accuracy With 2D DisplayContrary to our hypothesis, the 3D perspective guidance display did not result in more accurate targeting.On average, tip error was 170 % (95 % CI: 140?210 %) larger and tail error was 350 % (95 % CI: 300?400 %) larger with the 3D display.Although the primary difference between the two displays was intended to be their perspective,we believe that other, seemingly subtle, design factors had a larger impact. The most significant ofthese factors was the difference in minimum perceptible error. For simplicity, both of the guidancedisplays were based on different views of the same targeting box (Appendix C.6). As described inSection 2.6.4, the difference in perspective between the two display leads to a marked difference intargeting resolution. A single pixel change in the 2D display requires a real world movement of 0.16 mmhorizontally or 0.17 mm vertically; the 3D display requires 0.27 mm, 0.53 mm, 0.43 mm and 0.68 mmfor the tip horizontal, tip vertical, tail horizontal and tail vertical, respectively.In addition to the scaling differences as a result of the different views, differences in the targetingcues also affected how easy it was to detect whether the drill was aligned to the target. For the 3Ddisplay, the targeting cues were 10 mm spheres (Figure 2.7). The 2D had similar targeting cues initially,but these were changed to the offset cross-hairs to make them easier to see. Each conic point has aheight of 30 mm and a base of 20 mm (Figure 2.6). It is much easier to determine whether the tip of atriangle is centred on the frame than it is to determine if a sphere is centred.These differences in ability to discern error between the two displays may be one explanation forwhy subjects preferred the 3D display, and often felt like they were more accurate. Since the magnitudeof detectable error was smaller with the 3D display, it would be easier to achieve this higher error level.A similar explanation was proposed by Kassil [2009] whose subjects also preferred an orthographicdisplay over an axial display that yielded better performance.St. John [2001] tested 2D vs 3D perspective on a 2D display for air traffic control applications.They assessed several different tasks, categorized as either shape-understanding or relative-positioning.St. John found that ambiguity and distortion inherent to a 3D perspective makes relative-positioningtasks more difficult, but that a 3D perspective is better for shape understanding tasks. Since the task inour study is primarily a relative positioning task, our results seem consistent with their study; however,we can not say this with certainty because of the aforementioned differences in targeting resolution.95CHAPTER 3. NAVIGATED TARGETING USER STUDYFaster Targeting With 3D DisplayAlthough the final errors were larger, the 3D display did have a statistically detectable decrease in finetargeting time with an average savings of 2.4 s (95 % CI: 2.0?2.8 s). Two possible explanations forthis time savings are the additional context provided for the task and the difference in perceptible errordescribed above. We hypothesized that displaying a similar guidance view to the one the user wouldsee would make it easier to determine the visual motor correspondence and therefore improve targetingperformance. Unfortunately, the 3D display also had a larger minimum perceptible error, so anotherpossibility is that the error was reduced at the same rate, and subjects simply stopped when they couldno longer detect more error.There was no clear indication to the subject?s in our study about the magnitude of their currenttargeting error. Garvin developed a tool-mounted display for freehand navigated cutting in total kneearthroplasty (TKA), and provided different feedback depending on the magnitude of the error. Theychose not to supply corrective guidance for deviations above 10? or 10 mm since they should be detectedby the naked eye. They also ?deemed it futile to try to respond to corrective guidance for deviationsof less than 0.5? or 0.5 mm.? Applying a similar method to our study would likely have resulted inshorter fine positioning times with the 2D display, since the subject would not try to compensate forsmall differences caused by jitter.Depth Cue on 3D Display Made It Easier to Position TipSeveral subjects reported that it was easier to position the tip with the 3D display. This was likely dueto the inclusion of a depth cue on this display. The 3D display included a black cylinder that indicatedwhere the tip of the drill was with respect to the workpiece surface. This cue would enable the subjectto more closely control the distance of the tip from the workpiece while they adjusted the position.Since the 2D display did not provide any information on depth, subjects would have to approach theworkpiece slower, or use more trial and error to get the correct tip position. This may partially explainwhy the radial targeting time was an average of 0.5 s (95 % CI: 0.4?0.6 s) faster with the 3D display(Figure 3.27).Jitter Affected PerformanceThere are a variety of factors that influence human performance in interactive systems. Two main factorsare jitter and latency. Jitter is the undesired deviation from true measurement as a result of repeatedmeasurements. Latency is the time delay between measurement and display.The 3D displays the location of the target from a fixed viewpoint that roughly corresponded to theuser?s view of the actual target. One of the advantages of showing a 3D perspective is that it makes iteasier to determine which cue represents the tip position and which cue represents the bit orientation.There is little chance of having the cues overlap except in orientations with large deviations from thetarget trajectory. Although the separation of the cues may make the display more intuitive, it forces theuser to adjust their focus between the two locations, likely increasing the difficulty of simultaneouslyaligning both cues. The other main drawback in using a perspective view is that since more information96CHAPTER 3. NAVIGATED TARGETING USER STUDYmust be displayed, the resolution is decreased.Continuously measured quantities like the drill pose are subject to a type of random error calledjitter. This error causes chaotic movement of the target with respect to the drill; the targeting cueappears to move even if the drill is stationary. Combining transforms from several objects to representrelative transformations increases the amount of jitter. In a study on the performance of tool-mounteddisplays for surgical guidance, Kassil [2007] described how jitter ?limits the user?s ability to judge andcorrect alignment? in a drill targeting task. Our subjects reported a similar experience and frustration.Furthermore, the difference in resolution between the two displays would magnify the effect of jitter inthe 2D display, which was noted by several participants, and may help to explain the preference for the3D display where the jitter was less noticeable.Jitter can be reduced by applying smoothing, but this must be done cautiously. Smoothing canincrease latency, which can also negatively affect performance. Teather [2009] investigated the effect oflatency and spatial jitter on 2D and 3D pointing, and found that while latency had a stronger effect onpoint performance, erratic jitter can also significantly affect performance. Any attempt to reduce jitterwith smoothing must consider this performance trade-off.3.4.3 Participant FeedbackFeedback was elicited from participants informally during testing and afterwards using a debrief ques-tionnaire. All participants reported that the system was easy to learn how to use and all but one found itresponsive. The majority of participants reported that use of the forearm brace was intuitive (96 %), andbelieved that it improved drill tip positioning (88 %) and drill axis alignment (84 %).Informally, the majority of participants preferred the 3D display and believed there drill tip posi-tioning and drill axis alignment was easier. Although the results of the questionnaire did not show astatistically detectable difference using the Wilcoxon Signed-Rank test, a greater proportion of partic-ipants reported preference for the 3D display in terms of intuitiveness, ease of drill bit tip positioning,and ease of drill bit axis alignment. The results clearly show that positioning and alignment performanceas measured by final error was better with the 2D display. Since there is a large difference between theresolution of the two displays, the 3D display may have felt easier to use since users were unable to de-tect deviation from the intended target. Thus, it is not possible to comment on the effect of the improvedcontextual cues of the 3D display on targeting performance, but it is important to note that the design ofthe feedback display does have a large effect on targeting performance, and that a discrepancy may becreated between perceived performance and actual performance.3.4.4 Sources of Uncertainty and VariationWithin-trialThe main source of uncertainty within a trial is the uncertainty of the measured position of the drilltip. This uncertainty, or target registration error (TRE) is based on several sources: fiducial localizationerror (FLE), the uncertainty in the measure of a single marker; fiducial registration error (FRE), the97CHAPTER 3. NAVIGATED TARGETING USER STUDYuncertainty in determining the local coordinate system of a group of markers; and the drill bit calibration.Based on the FRE of the Polaris? system, and the geometry of our marker frames, we estimated theuncertainty of a single measurement to be on the order of 1.6 mm (Section 2.10).In addition to this random noise, there was also evidence of systematic error. The final error forthe tip showed a negative vertical bias for all conditions, with the magnitude primarily dependent ondisplay type. For 2D trials, this error was approximately ?1 mm on average for both the tip and tail.The average 3D display error was ?3 mm for the tip, and ?6 mm for the tail. We believe there are tworeasons for this error: compliance in the drill, and the design of the 3D display.There is a small amount of play between the body of the drill and the chuck of approximately 1?.Before the tip is in contact with the workpiece, the weight of the chuck and the drill bit would tend tocause it to hang downwards. When the tip is placed against the workpiece, part of the weight of the drillis supported through the drill bit. This upwards force would causing the chuck to tilt up relative to thedrill, and this would explain why the tip position is consistently 1?2 mm below the origin. This theory issupported by looking at the vertical tip error right at the moment contact is established (Figure 3.9). Forthis trial, we can see that the tip error increased slightly after contact was established at 8.5 s. Anotherpossible explanation is an error in the drill bit calibration. If the distance to the drill bit tip was incorrect,rotating about the tip while it is pressed into the workpiece would cause the measured tip position tochange.Based on the difference in targeting resolution between the two displays, we would expect thatthe magnitude and standard deviation of error would be larger for the 3D display than the 2D display.However, it is clear from Figure 3.29b and Figure 3.30b that there is a display-dependent increase in thevertical bias as well. Further, Figure 3.36 shows that this bias is larger for the 3D tail compared to the3D tip. We believe that the 3D perspective and size of the targeting cues is an explanation. The targetingspheres are relatively large, and are being viewed at a downwards angle which may have caused subjectsto target too low.Between-trialThere are several explanations for variation between trials, including fatigue and learning. The order ofcondition was randomized within blocks to help compensate for any systematic increase or decrease inperformance as a result of learning or fatigue. The subject also had an opportunity to rest which shouldhave further mitigated any fatigue effects. The only outcome where a learning effect was statisticallydetectable was gross targeting time, so this was unlikely to affect our results.Between-blockThe main source of variation between blocks is the difference in targeting resolution and minimumperceptible error as described above. It is possible that this difference masked any bracing effects.98CHAPTER 3. NAVIGATED TARGETING USER STUDYBetween-subjectThere are several sources of variation between subjects, including differences in height, visions, spatialability, and effort.To maintain a consistent posture between subjects, we adjusted the vertical position of the workpiecetarget and the forearm brace to match the subject?s height. Since the start position was fixed relative tothe worktable, adjusting the position of the workpiece changed the overall distance to the target. Thisdistance varied from approximately 450 mm to 600 mm. We defined a gross targeting threshold basedof within 100 mm to the target, with an accompanying gross targeting time to help account for thisdifference. 68 % of the variation in total gross targeting time was attributable to random subject effects.Subjects may have also differed in their spatial ability and in their experience with other hand-eyecoordination tasks, like video games. We can theorize that subjects with more experience or spatialability would have to concentrate less on the task, which could result in smaller differences between thebraced and unbraced cases. Conversely, subjects with less experience may have benefited more frombracing, since reducing the number of joints to control should free up some of their concentration.Although normal or corrected-to-normal vision was one of the inclusion criteria, we did not explic-itly test the subject?s vision. A subject?s ability to use the feedback provided by the guidance displaydepends on their ability to distinguish whether the targeting cues are aligned. Visual acuity is the abilityto distinguish two lines from one; The physiology of the eye limits normal visual acuity to between 0.3?and 1? (0.005?0.017?) [Levi 1990]. For the eye-to-screen distance of 1100 mm in our study, this meansthe minimum perceptible difference under ideal conditions was 0.1 mm?0.3 mm.3.4.5 LimitationsThere are several limitations to this study that may affect our ability to interpret and generalize theresults.JitterAs discussed above, random noise in the continuous measurement of the drill pose causes jitter of thetargeting cues on the guidance display, which makes targeting difficult. Several subjects mentioned thatjitter seemed worse in the 2D display, which makes sense since the greater resolution would magnifyany noise. Since the jitter is also recorded in the transforms, it limits our ability to determine if therewas any difference between the braced and un-braced conditions in terms of movement variability.Different Initial DistanceAs discussed earlier, instead of fixing the location of the start position relative to the environment, thestart position should change along with the height of the workpiece holder to ensure that the initial tip-goal distance is the same between participants. In this study, we defined a fixed distance threshold andgross targeting time to help control for the difference. Gross targeting time was the only metric wherewe found a statistically detectable influence of initial distance. Since gross targeting time was relatively99CHAPTER 3. NAVIGATED TARGETING USER STUDYsmall, was consistent between trials, and formed a small proportion (approximately 7 %) of the totaltrial time, we do not believe that these initial distance differences significantly affect our results.Time-Error Trade-offWe tested subject?s targeting performance with a time-limited task and a single set of instructions. Wechose to use a fixed trial length in order to standardize processing and make it easier to directly compareperformance, and selected a trial length of 15 s based on pilot testing to ensure subjects had enoughtime to complete the targeting and hold their position. Subject?s were instructed to achieve and hold themost accurate pose by the time limit. Our results therefore need to be considered with respect to theseinstructions and the time limit. It is likely that final accuracy results may have differed if a shorter, morechallenging time limit was imposed. Future studies should take this into account, to assess how differentinstructions influence the effect of display type and bracing on navigated targeting performance.3.4.6 Clinical RelevanceSince the task only involved targeting and no hole was actually drilled, the radial and angular errors wehave reported here are the best case scenario. When drilling into bone, ?especially at angles that are notperpendicular? skiving, or movement of the drill bit tip relative to the workpiece is a problem. Drill bitsare also susceptible to bending, further decreasing accuracy.The metric we have measured in this study represents the static targeting accuracy. It does not ac-count additional errors introduced in initiating the hole or deflections during drilling, nor how accuratelythe subject can obtain depth.Clinically, the required accuracy can vary considerably for different procedures. The maximum errortolerance for locking screw alignment in femoral intramedullary nailing was estimated in a previousstudy to be less than 8? in angulation and less than 0.75 mm radially [Szakelyhidi 2002: p.3]. Clinicalcollaborators for a previous study in our lab relaxed the radial requirement to approximately half of thedrill bit diameter, or 2.5 mm [Beadon 2007: p.42]. Our results show that our system is capable of meetingthe angular accuracy requirement, but only the 2D display is capable of meeting the relaxed radialaccuracy requirement. However, it is also important to note that the accuracy we report is between theplanned and measured drill bit trajectory, and does not include the possible error between the measuredand actual pose of the drill bit.SubjectsThe subjects we recruited in our study were not surgeons, and had no formal experience with a Com-puter Assisted Orthopaedic Surgery (CAOS) system. Since the experimental task did not actually involvedrilling, we do not expect that differences in experience with power or surgical tools would influenceperformance. We do expect that surgeons who are familiar with CAOS systems would also have en-hanced spatial ability and eye-hand coordination, allowing them to perform close to the limits of oursystem imposed by measurement noise.100CHAPTER 3. NAVIGATED TARGETING USER STUDYGuidance DisplayIn our study, we tested the targeting performance of a single guidance display view. Although the de-sign of our 2D guidance display is based on simple Computer Assisted Surgery (CAS) systems, mostcurrent CAS systems use a combination of several views. For example, the navigation display of theBrainLab? system for femoral hip resurfacing has three views: two cross-sectional views and an axialview (Figure 1.15). The axial view is similar to the 2D view tested in our study. In addition to havingmultiple views, the clinical guidance display also has a model of anatomy, which should provide bettercontext. The biggest difference that would likely influence performance is the inclusion of a numericalrepresentation of the desired angle. This numeric value would provide a discrete indicator of perfor-mance as opposed to the continuous indicator of our targeting cues. The number of decimals of thisvalue provides an indication of the desired threshold; the BrainLab? system rounds the angle to thenearest degree, implying a desired accuracy of ?0.5?. If our display had a discrete indicator, it is likelythat subjects would have spent less time trying to achieve a ?perfect? alignment. This is especially thecase with the 2D display, where subjects took an average of 2.4 s (95 % CI: 2.0?2.8 s) longer to positionthe tip than they did with the 3D display.TaskIn our study, subjects were asked to align the drill bit to the desired trajectory and maintain that pose.The next step in a typical navigated drilling task would be to actually start drilling and create a hole.Our data demonstrated that bracing the forearm did not improve targeting accuracy, but, at least for thetwo-dimensional (2D) display, it did reduce the amount of variation in the final position. This suggeststhat the brace made it easier for the subject to maintain the pose of the drill bit. Drilling into bone rarelyinvolves drilling perpendicular to a flat surface; trying to drill at an angle on curved surfaces commonlyresults in skiving. We can theorize that since bracing makes it easier to maintain the desired position ofthe drill, it may reduce the amount of skiving that occurs and result in a hole that is closer to the desiredentry point. Bracing may also make it easier to maintain the desired trajectory.Dividing the task into tip positioning and angular positioning is another item that may differ clin-ically. In our study, subjects were able to position the tip against the workpiece first, and then adjustthe angle independently. Clinically, it might not be possible to position and pivot the tip against theanatomy, and it may be necessary to position both the tip and the angle simultaneously before advanc-ing the drill. A forearm brace could make this simultaneous adjustment easier by providing support tothe arm or the tool.Once a hole is started, drilling efficiently in bone requires substantial force levels. Drilling is an in-herently unstable task and the amount of force a user can apply is limited by the body?s ability to main-tain stability [Rancourt 2001b]. To deal with this instability, user?s rely on the mechanical impedanceof their upper limb which depends on a number of factors including posture [Mussa-Ivaldi 1985; Tsuji1995] and muscle activation [Mussa-Ivaldi 1985; Dolan 1993; Gomi 1998]. Roy [1999] showed thatthe maximum force a user can apply to a pivoting stick, which is equivalent to a drill, is about 50 %less than what the user can apply to a fixed wall; Muscles can be co-contracted to provide the necessary101CHAPTER 3. NAVIGATED TARGETING USER STUDYlateral stiffness to overcome the instability, but this reduces the total force output. Not only is there afinite limit to the amount of stiffness that can be gained through co-contraction, but this muscle activa-tion requires energy which could expedite fatigue. The forearm brace we tested in this study appears toprovide some vertical stability that reduced vertical variability. We theorize that this augmented stabilitywould also allow a user to apply great thrust force.3.4.7 Future WorkThis study could be improved upon and expanded by considering some of the following:Limitations to address:? Fix the start position relative to the target so the distance is consistent between subjects.? Add a constraint so the angular start position is consistent between trials and subjects.? Reduce uncertainty in tracker measurements by optimizing marker geometry.? Reduce flicker through filtering.? Change transparency of 2D targeting cues so tail cue does not obstruct tip cue.? Adjust guidance displays so that visual resolution is similar.? Test speed-based and accuracy-based subject instructions.? Match targeting cues between displays (i.e., change 3D from spheres to cross-hair).? Explicitly assess fatigue, for example, with a visual analogue scale after each trial, or with elec-tromyography.? Assess discomfort of different body parts using visual analogue scale questionnaire (e.g. Galleano[2006]).? Assess what proportion of time subjects kept in contact with the brace (e.g. Galleano [2006]).? Test with a clinical population, surgical tools, and bones.Outstanding guidance display questions:1. How do different guidance display perspectives influence performance under non-ideal visuomo-tor correspondence?2. What influence does a tool-mounted guidance display have? [Garvin 2013]3. Does an ego-centric or exo-centric view lead to greater performance?Outstanding bracing questions:1. Does forearm bracing reduce drill bit skiving? Does this lead to improved accuracy of the drilledhole?2. Does forearm bracing enable subject?s to use higher drilling forces by providing lateral stability?3. Does forearm bracing have a greater influence on performance in stressed postures?4. Does forearm bracing reduce discomfort and fatigue?102CHAPTER 3. NAVIGATED TARGETING USER STUDY3.4.8 ApplicationsThe hardware and methodology developed for this study could easily be applied to investigate a numberof related research questions as described above. In addition to supporting future research, this studyhas also provided evidence that subtle changes to the design of visual feedback displays can have asignificant impact on performance. Designers of these types of navigation systems need to considermultiple factors, including display resolution, visual acuity, and targeting system noise.3.5 ConclusionsIn this chapter we described a user study designed to test the influence of an simple brace and guidancedisplay design on navigated targeting performance.Although braced 2D trials tended to be more accurate than unbraced 2D trials, there was no sta-tistically detectable difference in the final radial error or final angular error for this task (H1.1a, H1.1brejected). The short duration of the trial, ideal posture, and significant levels of measurement noise mayexplain why greater differences in final error were not observed. There were statistically detectabledecreases of 30 % in the vertical variability of the tip within a trial (H1.1c supported) and decreases of15 % to 25 % in the variability of error within a test block. Subjects reported greater positioning andalignment ease when using the forearm brace. There was a small, statistically detectable increase ingross targeting time of approximately 0.1 s, which is unlikely to be clinically relevant and no detectableinfluence on fine targeting time (H1.1c rejected). The 2D axial guidance display enabled significantlymore accurate positioning of both the tip and the angle: on average, tip error was 170 % (95 % CI:140?210 %) larger and tail error was 350 % (95 % CI: 300?400 %) larger with the 3D perspective dis-play (H1.2a, H1.2b rejected). The 3D display did exhibit faster fine targeting (H1.2c supported), butthere was no detectable influence on variation (H1.d rejected). We believe the difference in performancebetween the two display types can be attributed to a marked difference in the visual resolution. Theresolution of the 3D viewpoint display varies from 0.4 mm to 1.1 mm, whereas the resolution of the 2Dviewpoint display varies from 1.8 mm to 1.9 mm. This difference means that the minimum detectableerror based on the visual acuity of the user is much smaller on the 2D screen. This also may explainswhy the majority of users preferred the 3D screen: it felt easier to use because they were unable to detectthat there was still an error in the positioning. Because of the difference in resolution between the twodisplays, it is difficult to make recommendations regarding the viewpoint, although it is likely that thepreference for the 3D display was a result of the displays enhanced contextual cues.There are three main conclusions from this study:? Guidance display and subtle differences in targeting cue design can have a significant influenceon targeting performance;? Simple forearm bracing can improve targeting variability and repeatability; and,? Implementing an effective bracing strategy requires careful consideration of the motor task.103Chapter 4Design of a Damper-Based Brace toMinimize Cortical Drill PlungeIf we knew what it was we were doing,it would not be called research, would it?? Albert EinsteinCortical drilling was selected as a surgically relevant task where we could test whether a brac-ing strategy could improve performance. This chapter describes the development of an experimentaldamper-based brace designed to minimize drill plunge with minimal effect on the drilling process.We performed a series of pilot tests and developed a model of the drilling and plunge behaviourto inform the design process. Pilot testing identified typical human drilling thrust force and plungekinematics. Model simulations were used to predict drilling duration and plunge depth for a range ofhuman drilling thrust force and brace damping level. These simulations were then used to select anoptimal range of damping values for the brace. Based on the results of pilot testing and simulation, wedesigned a brace based on an adjustable dashpot. After characterizing the range of damping provided bythe dashpot, we chose three discrete damping levels. The ability of this brace to improve performanceof a simulated cortical drilling task is assessed in a user study described in Chapter 5.4.1 IntroductionCortical drilling is a challenging surgical task where the goal is to create a hole through one or bothcortices of a long bone. Cortical bone requires significant drilling thrust forces. Due to anatomicalvariation, complex geometry and limited visualization, it can be difficult to accurately gauge the bonethickness, which, when coupled with the required high forces, can result in sudden movement when thedrill bit penetrates through the bone surface. This penetration, or drill plunge, can result in injury to softtissue, vasculature, nerves, and tendons [Alajmo 2012]. It can also lead to a broken drill bit, which isoften very difficult, if not impossible, to remove. Simply drilling with lower force magnitude is not anoption due to the danger of excessive temperature generation which can lead to osteonecrosis. Althoughthere is little clinical evidence of complications caused by excessive drilling temperatures, there is ample104CHAPTER 4. DAMPER-BASED BRACE DESIGNin vitro evidence that temperature-induced osteonecrosis can affect the stability of a fixation or implant[Bertollo 2011].Previous researchers have found that drill plunge depth depends primarily on the force applied to thedrill immediately before breakthrough (pre-breakthrough force (PBF)), which is influenced by severalfactors. Experienced surgeons use an anticipatory rather than a reactionary control scheme to reduceforce [Dubrowski 2004] and rely on audible feedback of the drilling sounds to detect impending break-through [Praamsma 2008]. Drill bit sharpness and bone quality can also influence plunge: dull drill bitsrequire more force, while low-density osteoporotic bone require less force [Alajmo 2012].Although the primary purpose is not to develop a specific device for reducing drill plunge, it ishelpful to look at what approaches have been tried. Most surgeons rely solely on sensory feedback todetect impending breakthrough, but there are several other approaches. In certain anatomical locations,especially those with high accuracy requirements like the spine, a drill stop is used to limit penetration.The drill stop is pre-set to an estimated depth, but they can be time consuming and cumbersome toadjust. There are also specialized bits for perforating the skull, such as the ACRA-CUT1. This deviceuses a pressure-clutch mechanism to arrest penetration after breakthrough. Unfortunately, it is specificto brain surgery and is too large and specialized for general use.Several researchers have developed intelligent tools to detect breakthrough and stop drill motion.Early work in detecting breakthrough was motivated by limiting penetration of spherical bits in stape-dotomy [Brett 1995]. This work was extended for detecting breakthrough using twist drills by Allotta[1996] who later developed a novel mechatronic drill to control and arrest the drill feed rate usingforce sensors [Allotta 1997]. Fully automated systems have also been developed, including a three-axis robotic drilling system [Lee 2006]. Although these devices were shown to limit drill plunge, thecomplexity and cost of specialized tools may be limiting their widespread adoption.The goal of this chapter is to describe the development of an experimental device to assess whethera bracing strategy can improve performance. A secondary, parallel loading pathway should help thesurgeon better control the relative motion between the tool and the target anatomy. This bracing strategyshould minimize drill plunge without markedly increasing the risk of osteonecrosis by extending drillingduration.4.2 Materials and MethodsThis section describes the methodology and materials used to develop an experimental brace to reducecortical drill plunge. The design process included a series of pilot testing and the development of anumerical drilling model (Table 4.1). Pilot testing and drilling model development and simulation weredone in parallel with development of the research Computer Assisted Surgery (CAS) system described inChapter 2. We first developed a model to predict the behaviour of freehand drill plunge. Once we wereconfident that this model predicted a similar amount of drill plunge to those measured experimentally,we extended this model to include a bracing device. The braced model was then used to simulate arange of brace configurations and parameters to inform the type and impedance of an experimental1ACRA-CUT Smart Drill Model 200-500 http:\/\/www.acracut.com\/perforators.html105CHAPTER 4. DAMPER-BASED BRACE DESIGNbrace design. Finally, we built, characterized, and calibrated an experimental bracing device.Table 4.1 Braced Cortical Drilling DesignPhase Section ReferenceDesign Input Design Requirements Section 4.2.1Design Process Pilot Testing Section 4.2.2Model Development Section 4.2.3Simulations Section 4.2.4Design Output Braced Cortical Drilling Model Section 4.2.3Experimental Brace Section 4.2.54.2.1 Design RequirementsWe want to develop an experimental bracing device to test whether a bracing strategy can improve theperformance of a clinically relevant motor task. We first needed to define the goal of the motor task andidentify which performance metrics we wished to improve.Motor Task GoalWe are primarily interested in the breakthrough phases of the drilling task, where the goal is to minimizethe penetration of the drill relative to the anatomy after breakthrough. The goal of the drilling phase isto maintain an efficient drilling force to minimize both drilling duration and temperature generation.Performance MetricsFor cortical drilling, the main outcome measures are the drilling duration and the drill plunge depth.There are a number of different process measures, including drilling force, pre-breakthrough force,drilling velocity, and post-breakthrough velocity.Experimental Brace Design RequirementsWe generated a list of requirements for an experimental damping brace to minimize drill plunge withoutmarkedly increasing drilling duration (Table 4.2). In addition to the requirements necessary for deviceperformance, there are also several requirements to facilitate user testing.4.2.2 Pilot TestingThe goal of the pilot testing was to experimentally characterize the user, the tool, and the interactionsbetween them. Pilot testing was an iterative process that occurred in parallel with development of theresearch Computer Assisted Orthopaedic Surgery (CAOS) system and development of the drilling model.Experimental data was used to validate the model, enhance the research CAOS system to adequately106CHAPTER 4. DAMPER-BASED BRACE DESIGNTable 4.2 Experimental Brace Design RequirementsRequirement Description SourceR1 Exert sufficient force to restrict drill motion PerformanceR2 Implement a range of impedance levels Performance \/ TestingR3 Set damping levels repeatably TestingR4 Set damping levels quickly TestingR5 Set damping levels with minimal user intervention TestingR6 Quickly detach from drill Testingmeasure drill plunge performance, and generate the necessary parameters to inform the design of anexperimental bracing device.We performed a number of drilling trials under a variety of conditions: material type, materialthickness, material mounting, drill bit length and drill rotation speed. Several types of wood weretested, including balsa, pine, and oak, to investigate the effect of increased drilling resistance. We alsoexperimented with food-grade porcine spinous processes and bovine femur.We collected a variety of different data from the drilling trials, including video, kinematics, andforce. Kinematic data was captured using the optical tracking system described in Section 2.5. Fromthis data we were able to calculate maximum drill plunge, as well as velocity during drilling and afterbreakthrough. Later pilot work included a uniaxial force sensor, as described in Section 2.7, to measurethe drilling force. Some trials were recorded with a consumer-grade high speed camera (Casio EX-FC150). These videos were used to check that the optical tracking system was accurately measuring themaximum plunge depth. By marking drill bits with paint, we were also able to estimate the rotationalspeed of the drill.4.2.3 Model DevelopmentThis section outlines the motivations and approach we used to develop a model of braced cortical drillingto predict drilling duration and drill plunge. There were two reasons for developing a model of corticaldrilling:1. Gain a better understanding of the parameters that influence freehand drill plunge; and2. Use the model to predict the type and value of brace mechanical impedance to best improveperformance.We first created a model of freehand cortical drilling in conjunction with pilot testing. Then, oncethis model was able to predict similar levels of drill plunge to what we measured experimentally, weadded bracing to explore its effect on drill plunge and drilling duration. We selected a damper-basedbracing configuration and then used simulations to predict the optimal damping level of an experimentaldamper-based bracing device.107CHAPTER 4. DAMPER-BASED BRACE DESIGNTo create the model we used a lumped-parameters approach and a bond graph based on a simplifiedrepresentation of the user, drill, anatomy, and ground (Figure 4.1). Using lumped parameters simplifiesthe state space of the system to a finite number and enables us to model the system using ordinarydifferential equations with a finite number of parameters. These state equations were determined fromthe bond graph by inspection and then solved using MATLAB? (Version 7.14.0.739, The Mathworks,Natick, MA, USA). The model predicts the movement of the drill bit tip based on the applied force, theempirically measured drilling relationship relating force and feed, and in the braced case, the impedanceof the brace. After breakthrough occurs, we assume that the drill trajectory depends primarily on thepassive properties of the user?s arm. For simplicity, we assume that the anatomy is rigidly fixed relativeto the environment2.We chose to use a bond graph approach because of their inherent modularity and ability to representmultiple domains. Other researchers have also used bond graphs to model musculoskeletal structureand function [Wojcik 2003]. A bond graph is a graphical representation of a dynamic physical system[Paynter 1961]. The elements in a bond graph are connected by bonds that either transmit power orinformation. Power bonds are bidirectional with effort in one direction and flow in the other. In a linearmechanical system, the effort is a force and the flow is a velocity. Signal bonds carry unidirectionalmeasurements. We used the inward power sign convention to assign positive sign to bonds enteringa junction, and the causal stroke indicates the effort signal direction. To generate a bond graph, eachcomponent is identified and connected together with the appropriate bonds. Next, the effort and flowvariables are related by appropriate relations. Once causality is defined, the state equations can bedetermined by inspection.In order to perform the simulations, we needed to model the dynamics of the user?s arm, the drill,and the brace. The following sections describe how we:? modelled user force generation with the equilibrium point hypothesis,? estimated the impedance of a user?s arm based on anthropometric data and experimentally mea-sured joint stiffness,? modelled the user?s post breakthrough reaction,? modelled the drilling process with empirically measured parameters,? modelled the dynamics of a brace, and finally? combined these into a model of braced cortical drilling.Human ForceIn this section we describe how the user?s motor control was modelled. During drilling the user utilizesvisual, audible, and proprioceptive feedback to control the position and force of the drill, which involvessensorimotor and higher cognitive functions. When breakthrough occurs, the sudden force imbalanceresults in passive motion of the arm before the user is able to voluntarily react. The human model needsto predict the forces and motion of the user during both phases.2Clinically, it can be quite difficult or invasive to rigidly fix the target anatomy, and in general there will be some viscoelasticbehaviour based on the soft tissue.108CHAPTER 4. DAMPER-BASED BRACE DESIGN+)GroXQGAQatoP\\Drill+XPaQYD(a) Cortical drilling schematic.BraFHEBNBGroXQGAQatoP\\Drill+XPaQ\u000eI \u000bY \fDYDE+PDYAN+P++YYG(b) Lumped parameter model of cortical drilling with brace between drill andanatomy.S f : VH 110213C : kH4R : bH516vD..I : mHD70819C : kB10R : bB11R : f (vD)12113 S f : VG14(c) Braced cortical drilling bond graphFigure 4.1 Schematic, lumped-parameter model, and bond graph of braced cortical drilling withrigidly mounted anatomy. User applied force, FH , is generated by movement of the equilib-rium point, xH =?vH dt.109CHAPTER 4. DAMPER-BASED BRACE DESIGNEven a seemingly simple motor task like controlling drilling force involves the coordination andcontrol of many muscles across many joints. Human motor control is complicated, and an active areaof research. Two assumptions were used to simplify the model. First, we assumed that the user appliesa constant force during the drilling phase. Second, we assume that drill plunge behaviour is primarilya result of the passive viscoelastic properties of muscles, and that an equilibrium point shift is used togenerate drilling force.The equilibrium point hypothesis [Feldman 2007] was first proposed in the 1960?s as a model forsingle-joint human motor control and has since been expanded for multiple joints. The hypothesis isthat motion and force results from changes in the equilibrium, or set point of the end of a spring. Inorder for a user to generate force against a surface, an equilibrium point is projected into the surface,and the natural stiffness of the muscle results in an applied force. If the surface is suddenly removed,the arm will move and come to rest at the equilibrium point.We assumed that the user applies a constant force during the drilling phase. This is essentiallyequivalent to a reactionary mode of control that Dubrowski 2004 proposed most junior residents employ.Experienced surgeons vary their force levels by utilising anticipatory control to reduce force levels whenbreakthrough is imminent. At breakthrough, we assume that the user?s equilibrium point is set based onthe pre-breakthrough force (PBF) and the effective arm stiffness, kH :xH,0 =PBFkH. (4.1)The next section describes how the effective impedance parameters of the arm were estimated.Human ImpedanceWe estimated the effective horizontal impedance of the user?s hand based on experimental work fromthe literature. The user?s arm is modelled as a two link manipulator based on anthropometric data. For aparticular posture and drilling force, we calculated joint torque and used experimentally measured rela-tions to estimate joint stiffness and damping. The stiffness, damping, and inertia are then converted fromjoint coordinates into end-effector hand coordinates. Finally, we extracted the horizontal components asan estimate of the effective impedance.We modelled the arm using a kinematic chain ? a series of segments connected together by joints(Figure 4.2). All segments are treated as rigid bodies and are assumed to interact via joints, springs, anddampers. We assume that the trunk is stationary and that all motion occurs in the arm, which reducesthe system to two degrees of freedom (DOF).Experimental work has demonstrated that the impedance of the arm depends on numerous factors,including force, posture, instability, muscle contraction, muscle arrangement, and spinal reflex sensitiv-ity [Mussa-Ivaldi 1985; Gomi 1997; Gomi 1998; Burdet 2001]. These groups measured the impedanceproperties of the human arm by approximating it as a two-link serial manipulator (Figure 4.3). Motion istypically modelled in a horizontal plane, whereas this figure shows motion in a sagittal plane. The upperarm and forearm are modelled as rigid bodies with mass, length, centre of mass, and mass moment ofinertia from anthropometric data. The shoulder and elbow are assumed to act like revolute joints. Both110CHAPTER 4. DAMPER-BASED BRACE DESIGNforward and inverse kinematics and dynamics can be calculated using the model.Our goal is to estimate the effective 1 DOF impedance for a particular posture of the arm (Figure 4.4).We selected a standing posture with the shoulder in neutral position and the elbow flexed to 90?posture,as if one is preparing to shake hands. This posture is similar to how a surgeon would position theirbody during in a lateral approach for a femur fracture repair. For the two-link manipulator, this posturecorresponds to joint angles of ?s = ?pi2 and ?e =pi2 .We use the same link lengths and mass properties as Tee [2004], summarized in Table 4.3.For the selected posture, drill mass, and applied force, we then use these equations to estimate thejoint torques. The estimated joint torques are then used with the experimentally determined torque-Figure 4.2 Illustration of a human modelled as a kinematic chain. Body segments are replacedby rigid bodies connected together by joints, which enables the motion of the body to berepresented as a series of mathematical equations.?Hy?y?y?x??Vx??Hx?DF ?DF ?FP ? J(D ?D ??VP ? JFigure 4.3 Schematic of a two-link sagittal planar manipulator used to model the arm. The shoul-der and elbow are assumed to act like revolute joints with angles ?s and ?e, respectively.111CHAPTER 4. DAMPER-BASED BRACE DESIGNy?x??????????????????F'N ??????P\u0003J'N ??????F'PKEKNK????Figure 4.4 The effective 1 DOF impedance of the arm and drill is estimated using the rigid bodydynamics of a two-link representation of the human arm. Inertia is estimated based on limbproperties and posture. Damping and stiffness are based on the muscle torques required tosupport the mass of the drill and apply a force, FH .dependent joint stiffness and joint damping relations to estimate the joint stiffness and joint dampingmatrices. We then apply a Jacobian based transformation to find the equivalent stiffness, damping, andinertia in the end-effector coordinate system. We then extract the components corresponding to the 1DOF model.Table 4.3 Human Arm Anthropometric DataSegment Mass Length Centre of Massa Mass Moment of In-ertia(kg) (m) (m) (kg m2)Upper Arm m1 =1.93 a1 =0.31 ac1 =0.165 I1 =0.01410Forearm m2 =1.52 a2 =0.34 ac2 =0.19 I2 = 0.0188Source: Tee [2004]a Referenced from proximal joint.The position of the hand in the shoulder coordinate frame can be found usingx =[xy]=[a1 cos(?1)+a2 cos(?1 +?2)a1 sin(?1)+a2 sin(?1 +?2)](4.2)where a1 and a2 are the lengths of the upper arm and forearm, respectively. We define q as the vectorof joint angles, i.e. ?= [?1,?2]T . The velocity of the hand can be found usingx? =[x?y?]= J(?)??, (4.3)where J is the Jacobian, the transformation between Cartesian and joint space:112CHAPTER 4. DAMPER-BASED BRACE DESIGNJ(?) =[?a1 sin(?1)?a2 sin(?1 +?2) ?a2 sin(?1 +?2)a1 cos(?1)?a2 cos(?1 +?2) a2 cos(?1 +?2)]. (4.4)Experimental work has found that joint stiffness is linearly related to torque magnitude [Gomi1998]. The joint torque generated by the muscles ? consists of the torque to compensate for the ex-ternal force FE applied to the hand and the torque ?B required to move the limbs,? =?J(?)T FE + ?B. (4.5)We estimate ?B by assuming the rigid body dynamics of a two-link manipulator:?B = I(?)??+C(?,??)??+G(?), (4.6)where ?? is the joint acceleration vector, I(?) is the position-dependent inertia matrix, C(?,??)?? is theCoriolis and centrifugal velocity dependent forces, and G(?) is the torques due to gravity.Spong [2006: p. 259-262] derived the dynamics of a two-link manipulator:I(?) =[I11 I12I21 I22](4.7)I11 = m1a2c1 +m2(a21 +a2c2 +2a1ac2 cos(?2))+ I1 + I2I12 = I21 = m2(a2c2 +a1ac2 cos(?2))+ I2I22 = m2a2c2 + I2C(?,??) =[h??2 h??1 +h??2?h??1 0], h =?m2a1ac2 sin(?2) (4.8)G(?) =[(m1ac1 +m2a1)gcos(?1)+m2ac2gcos(?1 +?2)m2ac2gcos(?1 +?2)](4.9)Gomi [1998] experimentally quantified the viscoelastic behaviour of the upper arm during posturemaintenance and force regulation tasks. They found a torque-dependent joint stiffness, K?, and a torque-dependent viscosity, B?. The mean linear relations for five adult subjects were:K? =[10.8+3.18 |?s| 2.83+2.15 |?e|2.51+2.34 |?e| 8.67+6.18 |?e|]N m\/rad, (4.10)B? =[0.10+0.63 |?s| 0.04+0.18 |?e|0.04+0.18 |?e| 0.19+0.76 |?e|]N m s\/rad, (4.11)where ?s (N m) is the shoulder torque, and ?e (N m) is the elbow torque. Although this study took placewith the shoulder and elbow in a horizontal plane, these results should be a good approximation for thepurposes of the model.113CHAPTER 4. DAMPER-BASED BRACE DESIGNWe use Equation 4.5 to estimate the joint torque necessary to generate a 35 N drilling force andsupport the weight of the 1.38 kg drill, i.e. FE = [?35,?1.38 ? 9.81]T , ? = [?pi\/2,pi\/2]T , ?? = ?? =[0,0]T . This yields joint torques of ? = [18,7] and an inertia matrix, I? . These joint torques are thenused in Equation 4.10 and Equation 4.11 to calculate the joint stiffness and damping. To determine theeffective stiffness and damping in Cartesian coordinates we applied the Jacobian:K =(JT)?1(K??dJTdqF)(J)?1 (4.12)B =(JT)?1B? (J)?1 (4.13)M =(JT)?1I? (J)?1 , (4.14)and then isolated the x?component of the transformed matrices to determine kha, bha, and mh.The inertia of the arm was set as the sum of the mass of the drill and the equivalent mass of thehuman arm. The drill mass is set to the same weight as the experimental drill: 1.38 kg. Anthropometricdata from Tee [2004] was used to model the human arm as described in Table 4.3.We calculated the effective one-dimensional stiffness, damping, and inertia over a range of externalforces from 5 N to 150 N (Figure 4.5). As expected, the effective human stiffness has a positive linearrelationship with the drilling force, ranging from approximately 0.5 N\/mm to 21 N\/mm. Similarly, theeffective human damping level varies linearly from 0.080 N s\/mm to 0.390 N s\/mm. The effective humaninertia does not depend on external load; for this posture, the effective mass of the arm is 2.2 kg. Thecombined mass of the arm and the drill is 3.6 kg.Human ReactionWe assumed that the user perceives or detects breakthrough immediately, but that their reaction is de-layed by sensory, processing, and motor execution delays. We also assumed that their reaction is a returnof the equilibrium point to the surface of the work piece.We modelled this task as a simple reaction: there is a single response ? retract the drill ? to a singlestimulus ? breakthrough has occurred. Modelling the reaction requires an estimate for the reaction timeand a reaction duration. Human reaction time is well studied and depends on a number of factors,including age, stimulus type, and stimulus intensity [Kosinski 2012]. A recent study of 150 subjectsfound a mean of 255.7 ms and a standard deviation of 37.5 ms for a simple reaction test performed on acomputer [Deary 2011]. Based on these results, we chose a value of tR = 250ms for the human reactiontime. A reaction duration of tRD = 250ms was selected based on the ability of the arm to apply cyclicforce at a maximum frequency of approximately 4 Hz [Guiard 1987].114CHAPTER 4. DAMPER-BASED BRACE DESIGNFigure 4.5 Estimated components of linearized effective horizontal impedance under varying forcelevels of a human arm with upper arm perpendicular to ground and forearm parallel to ground.115CHAPTER 4. DAMPER-BASED BRACE DESIGNThe change in virtual equilibrium position was modelled using a sinusoid (Figure 4.6):Vh(t) =?????????0 0 < t < td ,piz0 sin(pi\/tr(t?td))2trtd ? t ? td + tr,0 t > td + tr.(4.15)Figure 4.6 Illustration of human reaction model. Drilling thrust force is generated by setting theequilibrium point z0 =? PBFkH into the work piece When breakthrough occurs, we assume thereis a delay of tR = 250ms before the user begins to react, and that it takes tRD = 250ms to movethe equilibrium point back to the starting point.Empirical Drilling ModelThe drilling model relates the kinetics and kinematics of the drill bit, user, and workpiece. Typically,drilling models predict thrust force based on feed rate, drill bit geometry, and material properties. Whilethis is appropriate for situations where the feed rate is controlled like an automated drill press or robot,a human user is typically monitoring and controlling thrust force rather than feed rate, so we need amodel that predicts feed rate based on applied thrust force.Wiggins [1976] experimentally demonstrated that specific cutting energy u, the energy expended perunit volume material removed, increases as drill feed velocity vD (mm\/s) decreases. It is also known thatthrust force FD (N) is directly related to vD: larger thrust forces result in larger feed rate. Experimentaldata with several different types of drill bits demonstrated a power function relationship:f = Bpx, (4.16)116CHAPTER 4. DAMPER-BASED BRACE DESIGNwhere f is the feed (mm\/rev) and p is the pressure (N\/mm2). B (mm) and x are experimentally de-termined constants found through regression. The pressure is defined using the thrust force and crosssectional area of the hole:p =FDA=4FDpiD2 (4.17)where D is the drill bit diameter (mm). The feed is estimated from the drill feed velocity and rotationspeed:f =60 ? vDRPM. (4.18)Equation 4.16, Equation 4.17, and Equation 4.18 are combined and rearranged to express drillingforce as a function of drill feed velocity:FD =piD24[60 ? vDRPM ?B] 1x .(4.19)Drilling parameters were obtained from the literature and measured experimentally (Table 4.4). Weexperimentally measured drilling parameters for a 3?16 inch (4.76 mm) high speed steel (HSS) drill bitinto 6.35 mm oak. Drilling force and drilling velocity were extracted from the linear drilling portion ofeach trial. We assumed a constant drill speed of 1200 RPM and calculated the feed and pressure usingEquation 4.17 and Equation 4.18. The constants B = 0.19mm and x = 1.45 were then estimated usinga non-linear least square fitting algorithm in MATLAB?. Detailed data can be found in Appendix A.3.Table 4.4 Empirical Drilling ParametersMaterial Bit Type RPM B (mm) x SourceOak HSS 1200 0.190 1.45 Appendix A.3Oak BRAD 1200 0.066 1.32 Appendix A.3Human cadaver femur Twist Drill 1150 0.00037 1.8 Wiggins [1976]Brace ModelAdding a bracing strategy to a system involves two parts: selecting the components to connect, anddesigning the dynamics of the brace.A secondary, parallel connection could be applied between any of the following components:? drill ?? anatomy? drill ?? user? drill ?? ground? anatomy ?? user? anatomy ?? ground? drill ?? anatomy117CHAPTER 4. DAMPER-BASED BRACE DESIGNWe chose to apply a brace between the drill and the anatomy for this application because it isthe movement of the drill bit relative to the anatomy that we wish to minimize. In a typical clinicalscenario, there will be motion of both the anatomy and the tool relative to the environment. To simplifythe problem, we assume that the anatomy is rigidly fixed relative to the environment. This enables us toshift the connection from the anatomy to the environment.We selected the dynamics of the brace based on the characteristics of the task and the aspect ofperformance we are trying to improve. Based on pilot testing and previous research, drill plunge resultsin motion of the drill bit relative to the anatomy primarily due to the passive spring-like properties of thehuman arm and a sudden imbalance of force. In order to reduce motion after breakthrough, we need thebracing device to impose a balancing force until the user detects breakthrough and voluntarily reducestheir drilling force.The brace can be passive, semi-active or active. We chose to explore a purely passive approach forsimplicity, and since other researchers have explored more active methods of breakthrough detectionand plunge minimization.We experimented with a variety of methods to passively reduce drill plunge, with the general ideaof minimizing acceleration of the drill by generating a balancing force. A spring seemed as if it wouldbe a logical choice, setup in a configuration such that it balanced out the human force at the position ofbreakthrough. In reality, this posed two problems: one, it required accurate knowledge of the workpiecedepth, and two, as the drill approached breakthrough, the drilling force would approach zero. Thesecond problem is more important: although drill plunge could be reduced to almost zero in an idealcase, the diminishing drilling force would markedly increase drilling duration. Instead of relying onaccurately knowing position relative to the breakthrough point, which is one of the inherent challengesof cortical drilling, we chose to focus on velocity, which led to experimentation with a damper.We identified that a damper-based brace had the greatest potential, since it would apply a velocity-dependent balancing force. The use of a damper with a drill is not novel. Dampers are sometimesmounted to a drill press to ensure a consistent feed rate. Since drilling velocity is relatively slowcompared to post-breakthrough velocity, the damper should only require a small force to move duringdrilling. A spring-based damper is also capable of producing a balancing force, but since it is positiondependent, it would also have a larger impact on the drilling process, and it would be difficult to set theun-stretched length appropriately.We modelled the brace as a linear damper,FB = bB ? y?, (4.20)where FB is the force exerted by the damper when it is moved at a velocity of y? and bB is the dampingcoefficient.In the next section, we combine the user, drilling, and brace models together to analyse the overallbehaviour of a braced drilling task.118CHAPTER 4. DAMPER-BASED BRACE DESIGNBraced Cortical Drilling ModelIn this section, we describe how the human and drilling models are combined into an overall freehandcortical drilling model, and how the brace model is added to form the braced cortical drilling model.We make several assumptions to simulate the drilling and breakthrough phases of the task separately.The drilling duration is found by solving the steady-state velocity so that the drill, damper, and appliedthrust force balance,?F = FH ?FB (v)?FD (v) = 0. (4.21)We include Equation 4.19 and Equation 4.20 to yield the following non-linear minimization:vd = argminv ? (0,?)?FH ?FB (v)?FD (v)?= argminv ? (0,?)?????FH ?bB ? v?piD24[60vRPM ?B] 1x?????. (4.22)The drilling duration, tD can then be determined from simple kinematics,tD =dwvD, (4.23)where dw is the depth of the workpiece.By assuming no post-breakthrough interaction between the drill bit and the workpiece, the motionof the drill tip is strictly a result of the passive dynamics of the arm. We ignore the drilling elementfrom the bond graph and define the state vector as X = [phd ,qb]T , where phd is the integrated effort, ormomentum, of the arm mass. We assign the other integrated flow, qb, as an observer which representsthe displacement of the drill relative to the work piece (equivalent to tz).The state equations are:dpHDdt=?kB ?qB +bB[VG?pHDmHD]+piD24??60[pHDmHD?VG]RPM ?B??1x(4.24)dqBdt=p7mHD?VG. (4.25)Our model is based on several assumptions (Table 4.5). These assumptions are mainly intended tosimplify the representation of the user.In the next section, we describe how these equations were used to predict duration and plunge.119CHAPTER 4. DAMPER-BASED BRACE DESIGNTable 4.5 Drilling Model AssumptionsAssumption DescriptionA1 Limb force and motion result from changes in Equilibrium-Point positionA2 User maintains constant drilling forceA3 Human arm impedance remains constantA4 User detects breakthrough immediatelyA5 No post-breakthrough interaction between drill bit and workpieceA6 Workpiece is rigidly fixed4.2.4 SimulationsWe used the MATLAB? functions fminbnd for the minimization to determine the drilling velocityand duration and ode15s to solve the ordinary differential equations of the post-breakthrough plungebehaviour.The determine the initial conditions, or breakthrough conditions, we set the displacement of thehuman spring to generate the desired pre-breakthrough force (PBF) using Equation 4.26. For simplicity,we assume that the drill starts from rest, so the initial value of the drill momentum, pHD, is zero.qH,0 =PBFkH(4.26)Freehand Cortical Drilling SimulationWe simulated freehand drilling by setting the brace stiffness, kB, and brace damping, bB, to zero. Appliedforce was varied from 5 N to 150 N.Braced Cortical Drilling SimulationWe simulated different combinations of thrust force level and brace damping. Applied force was variedfrom 5 N to 150 N and brace damping was varied from 0 N s\/mm to 40 N s\/mm.Damping Level OptimizationUltimately, the goal of the model is to predict an optimal brace damping level that minimizes drillplunge depth with minimal effect on drilling duration. We expect that as damping increases, plungewill decrease and drilling duration will increase. We define the optimal damping level as the value thatminimizes a cost function based on the drill plunge depth and duration,C = wp ?mZ +wt ? tD, (4.27)120CHAPTER 4. DAMPER-BASED BRACE DESIGNwhere wp and wt represent the relative weights applied to the plunge depth and drilling duration, respec-tively. For simplicity, we chose wp = wt = 1, which applies equal weighting to 1 mm of plunge and 1 sdrilling duration.The optimal damping level was determined for a range of FH using a minimization approach:bB,opt = argminbB ? (0,50)?C(FH ,bB,x,dw,)? (4.28)Equation 4.28 was minimized in MATLAB? using the function fmincon.4.2.5 Experimental Brace ImplementationResults of the pilot testing and model simulations suggested that a damper-based brace could reduce drillplunge depth with varying increases in drilling duration. The next sections describe the construction,and calibration of an experimental bracing device.Optimal Damping RangeDashpotA dashpot is a mechanical piston and cylinder device used to control velocity and dampen vibration. Thedevices dissipate energy by forcing a fluid through an orifice. Based on the required pulling force andstroke as determined from pilot testing (Table 4.6), we selected an Airpot? 2KS444 B 2.0 TX (AirpotCorporation, Norwalk, CT, USA) as shown in Figure 4.7a. This dashpot is constructed from a graphitepiston and pyrex glass cylinder and uses air as the working fluid. It has a 1.75 inch (44.45 mm) bore anda 2 inch (50.80 mm) stroke. The airpot exerts a roughly linear force with velocity, but differs slightlyfrom a traditional fluid dashpot because air is compressible. The maximum pull force for this modelis approximately 130 N. The model we chose has a one-way valve that provides damping in the pulldirection and minimal resistance in the push direction. It also includes an adjustable orifice that allowsthe damping level to be adjusted by turning a knob.MountingThe Airpot? was mounted inside a wooden frame to provide a rigid connection to ground and to limitthe travel of the piston. The drill was modified with a bracket to provide a connection point to theexperimental bracing device. A small aluminium bracket was designed, constructed, and attached to therear of the drill. This bracket provided a convenient point to easily connect and disconnect the damperpull rod. Figure 4.7b illustrates the experimental brace and the drill mounting.Damping Level CalibrationWe attached an angular indicator to the orifice adjustment knob in order to repeatably set damping levels.We performed a series of drop tests to characterize the damping level for different settings of the angularindicator.121CHAPTER 4. DAMPER-BASED BRACE DESIGN(a) (b)Figure 4.7 The experimental damping brace consists of a 2KS444B2.0TX Airpot? mounted insidea wooden frame. (a) An adjustable orifice on the top is used to provide a range of dampinglevels. The damping is one-way; this model only provides resistance while being extended.(b) An aluminium bracket mounted to the drill provides a detachable connection.To perform the drop test, the dashpot was mounted vertically. Optical markers were attached to am = 2.840kg steel block, which was then attached to the dashpot rod. We did a pivot calibration todetermine the offset of the ball connection relative to the local coordinate frame of the block.For each trial, the block started at rest in the fully retracted position and came to rest against a stopbefore reaching the end of the cylinder stroke. The optical tracker measured the vertical height of theblock as it descended.When a constant external force is applied to the dashpot with a mass, the pressure quickly drops inthe cylinder until the force balances and there is zero acceleration,FB?m ?g = 0, (4.29)which results in a nearly constant velocity. Assuming a linear damping relation as in Equation 4.30, thedamping coefficient can be estimated by rearranging the equations to formbB ?m ?gy?. (4.30)The velocity of each experimental trial was calculated by fitting a line to the linear portion of theheight-time response , y?. The damping coefficient, bB, was then calculated using Equation 4.30.Experimental Brace SimulationWe performed simulations of the model at each of the characterized damping levels in order to predictthe performance of the experimental brace. Simulations were performed at damping levels of 0 N s\/mm,122CHAPTER 4. DAMPER-BASED BRACE DESIGN0.2 N s\/mm, 10 N s\/mm and 30 N s\/mm over an applied force range of 5 N to 150 N. We also repeatedthe simulations using the drilling parameters for bone.4.3 ResultsIn this section we describe the results of the various stages of the brace development. First, we describea series of pilot testing that was used to identify typical ranges of cortical drilling metrics. We thenprovide results of the simulations using the model of cortical drilling we developed to predict drillplunge and duration. We compare the performance metrics predicted by the simulations to performancemetrics extracted from experimental trials, and then use the model to predict an optimal bracing level tominimize drill plunge and drilling duration. Finally, we illustrate the design of the experimental bracingdevice and characterize its damping level and predicted performance.4.3.1 Pilot TestingDrill plunge behaviour was explored by performing pilot tests in a variety of materials. Figure 4.8 illus-trates drill plunge after the far cortex of a bovine femur is penetrated. From the time of breakthrough, ittakes less than 0.2 s for the drill to travel 35 mm to 40 mm and bottom out against the top surface of thebone. During this time, the bone is also visibly pulled towards the drill.Previous studies have defined breakthrough as the time when the measured force applied to the workpiece is zero [Dubrowski 2004; Praamsma 2008]. We found that although there is a drop in force level,zero force did not always correspond with breakthrough if there was some sort of interaction betweenthe drill bit and the work piece. In order to quantify breakthrough time more accurately, we used themeasured tip position with respect to the registered rear surface of the work piece material.Figure 4.9 illustrates a typical drilling trial performed by an experienced subject using a 3?16 inch(4.76 mm) HSS drill bit in 6.35 mm oak. Figure 4.10 and Table 4.6 illustrate and provide summarymetrics for 10 pilot trials. Although the applied force is fairly consistent, there is substantial variation inthe plunge kinematics with drill plunge ranging from 10 mm to 38 mm. Maximum drill plunge occurredon the first trial, suggesting some learning took place.123CHAPTER 4. DAMPER-BASED BRACE DESIGNPre-breakthrough(a)During Breakthrough(b)Bottomed-out(c)Drill stop(d)Figure 4.8 Frames extracted from a video of drilling through the far cortex of the distal end of abovine femur: (a) immediately before breakthrough; (b) drill plunges downwards and bone ispulled upwards, (c) drill is bottomed out against bone; and (d) user stops drill. Each frame isseparated by approximately 0.13 s.Table 4.6 Pilot Testing SummaryDrill Trial Metric Min Max Mean ? SDAverage Thrust Force (N) 23 30 27 ? 2Average Drilling Velocity (mm\/s) 7 9 8 ? 1Drilling Time (s) 0.71 0.96 0.83 ? 0.07Pre-breakthrough Force (N) 20 42 30 ? 7Drill Plunge (mm) 10 38 16 ? 8Max Drill Plunge Delay (s) 0.14 0.17 0.15 ? 0.01Max Plunge Velocity (m\/s) 96 313 156 ? 60Experienced subject, 3?16 inch (4.76 mm) HSS drill bit,6.35 mm oak124CHAPTER 4. DAMPER-BASED BRACE DESIGNFigure 4.9 Work piece force and tip position of a typical drill plunge trial using a 3?16 inch (4.76 mm)HSS drill bit in 6.35 mm oak. Breakthrough is defined when tip crosses zero, pre-breakthroughis defined as maximum force in a 200 ms window before breakthrough, and drill plunge isdefined as maximum penetration of drill tip.Figure 4.10 Work piece forces and tip positions for a single subject series of 10 drill plunge trialusing a 3?16 inch (4.76 mm) HSS drill bit in 6.35 mm oak. Trials are shifted to align break-through with t = 0s. Drill plunge varies from 10 mm to 38 mm. Maximum drill plungeoccurred on the first trial.125CHAPTER 4. DAMPER-BASED BRACE DESIGN4.3.2 Freehand Plunge SimulationA typical simulation at an average drilling force of 30 N predicts a drilling duration of 2.6 s and amaximum drill plunge of 29 mm (Figure 4.11). At 30 N, the effective horizontal impedance of the user?sarm is kH = 0.831N\/mm, bH = 0.143N s\/mm, and mHD = 3.6kg. Maximum drill plunge occurs slightlyafter the 250 ms reaction time.As the applied force level increases from 5 N to 150 N, the predicted drill velocity increases from0.6 mm\/s to 80 mm\/s (Figure 4.12), which decreases the drilling duration from approximately 8 s to0.06 s. Increasing applied force levels leads to greater drill plunge (Figure 4.14), increasing from 7 mmto 55 mm and appearing to approach an asymptote at forces beyond those that are physiologically re-alistic (Figure 4.15). Drilling duration and maximum drill plunge are related by an inverse function(Figure 4.16).Figure 4.11 Drill bit tip trajectory of a typical drilling duration simulation. At a drilling force of30 N, the effective human arm impedance values are kH = 0.831N\/mm, bH = 0.143N s\/mm,and mHD = 3.6kg. The maximum predicted plunge for this simulation was 29 mm and occursnear the 250 ms reaction time, indicated with the vertical dashed line.ValidationPre-breakthrough force and average drilling force were extracted from a series of experimental trials andused as inputs to the model. A typical first experimental trial with a PBF of 42 N and mean drilling forceof 31 N predicts a drilling duration of 0.6 s and a maximum drill plunge of 35 mm. The corresponding126CHAPTER 4. DAMPER-BASED BRACE DESIGNFigure 4.12 Simulated drill trajectory as PBF increases from 5 N to 150 N. Drilling duration de-creases as PBF increases.Figure 4.13 Predicted drilling duration with increasing pre-breakthrough force (PBF). Durationdecreases as PBF increases.127CHAPTER 4. DAMPER-BASED BRACE DESIGNFigure 4.14 Simulated drill plunge trajectory as PBF increases from 5 N to 150 N. Maximum drillplunge increases as PBF increases.Figure 4.15 Predicted drill plunge with increasing pre-breakthrough force (PBF). Drill plunge in-creases as PBF increases, approaching a limit beyond physiologically realistic values of force.128CHAPTER 4. DAMPER-BASED BRACE DESIGNFigure 4.16 Predicted freehand drilling duration and drill plunge over a range of pre-breakthroughforce (PBF) from 5 N to 150 N.experimental drilling duration was 0.8 s and drill plunge was 40 mm. The maximum drill plunge occursslightly earlier in the experimental trial. The other noticeable difference is lack of symmetry betweenthe plunge and withdrawal in the experimental trial.The model consistently under-predicts the drilling duration of subsequent trials by 15 % to 20 %(Figure 4.18). After slightly under-predicting drill plunge by about 12 % in the first trial, the modeltends to over-predict drill plunge in subsequent trials by 70 % to 150 % (Figure 4.18). This deviationsuggests that the model is not accounting for learning effects.129CHAPTER 4. DAMPER-BASED BRACE DESIGNFigure 4.17 Comparison of simulated and experimental drilling.Figure 4.18 Comparison of simulated and experimental drilling duration. The model predicts upto a 15 % to 20 % shorter drilling duration than found in experiments.130CHAPTER 4. DAMPER-BASED BRACE DESIGNFigure 4.19 Comparison of simulated and experimental drill plunge. The model predicts the firsttrial in the pilot testing set within 12 %, but then overestimates plunge for the rest of the trialsin a block of 10 by roughly a factor of 2.131CHAPTER 4. DAMPER-BASED BRACE DESIGN4.3.3 Braced Cortical Drilling SimulationUsing our simple lumped parameter model, we predicted the drill plunge depth after cortical break-through. The inputs to the model are the pre-breakthrough force, the impedance of the surgeon?s arm,and the impedance of a bracing device between the drill and the work piece. At a typical drilling forcelevel of 30 N, applying a damping level of 10 N s\/mm increased drilling duration from 0.6 s to 3.4 sand decreased drill plunge from 29 mm to 0.8 mm (Figure 4.20). There is a slight increase in time tomaximum drill plunge from 0.28 s to 0.32 s.Figure 4.20 Drill bit tip trajectory of a typical braced drilling simulation. At a drilling force of30 N, the effective human arm impedance values are 0.831 N\/mm, 0.143 N s\/mm, and 3.6 kg.The experimental drilling resistance for a 3?16 inch (4.76 mm) high speed steel (HSS) drill bitin 6.35 mm oak. Drill plunge is reduced from 29 mm to 0.8 mm while drilling duration isincreased from 0.6 s to 3.4 s.At a fixed force level of 30 N, increasing the brace damping from 0 N s\/mm to 40 N s\/mm decreaseddrilling velocity from 8.1 mm\/s to 0.7 mm\/s (Figure 4.21), which increased drilling duration from 0.61 sto 6.45 s (Figure 4.22). Increasing brace damping reduced plunge depth (Figure 4.23) and decreasedmaximum drill plunge from 29 mm to 0.2 mm (Figure 4.24). As the damping level increased, a growingproportion of the force is required to move the damper, reducing the drilling force (Figure 4.25). Thisleads to decreased drilling velocity and longer drilling duration.132CHAPTER 4. DAMPER-BASED BRACE DESIGNFigure 4.21 Simulated drilling duration for a thrust force of 30 N and brace damping from0 N s\/mm to 40 N s\/mm.Figure 4.22 Simulated drilling duration for a thrust force of 30 N and brace damping from0 N s\/mm to 40 N s\/mm.133CHAPTER 4. DAMPER-BASED BRACE DESIGNFigure 4.23 Simulated plunge depth for a thrust force of 30 N and brace damping from 0 N s\/mmto 40 N s\/mm. Note that even relatively low levels of damping can have significant effects.Figure 4.24 Simulated plunge depth for a thrust force of 30 N and brace damping from 0 N s\/mmto 40 N s\/mm.134CHAPTER 4. DAMPER-BASED BRACE DESIGNFigure 4.25 Simulated braced drilling forces for a constant applied human force of 30 N, bracedamping from 0 N s\/mm to 40 N s\/mm and the empirically estimated drilling parameter ofthe HSS drill bit in oak. Note that as the damping level increases, a portion of the appliedforce is required to move the brace, reducing the drilling force and therefore reducing thedrilling velocity.4.3.4 Optimal Brace DampingAt a given force level, there is a trade-off between drill plunge and drilling duration as damping levelincreases (Figure 4.26a). We found an optimal bracing level at a particular applied force level by ap-plying a weighted cost function (Equation 4.27). With an applied drilling force of 30 N and an arbitraryweighting of wp = wt = 1 (i.e., 1 mm = 1 s) for illustrative purposes, the optimal damping level is ap-proximately 5 N s\/mm (Figure 4.26b). The optimal damping level increases linearly with human thrustforce, ranging from 1.0 N s\/mm to 30 N s\/mm (Figure 4.27).4.3.5 Brace Damping Level CalibrationAn angular indicator was added to the Airpot? so we could repeatedly set the damping level. We chosethree orifice adjustment positions and performed two additional sets of 10 drop trials for each. For thefirst set, the orifice adjustment knob was left at the same angle to quantify the intra-angle repeatability.During the second set of drop trials, the orifice adjustment knob was readjusted between each trial toquantify the inter-angle repeatability. One drop trial at each of the chosen damping levels is illustratedin Figure 4.28. The results of the characterization can be found in Table 4.7. There is markedly morevariation in the damping coefficient as the damping level increases.135CHAPTER 4. DAMPER-BASED BRACE DESIGN(a) Performance Trade-off(b) Weighted Cost FunctionFigure 4.26 Trade-off and optimal damping: (a) trade-off between drill plunge and drill durationfor a range of damping levels at 30 N and (b) optimal brace damping for equally weightedplunge depth (mm) and drilling duration (s) (i.e. wp = wt = 1).136CHAPTER 4. DAMPER-BASED BRACE DESIGNFigure 4.27 Optimal brace damping for equally weighted plunge depth (mm) and drilling duration(s) (i.e. wp = wt = 1).Figure 4.28 Plot of three typical drop trials. A 2.840 kg mass suspended from the damper wasreleased from rest. The vertical position of the mass was measured using an optical tracker.The damping level was estimated from the linear portion of the distance-time data for eachorifice position of the Airpot?.137CHAPTER 4. DAMPER-BASED BRACE DESIGNTable 4.7 Experimentally Measured Damping LevelsLevel Damping (N s\/mm)Low 0.2 ? 2%Medium 10 ? 2%High 30 ? 10%Based on 10 drops trials us-ing a 2.840 kg mass at eachorifice adjustment angle.138CHAPTER 4. DAMPER-BASED BRACE DESIGN4.3.6 Simulated Experimental Brace PerformanceWhen simulating drilling through oak at a typical applied force of 30 N, the model predicts that the ex-perimental damper-based bracing device should reduce the freehand drill plunge of 29 mm by approxi-mately 40 %, 97 %, and 99 %, at the low, medium, and high damping levels, respectively (Figure 4.29b).There is a corresponding 0.1 s, 2.5 s, and 7.1 s increase in drilling duration (Figure 4.29a).(a)(b)Figure 4.29 Simulated performance of experimental brace for each characterized Airpot? dampinglevel using drilling parameters derived for a 3?16 inch (4.76 mm) HSS drill bit in 6.35 mm oak:(a) drilling duration and (b) drill plunge.139CHAPTER 4. DAMPER-BASED BRACE DESIGNIn order to predict how the experimental brace would perform in bone, we repeated the simulationsusing empirical drilling parameters for human femur measured by Wiggins [1976]. At a given forcelevel, our model predicts identical levels of drill plunge (Figure 4.30b). This is expected, since we areassuming no interaction between the drill bit and the workpiece. It is important to note that since boneis more difficult to penetrate, we expect higher drilling forces would be required, leading to higher drillplunge and much longer drilling duration (Figure 4.30a). Based on the empirical drilling parametersfor twist drills in bone, the model predicts a drilling duration of 330 s at a force of 30 N, over 400times longer than oak. This lower feed leads to lower brace forces, so there is much less time variationbetween damping levels.140CHAPTER 4. DAMPER-BASED BRACE DESIGN(a)(b)Figure 4.30 Simulated performance of experimental brace for each characterized Airpot? dampinglevel using drilling parameters derived from human cadaver femur: (a) drilling duration and(b) drill plunge.141CHAPTER 4. DAMPER-BASED BRACE DESIGN4.4 DiscussionCan a bracing strategy improve the performance of a clinically relevant task? What type and levelof brace impedance can minimize drill plunge during cortical drilling? Based on pilot testing, wedeveloped a numerical model to predict plunge and duration of freehand cortical drilling. We thenextended this model to include a bracing element to demonstrate that plunge could be minimized withminimal increase in drilling duration. By applying a suitable weighting function, we were able todetermine optimal brace damping levels and then used these results to design, construct, characterize andcalibrate an experimental brace damping device. Numerical simulations demonstrated that a damper-based brace can markedly reduce drill plunge without markedly increasing drilling duration.Since the dynamics of cortical drilling have not been studied in much detail, we performed a varietyof pilot testing. One of our key findings is that even under ideal conditions ? when the workpiece depthis accurately known and the workpiece is rigidly mounted ? minimizing drill plunge is a surprisinglydifficult task. Even after gaining considerable experience, it was not uncommon to plunge 30 mm to40 mm. The high thrust forces required for drilling results in considerable build up of potential energyin the muscles of the arm. It is easy to understand how this sudden release of energy before the userhas a chance to voluntarily react can cause significant damage to soft tissue, vasculature, nerves, andtendons as reviewed by Alajmo [2012], especially since the drill bit is likely still turning. The highdrilling forces, passive properties of muscles and significant sensorimotor delays make manual corticaldrilling difficult.The freehand cortical drilling model we developed was able to reasonably predict unlearned drillingduration and drill plunge within about 20 %. Our model uses anthropometric values and experimentallydetermined joint stiffness and damping values from the literature to determine the impedance propertiesof the user?s arm. This model provides a reasonably good prediction of the amount of motion that resultsduring an initial, or unlearned, breakthrough event, but does not account for any learning.To model drilling, we used a power law relation with experimentally measured parameters. Thevalue we measured for x in oak is comparable to the value in bone estimated in the literature. Asexpected, the B values differ considerably, which represents the difference in hardness between the twomaterials. The relatively low correlation coefficient of 0.68 for the oak drilling parameters is likely aresult of drilling through the relatively thin sections.The damper-based brace should minimize drill plunge by providing a balancing force after break-through and dissipating energy until the user has a chance to react. This secondary, parallel loadingpathway between the drill and the workpiece should have minimal impact on drilling duration sincepre-breakthrough drilling velocities are relatively small compared to post-breakthrough plunge velocity.4.4.1 Modelling Assumptions and LimitationsWe made several assumptions to simplify the model and simulations. The following sections addressthe validity and impact of theses assumptions on the conclusions, and provide additional detail on otherlimitations that may explain the difference between simulated and experimental results.142CHAPTER 4. DAMPER-BASED BRACE DESIGNUser maintains constant drilling forceWe chose to use a constant drilling force to avoid the complexity of including a model of human feed-back control. Based on pilot testing, we knew that the applied thrust force varies, especially since theremust be some sort of force build up as drilling is first initiated. However, despite this limitation, themodel was still able to predict drilling duration within 20 % to 30 %. The use of a constant drilling forceis also a likely explanation for why the model consistently over-predicted duration when compared tothe experimentally measured duration from pilot testing. The average drilling force of the pilot trial wasused as an input to the model. Since the relation between drilling force and feed velocity is non-linear,time spent drilling at levels above or below the mean drilling force will not contribute equally to thedrilling duration.Human arm impedance remains constantWe assumed that over the course of a single trial, the impedance of the human arm remained constant.It is likely that when the person detects breakthrough, they change the impedance of the arm, i.e., theystiffen up through co-contraction, or they relax their arm. The primary driver of this is probably a low-latency reflex loop, i.e. a large extension is detected in the stretch receptors in the muscles, which leadsto a contraction of the antagonist. This would happen before any conscious attempt to retract the drill.Although the arm impedance may remain relatively constant during the passive plunge motion,there are almost definitely differences between subsequent trials through learning. Other researchershave demonstrated that voluntary control over the stiffness of the hand is possible [Darainy 2004].User detects breakthrough immediatelyWe assumed that the user detects breakthrough immediately as it occurs, and that there is a finite andfixed delay before they react by adjusting their equilibrium point. The underlying assumption is thatwhatever stimulus the human is using to detect breakthrough is unaffected by the damping level. Prop-erly assessing this assumption will require testing with the experimental bracing device, and we revisitthis issue in Chapter 5.No post-breakthrough drill bit interactionOne of the major assumptions was that there is no interaction between the drill bit and the workpieceafter breakthrough. During some pilot trials, we observed that standard twist drill bits would be pulledtowards the material after breakthrough. Trials that exhibited this ?corkscrew? behaviour had differ-ent post-breakthrough velocities. Furthermore, the tip plunge depth showed a linear trend immediatelyafter breakthrough, indicating a nearly constant velocity, followed by a conventional peak before with-drawal. Analysis of high speed video confirmed this coupled motion in a variety of materials, includingwood, bovine femur, porcine spinous processes, and plastic. This behaviour was much more commonin materials that were less likely to cut cleanly, like plastic. An incomplete breakthrough leaves smallprotrusions on the side of a hole which can engage the edges of a twist drill bit (Figure 4.31).143CHAPTER 4. DAMPER-BASED BRACE DESIGN(a) Incomplete breakthrough (b) CorkscrewFigure 4.31 Illustration of corkscrew mechanism. Incomplete breakthrough results in small pro-trusions on the side of the hole. These protrusions behave like threads, engaging the bit andpulling it into the work piece as it rotates. The translation remains coupled to the rotationuntil the protrusions break off or the drill stops spinning.We performed a series of trials at two different drill speeds, 350 RPM and 1200 RPM using a 3?16 inch(4.76 mm) aircraft drill bit in 3.5 mm polyethylene plastic. The feed rate of the drill bit, vz (mm\/s)expected by the rotational speed of the drill and the helix angle of the drill bit (30.5?),vz = b ?? =piDtan(?)?, (4.31)where D is the bit diameter (mm), ? is the helix angle (?), and ? is the rotational speed of the drill(RPM) shows good agreement with the post-breakthrough velocity (Figure 4.32).Based on these observations, we can theorize what happens during a corkscrew event. First, the tipstarts to break through the work piece. The force on the drill bit causes small remaining parts to fractureinstead of being cut, leading to an incompletely drilled hole. Small remaining pieces around the holeact like internal threads that transfer the rotational velocity of the drill bit into translation like a screw.The coupled corkscrew motion continues until one of the following occurs:? The protrusions or attached chips break off. This can occur as a result of a negative thrust forceapplied to the drill, or when the end of the flutes are reached in an extended drill bit.? The drill bit stops spinning after the drill motor is turned off.Based on these results, we expected that some drill bit geometries ? particularly a negative rake angle? might exacerbate plunge. Since the model does not consider any work piece-drill bit interaction, itwould likely under-predict drill plunge in the case of a corkscrewing bit. However, since we believe thatwhen a sufficient resistive force on the drill is reached, the incomplete parts of the hole are broken offcausing corkscrewing to stop. A damper-based brace should then still limit drill plunge and potentiallyshorten the amount of corkscrew by providing this resistive force.Rigidly fixed workpieceWe further simplified the model by assuming the workpiece was rigidly attached to the ground. Clin-ically, it can be challenging to rigidly fix the target anatomy, and the viscoelastic nature would intro-duce some additional dynamics. Preliminary pilot testing and simulations suggested greater amounts of144CHAPTER 4. DAMPER-BASED BRACE DESIGN(a)(b)Figure 4.32 Drilling trials using a 3?16 inch (4.76 mm) aircraft drill bit in polyethylene plastic at ap-proximate drill speeds of (a) 350 RPM and (b) 1200 RPM . Trials are aligned at breakthrough.Note how the post breakthrough velocity of the drill is nearly identical to the velocity ex-pected by corkscrew.145CHAPTER 4. DAMPER-BASED BRACE DESIGNplunge in a non-rigidly fixed workpiece. Although the drill bit travelled a similar distance relative tothe ground, the ?spring-back? of the workpiece after breakthrough resulted in greater relative motion. Abracing device between the drill and the workpiece should minimize drill plunge in a similar manner tothe rigidly mounted case.Estimated arm impedanceWe estimated the effective impedance of the human arm by using anthropometric data and joint impedancevalues from the literature [Gomi 1998]. There are three limitations to these joint impedance relations.First, the measurements were made on a relatively small group of 5 subjects. Second, there is a dif-ference in posture: the study measured impedance during arm motion in the horizontal plane, whereaswe modelled arm motion in the sagittal plane. Third, and perhaps most importantly, the torque stiffnessrelation is valid up to 30% maximum voluntary contraction (MVC). Assuming a maximum force around100 N, forces above 30 N will likely deviate from model.Learned StiffnessAlthough the model does a reasonably good job at approximating the first few trials, there is no ex-plicit learning included, and the model over-predicts drill plunge after several subsequent trials. Forexample, the experimental trials in Figure 4.19 show little variation in drill plunge with increased pre-breakthrough force, which can likely be explained by some sort of learning effect.At a fixed level of applied force, maximum drill plunge decreases with increased levels of learnedstiffness (Figure 4.33). At 30 N, increasing the learned stiffness from 0 N\/mm to 2.0 N\/mm reduces drillplunge from 29 mm to 11 mm. This reduction is a direct consequence of the equilibrium point theory;increased total stiffness at the same force yields smaller motion.Researchers have demonstrated that humans are able to adjust the size and orientation of their armstiffness, independently of force, to deal with instabilities in their environment [Burdet 2001]. Thismay offer a possible explanation for why similar levels of applied force result in reduced drill plunge insubsequent trials.4.4.2 Future WorkThis study could be improved upon and expanded by considering some of the following:Limitations to address:? Explicitly model human force control during drilling instead of assuming constant force.? What influence does adding viscoelastic dynamics to the target anatomy have on simulated brac-ing performance?? What difference does adding Airpot? non-linearities have on bracing performance?? How much does performance differ depending on user posture?? How sensitive is performance to variation in each parameter?? Utilize conservative congruence transformation to determine effective stiffness [Chen 2000].146CHAPTER 4. DAMPER-BASED BRACE DESIGNFigure 4.33 Maximum drill plunge simulated under increasing levels of learned stiffness at a forcelevel of 30 N.Outstanding questions:? What are the key factors that lead to corkscrew behaviour?? To what degree can the user augment stiffness through co-contraction?These questions are outside the scope of the present study.4.5 ConclusionThis chapter described the development of an experimental bracing device to reduce cortical drill plunge.A model of freehand cortical drilling was developed through pilot testing, and then extended to include abracing element. Experimentation and simulation identified a damper-based brace as the most effectiveway to reduce drill plunge with minimal affect of the drilling process. A range of optimal dampinglevels were identified through a series of simulations. We then designed, constructed, characterized andcalibrated an experimental brace damping device to implement four damping levels.We performed a series of pilot testing in a variety of materials including wood, plastic, bovine femurand porcine spinous processes. Oak wood was selected as a cost-effective and convenient work piece.An early version of the research CAS system described in Chapter 2 was used to quantify the forceand plunge depth. For a 3?16 inch (4.76 mm) high speed steel (HSS) drill bit in oak, pre-breakthroughforce ranged from 20 N to 42 N, drilling duration ranged from 0.71 s to 0.96 s and drill plunge rangedfrom 10 mm to 38 mm. Another significant finding of the pilot testing was we observed that certaincombinations of material and drill bit geometry resulted in a corkscrew behaviour that dominated initialplunge behaviour.The freehand cortical drilling model predicts plunge depth and drilling duration based on user pos-147CHAPTER 4. DAMPER-BASED BRACE DESIGNture and anthropometry, drill mass, and drilling force, and empirically determined drilling parameters.The drilling process was modelled as a power function with parameters derived from pilot testing. Fora 3?16 inch (4.76 mm) high speed steel (HSS) drill bit in oak, the constants were B = 0.19 and x = 1.45.We estimated the impedance parameters for a human subject in a standing posture with their upper armhanging to the side and the forearm parallel to the floor. Linear torque-based joint stiffness and dampingrelations and anthropometric data from the literature were used to determine the effective horizontalend-point impedance parameters for a range of external loadings. The external loading consisted of thedrill weight and axial thrust drilling forces that ranged from 0 N to 150 N. As force increases, plungeincreases and drilling duration decreases.A bracing element was added to cortical drilling model. Experimentation and simulations suggestedthat a damping element could effectively reduce drill plunge with minimal effect on drilling duration.The braced cortical drilling model was simulated with drilling forces of 0 N to 150 N and brace dampinglevels from 0 N s\/mm to 40 N s\/mm. For a given force level, increased brace damping level decreasesplunge and increases drilling duration.A simple weighting function was applied to the simulated drill plunge and drill duration results togenerate a series of optimal damping level based on human thrust force level. For a typical drilling forcerange of 30 N to 100 N, the optimum damping ranges linearly from 6.0 N s\/mm to 20 N s\/mm.An experimental damping brace based on a 2KS444B2.0TX Airpot? was designed and constructed.We characterized the dashpot and calibrated the adjustable knob at three damping levels: Low - 0.2 N s\/mm,Medium - 10 N s\/mm, and High - 30 N s\/mm.There are three main conclusions from this work:? A simple numerical model can predict drill plunge depth;? A brace with an optimal level of damping should markedly reduce plunge depth without markedlyincreasing drilling duration; and,? Twist drills occasionally catch on and corkscrew into a workpiece, affecting plunge behaviour.148Chapter 5User Study on Influence of Damper-basedBrace on Simulated Cortical DrillingThe true method of knowledge is experiment.? William BlakeIn order to assess the performance of the experimental damper-based brace for minimizing plungedeveloped in Chapter 4, we designed a drilling task to simulate cortical drilling. The goal of the clinicalprocedure is to drill though the bone cortex and stop before penetrating into soft tissue. We designedand conducted a user study in which subjects performed a simulated cortical drill task while the drill tipposition and task duration were measured. We compared the effect of brace damping level and drill bittype on the maximum drill plunge depth and drilling duration.5.1 HypothesesAs described in Section 1.4, we hypothesized that:H2.1 Increased levels of brace damping will markedly reduce drill plunge compared to freehand.H2.2 Increased levels of brace damping, at a level that markedly reduces drill plunge, will not markedlyincrease drilling duration.H2.3 A brad point type drill bit will enable markedly reduced drill plunge compared to a HSS drill bit.The expected reduction in drill plunge with increased brace damping is based on simulations ofthe braced cortical drilling model we developed in Chapter 4. These simulations demonstrated that,as damping level increases, drill plunge decreases and drilling duration increases. Since the predictedoptimal damping depends on drilling force, which will likely vary between subjects, we chose to assessthree damping levels to cover the range of expected drilling forces.Although our drilling model assumed that there was no interaction between the drill bit and work-piece, certain pilot trials with a standard twist drill bit (i.e., high speed steel (HSS)) demonstrated a149CHAPTER 5. PLUNGE DEPTH USER STUDYcorkscrewing behaviour which indicated coupled motion that exacerbated drill plunge. To ensure anypotential reduction in drill plunge was not limited to a particular drill bit geometry, we chose to test asecond drill bit type with a geometry that should not lead to corkscrewing, and therefore should resultin less drill plunge.5.2 Materials and Methods5.2.1 Study DesignWe designed a user study to test the effects of brace damping level and drill bit geometry on maximumdrill plunge and drilling duration. Subjects participated in both this study and the navigated targetingstudy described in Chapter 3 during a single session in a randomly assigned order.We adopted a within-subjects design. The conditions were nested instead of fully randomized be-cause changing the drill bit and adjusting the damping level takes time and manual intervention from theresearcher, which would have a significant effect on the total testing time. The experiment consisted ofa total of 8 blocks, with four damping levels (0 N s\/mm, 0.2 N s\/mm, 10 N s\/mm and 30 N s\/mm) nestedwithin two drill bit geometries (HSS and brad point (BP)); 10 holes were drilled per block (Figure 5.1).This 2x4x10 design yielded 80 drilling trials per subject. The number of repetitions was chosen so thatsubjects could complete both the drill targeting task and the cortical drilling task in approximately onehour.Participant+SS5010502 510Brad\u0003Point\/ + 0 \/ + 00Drill\u0003BitSubjectDamping5epetitionFigure 5.1 Illustration of cortical drilling study design. Each participant is assigned a task schedulewith a randomized drill bit order and damping order. Ten drilling trials are completed for eachcombination. The damping level order is then repeated for the second drill bit type.5.2.2 Experimental SetupThe experiment was conducted in the Neuromotor Control lab, located at the Point Grey Campus ofthe University of British Columbia. Subjects stood in front of a work table where a piece of woodwas clamped to the workpiece holder. The experimental damping brace for plunge minimization (Sec-tion 4.2.5) was mounted to the rigid frame and attached to the drill (Figure 5.2).150CHAPTER 5. PLUNGE DEPTH USER STUDY)orFH 6HQsor:orNSiHFH +olGHr:orNSiHFH2StiFall\\ 7raFNHG DrillAGMXstaElH DaPSHr(a) Schematic(b) Experimental SetupFigure 5.2 Experimental setup for the drill plunge task. The position of the tip of the drill ismeasured with respect to the breakthrough plane on the rear surface of the wood. The axialforce on the workpiece applied by the drill is measured with a uniaxial force sensor. TheAirpot? is mounted to the environment and provides a velocity-dependent damping force tothe rear of the drill. The drill is shown in the rest position. The image is taken from theviewpoint of the optical tracker.151CHAPTER 5. PLUNGE DEPTH USER STUDYDrill BitsDuring pilot testing, we observed that twist drills would often ?corkscrew? after forming an incompletehole through wood and bovine femur, so we decided to test the effect of drill bit geometry. Two typesof drill bit commonly used to drill wood were selected (Figure 5.3): a 3?16 inch (4.76 mm) BP bit and a3?16 inch (4.76 mm) HSS bit. New bits were used for approximately every 5 subjects.? A high speed steel (HSS) steel drill bit (Model 054-3008-8, Mastercraft, Toronto, Canada) is ageneral purpose bit for drilling in metal, plastics, and wood. This bit has a 135? split point that isdesigned to start on contact to avoid walking. It has a fast spiral, with a helix angle of 30.5?. Thisgeometry is similar to the one normally used to drill bone in surgery.? A brad point (BP) bit (Model 48-15-0185, Milwaukee Electric Tool Corp., Brookfield, WI 53005,USA) is specifically designed to cut through wood. It features a prominent tip to aid in precisepositioning and also features lines marked on the flutes for visual depth reference. This geometryhas a negative rake angle and is not expected to exhibit any corkscrew behaviour.(a)(b)Figure 5.3 Drill bit geometries tested in the study: (a) 135? high speed steel (HSS), (b) brad point(BP)Damping LevelsWe tested freehand (i.e., undamped, normal) drilling along with three levels of damping. The dampinglevel was changed by setting the adjustment knob on the Airpot? to the predetermined angles at whichthe device was characterized, as described in Section 4.3.5. For the freehand case, the adjustment knobwas completely removed, so the only resistance to movement would be negligible friction 1.1The Airpot? has a piston friction of < 8g.152CHAPTER 5. PLUNGE DEPTH USER STUDYWorkpieceSubjects drilled a series of holes through a 135 mm by 135 mm by 1?4 inch (6.35 mm) section of redoak plank. Since we wanted to simulate cortical drilling, we chose the thickness of the workpieceto represent a typical cortical thickness in the femur, which is known to vary considerably (e.g., 1.6?12.0 mm [Noble 1995]). We chose to use oak for several reasons: it is inexpensive, does not requirespecial storage or handling, and has comparatively consistent geometry and material properties. Theflat rear surface of the workpiece also provided a means for more accurately quantifying the time ofbreakthrough. Previous studies have used oak as a reasonable substitute for bone (e.g., Haug [1999]) anda comparative study showed that red oak had a statistically similar screw pull-out strength to cadaverichuman mandible [Bredbenner 2000]. However, bone is denser and stronger than oak, so we expectsmaller drilling forces will be required in our study (Table 5.1).Table 5.1 Approximate Workpiece Material PropertiesMaterial Density Bending Strength Modulus of Elasticityg\/cm3 MPa GPaRed Oaka 0.5-1.0 40?150 1.6?6.6Femoral Cortical Boneb 1.8 160?225 8.2?15.4a Mun?oz [2011]b Carter [1978]Each workpiece weighed approximately 0.10 kg and was attached to the workpiece holder describedin Section 2.4 with two clamps. To ensure subjects did not drill into the workpiece holder and to reducethe chance of drilling too close to a previous hole, each workpiece was marked using a targeting template(Figure 5.4). Subjects were instructed to use these marks as a guide, but not to be concerned aboutprecise targeting.5.2.3 Experimental Drilling TaskA drilling trial was defined as a single hole drilled under a certain combination of drill bit type anddamping level. The subject was verbally instructed to attempt to minimize both drilling duration anddrill plunge.5.2.4 SubjectsTwenty-five subjects (thirteen males; twelve females; age range 25?44; mean age 30) were recruitedfrom the University of British Columbia Point Grey Campus. The inclusion criteria was an age of 19-65years, normal or corrected-to-normal vision, and no history of neuromuscular injury to the upper ex-tremities. Subjects reviewed the Subject Consent Form (Appendix B.1) and provided informed consentbefore participation. Each subject completed the drill targeting and cortical drilling studies in a sin-gle session that lasted approximately one hour. A $10 gift card was provided as compensation for the153CHAPTER 5. PLUNGE DEPTH USER STUDYFigure 5.4 A 1?4 inch thick piece of oak clamped to the workpiece holder. The targeting marks areused to keep subjects from drilling into the workpiece holder or too close to previous holes;targeting accuracy was not important in this study.subject?s time. This study was approved by the UBC Behavioural Research Ethics Board (H09-01080).5.2.5 Conducting the ExperimentAfter providing informed consent, subjects were asked to provide their age, gender, and dominant hand.In order to ensure their safety, subjects were required to wear safety glasses, roll up long sleeves, removeany jewellery from the hands, and tie back any long hair.Each subject was assigned a unique subject identification number to anonymise their data and acorresponding task schedule (Table 5.2). This task schedule dictated the order in which subjects wouldcomplete the two experimental tasks, and the corresponding order of damping levels and drill bit types.A complete list of testing schedules can be found in Appendix D.1.Table 5.2 Example Testing ScheduleSubject ID Task Drill Bit Type Damping Level12 Plunge,Target BP, HSS L,H,0,MEach subject was assigned to a predetermined task schedule which dictated the order inwhich the task conditions were completed.We attempted to control for changes in posture between subjects. The vertical height of the work-piece holder was adjusted in order to maintain similar arm positioning. Subjects were instructed to standwith their feet approximately shoulder width apart, with their toes in a line perpendicular to the directionof drilling. The workpiece holder was adjusted so that the subject?s forearm was parallel to the floor andapproximately 90? relative to the upper arm (Figure 5.5).Participants were instructed to drill several holes to get a feel for determining breakthrough beforeattempting several practise trials with the audible signals. Once they were comfortable with the system,154CHAPTER 5. PLUNGE DEPTH USER STUDYFigure 5.5 The height of the workpiece holder was adjusted so the subject?s forearm was parallelto the floor and approximately 90? relative to the upper arm.the study proceeded.Trials were completed according to the task schedule. The researcher installed the appropriate drillbit, set the appropriate damping level and attached the marked workpiece to the workpiece holder.The beginning and end of each trial were indicated with audible beeps. When the subject was readyto begin, they were instructed to move the drill from the rest position to the start position. The startposition was defined as the drill pointed towards the workpiece with the damper in the fully retractedposition. The start of the trial was indicated by a set of three audible beeps. On the third beep, the subjectmoved the drill to the workpiece and started drilling. After the hole was complete, the subject returnedthe drill to the start position at which point the researcher would manually end the trial, signalled by asingle beep.Subjects were told that if they felt fatigued after completing a trial, they could take a break byreturning the drill to the rest position. Subjects also had an opportunity to rest after every 10 trials whenthe damping level was adjusted, after every 20 trials when the workpiece was detached, rotated, andreattached, and after every 40 trials when the drill bit was changed.After completing all the drilling trials, subjects were asked to complete the drilling portion of theDebrief Questionnaire (Appendix B.2).5.2.6 Acquiring and Processing the DataData AcquisitionDuring each trial, data from the tracker, the force sensor, and the power supply were recorded witha common time signature. The tracker data consisted of the static reference frame (SRF),the dynamicreference frame (DRF) and the tool recorded at 60 Hz. The computed transforms of the drill bit tip inthe target coordinate frame, T targettip , were also recorded. Each of these transforms consisted of three155CHAPTER 5. PLUNGE DEPTH USER STUDYCartesian coordinates, a quaternion and a measure of uncertainty. The axial force on the workpiece andthe current supplied to the drill were recorded at 1000 Hz. Each type of measurement was saved to itsown file and organized by a unique trial identification number.Data ProcessingData from each trial were processed using custom routines written in MATLAB? (Version 7.14.0.739,The Mathworks, Natick, MA, USA). After interpolating any missing frames2, the transforms were fil-tered with a low pass, fourth order, zero-lag Butterworth filter with a cut-off frequency of 5 Hz. Theforce and current data were filtered with a low pass, fourth order, zero-lag Butterworth filter with acut-off frequency of 60 Hz. Cutoff frequencies were selected to achieve a signal-to-noise ratio of ap-proximately one at the cutoff frequency. Illustrative examples of the raw and filtered force, current, andposition data can be found in Section 2.7, Section 2.8, and Section 2.10, respectively.Performance MetricsIn order to quantify task performance and compare experimental conditions, a number of metrics wereextracted from the processed data.The maximum drill plunge (mm) was calculated as the maximum distance of the tip beyond thebreakthrough plane. Since, the target coordinate frame was defined with its origin on the breakthroughplane and its z-axis aligned with the breakthrough plane normal vector, the maximum drill plunge wasavailable directly as the maximum value of the z-component of T GOALT IP , i.e. tz,max. Figure 5.6 illustrateshow breakthrough and drill plunge are determined.Drilling duration (s) was defined as the amount of time from the onset of drilling until break-through. Drilling onset, tS, was defined as the first instance when the drill was on and in contact withthe workpiece, as determined by a force threshold3 of 5 N and a drill current threshold of 0.2 A. Break-through was determined as the time when the drill bit crossed the breakthrough plane, i.e. when thez-coordinate of T GOALT IP crossed zero (Figure 5.7). In this example, tB = 5.3s, tS = 3.1s and tD = 2.2s.We calculated several secondary metrics to explore drilling behaviour in more detail (Figure 5.8).The mean drilling velocity was calculated from a best fit line of the z-component of T GOALT IP . Thepre-breakthrough force (PBF) was defined as the maximum force applied in a 200 ms window be-fore breakthrough. We also calculated the maximum drilling force, mean drilling force and drillingforce-time integral. Finally, the human breakthrough force exerted by the participant at a particulardamping level was estimated using the sum of the average force applied to the workpiece FD and theforce required to move the damper FB. The force required to move the damper was found using thedamping levels characterized in Chapter 4 bb and the mean drilling velocity extracted from the trackedtrip movement:2We used the MATLAB? function interp1 to replace missing frames and ensure the data was spaced uniformly in timeusing the piecewise cubic spline method. The median percentage of missing frames was 5 % (IQR: 4?7 %, Range: 1?29 %)3Force and current thresholds were selected based on pilot testing. See Sections 2.7 and 2.8.156CHAPTER 5. PLUNGE DEPTH USER STUDYFigure 5.6 Drill plunge is defined as the maximum distance of the tip beyond the rear plane of theworkpiece after breakthrough occurs.FH = F?B + F?D = v?z ?bb + F?D. (5.1)5.2.7 Model ComparisonIn order to assess how well our model from Chapter 4 predicted drill plunge across a variety of sub-jects, we performed simulations based on the metrics calculated for each trial. The mean drilling force,estimated human force, and damping level from each trial were input into the model along with anthro-pometric parameters from the literature (Table 4.3). We assumed that there was no learned stiffness.Simulations yielded a predicted drilling duration, td p and predicted drill plunge, mZp, for each trial.5.2.8 Statistical AnalysisStatistical analyses were conducted with R statistical software( Version 2.15.1, R Foundation for Statisti-cal Computing, R Development Core Team, 2012). Since our data involved repeated measures on blocksnested within subjects and the response variables are continuous, we used a linear mixed model (LMM)for analysis.Linear Mixed ModelsA mixed-effects model is a type of statistical model that contains both fixed effects and random effects.Fixed effects are parameters associated with an entire population or with certain repeatable levels ofexperimental factors, while random effects are associated with individual experimental units drawn atrandom from a population [Pinheiro 2000]. Mixed-effects models are particularly useful when data157CHAPTER 5. PLUNGE DEPTH USER STUDYFigure 5.7 Drilling duration, tD, is defined from drilling onset, tS, until breakthrough. Drillingonset is defined as the time when the drill bit is both in contact with the workpiece and rotating.The contact onset,tC, is defined as the time when workpiece force exceeds a threshold of 5 N.The power onset, tP, is defined as the time when drill current exceeds a threshold of 0.2 A.Breakthrough time, tB, is defined as the time when the tip position crosses zero. For this trial,tB = 5.3s, tS = 3.1s and tD = 2.2s.158CHAPTER 5. PLUNGE DEPTH USER STUDYFigure 5.8 Calculation of secondary drill plunge metrics. Mean drilling velocity is calculated asthe slope of a linear fit of the tip position during drilling. pre-breakthrough force (PBF) iscalculated as maximum force 200 ms before breakthrough. Human force, FH , is calculatedas the sum of bracing force and PBF, where bracing force is estimated using mean drillingvelocity and brace damping level.159CHAPTER 5. PLUNGE DEPTH USER STUDYis grouped, such as longitudinal data, repeated measures, blocked designs, and multilevel data. Mea-surements grouped within a statistical unit are typically correlated, which violates the assumption ofindependent measurements in analyses like analysis of variance (ANOVA). Mixed-effects models arealso capable of handling both balanced and unbalanced data, which prevents the exclusion of subjectswith one or more missed data points.A LMM approach was used for several reasons:? We wish to generalize our results to a larger population, so SUBJECT should be treated as a randomeffect.? DAMPING and DRILLBIT were fixed effects.? We have a mixture of continuous and categorical covariates.? The study followed a nested design, so trials within a block could not be considered independent.? We expected and observed unequal variances between groups.? Some trials were missing or had to be removed, so the data were not balanced.We based our analysis on the ?top-down? modelling approach described in West [2006] for a three-level LMM and performed the modelling using the R package nlme [Pinherio 2013]. We chose betweenmodels by comparing the values of the Bayesian Information Criterion (BIC) and by calculating likeli-hood ratio statistics with a significance level of ? = .05. A detailed description of the analysis can befound in Appendix E.1.Analysis of the drill plunge data must consider three levels (Table 5.3). We included fixed effectsfor all covariates under consideration (REP, DRILLBIT, DAMPING, AGE, and GENDER). HAND was notincluded since there were only 3 left handed subjects in the study, and we did not expect any effect.Since we want to make inferences regarding the population that our subjects were drawn from, we useda random effect to model the SUBJECT factor. Based on our study design, we also included a randomintercept and slope for each block nested within a subject.Table 5.3 Drill Plunge Data StructureLevel of Data VariableCluster of Units(Level 3)Cluster ID (Random) SubjectCovariates Age, dominant hand, genderAnalysis Unit(Level 2)Unit ID (Random) BlockCovariates Damping level , drill bit typeTime(Level 1)Time variable RepetitionDependent variables Drill plunge, drilling duration, plunge delayTime-varying covariates Force-integral, pre-breakthrough forceSource: adapted from Li [2012: p. 274].160CHAPTER 5. PLUNGE DEPTH USER STUDY5.3 ResultsIn this section, we present the results from the user study. The 25 participants (thirteen males; twelvefemales; age range 25?44; mean age 30) in the study performed ten drilling tasks for each combinationof four damping levels and two drill bit types. For each trial we recorded the drill bit position, drillingforce, and drill current and we computed the maximum drill plunge and drilling duration.During some of the trials, the participant mistakenly stopped drilling before the hole was complete.These trials were excluded from further analysis, though we do address whether these problem trialswere more common under certain damping levels in the limitations section. A list of the problem trialscan be found in Appendix D.2.Since many of the metrics do not follow a normal distribution, descriptive statistics are reported hereas median and inter-quartile range (IQR), or as a 95 % confidence interval (CI).5.3.1 Typical TrialA typical braced drilling trial has three phases: targeting, drilling, and withdrawal (Figure 5.9). In thisexample, contact occurs at 2.7 s and the drill is powered on shortly after at 3.0 s. The user applies amean force of approximately 43 N which yields a mean drilling force of 12 N and a mean velocity of2.9 mm\/s. The drilling duration is 2.3 s when breakthrough occurs at 5.3 s. The pre-breakthrough forceis 15 N and a drill plunge of 3 mm. The drill is powered off approximately 0.8 s after breakthroughoccurs, as the drill bit is being retracted.Figure 5.9 Tip position, tip force and drill current of a typical drilling trial using a high speedsteel (HSS) drill bit and a brace damping level of 10 N s\/mm.161CHAPTER 5. PLUNGE DEPTH USER STUDY5.3.2 Typical ConditionDrilling duration, force levels and drill plunge vary within a single block for a typical subject (Fig-ure 5.10). In this example, drilling duration ranges from 1.9 s to 3.5 s with a median value of 2.3 s(Figure 5.11a) and drill plunge varies from 1.9 mm to 3.9 mm with a median value of 2.8 mm (Fig-ure 5.11b). Drill feed ranges from 1.8 mm\/s to 3.4 mm\/s with a median value of 2.7 mm\/s.Figure 5.10 Variation in tip position, tip force, and drill current for a block of HSS drill bit andmedium damping level drilling trials for a typical subject. Trials are aligned at the time ofbreakthrough.5.3.3 Typical SubjectFigure 5.12a and Figure 5.12b illustrate the drilling duration and drill plunge for all trials performedby a typical subject. The subject shown started with the HSS drill bit and tested low, high, zero, thenmedium damping, before repeating the same sequence with the BP drill bit. Most of the sets show anegative trend, indicating that the subject completed the drilling more quickly for trials later in a block.The following figures illustrate the performance metrics for each trial of a typical subject. Fig-ure 5.13a illustrates the drilling duration for each trial for a typical subject. At the high damping level,there is a visible trend towards longer drilling durations.Figure 5.14b illustrates the pooled drilling duration and drill plunge for a typical subject. Eachpoint represents the median and IQR at each combination of drill bit type and damping level. Bothdrill bit types at the medium damping level are located closer to the origin than any other combination,indicating improved performance. There is noticeable difference in the amount of inter-trial variationbetween different conditions.162CHAPTER 5. PLUNGE DEPTH USER STUDY(a)(b)Figure 5.11 Typical set of braced drilling trials: (a) drilling duration and (b) drill plunge. Themedian and interquartile range are shown with the dotted line and shaded region.163CHAPTER 5. PLUNGE DEPTH USER STUDY(a)(b)Figure 5.12 Trial order for typical subject: (a) drilling duration and (b) drill plunge. Drill bit orderwas HSS, BP and damping level order was medium, zero, high, low.164CHAPTER 5. PLUNGE DEPTH USER STUDY(a)(b)Figure 5.13 Typical subject performance by condition: (a) drilling duration and (b) drill plunge.There appears to be a trend towards increased duration and decreased drill plunge as dampinglevel increases. There also appears to be a reduction in inter-trial drill plunge variation asdamping level increases.165CHAPTER 5. PLUNGE DEPTH USER STUDY(a)(b)Figure 5.14 Drilling duration and drill plunge by condition for a typical subject: (a) individual tri-als and (b) pooled by condition, showing the median and IQR. Note how trials at the mediumdamping level are clustered towards the origin, indicating better overall performance. Alsonote how there is less variation between trials at higher damping levels.166CHAPTER 5. PLUNGE DEPTH USER STUDY(a)(b)Figure 5.15 Forces for typical subject: (a) mean drilling force and (b) pre-breakthrough force(PBF). Note how trials at a given damping level have a higher force with the BP drill bitthan trials with the HSS drill bit. Also note how forces appears to decrease somewhat withincreasing damping level.167CHAPTER 5. PLUNGE DEPTH USER STUDY5.3.4 All SubjectsIn this section, we present descriptive data from all subjects. Of the 2000 trials that were recorded, only14 (<1 %) were excluded (Appendix D.2), leaving 1991 valid trials for analysis. The excluded trialswere not completed as expected, the reasons for which are addressed in Section 5.3.6.Performance MetricsMedian drilling duration was 2.3 s (IQR: 1.5?3.6 mm) and ranged from 0.6 s to 22.9 s (Figure 5.16a).The data are heavily skewed to the right.Drill plunge appears to decrease with increased damping level (Figure 5.16b). The overall mediandrill plunge was 9 mm (IQR: 4?16 mm). Drill plunge ranged from under 1 mm to 45 mm, which is theupper limit imposed by the experimental brace setup reached by bottoming out the damper.Secondary MetricsOverall median mean drilling force was 20 N (IQR: 15?26 N), and ranged from less than 2 N to 68 N(Figure 5.17a). At each damping level, there appears to be a trend towards an increased mean drillingforce with the BP drill bit compared to the HSS drill bit (Figure 5.17a). There also appears to be a slightapparent trend towards decreased mean drilling force at the high damping level.The values and behaviour of PBF are similar to mean drilling force. Overall median PBF was 21 N(IQR: 15?30 N), and ranged from less than 1 N to 74 N (Figure 5.17b). PBF appears to decrease slightlywith increased damping, and increase with the BP drill bit (Figure 5.17b). Similarly to mean drillingforce, PBF is about 8.5 N higher when using the BP drill bit and tends to decrease with increase bracedamping level.The mean drilling velocity appears to decrease slightly with increased brace damping level (Fig-ure 5.18a). There also appears to be a reduction when the BP drill is used, and a more consistent drillingvelocity, especially at higher damping level. On average, the mean drilling velocity increases from high,medium, no, and low damping.The human force estimated from Equation 4.2.3 using the mean drilling force and mean drillingvelocity appears to increase with greater brace damping levels (Figure 5.18b). There also appears to bea trend towards higher human force with the BP drill bit, especially at the zero and low damping levels.As damping level increases, the time delay from breakthrough to maximum drill plunge tends toincrease (Figure 5.19). Median drill plunge delay is 0.26 s and the IQR is 0.21?0.37 s, which means themajority of trials fall within the expected range of human reaction time delays. Longer delays appear tooccur more often at the medium and high damping levels.5.3.5 Comparison to SimulationWe compared the experimental results to the model we developed in Chapter 4. The estimated humanforce for each trial was extracted from each trial and used as an input to the model along with theempirically determined drilling constants (Appendix A.3).168CHAPTER 5. PLUNGE DEPTH USER STUDY(a)(b)Figure 5.16 Performance metrics by condition for all plunge trials: (a) drilling duration and (b)drill plunge. The first quartile, median, and third quartile for each condition are shown withan up-triangle, circle, and down-triangle, respectively. Note that as damping level increases,drilling duration increases slightly and drill plunge decreases and becomes less variable.169CHAPTER 5. PLUNGE DEPTH USER STUDY(a)(b)Figure 5.17 Subject-pooled metrics: (a) average drilling force and (b) pre-breakthrough force(PBF). The first quartile, median, and third quartile for each condition are shown with anup-triangle, circle, and down-triangle, respectively. Note how forces are consistently higherwith the brad point (BP) drill bit.170CHAPTER 5. PLUNGE DEPTH USER STUDY(a)(b)Figure 5.18 Secondary metrics: (a) drilling velocity and (b) estimated applied human force. Thefirst quartile, median, and third quartile for each condition are shown with an up-triangle,circle, and down-triangle, respectively. Note that mean drill feed tends to decrease and esti-mated human force tends to increase as damping level increases.171CHAPTER 5. PLUNGE DEPTH USER STUDYThe relationship between mean drilling force and drilling duration is captured well, although themodel tends to overestimate the drilling duration (Figure 5.20). This difference is more pronounced atthe medium and high damping levels.The experimental drill plunge data have a similar relationship to PBF as the model (Figure 5.21). Themodel does a better job predicting trials at the zero and low damping levels compared to the mediumand high damping levels.The model consistently over-predicts drilling duration across damping levels (Figure 5.22a). Themedian percent modelling error is 160 % (IQR: 75?300 %). The model predicts drilling duration withthe BP more accurately.Besides a few outliers, the percent error for predicting drill plunge are less than 200 % (Figure 5.22b).The overall median is ?35 % (IQR: ?75?30 %), however the model tends to over-predict drill plunge atthe zero and low damping levels and under-predict drill plunge at the medium and high damping levels,skewing the results.5.3.6 Atypical and Notable TrialsIn this section, we present examples of atypical and notable trials. These trials were not completed asoriginally anticipated. The reasons for atypical trials include incomplete breakthrough, and incompletebreakthrough that was later corrected. We also present trials where the drill plunge was so severe that itbottomed out the damper, as well as trials that demonstrate corkscrew behaviour. It is important to noteFigure 5.19 Drill plunge delay for all trials. The first quartile, median, and third quartile foreach condition are shown with an up-triangle, circle, and down-triangle, respectively. Atthe medium and high damping levels, the delay between breakthrough and maximum drillplunge tends to occur later, and sometimes markedly after breakthrough, which may indicatedifficulty in detecting breakthrough.172CHAPTER 5. PLUNGE DEPTH USER STUDYFigure 5.20 Comparison of experimental drilling duration to modelling results. The predicted du-ration from the model is shown as a solid line and the experimental trials are shown asindividuals points.173CHAPTER 5. PLUNGE DEPTH USER STUDYFigure 5.21 Comparison of experimental drill plunge to predicted drill plunge. The predictedplunge depth from the model is shown as a solid line and the experimental trials are shownas individuals points. Note how the model predicts higher than measured drill plunge depthfor the zero and low damping levels and lower than measured plunge depth for the mediumand high damping levels.174CHAPTER 5. PLUNGE DEPTH USER STUDY(a)(b)Figure 5.22 Modelling errors for all plunge trials: (a) drilling duration and (b) drill plunge. Thefirst quartile, median, and third quartile for each condition are shown with an up-triangle,circle, and down-triangle, respectively.175CHAPTER 5. PLUNGE DEPTH USER STUDYthat these trials represent a small proportion of the total trials recorded (<1 %).Incomplete drillingDuring some trials, the subject stopped drilling before the hole was complete, so there was no break-through (Figure 5.23). There were a total of four incomplete trials, and all of them occurred with the BPstyle drill bit: they happened with one subject at the medium damping level and one subject at the highdamping level.Figure 5.23 Example of a trial where the subject retracted the drill and stopped before the work-piece was completely drilled.Incomplete hole re-drilledA similar event happened with 8 different subjects over 12 additional trials, except that the participantrealized they had not finished drilling before the trial was stopped and went back to complete the hole(e.g., Figure 5.24). The drilling duration of these trials was manually corrected to remove the time takento reinsert the drill.Delayed maximum plungeWe also observed some trials where the user continued applying force well after breakthrough occurred(e.g., Figure 5.25). This suggests that there was a delay in the detection of breakthrough.Sufficient plunge to bottom-out damperDuring a couple of trials, plunge motion of the drill was limited by the hard stop on the experimentalbrace (Figure 5.26). The Airpot? has a stroke of 2 inch (50.8 mm); due to the experimental setup, the176CHAPTER 5. PLUNGE DEPTH USER STUDYFigure 5.24 Example of a trial where the participant retracted the drill before the hole was com-plete, and then returned to complete the hole.Figure 5.25 Example of a trial where the participant continues to apply force to the drill well afterbreakthrough occurred. This is noticeable as a nearly constant pre- and post-breakthroughvelocity.177CHAPTER 5. PLUNGE DEPTH USER STUDYmaximum possible plunge was approximately 45 mm. We installed a hard stop to prevent the pistonfrom being pulled out of the cylinder, which would cause damage.Figure 5.26 Example of a trial where the participant bottomed out the brace, limiting drill plungeto approximately 44 mm.Drill bit-workpiece interactionWe observed several trials where the drill was pulled into the workpiece (Figure 5.27). This ?corkscrew?behaviour was identified during the pilot study in Chapter 4. It is not clear how often this behaviouroccurred since it was only possible to visually observe it in extreme cases, but we believe it was limitedto only a few trials.Although the total number of affected trials form a small proportion of trials in the study (< 1%),they do illustrate two themes that are consistent with our observations: at higher damping levels, thedrill is more difficult to manoeuvre into position, and breakthrough is more difficult to detect.178CHAPTER 5. PLUNGE DEPTH USER STUDYFigure 5.27 Example of a trial where the drill bit was engaged and pulled in by the work-piece, dominating drill plunge with a corkscrew behaviour. The line at breakthrough in-dicates the expected velocity of the drill bit screwing into the workpiece while rotating at1200 rotations per minute (RPM). Note how the post-breakthrough motion is nearly linearand has a nearly identical slope to the expected velocity.179CHAPTER 5. PLUNGE DEPTH USER STUDY5.3.7 Statistical AnalysisIn this section, we describe the linear mixed effects analysis of the data. We fit a three-level LMM to eachmetric, with trials nested within blocks, and blocks nested within subjects. We fit each model with themaximal random effect structure justified by the data. Diagnostic plots can be found in Appendix E.2.Drilling DurationWe found that drilling time was statistically dependent on REP, DAMPING, DRILLBIT, and the interac-tions REP-DAMPING. There was insufficient evidence to include AGE, GENDER, or any other higher levelinteractions (?2(42) = 44, p = 0.38). We applied a log base-10 transform to correct for heteroscedastic-ity in the residuals. The random slope for BLOCK was retained; There was sufficient evidence to rejectthe null hypothesis that it should be removed (?2(2) = 54, p = 2 ? 10?12). There was also sufficientevidence to adopt a residual covariance structure that varied by BLOCK (?2(7) = 130, p = 0).There was no statistically detectable difference in drilling duration between the zero and low damp-ing level (p = 0.23) or the zero and medium damping level (p = 0.50) for a particular drill bit type(Figure 5.28). There are differences in drilling duration between each of the other damping level combi-nation (p < .001), and between drill bit types at a given damping level (p < .001). There is also a smalllearning effect; on average, there is a 16 % reduction in drilling duration from the first trial in a block tothe last.The intraclass correlation coefficient (ICC) for SUBJECT and BLOCK was 36 % and 84 %, respec-tively.Figure 5.28 Conditional expectations of drilling duration fixed effects from linear mixed effectsmodel. Note that there is no statistically detectable difference between the zero and lowdamping level and zero and medium damping level.180CHAPTER 5. PLUNGE DEPTH USER STUDYPlunge DepthWe found that plunge depth (PD) was statistically dependent on REP, DAMPING, DRILLBIT. There wasinsufficient evidence to include AGE, GENDER, or any other higher level interactions (?2(39) = 59, p =0.02). We applied a log base-10 transform to correct for heteroscedasticity in the residuals. The randomslope for BLOCK was retained; There was sufficient evidence to reject the null hypothesis that it shouldbe removed (?2(2)= 64, p= 2 ?10?14). There was also sufficient evidence to adopt a residual covariancestructure that varied by BLOCK (?2(7) = 50, p = 1.5 ?10?8).There was a statistically detectable difference in plunge depth between each of the damping levelsand the freehand case (p < .001) and between drill bit types at each level (p < .001) (Figure 5.29).There was also a small learning effect; on average, there was a 4 % reduction in plunge depth from thefirst trial in a block to the last.Approximately 14 % of the variation in plunge depth can be attributed to subject effects and another76 % to the combination of drill bit and damping level. Four subjects had unusually different intercepts:S19, S10, and S16 had unusually high intercepts, while S9 had an unusually low intercept.Figure 5.29 Conditional expectations of drill plunge depth fixed effects from linear mixed effectsmodel. Note the reduction in fine targeting time with the 3D display.Mean Drilling ForceWe found that mean drilling force was statistically dependent on DRILLBIT, DAMPING, the REP-DAMPINGinteraction and the DRILLBIT-DAMPING interaction. The effect of REP was not significant, but it was re-tained because of the higher order term. There was insufficient evidence to include AGE, GENDER, or anyother higher level interactions (?2(39)= 50, p= 0.11). We applied a log base-10 transform to correct forheteroscedasticity in the residuals. The random slope for BLOCK was retained; there was sufficient evi-181CHAPTER 5. PLUNGE DEPTH USER STUDYdence to reject the null hypothesis that it should be removed (?2(2) = 35, p = 3 ?10?8). There was alsosufficient evidence to adopt a residual covariance structure that varied by BLOCK (?2(7) = 110, p = 0).There is no statistically detectable difference in mean drilling force between the zero and low damp-ing level (p = 0.13) or the zero and medium damping level (p = 0.70) for a particular drill bit type(Figure 5.17a). There was a statistically detectable increase of 33 % to 63 % higher mean drilling forcefor trials with the BP drill bit compared to those with the HSS drill bit (p < .001). There is also evidenceof a small learning effect that varied by damping level: ?1 %, ?6 %, 4 % and 10 % for the zero, low,medium, and high damping levels, respectively.Figure 5.30 Conditional expectations of mean drilling force fixed effects from linear mixed effectsmodel. Note that there is no statistically detectable difference between the zero and low, andzero and medium damping level. Also note how mean drilling force is significantly higher ateach damping level.Pre-breakthrough ForceWe found that pre-breakthrough force (PBF) was statistically dependent on DRILLBIT, DAMPING, theREP-DAMPING interaction and the DRILLBIT-DAMPING interaction. The effect of REP was not sig-nificant, but it was retained because of the higher order term. There was insufficient evidence to in-clude AGE, GENDER, or any other higher level interactions (?2(39) = 43, p = 0.31). We applied alog base-10 transform to correct for heteroscedasticity in the residuals. The random slope for BLOCKwas retained; there was sufficient evidence to reject the null hypothesis that it should be removed(?2(2) = 12, p = 0.003). There was also sufficient evidence to adopt a residual covariance structurethat varied by BLOCK (?2(7) = 400, p = 0).There was no statistically detectable difference in prebreakthrough force between the zero and low182CHAPTER 5. PLUNGE DEPTH USER STUDYdamping level (p = .09), but there was a statistically detectable decrease at both the medium (p = .004)and high (p < .001) damping levels (Figure 5.31). There was a statistically detectable increase of 36 %to 65 % higher prebreakthrough force for trials with the BP drill bit compared to those with the HSS drillbit (p < .001). There is also evidence of a small learning effect that varied by damping level: ?3 %,?7 %, 13 % and 12 % for the zero, low, medium, and high damping levels, respectively.The ICC for subjects and blocks nested within subjects was 32 % and 75 %, respectively.Figure 5.31 Conditional expectations of prebreakthrough force fixed effects from linear mixed ef-fects model. Note that there is a statistically detectable reduction between the zero andmedium and zero and high damping levels.Drill Plunge DelayWe found that drill plunge delay was only statistically dependent on DAMPING. Using an maximum-likelihood (ML)-based likelihood ratio test, we determined that the additional fixed effects in the generalmodel were nonsignificant (?2(13) = 17.1, p = .19). We added PBF and the interaction DAMPING-PBFto improve the model (?2(4) = 66.8, p =< .0001).We allowed the standard deviation to vary by damping level. The ICC for subjects and blocks nestedwithin subjects was 45 % and 89 %, respectively. The expected value of drill plunge delay with nodamping and an average PBF of approximately 23 N is 0.24 s (95 % CI, 0.22?27 s).5.3.8 Observations and Subject FeedbackEach participant completed the instrument bracing section of the debrief questionnaire (Appendix B.2)after completing the drilling trials (Table 5.4).The majority of subjects reported that the damping brace was intuitive (96 %) and the increased183CHAPTER 5. PLUNGE DEPTH USER STUDYbracing helped reduce drill plunge (96 %). However, the majority of subjects also reported that increasedbracing increased drilling time (88 %) and was more fatiguing (96 %).Table 5.4 Debrief Questionnaire Bracing SummaryQuestionResponseaSD D A SAThe drill bracing was intuitive. 0 (0) 4 (1) 36 (9) 60 (15)Increased bracing increased drilling time. 4 (1) 8 (2) 32 (8) 56 (14)Increased bracing was more fatiguing. 4 (1) 0 (0) 40 (10) 56 (14)Increased bracing reduced drill plunge. 4 (1) 0 (0) 28 (7) 68 (17)a Values are percentages (number of subjects).The following is a list of observations made during and after testing:? There was some evidence of fatigue - sore back, sore hands, etc. Several subjects reported a sorehand from gripping the tool tightly.? Several subjects reported having a harder time detecting when breakthrough had occurred athigher damping levels. A small number of trials were stopped before breakthrough occurred, andthere were also a few times when subjects continued to advance the drill long after breakthroughhad occurred.? Some subjects (e.g., S14) modulated drill speed instead of axial force.? We often observed subjects adjusted their posture at higher damping levels, typically by shiftingtheir foot position.? Some subjects leaned with their body to generate more force (e.g., S19).? At higher damping levels, subjects had greater difficulty positioning the drill against the work-piece and starting drilling.? Moving the drill from the starting position to being in contact with the workpiece was reported tobe more difficult under higher damping.? We observed one subject in particular who noticeably flexed and co-contracted the muscles intheir arms (S27).5.4 DiscussionThe purpose of the user study presented in this chapter was to experimentally assess whether a bracingstrategy could improve the performance of a surgically relevant task. We created a simulated corti-cal drilling task to measure the influence of different experimental bracing device damping levels anddifferent drill bit geometries on drill plunge and drilling duration.184CHAPTER 5. PLUNGE DEPTH USER STUDY5.4.1 Influence of Brace Damping LevelGenerally, increased levels of brace damping decreased drill plunge and increased drilling duration. Ourdata demonstrated that compared to freehand drilling, a damping level of 10 N s\/mm markedly reduceddrill plunge without markedly increasing drilling duration for both drill bit types.Increased damping reduces drill plungeAs predicted, drill plunge decreases significantly as brace damping level increases. When breakthroughoccurs, the unbalanced forces due to the passive spring-like properties of the arm accelerate the drillbefore the user has a chance to react. The damper provides a velocity-dependent force that can resist thismotion and reduce drill plunge. Our data shows that a damper-based brace can help reduce drill plungefor inexperienced non-surgeons in wood to the same level as expert surgeons in bone (Figure 5.32).Figure 5.32 Experimental drill plunge results from a previous study on influence of experienceand use of audible feedback. (Source: reprinted from Praamsma [2008], ?2008 Associationme?dicale canadienne. Copied under license from the Canadian Medical Association andAccess Copyright. Further reproduction prohibited.)185CHAPTER 5. PLUNGE DEPTH USER STUDYMinimal change in drilling duration with increased dampingWhen a damper is connected to the drill during drilling, a portion of the total force applied by the user isrequired to move the damper. At the medium and high damping level, drilling duration only decreasedslightly, implying that the subjects tended to compensate by applying more force to maintain the samedrilling force and velocity.Subjects appeared to use several strategies to generate additional force. Some subjects adjustedtheir posture by moving their feet from a ?parallel-feet posture? to a ?feet-apart posture?. This wouldcreate a larger base of support. Some subjects also pulsed the drilling force, using a momentum strategyto generate higher forces. These strategies are similar to those explored by Rancourt [2001a], whodeveloped a human motor control model to analyse the dynamics of pushing in a standing posture.Increased fatigueThe majority of participants reported an increase in fatigue (96 %) with increasing damping level. Sincethe debrief questionnaire did not address damping levels individually, the subjects? experience with thehighest damping level likely biased the results, as significant force was required to move the damper.Some subjects were barely able to generate sufficient force to both move the damper and drill through theworkpiece. At a more appropriate damping level, more experienced users may actually see a reductionin fatigue since less muscular co-contraction should be required to limit drill plunge.In order to avoid the effects of fatigue, subjects were encouraged to take breaks between drillingblocks. The force required to move the drill against the resistance of the damper, especially at thehigher damping levels, did cause fatigue in some subjects. For some subjects, this meant resting morefrequently during the higher-braced blocks (2-4 trials).Delayed breakthrough detectionThere were several trials where the delay between breakthrough and maximum drill plunge was muchlarger than that expected from reaction time (Figure 5.25). Simple voluntary reaction time is on theorder of 250 ms [Deary 2011], but there were several trials where the subject continued to apply forceand advance the drill for 1 s to 8 s after breakthrough. The vast majority of these long reaction delaysoccurred at the medium and high damping levels.Reaction time is known to be affected by age, stimulus type, stimulus intensity, arousal level andstate of attention. Of these factors, stimulus type and stimulus intensity are likely the most relevantexplanation for long reaction delays. When breakthrough occurs, there is a drop in drilling force fol-lowed by motion. Previous studies have suggested that novices tend to use a reactionary control scheme,whereas experts use an anticipatory control scheme [Dubrowski 2004] and use the change in audibledrilling tone as a signal of impending breakthrough [Praamsma 2008]. Since most of the subjects inour study were inexperienced with this type of task, they likely relied primarily on haptic feedback ofthe changing drilling force. At higher damping levels, the magnitude of this change in force would besmaller and could be missed altogether.We believe that vision and proprioception are also used, but that they require a relatively large186CHAPTER 5. PLUNGE DEPTH USER STUDYchange in position for detection and have relatively long reaction times. In general, sensory delays forvision are longer than proprioception. This means that relying on vision for breakthrough detection willhave longer delay, and thus, greater plunge distances than when relying on proprioception.In our drilling model in Chapter 4, we assumed that a user?s ability to detect breakthrough wouldnot be affected by damping level. Although we did not have a way to measure breakthrough reactiontime directly, the user study data suggests that bracing may have impeded breakthrough detection.Difficulty targetingSeveral subjects reported or were observed having difficulty targeting the drill. Although accurate posi-tioning was not part of the study, we did provide a template to help properly space out the holes to avoiddrilling into the workpiece holder or on top of a previously drilled hole.Targeting difficulty was mainly a result of the requirements of the experimental setup. Since thebrace was fixed relative to the ground and mounted behind the drill, a damping force was applied beforethe drill was in contact with the workpiece. The starting position was several centimetres from thesurface of the workpiece. In the un-damped case, there was no force resisting motion, so the subjectcould simply place the tip against the workpiece in the desired location. When the brace was engaged,it exerted a velocity dependent force restricting motion towards the workpiece. Some participants foundthis frustrating, as it was difficult to move the drill into position quickly. At higher damping levels, thedamping force made it difficult to apply enough force to get the tip to engage into the workpiece, and theone-way damping made the situation worse. If the participant tried to readjust the position by movingthe drill backwards, there was no resistance, and the drill tip would move further than expected. Theuser would then have to move the damper again to regain contact with the workpiece.Targeting was also more difficult because of where the brace connected to the drill. The damperwas connected to the drill approximately in line with the drill bit axis with a ball joint. As the drill wasadvanced towards the workpiece, the horizontal force applied by the person tends to cause rotation ofthe drill bit towards the ceiling unless a counteracting moment was exerted by the hand (Figure 5.33).As damping level increased, a larger moment was required to keep the drill straight, and some subjectshad difficulty exerting enough torque.For simplicity, the experimental setup mounted the brace between the rear of the drill and framerigidly connected to the environment and the workpiece instead of directly between the drill and theworkpiece. Under higher damping levels, appreciable force or time were required to bring the tip of thedrill in contact with the workpiece from the fully retracted starting position. Since there is a ball jointat the piston and at the drill connection, there is also some instability created similar to a pulling on arope task. If a subject tried to move too quickly, large resistive forces made it hard to accurately positionthe tip against the workpiece, since only a small portion of the user?s force is pressing the tip into theworkpiece. This phenomenon was further aggravated by the one-way nature of the dashpot: there isbasically no resistance to moving away from the workpiece.This additional task time was not included in the analysis because the intended implementation ofthe device would not have the brace engage until the tip was brought into contact with the workpiece.187CHAPTER 5. PLUNGE DEPTH USER STUDY5.4.2 Influence of Drill Bit TypeBP drill bits result in greater drill plungeContrary to our hypothesis, our data demonstrated that for a given damping level, there was a smallbut statistically detectable increase in plunge depth using BP drill bits, compared to HSS drill bits. Webelieved that BP bits would lead to smaller amounts of drill plunge since the geometry was less likelyto catch the material and corkscrew. We did not have a reliable way of determining whether corkscrewoccurred during a particular trial, so it was not possible to assess how much of an effect it had on HSStrials or how often it occurred. We did find a statistically detectable increase in PBF when using theBP drill bit. Mean drilling force was an average of 8 N (44 %) higher than the HSS drill bit. Increasingdrill plunge with increased applied force is consistent with previous research and our modelling results.Based on these results, we can only conclude that the difference in applied force required to drill with BPtype drill bits has a greater influence on drill plunge than prevention of corkscrew. Further investigationis required to quantify the factors that contribute to corkscrew behaviour.5.4.3 Comparison to Cortical Drilling ModelThe predicted and experimental drilling duration show a similar trend with drilling force, but the modelconsistently predicts a longer drilling duration (Figure 5.22a). The model also tended to predict higherthan measured drill plunge depths at the zero and low damping level and lower than measured drillplunge depths at the medium and high damping levels (Figure 5.22b).The difference in drilling duration is likely because the force applied to the workpiece is not con-stant, and the non-linear relation between force and duration yields comparably faster drilling rates athigher forces. The model also assumed that drill rotation speed remained constant. Several subjects,particularly S15, varied the speed of the drill during the trial, which could lead to longer durations.The most likely source of variation between the experimental data and the plunge modelling resultswas learning, which was not accounted for in the model. As the subject adapts to the instability, they)D)+0+YG)D)+YG?GFigure 5.33 Free body diagram of the drill as drill is advanced towards workpiece. When thedamper is engaged, a velocity-dependent force resists the forward motion of the drill. Theparticipant must exert a horizontal force to advance the drill and a moment to keep the drillbit straight.188CHAPTER 5. PLUNGE DEPTH USER STUDYlikely increase their endpoint stiffness [Franklin 2003], which results in less plunge for the same appliedforce. Other factors related to the limitations addressed in Chapter 4 could also explain differences.Subjects in the study varied in height and weight, so their anthropometric parameters and thereforeimpedance parameters would vary. We experimented with ways to estimate the impedance parametersfor each subject, but developing the appropriate methodology and hardware was beyond the scope ofthis project. Another possible source of variation is that the model assumes a constant, linear dashpot,while the Airpot? has a non-linear air-spring behaviour.5.4.4 Comparison to Other WorkSince many of the factors that could affect drill plunge are not consistent between or necessarily con-trolled within these studies, it is difficult to compare results directly. However, our data supports trendsidentified by others: plunge depth depends largely on force, which is affected by drill bit geometry, drillbit sharpness, material properties, and user control.Previous studies have used a variety of methods and subjects to quantify or access plunge depth (Ta-ble 5.5). Earlier studies used an optical tracker to measure the movement of the wrist or drill, and useda drop in force to define the instant of breakthrough [Dubrowski 2004; Praamsma 2008; Khokhotva2009]. One limitation of this technique is that any interaction between the bit and the bone duringbreakthrough will result in non-zero forces, and could potentially affect the accuracy of breakthroughdefinition and plunge depth. The present study also tracked and registered the workpiece so that plungedepth could be measured explicitly and separately from force. Several other methods for quantifyingplunge depth have been used. Alajmo [2012] measured plunge depth using a sleeve positioned overthe drill bit. The sleeve would slide up the bit as the drill penetrated into the bone and then remainin place when the drill bit is withdrawn. This technique could lead to smaller plunge depths if move-ment of the sleeve requires any appreciable force, but this is unlikely. Clement [2012] measured plungedepth by mounting an expanded styrene plate to the rear surface of the cortex. While this method hasthe advantage of creating a cavity that can be accurately measured with a depth gauge, it is unclear howdrilling into the styrene effects plunge depth, but it likely provides greater resistance than soft tissue, andtherefore would lead to smaller plunge depth. Since they do not require an optical tracking system, themethods employed by Alajmo [2012] and Clement [2012] are comparably simpler and less expensivethan in the present study; however, they are not likely to be as accurate.Khokhotva [2009] investigated the influence of three different types of feedback during corticaldrilling training with second-year medical students: no feedback, intrinsic, and extrinsic. Subjects inthe no feedback group used a drill collar that prevented drill plunge from occurring. In the intrinsicfeedback group, subjects were able to plunge freely but did not receive any other feedback other thanwhat they experienced or observed. In the extrinsic feedback group, an audible signal was generatedto augment feedback when the subject plunged more than 5 mm. The study found that both groupsimproved performance with practice, but that there was no difference between the groups when theywere retested a week later (Figure 5.34). Interestingly, the ?experienced? group, a small number (n = 4)of third-year postgraduate surgical trainees, did not show improvement over the course of 60 practice189CHAPTER 5. PLUNGE DEPTH USER STUDYtrials. The study concluded that a relatively short practise session on a bench model could lead toskill improvement, and also that the inability to make errors does not necessarily undermine learning.Unfortunately, the Khokhotva [2009] study does not report drilling forces or drilling duration, so it ispossible that plunge depth is being minimized by increasing the risk of osteonecrosis. It is also importantto note that there is still appreciable levels of 5 mm to 10 mm plunge depth after learning and by the moreexperienced group.Figure 5.34 Experimental drill plunge results from a previous study on influence of different feed-back types on task learning. Each boxplot shows the median, 95 % confidence interval andrange. The left panel shows the results from trials 1-10 and the results from trials 51-60in the acquisition phase. The right panel shows the results one week later in the retentionphase. (Source: reprinted from Khokhotva [2009], ?2009 Association me?dicale canadienne.Copied under license from the Canadian Medical Association and Access Copyright. Furtherreproduction prohibited.)The Alajmo [2012] study demonstrated that plunge depth depends on experience, drill bit sharpnessand bone quality. The study found that when using sharp bits, surgeons with 5 or more years of expe-rience tended to plunge about 5 mm, 2.5 mm less than surgeons with less than 2 years of experience.Using blunt drill bits not only significantly increases plunge depth, but also negates the effect of expe-rience, with an average plunge depth of 21 mm in normal bone and 15 mm in osteoporotic bone. Weexpect that these findings are primarily a result of different drilling force levels, which unfortunatelywas not measured or controlled for. One of the strengths of the Alajmo [2012] study was the use ofa foam bone holder. As discussed in Chapter 4, plunge depth may increase when viscoelastic tissuecauses the bone to ?rebound? after breakthrough. The addition of a non-rigid bone mounting makes thetesting more realistic, although it is unclear how well the foam mimics the behaviour of real soft tissue.190CHAPTER 5. PLUNGE DEPTH USER STUDYThis Clement [2012] is the largest study to date, with 153 subjects. The study found no statisticallydetectable difference based on gender, surgical specialty, or experience, with an overall mean plungedepth of 6.31 mm and a range from 0.33 mm to 18.67 mm. Again, one of the limitations is the lack ofmeasured force or duration, especially since the subjects knew that minimizing plunge depth was thegoal of the study.While the studies to date have had consistent findings in terms of the importance of force on drillplunge depth, there has been no comprehensive evaluation of typical freehand drilling forces in theoperating room or on human bone. A recent study provides a comprehensive list of typical bone drillingforces from a number of studies [MacAvelia 2012]. Most of the studies have used a fixed feedrate,which does not accurately portray a freehand drilling task.191CHAPTER5.PLUNGEDEPTHUSERSTUDYTable 5.5 Drill Plunge Study ComparisonStudy Purpose Subjects Bone Model Mounting Forces (N) Plunge Depth (mm)Dubrowski[2004]ExplorationSurgeons (n=11)Junior residents (n=15)Lamb femur Rigid N\/R N\/RPraamsma[2008]Effect of drillingsounds andexperienceMedical student (n=11)Experienced residents(n=10)Surgeons (n=8)Lamb femur Rigid N\/R Figure 5.32Khokhotva[2009]Effect of differentperformancefeedback on taskretentionMedical students (n=22)Experienced residents(n=4)Lamb femur Rigid N\/R Figure 5.34Alajmo[2012]Effect of bitsharpness and bonequalityInexperienced surgeons(n=17)Experienced surgeons(n=20)Generic andosteoporoticsyntheticboneaFoam N\/A>20mm NormalBone>10mm OsteoporoticBoneClement[2012]Quantify plungedepthSurgeons andphysicians (n=153)GenericsyntheticboneRigid N\/A (6.3?3.2)mmPresent:FreehandEffect of bracedamping and drill bitgeometryNovice (n=25) Red oak Rigid 21N (15?28N)b 18mm (13?25mm)bPresent:10N s\/mmDamping?? ?? ?? ?? 20N (15?26N)b 4mm (3?6mm)ba Tube diameter 25 mm, canal diameter 9 mm, length: 400 mm; Synbone, Malans, Switzerland.b Median (Q1-Q3)N\/A: not applicable, N\/R: not reported192CHAPTER 5. PLUNGE DEPTH USER STUDY5.4.5 Sources of Variation and UncertaintyWe attempted to limit uncertainty as much as possible by randomizing the order in which conditionswere presented, however there is still the potential of uncertainty within trials, between trials, betweenblocks, and between subjects.Within-trialWithin a trial, there are several sources of measurement uncertainty.The optical tracker used in the study is limited to 60 Hz. Although this is appropriate for the rela-tively slow movements in targeting and alignment, it has a limited ability to capture the rapid drill plungemovement after breakthrough. However, in this study we were primarily interested in the maximumplunge depth. Since the drill must slow down and reverse direction, this event is captured adequately.The total uncertainty in the drill plunge metric ? the distance of the drill bit tip from the breakthroughplane ? depends on a series of measurements and calibrations. The measured pose of each rigid bodyis susceptible to noise introduced by the optical tracker, which is combined when the relative positionbetween two bodies is calculated. Additional sources of error include the drill bit tip calibration andthe plane calibration. We estimate that the total uncertainty in drill plunge is approximately 1.6 mm.Although this is relatively high, it is much smaller than the differences in drill plunge between differentdamping levels, so we believe there is minimal impact on our findings.Between-trialThere are several factors that may explain variation between trials.The most relevant consideration for any repetitive motor task is learning. We tried to control forlearning effects by giving each subject several practise trials at each damping level and presenting theblocks in a random order. As more holes were drilled in a particular block, it would have become easierto see the depth of the workpiece, which could have resulted in less drill plunge.Fatigue could also affect performance over the coarse of a block of trials. If the subject fatigued,we would expect a reduction in drilling force and a reduction in their ability to augment their stiffness.The decrease in drilling force would lead to longer drilling duration. It is difficult to say what the effectwould be on drill plunge: reduced force would lead to smaller drill plunge, while less stiffness wouldlead to more. Since the impedance of the task changed at each damping level, it is likely that somelearning occurred.Another source of inter-trial variation is drill bit sharpness. As a drill bit dulls, more force is requiredto drill and this has been shown to increase drill plunge [Alajmo 2012]. We attempted to control forthis uncertainty by randomizing the order of conditions and by replacing the drill bits for approximatelyevery five subjects. We believe this was a reasonable compromise between controlling for sharpnessand cost.193CHAPTER 5. PLUNGE DEPTH USER STUDYBetween-blockThe damping level could have varied between drill bit types and subjects by as much as 10 %, basedon the repeatability of manually setting the adjustment knob on the Airpot? (see Section 4.3.5). Thisvariation was unavoidable based on the current apparatus. In a future study, this variation could bereduced by replacing the adjustment knob with orifices of a fixed size. Since the difference betweendamping levels was much larger than the variation within a damping level, this likely had a minimaleffect on the results.The BP drill bit we used in the study had depth markings along the shaft, while the HSS drill bitwas unmarked (Figure 5.3). Only one user reported noticing these markings, but it is possible that itprovided additional feedback to gauge depth.Between-subjectIn addition to age, gender, and dominant hand, there are several additional factors that may explainvariation between subjects, mainly physical size and strength. Although we did adjust the height of theworkpiece to match the subject, their arm impedance would have still varied. Depending on the strengthof the subject, the portion of force required to move the damper may reduce the force being applied tothe workpiece by the drill bit below the threshold required to drill, or reduce it to a rate slow enoughthat fatigue became a factor.Although we did not formally quantify power tool experience, it varied from subjects who had neverused a cordless drill to those who had used drills regularly as part of their employment. Subjects withmore experience (e.g., S10, S19) tended to use higher force levels, which resulted in shorter drilling du-ration and larger drill plunge. Since minimizing drill plunge is rarely a concern outside of the operatingroom, these subjects likely weighted the reduction of drilling duration more strongly.5.4.6 LimitationsThere are several limitations to this study that may affect our ability to interpret and generalize theresults.PostureBased on the literature and our modelling results, we knew that posture can influence impedance andtherefore performance [Mussa-Ivaldi 1985; Rancourt 2001a]. We attempted to control for the postureof the user by adjusting the height of the task and by providing guidelines for feet placement. We didobserve several subjects adopt a more open posture by adjusting the position of their feet. This increasedbase of support would have made it easier to maintain stability, potentially leading to less drill plunge.However, we believe the primary reason for this posture change was to make it easier to apply force.Changes in foot position were observed more often at the high damping level, where subjects had toapply higher forces to the drill in order to achieve the same drilling speed as other conditions.Posture could be explicitly measured with motion tracking hardware. The limited working volume194CHAPTER 5. PLUNGE DEPTH USER STUDYof the Polaris? is not large enough, but an additional or alternative motion capture system could beused to measure the movement of the user. Having posture data may help explain differences betweensubjects, and could also be used to see how well the experimental posture compares to those predictedby models like the one developed by Jones [2008].Learning EffectsAny repetitive human motor task is likely to be affected by learning, and there was evidence of changein force, drilling duration, and drill plunge depth over the course of repeated trials. In addition to theexpected adaptation in stiffness, it became easier to see the thickness of the workpiece as holes weredrilled. Since we randomized the order of conditions, there should not be a significant impact on theoverall results of the study.Warped WorkpiecesSome of the test pieces had a slight bow and although we tried to ensure the workpiece was mountedwith the convex side against the workpiece holder, some trials were completed with the concave sideagainst the workpiece holder. This resulted in a gap between the rear surface of the workpiece and thebreakthrough plane defined on the workpiece holder. This should not have markedly affected the plungedepth, as the force required to drill was normally sufficient to compress the workpiece flat against theworkpiece holder. There would likely be a different force profile immediately after breakthrough asthe compressed workpiece ?springs? back after the drilling force is removed. The most bowed piecescould have resulted in an unloaded gap of approx 3.5 mm between the rear workpiece surface andthe workpiece holder. Spring back of a bowed workpiece after breakthrough may have also providedadditional visual and audible feedback that breakthrough had occurred, although this feedback wouldhave a similar delay. Since the magnitude of changes between the damping levels is considerably largerthan the gap, we do not believe this significantly affected our findings.Force MeasurementThe force applied by the subject to the drill was not measured directly and was estimated from thedirectly measured axial force on the workpiece and the estimated bracing force. The uncertainty inestimating the bracing force is quite large since we use a linear damper assumption, the mean drillingvelocity measured from the tracker and the experimentally measured damping level. The type of damperused in the study uses air as the working fluid and as a result has some nonlinear behaviour. Further,drilling velocity is not constant during the trial. Our estimates suggest that users applied higher forcelevels as damping level increased; however, the uncertainty described above makes it difficult to makeany conclusions. Future studies should consider measuring the force applied by the user directly in orderto determine the affect of bracing on muscle activation and fatigue.Similarly, we did not quantify the maximum pushing force of each subject. This would have beena useful metric to compare how close subjects were to their exertion limits at higher damping levels.We measured the maximum pushing force of a few subjects informally, and there was considerable195CHAPTER 5. PLUNGE DEPTH USER STUDYvariation (80?160 N). If the force required for drilling under high levels of damping exceeded thesubjects strength, it would likely lead to excessive drilling durations.5.4.7 Clinical RelevanceThere are a number of differences between the simulated cortical drilling task we assessed in this userstudy and a typical cortical drilling performed clinically (Table 5.6).Table 5.6 Comparison Between Simulated and Clinical Cortical Drilling TaskSimulated ClinicalWorkpiece Oak BoneThickness 5 mm 1.6?12.0 mmaUser Novice Layperson SurgeonDrill Commercial Drill Surgical DrillDrill bit HSS and Brad Point Orthopaedic BitWorkpiece support Rigid ViscoelasticPlunge material Air Soft-tissuea Source: Noble [1995]SubjectsThe subjects we recruited were of a similar age to junior surgeons but they did not have the samelevel of experience with the task. Previous studies have shown that when compared to junior residents,experienced surgeons use additional feedback to predict when breakthrough will occur and are betterat controlling their drilling force to minimize drill plunge [Dubrowski 2004; Praamsma 2008]. Basedon these results, we expect that experienced surgeons may experience less of a benefit from bracing.However, since there are still physiological limits in terms of voluntary reaction delays, bracing couldhelp to further reduce the amount and likelihood of drill plunge. Further, we demonstrated that usinga bracing strategy can help novices achieve a level of performance similar to, or perhaps better, thanexperts.WorkpieceThere are two aspect of the workpiece that affect the clinical relevance of this study: the choice ofmaterial and the rigid mounting.It is not uncommon to use bone substitutes in biomechanical research for ethical, practical, andmonetary reasons. In addition to being expensive, and requiring special handling procedures, bonespecimens would vary in geometry and material properties and it would be difficult to characterize thesurface to measure drill plunge depth. Although we chose one of the densest varieties of wood readilyavailable, the force required to drill through the oak is still less than that of bone. Since our data founda positive correlation between drilling force and plunge depth, we suspect that the plunge depths would196CHAPTER 5. PLUNGE DEPTH USER STUDYbe slightly higher in bone than what we measured. However, our drill plunge depths are consistent withanother study that used lamb femurs [Praamsma 2008].Artificial bone substitutes are available, but although they have realistic geometry, they may notaccurately replicate drilling loads in human bone. Synthetic composite femurs have been shown to havesimilar bending and torsional testing behaviours and 20-200 times less variability between specimenscompared to cadaveric specimens [Cristofolini 1996]. Recently however, MacAvelia [2012] compareddrilling loads between human cadaver femurs and artificial femurs (Model #3406, Sawbones, Vashon,WA, USA) in a unicortical drilling task and found statistically detectable and significant differences inboth thrust force and torque. Using parameters similar to our study, with a spindle speed of 1250 RPMand a fixed feed rate of 2.0 mm\/s, they found thrust forces in the human femur specimens ranged from175 N to 200 N, compared to 75 N to 87 N for the artificial femur. Based on these results, the authorsconcluded that ?for the present range of experimental parameters used, these artificial bones do notreplicate surgical drilling loads on human bone.? In our study, the mean drilling force was approximately20 N and measured as high as 88 N. Feed rate was 3.0 mm\/s on average, but varied considerably.In the experimental setup, the workpiece was rigidly affixed with respect to the environment. Thisdiffers from most scenarios seen clinically, where we would expect the target tissue to move withsome sort of viscoelastic behaviour due to the soft tissue supporting the bone. We would expect thatin a configuration with high tissue stiffness, drill plunge could actually be made worse as the targetanatomy recoils after breakthrough. A bracing device influencing the interaction between the tool andthe environment as in our experimental setup should still help mitigate the plunge generated by thehuman-environment interaction, but would not offer much benefit for the tissue-environment interac-tion. Mounting the brace between the environment and the tool was really done for simplicity. Ourintention is that an actual bracing device would be designed to influence the tool-anatomy interactiondirectly. The performance of such a device should be similar to what we saw experimentally.Another consideration related to the mounting of the workpiece is the lack of any material behindit. Although other plunge studies have used similar experimental set-ups [Dubrowski 2004; Praamsma2008], in a clinical setting, there would be soft tissue immediately adjacent to the bone, not air. Thissoft tissue would provide resistance, limiting the amount of plunge. This means that we can not directlyuse the drill plunge depths found in this study to predict whether injury would occur at a particularanatomical location.InstrumentsAlthough the drill used in the study was not an orthopaedic bone drill, it is similar in mass, style, anddrill speed to battery-powered models used clinically4. Pneumatic and electrically powered drills willbe lighter, but we do not expect that this would markedly affect the results.Conventional bone drilling bits are similar to, and were originally based on, HSS drill bits like theone used in this study. A variety of different designs have since been developed and tested. Typically,modern orthopaedic drill bits have a sharper point angle (90? versus 135?) and a slower spiral (smaller4Such as the Zimmer? Universal Power System, for example.197CHAPTER 5. PLUNGE DEPTH USER STUDYhelix angle). There is no clear consensus in the literature about the optimal parameters, but a recentreview summarized a number of recommendations based on the literature [Pandey 2013]:? High drill rake angle (20??30?).? Quick helix or worm spiral (25??35?).? Large point angle (100??130?).The choice of helix angle is primarily based on removal of debris and chips. We were able to demon-strate that when corkscrew did occur, the velocity of the drill after breakthrough was related to helixangle. If a future study was able better understand why and when corkscrew occurs, this may be asecondary consideration for drill bit selection.BP drill bits are specifically designed and optimized for cutting efficiently in wood, and especiallyacross the grain. The sharp centre point, or spur, is designed to be pushed into the soft wood to keep thedrill bit in position. In contrast to the HSS bit, the BP cuts the periphery of the hole first. This maximizesthe chance of the long wood fibres being cut cleanly, rather than being pulled out messily. Althoughbone has a similar heterogeneous structure, the large difference in hardness would make it extremelydifficult to use a BP bit to drill bone: the spur is not designed to cut into hard materials.One drill bit characteristic that does differ is bit length: orthopaedic drill bits tend to be quite longin order to access deep geometry and accommodate drill guides. During freehand drilling, the inherentlateral instability increases with bit length; maintaining stability can limit how much thrust force canbe applied [Rancourt 2001b]. It is therefore possible that using long drill bits with bracing levels highenough to effect drilling force could lead to even longer drilling durations.5.4.8 Future WorkThere are several outstanding questions related to addressing the limitations of the current study, devel-oping a specific device for minimizing cortical drill plunge, and applying bracing to other surgical tasks.Address limitations of current study:? Investigate how intermittent pulsing, rather than continuous drilling, affects drill plunge and du-ration.? Use a research-grade optical tracking system to track the drill tip position at higher frequency andfiner resolution.? Use high-speed video to identify when corkscrew occurs.? Explicitly assess fatigue. For example, with a visual analogue scale after each trial, or withelectromyography.? Assess performance of surgeons at different experience levels.? Assess impact of viscoelastic anatomy.? Perform trials in bone substitute or cadaver bone.? Improve model by including subject-specific anthropometry and impedance values.Outstanding questions and issues for development of specific plunge-minimization device:198CHAPTER 5. PLUNGE DEPTH USER STUDY? What are typical drilling forces used clinically?? When soft-tissue is present, is it harder to detect breakthrough?? How does plunge performance vary with workpiece thickness? What role does friction play?? What postures do surgeons typically employ while cortical drilling?? Does drill bit helix angle affect probability and severity of corkscrew?? Choose optimal damping range based on realistic bone and surgical bit drilling parameters.? Redesign device to mount to drill rather than ground.? Test active damping by controlling damping device orifice.Outstanding questions related to applying bracing to other tasks:? Test bracing strategies in similar clinical tasks.One of the biggest opportunities for future research is to quantify clinical freehand drilling forces.Although a few studies have quantified drilling force in human cortical cadaver bone, these have beenmeasured at a fixed feed rate instead of freehand where the surgeon controls the force [Wiggins 1976;Natali 1996; MacAvelia 2012]. Our system could be used to measure the magnitude and range ofdrilling forces in a typical freehand case. Ultimately, an instrument drill that measures drilling forcein-vivo would be the most accurate measure.5.4.9 ApplicationsAlthough the primary purpose of this study was to assess the feasibility of applying a bracing strategyto surgical tasks and not develop a specific device to minimize drill plunge, the results of this studydemonstrate that a damper-based bracing device may offer a simple, cost-effective solution. Previousresearch has identified experience as a major component of manual performance [Dubrowski 2004;Praamsma 2008; Alajmo 2012], while other research in this area has focussed on automated methodsof detecting and arresting breakthrough with specialized mechatronic tools [Ong 1998; Ong 1999; Ong2000] or robots [Lee 2006]. The cost and complexity of these specialized breakthrough preventiontools may explain their lack of adoption, and except for a few procedures with much higher risk, such ascraniotomy and stapendectomy, the majority of cortical drilling is still performed under manual control.Even the simplest devices require a specially-designed drill with integrated force or torque sensors, andthe necessary controllers to detect and arrest breakthrough. In this study, we showed that a relativelysimple and inexpensive mechanical bracing device could markedly reduce drill plunge regardless ofexperience level.With minimal changes, the measurement system could also be used to train and assess the drillingperformance of surgical residents and surgeons as well as assess different training methods. For exam-ple, Gofton [2007] used a similar system to assess the effect of using CAS on trainee learning of surgicalskills related to total hip replacement, while Khokhotva [2009] explored which type of task feedbackbest improved cortical drilling performance. Our system could also be used to help validate simpler,more inexpensive methods of quantifying plunge depth such as those described in Alajmo [2012] andClement [2012].199CHAPTER 5. PLUNGE DEPTH USER STUDY5.5 ConclusionsTo assess the performance of the experimental damping brace device developed in Chapter 4, we de-veloped a simulated cortical drilling task and designed a nested repeated measures user study. 25 non-experts were recruited to perform ten replications of the drilling task under each combination of twodrill bit geometries (HSS,BP) and four brace damping levels (0, 0.2, 10 and 30)N s\/mm. Holes weredrilled through a workpiece of 1?4 inch (6.35 mm) thick red oak.Drill plunge tended to decrease and drilling duration tended to increase with increased dampinglevel. Compared to the freehand condition, the medium damping level of 10 N s\/mm reduced drillplunge by an average of 74 % (95 % CI,71?76 %). At this damping level, there was no statisticallydetectable change in drilling duration (95 % CI,?6?25 %).A damper-based brace with the proper damping level can limit motion in the post-breakthroughphase of a simulated cortical drilling task without markedly affecting the time or force of the drillingphase. In more general terms, performance is increased without a corresponding increase task duration,and with limited additional cost or invasiveness.The results of this study provide evidence that the performance of a surgically relevant task can beimproved with an appropriately designed bracing device.There are three main conclusions from this study:? An appropriately design bracing strategy can improve the performance of a clinically relevanttask;? A mid-range level of damping of 10 N s\/mm can reduce drill plunge depth (PD) without a statisti-cally detectable increase in drilling duration (H2.1 and H2.2 supported); and,? Drill bit geometries that require higher drilling forces like the BP type tested in our study will leadto higher plunge depth (PD) (H2.3 rejected).200Chapter 6ConclusionsSuccess is sweet and sweeter if long delayedand gotten through many struggles and defeats.? Amos Bronson AlcottThe goal of this thesis was to assess the feasibility of applying a bracing strategy to a clinically rel-evant task. In this chapter, I revisit the research goals and hypotheses; summarize the contributions andkey findings; describe the strengths and limitations of the studies; propose avenues for future research;and, finally, present my overall conclusions.6.1 Research GoalsI hypothesized that bracing, an intuitive human motor behaviour used to enhance performance, may bea simple, cost-effective way to improve performance in certain surgical tasks. The goal of this thesiswork was to assess the feasibility of applying a bracing strategy to CAOS by:G1. Applying a bracing strategy to a surgically relevant task; andG2. Experimentally assessing whether the bracing strategy improved task performance.I applied bracing to two surgically relevant tasks: navigated drill targeting and cortical drilling.I developed a simple static rigid forearm brace for the navigated drill targeting task and developed apassive damper-based brace for the cortical drilling task.6.2 Experimental Computer Assisted Surgery SystemIn order to be able to run the intended experiments and to record the necessary performance metrics, Ideveloped a custom experimental Computer Assisted Orthopaedic Surgery (CAOS) system (Chapter 2).201CHAPTER 6. CONCLUSIONS6.2.1 Contributions and Key FindingsDeveloped experimental CAOS systemI developed a system using an optical tracker that is capable of tracking the tip and axis of a drill with anattached marker array at 60 Hz. The current optically tracked drill has a target registration error (TRE)of approximately 1.6 mm. The system displays a graphical user interface on a computer monitor withno perceptible latency.In addition to the functionality of a navigation system, the system has several other features tofacilitate research. The system is capable of measuring drill current and a force of up to 150 N appliedto a workpiece at 1000 Hz, and logging these measurements along with the tracker position data forfuture analysis. The system is also designed to manage the trials to implement the design of the currentand future user studies.I designed a device to rigidly hold and support a test workpiece and allow for the measurement offorce applied axially (Appendix C.5). Flexures maintain the position of the workpiece while allowingaxial force to be transferred to and measured by the axial force sensor. The workpiece holder is alsodesigned with an opening to allow for drill plunge and clamping surfaces to enable workpieces to bequickly and easily swapped out.Developed an unscented Kalman filter-based calibration for drill bit axis identificationI developed a unscented Kalman filter (UKF) based axis calibration algorithm to calibrate the primaryaxis of the drill bit (Appendix F). This method has a repeatability of 0.30?. This method does not requireany specially machined hardware to perform the calibration. Since it is based on an UKF, the calibrationcan be calculated in real time while the calibration movement is being performed and stopped when thedesired uncertainty is reached. In addition, the uncertainty parameters estimated during the calibrationprocess could be used in the future to enhance navigated targeting performance, as demonstrated bySimpson [2010].6.2.2 Strengths and LimitationsThe system is implemented in LabVIEW, which provides a convenient and modular environment forimplementing changes and acquiring data from different sensors. I used an NDI Polaris?, an opticaltracking system that has been used clinically and is able to wirelessly track several rigid bodies simul-taneously.There are two limitations related to the hardware: a relatively high target registration error (TRE)and the maximum tracking rate of 60 Hz. The TRE is related to both the inherent fiducial registrationerror (FRE) of the tracking system (0.35 mm) and the geometry of the marker arrays. There is someroom for optimizing the marker geometry, but there is an unavoidable trade-off between TRE and thetotal marker array size, which is roughly limited to the size of the tool. The tracking rate is not alimitation for navigation applications, since it is above the 30 Hz required for humans to perceive smoothmovement. However, the tracking rate does limit the ability to accurately measure fast motions such as202CHAPTER 6. CONCLUSIONSdrill plunge. This limited my ability to quantify initial drill plunge velocity, but this was a minor issuesince I was primarily interested in maximum plunge depth, the measurement of which was not affected.6.2.3 Future WorkOne of the factors that may have limited targeting accuracy was the magnitude of target registration error(TRE) and jitter. There are several ways that this could be reduced in a future study. First, the trackercoordinate frame (TCF) was defined by touching a tracked tool to 3 points that were asymmetricallyarranged around the workpiece plunge allowance hole. The simple 3-point method used in the presentstudy to determine the breakthrough plane resulted in a positional uncertainty that varied from 0.6 mmto 1.6 mm across the region of interest (Figure 2.14). The addition of at least one more point on thesurface on the opposite side of the hole would reduce the uncertainty and make it more consistent acrossthe region of interest.Second, the geometrical arrangement of the drill marker frame and the dynamic reference frame(DRF) could be optimized to find a better trade-off between TRE and the physical size and obtrusivenessof the marker array.Lastly, to minimize latency, I did not implement a jitter filter. A potential topic for future studyis investigating the trade-off between jitter and latency. Jitter can be reduced in the guidance displayby applying online filtering, but this will introduce a time delay that will increase latency. Since bothjitter and latency affect performance [Teather 2009], it may be possible to find a jitter filter that couldimprove performance.One design feature that could be added to the workpiece holder is hard stops. When the workpieceholder is not connected to the force sensor, it would be possible to plastically deform and damagethe flexures if too much force were accidentally applied. Such damage was avoided through carefultreatment of the apparatus.6.3 Navigated Drill Targeting User StudyI designed and performed a user study to assess whether a static, rigid forearm brace would improve theperformance of a navigated drill targeting task (Chapter 3). In this study, 25 subjects were given 15 s toalign the drill bit of an optically tracked drill with a virtual goal trajectory using visual feedback. Duringhalf of the trials, the subject?s forearm was supported by a rigid brace. I also assessed the influence oftwo different designs of guidance display that provided visual feedback to the user.6.3.1 HypothesesFor the navigated targeting task, I hypothesized that:H1.1 A passive rigid forearm brace will enable markedly improved targeting performance compared tofreehand:(a) Smaller final radial error;(b) Smaller final angular error;203CHAPTER 6. CONCLUSIONS(c) Smaller position variation; and,(d) Faster targeting.H1.2 A 3D perspective guidance display will enable markedly improved targeting performance com-pared to a 2D axial guidance display:(a) Smaller final radial error;(b) Smaller final angular error;(c) Smaller position variation; and,(d) Faster targeting.6.3.2 Contributions and FindingsThe design of guidance display markedly influences navigated targeting performanceThe 3D perspective guidance display led to quicker targeting, but larger errors in final accuracy. Ourdata showed that compared to the 2D axial display, using a 3D perspective guidance display resultedin faster targeting (H1.2d), with an average decrease of 2.4 s (95 % CI: 2.0?2.8 s). Unfortunately, thisdecrease in time was accompanied with a significant increase in final radial error (170 %, 95 % CI: 140?210 %), final angular error (350 %, 95 % CI: 300?400 %), and final position variation compared to the2D axial perspective display.Since there was a marked difference between the targeting resolutions of the two display types,I can not necessarily attribute the difference in performance to the different perspectives. However,it is clear that seemingly minor changes in the design of the display resulted in significant changes intargeting accuracy and speed. The interplay of viewpoint, resolution, and visual acuity must be carefullyconsidered by designers of these displays in order to optimize performance.These results also suggest that some sort of adaptive or hybrid display could potentially offer im-proved performance: a 3D perspective display that provides greater context and ease of spatial orienta-tion could result in greater initial targeting speed, while a simpler 2D perspective could provide optimalfinal accuracy.A rigid static forearm brace reduces angular variationMy data showed that using a passive rigid forearm brace resulted in a 30 % decrease in vertical an-gular variation and a 10 % decrease in horizontal angular variation during the final 0.5 s of the trial(H1.1b). This finding is in agreement with similar research that has reported subjective improvementsin perceived stability when using armrests [Ohta 2000].Bracing also led to a 10 % to 25 % increase in angular repeatability between trials, which is consis-tent with the 25 % improvement in positional repeatability measured by Zupanc?ic? [1998].These results suggest that a brace makes it easier to maintain the position of the drill, which mayhelp improve accuracy by providing greater resistance to perturbations when drilling is started. Dueto the preliminary nature of this work and to accommodate constraints on experiment time, the present204CHAPTER 6. CONCLUSIONSstudy task did not continue through to a drilling phase, so I did not investigate this possibility.A rigid static forearm brace does not improve final accuracy of navigated targetingI was unable to detectable any statistically significant difference in final targeting accuracy between thebraced and unbraced conditions.This finding suggests that in the absence of destabilizing interaction forces and given sufficient time,a human user is able to achieve levels of accuracy on the order of the resolution of the visual feedbackdisplay I used with or without bracing. Further research is required to determine if this trend holds witha more accurate display or with non-ideal visuomotor correspondence.6.3.3 Strengths and LimitationsIn this study, I developed and tested the performance of a clinically relevant navigated targeting taskwith a pair of clinically inspired guidance displays. A total of 25 surgeon-aged subjects participated inthe user study.The main limitation of this study was the difference in targeting resolution between the two guidancedisplay types, which may have overshadowed any performance improvements due to bracing. Althoughthe screens were the same size, a future study that controls for targeting resolution may be better able toaddress questions related to differences in guidance display perspective.6.3.4 ApplicationsThese findings suggest that the design of a guidance display for Computer Assisted Surgery (CAS)systems is not a trivial task, and that each element must be carefully considered. Specifically, overalltargeting resolution should be calculated and optimized, which requires consideration of the opticaltracker marker geometries, targeting cue design, monitor resolution, and monitor location relative to theuser.6.3.5 Future WorkThe next logical step of this work is to investigate the influence of forearm bracing on a completenavigated drilling task. In the present study, the enhanced support and stiffness provided by the bracereduced angular variation during targeting, and I believe that this may also keep the bit on target andaligned when more significant interaction forces are generated during drilling.In my study, the targeting resolution of the 3D visual feedback display was a limitation to targetingperformance. An optimized braced CAOS system should have the user?s ability to physically makethe alignment as the limiting factor. Therefore, one area for future study would be to more closelycontrol the differences between the targeting resolution of different displays in order to investigate theinfluence of perspective and determine the targeting resolution required to ensure that the display is notthe limiting factor.The physical setup of the experimental task was designed to have a near optimal visual-motor cor-205CHAPTER 6. CONCLUSIONSrespondence, meaning that the motion of the drill on the display matched the motion in real life, and nomental spatial rotations were required. Similar work in laparoscopic surgery has demonstrated that usingarm rests in stressed postures yields greater improvements in performance than under ideal, comfort-able postures [Galleano 2006]. Therefore, another area for investigation would be to repeat this studyand vary the position of the feedback monitor and target to explore the influence of guidance displaydesign and bracing on tasks performed under more surgically realistic situations where the visual-motorcorrespondence is not ideal.6.4 Modelling Manual Cortical DrillingIn order to develop an experimental bracing device to improve the performance of cortical drilling, Iperformed a variety of pilot testing and developed a numerical model of cortical drilling (Chapter 4).6.4.1 Contributions and Key FindingsA simple model can predict unlearned freehand drill plunge behaviourThe model uses drilling force, passive human arm impedance, and empirically measured drilling param-eters to predict drill plunge and drilling duration. I found using simulations that a passive, damper-basedbrace could markedly reduce drill plunge, and that it was possible to determine an optimal bracing levelthat balances drill plunge reduction and drilling duration increase with a suitable weighting function.6.4.2 Strengths and LimitationsThe model is simple, and uses experimentally measured human impedance and anthropometric param-eters from the literature. Since I used a bond graph approach, it is relatively simple to expand the modeland implement more complex models that could, for example, include more realistic human reactionand tissue dynamics.The main limitation to this model is that it does not take into account changes in learned stiffness.Although the model includes the ability to manually adjust learned stiffness, there is not a systematicway of modelling the learning process. Since the plunge depth is dependent on the overall limb stiffness,which is comprised of both passive and learned stiffness, this limits the model?s accuracy.Secondly, the model does not account for any interaction between the drill bit and the geometry afterbreakthrough, so it is unable to predict the influence of the corkscrew phenomenon I observed. Resultsfrom testing showed that this was relatively rare, so it unlikely to significantly affect our results.Lastly, the joint stiffness and damping relations derived from the literature were measured in thehorizontal plane and with a limited number of subjects. These provided a reasonable approximationwithin an order of magnitude. More accurate results could be obtained by experimentally measuringthe impedance of each subject?s arm in the relevant posture using a computer-controlled mechanicalinterface similar to the method presented in Burdet [2000]. At the least, a better understanding of thevariability in the impedance parameters would provide a better estimate for the amount of uncertainty206CHAPTER 6. CONCLUSIONSpossible in the model.6.4.3 ApplicationsThe model can be used to estimate the passive response of the human arm during drilling, and could bea valuable tool for developing a specific bracing device.6.4.4 Future WorkThe accuracy of the model could be improved in future studies by addressing some of the limitationsdiscussed earlier. As mentioned above, the user model could be extended to explore the variation inperformance expected under different levels of learned stiffness. The next most likely potential for im-provement is more accurate, and potentially user-specific, values for passive limb impedance properties.Finally, using a mechanistic model for the drilling process, like the one developed by Lee [2012], mayallow for greater investigation of interactions between the drill bit like the corkscrew behaviour I ob-served and could be used to identify under which conditions it is more likely to occur and how muchinfluence it has on plunge behaviour.6.5 Cortical Drilling User StudyI performed a user study to assess whether the experimental damper-based brace I developed would im-prove the performance of a simulated cortical drilling task (Chapter 5). In this study, 25 subjects drilleda series of holes through a 1?4 inch (6.35 mm) thick oak workpiece under 4 damping levels (0 N s\/mm,0.2 N s\/mm, 10 N s\/mm and 30 N s\/mm) and using 2 drill bit types (high speed steel (HSS) and bradpoint (BP)). I quantified maximum drill plunge depth (PD), drilling duration, the force applied to theworkpiece, and the current applied to the drill.6.5.1 HypothesesFor the cortical drilling task, I hypothesized that:H2.1 Increased levels of brace damping will markedly reduce drill plunge compared to freehand.H2.2 Increased levels of brace damping, at a level that markedly reduces drill plunge, will not markedlyincrease drilling duration.H2.3 A brad point type drill bit will enable markedly reduced drill plunge compared to a HSS drill bit.6.5.2 Contributions and Key FindingsA bracing strategy can improve the performance of a clinically relevant taskThe data showed that increased brace damping markedly reduced drill plunge compared to freehand,and that a medium damping level of 10 N s\/mm reduced plunge depth (PD) by an average of 74 %207CHAPTER 6. CONCLUSIONS(95 % CI: 71?76 %) (H2.1). Further, at the medium damping level, there was no statistically detectablechange in drilling duration (95 % CI: ?6?25 %) (H2.2).This is one of the first studies to explicitly and quantitatively assess whether a bracing strategycan improve the performance of a clinically relevant task. Most of the studies to date have relied onsubjective feedback from the surgeon as to whether stability was improved or fatigue was reduced. Inthis study, I was able to measure a marked improvement in a clinically relevant performance metric thatcan be related to injury risk. These results provide experimental evidence that a damper-based bracingdevice may be a cost-effective method for reducing the risk of vascular, nerve, and tendon damageduring cortical drilling.Certain drill bit geometries can exacerbate drill plungeI assessed two different drill bit geometries, and was able to demonstrate a statistically detectable dif-ference in drill plunge between a standard HSS drill bit and a BP drill bit. Contrary to my hypothesis,the data showed that, on average, brad point type drill bits actually resulted in larger amounts of drillplunge (H2.3). I hypothesized that brad type drill bits would result in less drill plunge since this typeof drill bit geometry is less likely to catch on the workpiece and corkscrew compared to typical HSStype drill bits. However, the pre-breakthrough force (PBF) for BP type drill bits was an average of 15 Nhigher, and I believe that applied force was a larger contributor to PD than corkscrewing behaviour.The optimal bit geometry for drilling through bone is an ongoing area of research and there is alack of consensus in the literature [Pandey 2013]. Only recently has drill plunge begun to receiveattention, and to the best of my knowledge, the influence of drill bit-workpiece interactions such ascorkscrewing has not been formally studied. While there are different types of drills and drill bitsthat will not corkscrew, such as oscillating drills, twist drills are still the most commonly used. Basedon these results, further study is required to determine whether the likelihood to corkscrew should beconsidered in future drill bit designs.6.5.3 Strengths and LimitationsIn this study, I developed a clinically relevant simulated cortical drilling task that generally mimics alateral approach for surgery on the femur. I performed the user study with a total of 25 surgeon-agedsubjects.One of the main strengths of the present study is that I quantified drilling time and drilling force inaddition to drill plunge depth. This allows me to better assess the relative trade-off between the risk ofgenerating too much heat and causing osteonecrosis and the risk of injury to drill plunge.Although this study provided encouraging results, there are several limitations that must be kept inmind in order to apply them clinically. There are several differences between the experimental task Istudied and the clinical situation.First, I used a convenience sample of novice non-surgeons with a variety of drilling experience.Based on previous studies, I expect that experienced surgeons would be better at minimizing freehanddrill plunge [Praamsma 2008]. However, similar studies have shown that even expert surgeons can208CHAPTER 6. CONCLUSIONSroutinely plunge 20 mm or more [Alajmo 2012], therefore they would likely still benefit from bracing.Second, I used oak and standard drill bits instead of bone and specialized orthopaedic drill bits.Based on pilot testing and experimental results in the literature, I expect the necessary force to drillthrough bone to be considerably higher than drilling through oak. The average drilling force in ourstudy was approximately 20 N, whereas one study measured forces ranging from 175 N to 200 N ata fixed feed rate in human cadaver femurs [MacAvelia 2012]. Since that study measured the forceusing a fixed feed rate, they are likely slightly higher than the forces I would expect a surgeon to applyclinically. Still, the link between larger drill forces and large plunge is well established, and the higherforces required to drill through bone would lead to larger drill plunge depth.6.5.4 ApplicationsThese results suggest that a bracing device designed to limit drill plunge should seriously be considered,especially when drilling in anatomical locations where vulnerable structures lie within a zone of dangerof being penetrated, i.e., the drill plunge ?danger-zone? [Alajmo 2012].A similar system could be used to help train and assess the learning and performance of surgicalresidents on minimizing drill plunge depth. Bench-top training has been shown to be a cost-effectiveand safe way for residents to improve performance. Results of one small study showed that althoughfeedback on plunge depth during a simulated bicortical drilling task improved short term performance,it had a similar effect on retention to practise without feedback [Khokhotva 2009]. The authors suggestthat focussing on drilling force may be more important, which is feedback our system could provide.6.5.5 Future WorkSince I began this study, several studies on drill plunge have been reported. All of the studies to date,including this one, have used either an artificial or animal bone model. There is a lack of data in theliterature on typical freehand drilling forces in real human cortical bone or in a realistic clinical situation.Properly quantifying the forces and surgeon posture are key steps in better understanding drill plungebehaviour.My results suggest that a damper-based bracing device might affect a user?s ability to detect break-through. A previous study quantified the influence of drilling sounds of PD, and concluded that expertswere able to use this feedback to predict breakthrough and reduce PD [Praamsma 2008]. A similar,more comprehensive investigation of which types of feedback (sounds, vision, proprioceptive) differentuser?s rely on is an important step in developing any sort of plunge-minimization device.6.6 Overall Implications and SignificanceBased on the this current study, I have several recommendations about applying bracing to and designingguidance displays for surgical tasks.209CHAPTER 6. CONCLUSIONS6.6.1 Recommendations for PracticeDevelop bracing device for drill plunge minimizationThe results of the user study described in Chapter 5 show that a damper-based brace with a mediumdamping level of 10 N s\/mm significantly reduced drill PD with minimal effect on drilling duration.These results suggest that a bracing device may offer a cost-effective way to improve performance andreduce the chance of injury. Such a device may be especially effective in anatomical locations wherevulnerable nerves, tendons, and vasculature are in close proximity to the bone being drilled, such asthe tip of the coracoid [Lo 2004], the midshaft and lateral epicondyle of the humerus [Carlan 2007;Apivatthakakul 2005; Apivatthakakul 2010], and the posterior cortex of the tibia (Hansen [2010] ascited in Alajmo [2012]).Explicitly optimize display design for time and accuracyThe results of the user study described in Chapter 3 show that seemingly small changes in guidancedisplay design can have a significant impact on navigated targeting performance. The design of theseguidance displays should be optimized so that it is not the limiting factor for accuracy.6.6.2 Recommendations for Future ResearchInvestigate influence of bracing on learned stiffness and fatigueI believe that the most important area for future studies is to investigate the relationship between bracing,learned stiffness, fatigue, and performance. Previous studies have shown that humans are able to adjustthe impedance of the arm independently of trajectory by co-contracting antagonistic muscles [Darainy2004]. This co-contraction is important for maintaining stability in unstable force-production tasks likedrilling [Rancourt 2001b], and limits the total amount of force available [Rancourt 2001a]. Increasingstiffness through co-contraction increases metabolic cost, and fatigue is known to increase force vari-ability [Selen 2007]. Humans likely use some form of impedance control to balance and optimize thistrade-off between stability and metabolic cost [Franklin 2003]. The inclusion of a brace may provideextra stability without the metabolic cost, potentially reducing the effects of fatigue and allowing forbetter performance.In the present study, I experimentally demonstrated that using a simple fixed forearm bracing strat-egy to augment the impedance of the limb could improve at least one aspect of performance. In thetargeting study, the support provided by the forearm brace effectively increased the lateral stability ofthe limb, which reduced angular variation. Subjects also subjectively reported less fatigue. More signif-icantly, in the cortical drilling study, the experimental damper-based bracing device provided increaseddamping to the arm to minimize the amount of overshoot that occurred when the drilling reaction forcesuddenly disappeared after breakthrough, which reduced drill plunge depth.Over the course of repeated freehand trials, subjects were able to reduce PD independently of pre-breakthrough force, suggesting that the subjects were modifying their impedance to increase stiffness210CHAPTER 6. CONCLUSIONSand accommodate the instability created by the uncertain breakthrough time. Internally increasing stiff-ness requires muscle co-activation, so not only is there a finite limit, but there is also greater metaboliccost. It is unclear how quickly or to what extent this co-activation leads to fatigue or how much increasedfatigue could affect performance.Depending on the task, the augmented impedance provided by bracing should allow larger forcesto be applied (which would otherwise be limited by the need to maintain stability), or reduce fatigue.Future studies involving bracing of unstable tasks should explicitly measure fatigue through electromyo-graphy or other subjective means, and should consider explicitly tracking posture as it has a significanteffect on limb impedance.Investigate influence of non-ideal visuomotor correspondenceIn the present study, the navigated targeting task was designed with ideal visuomotor correspondence:motion of the tool in the real world matched the motion on the guidance display and the guidance displaywas oriented directly in front of where the subject was manipulating the tool. This is rarely the case ina surgical scenario, where the guidance display is often positioned off to one side.Bracing and the design of the guidance display will likely play a more important role in targetingperformance when the relationship between motion in the real world and motion of the targeting cuesrequires an internal transformation. This should be investigated.Characterize clinical cortical drillingAs discussed above, a clinical assessment of drill plunge depth, drilling forces, and posture is the nextlogical step in understanding and developing ways to minimizing drill plunge.6.7 ConclusionsThis thesis represents one of the first studies in applying bracing to orthopaedic surgery, and providesexperimental evidence both that an appropriately designed bracing strategy can improve the performanceof a clinically relevant task and that targeting display design may play a significant role in overall systemaccuracy. 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English. In:Recent Advances in Robot Kinematics SE - 31. Ed. by Jadran Lenarc?ic? andVincenzo Parenti-Castelli. Springer Netherlands, pp. 307?316. ISBN: 978-94-010-7269-4. DOI:10.1007\/978-94-009-1718-7\\ 31 (page 12).Zupanc?ic?, Jure and Tadej Bajd (1998). ?Comparison of position repeatability of a human operator andan industrial manipulating robot?. In: Computers in biology and medicine 28.4, pp. 415?421. ISSN:0010-4825 (pages 13, 14, 20, 48, 49, 93, 204).221Appendix ADetailed MethodsA.1 Radial Axis ErrorThe distance between two axes in 3D space can be determined by finding the line that is mutuallyperpendicular to both (Figure A.1). The following section is rephrased from Bourke [1996].3E3\u00143\u00173\u00153\u00163AFigure A.1 The shortest distance between two lines in 3D space can be found by finding the linethat is mutually perpendicular.Points Pa and Pb are defined as points lying on their respective lines:Pa = P1 +?aP21 (A.1)Pb = P3 +?bP43 (A.2)The dot product of two perpendicular lines is zero:222APPENDIX A. DETAILED METHODSPab ?P21 = 0 (A.3)Pab ?P43 = 0 (A.4)These equations are expanded and solved for ?a and ?b:?a =(P13 ?P42)(P43 ?P21)? (P13 ?P21)(P43 ?P43)(P21 ?P21)(P43 ?P43)? (P43 ?P21)(P43 ?P21)(A.5)?b =(P13 ?P43)+?a(P43 ?P21)P43 ?P43(A.6)If the denominator of Equation A.5 is zero, the lines are either parallel or coincident. The valuesfor ?a and ?b found using Equation A.5 and Equation A.6 are plugged back into Equation A.1 andEquation A.2 to determine the shortest line.A.2 Angular Targeting TimeWe wanted a metric that could be used to indicate at what time a subject transitioned from angulartargeting to holding (Figure A.2a). Due to the number of trials to analyse, the method needed to beconsistent and not require manual intervention. The method also needed to be insensitive to the finalerror and able to deal with noisy data, which ruled-out a simple error threshold technique.We define a time-averaged reverse time-angular error integral:IteA(t) =? 15t eA(t)dt15? t, (A.7)which represents the average absolute error over the interval from t to the end of the hold period . Thevalue of this function will be large when the subject is adjusting the angular orientation of the drill atthe beginning of the trial, then drop and remain relatively constant as the subject holds the drill in place(Figure A.2b).We characterize the steady state error as the minimum value of IteA. In order to avoid false minimathat arise from random variations over short periods of time at the end of the trial, we apply a weightingfunction that rises at high values of t:weA =(1+t015? t), (A.8)where t0 is set to a constant value of 0.5 s to encourage inclusion of at least 0.5 s of data in the estimate.The minimum value of the weighted integral represents the root mean square (RMS) error of theangular error (Figure A.2c):meA = min(IteA(t) ?(1+t015? t)). (A.9)223APPENDIX A. DETAILED METHODSThe angular targeting time is then determined by finding the intersection of the time-angular errorintegral and an offset linear line (Figure A.2d):y = meA ? (15? t)+?eA, (A.10)where ?eA is set to mwea ?1s in order to clearly identify the time when the angular orientation settled.A.3 Empirical Drilling Parameter EstimationWe estimated the empirical drilling parameters by measuring force and velocity during a series ofdrilling trials. For each trial, the feed and pressure were calculated during the linear drilling portion(Figure A.3). Fitting the data from 10 trials of a 3?16 inch (4.76 mm) HSS drill bit in 6.35 mm oak at1200 RPM yielded constants of x = 1.45 and B = 1.9?10?1 mm (Figure A.4). A similar approach from10 trials of a 3\/16 inch (4.76 mm) BP drill bit in 6.35 mm oak at 1200 RPM yielded constants of x = 1.32and B = 6.6?10?2 mm (Figure A.5).A.4 Effective ResolutionThe two-dimensional (2D) representation of three-dimensional (3D) modelled world is based on theview from a notional camera. The field of view of this notional camera is called the viewing frustrum(Figure A.6). In general, six parameters are required to specify the left, right, bottom, top, near, and farclipping planes of this frustrum. In an orthographic view the bounds of the far plane are the same asthe near plane. For a perspective view, the parameters are the vertical field frame of view, aspect ratioof width to height, near plane distance, and far plane distance.A graphics pipeline describes how the 3D vertex of an object in the scene is transformed into a 2Dpixel location in the window.Vertex?????Ob jectModelView???EyeProjection???ClipPerspective???????NormalizedViewport?????Window(A.11)LabVIEW handles these calculations internally. To determine the pixel size of targeting cues on thedisplay, these equations from the graphics pipeline can be applied manually. The following equationsare adapted from the Open GL Modeling Pipeline1.Eye Coordinates:??????xeyeyeyezeyeweye??????= MmodelView ???????xob jyob jzob jwob j??????= Mview ?Mmodel ???????xob jyob jzob jwob j??????(A.12)1Described by http:\/\/www.songho.ca\/opengl\/gl transform.html224APPENDIX A. DETAILED METHODS(a) Angular error.(b) Reverse angular error integral.(c) Minimum time-weighted integral.(d) Angular targeting time.Figure A.2 Determination of angular targeting time for a typical trial.225APPENDIX A. DETAILED METHODSFigure A.3 Typical drilling trial for determining experimental drilling parameters. A 3?16 inch(4.76 mm) high speed steel (HSS) drill bit was used in 6.35 mm oak at approximately1200 RPM. The mean thrust force and drilling velocity are estimated from the linear forcerange.Figure A.4 Empirical drilling constants for a 3?16 inch (4.76 mm) high speed steel (HSS) drill bit in6.35 mm oak.226APPENDIX A. DETAILED METHODSFigure A.5 Empirical drilling constants for a 3?16 inch (4.76 mm) brad point (BP) drill bit in 6.35 mmoak.Figure A.6 OpenGL Perspective viewing frustum.Clip Coordinates: ??????xclipyclipzclipwclip??????= Mpro jection ???????xeyeyeyezeyeweye??????(A.13)Normalized Device Coordinates???xndcyndczndc???=???xclip\/wclipyclip\/wclipzclip\/wclip??? (A.14)227APPENDIX A. DETAILED METHODSWindow Coordinates (Screen Coordinates)???xwywzw???=???w2 xndc +(x+w2 )h2 yndc +(y+h2)f?n2 zndc +f+n2??? (A.15)Since we also know the size of the window and the display resolution,2D DisplayFor the 2D perspective display, the camera position is defined as [0,0,?300]T , the target is [0,0,0]T andthe up direction is [0,1,0]T . The ModelView Matrix is???????1 0 0 00 0.83205 0.5547 ?83.2050 0.5547 ?0.83205 ?416.0250 0 0 1??????(A.16)and the projection matrix is??????2.41421 0 0 00 2.41421 0 00 0 ?1.0002 ?2.00020 0 ?1 0??????(A.17)3D DisplayFor the 3D perspective display, the camera position is defined as [0,300,?300]T , the target is [0,0,150]Tand the up direction is [0,1,0]T .The ModelView Matrix is???????1 0 0 00 0.83205 0.5547 ?83.2050 0.5547 ?0.83205 ?416.0250 0 0 1??????(A.18)and the projection matrix is??????2.41421 0 0 00 2.41421 0 00 0 ?1.0002 ?2.00020 0 ?1 0??????(A.19)228Appendix BEthicsB.1 Ethics Consent Form229Version:  December 4, 2009  Page 1 of 3  Subject Consent Form \u0001\u0002\u0003\u0004\u0005\u0006\u0007\u0002\b\t\u000b\f\b\u000e\b\u0006\u000f\u0010\u0011\t\u0007\u000e\u0012\u0004\f\f\u0013\f\t\u0007\u0002\b\u000e\t\u0014\u0010\u0007\u0002\u0013\u0006\b\f\u0011\u000e\u0015\u0007\u000e\u0016\u0017\b\u0018\u0007\u0006\t\b\b\u0003\u0013\f\u0011\u0004\u000b\b\u0007\u0007\u0002\u0019\u0004\u0006\u001a\b\u0002\u0013\f\u0010\u000b\u0004\u0016\b\u0004\u0005\u0002\b\u0013\u0005\f\t\u000e\u0011\u000f\u0007\u0005\t\b\u0019\u000e\u0004\u0006\u0013\u0005\u0015\b\u0005\b\u0004\u0006\u0006\u0011\u000e\u0004\u0006\u0016\b\u0004\u0005\u0002\b\t\u0013\u000f\u0007\b\b\u0004\b\u0002\u000e\u0013\u000b\u000b\u0013\u0005\u0015\b\t\u0004\f\u001a\b  Principal Investigator:  Antony Hodgson, Professor, Department of Mechanical Engineering, (604) 822-3240.  Co-Investigator(s):  Jacob McIvor, M.A.Sc. Candidate, Department of Mechanical Engineering, (604) 822-2648.  This research is being done as part of a Master?s thesis.  Sponsor:  NSERC Discovery Grant: Advanced tools for computer-assisted orthopedic surgery.  Purpose: The purpose of this study is to investigate how visual feedback display design and instrument bracing affect the performance of a computer-assisted drilling task performed by a human operator.    Study Procedures: Participation in this study involves a single session that will take approximately one hour.  You will be asked to provide your age, gender, and dominant hand.  You will receive instructions on how to operate the computer-assisted drilling system.  This system consists of a standard handheld drill, a stereo camera position sensor and a targeting screen on a computer.  You will use the information displayed on the targeting screen to help position and align the drill.  Once you feel comfortable using the system, you will then use the system to drill a number of holes in a foam workpiece.  Each trial will be videotaped, and the movement of the drill will be recorded along with the time taken to drill the hole.  In addition to different designs of the targeting screen, some trials will also use a passive brace to help position and steady the drill.  After the drilling trials, you will fill out a short questionnaire on your experiences with the system. Version:  December 4, 2009  Page 2 of 3  Potential Risks: There is a minor risk of physical injury associated with the use of a power drill.   For your safety, you will be required to wear safety glasses, roll up long sleeves, remove any jewelry on your hands, and tie back any long hair.    Potential Benefits: No individual benefits are expected.  Confidentiality: Your identity will be kept strictly confidential and you will not be identified by name in any reports of the completed study.  Data from the study will be identified by a unique code number and accessible only by the Co-Investigator and Principal Investigator on a password protected PC in a locked office.   Remuneration\/Compensation: You will receive a $10 gift card for compensation of your time.   Contact for information about the study: If you have any questions or desire further information with respect to this study, you may contact Antony Hodgson at 604-822-3240.    Contact for concerns about the rights of research subjects: If you have any concerns about your treatment or rights as a research subject, you may contact the Research Subject Information Line in the UBC Office of Research Services at 604-822-8598 or if long distance e-mail to RSIL@ors.ubc.ca.   Photo Release  I authorize the researchers to use photographs and\/or video acquired during the study with identifiable features obscured for: ? scholarly reports and presentations ? future comparative studies Initial: ______ Version:  December 4, 2009  Page 3 of 3  Consent: Your participation in this study is entirely voluntary and you may refuse to participate or withdraw from the study at any time without consequence.   Your signature indicates that you consent to participate in this study.        ____________________________________________________ Subject Signature     Date   ____________________________________________________ Printed Name of the Subject signing above   Version: June 14, 2012  Page 1 of 1 Advanced tools for computer-assisted orthopedic surgery:  Effect of visual feedback display and instrument bracing on accuracy and time of a drilling task  Debrief Questionnaire  Please circle your response to each statement.  Statement SD D A SA It was easy to learn how to use the system. 1 2 3 4 The system is responsive. 1 2 3 4 2D Targeting Screen The 2D targeting screen was intuitive. 1 2 3 4 The 2D targeting screen made it easier to position the drill tip. 1 2 3 4 The 2D targeting screen made it easier to position the drill axis. 1 2 3 4 3D Targeting Screen The 3D targeting screen was intuitive. 1 2 3 4 The 3D targeting screen made it easier to position the drill tip. 1 2 3 4 The 3D targeting screen made it easier to position the drill axis. 1 2 3 4 Braced Targeting The instrument bracing was intuitive. 1 2 3 4 The instrument bracing made it easier to align the drill tip. 1 2 3 4 The instrument bracing made it easier to align the drill axis. 1 2 3 4 Braced Drilling     The instrument bracing was intuitive. 1 2 3 4 Increased bracing increased drilling time. 1 2 3 4 Increased bracing was more fatiguing. 1 2 3 4 Increased bracing reduced drill plunge. 1 2 3 4  How could the targeting screen be improved?       How could the instrument bracing be improved? 1 ? SD Strongly Disagree 2 ? D Disagree 3 ? A Agree 4 ? SA Strongly Agree B.2 Debrief QuestionnaireAPPENDIXB.ETHICSTable B.1 Debrief Questionnaire SummaryStatement Response Frequency (%(n))aSD D A SA1. It was easy to learn how to use the system. 0(0) 0(0) 17(4) 83(19)2. The system is responsive. 0(0) 4(1) 22(5) 74(17)3. The 2D targeting screen was intuitive. 0(0) 8(2) 40(10) 52(13)4. The 2D targeting screen made it easier to position the drill tip. 0(0) 36(9) 24(6) 40(10)5. The 2D targeting screen made it easier to position the drill axis. 0(0) 12(3) 56(14) 32(8)6. The 3D targeting screen was intuitive. 0(0) 8(2) 20(5) 72(18)7. The 3D targeting screen made it easier to position the drill tip. 4(1) 8(2) 28(7) 60(15)8. The 3D targeting screen made it easier to position the drill axis. 4(1) 12(3) 24(6) 60(15)9. The instrument bracing was intuitive. 0(0) 4(1) 36(9) 60(15)10. The instrument bracing made it easier to align the drill tip. 0(0) 12(3) 40(10) 48(12)11. The instrument bracing made it easier to align the drill axis. 0(0) 16(4) 32(8) 52(13)12. The drill bracing was intuitive. 0(0) 4(1) 36(9) 60(15)13. Increased bracing increased drilling time. 4(1) 8(2) 32(8) 56(14)14. Increased bracing was more fatiguing. 4(1) 0(0) 40(10) 56(14)15. Increased bracing reduced drill plunge. 4(1) 0(0) 28(7) 68(17)a SD-Strongly Disagree, D-Disagree, A-Agree, SA-Strongly Agree.A few questions were left unanswered, so not all rows sum to the total number of participants.234Appendix CEquipmentC.1 Optical TrackerC.1.1 Working VolumeThe NDI Hybrid Polaris? optical tracking has a silo-shaped working volume 1 m in diameter and 1 m inlength (Figure C.1).235APPENDIXC.EQUIPMENTFigure C.1 NDI Hybrid Polaris? working volume.236APPENDIX C. EQUIPMENTC.2 Marker Coordinate FramesWe characterized the local coordinate systems of the optical marker frames using NDI 6D Architect(Version 2.02.11, NDI, Waterloo, ON, Canada). This program creates a Tool Definition File for eachrigid body, which contains the marker positions in the local coordinate system (Table C.1), the markernormals, and the face normal.Table C.1 Definition of Optical Marker Local Coordinate SystemsRigid Body Marker x (mm) y (mm) z (mm)Drill A 0.00 0.00 0.00B 0.00 0.00 -96.74C 0.00 -50.44 -0.33D -2.12 -159.68 -94.28DRFa A 0.00 0.00 0.00B 53.92 0.00 0.00C 50.54 -108.40 -0.43D 4.26 -69.13 0.00SRFb A 0.04 0.04 0.00B -0.04 108.21 0.00C 100.12 130.27 0.50D 113.33 -0.04 0.00Damper Block A -109.95 -34.16 28.43B -109.95 25.88 28.43C -15.35 -33.76 28.43D -10.53 34.77 28.03a DRF-Dynamic Reference Frame, fixed relative to work-piece.b SRF-Static Reference Frame, fixed relative to ground.C.3 Targeting Display BoxBoth the 2D display (Section 2.6.2, Figure 2.6) and 3D display (Section 2.6.3, Figure 2.7) are based ondifferent views of the same targeting box (Figure C.6).C.4 Experimental DamperAn Airpot? model 2KS444 dashpot was selected for the experimental bracing device (Figure C.7).237APPENDIX C. EQUIPMENTC.5 Workpiece HolderA workpiece holder was designed and constructed to satisfy the following requirements:? position the workpiece repeatably? install new workpieces quickly? accommodate drill plunge? measure axial force? track the position of the targetWe used rapid prototyping manufacturing techniques to construct the workpiece holder. Individualparts were cut out of sheet metal, bent into shape, and assembled with spot welding. The holder isan open box with an opening to allow the drill bit to plunge freely. A raised lip provides an index toposition the workpiece in a repeatable position, and clamps are used to fix it in place. A marker frameis attached to the workpiece holder to track its position.In order to measure axial force, flexural bearings were used to provide five degrees of support forthe holder while allowing axial force to be transmitted unimpeded to a force sensor.The workpiece holder base is rigidly attached to a frame to maintain its position with respect to thework table. The vertical position of the workpiece holder is adjustable to maintain a consistent posturefor subjects of different heights.C.5.1 Flexure DesignSince our flexures were originally designed to be loaded in compression, we considered both the elasticlimit and resistance to buckling. Since we were trying to measure force in the direction of loading,instead of specifying a desired range of motion we considered stiffness.Elastic LimitWe have a rectangular shaped beam with thickness t, width w, and length L, that is loaded transverselyat the tip (Figure C.8). The moment inertia of this beam I is given by:I =wt312. (C.1)The bending stress ? in the outer fibres of the beam are given by the equation:? = MyI, (C.2)238APPENDIX C. EQUIPMENTwhere M is the moment at a particular point along the beam and y is the distance from the neutral axisto the outer fibres. Since the force is applied to the end of the beam, the moment is given by:M = FL. (C.3)Combining these equations together produces an expression that relates the geometry and loadingto the elastic limit:?e =6FLbt2. (C.4)The angular deflection ? of the loaded beam is given by:? = 2FL2EI, (C.5)where E is the modulus of elasticity.StiffnessThe stiffness of a cantilever beam is given by:k =CEIL3, (C.6)where:? I is the moment of inertia;? C is the a constant that describes the end condition;? E is the elastic modulus; and? L is the length of the beam.From the manufacturer?s literature, the axial force sensor has a stiffness of 583 N\/mm.BucklingFor a beam with one fixed and one end free, the critical compressive load for buckling is given by:Fc =piEI4L2(C.7)239APPENDIX C. EQUIPMENTC.5.2 Flexure ConstructionWe chose to use 17-7 PH stainless steel. The material properties for this alloy in the mill annealed andheat treated condition are listed in Table C.2. Each flexure is 0.386 mm thick and 80 mm wide, with aneffective length of 30 mm.Table C.2 Flexure Properties: 17-7 PH Stainless SteelConditionProperty Mill Annealed Heat Treated (TH 1050)Ultimate Tensile Strength UT S 1034 MPa 1241 MPa0.2 % Yield Strength ?Y 379 MPa 1034 MPaModulus of Elasticity E 200 GPa 200 GPaBuckling Load Fc 210 N 210 NMaximum Axial Load Fa,max 11.70 kN 31.9 kNMaterial properties: AK Steel Corporation 2007240APPENDIX C. EQUIPMENTAB&D]x \\Figure C.2 Labelled retroreflective markers for local drill coordinate frame definition. The originis centred at Marker A. The z-axis is aligned through Marker B, and Marker C is located inthe yz-plane.A]x\\B&DFigure C.3 Labelled retroreflective markers for Dynamic Reference Frame (DRF). The origin iscentred on Marker A, with the x-axis aligned through Marker B. Marker D is located on thexy-plane.241APPENDIX C. EQUIPMENTFigure C.4 Labelled retroreflective markers for Static Reference Frame (SRF). The origin is ap-proximately centred at Marker A, with the y-axis approximately aligned through Marker Band Marker D located on the yz plane.AB&D]\\xFigure C.5 Labelled retroreflective markers for damper characterization block. A pivot calibrationwas performed to align the origin with the center of the ball joint. The z-axis is perpendicularto the face of the block and the y-axis is parallel to the bottom surface of the block.242APPENDIX C. EQUIPMENTFigure C.6 Targeting box for guidance displays. The targeting box is aligned so that the origin iscoincident with the cross on the front face. The target axis is aligned with the long axis of thebox.243APPENDIX C. EQUIPMENTFigure C.7 Schematic of model 2KS444 Airpot? dashpot used in the cortical drilling study. Thestroke for this model is 2 inch (50.8 mm). (Source: Airpot Corporation.)Figure C.8 A rectangular beam transversely loaded at the tip.244APPENDIX C. EQUIPMENT)Figure C.9 The workpiece holder flexures provide 5 degrees of freedom (DOF) support while al-lowing the axial force to be transmitted to the force sensor.245Appendix DDataD.1 SubjectsD.2 Missing\/Problem TrialsD.2.1 Problem Targeting TrialsD.2.2 Problem Plunge TrialsD.3 Plunge Study246APPENDIX D. DATATable D.1 Subject Info and Task ScheduleSubjectIDAge Gender DominantHandTrialOrderaDisplayOrderbBraceOrdercDampingOrdereDrillbitf01g 27 M L n\/a n\/a n\/a n\/a n\/a02h 27 M R T,P 3D,2D U,F 0,L,M,H BP,HSS03 28 F R T,P 3D,2D F,U 0,L,M,H HSS,BP04 27 F R T,P 2D,3D U,F L,H,0,M BP,HSS05 30 M R T,P 2D,3D F,U L,H,0,M HSS,BP06 27 F R T,P 3D,2D U,F H,L,M,0 BP,HSS07 27 F L T,P 3D,2D F,U H,L,M,0 HSS,BP08 44 F R T,P 2D,3D U,F M,L,H,0 BP,HSS09 38 F L T,P 2D,3D F,U M,L,H,0 HSS,BP10 29 M R P,T 3D,2D U,F 0,L,M,H BP,HSS11 36 M R P,T 3D,2D F,U 0,L,M,H HSS,BP12 28 F R P,T 2D,3D U,F L,H,0,M BP,HSS13 31 F R P,T 2D,3D F,U L,H,0,M HSS,BP14 26 M R P,T 3D,2D U,F H,L,M,0 BP,HSS15 27 M R P,T 3D,2D F,U H,L,M,0 HSS,BP16 43 F R P,T 2D,3D U,F M,L,H,0 BP,HSS17 29 M L P,T 2D,3D F,U M,L,H,0 HSS,BP18 31 M R T,P 3D,2D U,F 0,L,M,H BP,HSS19 27 M R P,T 3D,2D F,U 0,L,M,H HSS,BP20 28 F R T,P 2D,3D U,F L,H,0,M BP,HSS21 26 F R P,T 2D,3D F,U L,H,0,M HSS,BP22 28 M R T,P 3D,2D U,F H,L,M,0 BP,HSS23 28 M R P,T 3D,2D F,U H,L,M,0 HSS,BP24 25 M R T,P 2D,3D U,F M,L,H,0 BP,HSS25 34 F R P,T 2D,3D F,U M,L,H,0 HSS,BP26 34 M R T,P 3D,2D U,F 0,L,M,H BP,HSS27 28 M R P,T 3D,2D F,U 0,L,M,H HSS,BPa T-Targeting, P-Drill Plungeb U-Unbraced, F-Forearm Bracec 2D-2D Axial Guidance Display, 3D-3D Box Guidance Displayd 0-Zero Damping, L-Low Damping, M-Medium Damping, H-High Dampinge HSS-High Speed Steel, BP-Brad Pointf Subject 01 completed a pilot version of the user study.g Subject 02 was removed from analysis due to problems with data acquisition.247APPENDIX D. DATAFigure D.1 Problem Targeting TrialsTable D.2 Problem Targeting TrialsTrial Id Subject Test Bracing Display Type Rep Problem973 6 8 U 3D 8 incorrect angular target cue974 6 9 U 3D 9 incorrect angular target cue986 6 21 B 3D 1 incorrect angular target cue987 6 22 B 3D 2 incorrect angular target cue2746 14 20 U 2D 10 high tuf3250 17 8 B 2D 8 bad target3260 17 18 B 3D 8 bad target3270 17 28 U 2D 8 bad target3280 17 38 U 3D 8 bad target3605 20 11 U 3D 1 wrong target248APPENDIX D. DATAFigure D.2 Problem Plunge TrialsTable D.3 Removed Plunge TrialsTrial Id Subject Test Damping Drill Bit Problem473 3 37 High HSS Incomplete holeb867 5 27 Zero HSS Overdrilla1006 6 1 High Brad Incomplete hole1012 6 7 High Brad Incomplete hole1159 7 10 Low HSS Overdrill2030 9 1 Med Brad Incomplete hole2038 9 9 Med Brad Incomplete hole2170 11 16 Low HSS Overdrilla Hole was drilled over top of, or too close to previous hole.b Drill was retracted and trial was ended before hole was complete.249APPENDIX D. DATATable D.4 Problem TrialsTrial Id Subject Test Damping Drill Bit Rep Problem473 3 37 H HSS 7 Re-drilla767 4 51 H HSS 1 Re-drill885 5 45 L BRAD 5 Re-drill1012 6 7 H BRAD 7 Re-drill2030 9 1 M BRAD 1 Re-drill2095 9 66 H HSS 6 Re-drill2098 9 69 H HSS 9 Re-drill2161 11 7 0 HSS 7 Re-drill2178 11 24 M HSS 4 Re-drill2181 11 27 M HSS 7 Re-drill2185 11 31 H HSS 1 Re-drill3188 17 26 H BRAD 6 Re-drill3225 17 63 H HSS 3 Re-drill3675 20 41 L HSS 1 Re-drill3733 21 15 H HSS 5 Missed breakthrough3775 21 57 H BRAD 7 Re-drilla Subject returned to drill incomplete hole.250APPENDIX D. DATAFigure D.3 Drilling Duration251APPENDIX D. DATAFigure D.4 Drill plunge depth252APPENDIX D. DATAFigure D.5 Mean drilling force253APPENDIX D. DATAFigure D.6 Estimated human force254APPENDIX D. DATAD.4 Targeting StudyFigure D.7 Gross targeting time255APPENDIX D. DATAFigure D.8 Fine targeting time256APPENDIX D. DATAFigure D.9 Tip targeting time257APPENDIX D. DATAFigure D.10 Angular targeting time258APPENDIX D. DATAFigure D.11 Tip targeting error259APPENDIX D. DATAFigure D.12 Angular targeting error260APPENDIX D. DATAFigure D.13 Total targeting error261APPENDIX D. DATAFigure D.14 Horizontal tip variation262APPENDIX D. DATAFigure D.15 Vertical tip variation263APPENDIX D. DATAFigure D.16 Horizontal tail variation264APPENDIX D. DATAFigure D.17 Vertical tail variation265Appendix EStatistical AnalysisE.1 Modelling ApproachWe based our analysis on the ?top-down? modelling approach described in West [2006] for a three-levellinear mixed model (LMM) and performed the modelling using the R package nlme [Pinherio 2013].We chose between models by comparing the values of the Akaike Information Criterion (AIC) andBayesian Information Criterion (BIC) and by calculating likelihood ratio statistics with a significancelevel of ? = .05.Analysis overview:1. Fit a general model with a ?loaded? mean structure1.2. Select a structure for the random effects.3. Select a covariance structure for the residuals.4. Reduce the model by removing non-significant fixed effects.5. Check model diagnostics.6. Interpret results.1. General Model SpecificationAn individual response Y for target t (t = 1 . . .10) within block i nested within subject j is given by:Yti j = ?0 +?1 ? REPt +?2 ?DISPLAYi +?3 ? BRACEi +?4 ?AGE j +?5 ?GENDER j +?6 ?d0t+?12 ? REPt ?DISPLAYi +?13 ? REPt ? BRACEi +?14 ? REPt ?AGE j+?15 ? REPt ?GENDER j +?23 ?DISPLAYi ? BRACEi+b0 j +b0i| j +b1i| j ? REPt + ?ti j (E.1)1A loaded mean structure contains all possible covariates as fixed effects.266APPENDIX E. STATISTICAL ANALYSISThe ? parameters represent fixed effects associated with the intercept, repetition, the block- andsubject-level covariates, and their two-way interactions; b0 j is a random subject intercept; b0i| j andb1i| j represent a random intercept and a random slope for each block nested within a subject; and ?ti jrepresents a residual.The distribution of random effects associated with subject j isb j ?N(0,?2int:sub ject). (E.2)where N(0,?2int:sub ject)represents a normal distribution with a mean of zero and a variance of?2int:sub ject . The distribution of random effects associated with block i nested within subject j isbi| j =(b0i| jb1i| j)?N(0,D(2)), (E.3)where the variance-covariance matrix D(2) is an unstructured matrix defined as:D(2) =(?2int:block ?2int,rep:block?2int,rep:block ?2rep:block). (E.4)The distribution of the residuals, ?ti j, associated with measurements within the same block is?ti j =?????1i j...?10i j?????N (0,Ri j) . (E.5)The variance-covariance matrix for the residuals, Ri j, is parametrized differently depending on themodel of correlation within a block. These are discussed in more detail below.2. Random Effects StructureWe assessed whether the block-level random slope could be omitted by using a restricted maximum-likelihood (REML)-based likelihood ratio test. For each model, the test statistic is the difference be-tween the -2 REML log-likelihoods of the reference and nested model [West 2006: p. 286]. A p-valueis obtained from a ?2 distributions with the degrees of freedom corresponding to the difference in thenumber of variance parameters. In cases where it was not possible to compare nested models, we chosethe model with the smallest BIC.3. Residual Covariance StructureWe tested several different structures for the residual covariance. The default structure assumes that allresiduals are independent and homoscedastic and uses a single parameter:267APPENDIX E. STATISTICAL ANALYSISRi j =???????2 0 . . . 0?2 . . . 0. . ....?2??????= ?2I10. (E.6)Since each block consisted of a 10 trials performed sequentially in time, we expect that measure-ments made closer in time will be more correlated than those further apart, and that they should not becorrelated with measurements from a different block. This type of temporal correlation can be describedwith a first order autoregressive correlation matrix with the form:??????????1 ? ?2 . . . ?101 ? . . ....1 . . .......1??????????. (E.7)4. Model ReductionWe used a maximum-likelihood (ML)-based likelihood ratio test to decide whether fixed effects couldbe removed from the model. The test statistic is the difference between the -2 ML log-likelihoods of thereference and nested model [West 2006: p. 286].5. Model DiagnosticsWe checked modelling assumptions related to both the residuals and the random effects. Where appro-priate, we applied a base-10 logarithm transform to correct for non-homogeneity in the residual vari-ance. This transformation was chosen because it makes it easier to interpret the estimated coefficientsas a percentage change.The residuals were assumed to be drawn from a normal distribution with constant variance. Wechecked the homogeneity of variance assumption by visually inspecting a plot of residuals versus fittedvalues. We checked the normality assumption by visually inspecting a quantile-quantile plot of themodel?s residuals.The random effects were also checked for normality and outliers by visually inspecting quantile-quantile plots. We also plotted random effects against the other covariates to ensure there was no sys-tematic bias.6. Model InterpretationWe expect correlated measurements within a block and within a subject; this correlation is called theintraclass correlation coefficient (ICC) [Li 2012: p. 222]. The ICC for subjects represents the percentage268APPENDIX E. STATISTICAL ANALYSISof total variance accounted for by subject clusters and the ICC for block represents the percentage oftotal variance for blocks nested within subjects. Theses variances should be calculated based on a modelfit without any covariates Li 2012.ICC j =?2subject?2subject +?2block +?2rep:block +?2. (E.8)Similarly, the percentage of total variance accounted for by block nested within subject isICCi| j =?2block +?2rep:block?2subject +?2block +?2rep:block +?2. (E.9)We also used multiple comparison of means and Tukey contrasts to compare factor levels.E.2 Plunge StudyE.2.1 Drilling DurationLinear mixed-effects model fit by REMLData: plungeAIC BIC logLik-3342.4 -3191.5 1698.2Random effects:Formula: ?1 | Subject(Intercept)StdDev: 0.11808Formula: ?Rep5 | Block %in% SubjectStructure: General positive-definite, Log-Cholesky parametrizationStdDev Corr(Intercept) 0.1006543 (Intr)Rep5 0.0092196 -0.068Residual 0.0813968Variance function:Structure: Different standard deviations per stratumFormula: ?1 | BlockParameter estimates:HSS0 BP0 HSSL BPL HSSM BPM HSSH BPH1.00000 1.25513 0.96864 1.25648 0.74778 0.86505 1.07317 1.00932Fixed effects: log10(td) ? Rep5 + Drillbit + Damping + cmeanF + Rep5:Damping+ Rep5:cmeanF + Drillbit:cmeanF + Damping:cmeanFValue Std.Error DF t-value p-value(Intercept) 0.213037 0.0288955 1775 7.3727 0.0000Rep5 -0.008817 0.0019357 1775 -4.5551 0.0000DrillbitBP 0.267828 0.0152546 171 17.5571 0.0000269APPENDIX E. STATISTICAL ANALYSISDampingL -0.019289 0.0212021 171 -0.9098 0.3642DampingM 0.016700 0.0208106 171 0.8025 0.4234DampingH 0.137684 0.0217301 171 6.3361 0.0000cmeanF -0.016845 0.0010112 1775 -16.6593 0.0000Rep5:DampingL 0.000699 0.0027269 1775 0.2564 0.7976Rep5:DampingM 0.003779 0.0025555 1775 1.4788 0.1394Rep5:DampingH -0.001806 0.0027456 1775 -0.6578 0.5108Rep5:cmeanF 0.000151 0.0000954 1775 1.5801 0.1143DrillbitBP:cmeanF -0.004488 0.0010235 1775 -4.3852 0.0000DampingL:cmeanF 0.002054 0.0013301 1775 1.5445 0.1227DampingM:cmeanF 0.005126 0.0013124 1775 3.9060 0.0001DampingH:cmeanF -0.006039 0.0015757 1775 -3.8327 0.0001Correlation:(Intr) Rep5 DrllBP DmpngL DmpngM DmpngH cmeanFRep5 -0.041DrillbitBP -0.251 -0.003DampingL -0.364 0.058 0.013DampingM -0.366 0.060 -0.010 0.501DampingH -0.339 0.058 -0.061 0.478 0.491cmeanF 0.009 0.060 -0.104 0.040 0.048 0.057Rep5:DampingL 0.030 -0.702 -0.002 -0.089 -0.042 -0.038 -0.042Rep5:DampingM 0.028 -0.758 0.008 -0.044 -0.079 -0.045 -0.054Rep5:DampingH 0.026 -0.715 0.014 -0.042 -0.043 -0.104 -0.041Rep5:cmeanF 0.010 -0.069 -0.030 -0.009 -0.007 -0.015 0.056DrillbitBP:cmeanF -0.048 -0.021 -0.064 -0.003 0.006 0.029 -0.284DampingL:cmeanF 0.031 -0.042 0.002 -0.130 -0.036 -0.036 -0.621DampingM:cmeanF 0.030 -0.033 0.011 -0.034 -0.041 -0.034 -0.644DampingH:cmeanF 0.041 -0.029 -0.065 -0.031 -0.029 0.175 -0.520Rp5:DL Rp5:DM Rp5:DH Rp5:cF DrBP:F DmpL:F DmpM:FRep5DrillbitBPDampingLDampingMDampingHcmeanFRep5:DampingLRep5:DampingM 0.532Rep5:DampingH 0.487 0.544Rep5:cmeanF -0.055 0.058 0.191DrillbitBP:cmeanF 0.009 0.036 0.016 -0.006DampingL:cmeanF 0.075 0.030 0.034 0.038 -0.092DampingM:cmeanF 0.034 -0.010 0.009 -0.095 -0.101 0.510DampingH:cmeanF 0.028 0.018 -0.060 -0.056 -0.054 0.425 0.448Standardized Within-Group Residuals:Min Q1 Med Q3 Max-3.623486 -0.561968 -0.043438 0.488233 5.561662270APPENDIX E. STATISTICAL ANALYSISNumber of Observations: 1985Number of Groups:Subject Block %in% Subject25 200Approximate 95% confidence intervalsFixed effects:lower est. upper(Intercept) 0.15636451 0.21303729 0.2697101Rep5 -0.01261404 -0.00881747 -0.0050209DrillbitBP 0.23771591 0.26782754 0.2979392DampingL -0.06114097 -0.01928950 0.0225620DampingM -0.02437904 0.01669965 0.0577783DampingH 0.09479056 0.13768425 0.1805780cmeanF -0.01882864 -0.01684543 -0.0148622Rep5:DampingL -0.00464899 0.00069932 0.0060476Rep5:DampingM -0.00123301 0.00377916 0.0087913Rep5:DampingH -0.00719085 -0.00180593 0.0035790Rep5:cmeanF -0.00003635 0.00015068 0.0003377DrillbitBP:cmeanF -0.00649559 -0.00448822 -0.0024808DampingL:cmeanF -0.00055443 0.00205432 0.0046631DampingM:cmeanF 0.00255227 0.00512632 0.0077004DampingH:cmeanF -0.00912962 -0.00603918 -0.0029487Random Effects:Level: Subjectlower est. uppersd((Intercept)) 0.086516 0.11808 0.16115Level: Blocklower est. uppersd((Intercept)) 0.0896631 0.1006543 0.112993sd(Rep5) 0.0075705 0.0092196 0.011228cor((Intercept),Rep5) -0.2861013 -0.0684870 0.155846Variance function:lower est. upperBP0 1.08876 1.25513 1.44692HSSL 0.83954 0.96864 1.11759BPL 1.08945 1.25648 1.44911HSSM 0.64713 0.74778 0.86408BPM 0.74743 0.86505 1.00119HSSH 0.92925 1.07317 1.23938BPH 0.87367 1.00932 1.16604Within-group standard error:lower est. upper0.073356 0.081397 0.090319Simultaneous Tests for General Linear Hypotheses271APPENDIX E. STATISTICAL ANALYSISMultiple Comparisons of Means: Tukey ContrastsFit: lme.formula(fixed = log10(td) ? Rep5 + Block + Rep5:Block, data = plunge,random = list(Subject = ?1, Block = ?Rep5), weights = varIdent(form = ?1 |Block), method = \"REML\", control = ctrl)Linear Hypotheses:Estimate Std. Error z value Pr(>|z|)BP0 - HSS0 == 0 0.1488 0.0375 3.97 <0.01 **HSSL - HSS0 == 0 -0.0436 0.0371 -1.18 0.939BPL - HSS0 == 0 0.0919 0.0375 2.45 0.218HSSM - HSS0 == 0 0.0376 0.0369 1.02 0.972BPM - HSS0 == 0 0.1839 0.0370 4.97 <0.01 ***HSSH - HSS0 == 0 0.2722 0.0372 7.31 <0.01 ***BPH - HSS0 == 0 0.4113 0.0372 11.06 <0.01 ***HSSL - BP0 == 0 -0.1924 0.0373 -5.16 <0.01 ***BPL - BP0 == 0 -0.0569 0.0377 -1.51 0.804HSSM - BP0 == 0 -0.1112 0.0371 -3.00 0.055 .BPM - BP0 == 0 0.0351 0.0372 0.94 0.982HSSH - BP0 == 0 0.1234 0.0374 3.30 0.022 *BPH - BP0 == 0 0.2625 0.0374 7.02 <0.01 ***BPL - HSSL == 0 0.1356 0.0373 3.63 <0.01 **HSSM - HSSL == 0 0.0812 0.0367 2.21 0.344BPM - HSSL == 0 0.2275 0.0368 6.19 <0.01 ***HSSH - HSSL == 0 0.3158 0.0370 8.53 <0.01 ***BPH - HSSL == 0 0.4550 0.0370 12.31 <0.01 ***HSSM - BPL == 0 -0.0543 0.0371 -1.46 0.827BPM - BPL == 0 0.0920 0.0372 2.47 0.208HSSH - BPL == 0 0.1803 0.0375 4.81 <0.01 ***BPH - BPL == 0 0.3194 0.0374 8.54 <0.01 ***BPM - HSSM == 0 0.1463 0.0366 4.00 <0.01 **HSSH - HSSM == 0 0.2346 0.0368 6.37 <0.01 ***BPH - HSSM == 0 0.3738 0.0367 10.17 <0.01 ***HSSH - BPM == 0 0.0883 0.0369 2.39 0.245BPH - BPM == 0 0.2274 0.0368 6.17 <0.01 ***BPH - HSSH == 0 0.1391 0.0371 3.75 <0.01 **---Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.1 1(Adjusted p values reported -- single-step method)E.2.2 Drill PlungeLinear mixed-effects model fit by REMLData: plungeAIC BIC logLik-2080.2 -1985.1 1057.1Random effects:272APPENDIX E. STATISTICAL ANALYSIS(a) Residuals (b) QQ-Block Residuals(c) QQ-Subject Intercept (d) FittedFigure E.1 LME Model Diagnostics - Drilling Force273APPENDIX E. STATISTICAL ANALYSISFormula: ?1 | Subject(Intercept)StdDev: 0.17518Formula: ?Rep5 | Block %in% SubjectStructure: General positive-definite, Log-Cholesky parametrizationStdDev Corr(Intercept) 0.120382 (Intr)Rep5 0.015763 -0.065Residual 0.129541Variance function:Structure: Different standard deviations per stratumFormula: ?1 | BlockParameter estimates:HSS0 BP0 HSSL BPL HSSM BPM HSSH BPH1.00000 0.97433 0.81739 0.70700 0.87472 0.84179 1.05090 1.03096Fixed effects: log10(mZ) ? Drillbit + DampingValue Std.Error DF t-value p-value(Intercept) 1.23073 0.040357 1785 30.4962 0.0000DrillbitBP 0.04912 0.017807 171 2.7583 0.0064DampingL -0.14417 0.025094 171 -5.7453 0.0000DampingM -0.59644 0.025201 171 -23.6675 0.0000DampingH -0.68269 0.025435 171 -26.8405 0.0000Correlation:(Intr) DrllBP DmpngL DmpngMDrillbitBP -0.221DampingL -0.317 -0.002DampingM -0.316 0.000 0.508DampingH -0.313 0.000 0.504 0.502Standardized Within-Group Residuals:Min Q1 Med Q3 Max-4.829509 -0.597304 -0.013428 0.543319 4.871540Number of Observations: 1985Number of Groups:Subject Block %in% Subject25 200Approximate 95% confidence intervalsFixed effects:lower est. upper(Intercept) 1.151580 1.230732 1.309883DrillbitBP 0.013966 0.049115 0.084264DampingL -0.193707 -0.144173 -0.094639DampingM -0.646185 -0.596440 -0.546695DampingH -0.732897 -0.682690 -0.632483274APPENDIX E. STATISTICAL ANALYSISRandom Effects:Level: Subjectlower est. uppersd((Intercept)) 0.12953 0.17518 0.2369Level: Blocklower est. uppersd((Intercept)) 0.107133 0.120382 0.135270sd(Rep5) 0.013303 0.015763 0.018678cor((Intercept),Rep5) -0.256125 -0.065413 0.130200Variance function:lower est. upperBP0 0.84861 0.97433 1.11867HSSL 0.71200 0.81739 0.93837BPL 0.61527 0.70700 0.81241HSSM 0.75935 0.87472 1.00763BPM 0.73204 0.84179 0.96799HSSH 0.91572 1.05090 1.20603BPH 0.89873 1.03096 1.18264Within-group standard error:lower est. upper0.11736 0.12954 0.14298Simultaneous Tests for General Linear HypothesesMultiple Comparisons of Means: Tukey ContrastsFit: lme.formula(fixed = log10(mZ) ? Rep5 + Block + Rep5:Block, data = plunge,random = list(Subject = ?1, Block = ?Rep5), weights = varIdent(form = ?1 |Block), method = \"REML\", control = ctrl)Linear Hypotheses:Estimate Std. Error z value Pr(>|z|)BP0 - HSS0 == 0 0.0665 0.0361 1.84 0.5922HSSL - HSS0 == 0 -0.1312 0.0359 -3.66 0.0063 **BPL - HSS0 == 0 -0.0968 0.0357 -2.71 0.1194HSSM - HSS0 == 0 -0.5811 0.0360 -16.15 <0.001 ***BPM - HSS0 == 0 -0.5585 0.0359 -15.55 <0.001 ***HSSH - HSS0 == 0 -0.6946 0.0363 -19.14 <0.001 ***BPH - HSS0 == 0 -0.6197 0.0363 -17.09 <0.001 ***HSSL - BP0 == 0 -0.1977 0.0358 -5.52 <0.001 ***BPL - BP0 == 0 -0.1633 0.0357 -4.58 <0.001 ***HSSM - BP0 == 0 -0.6476 0.0359 -18.03 <0.001 ***BPM - BP0 == 0 -0.6250 0.0359 -17.43 <0.001 ***HSSH - BP0 == 0 -0.7611 0.0362 -21.00 <0.001 ***BPH - BP0 == 0 -0.6863 0.0362 -18.95 <0.001 ***BPL - HSSL == 0 0.0344 0.0354 0.97 0.9782HSSM - HSSL == 0 -0.4499 0.0357 -12.62 <0.001 ***275APPENDIX E. STATISTICAL ANALYSISBPM - HSSL == 0 -0.4273 0.0356 -12.00 <0.001 ***HSSH - HSSL == 0 -0.5633 0.0360 -15.66 <0.001 ***BPH - HSSL == 0 -0.4885 0.0359 -13.59 <0.001 ***HSSM - BPL == 0 -0.4843 0.0355 -13.65 <0.001 ***BPM - BPL == 0 -0.4617 0.0354 -13.03 <0.001 ***HSSH - BPL == 0 -0.5978 0.0358 -16.69 <0.001 ***BPH - BPL == 0 -0.5229 0.0358 -14.61 <0.001 ***BPM - HSSM == 0 0.0226 0.0357 0.63 0.9984HSSH - HSSM == 0 -0.1135 0.0361 -3.15 0.0356 *BPH - HSSM == 0 -0.0387 0.0360 -1.07 0.9625HSSH - BPM == 0 -0.1360 0.0360 -3.78 0.0040 **BPH - BPM == 0 -0.0612 0.0360 -1.70 0.6868BPH - HSSH == 0 0.0748 0.0364 2.06 0.4434---Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.1 1(Adjusted p values reported -- single-step method)E.2.3 Mean Drilling ForceLinear mixed-effects model fit by REMLData: plungeAIC BIC logLik-4565 -4447.7 2303.5Random effects:Formula: ?1 | Subject(Intercept)StdDev: 0.12227Formula: ?Rep5 | Block %in% SubjectStructure: General positive-definite, Log-Cholesky parametrizationStdDev Corr(Intercept) 0.0741798 (Intr)Rep5 0.0055565 -0.005Residual 0.0774994Variance function:Structure: Different standard deviations per stratumFormula: ?1 | BlockParameter estimates:HSS0 BP0 HSSL BPL HSSM BPM HSSH BPH1.00000 0.68094 0.91071 0.66770 0.81549 0.55335 1.20172 0.75380Fixed effects: log10(meanF) ? Rep5 + Drillbit + Damping + Rep5:DampingValue Std.Error DF t-value p-value(Intercept) 1.24342 0.0273561 1782 45.453 0.0000Rep5 -0.00041 0.0012623 1782 -0.321 0.7483DrillbitBP 0.15920 0.0108970 171 14.609 0.0000276APPENDIX E. STATISTICAL ANALYSIS(a) Residuals (b) QQ-Block Residuals(c) QQ-Subject Intercept (d) Fitted vs. MeasuredFigure E.2 LME Model Diagnostics - Drill Plunge Depth277APPENDIX E. STATISTICAL ANALYSISDampingL 0.03660 0.0153936 171 2.378 0.0185DampingM -0.02018 0.0153339 171 -1.316 0.1900DampingH -0.13509 0.0155379 171 -8.694 0.0000Rep5:DampingL -0.00232 0.0017576 1782 -1.322 0.1864Rep5:DampingM 0.00231 0.0016954 1782 1.362 0.1733Rep5:DampingH 0.00452 0.0018700 1782 2.418 0.0157Correlation:(Intr) Rep5 DrllBP DmpngL DmpngM DmpngH Rp5:DL Rp5:DMRep5 -0.015DrillbitBP -0.205 0.002DampingL -0.283 0.027 0.003DampingM -0.284 0.027 0.003 0.504DampingH -0.279 0.026 -0.006 0.498 0.500Rep5:DampingL 0.011 -0.718 0.000 -0.037 -0.019 -0.019Rep5:DampingM 0.011 -0.745 0.000 -0.020 -0.034 -0.020 0.535Rep5:DampingH 0.010 -0.675 0.001 -0.018 -0.018 -0.042 0.485 0.503Standardized Within-Group Residuals:Min Q1 Med Q3 Max-8.481314 -0.481330 0.010115 0.496646 4.405674Number of Observations: 1986Number of Groups:Subject Block %in% Subject25 200Approximate 95% confidence intervalsFixed effects:lower est. upper(Intercept) 1.18976908 1.24342255 1.2970760Rep5 -0.00288098 -0.00040514 0.0020707DrillbitBP 0.13768879 0.15919872 0.1807087DampingL 0.00621614 0.03660209 0.0669881DampingM -0.05044568 -0.02017755 0.0100906DampingH -0.16575828 -0.13508750 -0.1044167Rep5:DampingL -0.00577010 -0.00232299 0.0011241Rep5:DampingM -0.00101556 0.00230953 0.0056346Rep5:DampingH 0.00085451 0.00452204 0.0081896Random Effects:Level: Subjectlower est. uppersd((Intercept)) 0.090849 0.12227 0.16455Level: Blocklower est. uppersd((Intercept)) 0.0660710 0.0741798 0.0832839sd(Rep5) 0.0042878 0.0055565 0.0072007cor((Intercept),Rep5) -0.2223696 -0.0048211 0.2131848278APPENDIX E. STATISTICAL ANALYSISVariance function:lower est. upperBP0 0.59528 0.68094 0.77893HSSL 0.79495 0.91071 1.04332BPL 0.58353 0.66770 0.76402HSSM 0.71178 0.81549 0.93432BPM 0.48335 0.55335 0.63348HSSH 1.05073 1.20172 1.37440BPH 0.65915 0.75380 0.86203Within-group standard error:lower est. upper0.070514 0.077499 0.085177Simultaneous Tests for General Linear HypothesesMultiple Comparisons of Means: Tukey ContrastsFit: lme.formula(fixed = log10(meanF) ? Rep5 + Block + Rep5:Block,data = plunge, random = list(Subject = ?1, Block = ?Rep5),weights = varIdent(form = ?1 | Block), method = \"REML\", control = ctrl)Linear Hypotheses:Estimate Std. Error z value Pr(>|z|)BP0 - HSS0 == 0 0.14732 0.02167 6.80 <0.001 ***HSSL - HSS0 == 0 0.04774 0.02189 2.18 0.3631BPL - HSS0 == 0 0.17285 0.02167 7.98 <0.001 ***HSSM - HSS0 == 0 -0.02343 0.02179 -1.08 0.9620BPM - HSS0 == 0 0.12926 0.02159 5.99 <0.001 ***HSSH - HSS0 == 0 -0.16737 0.02192 -7.63 <0.001 ***BPH - HSS0 == 0 0.04395 0.02174 2.02 0.4676HSSL - BP0 == 0 -0.09958 0.02158 -4.62 <0.001 ***BPL - BP0 == 0 0.02553 0.02135 1.20 0.9334HSSM - BP0 == 0 -0.17075 0.02148 -7.95 <0.001 ***BPM - BP0 == 0 -0.01805 0.02127 -0.85 0.9902HSSH - BP0 == 0 -0.31468 0.02161 -14.56 <0.001 ***BPH - BP0 == 0 -0.10337 0.02143 -4.82 <0.001 ***BPL - HSSL == 0 0.12511 0.02157 5.80 <0.001 ***HSSM - HSSL == 0 -0.07117 0.02169 -3.28 0.0232 *BPM - HSSL == 0 0.08152 0.02149 3.79 0.0038 **HSSH - HSSL == 0 -0.21511 0.02183 -9.86 <0.001 ***BPH - HSSL == 0 -0.00379 0.02164 -0.18 1.0000HSSM - BPL == 0 -0.19628 0.02147 -9.14 <0.001 ***BPM - BPL == 0 -0.04359 0.02126 -2.05 0.4481HSSH - BPL == 0 -0.34022 0.02161 -15.75 <0.001 ***BPH - BPL == 0 -0.12890 0.02142 -6.02 <0.001 ***BPM - HSSM == 0 0.15269 0.02139 7.14 <0.001 ***HSSH - HSSM == 0 -0.14394 0.02173 -6.62 <0.001 ***BPH - HSSM == 0 0.06738 0.02155 3.13 0.0373 *279APPENDIX E. STATISTICAL ANALYSISHSSH - BPM == 0 -0.29663 0.02153 -13.78 <0.001 ***BPH - BPM == 0 -0.08531 0.02134 -4.00 0.0018 **BPH - HSSH == 0 0.21132 0.02168 9.75 <0.001 ***---Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.1 1(Adjusted p values reported -- single-step method)E.2.4 Prebreakthrough ForceLinear mixed-effects model fit by REMLData: plungeAIC BIC logLik-2950.9 -2833.5 1496.5Random effects:Formula: ?1 | Subject(Intercept)StdDev: 0.12968Formula: ?Rep5 | Block %in% SubjectStructure: General positive-definite, Log-Cholesky parametrizationStdDev Corr(Intercept) 0.0818239 (Intr)Rep5 0.0073682 0.093Residual 0.0886243Variance function:Structure: Different standard deviations per stratumFormula: ?1 | BlockParameter estimates:HSS0 HSSL HSSM HSSH BP0 BPL BPM BPH1.00000 0.99451 0.86684 1.90513 0.83259 0.78120 1.83057 1.03145Fixed effects: log10(pbf) ? Rep5 + Drillbit + Damping + Rep5:DampingValue Std.Error DF t-value p-value(Intercept) 1.27888 0.0293434 1781 43.583 0.0000Rep5 -0.00130 0.0016334 1781 -0.794 0.4272DrillbitBP 0.17175 0.0125570 171 13.678 0.0000DampingL 0.03997 0.0171591 171 2.330 0.0210DampingM -0.05965 0.0176893 171 -3.372 0.0009DampingH -0.13951 0.0178236 171 -7.827 0.0000Rep5:DampingL -0.00244 0.0022861 1781 -1.069 0.2851Rep5:DampingM 0.00718 0.0025394 1781 2.829 0.0047Rep5:DampingH 0.00670 0.0026810 1781 2.501 0.0125Correlation:(Intr) Rep5 DrllBP DmpngL DmpngM DmpngH Rp5:DLRep5 0.006DrillbitBP -0.218 0.004DampingL -0.293 -0.012 -0.001280APPENDIX E. STATISTICAL ANALYSIS(a) Residuals (b) QQ-Block Residuals(c) QQ-Subject Intercepts (d) Fitted vs. MeasuredFigure E.3 LME Model Diagnostics - Mean Drilling Force.281APPENDIX E. STATISTICAL ANALYSISDampingM -0.295 -0.012 0.051 0.486DampingH -0.274 -0.012 -0.036 0.483 0.466Rep5:DampingL -0.005 -0.714 0.001 0.019 0.009 0.008Rep5:DampingM -0.001 -0.643 -0.015 0.008 0.004 0.008 0.460Rep5:DampingH -0.006 -0.609 0.007 0.008 0.008 -0.004 0.435Rp5:DMRep5DrillbitBPDampingLDampingMDampingHRep5:DampingLRep5:DampingMRep5:DampingH 0.392Standardized Within-Group Residuals:Min Q1 Med Q3 Max-12.712281 -0.435584 0.051708 0.496546 3.938728Number of Observations: 1985Number of Groups:Subject Block %in% Subject25 200Approximate 95% confidence intervalsFixed effects:lower est. upper(Intercept) 1.2213261 1.2788771 1.3364282Rep5 -0.0045006 -0.0012971 0.0019064DrillbitBP 0.1469628 0.1717494 0.1965361DampingL 0.0061020 0.0399729 0.0738439DampingM -0.0945708 -0.0596534 -0.0247359DampingH -0.1746960 -0.1395133 -0.1043306Rep5:DampingL -0.0069283 -0.0024445 0.0020392Rep5:DampingM 0.0022040 0.0071845 0.0121650Rep5:DampingH 0.0014460 0.0067041 0.0119623Random Effects:Level: Subjectlower est. uppersd((Intercept)) 0.096101 0.12968 0.17498Level: Blocklower est. uppersd((Intercept)) 0.0722169 0.0818239 0.0927090sd(Rep5) 0.0055368 0.0073682 0.0098054cor((Intercept),Rep5) -0.1566943 0.0931978 0.3318753Variance function:282APPENDIX E. STATISTICAL ANALYSISlower est. upperHSSL 0.86846 0.99451 1.13885HSSM 0.75651 0.86684 0.99326HSSH 1.66657 1.90513 2.17785BP0 0.72847 0.83259 0.95159BPL 0.68276 0.78120 0.89383BPM 1.60291 1.83057 2.09057BPH 0.90351 1.03145 1.17751Within-group standard error:lower est. upper0.080651 0.088624 0.097385Simultaneous Tests for General Linear HypothesesMultiple Comparisons of Means: Tukey ContrastsFit: lme.formula(fixed = log10(pbf) ? Rep5 + Block + Rep5:Block, data = plunge,random = list(Subject = ?1, Block = ?Rep5), weights = varIdent(form = ?1 |Block), method = \"REML\", control = ctrl)Linear Hypotheses:Estimate Std. Error z value Pr(>|z|)BP0 - HSS0 == 0 0.15330 0.02402 6.38 <0.01 ***HSSL - HSS0 == 0 0.05019 0.02422 2.07 0.432BPL - HSS0 == 0 0.18360 0.02396 7.66 <0.01 ***HSSM - HSS0 == 0 -0.07761 0.02406 -3.23 0.028 *BPM - HSS0 == 0 0.11544 0.02576 4.48 <0.01 ***HSSH - HSS0 == 0 -0.17486 0.02596 -6.74 <0.01 ***BPH - HSS0 == 0 0.04328 0.02428 1.78 0.631HSSL - BP0 == 0 -0.10311 0.02400 -4.30 <0.01 ***BPL - BP0 == 0 0.03030 0.02375 1.28 0.908HSSM - BP0 == 0 -0.23091 0.02385 -9.68 <0.01 ***BPM - BP0 == 0 -0.03785 0.02556 -1.48 0.818HSSH - BP0 == 0 -0.32816 0.02576 -12.74 <0.01 ***BPH - BP0 == 0 -0.11002 0.02407 -4.57 <0.01 ***BPL - HSSL == 0 0.13341 0.02395 5.57 <0.01 ***HSSM - HSSL == 0 -0.12780 0.02405 -5.31 <0.01 ***BPM - HSSL == 0 0.06525 0.02575 2.53 0.180HSSH - HSSL == 0 -0.22506 0.02595 -8.67 <0.01 ***BPH - HSSL == 0 -0.00691 0.02427 -0.28 1.000HSSM - BPL == 0 -0.26121 0.02379 -10.98 <0.01 ***BPM - BPL == 0 -0.06816 0.02551 -2.67 0.131HSSH - BPL == 0 -0.35847 0.02571 -13.94 <0.01 ***BPH - BPL == 0 -0.14032 0.02401 -5.84 <0.01 ***BPM - HSSM == 0 0.19305 0.02560 7.54 <0.01 ***HSSH - HSSM == 0 -0.09726 0.02580 -3.77 <0.01 **BPH - HSSM == 0 0.12089 0.02411 5.01 <0.01 ***HSSH - BPM == 0 -0.29031 0.02739 -10.60 <0.01 ***BPH - BPM == 0 -0.07216 0.02580 -2.80 0.095 .283APPENDIX E. STATISTICAL ANALYSISBPH - HSSH == 0 0.21815 0.02600 8.39 <0.01 ***---Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.1 1(Adjusted p values reported -- single-step method)(a) Residuals (b) QQ-Block Residuals(c) QQ-Subject Intercept (d) Fitted vs. MeasuredFigure E.4 LME Model Diagnostics - Prebreakthrough Force284APPENDIX E. STATISTICAL ANALYSISE.2.5 Estimated Human ForceLinear mixed-effects model fit by REMLData: plungeAIC BIC logLik-4445.9 -4217.1 2263.9Random effects:Formula: ?1 | Subject(Intercept)StdDev: 0.049794Formula: ?Rep5 | Block %in% SubjectStructure: General positive-definite, Log-Cholesky parametrizationStdDev Corr(Intercept) 0.0603394 (Intr)Rep5 0.0050983 0.033Residual 0.0603323Variance function:Structure: Different standard deviations per stratumFormula: ?1 | BlockParameter estimates:HSS0 HSSM BP0 BPM HSSL HSSH BPL BPH1.00000 0.83506 0.96726 0.86428 0.87280 1.92056 0.80596 1.24462Fixed effects: log10(Fh) ? Rep5 + Drillbit + Damping + cmeanF + Drillbit:Damping +Rep5:Drillbit + Rep5:Damping + Rep5:cmeanF + Drillbit:cmeanF + Damping:cmeanF +Rep5:Drillbit:Damping + Rep5:Damping:cmeanF + Rep5:Drillbit:Damping:cmeanFValue Std.Error DF t-value(Intercept) 1.31925 0.0161929 1765 81.471Rep5 0.00060 0.0017027 1765 0.351DrillbitBP 0.06300 0.0184495 168 3.415DampingL 0.03866 0.0178933 168 2.160DampingM 0.41257 0.0180143 168 22.902DampingH 0.71053 0.0212785 168 33.392cmeanF 0.01546 0.0007066 1765 21.873DrillbitBP:DampingL -0.03339 0.0257731 168 -1.296DrillbitBP:DampingM -0.14953 0.0259705 168 -5.758DrillbitBP:DampingH -0.29149 0.0282164 168 -10.330Rep5:DrillbitBP -0.00211 0.0026211 1765 -0.805Rep5:DampingL -0.00172 0.0023012 1765 -0.749Rep5:DampingM 0.00056 0.0023525 1765 0.239Rep5:DampingH 0.00580 0.0042627 1765 1.360Rep5:cmeanF -0.00011 0.0001684 1765 -0.642DrillbitBP:cmeanF -0.00183 0.0006914 1765 -2.651DampingL:cmeanF 0.00112 0.0008610 1765 1.303DampingM:cmeanF -0.00159 0.0009400 1765 -1.689DampingH:cmeanF 0.01108 0.0012798 1765 8.661Rep5:DrillbitBP:DampingL 0.00250 0.0035417 1765 0.705285APPENDIX E. STATISTICAL ANALYSISRep5:DrillbitBP:DampingM 0.00713 0.0035050 1765 2.033Rep5:DrillbitBP:DampingH 0.00391 0.0050784 1765 0.770Rep5:DampingL:cmeanF 0.00065 0.0002318 1765 2.815Rep5:DampingM:cmeanF -0.00051 0.0002385 1765 -2.156Rep5:DampingH:cmeanF 0.00039 0.0003861 1765 1.023Rep5:DrillbitBP:Damping0:cmeanF 0.00033 0.0002732 1765 1.216Rep5:DrillbitBP:DampingL:cmeanF -0.00048 0.0002163 1765 -2.241Rep5:DrillbitBP:DampingM:cmeanF 0.00028 0.0002534 1765 1.124Rep5:DrillbitBP:DampingH:cmeanF -0.00061 0.0004328 1765 -1.418p-value(Intercept) 0.0000Rep5 0.7254DrillbitBP 0.0008DampingL 0.0322DampingM 0.0000DampingH 0.0000cmeanF 0.0000DrillbitBP:DampingL 0.1969DrillbitBP:DampingM 0.0000DrillbitBP:DampingH 0.0000Rep5:DrillbitBP 0.4209Rep5:DampingL 0.4537Rep5:DampingM 0.8113Rep5:DampingH 0.1741Rep5:cmeanF 0.5208DrillbitBP:cmeanF 0.0081DampingL:cmeanF 0.1927DampingM:cmeanF 0.0914DampingH:cmeanF 0.0000Rep5:DrillbitBP:DampingL 0.4807Rep5:DrillbitBP:DampingM 0.0422Rep5:DrillbitBP:DampingH 0.4413Rep5:DampingL:cmeanF 0.0049Rep5:DampingM:cmeanF 0.0312Rep5:DampingH:cmeanF 0.3065Rep5:DrillbitBP:Damping0:cmeanF 0.2241Rep5:DrillbitBP:DampingL:cmeanF 0.0252Rep5:DrillbitBP:DampingM:cmeanF 0.2612Rep5:DrillbitBP:DampingH:cmeanF 0.1562Correlation:(Intr) Rep5 DrllBP DmpngL DmpngMRep5 -0.003DrillbitBP -0.555 -0.009DampingL -0.562 0.003 0.503DampingM -0.556 0.006 0.502 0.504DampingH -0.466 0.011 0.427 0.423 0.431cmeanF 0.091 0.112 -0.187 -0.080 -0.053DrillbitBP:DampingL 0.399 0.009 -0.708 -0.703 -0.358286APPENDIX E. STATISTICAL ANALYSISDrillbitBP:DampingM 0.394 0.006 -0.708 -0.357 -0.714DrillbitBP:DampingH 0.358 -0.001 -0.658 -0.325 -0.334Rep5:DrillbitBP -0.001 -0.654 0.011 0.001 0.001Rep5:DampingL 0.004 -0.738 0.009 -0.010 -0.003Rep5:DampingM 0.000 -0.727 0.004 -0.001 -0.029Rep5:DampingH -0.001 -0.402 0.001 0.000 -0.005Rep5:cmeanF 0.034 0.150 -0.043 -0.030 -0.027DrillbitBP:cmeanF -0.033 -0.040 -0.074 0.024 -0.032DampingL:cmeanF -0.057 -0.070 0.176 0.058 0.059DampingM:cmeanF -0.053 -0.065 0.158 0.048 0.145DampingH:cmeanF -0.035 -0.044 0.111 0.033 0.045Rep5:DrillbitBP:DampingL 0.000 0.483 -0.009 0.004 -0.002Rep5:DrillbitBP:DampingM 0.002 0.491 -0.007 -0.002 0.017Rep5:DrillbitBP:DampingH 0.002 0.340 -0.003 -0.002 0.001Rep5:DampingL:cmeanF -0.021 -0.104 0.036 0.034 0.023Rep5:DampingM:cmeanF -0.026 -0.109 0.027 0.023 -0.011Rep5:DampingH:cmeanF -0.016 -0.067 0.016 0.014 0.010Rep5:DrillbitBP:Damping0:cmeanF -0.015 -0.085 0.002 0.013 0.008Rep5:DrillbitBP:DampingL:cmeanF -0.005 -0.006 -0.009 -0.011 -0.005Rep5:DrillbitBP:DampingM:cmeanF 0.003 0.004 0.006 -0.002 0.021Rep5:DrillbitBP:DampingH:cmeanF 0.001 0.002 0.003 -0.001 0.002DmpngH cmeanF DBP:DL DBP:DM DBP:DHRep5DrillbitBPDampingLDampingMDampingHcmeanF 0.009DrillbitBP:DampingL -0.301 0.153DrillbitBP:DampingM -0.309 0.126 0.503DrillbitBP:DampingH -0.755 0.063 0.460 0.470Rep5:DrillbitBP 0.000 -0.111 -0.006 -0.007 -0.007Rep5:DampingL -0.002 -0.066 -0.009 -0.006 -0.006Rep5:DampingM -0.018 -0.106 -0.007 0.024 0.011Rep5:DampingH -0.124 -0.067 -0.004 0.001 0.090Rep5:cmeanF -0.017 0.125 0.034 0.030 0.021DrillbitBP:cmeanF -0.117 -0.361 -0.022 0.046 0.163DampingL:cmeanF 0.061 -0.628 -0.210 -0.124 -0.129DampingM:cmeanF 0.063 -0.584 -0.107 -0.244 -0.120DampingH:cmeanF 0.406 -0.390 -0.078 -0.089 -0.336Rep5:DrillbitBP:DampingL -0.003 0.073 0.003 0.006 0.009Rep5:DrillbitBP:DampingM 0.006 0.097 0.005 -0.019 -0.001Rep5:DrillbitBP:DampingH 0.089 0.077 0.004 0.001 -0.072Rep5:DampingL:cmeanF 0.027 -0.050 -0.051 -0.026 -0.032Rep5:DampingM:cmeanF 0.002 -0.115 -0.025 0.012 -0.004Rep5:DampingH:cmeanF -0.071 -0.069 -0.015 -0.011 0.049Rep5:DrillbitBP:Damping0:cmeanF -0.001 -0.011 -0.009 -0.002 0.009Rep5:DrillbitBP:DampingL:cmeanF -0.018 -0.055 0.024 0.006 0.023287APPENDIX E. STATISTICAL ANALYSISRep5:DrillbitBP:DampingM:cmeanF 0.013 0.036 0.002 -0.022 -0.016Rep5:DrillbitBP:DampingH:cmeanF 0.058 0.015 0.001 -0.002 -0.050Rp5:DBP Rp5:DL Rp5:DM Rp5:DH Rp5:cFRep5DrillbitBPDampingLDampingMDampingHcmeanFDrillbitBP:DampingLDrillbitBP:DampingMDrillbitBP:DampingHRep5:DrillbitBPRep5:DampingL 0.484Rep5:DampingM 0.473 0.534Rep5:DampingH 0.261 0.295 0.295Rep5:cmeanF -0.102 -0.109 -0.111 -0.062DrillbitBP:cmeanF -0.010 -0.007 0.083 0.064 -0.046DampingL:cmeanF 0.091 0.093 0.044 0.022 -0.080DampingM:cmeanF 0.083 0.052 -0.037 0.019 -0.074DampingH:cmeanF 0.058 0.038 0.021 -0.107 -0.051Rep5:DrillbitBP:DampingL -0.740 -0.653 -0.348 -0.192 0.074Rep5:DrillbitBP:DampingM -0.748 -0.362 -0.673 -0.198 0.078Rep5:DrillbitBP:DampingH -0.516 -0.249 -0.249 -0.836 0.055Rep5:DampingL:cmeanF 0.074 0.076 0.072 0.038 -0.721Rep5:DampingM:cmeanF 0.072 0.077 0.245 0.049 -0.709Rep5:DampingH:cmeanF 0.044 0.047 0.052 0.606 -0.438Rep5:DrillbitBP:Damping0:cmeanF -0.279 0.060 0.066 0.038 -0.608Rep5:DrillbitBP:DampingL:cmeanF -0.001 0.007 0.012 0.010 -0.007Rep5:DrillbitBP:DampingM:cmeanF 0.001 0.001 -0.152 -0.007 0.004Rep5:DrillbitBP:DampingH:cmeanF 0.000 0.000 -0.004 -0.513 0.002DrBP:F DmpL:F DmpM:F DmpH:FRep5DrillbitBPDampingLDampingMDampingHcmeanFDrillbitBP:DampingLDrillbitBP:DampingMDrillbitBP:DampingHRep5:DrillbitBPRep5:DampingLRep5:DampingMRep5:DampingHRep5:cmeanFDrillbitBP:cmeanFDampingL:cmeanF -0.132288APPENDIX E. STATISTICAL ANALYSISDampingM:cmeanF -0.084 0.518DampingH:cmeanF -0.093 0.383 0.369Rep5:DrillbitBP:DampingL 0.027 -0.099 -0.063 -0.046Rep5:DrillbitBP:DampingM -0.021 -0.064 0.004 -0.037Rep5:DrillbitBP:DampingH -0.043 -0.040 -0.037 0.050Rep5:DampingL:cmeanF -0.058 0.161 0.061 0.050Rep5:DampingM:cmeanF 0.091 0.049 -0.040 0.025Rep5:DampingH:cmeanF 0.056 0.030 0.028 -0.070Rep5:DrillbitBP:Damping0:cmeanF 0.092 -0.029 -0.024 -0.020Rep5:DrillbitBP:DampingL:cmeanF 0.139 -0.069 -0.011 -0.015Rep5:DrillbitBP:DampingM:cmeanF -0.092 0.012 0.039 0.012Rep5:DrillbitBP:DampingH:cmeanF -0.041 0.006 0.005 0.057Rp5:DBP:DL Rp5:DBP:DM Rp5:DBP:DHRep5DrillbitBPDampingLDampingMDampingHcmeanFDrillbitBP:DampingLDrillbitBP:DampingMDrillbitBP:DampingHRep5:DrillbitBPRep5:DampingLRep5:DampingMRep5:DampingHRep5:cmeanFDrillbitBP:cmeanFDampingL:cmeanFDampingM:cmeanFDampingH:cmeanFRep5:DrillbitBP:DampingLRep5:DrillbitBP:DampingM 0.553Rep5:DrillbitBP:DampingH 0.381 0.388Rep5:DampingL:cmeanF -0.055 -0.053 -0.035Rep5:DampingM:cmeanF -0.051 -0.167 -0.042Rep5:DampingH:cmeanF -0.031 -0.035 -0.507Rep5:DrillbitBP:Damping0:cmeanF 0.208 0.206 0.140Rep5:DrillbitBP:DampingL:cmeanF -0.199 -0.004 -0.007Rep5:DrillbitBP:DampingM:cmeanF -0.002 -0.035 0.004Rep5:DrillbitBP:DampingH:cmeanF -0.001 0.001 0.445R5:DL: R5:DM: R5:DH: R5:DBP:D0Rep5DrillbitBPDampingLDampingMDampingHcmeanF289APPENDIX E. STATISTICAL ANALYSISDrillbitBP:DampingLDrillbitBP:DampingMDrillbitBP:DampingHRep5:DrillbitBPRep5:DampingLRep5:DampingMRep5:DampingHRep5:cmeanFDrillbitBP:cmeanFDampingL:cmeanFDampingM:cmeanFDampingH:cmeanFRep5:DrillbitBP:DampingLRep5:DrillbitBP:DampingMRep5:DrillbitBP:DampingHRep5:DampingL:cmeanFRep5:DampingM:cmeanF 0.506Rep5:DampingH:cmeanF 0.312 0.313Rep5:DrillbitBP:Damping0:cmeanF 0.434 0.435 0.269Rep5:DrillbitBP:DampingL:cmeanF -0.502 0.013 0.008 0.013Rep5:DrillbitBP:DampingM:cmeanF 0.006 -0.465 -0.006 -0.008Rep5:DrillbitBP:DampingH:cmeanF 0.002 -0.004 -0.719 -0.004R5:DBP:DL: R5:DBP:DM:Rep5DrillbitBPDampingLDampingMDampingHcmeanFDrillbitBP:DampingLDrillbitBP:DampingMDrillbitBP:DampingHRep5:DrillbitBPRep5:DampingLRep5:DampingMRep5:DampingHRep5:cmeanFDrillbitBP:cmeanFDampingL:cmeanFDampingM:cmeanFDampingH:cmeanFRep5:DrillbitBP:DampingLRep5:DrillbitBP:DampingMRep5:DrillbitBP:DampingHRep5:DampingL:cmeanFRep5:DampingM:cmeanFRep5:DampingH:cmeanFRep5:DrillbitBP:Damping0:cmeanF290APPENDIX E. STATISTICAL ANALYSISRep5:DrillbitBP:DampingL:cmeanFRep5:DrillbitBP:DampingM:cmeanF -0.013Rep5:DrillbitBP:DampingH:cmeanF -0.006 0.004Standardized Within-Group Residuals:Min Q1 Med Q3 Max-9.783626 -0.449869 0.049669 0.555054 5.659678Number of Observations: 1986Number of Groups:Subject Block %in% Subject25 200Approximate 95% confidence intervalsFixed effects:lower est. upper(Intercept) 1.28749100 1.31925023 1.3510e+00Rep5 -0.00274136 0.00059825 3.9379e-03DrillbitBP 0.02657423 0.06299693 9.9420e-02DampingL 0.00333165 0.03865628 7.3981e-02DampingM 0.37700780 0.41257139 4.4813e-01DampingH 0.66851760 0.71052537 7.5253e-01cmeanF 0.01406991 0.01545577 1.6842e-02DrillbitBP:DampingL -0.08427088 -0.03339006 1.7491e-02DrillbitBP:DampingM -0.20080237 -0.14953181 -9.8261e-02DrillbitBP:DampingH -0.34719208 -0.29148763 -2.3578e-01Rep5:DrillbitBP -0.00725120 -0.00211032 3.0305e-03Rep5:DampingL -0.00623812 -0.00172466 2.7888e-03Rep5:DampingM -0.00405226 0.00056163 5.1755e-03Rep5:DampingH -0.00256388 0.00579660 1.4157e-02Rep5:cmeanF -0.00043847 -0.00010817 2.2214e-04DrillbitBP:cmeanF -0.00318887 -0.00183291 -4.7695e-04DampingL:cmeanF -0.00056659 0.00112213 2.8109e-03DampingM:cmeanF -0.00343122 -0.00158768 2.5587e-04DampingH:cmeanF 0.00857472 0.01108480 1.3595e-02Rep5:DrillbitBP:DampingL -0.00444820 0.00249810 9.4444e-03Rep5:DrillbitBP:DampingM 0.00025137 0.00712580 1.4000e-02Rep5:DrillbitBP:DampingH -0.00604927 0.00391108 1.3871e-02Rep5:DampingL:cmeanF 0.00019789 0.00065259 1.1073e-03Rep5:DampingM:cmeanF -0.00098203 -0.00051420 -4.6372e-05Rep5:DampingH:cmeanF -0.00036236 0.00039492 1.1522e-03Rep5:DrillbitBP:Damping0:cmeanF -0.00020357 0.00033228 8.6814e-04Rep5:DrillbitBP:DampingL:cmeanF -0.00090874 -0.00048459 -6.0445e-05Rep5:DrillbitBP:DampingM:cmeanF -0.00021220 0.00028477 7.8173e-04Rep5:DrillbitBP:DampingH:cmeanF -0.00146261 -0.00061383 2.3494e-04Random Effects:Level: Subject291APPENDIX E. STATISTICAL ANALYSISlower est. uppersd((Intercept)) 0.035314 0.049794 0.07021Level: Blocklower est. uppersd((Intercept)) 0.0530656 0.0603394 0.0686101sd(Rep5) 0.0038365 0.0050983 0.0067751cor((Intercept),Rep5) -0.2025553 0.0328312 0.2646312Variance function:lower est. upperHSSM 0.72802 0.83506 0.95784BP0 0.84234 0.96726 1.11070BPM 0.75242 0.86428 0.99277HSSL 0.76266 0.87280 0.99886HSSH 1.67424 1.92056 2.20313BPL 0.70281 0.80596 0.92425BPH 1.08645 1.24462 1.42583Within-group standard error:lower est. upper0.054829 0.060332 0.066388E.3 Targeting StudyE.3.1 TimeGross Targeting TimeLinear mixed-effects model fit by REMLData: targetAIC BIC logLik-1745.5 -1697 882.73Random effects:Formula: ?1 | Subject(Intercept)StdDev: 0.13485Formula: ?Rep5 | Block %in% SubjectStructure: General positive-definite, Log-Cholesky parametrizationStdDev Corr(Intercept) 0.042325 (Intr)Rep5 0.007910 0.013Residual 0.080518Fixed effects: log10(tg) ? Rep5 + Display + Brace + dsValue Std.Error DF t-value p-value292APPENDIX E. STATISTICAL ANALYSIS(a) Residuals (b) QQ-Block Residuals(c) QQ-Subject Intercept (d) Fitted vs. MeasuredFigure E.5 LME Model Diagnostics - Estimated Human Force293APPENDIX E. STATISTICAL ANALYSIS(Intercept) -1.27658 0.118438 841 -10.7785 0.0000Rep5 -0.00476 0.001222 841 -3.8978 0.0001Display3D 0.00871 0.010018 73 0.8698 0.3873BraceArm 0.04920 0.010020 73 4.9103 0.0000ds 0.00246 0.000223 841 11.0328 0.0000Correlation:(Intr) Rep5 Dspl3D BrcArmRep5 -0.008Display3D -0.019 -0.009BraceArm -0.060 0.003 -0.004ds -0.971 0.005 -0.023 0.018Standardized Within-Group Residuals:Min Q1 Med Q3 Max-4.641179 -0.493232 0.010317 0.527643 4.326475Number of Observations: 943Number of Groups:Subject Block %in% Subject25 100Fine Targeting TimeLinear mixed-effects model fit by REMLData: targetAIC BIC logLik-596.29 -562.37 305.15Random effects:Formula: ?1 | Subject(Intercept)StdDev: 0.068082Formula: ?1 | Block %in% Subject(Intercept) ResidualStdDev: 0.046933 0.13867Variance function:Structure: Different standard deviations per stratumFormula: ?1 | DisplayParameter estimates:2D 3D1.000 1.413Fixed effects: log10(tf) ? Display + BraceValue Std.Error DF t-value p-value(Intercept) 0.88053 0.017947 843 49.063 0.0000294APPENDIX E. STATISTICAL ANALYSISDisplay3D -0.19111 0.014531 73 -13.152 0.0000BraceArm -0.00592 0.014262 73 -0.415 0.6793Correlation:(Intr) Dspl3DDisplay3D -0.325BraceArm -0.400 -0.002Standardized Within-Group Residuals:Min Q1 Med Q3 Max-3.415354 -0.693787 0.020312 0.728689 2.306248Number of Observations: 943Number of Groups:Subject Block %in% Subject25 100Approximate 95% confidence intervalsFixed effects:lower est. upper(Intercept) 0.845307 0.88053 0.915759Display3D -0.220074 -0.19111 -0.162153BraceArm -0.034344 -0.00592 0.022504Random Effects:Level: Subjectlower est. uppersd((Intercept)) 0.047403 0.068082 0.09778Level: Blocklower est. uppersd((Intercept)) 0.032038 0.046933 0.068755Variance function:lower est. upper3D 1.2843 1.413 1.5546Within-group standard error:lower est. upper0.12971 0.13867 0.14825Tip Targeting TimeLinear mixed-effects model fit by REMLData: targetAIC BIC logLik-327.06 -293.14 170.53Random effects:295APPENDIX E. STATISTICAL ANALYSISFormula: ?1 | Subject(Intercept)StdDev: 0.11628Formula: ?1 | Block %in% Subject(Intercept) ResidualStdDev: 0.078237 0.17446Variance function:Structure: Different standard deviations per stratumFormula: ?1 | DisplayParameter estimates:2D 3D1.000 1.131Fixed effects: log10(tr) ? Display + BraceValue Std.Error DF t-value p-value(Intercept) 0.63442 0.028768 843 22.0529 0.0000Display3D -0.14257 0.019838 73 -7.1868 0.0000BraceArm 0.01880 0.019822 73 0.9483 0.3461Correlation:(Intr) Dspl3DDisplay3D -0.328BraceArm -0.346 -0.002Standardized Within-Group Residuals:Min Q1 Med Q3 Max-2.91067 -0.65337 -0.07331 0.63945 3.63163Number of Observations: 943Number of Groups:Subject Block %in% Subject25 100Approximate 95% confidence intervalsFixed effects:lower est. upper(Intercept) 0.577953 0.634419 0.690884Display3D -0.182111 -0.142573 -0.103036BraceArm -0.020708 0.018797 0.058303Random Effects:Level: Subjectlower est. uppersd((Intercept)) 0.083181 0.11628 0.16255Level: Blocklower est. uppersd((Intercept)) 0.060233 0.078237 0.10162296APPENDIX E. STATISTICAL ANALYSISVariance function:lower est. upper3D 1.0282 1.131 1.2442Within-group standard error:lower est. upper0.16315 0.17446 0.18655Tail Targeting TimeLinear mixed-effects model fit by REMLData: targetAIC BIC logLik4382.1 4411.2 -2185.1Random effects:Formula: ?1 | Subject(Intercept)StdDev: 0.82673Formula: ?1 | Block %in% Subject(Intercept) ResidualStdDev: 0.55472 2.3553Fixed effects: (ta) ? Display + BraceValue Std.Error DF t-value p-value(Intercept) 7.9837 0.23344 843 34.200 0.00Display3D -2.7372 0.18967 73 -14.432 0.00BraceArm -0.1785 0.18979 73 -0.941 0.35Correlation:(Intr) Dspl3DDisplay3D -0.405BraceArm -0.410 -0.002Standardized Within-Group Residuals:Min Q1 Med Q3 Max-2.19040 -0.71908 -0.15363 0.63944 3.01096Number of Observations: 943Number of Groups:Subject Block %in% Subject25 100Approximate 95% confidence intervalsFixed effects:lower est. upper(Intercept) 7.52555 7.98375 8.44195297APPENDIX E. STATISTICAL ANALYSISDisplay3D -3.11526 -2.73725 -2.35924BraceArm -0.55678 -0.17853 0.19971Random Effects:Level: Subjectlower est. uppersd((Intercept)) 0.56288 0.82673 1.2143Level: Blocklower est. uppersd((Intercept)) 0.3413 0.55472 0.90157Within-group standard error:lower est. upper2.2456 2.3553 2.4704298APPENDIX E. STATISTICAL ANALYSIS(a) Residuals (b) QQ-Block Residuals(c) QQ-Subject Intercept (d) Fitted vs. ExperimentalFigure E.6 LME Model Diagnostics - Gross Targeting Time299APPENDIX E. STATISTICAL ANALYSIS(a) Residuals (b) QQ-Block Residuals(c) QQ-Subject Intercept (d) Fitted vs. ExperimentalFigure E.7 LME Model Diagnostics - Fine Targeting Time300APPENDIX E. STATISTICAL ANALYSIS(a) Residuals (b) QQ-Block Residuals(c) QQ-Subject Intercepts (d) Fitted vs. ExperimentalFigure E.8 LME Model Diagnostics - Tip Targeting Time301APPENDIX E. STATISTICAL ANALYSIS(a) Residuals (b) QQ-Block Residuals(c) QQ-Subject Intercepts (d) Fitted vs. ExperimentalFigure E.9 LME Model Diagnostics - Tail Targeting Time302APPENDIX E. STATISTICAL ANALYSISE.3.2 AccuracyHorizontal Tip ErrorLinear mixed-effects model fit by REMLData: targetAIC BIC logLik2492.2 2550.3 -1234.1Random effects:Formula: ?1 | Subject(Intercept)StdDev: 0.14885Formula: ?1 | Block %in% Subject(Intercept) ResidualStdDev: 0.19894 0.75209Variance function:Structure: Different standard deviations per stratumFormula: ?1 | BlockParameter estimates:None2D Arm2D None3D Arm3D1.00000 0.85007 1.44598 1.38507Fixed effects: txe ? Rep5 + Display + Brace + Gender + Rep5:Gender - 1Value Std.Error DF t-value p-valueRep5 0.040671 0.012390 842 3.2827 0.0011Display2D 0.083313 0.075765 73 1.0996 0.2751Display3D -0.222180 0.083545 73 -2.6594 0.0096BraceArm 0.028202 0.068324 73 0.4128 0.6810GenderF 0.142157 0.091760 24 1.5492 0.1344Rep5:GenderF -0.053574 0.018919 842 -2.8317 0.0047Correlation:Rep5 Dspl2D Dspl3D BrcArm GendrFDisplay2D -0.084Display3D -0.082 0.608BraceArm 0.000 -0.496 -0.427GenderF 0.071 -0.530 -0.478 0.002Rep5:GenderF -0.655 0.059 0.054 -0.005 -0.107Standardized Within-Group Residuals:Min Q1 Med Q3 Max-3.521066 -0.654726 -0.035871 0.637932 2.742101Number of Observations: 943Number of Groups:Subject Block %in% Subject25 100303APPENDIX E. STATISTICAL ANALYSISApproximate 95% confidence intervalsFixed effects:lower est. upperRep5 0.016353 0.040671 0.064990Display2D -0.067687 0.083313 0.234312Display3D -0.388684 -0.222180 -0.055676BraceArm -0.107967 0.028202 0.164370GenderF -0.047228 0.142157 0.331541Rep5:GenderF -0.090708 -0.053574 -0.016440Random Effects:Level: Subjectlower est. uppersd((Intercept)) 0.071649 0.14885 0.30922Level: Blocklower est. uppersd((Intercept)) 0.12221 0.19894 0.32384Variance function:lower est. upperArm2D 0.74355 0.85007 0.97186None3D 1.26439 1.44598 1.65365Arm3D 1.21178 1.38507 1.58314Within-group standard error:lower est. upper0.68285 0.75209 0.82836Vertical Tip ErrorLinear mixed-effects model fit by REMLData: targetAIC BIC logLik3258.5 3311.8 -1618.3Random effects:Formula: ?1 | Subject(Intercept)StdDev: 0.59365Formula: ?Rep5 | Block %in% SubjectStructure: General positive-definite, Log-Cholesky parametrizationStdDev Corr(Intercept) 0.796334 (Intr)Rep5 0.060952 -0.099Residual 0.698453304APPENDIX E. STATISTICAL ANALYSISVariance function:Structure: Different standard deviations per stratumFormula: ?1 | BlockParameter estimates:None2D Arm2D None3D Arm3D1.00000 0.85679 3.43025 2.87847Fixed effects: tye ? Display + BraceValue Std.Error DF t-value p-value(Intercept) -0.93259 0.19060 843 -4.8928 0.0000Display3D -2.03196 0.19106 73 -10.6352 0.0000BraceArm 0.06797 0.18468 73 0.3681 0.7139Correlation:(Intr) Dspl3DDisplay3D -0.353BraceArm -0.490 -0.036Standardized Within-Group Residuals:Min Q1 Med Q3 Max-4.207744 -0.630143 -0.013406 0.604357 3.560991Number of Observations: 943Number of Groups:Subject Block %in% Subject25 100Approximate 95% confidence intervalsFixed effects:lower est. upper(Intercept) -1.30670 -0.932586 -0.55847Display3D -2.41275 -2.031963 -1.65118BraceArm -0.30009 0.067972 0.43603Random Effects:Level: Subjectlower est. uppersd((Intercept)) 0.37377 0.59365 0.94288Level: Blocklower est. uppersd((Intercept)) 0.615243 0.796334 1.03073sd(Rep5) 0.036717 0.060952 0.10118cor((Intercept),Rep5) -0.714079 -0.098989 0.60235Variance function:lower est. upperArm2D 0.74468 0.85679 0.98577None3D 2.98237 3.43025 3.94539Arm3D 2.49939 2.87847 3.31506305APPENDIX E. STATISTICAL ANALYSISWithin-group standard error:lower est. upper0.63283 0.69845 0.77089Horizontal Tail ErrorLinear mixed-effects model fit by REMLData: targetAIC BIC logLik3433.8 3487.1 -1705.9Random effects:Formula: ?1 | Subject(Intercept)StdDev: 0.24231Formula: ?Rep5 | Block %in% SubjectStructure: General positive-definite, Log-Cholesky parametrizationStdDev Corr(Intercept) 0.159923 (Intr)Rep5 0.058328 -0.353Residual 1.029921Variance function:Structure: Different standard deviations per stratumFormula: ?1 | BlockParameter estimates:None2D Arm2D None3D Arm3D1.00000 0.78193 2.29702 2.09094Fixed effects: tue ? Display + BraceValue Std.Error DF t-value p-value(Intercept) 0.15799 0.085457 843 1.8488 0.0648Display3D -0.40781 0.115879 73 -3.5193 0.0007BraceArm 0.04032 0.087301 73 0.4618 0.6456Correlation:(Intr) Dspl3DDisplay3D -0.244BraceArm -0.614 0.037Standardized Within-Group Residuals:Min Q1 Med Q3 Max-4.2575126 -0.5678580 -0.0090161 0.5796180 3.8267442Number of Observations: 943Number of Groups:Subject Block %in% Subject25 100Approximate 95% confidence intervals306APPENDIX E. STATISTICAL ANALYSISFixed effects:lower est. upper(Intercept) -0.0097426 0.157991 0.32572Display3D -0.6387526 -0.407807 -0.17686BraceArm -0.1336738 0.040318 0.21431Random Effects:Level: Subjectlower est. uppersd((Intercept)) 0.13944 0.24231 0.42107Level: Blocklower est. uppersd((Intercept)) 0.039354 0.159923 0.64988sd(Rep5) 0.023828 0.058328 0.14278cor((Intercept),Rep5) -0.961456 -0.353231 0.84158Variance function:lower est. upperArm2D 0.67911 0.78193 0.90031None3D 1.99660 2.29702 2.64264Arm3D 1.81849 2.09094 2.40421Within-group standard error:lower est. upper0.92413 1.02992 1.14782Vertical Tail ErrorLinear mixed-effects model fit by REMLData: targetAIC BIC logLik4224.4 4268.1 -2103.2Random effects:Formula: ?1 | Subject(Intercept)StdDev: 0.42138Formula: ?1 | Block %in% Subject(Intercept) ResidualStdDev: 0.32875 0.99315Variance function:Structure: Different standard deviations per stratumFormula: ?1 | BlockParameter estimates:None2D Arm2D None3D Arm3D307APPENDIX E. STATISTICAL ANALYSIS1.00000 0.70147 5.61066 5.67786Fixed effects: tve ? Display + BraceValue Std.Error DF t-value p-value(Intercept) -1.0606 0.12427 843 -8.5352 0.0000Display3D -4.5819 0.26930 73 -17.0145 0.0000BraceArm 0.0745 0.11915 73 0.6254 0.5336Correlation:(Intr) Dspl3DDisplay3D -0.127BraceArm -0.550 0.032Standardized Within-Group Residuals:Min Q1 Med Q3 Max-3.2471745 -0.6491139 0.0034389 0.6142933 5.3228706Number of Observations: 943Number of Groups:Subject Block %in% Subject25 100Approximate 95% confidence intervalsFixed effects:lower est. upper(Intercept) -1.30456 -1.060646 -0.81674Display3D -5.11864 -4.581932 -4.04523BraceArm -0.16294 0.074515 0.31197Random Effects:Level: Subjectlower est. uppersd((Intercept)) 0.27545 0.42138 0.64461Level: Blocklower est. uppersd((Intercept)) 0.17009 0.32875 0.6354Variance function:lower est. upperArm2D 0.61357 0.70147 0.80195None3D 4.91211 5.61066 6.40856Arm3D 4.97421 5.67786 6.48105Within-group standard error:lower est. upper0.90320 0.99315 1.09206Tip ErrorLinear mixed-effects model fit by REML308APPENDIX E. STATISTICAL ANALYSISData: targetAIC BIC logLik281.32 324.93 -131.66Random effects:Formula: ?1 | Subject(Intercept)StdDev: 0.11966Formula: ?1 | Block %in% Subject(Intercept) ResidualStdDev: 0.11253 0.2549Variance function:Structure: Different standard deviations per stratumFormula: ?1 | BlockParameter estimates:None2D Arm2D None3D Arm3D1.00000 0.84836 1.11759 1.09001Fixed effects: log10(tpe) ? Display + BraceValue Std.Error DF t-value p-value(Intercept) 0.02654 0.034150 843 0.7771 0.4373Display3D 0.43389 0.028204 73 15.3841 0.0000BraceArm -0.01745 0.028172 73 -0.6193 0.5376Correlation:(Intr) Dspl3DDisplay3D -0.394BraceArm -0.436 0.019Standardized Within-Group Residuals:Min Q1 Med Q3 Max-4.15074 -0.52239 0.20651 0.66352 2.09045Number of Observations: 943Number of Groups:Subject Block %in% Subject25 100Approximate 95% confidence intervalsFixed effects:lower est. upper(Intercept) -0.040491 0.026538 0.093566Display3D 0.377679 0.433889 0.490099BraceArm -0.073594 -0.017448 0.038699Random Effects:Level: Subjectlower est. upper309APPENDIX E. STATISTICAL ANALYSISsd((Intercept)) 0.081372 0.11966 0.17597Level: Blocklower est. uppersd((Intercept)) 0.087057 0.11253 0.14547Variance function:lower est. upperArm2D 0.74189 0.84836 0.97011None3D 0.97607 1.11759 1.27962Arm3D 0.95330 1.09001 1.24633Within-group standard error:lower est. upper0.23162 0.25490 0.28053Angular ErrorLinear mixed-effects model fit by REMLData: targetAIC BIC logLik244.99 288.61 -113.5Random effects:Formula: ?1 | Subject(Intercept)StdDev: 0.078143Formula: ?1 | Block %in% Subject(Intercept) ResidualStdDev: 0.11396 0.24602Variance function:Structure: Different standard deviations per stratumFormula: ?1 | BlockParameter estimates:None2D Arm2D None3D Arm3D1.00000 0.93765 0.99931 1.19795Fixed effects: log10(eAf) ? Display + BraceValue Std.Error DF t-value p-value(Intercept) -0.82677 0.028896 843 -28.6118 0.0000Display3D 0.61733 0.028262 73 21.8431 0.0000BraceArm -0.04175 0.028243 73 -1.4781 0.1437Correlation:(Intr) Dspl3DDisplay3D -0.488BraceArm -0.501 0.042Standardized Within-Group Residuals:310APPENDIX E. STATISTICAL ANALYSISMin Q1 Med Q3 Max-3.28302 -0.62109 0.14240 0.66560 3.91826Number of Observations: 943Number of Groups:Subject Block %in% Subject25 100Approximate 95% confidence intervalsFixed effects:lower est. upper(Intercept) -0.883488 -0.826771 -0.770054Display3D 0.561000 0.617326 0.673652BraceArm -0.098035 -0.041747 0.014541Random Effects:Level: Subjectlower est. uppersd((Intercept)) 0.045767 0.078143 0.13342Level: Blocklower est. uppersd((Intercept)) 0.088725 0.11396 0.14637Variance function:lower est. upperArm2D 0.81954 0.93765 1.0728None3D 0.87107 0.99931 1.1464Arm3D 1.04610 1.19795 1.3718Within-group standard error:lower est. upper0.22349 0.24602 0.27082Total Targeting ErrorLinear mixed-effects model fit by REMLData: targetAIC BIC logLik13.097 56.71 2.4516Random effects:Formula: ?1 | Subject(Intercept)StdDev: 0.10784Formula: ?1 | Block %in% Subject(Intercept) Residual311APPENDIX E. STATISTICAL ANALYSISStdDev: 0.10225 0.21971Variance function:Structure: Different standard deviations per stratumFormula: ?1 | BlockParameter estimates:None2D Arm2D None3D Arm3D1.00000 0.81092 1.12725 1.14044Fixed effects: log10(tte) ? Display + BraceValue Std.Error DF t-value p-value(Intercept) 0.39786 0.030633 843 12.988 0.0000Display3D 0.55906 0.025233 73 22.155 0.0000BraceArm -0.02735 0.025181 73 -1.086 0.2811Correlation:(Intr) Dspl3DDisplay3D -0.393BraceArm -0.437 0.030Standardized Within-Group Residuals:Min Q1 Med Q3 Max-4.10038 -0.59101 0.15187 0.68066 2.69771Number of Observations: 943Number of Groups:Subject Block %in% Subject25 100Approximate 95% confidence intervalsFixed effects:lower est. upper(Intercept) 0.337731 0.397856 0.45798Display3D 0.508765 0.559055 0.60935BraceArm -0.077531 -0.027346 0.02284Random Effects:Level: Subjectlower est. uppersd((Intercept)) 0.073412 0.10784 0.1584Level: Blocklower est. uppersd((Intercept)) 0.08003 0.10225 0.13063Variance function:lower est. upperArm2D 0.70901 0.81092 0.92748None3D 0.98471 1.12725 1.29041Arm3D 0.99701 1.14044 1.30449312APPENDIX E. STATISTICAL ANALYSISWithin-group standard error:lower est. upper0.19974 0.21971 0.24168E.3.3 VariabilityHorizontal Tip VariationLinear mixed-effects model fit by REMLData: targetAIC BIC logLik-545.56 -511.64 279.78Random effects:Formula: ?1 | Subject(Intercept)StdDev: 0.026226Formula: ?1 | Block %in% Subject(Intercept) ResidualStdDev: 0.011516 0.1846Variance function:Structure: Different standard deviations per stratumFormula: ?1 | BraceParameter estimates:None Arm1.00000 0.91298Fixed effects: log10(txfstd) ? Display + BraceValue Std.Error DF t-value p-value(Intercept) -1.10059 0.011735 843 -93.782 0.0000Display3D 0.00058 0.011695 73 0.050 0.9605BraceArm -0.02763 0.011758 73 -2.350 0.0215Correlation:(Intr) Dspl3DDisplay3D -0.498BraceArm -0.550 -0.001Standardized Within-Group Residuals:Min Q1 Med Q3 Max-2.963844 -0.627181 -0.014633 0.612032 4.475310Number of Observations: 943Number of Groups:Subject Block %in% Subject25 100Approximate 95% confidence intervals313APPENDIX E. STATISTICAL ANALYSISFixed effects:lower est. upper(Intercept) -1.123621 -1.10058640 -1.0775521Display3D -0.022728 0.00058153 0.0238907BraceArm -0.051062 -0.02762781 -0.0041939Random Effects:Level: Subjectlower est. uppersd((Intercept)) 0.013443 0.026226 0.051164Level: Blocklower est. uppersd((Intercept)) 0.00013864 0.011516 0.95655Variance function:lower est. upperArm 0.83264 0.91298 1.0011Within-group standard error:lower est. upper0.17273 0.18460 0.19729Vertical Tip VariationLinear mixed-effects model fit by REMLData: targetAIC BIC logLik-52.846 -18.925 33.423Random effects:Formula: ?1 | Subject(Intercept)StdDev: 0.06925Formula: ?1 | Block %in% Subject(Intercept) ResidualStdDev: 0.036448 0.24212Variance function:Structure: Different standard deviations per stratumFormula: ?1 | DisplayParameter estimates:2D 3D1.00000 0.86185Fixed effects: log10(tyfstd) ? Display + BraceValue Std.Error DF t-value p-value(Intercept) -1.72926 0.020287 843 -85.241 0.0000314APPENDIX E. STATISTICAL ANALYSISDisplay3D -0.01906 0.016450 73 -1.159 0.2503BraceArm -0.02431 0.016348 73 -1.487 0.1414Correlation:(Intr) Dspl3DDisplay3D -0.453BraceArm -0.407 -0.001Standardized Within-Group Residuals:Min Q1 Med Q3 Max-2.842722 -0.667971 -0.037832 0.587417 3.593796Number of Observations: 943Number of Groups:Subject Block %in% Subject25 100Approximate 95% confidence intervalsFixed effects:lower est. upper(Intercept) -1.769075 -1.729256 -1.689438Display3D -0.051850 -0.019065 0.013721BraceArm -0.056889 -0.024308 0.008274Random Effects:Level: Subjectlower est. uppersd((Intercept)) 0.04685 0.06925 0.10236Level: Blocklower est. uppersd((Intercept)) 0.015508 0.036448 0.085661Variance function:lower est. upper3D 0.7849 0.86185 0.94635Within-group standard error:lower est. upper0.22645 0.24212 0.25888Horizontal Tail VariationLinear mixed-effects model fit by REMLData: targetAIC BIC logLik-35.199 -1.278 24.6Random effects:315APPENDIX E. STATISTICAL ANALYSISFormula: ?1 | Subject(Intercept)StdDev: 0.084194Formula: ?1 | Block %in% Subject(Intercept) ResidualStdDev: 0.039677 0.24698Variance function:Structure: Different standard deviations per stratumFormula: ?1 | BraceParameter estimates:None Arm1.00000 0.83673Fixed effects: log10(tufstd) ? Display + BraceValue Std.Error DF t-value p-value(Intercept) -0.51264 0.022725 843 -22.5583 0.0000Display3D -0.01142 0.016679 73 -0.6847 0.4957BraceArm -0.04459 0.016873 73 -2.6428 0.0101Correlation:(Intr) Dspl3DDisplay3D -0.366BraceArm -0.426 -0.001Standardized Within-Group Residuals:Min Q1 Med Q3 Max-3.122043 -0.642355 -0.069055 0.537109 5.154678Number of Observations: 943Number of Groups:Subject Block %in% Subject25 100Approximate 95% confidence intervalsFixed effects:lower est. upper(Intercept) -0.557241 -0.512636 -0.468032Display3D -0.044661 -0.011420 0.021821BraceArm -0.078222 -0.044593 -0.010964Random Effects:Level: Subjectlower est. uppersd((Intercept)) 0.058995 0.084194 0.12016Level: Blocklower est. uppersd((Intercept)) 0.018863 0.039677 0.08346316APPENDIX E. STATISTICAL ANALYSISVariance function:lower est. upperArm 0.76124 0.83673 0.91971Within-group standard error:lower est. upper0.23090 0.24698 0.26419Vertical Tail VariationLinear mixed-effects model fit by REMLData: targetAIC BIC logLik520.41 554.33 -253.21Random effects:Formula: ?1 | Subject(Intercept)StdDev: 0.12511Formula: ?1 | Block %in% Subject(Intercept) ResidualStdDev: 0.072033 0.28088Variance function:Structure: Different standard deviations per stratumFormula: ?1 | BraceParameter estimates:None Arm1.0000 1.1422Fixed effects: log10(tvfstd) ? Display + BraceValue Std.Error DF t-value p-value(Intercept) -0.76269 0.032383 843 -23.5519 0.000Display3D -0.00468 0.024317 73 -0.1923 0.848BraceArm -0.16604 0.024404 73 -6.8039 0.000Correlation:(Intr) Dspl3DDisplay3D -0.375BraceArm -0.348 -0.002Standardized Within-Group Residuals:Min Q1 Med Q3 Max-3.244634 -0.597751 -0.065208 0.581631 4.133183Number of Observations: 943Number of Groups:Subject Block %in% Subject25 100317APPENDIX E. STATISTICAL ANALYSISApproximate 95% confidence intervalsFixed effects:lower est. upper(Intercept) -0.826250 -0.762689 -0.699127Display3D -0.053141 -0.004676 0.043789BraceArm -0.214680 -0.166043 -0.117406Random Effects:Level: Subjectlower est. uppersd((Intercept)) 0.087804 0.12511 0.17828Level: Blocklower est. uppersd((Intercept)) 0.044832 0.072033 0.11574Variance function:lower est. upperArm 1.039 1.1422 1.2557Within-group standard error:lower est. upper0.26225 0.28088 0.30084318APPENDIX E. STATISTICAL ANALYSIS(a) Residuals (b) QQ-Block Residuals(c) QQ-Subject Intercepts (d) Fitted vs. ExperimentalFigure E.10 LME Model Diagnostics - Final Horizontal Tip Error319APPENDIX E. STATISTICAL ANALYSIS(a) Residuals (b) QQ-Block Residuals(c) QQ-Subject Intercepts (d) Fitted vs. ExperimentalFigure E.11 LME Model Diagnostics - Final Vertical Tip Error320APPENDIX E. STATISTICAL ANALYSIS(a) Residuals (b) QQ-Block Residuals(c) QQ-Subject Intercepts (d) Fitted vs. ExperimentalFigure E.12 LME Model Diagnostics - Final Horizontal Tail Error321APPENDIX E. STATISTICAL ANALYSIS(a) Residuals (b) QQ-Block Residuals(c) QQ-Subject Intercepts (d) Fitted vs. ExperimentalFigure E.13 LME Model Diagnostics - Final Vertical Tail Error322APPENDIX E. STATISTICAL ANALYSIS(a) Residuals (b) QQ-Block Residuals(c) QQ-Subject Intercepts (d) Fitted vs. ExperimentalFigure E.14 LME Model Diagnostics - Final Tip Targeting Error323APPENDIX E. STATISTICAL ANALYSIS(a) Residuals (b) QQ-Block Residuals(c) QQ-Subject Intercepts(d) Fitted vs. Experimental(e) Fitted by blockFigure E.15 LME Model Diagnostics - Final Angular Targeting Error324APPENDIX E. STATISTICAL ANALYSIS(a) Residuals (b) QQ-Block Residuals(c) QQ-Subject Intercepts (d) Fitted vs. ExperimentalFigure E.16 LME Model Diagnostics - Final Total Targeting Error325APPENDIX E. STATISTICAL ANALYSIS(a) Residuals (b) QQ-Block Residuals(c) QQ-Subject Intercepts (d) Fitted vs. ExperimentalFigure E.17 LME Model Diagnostics - Final Horizontal Tip Variability326APPENDIX E. STATISTICAL ANALYSIS(a) Residuals (b) QQ-Block Residuals(c) QQ-Subject Intercepts (d) Fitted vs. ExperimentalFigure E.18 LME Model Diagnostics - Final Vertical Tip Variability327APPENDIX E. STATISTICAL ANALYSIS(a) Residuals (b) QQ-Block Residuals(c) QQ-Subject Intercepts (d) Fitted vs. ExperimentalFigure E.19 LME Model Diagnostics - Final Horizontal Tail Variability328APPENDIX E. STATISTICAL ANALYSIS(a) Residuals (b) QQ-Block Residuals(c) QQ-Subject Intercepts (d) Fitted vs. ExperimentalFigure E.20 LME Model Diagnostics - Final Vertical Tail Variability329Appendix FUKF Drill Axis CalibrationF.1 IntroductionThe goal of this project was to develop a method for calibrating the axis of a drill for use with a CASsystem. There are a variety of surgical procedures where the outcome is dependent on the ability of thesurgeon to create a hole quickly and accurately in the correct location, in the correct orientation, and tothe correct depth. CAS systems are designed to enhance the surgeon?s abilities by providing real-timefeedback on the location of the tool relative to the patient anatomy. Hardware is used to track the positionand orientation, or pose, of the tool and the anatomy. Current tracking hardware is unable to measurethe pose of the tip directly, so the tool body is tracked instead. In order to generate a visualization forthe surgeon, the unknown geometrical relationship, or transform, from where the tool is tracked to thetip must be determined.Figure F.1 illustrates an example of a CAS system for femoral hip resurfacing. An optical tracker (notshown) measures the pose of a static reference frame (SRF) attached to the ground, a DRF attached to theanatomy, and a drill coordinate frame attached to the drill. The SRF is used as a global reference frame,or ground frame. A registration process is used to align the DRF coordinate system to the anatomy.Similarly, a calibration is required to define the transform from the drill coordinate frame to the drill bitcoordinate frame, T DRILLT IP . The drill bit coordinate frame is defined with the origin at the drill bit tip, andthe z-axis aligned with the axis of the drill bit. The axis of the drill bit is commonly referred to as theprimary axis.Visual feedback is provided to the surgeon using a display like the one illustrated in Figure F.2. Theposition of the drill bit and its trajectory are displayed relative to the anatomy. The surgeon then usesthis display to adjust the position of the drill so that the desired entry point, trajectory, and depth can beachieved.The accuracy of the drill bit calibration directly affects the accuracy of the system; errors can causeserious consequences and can lead to an unsuccessful outcome. Depending on the procedure, theseconsequences might include injury to blood vessels or nerves, or misalignment of an implant. Forexample, when creating pilot holes in the vertebrae for inserting pedicle screws, inaccurate drilling can330APPENDIX F. UKF DRILL AXIS CALIBRATIOND5)7A1A77.5765)65)7D5)A1A777,37raFNiQJ\u001dD5,\/\/77,37raFNiQJ\u001d7raFNiQJ\u001d65)7D5,\/\/&aliEratioQ\u001d5HJistratioQ\u001dFigure F.1 Example coordinate systems of a CAS system used for femoral hip resurfacing. Anoptical tracker (not shown) measures the pose of the bone and drill relative to a static referenceframe (SRF). A calibration is required to determine the pose of the tip with respect to the drillcoordinate frame. A registration is required to determine to define the target with respect tothe dynamic reference frame (DRF).Figure F.2 Navigation display of the BrainLAB? CAS system for femoral hip resurfacing. Thedrill axis must be calibrated to properly display the drill bit trajectory, shown in blue, relativeto the target trajectory, shown in yellow.331APPENDIX F. UKF DRILL AXIS CALIBRATIONresult in penetration of the pedicle cortex, which can cause dural and neural injury. In order to ensurethe safety of the patient and increase the chances of a successful outcome, the drill calibration must beaccurate.Calibration algorithms can be divided into transformation methods and fitting methods. Transforma-tion methods rely on specialized, tracked calibration tools. The drill is placed in a machined hole with aknown relationship to the measured marker frame. A separate hole is required for each drill bit diameter,and accurately machining this part can be expensive. Fitting methods involve measuring the drill markerframe during a constrained motion, and then using an appropriate algorithm to estimate the calibrationparameters. Current calibration algorithms, such as a least-squares 3D circle fitting (LS3DCF), workwith a batch of data, i.e. a number of measurements are taken, and then processed at the same time. Ifthe desired accuracy is not achieved, the entire process must be repeated. Recent research demonstrateda 20 % reduction in targeting time when the user was provided with visual representations of uncer-tainty [Simpson 2007], but current calibration techniques do not provide the necessary information. Itis therefore desirable to develop a calibration that avoids the costs of a specialized tool, is capable ofbeing used in real-time, and generates the necessary information to estimate uncertainty.The UKF is a set of recursive mathematical equations that can be used for real-time parameter es-timation of non-linear systems [Wan 2000]. It has been applied to ultrasound calibration [Moghari2006], 3D rigid registration [Zamani 2008], and drill bit tip calibration [Simpson 2007]. However, tothe best of our knowledge, a UKF for primary axis calibration has not been reported.F.1.1 Project ObjectivesThe objectives of this project were to:1. Design a calibration procedure and UKF calibration algorithm for determining the primary axis ofan optically tracked drill bit;2. Compare the procedure and algorithm to an existing LS3DCF.F.1.2 Drill Calibration RequirementsYaniv [2008] defined 5 characteristics of an ideal registration algorithm:1. Fast: The result is obtained in real time.2. Accurate: After successful registration, the TRE, or distance between corresponding points in theregion of interest, is less than 0.1 mm.3. Robust: Has a breakdown point of N\/2, which means that more than half of the data elementsmust be outliers in order to throw the registration outside of reasonable bounds.4. Automatic: No user interaction is required .332APPENDIX F. UKF DRILL AXIS CALIBRATION5. Reliable: Given the expected clinical input, the registration always succeeds (or gives a clearindication that it is not accepted.)Item two does not translate directly to an accuracy requirement for an axis calibration. For a surgicalnavigation system, a commonly quoted accuracy requirement is 1 mm for a single point and 1? for atrajectory or cutting plane [Phillips 2007]. These values are an upper bound since the overall systemerror depends on a combination of a number of sources of error in addition to the drill calibration.These characteristics provide a base of comparison for the algorithm. The following requirementsare also considered:1. Minimal extra hardware ($300 budget)2. Works with different drill diameters and lengths3. Works with different types of position trackersF.1.3 OverviewThe remainder of this report is organized as follows: Section F.2 provides an overview of CAS and coversthe basics of transformations and calibration. This section also introduces UKFS. Section F.3 describesthe implementation and testing of the UKF axis calibration algorithm including a description of ourexperimental CAS system. Section F.4 contains the results of the validation and testing of the algorithm.Section F.5 provides analysis and discussion of the algorithm testing. Section F.6 summarizes theconclusions from our findings, addresses the limitations of the project, and describes potential futurework.F.2 BackgroundThis section provides a more detailed introduction to and background information on CAS, CAS hard-ware, CAS drilling, and the UKF.F.2.1 Computer-Assisted SurgeryCAS refers to the use of computer technology to improve the planning and execution of surgical proce-dures. The goal of these systems is to improve surgical outcomes by addressing some of the limitationsof the surgeon. One of the main focuses is to improve visualization; anatomical variation and a trendtowards smaller incisions and more minimally invasive procedures can make it difficult for a surgeon tosee what they are doing. Computer technology can be used to generate accurate models of the patient?sanatomy, enable the surgeon to create a plan before the surgery begins and provide guidance duringsurgery to execute (and if necessary, modify) the plan. CAS techniques have the potential to improveaccuracy, decrease operating times, and enable minimally invasive procedures which are all factors inimproving patient outcomes.333APPENDIX F. UKF DRILL AXIS CALIBRATIONTable F.1 Example Computer Assisted Surgery Proceduresablation therapy orthopedic implantsbrachytherapy spinal joint fusionbiopsy spinal screw insertioncraniotomy transcranial magnetic therapydeep brain stimulation tumour excisionThe following sections provide an overview of CAS. We describe the main operating principlesand review a number of systems in clinical use today and their advantages and challenges. The focusof this project is on an aspect of surgical navigation, so it is explored in more depth with a review ofthe hardware used to track surgical tools and the mathematics necessary to describe the geometricalrelations between tracked objects.CAS PrinciplesMost CAS systems involve some combination of the following three principles: patient modelling, plan-ning, and navigation. The purpose of patient modelling is to create an accurate geometrical model of thepatient?s anatomy. This model can either be created through medical imaging (e.g. computed tomog-raphy (CT), magnetic resonance imaging (MRI), x-ray, ultrasound) or by image-less techniques, suchas directly measuring the surface and morphing statistically based models. Once the patient model isgenerated, the surgeon can use it to diagnose, plan, and simulate the surgery during preoperative orintraoperative planning. This virtual model is then registered with the patient during surgery, enablingthe surgeon to visualize the location of surgical tools relative to the patient model. This guidance, ornavigation, enables the surgeon to carry out the surgical plan. In some cases, the movement of the toolis assisted or carried out by a mechanical device in robotic surgery.CAS Applications and Current SystemsThe development of CAS began in neurosurgery and has since expanded to a number of surgical do-mains. Table F.1 lists a variety of procedures that have benefited from the use of CAS systems thatspan across orthopaedics, Ear Nose and Throat (ENT), radiation therapy, and spinal surgery. Typically,these procedures involve high accuracy requirements and have significant consequences for mistakes.Reducing or replacing reliance on radiation-based imaging is another motivation for the implementationof CAS alternatives.Orthopaedics is particularly suited for CAS techniques since many of the procedures involves boneswhich can be treated like rigid bodies. Extensive exposure is often required to gain sufficient accessto deeply located tissue. The size of incisions is chosen to balance invasiveness with access, and as aresult there is often suboptimal visualization. Commonly target tasks utilizing CAS in orthopaedics arepedicle screw insertion [Merloz 1998], hip and knee replacement [Kanlic? 2006], and fracture alignment.Table F.2 lists a variety of commercially available CAOS systems [Craven 2005].334APPENDIX F. UKF DRILL AXIS CALIBRATIONTable F.2 Commercially Available CAOS SystemsCompany System Name Classification and DescriptionAcrobot (The Acrobot CompanyLtd.)Acrobot, MI-Navigation Semi-active robotic assistant,planning software. Resurfacing.Aesculap Orthopilot Image-less TKA and ACL, plan-ning and navigation.BrainLAB VectorVision Image-free and CT-based plan-ning and navigation.CASurgica Inc. HipNav, KneeNav CT-based. Preop. Plan-ning, RoM simulation, acetabu-lar placement for hips. Naviga-tion for TKA.DePuy\/BrainLAB iOrthopaedics Ci System Image-less, TKA and THA plan-ning and navigation.GE Healthcare FluoroTrak\/Flexiview Fluoroscopy navigation system\/-Mobile C-arm.Integrated Surgical Systems(ISS)ROBODOC\/ORTHODOC Active robotic system\/associ-ated planning system.Medivision Synthes SurgiGATE CT-based navigation system.Medtronic SNT (Surgical Navi-gation Technologies)StealthStation Image-based navigation system,TKA and MIS knee workingwith various third party C-arms,CT or MRI.PI Systems PiGalileo Image-free navigation sys-tem, TKA and THA, pluselectromechanical positioning?mini-robot? for TKA.Siemens Medical Solutions SIREMOBIL Iso-C\/Iso-C3D 2D\/3D C-arm Fluoroscopyworking with various third partynavigation systems.Smith & Nephew\/ORTHOsoft AchieveCAS, Navitrack Image-less navigation for TKAand THA (models derived fromCT).Stryker Orthopaedics\/Leibinger Navigation System Image-free THA\/TKA,withwireless tracking technology(can be image-based for otherprocedures.)Universal Robot Systems (URS)OrthoCASPAR Active robotic system for bonepreparation in TKA.Adapted from Craven [2005]335APPENDIX F. UKF DRILL AXIS CALIBRATIONAdvantages and ChallengesThe basic premise of CAS is that improved visualization will enable less invasive procedures to beachieved with the same or higher levels of accuracy. This should in turn result in a host of benefits,including less blood loss, faster recovery and shorter hospital stays leading to better patient outcomesand financial savings. In orthopaedic surgery, real time intraoperative feedback should result in higherprecision of bone cuts, better alignment of implants, easier fracture reductions, less radiation and betterdocumentation than classical manual techniques [Kanlic? 2006].Widespread adoption of CAS has been limited. A review by Craven [2005] of the factors influenc-ing acceptance of CAOS technologies concluded that there was ?poor validation of accuracy, lack ofstandardization, inappropriate clinical outcomes measures for assessing and comparing technologies,unresolved debated about the effectiveness of minimally invasive surgery, and issues of medical de-vice regulations, cost, autonomy of surgeons to choose equipment, ergonomics and training.? Severalstudies, e.g. Chauhan [2004], have demonstrated that although accuracy improved, it has come at theexpense of increased operating time and higher capital and per-procedure costs.Surgical NavigationSurgical navigation refers to the intra-operative guidance provided to the surgeon. The guidance pro-vided to the surgeon is typically information on the location of the surgical instrument relative to thetarget anatomy. This guidance can be provided through a variety of methods, such as visually, aurally,haptically, or using some combination. The most common method currently is a visual display on acomputer monitor. In order to provide information, the system must link the physical locations of thesurgical instrument and patient anatomy with their virtual representations. The location and orientationof surgical instruments and patient anatomy can be measured using medical imaging or using special-ized tracking hardware, or localizers. These measurements are then used to drive the position of themodels used on the display.Fluoroscopy is the most common medical imaging technique used for conventional navigation. Themain advantage is that the tip of a radio-opaque surgical instrument can be seen directly with respect tothe anatomy. The disadvantages are that the patient and the surgical team are exposed to radiation, andthat positioning the imaging equipment for the optimal viewpoint can be time consuming. In order toreduce unwanted radiation exposure and decrease operating room time, specialized tracking hardwarecan be used instead.There are several means of tracking the position and orientation of the patient anatomy and surgicalinstruments. Position can be measured directly, using rigid frames or mechanical linkages, or remotely,through several technologies including ultrasound, electromagnetic trackers, or optical trackers. Remotetracking technologies require reflective spheres, light-emitting diodes, ultrasound receivers, or magneticcoils to be attached to the anatomy to enable sensing. Each type of tracking hardware has its associatedadvantages and drawbacks.Mechanical linkages consist of articulated arms that are rigidly attached to the operating table andto the surgical instrument. By measuring the angles between segments and having known link lengths,336APPENDIX F. UKF DRILL AXIS CALIBRATIONFigure F.3 Figure 3 from Walker 2007 showing the Mark 1 instrumented linkage system. A - fix-ation stud,; B - first pair of revolute joints containing encoders; C - cable to connect encodersto computer; D - carbon tube link; E - third pair of revolute joints; F - handle; G - drill guide;H - digitizing tip. This system is used to accurately place pins for installing a cutting guide intotal knee replacement surgery.the position of the end-effector can be digitized. Mechanical systems have high acquisition rates andaccuracy on the order of 0.2mm, but suffer from a restricted workspace and often cause obstruction ofthe surgical area. An example of an instrumented linkage for total knee surgery from Walker [2007]is shown in Figure F.3. Mechanical linkages have largely been replaced by other types of trackinghardware.Optical Tracking System (OTS) are the most common type of tracking hardware, and are used byalmost all current clinical systems. OTS systems use photogrammetry to measure object geometry basedon images captured by one or more cameras. Some systems use videometric cameras, while infra-redcameras are more common. Both types of cameras use a specially designed marker attached to the objectbeing tracked. Videometric cameras use markers that includes elements of known length so the distancefrom the camera to the object can be determined. IR systems use active IR light emitting diode (LED) orpassive retroreflective spheres to reflect IR light generated near the camera. Active markers are availablein both wired and wireless versions. A minimum of three non-collinear markers are required to definethe pose of a rigid body in 6 DOF.OTS have several advantages, including high accuracy and reduced clutter in the operating room. Forexample, the NDI Polaris, shown in Figure F.4a, has an RMS error of 0.35mm, and is able to track bothwired and wireless tools. There are, however, several drawbacks. The main challenge is the that thesesystems rely on maintaining line-of sight between the camera and the markers. Any markers obstructedby the patient anatomy, the surgeon, or any fluid or debris generated by the surgery can decrease theaccuracy or prevent tracking altogether. One important consideration is therefore the need to mountmarkers on a location of the instrument away from where it will penetrate the body. A calibration is337APPENDIX F. UKF DRILL AXIS CALIBRATION(a) Tracking system and interface (b) Marker ArraysFigure F.4 Example of an optical tracking system. The NDI Hybrid Polaris Spectra (left) is ableto measure the 3D position of both active and passive markers (right).(a) Field Generators (b) 6DOF SensorFigure F.5 Example of an electromagnetic tracking system. The NDI Aurora? (Northern DigitalInc., Waterloo, ON, Canada) has two types of field generators (left) and is able to measure 5DOF and 6 DOF sensors (right).then required to relate the location of the markers to the point of interest (e.g. the instrument tip).Other drawbacks to OTS include the cost (good accuracy requires high-precision optics and fast trackingrequires expensive camera hardware) and limited working volumes.An Electromagnetic Tracking System (EMTS) tracks the position of sensor coils in an electromag-netic field. Most systems consist of four components: a field generator, tracked sensor coils, a sensorinterface, and a system control unit. Voltage is induced in the sensor coils when it is placed inside thecontrolled, varying magnetic field generated by the field generator. These voltages are measured andused by the system to determine the location and orientation of the coil. Since magnetic fields passthrough tissue, it is possible to track flexible instruments within the body. Furthermore, the sensorsare quite small so they can be embedded close to the tool tip. For example, as shown in Figure F.5,the smallest 6 DOF sensor for the Aurora system (NDI, Waterloo, Ontario, Canada) has a diameter of1.8mm. The main limitation of EMTS are their sensitivity to distortion. Anything that influences themagnetic field, such as the presence of conductive materials, can affect the accuracy. Compared to OTS,EMTS have a much smaller working volume, so the field generator must be placed carefully to ensureobjects can be tracked throughout the procedure.The next section describes how the transforms measured by the tracking hardware are representedand manipulated in software.338APPENDIX F. UKF DRILL AXIS CALIBRATIONRigid Body TransformsThis section provides an overview of the mathematics and notation used to describe the geometricalrelationship between rigid bodies. Throughout this report, scalars are represented in lowercase italics,vectors are represented in lowercase bold and matrices are represented in uppercase bold.A rigid body can be tracked in 3D space by defining a local coordinate system consisting of anorigin and three mutually perpendicular axes. The location and orientation of a coordinate frame withrespect to another coordinate frame is represented using a transform, which consists of a rotation and atranslation. The translation is represented as a vector of Cartesian coordinates, i.e.t = [tx, ty, tz]TThere are several different ways to represent rotation; here we chose to use the compact and com-putationally efficient unit quaternion, i.e.q = qw +qxi+qyj+qzk,where qw is called the scalar part and qxi+qyj+qzk is the vector part defined so thati2 = j2 = k2 = ijk =?1.We represent the quaternion as a vector:q = [qx,qy,qz,qw]T .A transform is then defined as a vector consisting of the quaternion and a translation:T = [qx,qy,qz,qw, tx, ty, tz]T .The transformation to object B in coordinate frame A is represented using the notation TBA. If thetransformation of a second object, C, is known in coordinate frame B, i.e. TCB, the transformation of Cin coordinate frame A can be found by composing the two transforms:TCA = TBA ?TCB,The composed rotation is found using the quaternion multiplication operation:qCA = qBA?qCB.The composed translation is found by adding the translation components rotated into the base frame339APPENDIX F. UKF DRILL AXIS CALIBRATIONusing quaternion conjugation:tCA = tBA +qBA ? tCB ? (qBA)?= tBA + tB?CA .The composition formula can be combined to calculate the transform of any coordinate frame withrespect to another coordinate frame as long as the intermediate transforms are known.A scene graph is a tree diagram used to represent the relationships between different coordinatesystems. Each node represents a coordinate system, and nodes are connected by known transforms. Thetransformation between any two coordinate systems can be determined by traversing connected nodesand composing the respective transform (or inverse, depending on direction).Figure F.6 shows an example scene graph for a CAS drilling system. The optical tracker measuresthe pose of three bodies directly with respect to the TCF: the drill (T drillTCF ), the SRF (TSRFTCF ), and the DRF(T DRFTCF ). The SRF is rigidly attached to the environment, and acts as a global reference for the othermarkers. The DRF is rigidly attached to the anatomy, and is used to track any relative motion of thepatient. The unknown transform from the drill to the tip, T DRILLT IP , is the goal of the calibration.75A&.(5D5,\/\/7,3 A1A720<D5)65)Figure F.6 Scene graph of a computer assisted surgical drilling system. Boxes represent coordi-nate systems; lines represent transforms. The goal of the system is to provide the user withinformation on the location of the tip relative to the target anatomy, T ANATT IP . The transformfrom the drill to the tip, T DRILLT IP , is unknown and must be calibrated.F.2.2 Computer Assisted DrillingThe previous sections provided a general overview of CAS. We now focus on a particular task of interest:surgical drilling.Drilling is one of the most commonly performed tasks in orthopaedic surgery. There are a varietyof reasons that a surgeon will create a hole in the bone, such as in preparation for a screw or implant,to relieve pressure, or to route tendons and ligaments. Although the relative importance of accuracy340APPENDIX F. UKF DRILL AXIS CALIBRATIONand speed will depend on the procedure, in general, the goal is to create a hole quickly with accurateposition, trajectory, and depth without causing excessive damage to the bone. This is often difficult toachieve, making drilling a good candidate for computer assistance.As discussed above, the primary motivation of CAS systems is to improve accuracy. Accuracy canbe difficult to achieve during drilling due to a combination of several factors: inadequate visualization,instability, and the nature of machining bone. Rancourt [2001b] demonstrated that drilling is an inher-ently unstable task. Lateral stiffness must be present to ensure that the force applied to the end of thedrill doesn?t cause an uncontrolled rotation if the force isn?t perfectly aligned with the drill axis. Thisinstability increases with larger drilling forces, such as those required to efficiently drill bone. Adequateforce levels must be used to reduce the risk of excessive heat generation that could cause damage tothe bone tissue, i.e. cause osteonecrosis. Maintaining adequate force and stability become competingrequirements.In order to reduce the risk of injury, many drilling tasks with high accuracy requirements are com-pleted under fluoroscopic guidance. Although fluoroscopy provides the surgeon with the actual positionof the drill bit relative to the anatomy, there are several drawbacks: only one perspective at a time isavailable, adjusting view positions is often difficult and time consuming, and both the patient and op-erating room team to are exposed to undesirable radiation. A CAS drilling system has the potential toreduce radiation exposure with comparable or improved accuracy.Distal locking of intramedullary nails, femoral head resurfacing and core decompression are exam-ple of surgical procedures that rely on accurate drilling. The success of each of these procedures involvea drilling task where the correct positioning and trajectory must be attained. Both distal locking andcore decompression typically rely on fluoroscopy to achieve the correct trajectory.ChallengesOne of the challenges of applying CAS techniques to drilling is tracking the position of the drill bit.It is difficult to directly track the tip of the drill bit using current technology. Optical systems rely online-of sight, so markers can not be placed on any part of the tool that will penetrate the body. Althoughelectromagnetic sensors could be installed in the tip of the drill bit, these would be expensive and thesensors would be susceptible to interference by the rotating drill motor. Some systems get around thisissue by tracking a drill guide instead, although this does not allow depth control, and can be lessconvenient.Instead of tracking the drill bit tip directly, it is common to attach a marker array to the drill itselfand determine the transform of the tip through a calibration. This method has the advantage of using asingle sensor for a variety of drill bits, but it does require a calibration each time the drill bit is changed.Drill CalibrationA drill calibration is necessary to describe the location and orientation of the drill bit with respect to themeasured drill coordinate frame. It is an important component of the overall accuracy of a CAS system;a difference between the actual position of the drill and what the surgeon is being shown can result in341APPENDIX F. UKF DRILL AXIS CALIBRATIONyxzxzy7iSDrillD5,\/\/77,3Figure F.7 The goal of the drill calibration is to determine the unknown transform from the coor-dinate system defined by the fiducial markers to the drill bit tip, T DRILLT IP .neurovascular injury or misalignment of screws or implants. Figure F.7 illustrates the two coordinatesystems and the unknown transform between them. The calibration process should be quick, accurate,require minimal user interaction and work reliably.The drill bit calibration is a transform that represents the translation to the drill bit tip and theorientation of the rotational axis, or primary axis, of the drill bit. The tip translation is required todetermine hole location and depth while the principal axis defines the trajectory of a hole. The additionalDOF representing rotation around the drill bit is not necessary, but is sometimes useful to indicate somemeaningful direction of the drill (e.g. ?up? on the drill body.)This calibration can be determined using a transform method with a specialized tool, or with afitting method. Transform methods use a special tool with a known geometrical relation to directlycompute the drill calibration. Figure F.8 shows an example of a special dedicated calibration tool usedwith the VectorVision system (BrainLAB Inc., Westcherster, Illinois, USA). The tool relies on highmanufacturing tolerances to determine the length, diameter, and position of the tip of the instrument.The drill calibration is calculated directly using the measurement of the drill coordinate frame, themeasurement of the calibration tool coordinate frame and the known transform from the calibrationcoordinate frame to the machined hole into which the drill is placed.Fitting methods rely on constraining the tool in the ground frame and recording data while the toolis moved. Errors can be introduced into the data through unwanted movement of the constraints andfrom random noise in the tracker measurements. The calibration parameters are estimated by using analgorithm to fit the noisy data to a known geometry.For example, one of the most commonly performed is a pivot calibration. Translation of the tip isconstrained by placing the tip of the drill bit in a divot that is fixed with respect to some coordinatesystem, as illustrated in Figure F.9. The position of the drill coordinate system is measured while thedrill is pivoted using the remaining 3 DOF. A sphere is fit to the resulting data, with the coordinates ofthe centre representing the tip location. The measurements are then used to determine the translation342APPENDIX F. UKF DRILL AXIS CALIBRATIONFigure F.8 Example of a special drill calibration tool. (Source: [Beckmann 2006], ?Springer2006, used with permission.)Figure F.9 Calibration data for tip translation is generated by a pivot procedure. The drill coor-dinate frame is measured while the drill is pivoted with the drill bit tip held fixed in a smalldivot.of the tip with respect to the drill coordinate frame. The inputs and outputs of a typical algorithm aresummarized in Table F.3. The goal is to find the centre, (x,y,z), and radius, r, that minimize the distancebetween the data points and the sphere.A similar approach can be used to determine the orientation of the primary axis. The drill bitis constrained to restrict 3 DOF of translation and 2 DOF of rotation. This restricts motion to 1 DOFrotation around the drill bit axis, as illustrated in Figure F.10, which limits the drill coordinate frame tomove along a 3D circle. In practice, this can be accomplished by clamping the drill bit to a v-groove,or by drilling into a work-piece fixed to the ground, and rotating the drill chuck. A LS3DCF algorithmcan then be used to determine the calibration. The goal of this algorithm is to find the centre point,343APPENDIX F. UKF DRILL AXIS CALIBRATIONTable F.3 3D Sphere Fitting AlgorithmName Type DescriptionInputs m integer number of data points(xi,yi,zi)mi=1 array(m) of vectors data points(x0,y0,z0),r0 vector,scalar initial valueOutputs (x,y,z),r vector,scalar fitted sphere(di)mi=1 array(m) distances of data from sphereFigure F.10 Data for an axis calibration can be generated by using a rotation calibration procedure.The drill coordinate frame is measured while the drill is rotated around the drill bit which isheld fixed or clamped.(x,y,z), normal vector, (a,b,c), and radius, r, that minimize the distance of the 3D data points from the3D circle, expressed in the fixed coordinate frame. The inputs and outputs are summarized in Table F.4.There are two sources of error that can cause the drill transforms to deviate from a perfect circle:constraint movement and measurement noise. If the constraints shift during the rotation procedure, therotation axis in the ground frame will move. Any translation or rotation perpendicular to the rotationTable F.4 3D Circle Fitting AlgorithmName Type DescriptionInputs m integer number of data points(xi,yi,zi)mi=1 array(m) of vectors data points(x0,y0,z0),(a0,b0,c0),r0 vector,vector,scalar initial valueOutputs (x,y,z),(a,b,c),r vector,vector,scalar fitted circle(di)mi=1 array(m) distances of data from circle344APPENDIX F. UKF DRILL AXIS CALIBRATIONaxis will introduce a radial error, or angular error, respectively. Translation along the rotation willintroduce axial error. The second source of error is the inherent noise in tracking the position of thefiducial markers which results in translational and rotational uncertainty in the drill coordinate frame.One of the limitations of this LS3DCF technique is that it does not take advantage of all availabledata. Although the tracker is able to determine both the translation and rotation of the drill coordinateframe, only the translation data is used. A different algorithm could be designed to incorporate rotationdata as well. Another limitation is that the algorithm requires blocks of data. A conservative number ofdata points must first be measured and then processed. If the desired accuracy is not achieved, the entireprocess must be repeated, which can take up valuable time.An unscented Kalman filter (UKF) is able to process data as it is measured and provide not only thecalibration parameter, but an estimate of the uncertainty. This enables real-time calibration which canbe terminated when the desired accuracy is reached. The following section describes the UKF in moredetail.F.2.3 Kalman FilterThe Kalman filter is a set of mathematical equations designed to recursively estimate the state of aprocess in a way that minimizes the mean of the squared error [Welch 2006]. The filter can be usedto estimate the past, present and even future states, and can do so with incomplete or noisy data. TheKalman filter was originally developed for linear systems [Kalman 1960], but has since been extendedto nonlinear systems by using the unscented transform [Julier 1997]. The UKF is required here to handlenonlinear rotations.The state of the process at a certain time i is described as a state vector xi. The UKF algorithmpredicts the state vector at some time i+1 and then corrects the estimate using noisy measurements asfeedback. A nonlinear process model describes the time time update and a nonlinear observation modeldescribes the measurement update.For parameter estimation, the state vector is formed using the L parameters, and is assumed toremain constant. The process model is thus stationary, with process noise Rk:xk+1 = xk +Rk (F.1)The observation model is defined with known input uk, and output yk. A nonlinear map between theG()?, is dependent on the parameters:yk = G(xk,uk)+Qk, (F.2)where Qk is the observation noise related to errors in the measurement system. The UKF uses adeterministic sampling approach to calculate the mean and covariance by generating and propagatingso called sigma points through the non-linear mapping and then computing a weighted mean and co-variance. Three parameters control these sigma points: the constant ? determines the spread of sigmapoints, ? is a secondary scaling parameter, and ? is used to incorporate prior knowledge about the dis-345APPENDIX F. UKF DRILL AXIS CALIBRATIONtribution of the state vector 1. Another parameter, ? , is used to apply exponential weighting on pastdata. A full description of the algorithm can be found in Appendix F.8.2.UKFS have been applied to a variety of relevant calibration and registration problems. Moghari[2006] developed a UKF algorithm for calibrating an optically tracked ultrasound probe, allowing the2D ultrasound images to be mapped to physical coordinates. Simpson [2007] used a UKF algorithmfor calibrating the tip of an optically tracked drill and providing real-time tracking and estimates ofuncertainty. Providing these uncertainty estimates to the surgeon via the visual guidance display led toan average 20 % reduction in navigated pedicle screw placement time. The UKF technique has also beenused for 3D point-based rigid registration [Zamani 2008].F.2.4 SummaryThis section provided background information on CAS, computer-assisted surgical drilling, drill calibra-tion, and the UKF. The following section describes how these elements were brought together to designan unscented Kalman filter for calibrating the primary axis of a drill for use in CAS.F.3 MethodsThis section describes the two components of the calibration: the procedure to generate the data, and thealgorithm to determine the calibration. We describe how we generated simulated calibration data andhow experimental calibration data was measured with our research CAS system. Next, we describe thedevelopment of an UKF for determining the axis calibration from the rotation data. Finally, we describehow the algorithm was validated and compared to a LS3DCF method.F.3.1 Calibration ProcedureThe goal of the calibration procedure is to generate data that can be used by the calibration algorithmto determine the calibration parameters. In order to determine the primary axis, we chose to use arotation procedure to constrain the measured motion to a 3D circle. The drill body (and measured localcoordinate frame) is rotated around a fixed drill bit. This section describes how rotation data weregenerated using computer simulation and measured with our research CAS system.Simulated Calibration ProcedureSimulated data were generated using a custom script in Matlab (Version 7.14.0.739, The Mathworks,Natick, MA, USA). The tool geometry was defined by a transform from the marker array to the tip ofthe tool, with the z-axis aligned with the drill bit axis. The calibration procedure was defined by a tiplocation in the ground frame. Data were then generated by rotating the tip around the drill axis in theground frame and calculating the resulting position of the drill coordinate frame. Axial, angular, andmeasurement error was introduced by generating random numbers from a normal distribution. A value1 ? typically ranges from 1e?4 ? ? ? 1; ? is typically set to 3?L for parameter estimation; and ? = 2 is optimal for aGaussian distribution [Wan 2000].346APPENDIX F. UKF DRILL AXIS CALIBRATIONof 0.35 mm\/?4 was used for the FRE of the tracker, where 0.35 mm is the rated volumetric uncertaintyof the NDI Polaris? trackers and 4 represents the number of markers. A copy of the code can be foundin Appendix F.8.1.1. Select T TIPDRILL, the transform that represents the rotation and translation from the drill markercoordinate system to the drill bit tip coordinate system.2. Select T TIP,0TCF , the initial position of the drill bit in the ground frame, or here, the TCF.3. Create a movement transform by combining axial angular rotation range (?z), axial error (?z), andtilt error (?? ). The axial error and tilt error are drawn from a zero-mean, normal distribution withstandard deviations of ?? and ?z, respectively.4. Compose movement transform with initial tip pose to get T TIP,iTCF .5. Calculate drill marker pose in TCF: T DRILL,iTCF = TTIP,iTCF ?TDRILLTIP .6. Apply zero-mean, normally distributed perturbations to the translational components of the drillmarker: T? DRILL,iTCF .7. Repeat steps 3-6 to produce N calibration points.Experimental Calibration ProcedureExperimental data were measured with a CAS research system using a commercially available drill anddrill bits.The experimental CAS system is based on an Polaris optical tracker (NDI, Waterloo, Ontario,Canada). Although this system is capable of tracking both passive and active markers, only passive,spherical retroreflective markers were used. Arrays of at least 3 markers in a pre-defined geometry wereattached to rigid bodies to measure their position and orientation. The Polaris communicates through aserial link to a PC (Intel Core 2 Quad CPU 2.40 GHz, internal storage 4 GB, NVIDIA GeForce 9500GT512MB Video Card). Transforms can be acquired up to a maximum rate of 60 Hz.The system uses a modified commercially available drill (Model DW907, DeWalt, Baltimore MD,U.S.A). This model is hand-held and battery-powered. Four of the screws that held the drill togetherwere replaced with threaded standoffs. The retroreflective markers were attached to each standoff usingthe standard threaded mounting posts. The modified drill is illustrated in Figure F.11. The markergeometry was characterized using the collection procedure of the NDI software. A local drill coordinatesystem was defined with the origin at marker A, the negative z-axis passing through marker B, and thex-axis perpendicular to the plane defined by the markers A, B, and C. The resulting coordinate systemhas the the z-axis approximately aligned in the direction of the primary axis of the drill bit. Markerpositions are listed in Appendix F.7.1.The calibration procedure was performed and measured 30 times. During each trial, the drill bit wasrigidly clamped relative to the ground while the drill body was rotated. It was not possible to completea full 360? rotation and maintain line of sight, so the drill was rotated approximately 90? and thenreversed to the original location. During the rotation, 500 measurements of the drill coordinate framewere recorded at 60 Hz.347APPENDIX F. UKF DRILL AXIS CALIBRATIONAB&D]x \\Figure F.11 Retroreflective markers were attached to a commercially available cordless drill toenable pose measurement with an optical tracker system. A local drill coordinate systemwas defined with the origin at marker A and the z-axis approximately aligned with the drillaxis. The USB accelerometer shown attached to the side of the drill was not part of thisproject.The next section describes the algorithm used to process the data.F.3.2 UKF Axis Calibration AlgorithmThe goal of this algorithm is to determine the location of the drill bit axis in the drill coordinate framefrom transform data produced by a rotation procedure. Several components are required in order to de-velop a UKF algorithm to determine the calibration parameters. We must determine how to parametrizethe axis and how to use the observations (i.e. the measured calibration data) to update the parameterestimate. All of the simulation, testing, and analysis was done using Matlab (Version 7.14.0.739, TheMathworks, Natick, MA, USA). The UKF algorithm framework was based on the paper by Wan [2000].Axis ParametrizationAn axis in 3D space can be defined by two 3D points or a single 3D point and a parallel vector, requiringa minimum of 5 parameters. Since any point along the line can be used, there are an infinite set of validparameters. In the case of tracked surgical tools, we can use a priori information about the approximatedirection of the axis with respect to the tool coordinate system to limit the range of valid parameters.Our parametrization uses two 3D points each restricted to a pierce plane. The two pierce planesare defined approximately normal to the desired axis. The axis intersects each plane at a single point,defined as the pierce point. This reduces the number of unknown parameters to four: two 2D pierce348APPENDIX F. UKF DRILL AXIS CALIBRATIONFigure F.12 Unique pierce points for a pre-defined distal and proximal plane.points. For simplicity, we use the xy plane and a parallel plane offset by 100 mm 2. The planes and anarbitrary axis are illustrated in Figure F.12.UKF Parameter EstimationA UKF can be used for parameter estimation by defining an appropriate state vector using the parameters.To map the axis in the ground frame from measurements of the tool, the rotation axis must be representedwith respect to both the tool and the ground. This require 8 parameters: two pierce points for theproximal and distal planes in each coordinate system and two components per pierce point,x = [(pproximal,pdistal)ground,(pproximal,pdistal)tool]T=[ugp,vgp,ugd ,vgd ,ut p,vt p,utd ,vtd]T. (F.3)xi = xi+1 +(0,?Q)(F.4)The state model defines how the state vector changes in time. In our case, the parameters aretime invariant with initial value and covariance matrix x0 and P0x , respectively. (0,?Q) is a zero meanGaussian random vector with a covariance matrix ?Q which represents noise in the calibration process.2This choice of offset keeps pierce points errors on similar scales: 1 mm angular pierce point error is equivalent to 1.7?349APPENDIX F. UKF DRILL AXIS CALIBRATIONObservation ModelThe observation model defines how external observations or measurements of the system are used tocorrect the estimate of the system state. For parameter estimation, a training set of known inputs anddesired outputs is typically used to solve for the parameters. Here, we define an observation model usinga direct-error formulation so that the expected output is always zero.Each observation is a measured transform of the drill coordinate frame with respect to ground. Theerror is computed as the difference between the rotation axis based on this measurement and the currentground rotation axis estimate. Figure F.13 illustrates the observation model.First, the pierce points in the ground frame and tool frame are extracted from current parameterestimate:ppTCF =???ugpvgp0??? ,pdTCF =???ugdvgd100??? (F.5)ppDRILL =???ut pvt p0??? ,pdDRILL =???utdvtd100??? (F.6)These pierce points are then transformed into the ground frame using the measured transform(TDRILLTCF ) of the drill with respect to ground:pp?TCF = ppDRILL ?(TDRILLTCF)?1(F.7)pd?TCF = pdDRILL ?(TDRILLTCF)?1. (F.8)The projected pierce points define an axis which intersects the pierce planes in the ground frame intwo places:nTOOLTCF =pd?TCF?pp?TCF???pd?TCF?pp?TCF???(F.9)?d =0?(pp?TCF)z(nTOOLTCF)z(F.10)?p =100?(pp?TCF)z(nTOOLTCF)z(F.11)pp??TCF = pp?TCF +?d ?nTOOLTCF (F.12)pd??TCF = pd?TCF +?p ?nTOOLTCF (F.13)350APPENDIX F. UKF DRILL AXIS CALIBRATIONFinally, the radial distance between the two pierce points on each plane is computed and summedtogether to calculate the error.e = rd + rp=???pdTCF?pd??TCF???+???ppTCF?pp??TCF??? (F.14)If the calibration parameters are correct, than the transformed tool rotation axis and its correspondingpierce points will be aligned with the ground rotation axis and both radial distances will be zero. Theunscented transform is necessary because the rotations make the observation model non-linear.Converting Pierce Points to Axis CalibrationOnce the algorithm has finished processing the data, the optimized pierce points must be convertedinto a more usable form. The pierce points define the primary axis of the drill bit: this does not includeinformation on the location of the drill bit tip along the axis or a rotation around the axis. The translationof the tip along the axis can be determined using a pivot calibration. The rotation around the axis is notimportant, and is typically set to something convenient, for example the y-coordinate aligned with thenatural ?up? direction of the drill body.In the absence of a pivot calibration, we can still convert the pierce points into a transform. Theorigin is selected as the point along the axis closest to the drill marker origin. The z-axis is definedusing the two pierce points and rotation around the axis is chosen arbitrarily.Ground Truth DifferenceThe accuracy of the calibration algorithm can be measured in simulation by calculating the groundtruth difference, i.e. the difference between the known parameters and the estimates produced by thealgorithm. In order to describe the difference between two axes, two error metrics are defined: anangular error and a radial error.The angular difference between two axes can be found by using the dot product and the directionvectors a and b:cos? =????a ?b|a| |b|????The radial error is defined as the minimum mutually perpendicular distance between the two axes.If the two axes coincide or intersect, the radial error will be zero, otherwise a finite distance exists. Theequations to calculate this distance can be found in Appendix A.1.It is often convenient to have a single scalar representation of error. This can be accomplished bymapping one of the error metrics into the space of another using a characteristic length. In this case, wemap the angular error into radial units using a characteristic length of 100 mm, which corresponds tothe chosen pierce plane offset. This applies equal weighting to an angular error of 1? and approximately351APPENDIX F. UKF DRILL AXIS CALIBRATIONFigure F.13 Illustration of observation model. The top figure shows the measured drill coordinateframe with its distal and proximal plane in cyan and magenta. The tool pierce points aretransformed using the measurement into the ground frame. The tool pierce points are foundin the ground frame on the blue distal and red proximal plane. The algorithm attempts tominimize the radial distance between the tool and ground pierce points (rd + rp).352APPENDIX F. UKF DRILL AXIS CALIBRATION1.7 mm.F.3.3 Testing, Validation and ComparisonThis section describes the testing, validation and comparison of the UKF axis calibration algorithm.The simulated data were used to optimize the filter tuning and provide a measure of how the internalerror metrics compared to the ground truth difference for different amounts of measurement error. Theexperimental data were used to estimate the repeatability of the algorithm. Finally, we compared theUKF axis calibration algorithm to a LS3DCF algorithm using both the simulated and experimental data.Filter TuningThe Kalman filter has several user-controlled parameters used to tune its performance: the sigma pointspread, ? , the measurement noise covariance matrix, R, and the past-data forgetting factor, ?RLS. Inorder to achieve optimal filter performance, we performed an optimization using simulated data to de-termine appropriate values for each parameter.Since the tuning parameters are bounded the optimization was set up as a constrained minimiza-tion. Table F.5 lists the tuning parameters and their upper and lower bounds based on values found inWan [2000]. We used the Matlab function fmincon with the interior-point algorithm. The objectivefunction is a sum of the final radial and (mapped) angular ground truth difference.min?RLS,?,R(eRt + eRg + eAt + eAg) (F.15)The optimization was applied to 100 simulated calibration data sets generated with a 0?? 90? 0?rotation; calibration errors of ?? = 0.25? axial and ?z = 1mm tilt; and marker measurement error of0.35\/?4mm FRE.Table F.5 Filter Tuning Parameter BoundsTuning Parameter Lower Bound Upper Bound?RLS 0.9 0.9999? 1e-3 1R 1e-6 1e-2Simulated Ground Truth DifferenceA second set of 100 simulated data sets were generated and used to evaluate and compare the groundtruth difference of the UKF axis and with the least-squares 3D circle fitting (LS3DCF) algorithm(LeastSquares Geometric Elements Library, National Physics Laboratory, Teddington, Middlesex, UK.3). TheLS3DCF implementation uses a Gauss-Newton method. The ground truth differences were tested with apaired t-test to assess any difference between the two algorithms using a significance level of ? = 0.05.3Available for download at http:\/\/www.eurometros.org\/metros\/packages\/lsge\/353APPENDIX F. UKF DRILL AXIS CALIBRATIONExperimental RepeatabilityWe wanted to quantify the performance of the UKF algorithm and compare it to the LS3DCF algorithmusing experimentally measured data. Since the ground truth is not known for experimental data, analternative metric is required. A measure of repeatability was obtained by determining an average cali-bration transform. The average calibration transform was calculated by combining the Euclidean meanof the translation with the norm-preserving average of the quaternions [Markley 2007]. The angularand radial error compared to the average were calculated for each trial and a Kolmogorov-Smirnofftest was applied to assess statistically detectable differences between the two calibration algorithms. Asignificance level of ? = 0.05 was used.F.3.4 SummaryWe successfully implemented a UKF algorithm to determine the primary axis of a tracked drill bit usinga rotation calibration procedure. We analysed the performance of our algorithm using simulated dataand measured a series of rotation procedures to test it experimentally. The next section presents theresults calibrations performed using the simulated and experimental data.F.4 ResultsThis section provides results of the creation, tuning, and testing of a rotation calibration procedure and aUKF-based axis calibration algorithm. The calibration is first demonstrated using simulated data. Next,simulated data is used to tune and assess the performance of the algorithm. Finally, we present theresults of a set of experimentally measured calibrations.F.4.1 ExampleIn this section, each step of the calibration process is illustrated using simulated data. Figure F.14 showsa tool defined with a tip calibration ofT T IPDRILL = [0.0868,0.0868,?0.0076,0.9924,?40,?20,120]Tand a tip position ofT T IPTCF = [0.0713,?0.0500,?0.8160,0.5714,100,60,50]T .These values were selected to represent an axis that has similar offsets to our experimental setup,with a rotation axis that is roughly in the z-direction of the tool and the tracker. The drill is rotated 90?around the drill axis then returned to its original position. Each measurement is perturbed with noisedrawn from a uniform distribution. As shown in the figure, the data lies approximately along a segmentof a 3D circle.The calibration ground truth is illustrated in Figure F.15. The ground truth consists of two sets oftwo pierce points which represent where the axis pierces the distal and proximal pierce planes. Each354APPENDIX F. UKF DRILL AXIS CALIBRATIONFigure F.14 Illustration of a particular tool geometry (left) and simulated calibration procedure(right). The tip is defined in the local tool coordinate system. Measurements in the trackercoordinate frame are generated by rotating the tool around the ground rotation axis. Thisfigure shows a 20 measurement sample of a 0?? 90?? 0? simulated calibration with 1 mmaxial error, 0.25? tilt error, and 0.18 mm FRE.plane is characterized by 5 parameters: a fixed plane offset, and two pierce points.The UKF-based algorithm is applied to the simulated data with a default set of filter parameters(? = 1?10?3,? = ?5,? = 2). The filter is iterated for each simulated measurement. Figure F.16illustrates the estimate of the pierce point parameters after each iteration. Even with a naive initialestimate, the parameters converge after 14-15 iterations.By comparing the known axes with the estimated parameters, the ground truth difference for eachiteration can be calculated, as illustrated in Figure F.17. The ground truth difference decreases andapproaches zero as expected. The final ground truth difference for the tool is 0.03 mm and 0.33?.When using experimental data, the ground truth isn?t known so an alternative measure must be usedto estimate the uncertainty. Figure F.18 illustrates convergence of the norm of the covariance matrix.This represents an combined estimate of the maximum uncertainty in the parameters.F.4.2 Filter TuningOptimization was performed on 100 sets of simulated data to determine the appropriate filter tuningparameters. The simulated data were a 0??90??0? rotation with N = 500 samples. Table F.6 lists thevalues of the tuning parameters resulting from the optimization.355APPENDIX F. UKF DRILL AXIS CALIBRATIONFigure F.15 Ground truth pierce points for example data. (Top) The rotation axis in the groundframe is shown with the tip coordinate frame and its corresponding distal (ugd ,vgd) andproximal (ugp,vgp) pierce points. (Bottom) The rotation axis in the tool frame is shown withthe tip coordinate frame and its corresponding distal (utd ,vtd) and proximal (ut p,vt p) piercepoints.F.4.3 Testing and ComparisonThe optimized tuning parameters were then used to evaluate the ground truth difference on an additional100 sets of simulated data. Summary statistics for the radial and angular ground truth difference arelisted in Table F.7. The most relevant metric is the radial and angular ground truth difference for thetool.356APPENDIX F. UKF DRILL AXIS CALIBRATIONFigure F.16 Convergence of pierce point locations with an initial estimate of x0 =[0,0,0,0,0,0,0,0]T . The parameter estimate stabilizes after about 10 iteration.Figure F.19 illustrates the angular and radial ground truth difference of each data set for both algo-rithms. The LS3DCF algorithm clearly has less radial ground truth difference for the tool axis. A pairedt-test was used to test whether the mean of the ground truth difference differed between the algorithms.Using a significance level of ? = 0.05, there was a statistically detectable difference in all four groundtruth differences. Figure F.20 shows the empirical cumulative distribution function comparing the twoalgorithms, which shows how the UKF algorithm has a smaller angular ground truth difference while theLS3DCF algorithm has a smaller radial ground truth difference.357APPENDIX F. UKF DRILL AXIS CALIBRATIONFigure F.17 Ground truth difference for simulated example data. The final ground truth differencefor this N=20 sample is 0.69 mm and 0.40? for the tracker rotation axis and 0.03 mm and0.33? for the tool rotation axis.Figure F.18 Covariance matrix norm for example data. The norm of the covariance matrix is usedto estimate uncertainty in the axis estimate in the absence of ground truth.F.4.4 Experimental Calibration DataThis section describes the results from the 30 experimental rotation procedures. Drill coordinate frametransforms from a typical trial are shown in Figure F.21. Like the simulation, these measurements liealong a portion of a 3D circle. At a localizer acquisition rate of 60Hz, each procedure takes just over 8seconds to complete. Over a total rotation of 180?, this corresponds to an average angular velocity of22?\/s, or approximately 0.4? per measurement.358APPENDIX F. UKF DRILL AXIS CALIBRATIONFigure F.19 Comparison of radial and angular ground truth difference for 100 sets of simulateddata using UKF axis algorithm and LS3DCF algorithm.Figure F.20 Empircal CDF of angular and radial ground truth difference for 100 simulated datasets. Using a paired t-test, there is a statistically detectable difference between the means ofeach component of the ground truth difference.359APPENDIX F. UKF DRILL AXIS CALIBRATIONTable F.6 Optimized Tuning ParametersTuning Parameter Simulation?RLS 0.98? 0.04R 0.0001Table F.7 Simulated Data Ground Truth DifferenceAlgorithm Parameter ??? 95% CIUKFRadial-Ground 0.19 ? 0.09 mm [0.17,0.21]Radial-Tool 0.50 ? 0.23 mm [0.45,0.55]Angular-Ground 0.16 ? 0.07? [0.14,0.17]Angular-Tool 0.16 ? 0.07? [0.14,0.17]LS3DCFRadial-Ground 0.14 ? 0.08 mm [0.12,0.15]Radial-Tool 0.13 ? 0.07 mm [0.11,0.14]Angular-Ground 0.24 ? 0.15? [0.21,0.27]Angular-Tool 0.24 ? 0.15? [0.21,0.27]Ground truth error statistics for 100 simulated data sam-ples with ?z = 1mm axial error, ?? = 0.25? tilt error and0.18 mm FRE.Figure F.21 Measured drill transform data from a typical experimental rotation. Every 10th mea-surement is shown for clarity. Each trial consisted of 500 measurements rotated over 90? andback again.Figure F.22 illustrates the pierce point estimates of a typical experimental dataset. The UKF was runwith the optimized tuning parameters.360APPENDIX F. UKF DRILL AXIS CALIBRATIONIn this case, the estimate converges after about 35 iterations, which corresponds to approximately14? of rotation. There is some variability between trials, as shown with the norm of the covariancematrix for all experimental trials in Figure F.23. This figure clearly shows that essentially all trialsconverge after 80 iteration, which corresponds to about 30? of tool rotation. An appropriate thresholdon the covariance matrix norm could be used to end the rotation when a desired level of uncertainty isreached.Figure F.22 Pierce point convergence behaviour for a typical experimental rotation. The top figureshows pierce points corresponding to the ground rotation axis whereas the bottom figureshows pierce points corresponding to the tool rotation axis. The first 75 iterations of 500 areshown.361APPENDIX F. UKF DRILL AXIS CALIBRATIONFigure F.23 Convergence of covariance norm for N=30 experimental rotations. All trials convergeafter approximately 80 iterations. The norm of the covariance matrix is a measure of themaximum uncertainty in the parameters.Since no ground truth is available for the experimental data, we calculated a measure of repeatability.The pierce point parameters estimate for each trial was found by averaging the results of the last 50iterations. Figure F.24 shows a set of boxplots representing the difference between the pierce pointsparameter for each trial and the mean over all trials. The repeatability of the pierce points varied from0.13 mm to 0.28 mm.Figure F.24 Repeatability of pierce points determined by unscented Kalman filter (UKF) algorithmfor N=30 experimental rotations.The average time taken to process each observation was 0.0028 s.362APPENDIX F. UKF DRILL AXIS CALIBRATIONFigure F.25 Calibrated tip pose (large coordinate frame) from typical experimental rotation data(small coordinate frames). Only every 10 data transforms are shown for clarity.363APPENDIX F. UKF DRILL AXIS CALIBRATIONF.4.5 Least-Squared Circle Fitting ComparisonFigure F.26 illustrates a paired comparison of the two calibration algorithms for 30 experimental rotationdata sets. A Brown-Forsythe Levene-type test was used to assess whether the calibration errors comesfrom groups with equal variances. A non-parametric test was used since the errors are all positive.Although the radial ground error was close to reaching significance, no statistically detectable differencewas found, suggesting that the two methods have comparable repeatability (Table F.8).Table F.8 Experimental Calibration Algorithm ComparisonParameter Test Statistica pRadial-Ground 3.85 0.054Radial-Tool 3.25 0.077Angular-Ground 1.03 0.31Angular-Tool 0.68 0.412a Brown-Forsythe Levene-type test forequal variances.F.4.6 SummaryThis section presented the results of the testing and comparison of the UKF axis algorithm. An illus-trative example was first used to demonstrate how the algorithm worked, followed by results of thetuning and comparison to a LS3DCF algorithm using simulated data. Finally, the results of applying thealgorithm to data obtained using the experimental CAOS system were presented.F.5 DiscussionWe developed a calibration method to determine the unknown transformation of the primary axis ofa drill bit with respect to a marker frame attached to the body of the drill. Data were generated witha rotation procedure and a UKF based algorithm was developed to process the data. The UKF basedalgorithm was able to determine calibration parameters with a comparable ground truth difference to astandard LS3DCF technique with the added benefit of being able to do it in real-time as well as provideuncertainty metrics which can be used to enhance visualization.F.5.1 PerformanceIn this section, we discuss the performance of the UKF axis calibration algorithm in the context of thecharacteristics of an ideal registration algorithm proposed by Yaniv [2008].Execution TimeThe ideal registration algorithm should occur in real-time. The Matlab implementation of the algorithmtook approximately 0.0028 seconds to process each data point, which is more than sufficient for real-time calibration using the NDI Polaris tracker, which is limited to an acquisition rate of 60 Hz. Based on364APPENDIX F. UKF DRILL AXIS CALIBRATIONFigure F.26 Comparison of radial and angular error for UKF algorithm and LS3DCF algorithm.this timing, this algorithm could be used for real-time calibration with a measurement update frequencyas high as 300 Hz. Code optimization and a programming language with lower overhead could extendthis range even further. The ability to perform the calibration in real-time is a significant gain over thestandard LS3DCF technique which operates on batch data.AccuracyWe adapted the original goal of a TRE less than 0.1 mm in the region of interest to better accommodatethe dual-errors associated with axes. For simulated data with realistic amounts of noise, the UKF axisalgorithm had a mean radial ground truth difference of 0.70 ? 0.29 mm (95% CI: 0.65?0.76) and a365APPENDIX F. UKF DRILL AXIS CALIBRATIONmean angular ground truth difference of 0.22 ? 0.10? (95% CI: 0.20?0.24). These errors are larger thanexpected.Breakdown PointAccording to Yaniv, an ideal registration algorithm must be able to handle more than half of the dataelements as outliers before results fall outside of reasonable bounds. This was not tested explicitly forthis algorithm. In the case of a real-time UKF calibration, any errors in the rotation procedure would bereflected in the uncertainty of the parameter estimates. If for example the drill slipped, the user couldsimply correct the mistake and continue the rotation procedure. It might take slightly longer for thecalibration to converge to the desired uncertainty, but the built-in data forgetting factor should take careof any outlying data points.AutomationAn ideal registration should not require user interaction. There are three aspects of the UKF calibrationthat require some user input. First, the normal vectors of the pierce planes must be approximatelyaligned with the rotation axis in order to work properly. The orientation of the pierce planes couldbe automated, or simply chosen based on a priori knowledge of the tool geometry. Second, the tuningparameters of the filter must be selected appropriately. A default set of tuning parameters should provideconvergence for an arbitrary condition. Once an application is selected, a developer could characterizethe tool and tracker to determine optimal parameters. Finally, the positive direction of the rotation axisis calculated arbitrarily and must be sometimes be flipped by the user to align with the navigated modelof the tool. The calibration could be set up to start in a particular direction, e.g., clockwise, in order togive the algorithm the necessary information to properly determine the positive direction.ReliabilityGiven the expected clinical input, an ideal registration should always succeed. For a drill with a similargeometry to the one used with our experimental CAOS system, the algorithm converged to a solutionfor each experimental rotation data set. Further testing is necessary to ensure the algorithm workssuccessfully with different tool geometries and with the rotation axis fixed in different location over theworking volume of the tracking hardware.F.5.2 Comparison to Other MethodsPart of the initial motivation of this project was difficulty in finding information on existing axis cal-ibration techniques. Clinical systems like the VectorVision? (BrainLAB, Munich, Germany) rely onspecially designed tracked calibration tools, which are expensive and inconvenient for a research envi-ronment. These calibration tools are manufactured with tolerances to achieve high levels of accuracy.The need to track the calibration tool will also introduce inaccuracies due to noise in measuring themarkers and uncertainty in registering the marker array.366APPENDIX F. UKF DRILL AXIS CALIBRATIONThe LS3DCF approach has been used by other researchers (e.g. Kassil [2007]), but limited detailswere provided on its implementation or validation. Since the algorithm relies on a preliminary 3D planefitting technique, it can be sensitive to axial error, and measurements with low radius of curvature (e.g.large radius and small rotation angle). Although some existing algorithms can return an estimate ofuncertainty, they definitely work on a batch of data. The other limitation is that the input is simply themeasurement translations. Any orientation information on the revolving rigid body is discarded.Based on the slightly lower ground truth differences, this LS3DCF algorithm batch-processed thesimulated data sets more accurately than the UKF algorithm processed the data iteratively. Part of thedifference in performance is that this UKF axis algorithm implementation uses a static value for theexponential weighting on past data. An intermediate value must be chosen to balance early convergencewith late susceptibility to noisy data.There is no statistically detectable difference in repeatability between the two algorithms whenusing experimentally measured data. Table F.7 demonstrates similar repeatability using simulated datain all measures except the radial tool ground truth difference. The UKF algorithm appears to have apositive relationship between radial and angular error, especially in the tool frame, whereas the LS3DCFalgorithm has a consistent level of radial error.SummaryThis section discussed the results of the UKF algorithm testing in the context of the characteristics of anideal registration algorithm and compared the UKF algorithms performance to a LS3DCF algorithm. TheUKF algorithm has similar levels of accuracy to a LS3DCF algorithm and has the advantage of being ableto complete the calibration in real-time. There is still room for improvement by reducing the need formanual user intervention to make the algorithm more automated and to ensure the algorithm is reliablewith other tool geometries and rotation locations.F.6 ConclusionsThis section summarizes the development of the calibration procedure, and the results of the simulationsand experimental repeatability. The strengths and limitations of the UKF algorithm are discussed alongwith opportunities for future work.F.6.1 ContributionsThe purpose of this project was to develop and test a method for calibrating the primary axis of anoptically tracked drill for use in CAS. We selected a simple rotation procedure to generate the data anddeveloped a calibration algorithm based on an unscented Kalman filter.Appropriate filter tuning parameters were determined by an optimization approach using simulateddata and the ground truth difference. The mean values for the tuning parameters for 100 simulated datasets with realistic error values were ? = 0.98 , ? = 0.04, and R = 0.0001.Using simulated data, the ground truth difference was found to be less than 1 mm and less than 1?.367APPENDIX F. UKF DRILL AXIS CALIBRATIONThe radial and angular ground truth difference were 0.50 ? 0.23 mm (95% CI: 0.45?0.55) and 0.16? 0.07? (95% CI: 0.14 ?0.17) respectively. The algorithm takes approximately 0.0028 seconds periteration, which is sufficient to perform real-time calibration up to 300 Hz. The UKF outperformed theLS3DCF algorithm in angular ground truth difference, but not radial ground truth difference.An experimental CAS system was used perform a repeatability assessment using real data. A totalof 30 rotation procedures were measured by a single operator, each spanning approximately 90? ofrotation. For each trial, 500 measurements were recorded at 60 Hz. The repeatability of the calibrationswere 0.23 mm and 0.30?. There was no statistically detectable difference between the repeatability ofthe UKF algorithm and the LS3DCF.Overall, the algorithm should reliably calibrate a rotation axis within <1 mm and 0.5?.F.6.2 Strengths and LimitationsThe main advantages of the UKF axis calibration algorithm are the ability to perform the calibrationin real-time and generate estimates of uncertainty. The real-time calibration should enable surgeons tosave time by enabling them to stop the procedure once the desired accuracy is reached. The uncertaintyestimates can be used to enhance the visualization and improve surgical navigation. Furthermore, anUKF can also be used for real-time tracking, and it is possible to develop a UKF for simultaneous trackingand calibration.The main limitation of the current implementation is the choice of axis parametrization. Given a setof pierce planes, not all rotations can be represented. In order to avoid convergence difficulties, priorknowledge of the tool geometry should be used to select an appropriate set of pierce planes, or the theorientation of the pierce planes could also be adjusted automatically by preliminary code. In the contextof a well-defined CAS application, with known tool and marker geometries, this issue should not pose aconcern.The tuning parameters to choose in advance are another limitation, since inappropriate values cannegatively affect the performance of the filter. This is another general limitation that can be addressedby focusing on a particular application, and doing pre-operative evaluations to determine the appropriatevalues. Adequate characterization of the noise associated with a given tracking system and tool wouldallow the developer to select appropriate tuning parameters.The main limitation of this study was the selection of a LS3DCF algorithm for comparison. Althoughit would have required the development of an additional algorithm, a transform-based block fittingmethod would have been a more appropriate choice, since it would incorporate both translation androtation information from the measurements.F.6.3 Future WorkRobustness TestingWe have shown that the UKF axis calibration algorithm produces satisfactory results for a tool withgeometry similar to the one used in our experimental CAOS system. In order to comfortably use the368APPENDIX F. UKF DRILL AXIS CALIBRATIONalgorithm with an arbitrary marker frame and tool geometry, further validation is required to ensure thatthe algorithm performs as expected. One of the main limitations of the LS3DCF algorithm is a sensitivityon the radial distance, i.e. the distance from the axis to the markers. The UKF axis calibration should beless sensitive to this distance since it uses not only marker translations like the 3D circle fitting but alsothe marker orientation information. The UKF algorithm should also be insensitive to axial translationerror for the same reason.Full Drill Bit CalibrationCurrently, the full drill calibration is found by taking the drill bit tip translation from a pivot calibrationand the drill bit orientation from a rotation calibration. The axis position information from the rotationcalibration is simply ignored. Performing each calibration separately and combining the results is sub-optimal. Ideally, the two methods should be combined so that instead of discarding information, theinformation is used to speed up the other portion of the algorithm.For example, since the tip should lie along the primary axis, the pivot procedure should be completedfirst. The resulting known tip translation could be incorporated into the rotation algorithm so that justthe orientation of the primary axis is determined.Axis ParametrizationThe use of pierce planes and pierce points is numerically convenient, but it does require some a prioriknowledge of the set up for the algorithm to work effectively. Ideally, the axis would be parametrizedwith a quaternion and a translation vector. This is possible to achieve, but it involves modifying theunderlying UKF algorithm in order to properly average the quaternions (i.e. a Euclidean average is notappropriate.) Using a quaternion and translation vector directly would make it easier to interpret theuncertainty in the calibration parameters produced by the algorithm.Appended Data ImplementationThe current implementation of the observation model only considers a single measurement of the drillmarker frame during each iteration of the filter. Better performance may be achieved by appendingeach new measurement to a list of previous measurements and changing the observation model so itworks on the entire set. This approach was utilized by Moghari [2006] to perform the calibration of afreehand ultrasound probe. Moghari ?s algorithm yielded x?, y? and z? error components of 0.61 mm,0.42 mm and 1.07 mm, respectively, which is comparable to block calibration algorithms. One potentialdrawback is that the current implementation applies an exponential weighting to past data; if a similarweighting method was not applied, erroneous measurements could continue to skew the data.F.6.4 ConclusionWe successfully developed a UKF based algorithm for calibrating the primary axis of an optically trackeddrill. Data is generated by rotating the drill body around a fixed drill bit, which requires minimal369APPENDIX F. UKF DRILL AXIS CALIBRATIONhardware. The algorithm works iteratively, enabling the calibration to be performed in real-time andstopped when the desired uncertainty is reached. Angular error is less than 0.2? and radial error isless than 0.6 mm which is within the required accuracy range for procedures like distal locking ofintramedullary nails and core decompression of osteonecrosis.F.7 Supporting MaterialsF.7.1 Experimental DrillThe position of the markers was characterized using NDI 6D Architect (Version 2.02.11, NDI, Waterloo,ON, Canada). A local drill coordinate frame was defined with the origin at marker A, ?z axis throughmarker B, and x perpendicular to plane defined by markers A, B, and C. The results are summarized inTable F.9 and markers illustrated in Figure F.27.Table F.9 Drill Marker PositionsMarker x [mm] y [mm] z [mm]A 0.00 0.00 0.00B 0.00 0.00 -96.74C 0.00 -50.44 -0.33D -2.12 -159.68 -94.28AB&D]x \\Figure F.27 Labelled retroreflective markers for local drill coordinate frame definition.370APPENDIX F. UKF DRILL AXIS CALIBRATIONF.8 CodeF.8.1 Simulationfunction [rotationPoses] = sim_Rotate2(calib, tool )% simRotate2 - simulate an ordered rotation calibration% nposes - number of poses to \"record\"% angle [zanglemin zanglemax]% error [ axialErr angErr]% rotationPoses [nPoses x 8] matrix [qx qy qz qw tx ty tz err]%number of calibration pointsnPoses = calib.n;%range of rotationzangle = calib.range;%intial drill marker positionstartPose = composeT(calib.tipPose,inverse(tool.tip));error = calib.error;zmin = zangle(1);zmax = zangle(2);axialErr = error(1);angErr = error(2);locErr = error(3);%initialize data variablesrotationPoses=zeros(nPoses,8);%create angles for rotation about the drill axis for its%calibration%random angles%anZ = zmin+(zmax-zmin).*rand(nPoses,1);%ordered anglesalphaZ = zmin:(zmax-zmin)\/(nPoses-1):zmax;% create random vertical error to simulate axial tip motionvertErr = -axialErr\/2+(2*axialErr).*rand(nPoses,1);%create random error for off-axis rotationanOff = -angErr\/2+(2*angErr).*rand(nPoses,1);anOffang = -pi + (2*pi).*rand(nPoses,1);xOffang = cos(anOffang);yOffang = sin(anOffang);371APPENDIX F. UKF DRILL AXIS CALIBRATION%calculate intial tip pose based on tool start posetipref = composeT(startPose,tool.tip);%for each pose, rotate the markers about the drill axisfor i=1:nPoses%generate deviations of tip from initial tip pose (in tip frame)rotT = [0 0 vertErr(i)];rotQ = [0 0 1*sin(alphaZ(i)\/2) cos(alphaZ(i)\/2)];errQ = [xOffang(i)*sin(anOff(i)\/2) ...yOffang(i)*sin(anOff(i)\/2) 0 cos(anOff(i)\/2)];err=0;if( exist(?qmult?)==2) %quaternion toolbox installedtotQ=qmult(rotQ,errQ);elseerror(?No quaternion toolbox installed?)endrottip = [ totQ rotT err];tip = composeT(tipref,rottip); %(deviated tip in world frame)%calculate position of tool in world framerotationPoses(i,:) = composeT(tip,inverse(tool.tip));endnoise = randn( nPoses, 3 );rotationPoses(:,5:7) = rotationPoses(:,5:7) + locErr*noise;endF.8.2 UKF AlgorithmUKFclassdef ukf%UKF Unscented Kalman Filter% Standard Unscented Kalman Filter algorithm for parameter% estimation.%% Based on the paper:% THE SQUARE-ROOT UNSCENTED KALMAN FILTER FOR STATE AND% PARAMETER-ESTIMATION% Rudolph van der Merwe and Eric A. Wan372APPENDIX F. UKF DRILL AXIS CALIBRATIONFigure F.28 Standard UKF Algorithm. (Source: Simpson [2007].)propertiesxEst % state mean estimate at time kPEst % state covariance at time kU % control input vectoQ % process noise covariance at time kffun % process Modelz % observation at time k+1R % measurement noise covariance at time k+1hfun % measurement modeldt % time step (passed to ffun\/hfun)alpha % sigma point scaling parameterbeta % higher order error scaling parameterkappa % scalar tuning parameter373APPENDIX F. UKF DRILL AXIS CALIBRATIONendmethodsfunction obj = step( obj)% This function performs one complete step of the Unscented Kalman Filter%% SYNTAX : [xEst, PEst] = standard_ukf(xEst, PEst, U, Q, ffun,% z, R, hfun, dt, alpha, beta, kappa )%alpha - spread of sigma points around xEst (1e-4 -> 1)%kappa - secondary scaling parameter 0 for state estimation,% 3 - L for parameter estimation%beta - used to incorporate prior knowledge of distribution of x% for gaussian distributions, beta = 2 is optimalstates = size( obj.xEst(:), 1 ); %size of state vector (L)observations = size( obj.z(:), 1 ); % size of observation vector% calculate the sigma points and their corresponding weights% using the scaled unscented transform%% equation 6%% note we return nsp+1 weights. first nsp weights are% w_i?m, and the last one is w_i?c%xSigmaPts - (L x 2L+1)%wSigmaPts - weights on estimates%nsp - number of points (2*L + 1)[xSigmaPts, wSigmaPts, nsp] = ...ukf.scaledSymmetricSigmaPoints( obj.xEst, obj.PEst, ...obj.alpha, obj.beta, obj.kappa );% work out the projected sigma points and their means% equation 7xPredSigmaPts = feval( obj.ffun, xSigmaPts(1:states,:), ...repmat(obj.U(:),1,nsp ), zeros( states, nsp ), obj.dt );%(L x 2L+1)% equation 8xPred = sum( repmat( wSigmaPts(1:nsp), states, 1 ) .* xPredSigmaPts, 2 );exSigmaPt = xPredSigmaPts - repmat( xPred, 1, nsp );wSigmaPts_xmat = repmat( [ wSigmaPts(nsp+1) wSigmaPts(2:nsp) ], states, 1 );374APPENDIX F. UKF DRILL AXIS CALIBRATIONPPred = ( wSigmaPts_xmat .* exSigmaPt ) * exSigmaPt? + obj.Q;%Q - process noise covariance% equation 9% redraw sigma points to incorporate effect of process noise[xPredSigmaPts, wSigmaPts, nsp] = ...ukf.scaledSymmetricSigmaPoints( xPred, PPred, obj.alpha, obj.beta, obj.kappa );zPredSigmaPts = feval( obj.hfun, xPredSigmaPts, repmat(obj.U(:),1,nsp), ...zeros( observations, nsp), obj.dt );% equation 10 alternative - 7.83?% zPredSigmaPts = feval( hfun, xPredSigmaPts, U(:),zeros(observations,nsp),dt);% equation 10zPred = sum( repmat( wSigmaPts(1:nsp), observations, 1 ) .* zPredSigmaPts, 2);% measurement update equationsezSigmaPts = zPredSigmaPts - repmat( zPred, 1, nsp );exSigmaPts = xPredSigmaPts - repmat( xPred, 1, nsp );wSigmaPts_zmat = repmat([ wSigmaPts(nsp+1) wSigmaPts(2:nsp) ],observations,1);% equation 11PxzPredPrime = ( wSigmaPts_zmat .* ezSigmaPts ) * ezSigmaPts? + obj.R;PxzPred = (wSigmaPts_xmat .* exSigmaPts) * ezSigmaPts?;% equation 12K = PxzPred \/ PxzPredPrime; % kalman gain% equation 13inovation = obj.z - zPred;obj.xEst = xPred + K * inovation;obj.PEst = PPred - K * PxzPredPrime * K?;endendmethods (Static)function [xPts, wPts, nPts] = scaledSymmetricSigmaPoints(x,P,a,b,k)% This function returns the scaled symmetric sigma point distribution.%% [xPts, wPts, nPts] =% scaledSymmetricSigmaPoints(x,P,alpha,beta,kappa)% Inputs:% x mean375APPENDIX F. UKF DRILL AXIS CALIBRATION% P covariance% (a) alpha scaling parameter 1% (b) beta extra weight on zero?th point% (k) kappa scaling parameter 2 (usually set to default 0)%% Outputs:% xPts The sigma points% wPts The weights on the points% nPts The number of points%%%% (C) 2000 Rudolph van der Merwe% (C) 1998-2000 S. J. Julier.% Number of sigma points and scaling termsL = size(x(:),1);nPts = 2*L+1; % we?re using the symmetric SUT% Recalculate kappa according to scaling parametersk = a?2*(L+k)-L;% Allocate space %unnecessary?%wPts=zeros(1,nPts);%xPts=zeros(L,nPts);% Calculate matrix square root of weighted covariance matrix% %originaltryPsqrtm=(chol((L+k)*P))?;catchsave error.mat x k P a -appendend%Psqrtm = (L+k)*chol(P)?; %modified% Array of the sigma pointsxPts=[zeros(size(P,1),1) -Psqrtm Psqrtm];% Add mean back inxPts = xPts + repmat(x,1,nPts);% Array of the weights for each sigma pointwPts=[k 0.5*ones(1,nPts-1) 0]\/(L+k);% Now calculate the zero?th covariance term weightwPts(nPts+1) = wPts(1) + (1-a?2) + b;end376APPENDIX F. UKF DRILL AXIS CALIBRATIONendendAxisUKFclassdef axisUKF < ukf%axisUKF Axis Calibration Unscented Kalman Filter% Derived from generic UKF class with parameters for calibrating the% primary axis of a rotated tool.propertiesxdim = 8;ydim = 1;lambdaRLS = 0.99;x0;P0;iteration = 0;PNorm;endmethodsfunction AU = axisUKF()% process noise covariance at time kAU.Q = 1e-6*eye(AU.xdim);% process ModelAU.ffun = ?axisUKF.ffun_axis?;% observation at time k+1AU.z = zeros(AU.ydim,1);% measurement noise covariance at time k+1AU.R = 1e-6*eye(AU.ydim);% measurement modelAU.hfun=?axisUKF.hfun_axis?;% time step (passed to ffun\/hfun)AU.dt = 1;AU.alpha= 1e-3; % sigma point scaling parameterAU.beta = 2.0; % higher order error scaling parameterAU.kappa = -5; % scalar tuning parameter% Initial valuesAU.P0 = 1*eye(AU.xdim);AU.x0 = zeros(AU.xdim,1);AU.PNorm = zeros(AU.xdim);AU = reset(AU);endfunction AU = reset(AU)AU.xEst=AU.x0;377APPENDIX F. UKF DRILL AXIS CALIBRATIONAU.PEst=AU.P0;AU.iteration = 0;endfunction AU = initialize(AU,x0,P0)AU.x0 = x0;AU.P0 = P0;endfunction AU = update(AU,data)AU.U = data;AU.Q = (AU.lambdaRLS?(-1)-1)*AU.PEst; %process noiseAU = step(AU); % UKF stepAU.iteration = AU.iteration + 1;endendmethods (Static)out = ffun_axis( x, u, n, t )out = hfun_axis( X, u, n, t )end %end static methodend %end classdeffunction [out] = ffun_axis( x, u, n, t )% Process Modelout = x;endfunction [out] = hfun_axis( X, u, n, t )% HFUN(X,u,n,t)% X - state vector [ua va ub vb uc vc ud vd]% u - control input, measurement (tool poses)% [qx qy qz qw tx ty tz err]% error function is radial error of each pierce pointsu = size(u);L = size(X,2); %number of sigma points%State Vector - > Pierce pointsGP = [X(1,:);X(2,:);zeros(1,L)]; %ground proximalGD = [X(3,:);X(4,:);100*ones(1,L)]; %ground distalTP = [X(5,:);X(6,:);zeros(1,L)]; %tool proximalTD = [X(7,:);X(8,:);100*ones(1,L)]; %tool distal378APPENDIX F. UKF DRILL AXIS CALIBRATION% Project tool points into ground frameTPg = qvqc(u(1:4,:),TP) + u(5:7,:);TDg = qvqc(u(1:4,:),TD) + u(5:7,:);%calculate tool rotation axis in groundntg = TDg - TPg;rtg = sqrt(ntg(1,:) .* ntg(1,:) ...+ ntg(2,:) .* ntg(2,:) ...+ ntg(3,:) .* ntg(3,:) );ntg = ntg .\/ repmat(rtg,3,1); %normalize%find tool rotation axis pierce points in ground planest1 = -TPg(3,:) .\/ ntg(3,:); %Cg2z = 0t2 = (100*ones(1,L) - TPg(3,:)) .\/ ntg(3,:); %Dg2z =100;TPg2x = TPg(1,:) + t1.*ntg(1,:);TPg2y = TPg(2,:) + t1.*ntg(2,:);TPg2z = TPg(3,:) + t1.*ntg(3,:); %zeros(1,L);TDg2x = TPg(1,:) + t2.*ntg(1,:);TDg2y = TPg(2,:) + t2.*ntg(2,:);TDg2z = TPg(3,:) + t2.*ntg(3,:); %100*ones(1,L);TPg2 = [TPg2x;TPg2y;TPg2z];TDg2 = [TDg2x;TDg2y;TDg2z];CA = TPg2 - GP;DB = TDg2 - GD;r1 = sqrt(CA(1,:) .* CA(1,:) ...+ CA(2,:) .* CA(2,:) ...+ CA(3,:) .* CA(3,:) );r2 = sqrt(DB(1,:) .* DB(1,:) ...+ DB(2,:) .* DB(2,:) ...+ DB(3,:) .* DB(3,:) );out(1,:)=r1+r2;end379","type":"literal","lang":"en"}],"http:\/\/www.europeana.eu\/schemas\/edm\/hasType":[{"value":"Thesis\/Dissertation","type":"literal","lang":"en"}],"http:\/\/vivoweb.org\/ontology\/core#dateIssued":[{"value":"2014-05","type":"literal","lang":"en"}],"http:\/\/www.europeana.eu\/schemas\/edm\/isShownAt":[{"value":"10.14288\/1.0072138","type":"literal","lang":"en"}],"http:\/\/purl.org\/dc\/terms\/language":[{"value":"eng","type":"literal","lang":"en"}],"https:\/\/open.library.ubc.ca\/terms#degreeDiscipline":[{"value":"Biomedical Engineering","type":"literal","lang":"en"}],"http:\/\/www.europeana.eu\/schemas\/edm\/provider":[{"value":"Vancouver : University of British Columbia Library","type":"literal","lang":"en"}],"http:\/\/purl.org\/dc\/terms\/publisher":[{"value":"University of British Columbia","type":"literal","lang":"en"}],"http:\/\/purl.org\/dc\/terms\/rights":[{"value":"Attribution-NonCommercial-ShareAlike 2.5 Canada","type":"literal","lang":"en"}],"https:\/\/open.library.ubc.ca\/terms#rightsURI":[{"value":"http:\/\/creativecommons.org\/licenses\/by-nc-sa\/2.5\/ca\/","type":"literal","lang":"en"}],"https:\/\/open.library.ubc.ca\/terms#scholarLevel":[{"value":"Graduate","type":"literal","lang":"en"}],"http:\/\/purl.org\/dc\/terms\/title":[{"value":"Effect of bracing and navigation display design on targeting accuracy and plunge depth during surgical drilling","type":"literal","lang":"en"}],"http:\/\/purl.org\/dc\/terms\/type":[{"value":"Text","type":"literal","lang":"en"}],"https:\/\/open.library.ubc.ca\/terms#identifierURI":[{"value":"http:\/\/hdl.handle.net\/2429\/45698","type":"literal","lang":"en"}]}}