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Effect of bracing and navigation display design on targeting accuracy and plunge depth during surgical… McIvor, Jacob Donald 2013

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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 	 &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+XPaQI Y DYDE+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 ??????PJ'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 510BradPoint/ + 0 / + 00DrillBitSubjectDamping5epetitionFigure 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