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Biomechanical comparison of two total ankle replacement designs : micromotion and kinematic patterns McInnes, Kurtis Anthony 2012

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Biomechanical Comparison of Two Total Ankle Replacement Designs: Micromotion and Kinematic Patterns by KURTIS ANTHONY MCINNES B.Eng. McGill University, 2009 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE STUDIES (Mechanical Engineering)  THE UNIVERSITY OF BRITISH COLUMBIA July 2012  © Kurtis Anthony McInnes, 2012  ABSTRACT  Introduction: Arthritis is a degenerative disease that causes irreversible damage to a joint’s  articular cartilage. Despite having high failure rates in early total ankle arthroplasty (TAA) models, recent improvements have increased the success of this procedure, providing end-stage ankle  arthritis patients a viable alternative to fusion with better functional outcomes. Currently, the most  prevalent cause of failure is aseptic loosening, which is believed to be affected by motion at the bone-implant interface. The objective of this study was to compare micromotion and kinematic patterns of two TAA designs.  Methods: A mechanical simulator was designed to apply compressive loads and bending moments to human cadaveric ankles, intact and replaced. It induced a maximal range of motion in the ankle  about 3 orthogonal axes: plantarflexion-dorsiflexion (PF-DF), inversion-eversion (INV-EV), and internal-external rotation (IR-ER). Six ankle pairs were tested and compared. The implants  analyzed were the Agility™ and the Scandinavian Total Ankle Replacement (S.T.A.R.®). Using an  optical motion capture system, tibiocalcaneal kinematics and the relative bone-implant motion for each implant were recorded and analyzed.  Results: The Agility exhibited a greater amount of micromotion between the bone and prosthesis  than the STAR for the tibial component in INV-EV (p=0.037), and for the talar component in PF-DF  (p=0.002) and IR-ER (p=0.038). Micromotion magnitudes were affected by loading direction and  compression. Kinematic changes were observed following replacement of the ankle joint. There  were decreases in the amount of motion coupling for both implants when loaded in INV-EV and IR-  ER. There were increases in joint translation for both implants in the medial/lateral direction under  INV-EV loading, and for the STAR in the anterior/posterior and compression/distraction directions under PF-DF loading. No significant ROM differences were found.  Discussion: Increased micromotion in the Agility supports the hypothesis that higher aseptic  loosening rates are correlated with reduced initial post-op fixation. The effect of loading direction  on micromotion magnitude confirms the need to apply a variety of loading conditions to obtain a comprehensive micromotion analysis. Kinematic differences between implanted and intact ankles  show that there is still room for improvement towards an ankle replacement design that replicates the performance of a healthy ankle.  1  PREFACE  UBC Research Ethics Board Approval:  Clinical Research Ethics Board  Certificate Number: H10-02860  2  TABLE OF CONTENTS  Abstract ......................................................................................................................................................................................... i  Preface.......................................................................................................................................................................................... ii Table of Contents .................................................................................................................................................................... iii  List of Tables............................................................................................................................................................................. vi  List of Figures .......................................................................................................................................................................... vii Acknowledgements ............................................................................................................................................................... xi 1  Introduction ..................................................................................................................................................................... 1  1.1  1.2  Overview .................................................................................................................................................................. 1  Foot and Ankle Anatomy ................................................................................................................................... 3  1.2.1  1.2.2  1.2.3  1.3 1.4  1.5  Joints ................................................................................................................................................................ 7  Articular Cartilage ...................................................................................................................................... 8  Arthritis .................................................................................................................................................................. 10  Total Ankle Arthroplasty................................................................................................................................. 13 Total Ankle Arthroplasty Designs ............................................................................................................... 15  1.5.1 1.5.2 1.5.3  Agility Total Ankle Replacement System ........................................................................................ 15 Scandinavian Total Ankle Replacement System .......................................................................... 16  Others ............................................................................................................................................................ 18  1.6  Clinical Outcomes of TAA ................................................................................................................................ 19  1.9  In Vitro Ankle Loading Apparatuses........................................................................................................... 31  1.7  1.8  1.10  Ankle Biomechanics .......................................................................................................................................... 22  Biomechanics of the Replaced Ankle ......................................................................................................... 25 Micromotion ......................................................................................................................................................... 35  1.10.1  1.10.2  2  Bones ............................................................................................................................................................... 5  1.11  Theory ........................................................................................................................................................... 35  Implant micromotion .............................................................................................................................. 38  Motivation ............................................................................................................................................................. 42  1.12  Objectives .............................................................................................................................................................. 42  2.2  Ankle Loading Apparatus................................................................................................................................ 44  Methods ........................................................................................................................................................................... 43  2.1  Experimental Design ......................................................................................................................................... 43  2.2.1  2.2.2  2.2.3  2.2.4  Foot-Plate..................................................................................................................................................... 46 Mounting Rig .............................................................................................................................................. 47  Counterbalances ....................................................................................................................................... 48  Loads .............................................................................................................................................................. 50  3  2.3  2.4  Specimen Selection ............................................................................................................................................ 53  Specimen Preparation ...................................................................................................................................... 54  2.4.1  2.4.2 2.4.3  2.5  2.6  2.9  Test Procedure........................................................................................................................................... 59  Data Analysis/Processing ............................................................................................................................... 67 Kinematic Analysis ............................................................................................................................................ 67  2.9.1  Joint Rotations ........................................................................................................................................... 69  2.9.4  Joint Translations ..................................................................................................................................... 71  2.11.1  Micromotion ............................................................................................................................................... 73  2.9.3  2.10  2.11  Range of Motion ........................................................................................................................................ 70 Motion Coupling ........................................................................................................................................ 70  Bone-Implant Relative Motion...................................................................................................................... 71  Statistical Analysis ............................................................................................................................................. 73  2.11.2  Kinematics ................................................................................................................................................... 74  Results .............................................................................................................................................................................. 76  3.1  Bone-Implant Relative Motion...................................................................................................................... 76  3.2  Kinematic Behaviour ........................................................................................................................................ 81  3.1.1  Tibial Component Micromotion ......................................................................................................... 78  3.2.1  Joint Rotations ........................................................................................................................................... 81  3.2.4  Joint Translation .................................................................................................................................... 107  3.1.2  3.2.2  4  Test Conditions .......................................................................................................................................... 58  Data Acquisition.................................................................................................................................................. 66  2.9.2  3  Joint replacement surgery .................................................................................................................... 56  Test Protocol ........................................................................................................................................................ 58  2.6.2  2.8  Fastening Foot-Plate ............................................................................................................................... 55  Measurement Method ...................................................................................................................................... 57  2.6.1  2.7  Potting ........................................................................................................................................................... 54  3.2.3  Talar Component Micromotion .......................................................................................................... 79  Range of Motion ........................................................................................................................................ 85  Motion Coupling ........................................................................................................................................ 92  Discussion .................................................................................................................................................................... 117  4.1  Loading Apparatus.......................................................................................................................................... 117  4.4  Implant Design Considerations ................................................................................................................. 129  4.2  4.3  4.5  Micromotion-Loosening Relation............................................................................................................. 124  Surgeon Skill...................................................................................................................................................... 128  Differences in Kinematic Behaviour ........................................................................................................ 132  4.5.1  Range of Motion ..................................................................................................................................... 132  4  4.5.2  4.5.3  Joint Origin Translation ...................................................................................................................... 136  4.6  Motion Dependence on Loading Direction ........................................................................................... 138  4.9  Limitations ......................................................................................................................................................... 144  4.7  4.8  Large Inter-Specimen Variance ................................................................................................................. 140  OptoTrak Measurements ............................................................................................................................. 140  4.9.1  4.9.2  PF-DF Angular limits ............................................................................................................................ 144 Foot Alignment ....................................................................................................................................... 144  4.9.3  Pure Moment Assumption ................................................................................................................. 145  4.10.1  Micromotion ............................................................................................................................................ 147  4.9.4  5  Coupled Motion ...................................................................................................................................... 134  Sample Size............................................................................................................................................... 146  4.10  Future Work ...................................................................................................................................................... 147  4.11  Contributions .................................................................................................................................................... 150  4.10.2  Kinematics ................................................................................................................................................ 149  Conclusion.................................................................................................................................................................... 151  References ............................................................................................................................................................................. 152 Appendix A: TAA Failures and their Causes ............................................................................................................ 159 Appendix B: Indications for TAA .................................................................................................................................. 160 Appendix C Mounting Rig................................................................................................................................................ 161 Appendix D: Agility Surgical Procedure .................................................................................................................... 171 Appendix E: STAR Surgical Procedure....................................................................................................................... 175 Appendix F: Optotrak Accuracy Study ....................................................................................................................... 179 F.1  F.2  Setup ..................................................................................................................................................................... 179  Protocol ............................................................................................................................................................... 181  F.3  Results.................................................................................................................................................................. 183  G.1  opt_ankle_angles.m ......................................................................................................................................... 187  F.4  Accuracy Study Data ...................................................................................................................................... 184  Appendix G: Matlab Data Analysis Programs ......................................................................................................... 187 G.2  G.3  G.4  ankle_angles.m ................................................................................................................................................. 201  trs.m ...................................................................................................................................................................... 203  vwd.m ................................................................................................................................................................... 204  Appendix H: JCS Angle Plots ........................................................................................................................................... 207  Appendix I: Applied Loading: Moment-Angle Plots ............................................................................................. 219 Appendix J: Data Tables ................................................................................................................................................... 231  5  LIST OF TABLES  Table 1: STAR clinical loosening rates .......................................................................................................................... 20  Table 2: Agility clinical loosening rates ........................................................................................................................ 21  Table 3: ROM values for the Agility and STAR........................................................................................................... 26  Table 4: Specimen data ....................................................................................................................................................... 54 Table 5: Loading conditions .............................................................................................................................................. 59  Table 6: Range of motion.................................................................................................................................................... 85  Table 7: Translation accuracy test increments ...................................................................................................... 182 Table 8: Rotation accuracy test increments ............................................................................................................ 182 Table 9: Combined translation and rotation accuracy test increments ....................................................... 182  Table 10: Relative displacement accuracy test increments .............................................................................. 182  Table 11: Results of the Optotrak accuracy study ................................................................................................ 183  Table 12: Repeatability .................................................................................................................................................... 184 Table 13: Precision ............................................................................................................................................................ 184 Table 14: Displacement error measurements ........................................................................................................ 184  Table 15: Rotation error measurements .................................................................................................................. 185 Table 16: Relative displacement error measurements....................................................................................... 185  Table 17: Combined translation and rotation error measurements ............................................................. 186 Table 18: Peak tibial micromotion magnitudes ..................................................................................................... 231  Table 19: Peak talar micromotion magnitudes ...................................................................................................... 231 Table 20: Motion Coupling Ratios for PF-DF........................................................................................................... 231 Table 21: Motion coupling ratios for INV-EV .......................................................................................................... 231 Table 22: Motion coupling ratios for IR-ER ............................................................................................................. 231 Table 23: Peak medial/lateral (q1) joint translations......................................................................................... 232  Table 24: Peak anterior/posterior (q2) joint translations ................................................................................ 232  Table 25: Peak compression/distraction (q3) joint translations ................................................................... 232  6  LIST OF FIGURES  Figure 1: Bones and joints of the foot and ankle ........................................................................................................ 4 Figure 2: Articular cartilage ................................................................................................................................................ 9  Figure 3: Normal and osteoarthritic knee articular cartilage ............................................................................. 11 Figure 4: Agility ankle replacement prosthesis ........................................................................................................ 16 Figure 5: STAR prosthesis .................................................................................................................................................. 17 Figure 6: Salto Talaris .......................................................................................................................................................... 18 Figure 7: Buechel-Pappas................................................................................................................................................... 18  Figure 8: Inbone ..................................................................................................................................................................... 18  Figure 9: Hintegra ................................................................................................................................................................. 18  Figure 10: AES......................................................................................................................................................................... 18 Figure 11: Eclipse .................................................................................................................................................................. 18  Figure 12: BOX ........................................................................................................................................................................ 18  Figure 13: Mobility................................................................................................................................................................ 18  Figure 14: PF-DF range of motion of the STAR as affected by different amounts of A/P misalignment and bearing thickness. ......................................................................................................................................................... 26 Figure 15: A/P laxity of the intact ankle and STAR ................................................................................................. 28  Figure 16: Ankle joint reaction force during walking............................................................................................. 29  Figure 17: FEA results of contact pressures for the Agility and Mobility ...................................................... 30 Figure 18: Robotic gait simulators ................................................................................................................................. 32 Figure 19: Ankle loading devices .................................................................................................................................... 34  Figure 20: Mechanoregulation concept proposed by Pauwels........................................................................... 35 Figure 21: Mechanoregulation concept proposed by D.R. Carter...................................................................... 36 Figure 22: Mechanoregulation concept proposed by Claes and Heigele ........................................................ 36  Figure 23: Biphasic mechanoregulation concept proposed by Prendergast and Huiskes...................... 37 Figure 24: Photomicrographs of porous coated implants showing osseointegration.............................. 39  Figure 25: Ankle loading apparatus ............................................................................................................................... 45 Figure 26: Foot-plate............................................................................................................................................................ 46  Figure 27: Mounting rig ...................................................................................................................................................... 47 Figure 28: Counter-balances ............................................................................................................................................. 49  Figure 29: Compressive load applicator ...................................................................................................................... 50 Figure 30: Compressive load line of force in PF-DF loading................................................................................ 51  7  Figure 31: Moment application apparatus .................................................................................................................. 52  Figure 32: Bone screws and cable ties .......................................................................................................................... 56  Figure 33: Optotrak Certus motion capture system ............................................................................................... 57  Figure 34: Test setup for IR-ER, PF-DF, and INV-EV ............................................................................................... 58 Figure 35: Marker mounting locations for the Agility............................................................................................ 61 Figure 36: Marker mounting locations for the STAR .............................................................................................. 62  Figure 37: Applied moment............................................................................................................................................... 65  Figure 38: Angular displacement of the servo motor ............................................................................................. 65 Figure 39: Joint coordinate system definition for the ankle ................................................................................ 68 Figure 40: Implant-specific coordinate frames. ........................................................................................................ 72 Figure 41: Micromotion magnitudes over 3 cycles of PF-DF for the talar component ............................ 76 Figure 42: Agility talar component lift-off .................................................................................................................. 77  Figure 43: Peak micromotion magnitudes for the tibial component ............................................................... 78 Figure 44: Peak micromotion magnitudes for the talar component ................................................................ 80 Figure 45: PF-DF joint angles ........................................................................................................................................... 82 Figure 46: INV-EV joint angles ......................................................................................................................................... 83 Figure 47: IR-ER joint angles ............................................................................................................................................ 84  Figure 48: Range of motion for INV-EV with a 15 N preload .............................................................................. 87 Figure 49: Range of motion for INV-EV with a 75 N preload. ............................................................................. 87 Figure 50: INV-EV ROM interaction between compression, condition, and implant type ...................... 88  Figure 51: Range of motion for IR-ER with a 15 N preload ................................................................................. 90  Figure 52: Range of motion for IR-ER with a 300 N preload ............................................................................... 90 Figure 53: IR-ER ROM interaction between compression, condition, and implant type ......................... 91 Figure 54: INV-EV motion coupling ratios in the PF-DF loading direction ................................................... 93  Figure 55: INV-EV:PF-DF motion coupling. ................................................................................................................ 93  Figure 56: INV-EV:PF-DF motion coupling ratios interaction between implant type, compression, and ankle condition .............................................................................................................................................................. 94  Figure 57: IR-ER motion coupling ratios for the PF-DF loading direction..................................................... 95  Figure 58: IR-ER:PF-DF motion coupling .................................................................................................................... 95  Figure 59: IR-ER:PF-DF motion coupling ratios interaction between implant type, compression, and  ankle condition ....................................................................................................................................................................... 96 Figure 60: PF-DF motion coupling ratios in the INV-EV loading direction ................................................... 98 Figure 61: PF-DF:INV-EV motion coupling. ................................................................................................................ 98  8  Figure 62: PF-DF:INV-EV motion coupling ratios interaction between implant type, compression, and ankle condition .............................................................................................................................................................. 99  Figure 63: IR-ER motion coupling ratios in the INV-EV loading direction ................................................. 100  Figure 64: IR-ER:INV-EV motion coupling ............................................................................................................... 101  Figure 65: IR-ER:INV-EV motion coupling ratios interaction between implant type, compression, and ankle condition. .......................................................................................................................................................... 101 Figure 66: PF-DF motion coupling ratios in the IR-ER loading direction ................................................... 103  Figure 67: PF-DF:IR-ER motion coupling ................................................................................................................. 103  Figure 68: PF-DF:IR-ER motion coupling ratios interaction between implant type, compression, and  ankle condition .................................................................................................................................................................... 104  Figure 69: INV-EV motion coupling ratios in the IR-ER loading direction ................................................. 105  Figure 70: INV-EV:IR-ER motion coupling ............................................................................................................... 106  Figure 71: INV-EV:IR-ER motion coupling ratios interaction between implant type, compression,  and ankle condition ........................................................................................................................................................... 106  Figure 72: Mean translation of the JCS origin along the medial/lateral axis ............................................. 107  Figure 73: Translation of the JCS origin along the medial/lateral axis due to PF-DF loading showing the interaction of compression, condition, and implant type .......................................................................... 108  Figure 74: Translation of the JCS origin along the medial/lateral axis due to INV-EV loading, showing the interaction of compression, condition, and implant type........................................................ 109 Figure 75: Mean translation of the JCS origin along the anterior/posterior axis .................................... 110  Figure 76: Translation of the JCS origin along the anterior/posterior axis due to PF-DF loading, showing the interaction of compression, condition, and implant type........................................................ 111  Figure 77: Translation of the JCS origin along the anterior/posterior axis due to IR-ER loading, showing the effect of compression.............................................................................................................................. 112 Figure 78: Mean translation of the JCS origin along the compression/distraction axis ....................... 113  Figure 79: Translation of the JCS origin along the compression/distraction axis due to PF-DF  loading, showing the interaction of compression, condition, and implant type ...................................... 114  Figure 80: Translation of the JCS origin along the compression/distraction axis due to PF-DF  loading, showing the interaction between condition and implant type ...................................................... 115  Figure 81: Translation of the JCS origin along the compression/distraction axis due to PF-DF  loading, showing the compression .............................................................................................................................. 116  9  Figure 82: Locations of instantaneous center of rotation for the ankle in the sagittal plane with the  location of cable guide and direction of compressive force at 23° plantarflexion, at 0° -neutral, and at 25° dorsiflexion .............................................................................................................................................................. 121  Figure 83: Sagittal plane schematic view of Agility and STAR with stars depicting the instantaneous center of rotation. ............................................................................................................................................................... 122  Figure 84: A schematic diagram of the loading apparatus in the frontal plane showing the stabilizing artefact moment about the ankle’s INV-EV center of rotation. ....................................................................... 123  Figure 85: A schematic diagram of the loading apparatus in the transverse plane showing the stabilizing artefact moment about the ankle’s IR-ER center of rotation. .................................................... 124  Figure 86: ROM in INV-EV (top) and tibial IR-ER (bottom) due to 100 Nm static applied torque with 200 N of axial compression ............................................................................................................................................ 133  Figure 87: Velmex A25 Unislide ................................................................................................................................... 179 Figure 88: Thorlabs PR01 ............................................................................................................................................... 180  Figure 89: Optotrak accuracy test setup ................................................................................................................... 180  Figure 90: Relative displacement accuracy test setup ........................................................................................ 182  10  ACKNOWLEDGEMENTS  I have so much respect and appreciation for Dr. Tom Oxland, who was a great supervisor that not only provided mentorship, support, and guidance, but also funded this project and my stipend through his personal research grant money.  I would like to thank Dr. Alastair Younger for providing crucial insight in the clinical aspect and implications of this research as well as performing the ankle replacement surgeries.  I would also like to thank my family, friends, and fellow lab mates at the Orthopaedic Injury Biomechanics Laboratory who were always there to provide support and encouragement when I needed it.  Without the help of all these people, none of this would have been possible. I consider myself truly blessed to have had the opportunity to perform this research.  11  1 INTRODUCTION 1.1 OVERVIEW  Arthritis is a leading cause of disability in Canada and is among the top three most common chronic  conditions. Across the country, nearly 4 million people suffer from arthritis and approximately 100,000 more Canadians are diagnosed each year. In 1998, the cost of arthritis to Canadians was  $4.4 billion, of which $908.9 million were direct co sts such as hospital stays, physician services,  and medications, and the other $3.5 billion were incurred from indirect costs like loss of productivity [1]. Even though the prevalence of ankle arthritis is much lower than hip and knee, at  4.4 percent of the total demographic [2], the costs related to ankle arthritis approach $200 million per year.  Arthritis is a degenerative joint disease affecting all joints in the body that causes pain and stiffness,  limits mobility, and decreases quality of life. When the ankle is affected by end stage arthritis, there  are two main surgical options. The more recent but less common treatment is total ankle  arthroplasty (TAA) [3], where joint articulation surfaces are replaced with metal and polyethylene  components (sometimes ceramic). The other option is ankle arthrodesis, which addresses the pain by fusing the tibiotalar joint (and occasionally other adjacent joints) with pins and screws,  eliminating all relative motion between the tibia and talus. Arthrodesis is a simpler and quicker procedure while TAA is more invasive, complex and costly. Recently, TAAs have been shown to  offer equivalent pain relief with a comparable reoperation rate, while additionally providing better function [4,5]. Although subject to similar reoperation rates, the complexity of revision in TAA is much higher and in some cases not possible, making it a slightly riskier operation in the short term.  1  A large number of contraindications for TAA exist, which result in a high risk of failure from  receiving an ankle replacement and reduce eligibility for the operation. Absolute contraindications  include avascular necrosis, active or recent infection, neuropathy, and severe deformity or malalignment of the ankle. There are also relative contraindications, in which it is subject to the surgeon’s discretion whether or not to perform a TAA on younger patients, extremely active or  heavy-labour individuals, those with prior infection in the ankle, or patients with  osteoporosis/osteopenia [6]. Even though success rates of TAA’s are continuing to increase, the history of inadequacy continues to impact the reputation of this procedure, making it a somewhat  controversial treatment option [7], which may influence some patients who would be good  candidates to opt for ankle fusions instead. Currently, fusion is still viewed as the standard  treatment for end-stage ankle arthritis [7], despite the reduction in mobility/function of the joint and high future complication rate in adjacent joints of the foot.  Based on statistics from a US healthcare database, the expected number of procedures performed  treating ankle arthritis in 2012 is approximately 20,000 [3]. Only one fifth (3,925) of these will be  TAAs (including revisions) and the rest will be ankle fusions [3]. This corresponds to an incidence  of 1.25 per 105 people, which is of a similar magnitude to incidence rates reported in Sweden  (.8/105)[8] and Finland (1.5/105)[9]. Assuming a similar demographic in Canada as in the US, there  would be approximately 435 total ankle replacement (TAR) and 1757 arthrodesis procedures performed in Canada this year addressing the problem of end-stage ankle arthritis.  Success rates of current ankle replacements are under 85% when looking at short to mid-term results in national joint registers (non-designer surgeons) [9-12]. This is still quite low when  compared to the survival rates of hip and knee replacement. A recent collation of data from joint  registers across the world shows that the revision rate of ankles is more than 2.5 times greater than  either hip or knee. This study used a metric of revisions per 100 observed component years, which 2  normalizes for follow-up period. Ankles were found to have a revision rate of 3.29, while hips and knees had rates of 1.29 and 1.26 respectively [13]. This corresponds to revision rates of 32.9%, 12.9%, and 12.6% at ten years. Historically, success rates for hip/knee devices have improved due  to a greater number of clinical and biomechanical studies compared to ankle replacement. Similar  benefits could be achieved for ankle replacements and comparable success rates will be reached as appropriate research is performed. As designs and success rates improve, it is expected that patient  candidacy will also expand and those with end-stage ankle arthritis will receive a higher level of care and experience a greatly improved quality of life.  The most prevalent cause of TAA failure is currently aseptic loosening (Appendix A). Aseptic  loosening results when bonding at the bone-implant interface fails. Successful bonding relies on osseointegration, which is bone ingrowth into the porous surface of the implant. When excessive  micromotion occurs between the bone and implant, it prevents osseointegration and leads to TAA failure via aseptic loosening.  The objective for this thesis was to analyze the biomechanical behaviour of two current ankle  replacement designs. Specific focus was given to measuring the micromotion between the implant components and their respective bone surfaces, and quantifying three-dimensional kinematic patterns.  1.2 FOOT AND ANKLE ANATOMY  The ankle joint complex consists of the talocrural and inferior tibiofibular joints, and sometimes includes the subtalar joint as well. These joints involve the tibia, fibula, talus, and calcaneus (refer to  3  figure 1). Because of its shape, the superior portion of the talocrural joint is commonly referred to as the ankle ‘mortise’. Although it may appear to be just a simple hinge-joint at first glance, it is  actually one of our most intricate joints, which involves coordination with numerous other joints in the forefoot in order to provide a balanced and stable foundation for all bipedal locomotion. Its  particular architecture enables it to withstand and transmit the largest loads of any joint in the  body. Loads up to as high as 13.3 times body weight (BW) have been predicted [14]. During daily  activities such as gait, it is common for ankle loads to double the magnitude of those in the hip and  knee while only having one-third of the contact area [15]. Despite experiencing much higher stresses, ankles are only accountable for approximately 7.5 percent of all lower extremity arthritis cases [16].  Tibiofibular joint  Figure 1: Bones and joints of the foot and ankle. Anatomy image courtesy and copyright of Primal Pictures Ltd – www.primalpictures.com  4  1.2.1  BONES  The tibia acts as the main weight-bearing long bone of the lower leg. Its diaphysis has a cross-  section that is roughly triangular in shape with posterior, medial, and lateral surfaces. It flares out at its superior aspect forming the tibial plateau which articulates with the femur at the knee. At its  inferior aspect called the tibial plafond, its cross-sectional area also increases and forms a concave surface with the medial maleolus extending beyond it to form the superior and medial portions of the ankle mortise.  The fibula is a long bone located laterally to the tibia and bears relatively little weight in comparison. Its primary function is to provide attachment for muscles. It has the most slender  aspect ratio of all long bones. The fibular head articulates with the tibia superiorly at the posterior aspect of the lateral condyle in an arthrodial (plane) synovial joint. Inferiorly, it articulates with the  tibia and extends past the tibia distally to articulate with the talus, forming the lateral portion of the ankle mortise.  The talus is the most superior bone of the foot. The talus is unique in having a large surface area of  articular cartilage and having no muscle origins and insertions. It is at risk of losing its blood supply in excessive dissection or after fracture. It can be subdivided into three parts: the head, neck,  and body. The head is the most anterior portion of the talus and it articulates with the navicular  bone. The neck is a rough, non-articulating segment that connects the head and body. On the  superior aspect of the body is the trochlea, which articulates superiorly with the tibia and fibula at the talocrural joint. It has an articular surface that is convex in the sagittal plane and quasirectangular (anterior aspect is slightly wider than posterior) in the frontal plane with medial and lateral articulate facets for the two malleoli. The radius of curvature of the trochlea is longer on its  posterior than its anterior articular surface [17]. The body of the talus also articulates inferiorly  with the calcaneus at three locations forming the subtalar joint. The posterior calcaneal articular 5  surface is separated from the middle and anterior calcaneal articular surfaces by a deep groove called the sulcus tali. The talus is the insertion point for the anterior talofibular ligament, the posterior talofibular ligament and the deep deltoid ligament that act as the main stabilizers of the ankle joint.  The calcaneus is the bone most commonly known as the heel. It is the largest bone in the foot, and it  is located directly beneath the ankle joint and extends out posterior to it. The posterior half of it is  called the tuber calcanei, providing attachment of the achilles tendon and the plantar fascia. The achilles tendon is the main plantar flexor of the ankle. The calcaneal fibular ligament inserts into the lateral aspect of the body and the sustentaculum tali has the deltoid ligament insertion. Both  stabilize the ankle joint. It articulates superiorly with the talus at the 3 locations previously mentioned, and it also articulates anteriorly with the cuboid.  The navicular articulates with the anterior aspect of the talus and forms part of the medial column of the foot. It provides the attachment for the tibialis posterior tendon and is the insertion of the  majority of the deltoid ligaments supporting the arch. It also articulates with the three cuneiforms  anteriorly and occasionally with the cuboid laterally. The 3 cuneiforms are situated anteriorly to  the navicular and connected to the first, second, and third metatarsals. The metatarsals make up the largest portion of the forefoot and are numbered one through five from medial to lateral. The fourth  and fifth metatarsals are anterior to the cuboid. The phalanges (or toes) project off the anterior aspect of the metatarsals.  6  1.2.2  JOINTS  While the number of joints in the foot and ankle number over 30, the predominant three providing ankle motion and included in the ankle joint proper are those of the inferior tibiofibular, talocrural  (tibiotalar and talofibular), and subtalar joints (refer to figure 1).  The inferior tibiofibular joint (aka: tibiofibular syndesmosis) is a slightly movable joint where the  fibula connects to the tibia at its most inferior aspect. At this location the convex fibula articulates with a concave groove on the lateral surface of the tibia. The fibula is attached to the tibia via  fibrous tissues such as the interosseus membrane and ligaments spanning the gap between the tibia  and fibula immediately proximal to this articulation. This syndesmosis holds the fibula in place next to the tibia to provide lateral stability to the ankle and form the lateral border of the ankle mortise.  The talocrural joint is the primary joint of the ankle complex and is formed by the articulation of the  talus with the tibia and fibula. The superior part of this joint makes up the ankle mortise and consists of the concave distal end of the tibia, the medial malleolus of the tibia, and the fibula  extending distally from the inferior tibiofibular joint as the lateral malleolus. The talus comprises  the inferior portion of this joint, fitting inside the mortise. The talocrural joint acts primarily as a  hinge and accounts for the majority of the foot’s plantar- and dorsi-flexion range of motion; however, this is a gross over-simplification. This joint also allows small amounts of inversion-  eversion (INV-EV) [18] and internal-external rotation (IR-ER) [19]. Additionally, calling it a hinge  joint is inaccurate because the flexion axis changes location as the ankle flexes [20]. In the sagittal  plane, the motion of the ankle is largely governed by the deltoid (especially tibiocalcaneal) and  calcaneofibular ligaments. A four-bar linkage geometrical model of the ankle quite accurately predicts its motion patterns and surface geometries, including that the instantaneous centre of  rotation moves from a posterior-inferior to an antero-superior position as the foot moves from plantar-flexion to dorsiflexion [21].  7  The subtalar joint is formed between the talus and calcaneus, and it articulates at three locations as  previously mentioned. The posterior calcaneal articular surface is concave in the direction along its  long axis, while the middle and anterior articular surfaces are slightly convex. The shapes of these joints primarily enable rotation in the frontal plane. The subtalar joint, along with the transverse tarsal joint (talonavicular and calcaneocuboid joint), accounts for the majority of INV-EV experienced by the foot.  1.2.3  ARTICULAR CARTILAGE  Articular cartilage is a form of hyaline cartilage found on the ends of bones in joints. Its function is to act as a bearing surface between the bones that move relative to each other. Its structure is perfectly suited to its purpose, which gives the joint an extremely low friction surface that is very  resistant to wear and compliant structure that will minimize stresses and absorb shock (see fig. 2  for a breakdown of its hierarchical structure). Its molecular makeup facilitates ideal lubrication interaction with the synovial fluid and its molecular constituents, namely hyaluronic acid and numerous proteoglycans. The biphasic nature of this tissue creates a highly compliant material that will expel water when compressed and reabsorb when decompressed. Its compliance works to  increase the contact area between bones and absorb shocks from impacts. This highly effective  bearing surface can withstand many millions of cycles over the course of a person’s life without breaking down for most healthy people. However, it is an avascular tissue with a very low cell division rate, resulting in a very limited ability to repair/regenerate damaged tissue.  8  Figure 2: Articular cartilage and its hierarchical structure and components. Reprinted with permission from Elsevier via Copyright Clearance Center (source: Mow VC et al. 1992[22])  Articular cartilage is composed mainly of water (60-70% of wet weight), collagen (10-30% of wet  weight), proteoglycans (3-10% of wet weight), and chondrocytes (<10% of tissue volume). Water is the fluid phase of cartilage that flows throughout the matrix and is absorbed or expelled depending  on external loads. Collagen occurs primarily in the type II form, and it is the main structural  component that gives cartilage its shape and attachment to the subchondral bone. It is responsible for cartilage’s tensile strength and resistance to swelling with water. Proteoglycans are hyaluronate  aggregates with numerous chains of glycosaminoglycans (mostly chondroitin sulfate and keratan sulfate). They are responsible for the hydrophilicity of articular cartilage, which gives it resiliency by decreasing its permeability. Finally, chondrocytes are the cells that govern the maintenance of 9  the cartilage. They synthesize the macromolecules of the matrix. They receive nutrients by diffusion and rarely divide/reproduce.  The thickness and mechanical properties of articular cartilage vary slightly between different joints. Of the lower extremities, the ankle’s cartilage is the thinnest and the knee’s is the thickest. Mean  thicknesses were found to range from 1.0 to 1.62 mm and 1.69 to 2.55 mm for the ankle and knee respectively. The compressive modulus was also found to be inversely related to the thickness of the cartilage in all joints. [23]  1.3 ARTHRITIS  Arthritis is literally defined as joint inflammation and typically refers to a number of diseases where joint pain is the primary ailment. Arthritis is a blanket term that covers over 100 maladies, but the  main classifications where joint pain is primary include: osteoarthritis, rheumatoid arthritis, ankylosing spondylitis, gout/pseudo-gout, juvenile idiopathic arthritis, septic arthritis, and Still’s  disease. Post-traumatic arthritis (PTA), rheumatoid arthritis (RA), and primary osteoarthritis (POA) are the types most commonly treated by TAA at 40.6%, 29.6%, and 26.9% respectively (see appendix B for details).  While POA is the most frequent diagnosis for patients receiving hip and knee replacements [16,24], it is much less common for it to affect the ankle. The low incidence of POA most likely plays a significant role in why the overall incidence of ankle replacements is so much lower than hip/knee.  Even though obesity, certain occupations, genetics, and a few other risk factors have been identified with its occurrence, POA is generally idiopathic and the underlying cause remains unknown. PTA is 10  when osteoarthritis occurs secondary to traumatic injuries such as dislocations and fractures,  especially a fracture transecting an articular surface. While POA and PTA differ in origin, the end result of both forms is essentially the same.  Osteoarthritis, whether primary or post-traumatic, is a degenerative process that is very difficult to  treat even if it is caught at an early stage. It is defined by mechanical breakdown or fibrillation of  the articular cartilage (see fig. 3), which initiates at a small localized area on the surface that  expands to affect broader and deeper areas eventually to the point where bone on bone articulation occurs. It is accompanied by a breakdown of the collagen framework, decrease in proteoglycan aggregation, and an increase in water content. In turn, this decreases the compressive stiffness and  increases the permeability of the cartilage, hindering its ability to absorb shock and distribute loads across the joint.  Figure 3: Normal knee articular cartilage with healthy, smooth surfaces (left) contrasted with osteoarthritic knee cartilage with rough, damaged surfaces (right). Image courtesy and copyright of Media Partners, Inc. from the patient education booklet "Total Knee Replacement: A Patient and Family Guide for Surgery and Recovery." (Source: http://healthpages.org/health-a-z/osteoarthritis-degenerative-joint-disease/)  11  RA, while entirely different in its mechanism, can result in similar consequences as the joint  surfaces become eroded. RA is an autoimmune disease that primarily causes the body’s immune  system to attack its synovial joints. Because it is a systemic problem, it will usually end up affecting multiple joints and will even damage other organs on occasion. It is usually accompanied by symptoms of swollen, tender, warm, and stiff joints that are most painful in the morning or after extended periods of inactivity.  Since arthritis is a degenerative disease by nature, the severity of a patient’s condition could lie anywhere along the continuum from initial onset to end-stage arthritis. Conservative treatments  are available for the milder cases including a number of natural treatments, medications, joint injections, and even some less aggressive surgical procedures. Unfortunately, these conservative treatments focus mainly on pain management and slowing the process of degeneration, and their  effectiveness at this is still suspect. We have yet to discover a treatment that can reverse the damage accumulated in the articular cartilage, leading most patients inevitably to end-stage  arthritis. Once the disease has progressed to this point, conservative treatments are rendered  completely ineffective and more aggressive surgical options are required.  For those with end-stage ankle arthritis, two options are available: arthrodesis and arthroplasty.  Arthrodesis is the surgical procedure commonly referred to as joint fusion. Surgeons use any combination of plates, screws, pins, wires, and rods to immobilize the joint until it eventually fuses  together. The end result of this operation is the elimination of all relative motion between the previously articulating surfaces, which allows weight bearing with effective pain relief at the cost of  flexibility and motion at the fused joint. Despite its obvious functional limitations and risk of provoking arthritis in the adjacent joints, it is still the standard treatment for ankle arthritis  because of its long track record of proven pain management and perception as a safer procedure.  12  However, total ankle arthroplasty has shown to be a comparably safe procedure in recent years with the added benefit of improved function [4].  1.4 TOTAL ANKLE ARTHROPLASTY  Total ankle arthroplasty (TAA) refers to the surgical replacement of degenerated/diseased ankle  joint. As with arthrodesis, the main objective is to eliminate the pain caused by arthritis, but in  addition it also aims to restore joint function. This procedure removes the damaged articular surfaces and inserts prosthesis components to replace them, which allow for relative motion.  Current TAA designs are generally successful at eliminating pain and enabling patients to regain  most of their ankle function [25,26]. Although this procedure might not restore ankle ROM to that of a normal ankle, patients can typically expect increases in ROM of between 5 to 10 degrees  depending on implant type, which results in a post-op ROM of between 25 and 35 degrees  depending on preoperative condition [27-29]. However, this procedure’s major drawbacks are its limited longevity due to bearing wear and relatively low success rates [13].  The first generation of TAA designs emerged in the 1970’s following the successes of hip and knee  replacements. However, the ankle’s complexity and its requirements for a successful joint  replacement design were underestimated. The resulting first generation of TAA designs released  were not anatomically accurate and produced disappointing outcomes. Even the most successful design of this generation, the Mayo total ankle arthroplasty, was reported to have a failure rate of  36% [30], while other designs’ failure rates were as high as 90% [31]. This generation was typified by cemented designs that were either: over-constrained and susceptible to early loosening at the  bone-cement interface, or under-constrained and prone to instability and displacement. By the 13  early 1980’s, these designs were removed from circulation and the concept of total ankle replacements had been all but abandoned for the more reliable arthrodesis.  It wasn’t until the second generation of TAA designs started showing improved mid-term outcomes  in the late 90’s and early 2000’s that people began to view TAA as an acceptable, albeit slightly more risky, alternative to fusion. Second generation designs included implants such as the Agility,  STAR, TNK, and Buechel-Pappas, some of which are still used today in their original or slightly modified form. Further attention to natural ankle kinematics [20] and attempts to replicate them  with the new devices has yielded considerable improvements in these second generation implants. Third generation TAA designs seem to be showing further improvements in success rates [8,26],  although more mid- and long-term follow-ups would be required to confirm this. Joint register data  for all total ankle arthroplasties currently in circulation worldwide reveals a 10 year survivorship  of around 70% [13]. This is a vast improvement on the previous designs and promotes optimism for even greater success rates with future generations of implants.  Every ankle replacement design has a different technique and uses its own set of specialized equipment. The similarities in surgical technique that can be drawn across the spectrum of designs are the following:  1. Incision to the anterior of the ankle joint to expose the bone/joint 2. Resurfacing cut(s) on the tibia  3. Resurfacing cut(s) on the talus  4. Cuts to facilitate fixation stems  5. Installation of metal (usually Ti or CoCr alloys) implants into tibia and talus 6. Insertion of polyethylene component (3-component designs)  14  Each different TAA system has also been designed with a unique combination of material selection,  implant geometry, and fixation method. The design features of the two TAA prostheses examined in  this study, the AgilityTM Total Ankle Replacement Sytem and the Scandinavian Total Ankle Replacement (STARTM Ankle), are described in detail in the following section.  1.5 TOTAL ANKLE ARTHROPLASTY DESIGNS 1.5.1  AGILITY TOTAL ANKLE REPLACEMENT SYSTEM  The Agility™ Total Ankle Replacement System was designed by Dr F.G. Alvine and is manufactured by DePuy Orthopaedics, (Warsaw, Indiana, USA). It was granted FDA approval in the USA in 1992 and was used in Canada from 1999 until 2006.  The Agility is a two-component semi-constrained total ankle prosthesis with a titanium tibial  component and a cobalt chromium talar component. A polyethylene (PE) liner is attached to the tibial component. An arthrodesis of the syndesmosis allows load sharing through the fibula and the tibia, to stabilize the tibial component and simplify the ankle to a hinge joint by eliminating tibio-  fibular motion. The talar component is tapered in the aagility nterior-posterior direction with its  widest edge anterior with the aim of maximising stability in stance.  Both components have a sintered bead surface (POROCOAT) intended to allow osseointegration at the prosthesis/bone interface. POROCOAT has been used extensively for hip replacements, in the AML stem, with excellent long term function and bonding [32-34]. The Agility has flat bone  interface surfaces on both the talus and the tibia, and fins are included to aid stability and increase surface area for bone ingrowth.  15  4 1 5  2 3  Figure 4: Agility ankle replacement prosthesis: 1) titanium tibial component 2) polyethylene bearing fixed to tibial component 3) CoCr talar component 4) POROCOAT sintered bead ingrowth surface 5) stabilization fins  1.5.2  SCANDINAVIAN TOTAL ANKLE REPLACEMENT SYSTEM  The Scandinavian Total Ankle Replacement (STAR®) is an unconstrained, three-component ankle  arthroplasty implant manufactured by Small Bone Innovations (SBi , New Jersey). It has been used for more than 19 years and in over 15,200 patients worldwide, and just received FDA approval in  2009. The STAR is the only FDA-approved total ankle replacement system for uncemented use.  The STAR’s tibial component is made from a cobalt-chromium-molybdenum (CoCrMo) alloy that has a titanium plasma spray coating on the proximal side for bone-ingrowth. It has a flat  articulation surface and two cylindrical fixation barrels on the superior side to anchor the implant in the subchondral bone. It uses an ultra-high molecular weight polyethylene (UHMWPE) mobile bearing, which has a flat surface articulating with the tibial component and a concave surface with a 16  groove for articulation with talar component. Similarly to the tibial component, the talar component is made from the CoCrMo alloy and has a titanium plasma spray ingrowth surface. Its ingrowth surface has 5 flat surfaces combining to form a concave structure that cups the talus with a stabilization fin in the middle. It has a convex shaped proximal articulating surface with a ridge to match the groove on the bearing.  4 1 6  2  3 5  Figure 5: STAR prosthesis: 1) flat CoCrMo tibial component 2) polyethylene mobile bearing insert 3) convex CoCrMo talar component 4) tibial fixation barrels with Ti plasma spray coating 5) talar interface surface with stabilization fin and Ti plasma spray coating 6) groove and ridge to guide mobile bearing and prevent M/L dislocation  17  1.5.3  OTHER ANKLE REPLACEMENTS  Including the Agility and STAR, there are 20 TAA designs currently in use [35], and several of the  other designs are shown in figures 6 through 13.  Figure 6: Salto Talaris  Figure 8: Inbone  Figure 10: AES  Figure 12: BOX  Figure 7: BuechelPappas  Figure 9: Hintegra  Figure 11: Eclipse  Figure 13: Mobility  As one will notice from a quick examination of these TAA models, there are a number of different  geometries employed at both the articular level and bone-interface. This fact indicates that further investigation is still required to consolidate these implants and agree on the most effective designs.  18  1.6 CLINICAL OUTCOMES OF TAA  The implants selected for this study, the Agility and STAR, are two of the five most prevalent ankle  replacement systems currently in use. Along with the notion that a larger population has interest in these results, this grants us the advantage that there is a wider range of background information on  them to provide context for the results. A number of clinical studies have reported on the short- and mid-term outcomes of these implants. Examination of these clinical results can show us trends in which implants are failing, when they failing, and how they are failing. This will eventually lead to studies of a more fundamental nature in order to determine failure mechanisms and how to prevent these failures.  One major challenge with comparing or collating data from studies originating from different research groups is dealing with variation in data collection and reporting methodology. It is important to be conscientious with the data to ensure it is all taken within the same context. In this  particular case, we have to be careful to maintain a consistent definition of key terms like failure  rates and aseptic loosening, as well as considering the follow-up period for each patient. Slight  variations to the implants and the surgical procedure have also occurred over the time frames of these studies, which cannot be accounted for. Unfortunately, some of these discrepancies cannot be  reconciled and we have to accept them as a limitation. However, a benefit to be gained from  synthesizing multi-study data is obtaining information from a wider demographic of surgeons and patients, which would give us a more comprehensive view of what would be occurring in practice. The following data should be considered with this in mind.  Failure of a TAA procedure is typically defined as when the patient requires a revision, arthrodesis, or below-knee amputation. Replacement of implant components, removal of one implant in  exchange for another, and realignment of one or both component(s) are examples of revision, 19  whereas débridement and extra-articular procedures would not be included. There are several  mechanisms for any type of joint replacement to fail or require some type of reoperation. The most common include aseptic loosening, instability, improper implant alignment, infection, polyethylene fracture, bone fracture, and persisting pain. A number of follow-up studies show that aseptic  loosening is the predominant mode of failure (46%), followed by instability (14%), mal-alignment (11%), infection (9%), polyethylene failure (8%), pain with unknown origin (8%), and periprosthetic bone fracture (4%). (see Appendix A for details)  The failure rates of the ankle replacements in total along with those due to aseptic loosening vary a great deal across studies, due to the infrequent nature of this procedure and large variations  between patients and surgeons. If we collate the data reported in all the different clinical outcome studies, we can achieve a respectable sample size that includes a range of surgeon skill levels and  patients from across the globe. The following tables summarize the outcomes of several different STAR and Agility follow-up studies:  Table 1: STAR clinical aseptic loosening rates  Author  Year  Anderson et al.[36]  2003  Henricson et al.[10]  2007  Skyttä et al.[9]  Karantana et al.[37] Wood et al.[38]  Saltzman et al.[4] Schutte et al.[39] Fevang et al.[12]  Hosman et al.[11] Total  N  51  Failures/ Revisions 12  Loosening Failures 7  Loosening Failure Rate 13.7  303  71  27  8.9  2010  217  2010  52  31 8  2008  200  24  2008  49  4  2009 2007 2007  593  16 2  14  7.4 3.8 7  28  <21  <3.5  216  21  7  3.2  1726  202  45  3  2 2  98  4.1 4.4 5.7  20  Table 2: Agility clinical aseptic loosening rates  Author  Year  Claridge et al.[40]  2009  Hosman et al.[11]  2007  Knecht et al.[41] Spirt et al.[42] Total  26  Failures/ Revisions 5  Loosening Failures 2  Loosening Failure Rate 7.7  117  8  6  5.1  N  2004  132  2004  306 581  14 33 60  5  28 41  3.8 9.1 7.1  This data sample suggests that the Agility TAR has a higher percentage of procedures failing  because of aseptic loosening than the STAR. While the difference may not be that large, another difference found in clinical follow-ups was that a much larger percentage of the Agilitys (78%)  [41,43] had radiolucencies at the bone-implant interface than the STARs (19%) [44]. This indicates  that there was only fibrous ingrowth due to excessive relative motion and is probably predictive of aseptic loosening failure in the future.  Of the second generation TAR designs (those originating in the late 80’s to early 90’s); the STAR, Agility, and Buechel-Pappas (BP) have had the most commercial success. The others falling into this  category include the Ramses, EKSA, and TNK, but the outcome studies for these implants are very limited if they exist at all. The mid-term failure rates reported for the BP device (11.6%) [8,26] fall in the same range as the STAR and Agility. The design improvements applied in third generation TAR implants, such as improved implant geometries and ingrowth surfaces, seem to be causing  slight increases in success rates [8,26], but the number of cases and duration to follow-up period is still quite limited for these implants.  21  1.7 ANKLE BIOMECHANICS  The range of motion of a normal ankle is approximately 70° in the sagittal plane, 50° of PF and 20° of DF, which has been shown to decrease with age [45,46]. However, this doesn’t represent its  absolute maximum ROM because stretching and certain activities can cause it to exceed these passive values by over 200% [47]. During daily activities, different subsets of the overall ankle ROM  are utilized. Level walking normally requires only about 15° of PF and 15° of DF [48], while running  uses 20° of DF and stepping down from a step requires slightly more ROM particularly in DF  (around 25° DF and 15° PF) [47]. The range of motion can get up to as high as 39.7° of DF, 24.7° of INV, 17.7° of EV, 11.7° of ER, and 27.5° of IR in specific daily activities that require a high range of  motion like squatting, kneeling, and sitting cross-legged [49]. By applying a fixed joint torque in cadaveric tests, the actual ROM may not necessarily be determined because the output values  depend on the magnitude and method of applied loads, but it provides a great way to systematically  compare different ankle joints and replacements. A cadaveric ROM test found PF-DF, INV-EV, and  IR-ER ROM limits of 28.2°-14.7°, 13.8°-5.0, and 15.2°-8.2° respectively in the intact ankle [50], however, this seems to be a quite conservative ROM limit when compared to previously mentioned  data.  One reason that kinematic replication of the ankle joint is so difficult is that the instantaneous axis of rotation is constantly changing depending on its relative orientation within the joint due to the  combination of sliding and rolling that occurs on the talar surface, which has a varying radius of  curvature. Changes in the ankle’s instantaneous axis of rotation occur in all three planes, and the axis affected by ankle motion in any of these planes. In the transverse plane, the axis generally  remains parallel to the line intersecting the two malleoli throughout a range of flexion angles [20].  In the sagittal plane, the instantaneous center of rotation moves from an antero-superior to a postero-inferior position as the foot rotates from DF to PF [21]. In the frontal plane, the axis of 22  rotation is oriented downward laterally in DF and either downward medially or horizontal in PF [20].  The rotations of the ankle joint complex along its three axes are naturally coupled together. For this  reason, ankle motion is sometimes described in terms of supination and pronation. Pronation involves the concurrent rotations of dorsiflexion, eversion, and external rotation, and supination is  the opposite, which involves plantarflexion, inversion, and internal rotation. During gait, the foot  pronates during midstance and supinates from heel rise to toe-off [51]. Motion coupling between axes has been classified in cadaveric experiments as rotation along a secondary axis due to applied rotation about a given axis. Although differences in motion coupling patterns are seen between  studies due to differences in loading apparatuses, the same patterns of coupling in the supination/pronation relationship were observed [52,53].  Very few direct measurements of kinetic parameters are available, but we can be quite confident  with indirect measurement techniques based on the strong agreement between studies analyzing  the same activities with different methods [54]. Indirect measurements require the use of in vivo  measurements to apply inverse dynamics calculations to a model of the ankle in order to predict joint loads or tissue stresses and strains depending on the complexity of the model. Considerable  differences in load magnitudes occur within ankles of different specimens, even those of similar size, due largely to anatomic variation – especially of structures affecting the musculotendinous  moment arms.  The ankle experiences the highest loads out of any joint in the entire body. Even during a relatively common and repetitive activity such as running, the ankle has been reported to transmit  compressive forces up to 11.1-13.3 BW (approximately 7-8 kN for the average person) [14,55]. The ankle is the most distal of the large joints, which requires it to support almost the entire body  weight. Compared to the hip and knee, the loads in the ankle are proportionally larger than one 23  would expect due solely to supporting a larger BW percentage. During walking, the tibiotalar joint  experiences a maximum compressive load of approximately 5-7BW during push-off (approx. 70%  of stance phase) whereas 3-4BW and 2-3BW are seen in the knee and hip respectively [15]. The  architecture of the foot is such that the moment arm of the forefoot about the ankle is considerably longer than that of the Achilles tendon. This increases the magnitude of plantar flexing moment required for forward propulsion, which requires a larger force in the Achilles tendon and increases the compressive load in the joint.  The moments generated about the ankle have been measured for different contraction velocities and forms and have also been calculated with models for several activities. The maximum plantar-  flexing moment in voluntary isometric contraction was found to be 232 Nm on average with a  corresponding Achilles tendon tension of just over 4.5 kN (approximately 7 BW) [56]. Similar measurements have been taken with muscle contraction being applied with maximum tolerated electrical stimulation in an attempt to better isolate and control the contraction, but the maximum  applied moment was much lower than the previously mentioned values (less than 75 Nm) [57]. The  plantarflexion moments calculated for activities such as running, walking, and jumping agreed reasonably well with these results with maximum moments of 240 Nm (1.2 BW·fl – 50th percentile  male), 120 Nm (0.6 BW·fl – 50th percentile male), and 250 Nm respectively [55,58].  In addition to the forces and moments experienced during gait, the contact pressures have also been examined with finite element models and pressure films in cadaveric experiments. While joint loads calculated for the ankle had quite reasonable agreement across a range of studies, there are  more discrepancies in the calculation of contact stresses. One FEA study found maximum stresses  in the talus of 3.55 MPa during push-off with a 3 kN compressive ankle load [59] whereas another  found peak stresses ranging from 9-14 MPa with a 2.8 kN compressive load [60]. A scaled down cadaveric gait simulation using a pressure sensing film, found a mean peak pressure of 4.8 MPa 24  using a ground reaction force of 350 N [61]. This result favours the latter FEA experiment’s values, but further validation is still necessary.  Possible explanations for differences in stress calculations are likely due to difficulties in modeling the behaviour of the contact surface. Inaccurate material properties, especially of the cartilage, can  lead to drastically different joint contact areas. Contact area will increase with a more compliant surface, and it has also been observed to increase significantly with increased compressive force  [62]. Because of the shape of the trochlea tali, an increase in contact area also occurs when the foot  is in dorsiflexion compared to plantar flexion [63,64]. A number of studies have looked at effective contact areas for different foot positions, and it is generally agreed upon that the average contact area of the ankle is in the range of 300 to 500 mm2 [62-66].  1.8 BIOMECHANICS OF THE REPLACED ANKLE  A successful total ankle replacement must fulfill three key requirements. It must reproduce the kinematic behaviour of the natural joint, be strong enough to endure the dynamic loading of the  ankle over many years of use, and be accepted by and fully integrated into the body.  It has been determined that the tibiocalcaneal and calcaneofibular ligaments are essential in  guiding the ankles motion in the sagittal plane during passive flexion, while the superficial  tibiotalar and anterior talofibular ligaments play a role in determining range of motion limits [67].  Because the articulating surfaces are removed in a joint replacement, the ligaments are the major constraining structures that remain constant, which makes it very important to understand their role and function in ankle motion. Modelling the motion of the ankle using a 4-bar linkage with 25  isometric ligaments reproduced observed motion with considerable accuracy [21]. Using this  model, an ankle replacement articulation geometry was designed that would be compatible with  the ligament structure and throughout the flexion range of motion [68]. Expansion of this concept to create more accurate three dimensional simulations, respecting all ligaments and structures has  proven to reproduce accurate kinematic behaviour essential to finite element analyses [69]. Being respectful of the ankle’s remaining structural components and designing a replacement that replicates normal kinematics within these constraints is crucial in creating an effective prosthesis.  While the usefulness of computer models has been demonstrated in this specific context of designing ligament compatible geometries, their biggest use is in determining stresses and strains in implant components with FEA, and more useful kinematic data can be found in cadaveric tests. Table 3: ROM values for the Agility and STAR as determined by Valderrabano et al. (2003)  Implant Agility STAR  PF  30.0 22.7  DF  10.0 10.6  Range of Motion (degrees) INV EV 17.4 7.8  11.9 7.5  IR  16.3 4.9  ER  10.0 15.6  The range of motion of replaced ankles has been  examined with cadaveric tests in two different studies: one by Valderrabano et al. that examined the ROM about  all three axes including analysis of the Agility and STAR among others [50], and the other by Tochigi et al. that looked at the PF-DF ROM of the STAR [70].  Valderrabano’s results pertaining to these two implants  are summarized in Table 3. In Tochigi’s experiment, the  Figure 14: PF-DF range of motion of the STAR as affected by different amounts of A/P misalignment and bearing thickness. Reproduced and adapted with permission and copyright © of the British Editorial Society of Bone and Joint Surgery [66].  26  STAR was found to have a ROM of 29.6° PF and 30.3° DF with proper installation, although it that  was found to be significantly affected by bearing thickness and A/P positioning of the talar component (fig. 14). Comparing the STAR PF-DF ROM of these two studies, we find that the  Tochigi’s values were considerably higher. There were differences in the loading apparatus and  definition of ROM limits that are likely the cause of this discrepancy. Valderrabano’s test used a 200 N axial load and a 100 Nm static moment, whereas Tochigi’s test used a 300 N axial load and  determined ROM limits by ligament strains or bearing lift-off. The ROM values determined by Valderrabano et al. for these implants are likely an underestimate since those of the intact ankle were quite conservative, as previously noted.  The amount of coupled rotation comparing implanted and intact ankles has been looked at also by  Valderrabano et al. [52] as well as by Michelson et al. [53]. Regardless of the TAA design in question, the motion transferred from one axis to the next was consistently reduced from the intact  ankle. The supination/pronation coupling relationship was still evident, but to a considerably lower degree, which varied between implant designs.  Along with coupled rotations about the other two axes, there is also mediolateral translation of the talus that accompanies PF-DF rotation. The amount of M/L translation in mobile bearing prostheses  (around 5mm) is similar to that found in the intact ankle while a semi-constrained device allows much less of this motion [18].  Another important kinematic parameter related to joint translation is joint laxity, which has been  examined in the intact ankle and one implanted with the STAR (fig 15). This study measured the  amount of A/P and M/L translation of the talus when the ankle in the neutral position was  subjected to a load limit of 150N with and without a compressive load. The joint laxity was  significantly higher in the STAR ankle, which was even more pronounced in the case where 27  compression of the joint was included, because the 700N compressive load drastically decreased the laxity in the intact ankle while only moderately reducing the laxity in the replaced ankle. [71]  Figure 15: A/P laxity of the intact ankle (black) and STAR (gray) with 5N (left) and 700N (right) axial compression. Reproduced with permission from Elsevier via Copyright Clearance Center, Inc. (Source: Watanabe et al. 2009 [71])  The joint reaction forces and moments within a replaced ankle are nearly the same as those of a normal ankle. However, slight differences are present in people suffering from ankle arthritis [72]  due to altered motion patterns of as a means of mitigating pain, which in turn reduces joint loads. After receiving an ankle replacement, the joint reaction forces within the ankle during gait were increased compared to the pre-operative condition but still lower than the normal loads (fig. 16).  Other gait studies have also confirmed the improvement of several other kinetic and kinematic  parameters following total ankle replacement in short to intermediate follow-up periods [25,73]. While the performance of TARs might not reach that of normal ankles, they should still be designed to withstand the loads of a normal ankle to provide a reasonable safety factor. Therefore, there is little need to explore the kinetic behaviour of the ankle much further, except with the intent of looking closer at the stresses and strains specific to the prosthesis.  28  Figure 16: Ankle joint reaction force in percent body weight as a function of percent stance phase during walking gait for normal subjects, preoperative patients, and patients who have received TAA. Reproduced with permission from Lippincott Williams & Wilkins via Copyright Clearance Center (Source: Stauffer et al. 1977 [72])  In comparison to the tibial and talar components, which are built from metals much stronger than bone, the UHMWPE meniscal or bearing component is quite fragile. A number of TAA failures have  been attributed to the fracture or abnormal wear of this component, giving cause for investigation into its stresses and wear rates. Finite element models are an excellent way to provide detailed  information on the stresses and strains experienced by all the components of an ankle replacement.  While cadaveric testing with pressure films is tedious and costly, they are necessary for validation of these models to ensure the proper parameters are used to get accurate results. Computer simulations can be used to test any number of potential loading scenarios very quickly and inexpensively once the model has been validated. In practice, this has been used to examine the effects of design modifications and improper implant alignment in existing devices, and the projected performance of a device under development.  Experimentally validated FEA models have been conducted in order to determine the stress  distribution throughout the polyethylene components during gait of the Agility and Mobility total ankle replacements (DePuy). It was found that wider talar components in the Agility decreased  stresses in the PE liners, but the decrease in pressure were not as much as would be expected if it 29  were proportional to the increase in contact area [74]. The Mobility was found to have much lower average contact pressures than the Agility for proper alignment, with the Agility (22 MPa) exceeding the yield stress of PE (18 MPa) (fig. 17). The effect of implant misalignments were looked at and marked increases in the articular contact pressures occurred when malaligned for both  implants, but the increase was more dramatic in the Mobility with severe edge loading in the PE  component, showing a two- to four-fold increase in maximum von Mises stresses on the inferior surface of the mobile bearing [75].  Figure 17: FEA results of contact pressures for the Agility (top/blue) and Mobility (bottom/red) in proper alignment. Image reprinted with permission from JBJS Am(Source: Espinosa et al. 2010 [75])  Additionally, the use of modelling as a preclinical design tool has also been implemented. The Box ankle prosthesis developed by Leardini et al. was subjected to an even more complex gait simulation, including the effects of ligaments. The design was determined to be capable of allowing  the necessary range of motion without overstraining any ligaments. The contact pressures also  remained below the yield stress of the polyethylene bearing throughout the simulation, reaching a maximum on the inferior surface of 16.1 MPa at 79% of the stance phase. [69]  Contact pressures are certainly linked to the wear behaviour of the PE, but these simulations cannot give us concrete evidence about the long term wear patterns or rates. In order to determine  this, in vitro tests must be performed on the prosthesis. Knee joint wear simulators were modified 30  to fit total ankle replacements and to apply loading conditions specific to ankle during the stance  phase of gait. A similar experimental procedure was performed simultaneously by two groups to  determine the wear behaviour of the aforementioned novel ankle replacement design [76], and to  compare the wear rates of the Buechel-Pappas with the Mobility [77]. The latter experiment found lower wear rates in the Mobility, albeit insignificant due to low sample size. This wear simulation procedure was verified to be effective by comparing the wear patterns from the simulator after 2 million cycles to those found in retrieved prostheses of the same design [78].  Despite the fact that aseptic loosening is the leading cause of total ankle replacement failure, and several studies have elucidated the role of micromotion in bone ingrowth, no studies have examined micromotion between the implant and bone to date.  1.9 IN VITRO ANKLE LOADING APPARATUSES  Cadaveric biomechanical tests on ankle replacements are lacking, but there are a good number of  experiments on the intact ankle joint complex that can aid in developing suitable testing methodologies and understanding ankle function. Due to the foot’s large number of bones and  joints, it is difficult to control and replicate in vivo mechanics and kinematics of the simplest activities. However, efforts put toward the reproduction of these forces and motions have yielded meaningful results that provide baseline data for the intact ankle that developers of TARs can aim to reproduce.  31  Recent advances in robotics and control have given us the ability to simulate muscle activation by applying forces to the tendons involved in foot and ankle locomotion (fig. 18). EMG and muscle  force data collected from in vivo gait experiments have exposed the state of muscle activity for a normal person. This technology combined with the knowledge of our natural ankle biomechanics has been synthesized to mimic gait within stance phase quite accurately [54].  Figure 18: Schematic of a robotic stance phase gait simulator from Pennsylvania State University (left) and sequences of images from a different cadaveric gait simulator from the University of Tubingen (right). Both figures reproduced with permission from Elsevier via Copyright Clearance Center (Source: left – Hamel et al. 2004 [79]; right – Suckel et al. 2008 [80])  Experiments with these types of simulators have been an invaluable tool with which we have been able to study and better understand how the bones in the foot move and interact with each other  with invasive measurement techniques [79,81,82] that provide much more accurate data than can be gathered from in vivo tests. This methodology has also been extrapolated to examine kinematics  in ankles with various injury models [83] as well as determining joint loads in healthy [61,80] and fused ankles [84].  32  Less complex models which employ a variety of configurations with differing levels of constraint in both static and dynamic loading have also given us a better understanding of the ankle joint  complex. The most obvious simplification from the above mentioned method is to break down the  motion into static postures of the movement of interest. This still allows us to evaluate the relative positions of bones [85] and even solving for certain muscle forces required for equilibrium [86].  Basic methods using manual manipulation while taking bone position measurements have shown  us which method of fracture fixation is more effective [87] and where different axes of the foot and  ankle are located [88]. Manual displacement control of an axially loaded, rotationally unconstrained  ankle has been used to show how ankle motion patterns change with varying fracture severities or TAA [53,89].  A few different methods of applying external loads by actuators or motors have been utilized to  dynamically test the ankle. An ankle tester developed at the University of Iowa (shown in fig. 19-1) uses an MTS system to apply axial compression and IR-ER torque and a pneumatic actuator to apply A/P force to the proximal tibia, and the foot orientation is controlled by a linear servohydraulic  cylinder on the PF-DF axis and pulley/weight system for the INV-EV axis. It is a 6 DOF system with  automated control of 4 motions and capability for constant torque to one axis, leaving only the M/L  translation axis with no loading capability [70,90-92]. A multi-axial testing device was used to test the ankle at the Mayo Clinic that is capable of applying an axial load to the proximal tibia with a linear actuator, A/P and M/L forces to the foot with a powered translation table, and an axial  moment to the foot via a rotary stage (fig. 19-2) [71]. Aside from these two devices and muscle actuated gait simulators, the only other dynamic ankle tester is one developed in our lab by Chad  Larson (fig. 19-3) which is capable of applying a pure moment to the foot with very minimal forces and off-axis moments.  33  1  2  3  Figure 19: Ankle loading devices designed to be able to 1) apply axial load, A/P force, PF-DF/INV-EV/IR-ER moments or leaving all axes unconstrained (Univ. of Iowa) 2) apply axial load, A/P and M/L force, and axial moments (Mayo Clinic) 3) apply pure moments to the unconstrained foot (C Larson – UBC). Fig. 19-1 (Source: Anderson et al. 2010 [90] & fig. 19-2 (Source: Watanabe et al. 2009 [71]) reprinted with permission from reprinted with permission from Elsevier via Copyright Clearance Center. Fig. 19-3 reprinted with permission from Younger AS (Source: Larson et al. 2005 [93])  As with all in vitro biomechanical tests, there is an inherent trade-off between the degree of  biofidelity and simplicity of the experiment. While more complex experiments allow for better  replication of finer details, they typically also require more costly and elaborate equipment along  with being technically more difficult to perform and collect data from. On the converse, simpler  experiments will usually be less expensive, and can be less complicated to allow for a more robust and clear conclusion. They can still reveal important information concerning trends or comparisons in which the precise values are not of paramount importance.  34  1.10 MICROMOTION  1.10.1 THEORY  It has been observed that all skeletal tissues, ranging from ligaments to bone, can form from the  same mesenchymal precursor cells. The environment in which the mesenchyme is cultivated,  including mechanical stimulus, plays a large role in determining what tissue it will differentiate  into. Within the field of mechanobiology, a few different theories exist on the driving mechanism(s) behind the growth and differentiation of skeletal tissue. They typically involve different  combinations of stress/strain tensors or invariants. The most prominent models include those by  Pauwels [94], Carter & Beaupré [95], Claes & Heigele [96], and Prendergast & Huiskes [97] illustrated in the following figures.  Figure 20: Mechanoregulation concept schematic of musculoskeletal connective tissue differentiation as proposed by Pauwels. Reproduced with permission from Elsevier via Copyright Clearance Center (Source: Weinans et al. 1996 [98])  35  Figure 21: Mechanoregulation concept controlled by hydrostatic stress and tensile strain history as proposed by D.R. Carter. Reproduced with permission from Lippincott Williams & Wilkins via Copyright Clearance Center (Source: Carter et al. 1998 [95])  Figure 22: Mechanoregulation concept controlled by hydrostatic pressure and strain as proposed by Claes and Heigele. Reprinted with permission from Elsevier via Copyright Clearance Center (Source: Claes et al. 1999 [96])  36  Figure 23: Biphasic mechanoregulation concept controlled by interstitial fluid velocity and solid shear deviatoric strain as proposed by Prendergast and Huiskes. Reprinted with permission from Elsevier via Copyright Clearance Center (Source: Lacroix et al. 2002 [99])  All of these theories, while differing in perspective on what the exact stimulus is behind the  differentiation, agree on the fact that large shear strains promote fibrous tissue and inhibit osseous formation.  These theories have been effectively used to model and predict phenomenon such as fracture  healing and fetal bone development. However, they not only apply to purely biological systems, but also to those interfacing with other materials such as orthopaedic implants. Uncemented joint  replacements have a porous surface to interface with the bone and rely on bone growth into that  surface for long term stabilization. The mechanical stimuli at the interface of uncemented joint  replacements and the host bone are in theory directly related to the type of tissue that will form in  and around the surface of the implant. Large relative motions between the implant and bone will create shear stresses in the tissue and lead to fibrous tissue differentiation, whose characteristics  are undesirable for implant fixation longevity. Smaller motions will reduce shear strains and allow for continuous bone ingrowth, providing a strong and durable interface between the implant and bone.  37  1.10.2 IMPLANT MICROMOTION  Studying the micromotion in total joint replacements in order to determine which designs are less  likely to fail is not a new concept, even though it has not been attempted in ankles. It has been proposed that such testing should be a requirement of new designs to ensure their quality [100]. There are several different methods that have been employed to examine the motion behaviour of different hip and knee replacements.  1.10.2.1  In vivo animal tests  Performing in vivo measurements is essentially the only way to observe the actual bone  remodelling response around implants. However, ethical considerations make performing this type  of experiment on humans undesirable. The next best approximation would be in vivo animal tests,  of which there have been a few dog experiments of note. For a series of beagles with hip replacements, it was found that the ones that had osseointegration produced maximum recoverable  deflections of 28 µm, whereas those with fibrous tissue ingrowth had maximum recoverable deflections of 150 µm in the least compliant specimen [101]. In another study all the foxhounds  with hip replacements were found to have osseointegration with initial fixation micromotion measurements of up to 56 µm. After periods of either .5, 1, or 2 years to allow for bone ingrowth,  the micromotion magnitudes observed dropped significantly [102]. In an effort to quantify the  amount of micromotion permitting bone ingrowth, another foxhound study was performed in which constant cyclical motions of different magnitudes (0, 20, 40, and 150 µm) were applied to implants in their femurs. Those with zero and twenty microns had continuous bone ingrowth, those  with forty showed partial bone ingrowth, and those with 150 µm only had fibrous ingrowth (fig. 24) [103].  38  Figure 24: Photomicrographs of porous coated implants subjected to 0 and 150 µm of cyclic micromotion showing complete osseointegration (left) and disconnected bone ingrowth and fibrous tissue (right). Reprinted with permission from JBJS Am (Source: Jasty et al. 1997[103]).  While we can’t draw a direct conclusion from these experiments on the threshold amount of initial micromotion separating human patients with bone vs. fibrous ingrowth, this does show us: a) That a stabilization of micromotion over the healing process occurs – even  though  exceeding 40µm where only partial ingrowth was observed, at 56µm of initial motion there  was still full osseointegration  b) A rough estimation for the order of magnitude of micromotion permitting continuous bone ingrowth. It is generally accepted now that the ingrowth threshold is between 100 - 200µm.  1.10.2.2  Ex vivo cadaveric tests  The micromotion patterns of joint replacements have been studied to analyze a number of different  design characteristics of joint replacements. Examples of these characteristics include stem  geometry (shape, length, diameter) [104,105], material [104], surface roughness [106], cementing  techniques [107,108]. By isolating the design features that improve and hamper the initial fixation of the prostheses, superior designs were able to be implemented that minimize the risk of aseptic loosening.  39  Experiments have been performed to improve the testing methodology for micromotion measurements as well. To improve the accuracy of the measurement, novel measurement techniques were developed [109,110] and protocols for the standardization of how and where the  measurements should be taken have been proposed [111]. A protocol for taking initial fixation measurements as a means to pre-clinically predict the loosening of hip replacements has also been put forward [100].  1.10.2.3  FEA modeling  The use of finite element modeling has proved useful in micromotion measurement. Models have  been validated with the use of in vitro experiments and have shown good agreement. However, caution should be taken when evaluating models, and they should be validated with experimental  data when possible because small changes in parameters that have no physical bearing can easily  throw off measurements by an order of magnitude [112]. The usefulness of accurate models is quite  broad, enabling subject specific tests [113], implant design tests with a large range of loading  conditions [114], large numbers of tests with statistical population variations (weight, height, bone  quality, and interface gap presence) [115], and a host of other possible applications with very detailed outcomes.  1.10.2.4  In vivo RSA  The use of models can also be applied to measurement techniques outside of the typical FEA  applications to be used in conjunction with RSA. By merging these two techniques, it is possible to achieve similar accuracy and precision to standard marker-based RSA without the requirement of  tantalum beads [116,117]. This expands the usefulness of RSA measurements to a much wider application base.  40  1.10.3 ASEPTIC LOOSENING  Aseptic loosening refers to the failure of orthopaedic implants by mechanical loosening in the absence of sepsis. There are two distinct methods by which this happens over different time frames.  One is caused by the production of polyethylene wear particles, which triggers an immune system  response that activates macrophages and sends them to the site to remove the foreign particles.  Peri-prosthetic osteolysis, or bone resorption, is an unfortunate byproduct of this process that can  weaken the bone-implant bond and result in mechanical loosening failure. Since this process is a  result of bearing wear, it usually only initiates after 5-7 years of use [118]. The other cause of  aseptic loosening, relative motion between the bone and implant, is present right from the outset and can lead to failure and revision much earlier. It has already been established that in an  environment where excessive micromotion is present, osseointegration of the implant is impossible  and fibrous tissue forms around the implant instead. The formation of fibrous tissue immediately  following implantation does not necessarily imply aseptic loosening will occur. Three typical outcomes can arise from this scenario: the micromotion decreases over time to enable osseointegration, the micromotion stabilizes at a level that neither allows bone ingrowth nor causes  circumstances requiring revision, or the micromotion increases over time and gives rise to  complications requiring revision surgery [4,41]. Implant migration patterns within the first couple of years have been shown to predict aseptic loosening behaviour whose symptoms would require  revision surgery quite soon or even after many years (up to ten years later) [119,120]. Although not always resulting in revision, it is commonly accepted that weak initial fixation (fibrous ingrowth) is a strong predictor of future aseptic loosening failures, similar to migration.  41  1.11 MOTIVATION  There is a general lack of research in the area of total ankle replacements in comparison to its hip and knee counterparts. In order to reduce their failure rate, it is important to produce similar  biomechanical analyses of the joint to better understand the ankle’s performance before and after replacement. Aside from the obvious outcomes of kinematic variables, the motion between the  implants and their anchoring bone is of particular interest because of the large proportion of total ankle arthroplasty failures that are attributable to aseptic loosening. Aseptic loosening can occur as  a result of excessive interfacial motion, which prevents continuous bone ingrowth right from the outset and fibrous tissue is formed at the interface instead. In order to prevent this from happening, it is imperative to reduce the amount of motion between the implant and bone by determining which designs are best suited to accomplish this.  1.12 OBJECTIVES  The primary objective of this study was to perform a biomechanical analysis of the cadaveric ankle to compare two commercially available total ankle replacement designs, the STAR and Agility. This analysis contained specific aims to:  1. Determine the difference in micromotion at the bone-implant interface between the Agility and STAR for both tibial and talar components  2. Determine the effect of applying a compressive load on the relative micromotion magnitudes  3. Quantify the kinematic changes imposed on the ankle by the joint replacement prostheses in comparison to each other and intact ankles  42  2 METHODS  2.1 EXPERIMENTAL DESIGN  This experiment was designed to simulate a range of loading scenarios in the ankle in order to  observe the performance of both the STAR and Agility total ankle replacements in comparison to  each other and intact ankles. The ankle testing apparatus was designed to apply a compressive load  and a pure moment to the otherwise unconstrained foot. Six bilateral pairs of human cadaver ankle  joints were tested in this simulator, which were initially analyzed intact and again after having  received total ankle arthroplasty. Each ankle received one TAR, such that one ankle of each pair had  the Agility and one had the STAR. Each test consisted of a sequence of 3 independent load applications about orthogonal axes. These axes coincided with those on the ankle defined as  plantarflexion-dorsiflexion (PF-DF), inversion-eversion (INV-EV), and internal rotation-external rotation (IR-ER). Each limb was subjected to a compressed and an uncompressed test for both intact and implanted conditions.  An optoelectronic motion capture system was used to determine the 3-dimensional positions and orientations of the bones and joint replacement components during these tests. These measurements were used for determining bone-implant micromotion as well as kinematic variables such as range of motion (ROM), motion coupling (MC), and joint translation (JT).  43  2.2 ANKLE LOADING APPARATUS  The ankle loading apparatus used in this study of total ankle replacements had five distinct  components: moment applicator, foot-plate, counterbalances, mounting rig, and follower load (fig. 25). The moment applicator was used to apply a pure moment to the foot-plate while leaving the other 5 DOF unconstrained. The foot-plate’s function was to attach rigidly to the bottom of the foot,  provide attachment points for the moment applicator’s fixture block and counterweight cables, and  facilitate the application of a compressive load. The counterbalances’ purpose was to counteract the weight of the footplate and moment applicator arm so that there were no external forces or  moments acting on the ankle other than the applied loads. The mounting rig was needed to fix the  proximal end of the foot to the test platform and supply a means to guide the compressive load cables through the centre of the ankle. The follower load used a linear hydraulic actuator and cable system to apply a constant compressive load to the foot-plate.  This apparatus was adapted from one originally designed for loading the spine [121]. It applies a  pure moment about a single axis to one end of the spinal segment while the other end was fixed to  the test platform. The moment was applied in such a way that allowed the superior end to be completely unconstrained except for the axis about which the moment was being applied. This apparatus was previously modified for testing with the ankle by Chad Larson, a former M.A.Sc.  student [93]. His study compared the relative strengths of different ligament grafting techniques by applying moments to the ankle about 3 orthogonal axes. The test apparatus he used was similar to  the one used in the present experiment, except that no compressive loads were applied in his  ligament study.  44  Cable Counterweight System  Moment Applicator Foot-Plate  Optotrak Marker Carrier Cable Guide Disc Counterweight  Steel Cable  Mounting Rig  Hydraulic Actuator  Figure 25: Ankle loading apparatus set up for PF-DF loading on the intact left foot of specimen 3  45  2.2.1  FOOT-PLATE  The foot-plate (fig. 26) was designed with an array of holes to provide locations to screw into the  foot and pass ties through to secure it to the plate for all sizes and shapes of feet. A slight square  recess and 10-24 threaded holes to each side were machined onto the plate bottom near the posterior end to accept the existing fixture block. A medial-lateral groove was milled out of the plate to allow the steel cable to pass underneath the block once attached. The groove was roughly underneath the ankle center when the foot was in the neutral position. Within the groove, two slots were made to hold polyethylene inserts for the cable to rest on to decrease the coefficient of sliding friction.  Figure 26: Foot-plate shown from the inferior aspect (left) and close up of the cable slot with polyethylene inserts (right)  46  2.2.2  MOUNTING RIG  The mounting rig built for this experiment was designed with three functions: to secure the  proximal end of the limb, to fix the limb to the test platform, and to provide an adjustable cable guide system for directing the compressive load (fig. 27).  Cable guide holes A/P Position Adjustment Set Screws  Vertical Position Adjustment Set Screws  Figure 27: Mounting rig used for potting the limb, mounting it to the test platform, and guiding the compression cables  The main body of the rig consisted of a hollow rectangular box with an open top. It was precisely  machined so that all joints were water-tight in order to prevent leakage while the liquid potting mixture was solidifying. The bottom plate of the rig had four holes which machine screws could pass through for attachment to the test platform. The rig was also designed with four posts in each 47  corner that had holes drilled through the center down its entire length. The holes in these posts were used to hold cylindrical rods, whose vertical position was adjusted and secured by means of  set screws. There were holes drilled through the tops of these rods to hold two smaller rods  perpendicular to them on the medial and lateral sides of the ankle. The smaller rods’ anterior/posterior position could also be adjusted and held in place by set screws. Cable guide holes were drilled through the small rods in order to accommodate a steel cable. The adjustment of  previously mentioned rods enabled the vertical and A/P translation of the guide holes. Details of the construction of the rig are given in Appendix C.  2.2.3  COUNTERBALANCES  The counterbalance system was calibrated once prior to biomechanical testing to ensure the elimination of all external loads/moments on the ankle caused by the weight of the system. This  was accomplished by connecting the foot-plate to the moment application apparatus and arranging the counterbalances such that the system was suspended motionless in the air.  The first such counterbalance supported the weight of the entire configuration with a cable and  pulley system. It used an aluminum box/receptacle filled with lead beads (loaded to approximately 1.8 kg), connected to a system of pulleys, which in turn were attached to anchor points on the  footplate. The pulley system was free to translate along all three planes and follow the translations of the footplate during the tests. The placement of cable anchor points on the footplate were also  calculated so that it did not create any additional moments and allowed it to operate optimally under a large range of angular rotations. It was determined that the optimal locations for the anchor points were as shown in figure 28.  48  Y X  Z  Cable Counterweight Anchor Points  Disc Counterweights  Figure 28: Foot-plate mounted to moment apparatus suspended by cable counterweight and balanced by disc counterweights (left), and counterweight pulley system attached to the test platform frame free to translate along the X, Y, and Z axes in accordance with footplate movements (right)  The second counterbalance component counteracts the moment caused by the arm of the moment  apparatus. It is a threaded rod with five disc-shaped steel weights (weighing approximately 96 g each) that extends out from the fixture block of the moment applicator. Nuts on either side of the  weights secure them in place and can be shifted along the length of the rod to fine tune the countermoment without changing the overall weight of the system. Gross adjustments can also be made by  adding or removing discs, but the change in total weight must then be reflected in the cable counterweight (refer to fig. 28).  49  2.2.4  LOADING  2.2.4.1 Compression As mentioned previously, the compressive loads were applied using a 1/16” steel cable looped  around the bottom of the foot-plate and a small pulley attached to a linear hydraulic actuator. The  actuator used was an Instron A591-4 (Instron, Norwood, MA) with a force capacity of ±1kN and an actuator stroke of ±25mm connected to the Labtronic 8800 control unit. The actuator was fixed to the test bed, directly underneath the platform to which the limb was mounted as shown in figure  29.  Cable Pulley Attachment Honeywell Model 75 Load Cell  Instron A591-4 Hydraulic Actuator  Figure 29: Instron A591-4 linear hydraulic actuator mounted below the test platform with the cable pulley attachment connected to the load cell.  There was a Honeywell Model 75 load cell (Honeywell Internaltional Inc., Columbus, OH) attached to the actuator’s end effector, which measured tension and compression to a capacity of 1kN with 50  an accuracy of ±1.4N. An aluminum bar was attached to the load cell with pulleys on either end free  to rotate about its transverse axis. The steel cable was looped around this pulley system to apply tension to the system.  Footplate Cable Groove  Cable Guide Rod  Figure 30: Foot in PF-DF loading with compressive load line of force applied directed downward from footplate cable groove through cable guide rod and down toward the hydraulic actuator  As described previously, the mounting rig was designed with a configuration of rods that enabled  the vertical and A/P position of a guide hole for the cable to be easily adjusted. This allowed the cable and hence the line of action for the compressive force to be directed from the groove on the bottom of the foot plate, through the cable guide hole on the mounting rig, and downward to the hydraulic actuator (fig. 30). The main function of the cable guide was to direct the force through the  axis of rotation of the ankle in the sagittal plane. This was necessary to minimize the artefact moment caused by the offset of the compressive force from the ankle axis. It was not possible to eliminate the artefact moment altogether because the ankle axis changes as the talus moves with respect to the tibia. During the experiment, constant compressive loads up to 300N were applied to 51  the foot. Because the location of the cable groove on the foot-plate moved along with the foot as it traveled through its range of motion, the line of force was changing throughout the test. As a result,  the force wasn’t a pure axial load but had a shear component as the foot rotated away from the neutral position.  2.2.4.2 Moment The device used to apply moments in this experiment (fig. 31) was essentially the same as the one originally designed by Goertzen et al. [121] with the exception that the hollow tube around the ball spline has since been upgraded to increase its axial travel (480mm vs. 300 mm) and improve its  torsional stiffness (6.5° vs. 14° angular deformation at 10 Nm applied torque). It utilized a servo  motor (D50R10-0243, Designatronics, New Hyde Park, NY) with a 55:1 low-backlash planetary  reduction gearbox (G23PI-0055-LB, Industrial Devices, Petaluma, CA) to apply torque to the  articulating arm. The arm consisted of two universal joints (UJ-SS1000, Belden, Broadview, IL)  connected by a ball spline (LBF15UU+300LE, THK, Mississauga, ONT). One U-joint was attached to the output shaft of the gearbox and the other to the torque load cell (TRT-200, Transducer Techniques, Temecula, CA), which in turn was connected to the fixture block. Optical Rotary Encoder Motor Latch  Gearbox  U-joint  Ball Spline  U-joint  Fixture Block  Figure 31: Moment application apparatus  52  This configuration allowed the motor to apply moments about a designated axis determined by the  orientation of the fixture block for a range of specimen translations and rotations. It was initially determined to apply pure moments about each of 3 orthogonal axes to within 0.15 Nm with a force component of 1.49 N [121], and was again verified after implementation of the new arm.  A LabVIEW (National Instruments, Austin, TX) program was used to input the test parameters such  as angular velocity, torque limits, and number of cycles. The servo motor control was facilitated by  this program in conjunction with a motion control card (Flexmotion 6C) and amplifier (nuDrive 4CF-001), with feedback inputs from the optical encoder (H32R85–L0306, SDP/SI, New Hyde Park,  NY) and conditioned torque cell signal (TMO-2, Transducer Techniques, Temecula, CA). A real time graphical output of the actuator angle and applied moment were displayed on the LabVIEW VI during tests.  2.3 SPECIMEN SELECTION  The specimens used in this study were fresh frozen human cadaveric foot and ankle joint  complexes cut off at mid-shank. They were obtained from the UBC Department of Cellular and  Physiological Sciences through the Body Donation Program. Both male and female specimens of all ages were accepted. Specimens excluded from this study were only those which had severe  ligament damage, deformities, or other conditions that would render a subject ineligible for a TAR surgery in clinical practice. There were 3 male and 3 female donors, which composed the demographic displayed in table 4.  53  Table 4: Specimen data  Specimen #  Sex  Age (yrs)  Weight (kg)  Height (cm)  H1347  M  67  60  175  H1351  M  93  73  168  H1349 H1350 H1352 H1353  Average  M F F F  90 68 59 68  74.2 ± 13.9  80 81 73 45  68.7 ± 13.8  168 168 165 173  169.5 ± 3.7  2.4 SPECIMEN PREPARATION  All specimens were kept frozen at -20°C when not in use. Prior to use, the limbs were transferred to  a refrigerator kept at 4°C until fully thawed, which in most cases was approximately 48 hours.  2.4.1  POTTING  In order to mount the limbs in the test rig, the proximal end of the tibia and fibula were potted in  dental stone. To ensure that the dental stone bonded rigidly to the specimen, bone was exposed on the proximal 3-4 inches of the tibia and fibula. All tissues including the periosteum were removed using a #22 scalpel and tissue forceps.  A large retort stand and two clamps were used to align and immobilize the limb in an upside down  position. The alignment of the limb was determined visually by setting the long axis of the tibia as normal to the ground (vertical in the X-Z and Y-Z planes) and setting the long axis of the foot (the line passing through the posterior most point of the calcaneus and the second metatarsal) as 54  parallel to the cable guides while the foot rested in the neutral position. The foot was suspended in  the air with all of the exposed bone within the potting jig except for the distal half inch to provide clearance for the soft tissues.  Four ¼-20 machine screws were placed in the holes at the bottom of the potting jig with a nut on  the bottom (outside of the jig) to hold the bolts in place while the potting set. The screws were  firmly fixed within the dental stone once it had hardened, after which they were used to fasten the  specimen to test platform.  The dental stone powder (Tru-Stone® Pink, Heraeus Kulzer, South Bend, Indiana) used has a compressive strength of 103.5 MPa and requires a liquid/powder ratio of 24 mL/100 g. It was  mixed with water to a consistency that was thick yet still able to be easily poured from the mixing  dish into the potting jig. The potting rig was filled to the top and the jig was disturbed to ensure it had a homogenous distribution and that no air bubbles were present.  The specimen was kept suspended upside down while the potting set. The set time according to the specifications is 9-11 minutes, but it was left to sit for approximately an hour before moving it to  ensure the dental stone was fully hardened. Because the potting was still hot at this point, the  specimen was placed in the refrigerator to cool before the specimen was loaded.  2.4.2  FASTENING FOOT-PLATE  A foot-plate was attached to the bottom of the limbs to enable attachment to the loading apparatus.  The center-line of the foot-plate was held in alignment with the long axis of the foot while two screws were put into the calcaneus through counter-bored holes in the plate (fig. 32-L). Pilot holes  were drilled into the calcaneus prior to inserting the 6.5 mm cancellous bone screws (45 mm long, 32 mm thread length). The forefoot was secured using two cable ties fed through holes in the foot55  plate strapped around the distal end of the metatarsals (fig. 32-R). The cable ties were cinched  down tight enough that no motion was observed between the forefoot and footplate during testing. Bone Screws  Cable Ties  Figure 32: Bone screws passing through the foot-plate into the calcaneus (left) and cable ties wrapping around forefoot and through footplate (right).  2.4.3  JOINT REPLACEMENT SURGERY  After each specimen was tested intact, one of two joint replacement surgeries was performed on it.  The surgeries were performed by foot and ankle surgeon, Dr. Alastair Younger, who has clinical experience with both of these procedures.  The surgical instrumentation included specialized cutting jigs, pins, guides, drill bits, measurement devices, and various other tools to ensure accurate alignment and installation of the implant donated by the manufacturer. Other generic tools used were oscillating and reciprocating saws, a drill, osteotomes, rongeurs, surgical tweezers and forceps, and scalpels.  The Agility total ankle replacement surgery was performed on the left limb and details of the  surgical technique can be found in Appendix D. The STAR implant was installed in the right limb of the pair, and the details of this first generation STAR procedure can be found in Appendix E.  56  2.5 MEASUREMENT METHOD  The Optotrak Certus® (Northern Digital Inc., Waterloo, ON) was used for taking bone and implant position measurements. It is an optoelectronic motion capture system that tracks the 3D position of  infrared LED diodes. These markers were grouped into arrays of 4 and attached to polyethylene  marker carriers. They were arranged in rectangular groupings to enable the calculation of rigid body translations and rotations. The Optotrak is specified to have a single marker 3D accuracy of  0.1 mm and a resolution of 0.01 mm. Further validation was performed to determine the accuracy of measurements taken with the four marker arrangement and transformation algorithm used in  this experiment (see Appendix F). The Optotrak measurements were found accurate to within 0.012 mm for translations and 0.09° for rotations, with a precision of 0.005 mm and a repeatability of 0.002 mm.  Figure 33: Optotrak Certus motion capture system. Optotrak camera (left) and PE marker carrier with 4 LED diodes (right)  57  2.6 TEST PROTOCOL  2.6.1  TEST CONDITIONS  A total of six pairs of limbs were tested in this experiment. One limb out of the pair was used to test  the Agility implant, while the other was used for the STAR implant in this bilateral comparison procedure. Each limb was subjected to four tests – two performed on the intact ankle and the same  two repeated after total ankle replacement (see table 5 for details). One test was with a constant  compressive preload representing ½ BW (or 1/8 BW for INV-EV) and the other one was with a minimal preload (15N). Each test comprised a sequence of three orthogonal load applications,  during which the ankle was cycled through its ROM about the given axis three times. The behaviour of ankles was found to be consistent from the third cycle onward; therefore, the test was stopped  after completion of the third cycle to minimize damage caused to soft tissues. The three orthogonal axes were chosen to be aligned as close as possible to those of PF-DF, INV-EV, and IR-ER (fig. 34).  Figure 34: Ankle test apparatus setup for the 3 loading directions: IR-ER (left), PF-DF (middle), and INV-EV (right)  58  For the uncompressed conditions, a 15 N compressive load was applied to stabilize the joint. For the compressed conditions in PF-DF and IR-ER, 300 N was chosen as it represented roughly ½ BW. Angular displacement limits for the implanted PF-DF tests were determined on a specimen by  specimen basis. They were defined based on either a percentage of the intact ROM, component/bone interference, or bearing lift-off. Table 5: Loading conditions  PF-DF INV-EV IR-ER  2.6.2  Intact: uncompressed  Intact: compressed  15 N compression 5 N·m torque limit  300 N compression 5 N·m torque limit  15 N compression 3 N·m torque limit 15 N compression 3 N·m torque limit  75 N compression 3 N·m torque limit 300 N compression 3 N·m torque limit  Implanted: uncompressed 15 N compression Angular displacement limit 15 N compression 3 N·m torque limit 15 N compression 3 N·m torque limit  Implanted: compressed 300 N compression Angular displacement limit 75 N compression 3 N·m torque limit 300 N compression 3 N·m torque limit  TEST PROCEDURE  2.6.2.1 Initial Test Prep Each specimen received from the UBC body donation program varied slightly in the shank length.  The depth of bone within the potting could be adjusted slightly to compensate for limb length; however, ensuring that the limb was securely fastened was of utmost importance and a minimum of  3 inches of bone depth would be required of the total 4 inch jig depth. This resulted in differences in the overall height of the mounted limbs between specimens. This difference was accounted for by  adjusting the height of the test platform such that the arm of the moment applicator was parallel to  the ground. This was required to maintain the alignment used to set the counterbalances and to  prevent interference between the moment applicator and the test platform.  59  At this point, the Instron and Optotrak were also set up. The Instron was powered on, warmed up, and calibrated. The Optotrak was plugged in and initialized with the LabVIEW program, and all the Optotrak markers were verified for connectivity and proper arrangement.  2.6.2.2 Markers There were a few methods employed to attach the Optotrak marker carriers to the rigid bodies of interest. In order to get accurate rigid body transforms, it is important that all four markers on a  given marker carrier are visible throughout the entire test. Since all the bodies that had to be  tracked were in such close proximity, the marker carriers had to be placed strategically to prevent  any markers from getting blocked.  K-wire pins were used for attaching the marker carriers to bone. The K-wire was bent prior to  insertion to avoid accidentally widening the hole and causing it to loosen. As a result, it was impossible to insert the pins with a drill in the conventional manner. A pilot hole considerably  smaller than the K-wire was drilled into the bone, and the pin was inserted into the hole with a snug friction fit. There was a steel block, which was connected to the K-wire and a small nail by set  screws. This K-wire/nail block prevented rotation of the pin within the bone.  Each Agility implant component had a 10-32 threaded hole that was designed to aid in the  installation of the implant during surgery. Machine screws, which had a flexible galvanized steel wire (ø = .0475 in) fixed to them with a nut, were threaded into these holes (fig. 35). The wire was  twisted about itself to increase its rigidity. The marker carriers were attached at the ends of these wires.  60  1  2  Figure 35: Marker mounting locations for the Agility TAR. Screws with mounting wires threaded into the tibial (1) and talar (2) installation holes are shown  The STAR components only had flat and curved surfaces that were accessible after the implant was  installed; hence, glue (Instant Krazy Glue®, One Easton Oval, Columbus, OH) was used to attach marker mounts. The tibial component had a space on the proximal aspect just anterior to the fixation barrels where a wire was able to sit without touching any bone. The wire was looped to create a larger surface contact area where it attached to the implant, and the portion that extended  outward was twisted to increase rigidity. On the talar component, the only available area was the convex articulating surface. A small steel block with a hole for a K-wire pin and a set screw was  glued onto the front corner of the talar implant where it had clearance from the mobile polyethylene bearing and bony elements throughout the entire range of motion (fig. 37).  61  1  2  Figure 36: Marker mounting locations for the STAR: twisted wire glued to the proximal side of tibial component (1) and mounting block glued to bottom corner of talar component (2)  The polyethylene marker carriers were built with a steel block fastened to the back. These blocks  have small holes parallel to the carrier surface to allow it to slide onto the K-wire pins or other wires protruding from the specimen and are held in place by a set screw. The pins were  strategically fixed to the specimen to reduce marker overlap. The fine adjustment of the marker carriers’ orientation with respect to the wire in conjunction with the wire positioning enabled us to  ensure that none of the LEDs were blocked. The final adjustments were made while the Optotrak was running with the LabVIEW program giving feedback of the whether or not the camera was  picking up the LED’s signal. At this point, adjustment of the K-wires themselves were kept to a minimum in order to reduce the chance of loosening their connection to the bone, and adjustments  in the camera orientation and the marker positions were used liberally instead. When a potential 62  setup had been configured, the foot was moved to its most extreme poses in its range of motion and  the marker signals were checked and further adjustments were made if there were any obstructions.  2.6.2.3 Ankle Axis of Rotation It is difficult to approximate the axis of rotation for the ankle joint in the sagittal plane because its  position and orientation changes as the ankle moves, but an optimal position was found for each specimen that best approximated it for all loading applications. As a starting point, the vertical  position of the cable guides was estimated based on the implant geometry or anatomical  landmarks, which was roughly around the distal tips of the malleoli. Subsequently, a 200 Newton  compressive load was applied to the ankle and an optimal configuration of the cable guides’ A/P positions was determined empirically. The configuration was evaluated by setting the cable guide  positions, rotating the foot about its flexion axis by hand, and feeling the magnitude of induced  moment caused by the compressive force. The guide positions were then adjusted slightly and the  process was repeated until the position was found that minimized the induced moment caused by the compressive load. After the optimal cable guide positions were found, the set screws were tightened down so that the guide positions wouldn’t shift when the ankle was loaded.  2.6.2.4 Reference Position  A reference position was required for the calculation of all the joint angular and translational  displacements. The foot was put into the neutral position and Optotrak data was collected for a few seconds without any motion. The neutral position was defined as the orientation when the footplate was parallel to the ground along the PF-DF axis, while the foot was allowed to take on its natural alignment about the INV-EV and IR-ER axes.  63  2.6.2.5 Digitize points It is necessary to know where certain points on the limb are in reference to the Optotrak coordinate  system. These are required to locate points of interest or define other coordinate systems for use in  post-processing. While the foot was still in the exact same position as in the static shot, a digitizing probe was used to identify the location of specific landmarks and record their position. The  Optotrak probe consists of a rigid plastic body housing six LED markers with a steel tip protruding from the body. While the tip touched the desired point and at least three of the markers were  visible to the Optotrak camera, the position could be captured with the press of a button in the Labview VI. Details of the digitized points will be shown in the following analysis sections.  2.6.2.6 Apply Loads Depending on which test was being run, the designated compressive load was applied. The position  of the foot was then moved as close to neutral as possible before initiating the test. A custom  Labview program designed and validated previously for similar studies was used to coordinate the  Optotrak data recording and the moment application. This program implemented a PID controller  to cause the servo motor to supply a torque that maintained a constant angular velocity until it  reached either the torque or angular displacement limit designated for the specific test. Following  this, it reversed the angular velocity until it reached the limit in the opposite direction and repeated  this process until it completed 3 cycles. The following figures show a typical example of the loading  applied to the foot displayed as time traces of the applied moment (fig. 37) and resulting angular displacement (fig. 38).  64  Applied Moment: Specimen H1352R Intact Uncompressed PF-DF 6 5.034  Moment (Nm)  4  2  0  -2  -4 -5.051  -6 0  50  100  150  200  250  300  Time (s) Figure 37: Sample of applied moment measured by the torque load cell for uncompressed PF-DF loading set to limits of 5Nm  Applied Rotation: Specimen H1352R Intact Uncompressed PF-DF 60 49.95  Angle (deg)  40  Slope = -1.98 deg/s  20  0  -20 -39.02  -40  -60 0  50  100  150  200  250  300  Time (s) Figure 38: Sample of angular displacement of the servo motor as measured by the optical encoder for uncompressed PF-DF loading set to an angular velocity of 2 deg/s.  65  2.7 DATA ACQUISITION  The 3D position data of the bones and implant components was recorded with the Optotrak Certus  system. The Optotrak camera was connected to its system control unit, which was connected to the computer with a specialized PCI card. The data from the Optotrak was collected and managed with  the LabVIEW (National Instruments, Austin, TX) virtual interface that was custom designed to  coordinate motion capture and control load application through the moment application apparatus.  The data from the moment application apparatus was not used for any of the outcomes of the study,  but it was used for feedback required to control the loading. The applied moment was measured by  the torque sensor (TRT-200, Transducer Techniques, Temecula, CA) connected to the fixture block.  The signal from the torque cell was first passed to the torque sensor signal conditioner (TMO-2,  Transducer Techniques, Temecula, CA) before it was sent to the DAQ unit (nuDrive 4CF-001, National Instruments, Austin, TX). The angular displacement of the foot was approximated by the  optical rotary encoder (H32R85-L0306, SDP, Designatronics, New Hyde Park, NY) connected to the  servo motor. The signal from the optical encoder was also sent to the DAQ unit. Both the angular  displacement and torque signals were sent through the motion control card (Flexmotion-6C, National Instruments, Austin, TX) from this unit to the computer. The LabVIEW VI used the  feedback signals from the motion control card to adjust the signal sent through the power amplifier (also the DAQ unit – nuDrive 4CF-001) to the servo motor.  66  2.8 DATA ANALYSIS/PROCESSING  The Optotrak .dat files were first converted to .csv files using NDI file conversion wizard. Matlab programs were written to manipulate and perform preliminary analysis on the .csv data (AppendixG). The 3D position data was analyzed by comparing each successive frame to the initial  static shot in order to determine the kinematic variables and relative bone-implant displacements. By assuming rigid bodies (including the markers with respect to their targets), it was possible to  determine the transformation matrix required to take the marker set (and by association the  bone/implant of interest) from the initial position to the final position. The method used in this study for this computation was the least-squares algorithm described by Veldpaus et al.[122]. This computation gives an estimate of the translation vector and rotation matrix of a moving body from  the spatial coordinates of at least three non-collinear markers. Joint rotations, joint translations,  and bone/implant motions were then determined by applying the rotation matrices and translation vectors of the rigid bodies to their local coordinate frames.  2.9 KINEMATIC ANALYSIS  All kinematic data was represented here in the joint coordinate system (JCS)[123], which  eliminated the angles’ dependence on the order of rotations about the joint axes. Although the JCS is  a non-orthogonal basis, it provides a more anatomically relevant definition of the rotations while  allowing for better comparison between different studies. Specifically, the definition of the ankle  joint coordinate system used landmarks and axes as proposed by Wu et al.[124] as shown in figure 39.  67  Figure 39: Joint coordinate system definition for the ankle. Reprinted with permission from Elsevier via Copyright Clearance Center (Source: Wu et al. 2002[124])  e1:  e3:  e2:  Flexion axis: fixed to the tibia/fibula, pointing laterally and passing through the tips of the medial and lateral malleoli. Rotation (α): dorsiflexion (positive) or plantar-flexion (negative) Displacement (q1): lateral (positive) or medial (negative) shift  Long axis: fixed to the calcaneus, pointing cranially and along the long axis of the tibia while in neutral position. Rotation (γ): internal rotation (positive) or external rotation (negative) Displacement (q3): compression (positive) or distraction (negative) Floating axis: normal to e1 and e3. Rotation (β): inversion (positive) or eversion (negative) Displacement (q2): anterior (positive) or posterior (negative) drawer  68  The only deviation from Wu’s coordinate system was in defining the long axis of the tibia. This axis  is pointing cranially along the line intersecting the midpoint of the medial and lateral condyles of  the tibial plateau and the midpoint of the medial and lateral malleoli. However, it was not possible to locate the condyles because the limb was cut off mid-shank. Instead, it was approximated by the line intersecting the midpoint of the malleoli and centroid of the most proximal segment of the tibia available[125].  The points that required digitizing for the JCS and all kinematic analysis were as follows: 1. Medial malleolus  2. Lateral malleolus  3. Medial edge of tibia  4. Lateral edge of tibia  5. Posterior edge of tibia  2.9.1  JOINT ROTATIONS  The joint rotations were calculated according to the joint coordinate system definition. Because the  reference axes rotate along with the joint, it allows for a more relevant description of the angular  displacements observed. In this specific experiment the tibia was essentially fixed (aside from slight  bone deformations due to loading), thus the flexion axis fixed to the tibia was the only axis that remained relatively stationary. For the ‘long’ and the ‘third’ axes, the effects of this coordinate  system were much more pronounced. The rotations calculated for a given axis were those of the rotations in the plane that contained this axis as its normal vector in the current frame’s orientation.  69  2.9.2  RANGE OF MOTION  The range of motion as defined in this experiment was the largest angle observed in both positive  and negative directions of rotation about the primary axis. That is to say, the primary axis was the  axis about which the testing apparatus was applying the moment. The range of motion is a good  way to compare different specimens because it is a very simple computation outputting a scalar value. As such, it is commonly reported and inter-study calculation differences are minimal.  2.9.3  MOTION COUPLING  In this study, coupled motion was defined as the rotation along axes that were not the primary axis.  While the primary axis was being cycled through its range of motion by the moment application  apparatus, the other two axes were unconstrained and free to rotate naturally. Because the joints of  the foot and ankle are interrelated in a complex manner and are not orthogonal unidirectional  hinges, motion along the other axes occurred as the primary motion was induced. The motion coupling ratio used to describe this motion was the maximum induced ROM about a secondary axis  divided by the maximum ROM of the primary axis during the third cycle of loading. The motion coupling plots show the mean value of the secondary axis angles as a function of the primary axis  angle for the uncompressed conditions when loaded in the forward and reverse directions separately. Because not all of the specimens had the same primary ROM as the others, the graphs displayed the ROM over which the majority of specimens had data.  70  2.9.4  JOINT TRANSLATIONS  The joint centre in neutral position was taken as the midpoint between the distal tips of the lateral and medial malleoli. The joint translations were defined as the movement of the joint centre fixed to  the calcaneus reference frame with respect to its initial position in the tibial reference frame. These were calculated by determining the transformation matrix between the calcaneus marker array in a  given frame and that of its initial static shot, and applying it to the joint center. After the displacement vector was determined in the Optotrak reference frame, it was decomposed into  components along the JCS axes. The JT magnitudes were taken as the difference between the maximum and minimum values of the final cycle.  2.10 BONE-IMPLANT RELATIVE MOTION  Along with the digitization of all the anatomical landmarks for defining the coordinate system in kinematic analysis, separate coordinate systems and reference points were created from digitized points on the implants for the analysis of the motion between the bone and implant. Separate  coordinate systems were necessary for both components of each implant, and were defined as shown in figure 40.  71  e3  2  7  1  e1  3  e3  e2  e3  e1  1 e1  4 5  e2  6 e2  2  e3  3 4  e1  5  e2  Figure 40: Implant-specific coordinate frames and the corresponding digitized points required to define them with the STAR on the left and Agility on the right.  STAR:  Agility:  Tibia: O: midpoint of 1 and 2 e1: 2-1 e3: (4-3) cross (5-4) e2: e3 cross e1  Tibia: O: midpoint of 1 and 2 e1: 2-1 e2: (2-1) cross (1-3) e3: e1 cross e2  Talus: O: midpoint of 6 and 7 e1: 7-6 e3: e3tibia e2: e3 cross e1  Talus: O: midpoint of 4 and 5 e1: 5-4 e3: e3tibia e2: e3 cross e1  72  The dimensions of the implants were measured, and the locations of the implant corners were determined within the implant coordinate system. This allowed us to calculate the 3D translations  of the four corners and determine their relative displacements. Calculating the motion of the corners was required to ensure that the reported micromotion magnitudes were the maximum  values across the entire surface of the implant interface. Rotation of the implant with respect to the bone could cause certain corners to experience larger micromotion magnitudes than others  depending upon the axis of rotation.  Comparing the motion between the implant and bone for the STAR and Agility was the main objective of this project. There are a number of different ways in this behaviour can be quantified. We chose to use the magnitude of displacement because it is a scalar quantity that easily translates  to the ingrowth tissue’s tensile strain. The primary outcome measure used was the maximum relative displacement magnitude of the third cycle.  2.11 STATISTICAL ANALYSIS 2.11.1 MICROMOTION  All statistical results were considered significant with p < 0.05. Errors are reported as one standard deviation.  Six two-way repeated measures ANOVA’s were performed on the micromotion data to determine  the effects of implant type and compression on the amount of motion between the implant and  bone. One of these ANOVAs was performed for each of the two implant components (tibial and talar) by three loading directions (PF/DF, INV/EV, and IR/ER).  73  The effect of compression was analyzed as a repeated measure, but the effect of implant type was  not because the differences between the left and right ankle are not necessarily negligible despite the fact that they are from the same person. Student-Newman-Keuls tests were used for post-hoc comparisons.  2.11.2 KINEMATICS  All kinematic variables were analyzed with three-way ANOVAs, which had 2 repeated measures and one factorial comparison. Analysis was performed on the range of motion, motion coupling  ratios, and joint translation magnitude measurements to assess the effect of implant type (Agility  vs. STAR), ankle condition (intact vs. implanted), and compression (uncompressed vs. compressed).  In the analysis, the three variables used were ‘Implant’, ‘Condition’, and ‘Compression’. As a main  effect, the implant variable represented the difference between the left and right ankles, including  the intact and implanted (Agility and STAR respectively) conditions. The condition variable referred to the difference between intact and implanted ankles (both implant types). The  compression variable referred to the difference between the uncompressed and compressed tests.  The interaction between condition and implant was the most intriguing because it showed the  effect that each of the two implant types had on the intact ankles. The interaction between compression and implant showed how compression affected the left and right ankles. The interaction between condition and compression showed the difference in how the implanted and intact ankles were affected by compression. The interaction between condition, compression, and  implant showed the differences in how the two implant types were affected by compression. Since  the differences between the left and right ankles were mainly due to specimen variation or caused by an interaction with implant type, the effect of implant and the interaction between implant and compression were not a focus of this analysis.  74  The two repeated measures within a specimen were compressive load and ankle condition. As  previously mentioned, the type of ankle replacement was not a repeated measure because they  were not performed on the same ankle and inter-specimen variability was not negligible. One  ANOVA was performed on the total ROM magnitude for each direction analyzed (two in total: INVEV and IR-ER). Two ANOVAs were performed for each loading direction since there were two axes  of coupled motion, which resulted in a total of six. Nine ANOVAs were performed on the JT data – three for each loading direction, which corresponded to the three JCS translations (q1, q2, and q3).  75  3 RESULTS  3.1 BONE-IMPLANT RELATIVE MOTION  The data from specimen H1351 in figure 41 shows a representative example of the relative motion magnitude seen at the corner of greatest motion for the talar implant. Each motion trace was  normalized in the x axis for cycle duration. Both compressed and uncompressed data are plotted in order to compare how compression and implant type affect the amount of motion observed.  PF-DF Micromotion (Specimen 4) 2.5  Micromotion (mm)  2.0  1.5  Agility (15N) Agility (300N) STAR (15N) STAR (300N)  1.0  0.5  0.0 0.0  0.5  1.0  1.5  2.0  2.5  3.0  Cycle  Figure 41: Specimen 4 micromotion magnitudes over 3 cycles of PF-DF for the talar component of both implants with and without compression. Ankles start in the neutral position and are plantarflexed initially, reaching their maximum PF angle just prior to 50% corresponding to their peak micromotion magnitudes. In the STAR another micromotion peak occurs at approximately 80% of the cycle, which corresponds to the maximum DF angle.  76  In this example, one can see that the uncompressed Agility component had a spike in which the  relative motion increased substantially, corresponding to its peak plantar-flexion range of motion.  Visual inspection showed that this spike was the result of the anterior two corners of the implant  lifting off the bone (see figure 42). This lifting off phenomenon occurred in 4 out of the 6 unloaded PF-DF tests for the talar component of the Agility. However, this same phenomenon did not occur during the same test when a compressive force was added.  Figure 42: Consecutive photos of the uncompressed PF-DF test for the Agility illustrating talar component lift-off from left to right.  Generally, the STAR implant components had lower mean micromotion magnitudes than the Agility, and the tibial components of the implants typically had lower magnitudes of relative motion than found in the talar components.  77  3.1.1  TIBIAL COMPONENT MICROMOTION  For the tibial component, the mean micromotion magnitudes the Agility displayed were larger than  the STAR in all loading configurations except for PF-DF with compression (fig. 43).  Tibial Micromotion 1.2 Agility STAR  Maximum Relative Displacement (mm)  1.0  0.8  0.6 # #  0.4  0.2  0.0 PF-DF 15N  PF-DF 300N INV-EV 15N INV-EV 75N  IR-ER 15N  IR-ER 300N  Figure 43: Peak micromotion magnitudes for the tibial component for all loading scenarios. Micromotion values are plotted as mean with error bars as one standard deviation. # p=0.040  In PF-DF, there were no significant differences in tibial component micromotion (main effects: ‘Implant Type’ p = 0.503, ‘Compression’ p = 0.151; interaction: ‘Implant Type’ x ‘Compression’ p =  0.520). In INV-EV loading, the difference between the mean micromotion magnitudes of the Agility and STAR, 0.248 and 0.125 mm respectively, was determined to be the only significant difference  (main effects: ‘Implant Type’ p = 0.037, ‘Compression’ p = 0.599; interaction: ‘Implant Type’ x  78  ‘Compression’ p = 0.321). In the IR-ER direction, the decrease in micromotion caused by applying a  compressive load was found be significant while the effect of implant type was not quite significant (main effects: ‘Implant Type’ p = 0.062, ‘Compression’ p = 0.019; interaction: ‘Implant Type’ x ‘Compression’ p = 0.602).  3.1.2  TALAR COMPONENT MICROMOTION  The mean micromotion magnitudes associated with the STAR were consistently lower than the Agility in the talar component (see fig. 44). In all three loading directions, applying a compressive  load decreased the mean micromotion in the Agility implants, but had varying effects on the STAR. In PF-DF, both effects and the interaction between them was found to be significant (main effects: ‘Implant Type’ p = 0.002, ‘Compression’ p = 0.037; interaction: ‘Implant Type’ x ‘Compression’ p =  0.027). The mean micromotion in the Agility was 1.235 mm higher than in the STAR. The inclusion of a compressive load in the test decreased the amount of micromotion for the talus in PF-DF, but  there was also a significant interaction between compression and implant type. In this test we saw  compression decreased the micromotion in the Agility (p = 0.006) but had no significant effects on  the STAR (p = 0.892). In INV-EV, the amount of micromotion observed in the Agility was almost  significantly higher than the STAR, but no significant differences were found due to either implant type, compression, or their interaction (main effects: ‘Implant Type’ p = 0.085, ‘Compression’ p =  0.242; interaction: ‘Implant Type’ x ‘Compression’ p = 0.263). Similarly to PF-DF, significant  differences were found due to both effects and their interaction in IR-ER (main effects: ‘Implant Type’ p = 0.040, ‘Compression’ p < 0.001; interaction: ‘Implant Type’ x ‘Compression’ p = 0.003).  Compression decreased the combined motion of the implants, but there was a significant difference  between how compression affected each implant such that the Agility motion was significantly  decreased (p < 0.001) but STAR motion was not (p = 0.138).  79  Talar Micromotion 5  *#  Agility STAR  Maximum Relative Displacement (mm)  4  3  2  # @ %  1  * @ %  0 PF-DF 15N  PF-DF 300N INV-EV 15N INV-EV 75N  IR-ER 15N  IR-ER 300N  Figure 44: Peak micromotion magnitudes for the talar component for all loading scenarios. Values given as mean with error bars as one standard deviation. * p<0.001; # p=0.006; @ p=0.001; % p<0.001  80  3.2 KINEMATIC BEHAVIOUR 3.2.1  JOINT ROTATIONS  The following sets of plots (fig. 45-47) are time traces of the joint angles according to the JCS  convention for the 3 rotational axes. Examples from the experimental set were selected that  appeared to be the most representative of the typical behaviour of most specimens. These plots give a good general idea of what is going on from the kinematics perspective. One can start to see  some of the quantities (ROM and MC) that will be looked at in further detail in the following  sections. Qualitatively, there were some similarities and some differences between the two  implants and the intact ankles. Even though there were exceptions and even contradictions due to large inter-specimen variability (even between the left and right intact feet from the same donor),  some general trends in the kinematic patterns were evident.  These plots showed that the primary axis in each of the loading directions had relatively constant  angular velocity, in accordance with the applied load. There were times when the slope of this curve  deviated from the norm, which usually coincided with rapid changes in the other axes or an increase in joint stiffness (required torque). Meanwhile, the other two axes were free to rotate to  their natural tendency. Each ankle had its own repeatable signature motions about these secondary  axes, but there was agreement in their general patterns. They followed a pronation/supination coupling behaviour as expected, but the degree of this coupling varied between the different groups.  81  Plantarflexion-Dorsiflexion Right Intact PF-DF  30  30  20  20  10  10  Angle (deg)  Angle (deg)  Left Intact PF-DF  0 -10 -20  0 -10 -20  -30  -30  -40  -40  -50  -50  0  1000  2000  3000  4000  5000  0  1000  2000  Time  4000  5000  PF-DF INV-EV IR-ER  PF-DF INV-EV IR-ER  Agility PF-DF  STAR PF-DF  30  30  20  20  10  10  Angle (deg)  Angle (deg)  3000  Time  0 -10 -20  0 -10 -20  -30  -30  -40  -40  -50  -50 0  500  1000  1500  2000  2500  3000  3500  4000  0  500  1000  Time PF-DF INV-EV IR-ER  1500  2000  2500  3000  3500  4000  4500  Time PF-DF INV-EV IR-ER  Figure 45: Representative sample of joint angles in uncompressed PF-DF loading for left and right intact, Agility, and STAR ankles. Black lines denote the primary/driven axis of rotation, where DF is positive and PF is negative. Red lines denote INV-EV rotations, where INV angles are positive. Green lines denote IR-ER rotations, where IR angles are positive.  82  Inversion-Eversion Right Intact INV-EV  40  40  30  30  20  20  10  10  Angle (deg)  Angle (deg)  Left Intact INV-EV  0 -10 -20  0 -10 -20  -30  -30  -40  -40 -50  -50 0  500  1000  1500  2000  2500  3000  3500  4000  0  4500  500  1000  1500  2500  3000  3500  4000  4500  Time  Time PF-DF INV-EV IR-ER  PF-DF INV-EV IR-ER  STAR INV-EV  Agility INV-EV 40  40  30  30  20  20  10  10  Angle (deg)  Angle (deg)  2000  0 -10 -20  0 -10 -20  -30  -30  -40  -40 -50  -50 0  500  1000  1500  2000  2500  3000  3500  4000  4500  0  500  1000  2000  2500  3000  3500  4000  4500  Time  Time PF-DF INV-EV IR-ER  1500  PF-DF INV-EV IR-ER  Figure 46: Representative sample of joint angles in uncompressed INV-EV loading for left and right intact, Agility, and STAR ankles. Red lines denote the primary/driven axis of rotation, where INV is positive and EV is negative. Black lines denote PF-DF rotations, where DF angles are positive. Green lines denote IR-ER rotations, where IR angles are positive.  83  Internal-External Rotation Right Intact IR-ER  40  40  30  30  20  20  Angle (deg)  Angle (deg)  Left Intact IR-ER  10  10  0  0  -10  -10  -20  -20 0  500  1000  1500  2000  2500  3000  3500  0  4000  500 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500  Time  Time PF-DF INV-EV IR-ER  PF-DF INV-EV IR-ER  STAR IR-ER  40  40  30  30  20  20  Angle (deg)  Angle (deg)  Agility IR-ER  10  0  -10  10  0  -10  -20  -20  0  500 1000 1500 2000 2500 3000 3500 4000 4500 5000  0  500  1000  Time PF-DF INV-EV IR-ER  1500  2000  2500  3000  3500  4000  4500  Time PF-DF INV-EV IR-ER  Figure 47: Representative sample of joint angles in uncompressed IR-ER loading for left and right intact, Agility, and STAR ankles. Green lines denote the primary/driven axis of rotation, where IR is positive and ER is negative. Black lines denote PF-DF rotations, where DF angles are positive. Red lines denote INV-EV rotations, where INV angles are positive.  84  In PF-DF (fig. 45), the foot went into inversion and external rotation as it was plantar-flexed, and it  became internally rotated and decreased its amount of inversion and in some cases increase again to another inversion peak as it was dorsiflexed. In INV-EV (fig. 46), the foot plantar flexed as it  became inverted. The IR-ER angle followed the INV-EV angle quite closely and became internally rotated while inverted and externally rotated while everted. When the foot went into eversion, it  naturally fell back to a neutral or slightly dorsiflexed orientation. In IR-ER (fig. 47), we found that it plantar-flexed as it became internally rotated and dorsiflexed when externally rotated. The INV-EV  angle followed the IR-ER angle, becoming inverted with IR and everted with ER, similar to the way  the IR-ER angle followed the INV-EV angle in the INV-EV test. The magnitude of plantar-flexion occurring in this test was much smaller than that seen in the INV-EV test.  3.2.2  RANGE OF MOTION  The range of motion was determined for both INV-EV and IR-ER; however, measurements for the  PF-DF ROM in the implanted ankles could not be attained due to the limitations of the testing setup (table 6).  Table 6: Range of motion in degrees along the three primary axes at applied moment limits (5 Nm for PF-DF and 3 Nm for INV-EV and IR-ER)  Compression PF-DF  INV-EV  IR-ER  Intact  Agility  STAR  15 N  -50.4 ± 7.2  26.5 ± 4.1  -  -  -  -  15 N  -8.1 ± 5.8  23.7 ± 6.3  -10.5 ± 3.0  27.4 ± 6.3  -5.7 ± 2.1  24.5 ± 4.4  28.4 ± 6.5  -16.6 ± 6.2  28.5 ± 8.2  -12.3 ± 6.2  25.3 ± 4.7  300 N 75 N 15 N  300 N  -40.4 ± 5.4 -6.8 ± 3.8  -12.2 ± 4.0 -5.3 ± 3.1  27.8 ± 5.0  22.8 ± 6.2 7.8 ± 4.4  -  -9.2 ± 3.9 -8.1 ± 2.1  -  29.5 ± 2.7 4.8 ± 3.3  -  -6.9 ± 2.3 -2.9 ± 2.0  -  23.2 ± 4.1 9.5 ± 3.0  85  Inversion-Eversion The INV-EV ROM was significantly decreased by compression, but none of the other factors had a  significant effect (main effects: ‘Implant’ p = 0.176, ‘Condition’ p = 0.197, ‘Compression’ p = 0.019; interactions: ‘Implant’ x ‘Condition’ p = 0.630, ‘Compression’ x ‘Implant’ p = 0.058, ‘Condition’ x ‘Compression’ p = 0.904, ‘Condition’ x ‘Compression’ x ‘Implant’ p = 0.769).  The mean ROM of the STAR was lower than the Agility in both inversion and eversion in  uncompressed and compressed loading (fig. 48-49); however, this observation could have been misleading if the intact baseline was overlooked because the STAR prosthesis actually showed a similar trend of increasing the total INV-EV ROM, which was quite evident in figure 50. The mean  intact range of motion for the right ankles (red) was lower than that of the left ankles (blue) by approximately 10 and 7 degrees in the 15 N and 75 N compression scenarios respectively. Despite being a relatively large difference (31.9% and 24.8% of the average ROM respectively), it was determined to be not significant (15N: p = 0.909; 75N: p = 0.948).  86  Uncompressed Inversion-Eversion Range of Motion  STAR  Agility  Intact  -20  -10  0  10  20  30  40  ROM (deg) Figure 48: Range of motion for INV-EV at 3 Nm torque limits with a 15 N preload, showing mean peak inversion (positive) and eversion (negative) angles. Error bars denote one standard deviation.  Compressed Inversion-Eversion Range of Motion  STAR  Agility  Intact  -20  -10  0  10  20  30  40  ROM (deg) Figure 49: Range of motion for INV-EV at 3 Nm torque limits with a 75 N preload, showing mean peak inversion (positive) and eversion (negative) angles. Error bars denote one standard deviation.  87  Total INV-EV Range of Motion 50 45  Range of Motion (deg)  40 35 30 25 20 15 10 COND:  Intact  Implanted COMP: 15 N  COND:  Intact  Implanted  Implant Agility Implant STAR  COMP: 75 N  Figure 50: Total INV-EV ROM showing the interaction between compression, condition, and implant type. Values shown are mean ROM in degrees, and vertical bars denote 0.95 confidence interval.  88  Internal-External Rotation The IR-ER ROM was only significantly affected by compression (main effects: ‘Implant’ p = 0.418,  ‘Condition’ p = 0.923, ‘Compression’ p < 0.001; interactions: ‘Implant’ x ‘Condition’ p = 0.495,  ‘Compression’ x ‘Implant’ p = 0.104, ‘Condition’ x ‘Compression’ p = 0.611, ‘Condition’ x ‘Compression’ x ‘Implant’ p = 0.919).  In the IR-ER loading direction, the inclusion of compression had a huge effect on the kinematics of the ankle, which was quite evident even to the naked eye. The compression inhibited supination of the foot, decreasing the range of motion about the IR-ER axis for all test conditions, which can be  clearly seen from comparing figure 51 to figure 52. This resulted in a decrease in mean combined  ROM from approximately 41° to 13° when compression was applied. The effect that the two ankle  replacements had on their intact counterparts was not the same. Although insignificant, the Agility increased the mean ROM by 2.3° (p = 0.300) and 1.0° (p =0.890) whereas the STAR decreased the ROM by 0.8° (p = 0.715) and 1.7° (p = 0.713) in the uncompressed and compressed cases respectively (see fig. 53).  89  Uncompressed Internal-External Rotation Range of Motion  STAR  Agility  Intact  -30  -20  -10  0  10  20  30  40  ROM (deg) Figure 51: Range of motion for IR-ER at 3 Nm torque limits with a 15 N preload, showing mean peak internal (positive) and external (negative) rotation angles of the foot. Error bars denote one standard deviation.  Compressed Internal-External Rotation Range of Motion  STAR  Agility  Intact  -30  -20  -10  0  10  20  30  40  ROM (deg) Figure 52: Range of motion for IR-ER at 3 Nm torque limits with a 300 N preload, showing mean peak internal (positive) and external (negative) rotation angles of the foot. Error bars denote one standard deviation.  90  Total IR-ER Range of Motion 60 55 50  Range of Motion (degrees)  45 40 35 30 25 20 15 10 5 0 COND:  Intact  Implanted COMP: 15 N  COND:  Intact  Implanted  Implant Agility Implant STAR  COMP: 300 N  Figure 53: Total IR-ER ROM showing the interaction between compression, condition, and implant type. Values shown are mean ROM in degrees, and vertical bars denote 0.95 confidence interval.  91  3.2.3  MOTION COUPLING  The motion coupling ratios for PF-DF were the smallest of the 3 loading directions. Both of the secondary rotation magnitudes in this loading direction were lower than 20% of the PF-DF ROM.  Also, the magnitudes of motion coupling in each direction were nearly equal (details in table 8). The  magnitude of total coupled motion was also the least in this loading direction, and values rarely exceeded 10 degrees about either axis.  Plantarflexion-Dorsiflexion Loading No significant differences were found in the INV-EV:PF-DF motion coupling ratios (main effects: ‘Implant’ p = 0.777, ‘Condition’ p = 0.468, ‘Compression’ p = 0.060; interactions: ‘Implant’ x  ‘Condition’ p = 0.167, ‘Compression’ x ‘Implant’ p = 0.253, ‘Condition’ x ‘Compression’ p = 0.937, ‘Condition’ x ‘Compression’ x ‘Implant’ p = 0.342).  Compression tended to decrease the amount of motion coupling and was nearly significant in its  effect (p = 0.0597) and it brought the mean combined MC ratio from 0.167 to 0.131 (fig. 54). The  Agility and STAR seemed to have a different effect on the MC ratio, which was a decrease caused by  the Agility and an increase caused by the STAR (fig. 56). Although there were no significant  differences between the coupling ratios, there are subtler differences that can be seen in the pattern  of their coupling (fig. 55). The minimum INV-EV angle is occurs part way into the PF cycle, and it  was found to occur around different angles of PF for each implant. Compared to the normal ankle, it  occurred sooner for the Agility and later for the STAR. During DF, both implants followed the normal pattern relatively well, but the Agility’s pattern was slightly closer.  92  INV-EV : PF-DF Motion Coupling 0.35 Intact Agility STAR  Coupling Ratio  0.30 0.25 0.20 0.15 0.10 0.05 0.00  Uncompressed  Compressed  Figure 54: Mean INV-EV motion coupling ratios in the PF-DF loading direction with error bars as one standard deviation.  Plantar-flexion: INV-EV Coupling  Dorsiflexion: INV-EV Coupling  16  16  14  Intact Agility STAR  14  Intact Agility STAR  12  INV-EV Angle (deg)  INV-EV Angle (deg)  12 10 8 6 4 2  10 8 6 4 2  0  0  -2  -2  -4  -4  -50  -40  -30  -20  -10  0  PF-DF Angle (deg)  10  20  30  -50  -40  -30  -20  -10  0  10  20  30  PF-DF Angle (deg)  Figure 55: INV-EV motion coupling mean values (±SD) plotted as a function of PF-DF angle in forward (PF, on left) and reverse (DF, on right) direction. Positive angles denote INV and DF.  93  Figure 56: INV-EV:PF-DF motion coupling ratios showing the interaction between implant type, compression, and ankle condition. Vertical bars denote 0.95 confidence intervals  Similarly to INV-EV:PF-DF, there were no significant differences in the IR-ER:PF-DF coupling ratios  caused by compression or implant type (fig. 57) (main effects: ‘Implant’ p = 0.396, ‘Condition’ p =  0.633, ‘Compression’ p = 0.697; interactions: ‘Implant’ x ‘Condition’ p = 0.194, ‘Compression’ x ‘Implant’ p = 0.405, ‘Condition’ x ‘Compression’ p = 0.995, ‘Condition’ x ‘Compression’ x ‘Implant’ p =  0.703).  In contrast with the previous MC direction, the Agility increased the IR-ER coupling and the STAR  decreased it (fig. 59), which was the most pronounced difference in this test, albeit insignificant (p = 0.194). Looking at the IR-ER angle as a function of PF-DF angle (fig. 58), the Agility curve seemed to resemble the intact curve more closely.  94  IR-ER : PF-DF Motion Coupling 0.35 Intact Agility STAR  Coupling Ratio  0.30 0.25 0.20 0.15 0.10 0.05 0.00  Uncompressed  Compressed  Figure 57: Mean IR-ER motion coupling ratios for the PF-DF loading direction with error bars as one standard deviation.  Dorsiflexion: IR-ER Coupling  8  8  6  6  4  4  2  2  IR-ER Angle (deg)  IR-ER Angle (deg)  Plantar-flexion: IR-ER Coupling  0 -2 -4 -6 Intact Agility STAR  -8  0 -2 -4 -6  Intact Agility STAR  -8  -10  -10  -12  -12 -50  -40  -30  -20  -10  0  PF-DF Angle (deg)  10  20  30  -50  -40  -30  -20  -10  0  10  20  30  PF-DF Angle (deg)  Figure 58: IR-ER motion coupling mean values (±SD) plotted as a function of PF-DF angle in forward (PF, on left) and reverse (DF, on right) direction. Positive angles denote IR and DF.  95  Figure 59: IR-ER:PF-DF motion coupling ratios showing the interaction between implant type, compression, and ankle condition. Vertical bars denote 0.95 confidence intervals  Inversion-Eversion Loading The MC ratios observed in INV-EV were the largest of the three loading directions. This is especially evident in PF-DF coupling, with the mean ratio of the intact limbs nearing 2. The PF-DF MC ratio  decreased from 1.866 to 1.120 when comparing intact and implanted ankles (p = 0.004). The IR-ER ratio was also significantly reduced by the replacement of the ankle joint with these prostheses, bringing the mean ratio from 0.786 to 0.540 (p = 0.002). Additionally for IR-ER coupling, there was  a significant interaction between compression and ankle condition (p = 0.010), which indicates that  96  the intact ankles’ ratio was increased by the compressive load whereas the implanted ankles’ ratio experienced a decrease due to compression.  In INV-EV loading, the PF-DF coupling ratios were significantly reduced by replacing the joint, but  no significant differences were found between the implants or due to compression. There were no significant interactions between the effects either (main effects: ‘Implant’ p = 0.540, ‘Condition’ p =  0.004, ‘Compression’ p = 0.131; interactions: ‘Implant’ x ‘Condition’ p = 0.743, ‘Compression’ x ‘Implant’ p = 0.797, ‘Condition’ x ‘Compression’ p = 0.074, ‘Condition’ x ‘Compression’ x ‘Implant’ p = 0.468).  The PF-DF MC ratio in INV-EV loading was clearly lower in the implanted cases, even to the point  that post-hoc tests found significant differences between intact and both implants in the  uncompressed and compressed loading scenarios (fig 60). Generally speaking, plantarflexion was linearly related to inversion, except for a plateau region that occurred close to the ankle’s  dorsiflexion limit. During inversion, the shape of the coupling curves was quite similar between the  implants and intact cases, but the slope change was more pronounced and occurred at a slightly larger angle for the intact case (8° vs. 6°) and DF plateau was at larger angle for the intact ankle (fig.  61 left). During eversion, the shapes of the implanted ankles deviated from the intact curve more  and lacked the distinguishable plateau region seen in inversion (fig. 61 right). For the most part,  the implants behaved similarly to each other and caused a comparable decrease in the MC ratio compared to the intact ankles in both compressed and uncompressed tests (fig. 62).  97  PF-DF : INV-EV Motion Coupling 4  Coupling Ratio  3  #  $  *  @  2  Intact Agility STAR  #  *  $ @  1  0  Uncompressed  Compressed  Figure 60: Mean PF-DF motion coupling ratios in the INV-EV loading direction with error bars as one standard deviation. * p=0.005; # p=0.017; @ p=0.001; $ p=0.004  Eversion: PF-DF Coupling  30  30  20  20  10  10  PF-DF Angle (deg)  PF-DF Angle (deg)  Inversion: PF-DF Coupling  0 -10 -20 Intact Agility STAR  -30 -40  0 -10 -20 Intact Agility STAR  -30 -40  -50  -50  -20  -10  0  10  INV-EV Angle (deg)  20  30  -20  -10  0  10  20  30  INV-EV Angle (deg)  Figure 61: PF-DF motion coupling mean values (±SD) plotted as a function of INV-EV angle in forward (INV, on left) and reverse (EV, on right) direction. Positive angles denote DF and INV.  98  Figure 62: PF-DF:INV-EV motion coupling ratios showing the interaction between implant type, compression, and ankle condition. Vertical bars denote 0.95 confidence intervals  The coupling ratios of IR-ER to INV-EV were significantly decreased from intact to implanted  ankles, and the interaction between ankle condition and compression was also found to be significant (main effects: ‘Implant’ p = 0.322, ‘Condition’ p = 0.002, ‘Compression’ p = 0.578;  interactions: ‘Implant’ x ‘Condition’ p = 0.918, ‘Compression’ x ‘Implant’ p = 0.893, ‘Condition’ x ‘Compression’ p = 0.010, ‘Condition’ x ‘Compression’ x ‘Implant’ p = 0.063).  IR-ER motion was coupled quite strongly to INV-EV motion, and they had a nearly linear  relationship throughout the ROM with the exception of the STAR. The MC curve of the Agility followed very closely to the intact pattern, but the STAR differed quite a bit, which had slope change  at around 17° of inversion not present in the other ankle conditions (fig. 64). There was a 99  significant difference in MC ratios between the STAR and intact conditions during the  uncompressed test, but both implants caused a decrease in MC during the compressed test (fig. 63). The interaction between compression, ankle condition, and implant type was almost significant since compression increased the mean MC ratio in the intact ankles, decreased it in ankles with the Agility, and had little effect on it in ankles with the STAR (fig. 65).  IR-ER : INV-EV Motion Coupling 1.4  *  #  Coupling Ratio  Intact Agility STAR  @  1.2 1.0 #  0.8  *  @  0.6 0.4 0.2 0.0  Uncompressed  Compressed  Figure 63: Mean IR-ER motion coupling ratios in the INV-EV loading direction with error bars as one standard deviation. * p<0.001; # p=0.007; @ p=0.003  100  Inversion: IR-ER Coupling  Eversion: IR-ER Coupling  30  30 25  Intact Agility STAR  20  IR-ER Angle (deg)  IR-ER Angle (deg)  25  15 10 5  15 10 5  0  0  -5  -5  -10  Intact Agility STAR  20  -10 -20  -10  0  10  INV-EV Angle (deg)  20  30  -20  -10  0  10  20  30  INV-EV Angle  Figure 64: IR-ER motion coupling mean values (±SD) plotted as a function of INV-EV angle in forward (INV, on left) and reverse (EV, on right) direction. Positive angles denote IR and INV.  Figure 65: IR-ER:INV-EV motion coupling ratios showing the interaction between implant type, compression, and ankle condition. Vertical bars denote 0.95 confidence intervals  101  Internal-External Rotation Loading The motion coupling patterns induced by IR-ER loading were similar to those of INV-EV, although  smaller ratios were observed in this type of loading, especially in PF-DF MC. The application of  compression during these tests reduced the overall motion in all axes by a large amount, which  produced some interesting results. In both PF-DF and INV-EV coupling, the effects of compression  and ankle condition had significant effects.  The PF-DF motion coupled to IR-ER was significantly decreased from intact to implanted ankles, and there was a significant decrease caused by compression. The mean motion coupling ratio was reduced by the compressive load from 0.589 to 0.453 and by implementing TAAs from 0.667 to  0.375. The Agility and STAR implants had nearly identical effects on the PF-DF motion coupling.  Surprisingly, we also found a that the MC ratio in the left ankles was decreased by compression more than the right ankles leading to significant interaction between compression and implant (main effects: ‘Implant’ p = 0.359, ‘Condition’ p < 0.001, ‘Compression’ p = 0.008; interactions: ‘Implant’ x ‘Condition’ p = 0.912, ‘Compression’ x ‘Implant’ p = 0.029, ‘Condition’ x ‘Compression’ p = 0.258, ‘Condition’ x ‘Compression’ x ‘Implant’ p = 0.998).  The mean PF-DF:IR-ER MC ratios were decreased by compression in all ankles, but those replaced  with the Agility prosthesis were the affected the most (fig. 66); however, the post-hoc analysis  didn’t find this to be significant (p = 0.059). As expected, the ankle plantar flexed during IR and  dorsiflexed during ER in accordance with the supination-pronation relationship. The motion  coupling curves of all conditions took on a similar shape, with a curve of downward concavity during IR and one with a less pronounced curvature and a slight inflection near the beginning of the cycle in ER (fig. 67). Although slight differences are visible between the implants in their MC curves,  their effects on the MC ratios are almost identical (fig. 68).  102  PF-DF : IR-ER Motion Coupling 1.2 Intact Agility STAR  1.0  Coupling Ratio  * 0.8  0.6  *  0.4  0.2  0.0  Uncompressed  Compressed  Figure 66: Mean PF-DF motion coupling ratios in the IR-ER loading direction with error bars as one standard deviation. *p=0.044  External Rotation: PF-DF Coupling  30  30  20  20  PF-DF Angle (deg)  PF-DF Angle (deg)  Internal Rotation: PF-DF Coupling  10  0 Intact Agility STAR  -10  10  0  Intact Agility STAR  -10  -20  -20 -20  -10  0  10  IR-ER Angle (deg)  20  30  -20  -10  0  10  20  30  IR-ER Angle (deg)  Figure 67: PF-DF motion coupling mean values (±SD) plotted as a function of IR-ER angle in forward (IR, on left) and reverse (ER, on right) direction. Positive angles denote DF and IR.  103  Figure 68: PF-DF:IR-ER motion coupling ratios showing the interaction between implant type, compression, and ankle condition. Vertical bars denote 0.95 confidence interval.  The MC ratio of INV-EV motion to IR-ER loading was found to be significantly decreased by joint replacement and significantly increased by compression (main effects: ‘Implant’ p = 0.786, ‘Condition’ p = 0.025, ‘Compression’ p = 0.024; interactions: ‘Implant’ x ‘Condition’ p = 0.588,  ‘Compression’ x ‘Implant’ p = 0.722, ‘Condition’ x ‘Compression’ p = 0.104, ‘Condition’ x ‘Compression’ x ‘Implant’ p = 0.347)  The application of compression increased the ratio of coupled INV-EV motion of all ankle conditions  and a significant difference was found for ankles with the STAR (fig. 69). Neither implant replicated the intact MC pattern very well (fig. 70). Despite reaching a similar maximum INV angle, the  104  Agility’s curve had a shallower curve and lower EV angle as a result. The STAR’s curve deviated more from the intact case than the Agility, and it exhibited an even shallower slope and a lower INV angle. In uncompressed loading, replacing the ankle joint with either implant resulted in  comparable decreases in INV-EV coupling. Under compression, however, the Agility caused a minor decrease in mean coupling ratio while the STAR caused a minor increase (fig. 71).  INV-EV : IR-ER Motion Coupling 1.2  1.0  Coupling Ratio  *  Intact Agility STAR  0.8  * 0.6  0.4  0.2  0.0  Uncompressed  Compressed  Figure 69: Mean INV-EV motion coupling ratios in the IR-ER loading direction with error bars as one standard deviation. *p=0.032  105  Internal Rotation: INV-EV Coupling  External Rotation: INV-EV Coupling  25  25  Intact Agility STAR  15  20  INV-EV Angle (deg)  INV-EV Angle (deg)  20  10 5 0 -5 -10  Intact Agility STAR  15 10 5 0 -5 -10  -15  -15  -20  -10  0  10  IR-ER Angle (deg)  20  30  -20  -10  0  10  20  30  IR-ER Angle (deg)  Figure 70: INV-EV motion coupling mean values (±SD) plotted as a function of INV-EV angle in forward (IR, on left) and reverse (ER, on right) direction. Positive angles denote INV and IR.  Figure 71: INV-EV:IR-ER motion coupling ratios showing the interaction between implant type, compression, and ankle condition. Vertical bars denote 0.95 confidence intervals  106  3.2.4  JOINT TRANSLATION  Medial/Lateral Joint Translation The mediolateral translation of the foot was calculated as the joint centre’s displacement along the  flexion axis, denoted q1 in the JCS. It was the largest when the ankle was loaded in INV-EV by approximately a factor of 2 (fig. 72).  Medial/Lateral (q1) Joint Translation 25 Intact Agility STAR  ##  Translation (mm)  20  @  ** @  **  $$  $$  ##  15 $ #  *  10  5  *  # $  0 PF-DF UC PF-DF C INV-EV UC INV-EV C IR-ER UC  IR-ER C  Loading Type Figure 72: Mean translation of the JCS origin along the medial/lateral axis with error bars as one standard deviation. UC denotes uncompressed loading and C denotes compressed loading. *p=0.005(L), 0.002 (R); #p=0.003; $p=0.007; @p=0.002; **p<0.001; ##p=0.001; $$p<0.001  107  In the PF-DF loading direction, compression was found to increase the amount of translation more in intact ankles than in the replaced ankles. The effects of compression and ankle condition were  found to cause significant increases and decreases in this motion respectively, but the previously mentioned effect played a large role in this result (fig. 73) (main effects: ‘Implant’ p = 0.158,  ‘Condition’ p = 0.019, ‘Compression’ p = 0.001; interactions: ‘Implant’ x ‘Condition’ p = 0.681, ‘Compression’ x ‘Implant’ p = 0.242, ‘Condition’ x ‘Compression’ p = 0.003, ‘Condition’ x  ‘Compression’ x ‘Implant’ p = 0.484). Post hoc analysis revealed that the only significant comparisons were those with the compressed intact ankles.  Figure 73: Translation of the JCS origin along the medial/lateral axis due to PF-DF loading showing the interaction of compression, condition, and implant type. Values shown are mean peak displacements in millimeters, and vertical bars denote 0.95 confidence intervals.  108  Under INV-EV loading, replacing the joint resulted in a larger amount of M/L translation, and the  effect was slightly more pronounced in the STAR than the Agility but not significant (fig. 74). This  also resulted in significant post-hoc tests between intact and Agility, and between intact and STAR for both the compressed and uncompressed tests (fig. 72) (main effects: ‘Implant’ p = 0.194,  ‘Condition’ p = 0.015, ‘Compression’ p = 0.653; interactions: ‘Implant’ x ‘Condition’ p = 0.246, ‘Compression’ x ‘Implant’ p = 0.497, ‘Condition’ x ‘Compression’ p = 0.518, ‘Condition’ x ‘Compression’ x ‘Implant’ p = 0.242).  Figure 74: Translation of the JCS origin along the medial/lateral axis due to INV-EV loading, showing the interaction of compression, condition, and implant type. Values shown are mean peak displacements in millimeters, and vertical bars denote 0.95 confidence intervals.  There were no significant effects found in this direction of joint translation when loaded in IR-ER (main effects: ‘Implant’ p = 0.304, ‘Condition’ p = 0.791, ‘Compression’ p = 0.623; interactions: ‘Implant’ x ‘Condition’ p = 0.537, ‘Compression’ x ‘Implant’ p = 0.216, ‘Condition’ x ‘Compression’ p = 0.419, ‘Condition’ x ‘Compression’ x ‘Implant’ p = 0.325).  109  Anterior/Posterior Joint Translation The anteroposterior translation of the foot was calculated as the joint centre’s displacement along the A/P axis of the foot, denoted q2 in the JCS. The largest difference in the A/P joint translation was found in the STAR under PF-DF loading (fig. 75).  Anterior/Posterior (q2) Joint Translation 12 #  *  Translation (mm)  10  Intact Agility STAR  @  $  8  $  6  * @  #  4  2  0 PF-DF UC PF-DF C INV-EV UC INV-EV C IR-ER UC  IR-ER C  Loading Type Figure 75: Mean translation of the JCS origin along the anterior/posterior axis with error bars as one standard deviation. *p=0.002; #p<0.001; $p=0.038 (L); @p=0.018  110  In PF-DF loading, there were significant differences in the A/P translation of the foot due to the effects of implant and condition, and the compression-condition and compression-condition-  implant interactions (main effects: ‘Implant’ p = 0.044, ‘Condition’ p = 0.017, ‘Compression’ p =  0.712; interactions: ‘Implant’ x ‘Condition’ p = 0.002, ‘Compression’ x ‘Implant’ p = 0.164, ‘Condition’  x ‘Compression’ p = 0.001, ‘Condition’ x ‘Compression’ x ‘Implant’ p = 0.032). When compression  was introduced, the amount of translation in the STAR ankles was significantly increased (fig. 76).  There was also a significant difference found in the compressed case between the intact ankles and those with the STAR (fig. 75).  Anterior/Posterior (q2) Joint Translation: PF-DF Loading 10  Displacement Magnitude (mm)  9 8 7 6 5 4 3 2 1 0 COND:  Intact  Implanted COMP: 15 N  COND:  Intact  Implanted  Implant Agility Implant STAR  COMP: 300 N  Figure 76: Translation of the JCS origin along the anterior/posterior axis due to PF-DF loading, showing the interaction of compression, condition, and implant type. Values shown are mean peak displacements in millimeters, and vertical bars denote 0.95 confidence intervals.  111  No significant differences were found in INV-EV loading (main effects: ‘Implant’ p = 0.637,  ‘Condition’ p = 0.613, ‘Compression’ p = 0.768; interactions: ‘Implant’ x ‘Condition’ p = 0.075, ‘Compression’ x ‘Implant’ p = 0.712, ‘Condition’ x ‘Compression’ p = 0.108, ‘Condition’ x ‘Compression’ x ‘Implant’ p = 0.492).  In IR-ER loading, compression was found to significantly decrease the amount of A/P translation (fig. 77) (main effects: ‘Implant’ p = 0.420, ‘Condition’ p = 0.720, ‘Compression’ p = 0.032; interactions: ‘Implant’ x ‘Condition’ p = 0.799, ‘Compression’ x ‘Implant’ p = 0.143, ‘Condition’ x  ‘Compression’ p = 0.439, ‘Condition’ x ‘Compression’ x ‘Implant’ p = 0.999). There were also significant post-hoc tests between the compressed and uncompressed tests for the left intact ankle and for the Agility.  Anterior/Posterior (q2) Joint Translation: IR-ER Loading 8  Displacement Magnitude (mm)  7 6 5 4 3 2 1 0 15 N  300 N COMPRESSION  Figure 77: Translation of the JCS origin along the anterior/posterior axis due to IR-ER loading, showing the effect of compression. Values shown are mean peak displacements in millimeters, and vertical bars denote 0.95 confidence intervals.  112  Compression/Distraction Joint Translation The compression/distraction translation of the foot was calculated as the joint centre’s  displacement along the C/D axis of the foot, denoted q3 in the JCS. The most C/D translation occurred in PF-DF loading, and the least occurred in IR-ER loading (fig. 78).  Compression/Distraction (q3) Joint Translation 20 $ #  18  Intact Agility STAR  Translation (mm)  16 #  14  *  12 10 8  $  *  6  @  4 2  @  0 PF-DF UC PF-DF C INV-EV UC INV-EV C IR-ER UC  IR-ER C  Loading Type Figure 78: Mean translation of the JCS origin along the compression/distraction axis with error bars as one standard deviation. *p<0.001; #p<0.001; $p<0.001; @p=0.031 (L)  113  In PF-DF, the main effects of compression and implant type were significant, but there were also significant interactions found between condition and compression and between implant type, condition, and compression (fig. 79) (main effects: ‘Implant’ p = 0.459, ‘Condition’ p = 0.062, ‘Compression’ p = 0.023; interactions: ‘Implant’ x ‘Condition’ p = 0.016, ‘Compression’ x ‘Implant’ p = 0.096, ‘Condition’ x ‘Compression’ p = 0.001, ‘Condition’ x ‘Compression’ x ‘Implant’ p = 0.001).  This is because compression was only significant in the ankles with the STAR. Post-hoc analysis revealed significant differences between the intact ankles and those implanted with the STAR for  both uncompressed and compressed cases, as well as between the compressed and uncompressed tests of the STAR (fig. 78).  Compression/Distraction (q3) Joint Translation: PF-DF Loading 18  Displacement Magnitude (mm)  16 14 12 10 8 6 4 2 0 COND:  Intact  Implanted COMP: 15 N  COND:  Intact  Implanted  Implant Agility Implant STAR  COMP: 300 N  Figure 79: Translation of the JCS origin along the compression/distraction axis due to PF-DF loading, showing the interaction of compression, condition, and implant type. Values shown are mean peak displacements in millimeters, and vertical bars denote 0.95 confidence intervals.  114  In INV-EV, there was a significant effect of implant type (main effects: ‘Implant’ p = 0.644, ‘Condition’ p = 0.842, ‘Compression’ p = 0.477; interactions: ‘Implant’ x ‘Condition’ p = 0.020,  ‘Compression’ x ‘Implant’ p = 0.987, ‘Condition’ x ‘Compression’ p = 0.282, ‘Condition’ x ‘Compression’ x ‘Implant’ p = 0.759). Implanting ankles with the Agility caused a decrease in C/D joint translation, whereas the STAR caused an increase (fig. 80).  Compression/Distraction (q3) Joint Translation: INV-EV Loading 10  Displacement Magnitude (mm)  9 8 7 6 5 4 3 2 1 0 Intact  Implanted  Implant Agility Implant STAR  CONDITION  Figure 80: Translation of the JCS origin along the compression/distraction axis due to PF-DF loading, showing the interaction between condition and implant type. Values shown are mean peak displacements in millimeters, and vertical bars denote 0.95 confidence intervals.  During IR-ER loading, compression was found to decrease the joint translation in this direction (fig.  81) (main effects: ‘Implant’ p = 0.145, ‘Condition’ p = 0.990, ‘Compression’ p = 0.0001; interactions: ‘Implant’ x ‘Condition’ p = 0.815, ‘Compression’ x ‘Implant’ p = 0.453, ‘Condition’ x ‘Compression’ p = 0.863, ‘Condition’ x ‘Compression’ x ‘Implant’ p = 0.358).  115  Compression/Distraction (q3) Joint Translation: IR-ER Loading 4.5  Displacement Magnitude (mm)  4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 -0.5 1  2 COMP  Figure 81: Translation of the JCS origin along the compression/distraction axis due to PF-DF loading, showing the compression. Values shown are mean peak displacements in millimeters, and vertical bars denote 0.95 confidence intervals.  116  4 DISCUSSION  Micromotion at the bone-implant interface of uncemented prostheses has been proven to be an  important factor in osseointegration and overall implant fixation. To my knowledge, this is the first  cadaveric experiment to analyze the micromotion patterns of total ankle replacements. It is important to know the micromotion behaviour of different TAAs in order to reduce the risk of  aseptic loosening failure by enabling clinicians to make educated decisions on which designs to use along with improving the performance of new designs under development.  Along with implant osseointegration, reproduction of normal ankle kinematics is another important  factor in the success of a joint replacement. Properly designed joint replacements will have articulating surface geometries that allow proper range of motion, motion coupling, and joint translation within the confines of the bony and ligamentous structure of the ankle joint.  This study found the Agility to exhibit patterns of larger micromotion than the STAR. Clinically, failure rates due to aseptic loosening are higher in the Agility (shown previously in tables 1 & 2),  which corroborates this finding and supports the idea that larger motions at the bone-implant interface translate to weakened implant fixation. Several kinematic differences were found between the intact and implanted ankles indicating that there is room for improvement on the articulation  geometry design for both of these models.  4.1 LOADING APPARATUS  The loading apparatus was designed with emphasis placed on maximizing the versatility of the testing rig in order to create a comprehensive loading protocol. As mentioned earlier, the device  117  used in this study was an adaptation of a loading apparatus previously developed in our lab by Chad Larson for studying the ankle, which was in turn an adaptation of one originally designed for applying loads to the human spine. This ankle loading apparatus proved to be a great method to  apply pure moments to the foot while leaving the 5 remaining DOF unconstrained. However, it was  believed to be important that micromotion patterns were studied with a compressive load applied to the ankle in this study. Consequently, modifications were made to his design to allow for compression to be applied via a steel cable tensioned by a hydraulic actuator.  It was imperative for this simulator to be able to induce a number of different types of loading scenarios for this project because there are a range of fundamentally different types of loading that  an ankle will be subjected to in vivo. It has been shown in total hip and knee replacements that  some loading types, associated with certain activities, induce greater amounts of micromotion and  are more critical to determining the quality of implant fixation [114,126,127]. It is currently unknown which loading types are the most critical for ankle replacements or whether it is  dependent on implant design, therefore, it was necessary to examine several different loading scenarios. Even though the ankle won’t be subjected to all of these loads on a regular basis, the potential for these loading scenarios to occur is evident. Testing the micromotion magnitude at the extreme ranges of motion provides a measure of the ‘worst case scenario’. Versatility of loading was  gained at the expense of complexity and biofidelity of each specific test. Accuracy in reproducing  the motions and loads of common specific tasks, such as gait, are important when determining long term effects because these are the loads experienced in a high frequency. Implementing these types  of loading is more suitable for studying polyethylene wear, implant migration, and specific details  about a certain task. Focusing on the specifics of a certain task wouldn’t contribute significantly to  the overall objective of determining the maximum micromotion magnitudes for each implant that  could be expected clinically. The loading apparatus design we settled on was able to manipulate the  ankle through its entire range of motion through a combination of rotations about 3 axes with and 118  without compression. At the level of the bone-implant surface, this would induce a wide spectrum of loads and give a well-rounded indication of the implant’s overall initial fixation.  Another advantage to this design that complements its versatility was its simple setup. This quality enabled quick transition between the different tests being performed. Since there were 6 loading variations on a given testing day, being able to carry out the tests rapidly was important to minimize the amount of time that the cadaveric limbs remained thawed.  In this experiment, there were two preload conditions. A 15 N preload was used for the  uncompressed loading scenario, while a 300 N preload was used for the compressed loading  scenario. Two different preloads were used to determine if the addition of a compressive load had an effect on the micromotion and kinematic behaviour of ankles with different total ankle replacements. For the compressed case, 300 N was chosen because it represents roughly half of the body weight of an average person. Other studies that have performed biomechanical testing on  cadaver ankles have also used this same preload [53,70], which makes using 300 N very desirable  for the purposes of comparing results with these studies. This is much lower than the compressive  forces the ankle experiences even in low intensity activity (walking is approximately 3-5 BW), but this load is justifiable because very minimal weight bearing is recommended in the first 2 weeks  following surgery. Due to the nature of the loading apparatus, applying a much larger compressive load would create excessive shear stresses, artefact moments, and pose a risk of causing damage to  the limb. The reason for using a 75 N compression for the INV-EV conditions instead of 300 N was  that this loading puts the ankle in a compromised position which limits its ability to withstand compression and this posed a risk of damaging the limb. Additionally, the higher load wouldn’t  allow the ankle to follow the same kinematic pattern or experience its full range of motion because the larger load made the foot more susceptible to becoming locked in plantarflexion due to the moment artefact.  119  Compared to maximum plantarflexion moment of 232 Nm previously measured[56], the applied moment of 5 Nm in this direction is no comparison. This is because the 232 Nm was an active moment (applied by muscle activation), whereas the applied moments in this experiment were  passive (applied externally). Since no muscle activation was simulated in this cadaveric test, the muscles and tendons were inconsequential, and the only structures resisting the applied moments  were the bones, ligaments, and other soft tissues of the ankle. These structures’ ability to resist moments is quite minimal in comparison, and damage to the limb would be inevitable if such large moments were applied to the joint. The benefit of applying pure moments in this manner is that it is  much more repeatable and consistent across specimens. It allows us to know the exact loads that are being applied regardless of specimen anthropometry.  One drawback of modifying the spine machine for the loading apparatus was that it required the  limb to be mounted upside down with the tibia fastened to the table. This means that the direction in which the force of gravity acted on the foot and implants was reversed. This could have had a minor effect on the kinematics of the foot as well as the micromotion of the implants in the  uncompressed loading scenarios where there were no other vertical forces acting. For example, the  Agility talar component lift-off that was observed during uncompressed PF-DF loading may not have occurred if the foot were oriented with the foot downward. If the foot was oriented right side up, the force of gravity likely would have kept the talar component in contact with the talus when  compression on the anterior portion was decreased. Although less micromotion would have been observed in this loading scenario if no lift-off occurred, it is very unlikely that the decrease would  be substantial enough to impact the overall outcome significantly.  The other consequence of this apparatus design was that it limited our options for how to apply the  compressive load. The most feasible option for the compressive load application with this setup was using steel cable and a hydraulic actuator. If we break it down for simplicity, the cable  120  essentially acts on the footplate as two point loads of constant magnitude, one on either side. The  line of force created by the tension in the cable is constantly changing direction as the foot rotates  through its range of motion. If we examine motion in the sagittal plane, we know that the  instantaneous flexion axis of a healthy ankle translates along an arc from a postero-inferior to an antero-superior position as the ankle goes from plantar-flexion to dorsiflexion (fig. 82) [21].  Figure 82: Locations of instantaneous center of rotation (IC denoted by yellow star) for the ankle in the sagittal plane with the location of cable guide (blue circle) and direction of compressive force (red arrow) at 23° plantarflexion (a), at 0° -neutral- (b), and at 25° dorsiflexion (c) as adapted from Leardini et al. 1999. Reprinted with permission from Elsevier via Copyright Clearance Center, Inc.  For ankles with arthroplasty, we can deduce where their axis of rotation will be based on the  geometry of the implant. For the two implants under investigation, their flexion axes are coincident  with the center of curvature of talar articulating surface. The Agility’s flexion axis remains for the most part stationary because it is a 2-component/fixed-bearing design, whereas the STAR’s flexion  axis is mobile relative to the tibia, allowing it to translate in the A/P direction and rotate about the axis perpendicular to the plane of the tibial component (fig. 83).  121  Figure 83: Sagittal plane schematic view of Agility (left) and STAR (right) with stars depicting the instantaneous center of rotation.  When the cable’s line of force was not passing directly through the ankle’s axis of rotation, the  compression caused an undesirable additional moment about the ankle. In PF-DF loading, this  artefact moment did not impede the loading apparatus from creating the desired kinematic pattern  because it was directly counteracted by the applied moment, although it did affect the torque  measurements obtained from the load cell governing the moment applicator. In INV-EV and IR-ER,  however, this created some difficulties because there was nothing to resist the artefact moment,  and the ankle could become locked in plantarflexion or dorsiflexion if the artefact moment  exceeded a certain threshold. The cable guides were implemented to reduce this effect by  decreasing the moment arm of the compression about the axis of rotation, which was investigated  in detail by Cripton et al. for the spine [128]. As shown in figure 83, this loading setup was designed to stabilize the ankle, with the artefact moment rotating the ankle back to the neutral position.  For the range of motion (23° PF to 25° DF), the intact specimens were found to be ‘stable’ with  minimal effects of the moment artefact. However, instances were encountered during testing where  this was not the case. Because locating the flexion axis was done empirically, it was not possible to  be entirely sure that the cable guides were at the ideal location. As such, at larger plantarflexion angles, such as those nearing its ROM limit, the effect of errors in the axis approximation was magnified. Additionally, the artefact moment was more problematic in the case of the STAR because  the shear force, which was caused by the compressive load as the foot deviates from neutral  122  position, translated the foot in the A/P direction. As the foot translated, so did its flexion axis and the plantarflexing moment was increased. Because of these effects, extreme care was required to prevent it from locking in either DF or PF, and in some cases testing had to be restarted with further adjustments to the cable guide locations.  The effect that this compressive load had about the other axes was stabilizing instead, such that the  further the foot rotated, the larger the moment caused by the compression was to return the foot  back to neutral position. In INV-EV, the geometry of the loading device caused the moment arm of  the steel cable to be slightly longer on the side opposite to the direction that it was rotating. This  created a moment in the frontal plane that rotated the foot back to neutral position (fig. 84). In IR-  ER, a stabilizing artefact moment was also created but by a different mechanism. As the foot  rotated, the cable slots on either edge of the foot-plate translated away from the cable guide holes  such that the tension in the cables had a component in the transverse plane perpendicular to the  foot’s IR-ER axis in the opposite direction to its rotation (fig. 85).  Figure 84: A schematic diagram of the loading apparatus in the frontal plane showing the lines of force for the steel cables (red arrows) and their moment arm lengths (orange/green lines) that illustrate the stabilizing artefact moment (blue arrow) about the ankle’s INV-EV center of rotation.  123  Figure 85: A schematic diagram of the loading apparatus in the transverse plane showing the projections of the cable tension (red arrows) directed from the cable slots toward the cable guide holes (orange circles) that illustrate the stabilizing artefact moment (blue arrow) about the ankle’s IR-ER center of rotation.  The approach used in this experiment was an approximation of the loading and resulting motion seen in live patients. Applying compression and a pure moment to the foot is not equivalent to the compression and moment created by tendon tension; however, it was not the intention to simulate this but instead to subject the bone-implant interface to a range of stresses that it may experience in vivo. The fact that it was a cadaveric test reduced the inter-subject variations on loading patterns,  and as in this particular study, reduced anatomical differences by comparing two implants on the  left and right ankles of the same subject. Despite its limitations, it is valuable as a pre-clinical testing tool that offers a means of applying repeatable loading patterns in cadaveric ankles.  4.2 MICROMOTION-LOOSENING RELATION  The topic of micromotion between bones and implants has been studied extensively in regards to  analyzing the bone-prosthesis interface and its initial fixation for both hip and knee replacements.  Since the link between the amount of motion at this interface and the strength of the bone-implant 124  bond in uncemented implants had been established, numerous studies have been performed in order to reduce the relative motion and improve the bond in total hip and knee arthroplasty. As  aseptic loosening continues to persist as the leading cause of revision surgery in total ankle arthroplasty, it is undeniable that the field would benefit from similar research.  The micromotion threshold for osseointegration originates from several studies concerning bone  ingrowth in canines. As mentioned earlier, Pilliar et al. measured the amount of relative motion after the initial healing phase, and those without bone ingrowth allowed 150 µm or more [101].  Jasty et al. found that complete, partial, and no osseointegration occurred when implants were  subjected to 20, 40, and 150 µm of constant oscillatory motion following implantation [103], and that full osseointegration occurred for implants exhibiting 56 µm of micromotion initially post-  implantation [102]. A direct link cannot be drawn between these experimental outcomes and this  study because they were performed on canines and they used slightly different measurement techniques. Due to the complex processes occurring within a live subject, we cannot suggest that initial post-op human cadaveric micromotion is equivalent either to a constant magnitude cyclic relative displacement or to the amount of recoverable displacement after complete integration.  However, the measurement in the latter of Jasty’s experiments is very similar to the measurement performed in the current study and others that look at the initial fixation of joint replacements. All  of the dogs in his experiment had full osseointegration and the largest micromotion observed was 56 µm, which shows that this level of micromotion is tolerable but does not give an absolute cut-off  value. With these findings and the results of initial fixation tests performed on hip/knee replacements, the threshold currently adopted by those in the field of total joint replacements is  around 150 microns. Regardless of what is accepted, it remains that there is no maximum  micromotion value that we can ascribe to an osseointegration threshold, but it can be stated for certain that lower micromotion magnitudes are favourable.  125  The amount of micromotion observed in this study was much larger than expected. There are currently no studies of micromotion in TAA prostheses in the literature to compare to, therefore,  our only basis for comparison was contemporary hip and knee micromotion measurements. Hip  and knee replacements typically exhibit micromotion magnitudes in the range of 100-200 µm when subjected to in vivo loading patterns [114,115,127]. Even the STAR, which had the lesser relative  motion of the two implants, had a mean maximum micromotion magnitude of 789 µm. These results exceed the 150 µm threshold by a factor of greater than 5.  The micromotion values from these tests were expected to be larger than the 150 µm characteristic  of hip and knee replacements for three reasons:  1) The aseptic loosening rates of these ankle replacements are higher than most hip/knee replacements;  2) The loading apparatus was designed to stress the bone-implant interface by pushing it to the limits of its ROM;  3) Relatively low compressive forces were applied.  However, the amount by which they exceeded this threshold was still surprising. It was found that  even a modest 300 N compressive load had a significant effect on the micromotion magnitudes. In vivo loading applies much larger compressive loads to the ankle joint than this value, by a factor of 6 to 10 during level walking. At this point we are unsure of what effect such a large compressive  load would have. Typically, larger loads are associated with larger bone-implant interface stresses, but it is possible that because the prostheses are designed with flat surfaces on both the tibia and  talus, which are normal to compressive axial loads for the majority of activities, that increased compression would reduce motion due to increased friction.  Clinically, the failure rate due to aseptic loosening is 5.7% for the STAR and 7.1% for the Agility, which indicates more than 90% of them are not failing by this mechanism. Therefore, it is safe to 126  assume that clinically these implants are either experiencing more than 150 µm and still achieving  osseointegration or not experiencing such large micromotions because the patient is careful and these tests are an overestimate of the actual in vivo micromotions. While this may seem to  contradict the findings of Jasty et al., it is important to remember that the process of implant  integration is time dependent and involves many complex biological factors that are not completely understood at this point. This implies that during the healing process, there are factors at work to reduce the amount of motion from what was observed during this experiment to a magnitude of  relative motion below the threshold for continuous bone ingrowth. These factors could include  inflammation to restrict range of motion, pain to discourage excessive use/weight-bearing, or intermediate ingrowth medium (such as fibrous tissue) or partial bone ingrowth to secure the implant.  Since the micromotion values found in this study were higher than the 150 µm threshold, it is  impossible to draw a direct relationship between these two values. However, it was determined that the implant with greater relative bone-implant motion, the Agility, was also the implant with  greater aseptic loosening rates. While it is possible that this correlation was coincidental, it is very unlikely that the two are not related due to the links previously confirmed between micromotion and bone ingrowth. Therefore, it is believed that higher aseptic loosening rates were attributable to a less secure initial fixation resulting in a larger magnitude of micromotion patterns. Consequently, the type of measurement obtained here was effective as a relative gauge to determining the implant’s ability to accept bone ingrowth and produce a strong bond between the bone and implant.  127  4.3 SURGEON SKILL  There is a substantial learning curve for foot and ankle surgeons in performing total ankle replacements. It has been shown that surgeon experience with a given ankle replacement plays a large role in the perioperative complication rate [129]. Success rates reported by the inventors of these devices exceed those of other foot/ankle surgeons as we can see by comparing independent  TAA survivorship studies with those of national joint registers. We can infer from these two facts, that surgeon skill would in all likelihood play a large role in affecting aseptic loosening rates. With this in mind, it is important for the surgeon(s) performing these to have similar skill/experience  with each implant to provide a meaningful comparison. Fortunately, the foot and ankle surgeon collaborator on this project was quite familiar with and proficient in the techniques of both procedures, and he performed all surgeries himself to eliminate surgeon variance.  Surgeon skill was important in this study since the success of these procedures relies heavily on both the alignment of the implants and the precision of the cuts. The position of each component has 6 degrees of freedom, 3 rotational and 3 translational, and all 6 of both implant components  must be properly aligned with respect to each other and the ankle in order for the joint replacement to function as designed [70]. Among many other things, misalignment will create abnormal ankle dynamics which can induce large stresses on the implant components or bone as  well as at the bone-prosthesis interface leading to micromotion. Although these jigs eliminate a great deal of the variability in the alignment of the cuts, the surgeon’s expertise is required to attach  and align the jig with respect to the ankle and usually also the talar component with respect to the tibia. Surgeon skill is also important in making the cuts straight and flat. It may seem trivial because  the jigs guide the saw blades, but in order to get a flat cut the surgeon often has to go in free hand afterwards because the blades are flexible and skive upwards toward the back. Because the  128  implants are manufactured with flat edges on their interfacial surfaces, the flatness of the cut is crucial to maximize surface contact area and ensure a tight and proper fit.  4.4 IMPLANT DESIGN CONSIDERATIONS  Stresses and strains at the bone-prosthesis interface will be largely determined by four separate  factors. These include external loads, load transfer between the implants at the articulation surfaces, load transfer between the implants and bones, and the quality of the fit and finish of the implant’s peripheral surfaces.  The first factor is the loading applied to the ankle joint. This is caused by the external loads on the  foot and is affected by the activity being performed. While restrictions on activity levels and types of movements can be given to patients, the external loading conditions are for the most part uncontrollable and should be seen as a constraint rather than a variable.  The second factor is how the external load is transferred across the ankle joint between the implant components. This is governed by the implant articulation geometries, and the main differences  between two- and three-component implants are evident in this area. In a two-component semiconstrained device such as the Agility, the two implant components are fixed in the A/P direction with respect to each and there are significantly more shear forces transferred between them as a  result. In a mobile bearing prosthesis such as the STAR, the talar and tibial components can translate with respect to each other and the shear forces are instead resisted by the ligaments and other soft tissues of the ankle. Along with these differences, there are also less dramatic differences  in load transfer that are affected by the component shapes. One issue of crucial importance is stress 129  concentration in the PE bearing because it has a relatively low yield stress. In order to reduce the  stresses, avoiding delamination and excessive wear, the articulation surfaces must be designed to maximize contact area and minimize edge loading.  The third factor is the implant geometry at the bone interface, which plays a more direct role in the  micromotion behaviour. The geometry of the implant surface in contact with the bone is a critical factor in determining its effectiveness at resisting interfacial motion. Ideally, the majority of the  implant will experience compression over the range of activities. Compression is desirable because  it will cause the implant to remain in close contact with the bone and increase the frictional force.  Shear loading, on the other hand, is detrimental because it creates tensile strains that inhibit bone ingrowth into the implant. Different geometries can produce varying combinations of interfacial stresses depending on the external load being applied and how they are transferred across the  joint. Given that the ankle will experience a range of external loading scenarios, the design must be  effective at resisting forces and moments about each axis to varying degrees. This is quite evident when we compare the micromotion patterns of the different loading directions.  The fourth factor is the fit and finish of the implant into the bone. Greater friction between the prosthesis and bone will help prevent slipping between the two surfaces and resist the forces  imposed by the implant loading. This can be affected by the implant surfaces, the surgical jig design,  and surgeon experience/skill. There have been a number of different types of coatings used on  implants to improve the bone ingrowth potential of an implant, including hydroxyapatite (and  other calcium phosphates), cobalt chromium alloys, and titanium to name a few. Along with  different coating materials, there are also a number of coating application techniques that result in varying pore sizes and shapes [130]. The Agility uses a sintered bead coating, and the STAR has a  titanium plasma spray coating. The uncemented version of the STAR implant was originally designed with a single coating plasma spray, but clinical evidence suggests higher osseointegration 130  rates after the transition to a dual coating of titanium and calcium phosphate [8,37]. Both coatings  have shown success in the past and since cadaveric studies cannot evaluate bone-ingrowth, they  could not be compared in this study. However, the plasma spray approach seemed to have a greater  surface roughness, which would be beneficial in increasing the friction factor. The jigging systems  for each implant were of similar quality, being from the same generation, and each had their own shortcomings. Where the jigs left room for error, surgeon skill and experience with the procedure came into play to ensure proper implant fit and alignment.  The results of the tests performed in this study showed that the Agility had larger micromotion magnitudes than the STAR in both tibial and talar components. This suggests that one or more of  the design differences between these two prostheses helps to reduce the tensile stresses and strains at the bone-implant interface. These implant designs differed in all three of the implant  related factors previously mentioned, which makes it hard to determine the precise effects of each variable. I believe that differences in all three areas made partial contributions to this result.  Because the STAR is an unconstrained 3-component prosthesis, the shear stresses transferred  between the implants were reduced. The geometry of the interface favours the STAR implant’s talar  component because it has a larger surface contact area that is concave rather than flat, which  increases the friction between the surfaces and provides greater resistance to motion in a wider range of loading scenarios. As for the tibial component geometry, the Agility’s had a larger surface  contact area and was better suited to resist A/P forces but required a large amount of bone  resection, while the STAR’s barrels provided good stability in all directions except A/P but were highly dependent on bone quality for fixation strength. Judging the overall fit by the amount of force  required to remove the implants after testing, the STAR’s talar component had a better fit, while the tibial components were fairly similar.  131  4.5 DIFFERENCES IN KINEMATIC BEHAVIOUR  Attempting to reproduce the kinematic behaviour of normal ankles in a prosthetic device is important in order to restore the patient’s normal motion and reduce the cascading effect that small  changes can have on the body. It is also important because the ankle and all of the structures around it (especially ligaments) have been optimized for its function from many decades of  remodelling. By replicating its normal patterns, the stresses in these structures, and consequently  the prosthesis, are able to be minimized. The kinematic parameters examined in this study were range of motion (ROM), motion coupling (MC), and joint translation (JT). Despite the challenges posed by a large variance between specimens and a low sample size (N = 6), it was possible to tease  out some significant differences between the intact ankles and ones that were replaced with the Agility and STAR prostheses.  4.5.1  RANGE OF MOTION  At the talocrural joint, the primary motion occurring is ankle flexion (PF-DF) or rotation in the  sagittal plane. Because of this, it would be expected that the main differences in ROM between  implants would be found about this axis. Despite being able to determine the PF-DF ROM limits with reasonable accuracy through other means, the test setup did not allow for the application of applied moment limits to implanted specimens. Therefore, this aspect of the kinematic analysis could not be included in this study. However, complete analysis of the INV-EV and IR-ER ROM was able to be performed.  Slight changes were observed between the mean INV-EV and IR-ER ROM values of the intact and replaced joints, but they were found to be well within the range of values expected from random  variation within the sample population. Although testing a larger sample size might reveal data that  132  proves otherwise, the absence of detectable differences implies that these joint replacements don’t hinder the function of the ankle substantially by either restricting its motion or making it unstable.  It cannot be concluded for certain that there was no difference between the STAR and intact ROM,  but it can still point toward some interesting implications. Considering the architecture of the STAR in the frontal and transverse planes, it is apparent that this prosthesis does not allow any INV-EV  motion, and it does not provide any resistance to IR-ER motion. This reinforces the fact that the majority of INV-EV motion occurs in the subtalar and transverse tarsal joints and not in the  talocrural joint. Concerning IR-ER rotation, it tells us the bony geometry of the talocrural joint plays  only a small role in restricting this motion and instead this responsibility lies with the soft tissues of the ankle.  Compared to the ranges of motion determined  by Valderrabano et al. (fig. 86), the range of  values found in this study (see table 6) were not surprising. The ROM in INV-EV found in this  study was slightly higher, but this is to be expected because compression was found to  significantly decrease total ROM and the applied  axial compressions (15 N and 75 N) were lower than the 200 N used in their study. The amount  of ROM in the IR-ER direction was also in agreement since the ROM for the uncompressed and  compressed  tests  in  this  Figure 86: ROM in INV-EV (top) and tibial IR-ER (bottom)  study due to 100 Nm static applied torque with 200 N of axial compression from Valderrabano et al. 2003 pt. 1.  encompassed the values found by Valderrabano Copyright © 2012 by the American Orthopaedic Foot and in accordance with the applied compression (15  Ankle Society, Inc., originally published in Foot & Ankle International, 24(12):881-886 and reproduced here with permission.  133  < 200 < 300 N). The effects that the Agility and STAR had in comparison to the intact ankle, despite  being insignificant, were in agreement with these previous observations in all but one case.  Replacement of the ankle with an Agility prosthesis caused increases in ROM for both INV-EV and IR-ER, and replacement with the STAR caused a decrease in ROM for IR-ER. The disagreement  occurred in INV-EV for the STAR, and it was found to cause an increase in ROM for this study in contradiction to the observation of a decrease by them. Some differences here can be accounted for with the different coordinate frame definitions, since we used a JCS based off anatomical landmarks but they used orthogonal axes coincident with the applied moments.  Valderrabano et al. also found that use of the STAR was accompanied by a shift toward ER (or  internal tibial rotation), which was the opposite of what was observed in the compressed IR-ER test  of this study (fig. 52). However, this effect can be convoluted by differences in the definition of  neutral position. Because only the PF-DF axis was constrained during the initial static shot, the INV-  EV and IR-ER axes were left to align to the most stable position rather than aligning to the same neutral position as the intact case.  4.5.2  COUPLED MOTION  The motion coupling ratios were smallest when the ankle was loaded in PF-DF. This result makes  sense because the PF-DF has the largest ROM, which created a large denominator in the coupling  ratio. Despite this, the magnitude of coupled motion was also the least in PF-DF, which tells us that motion coupling to the flexion axis is generally the weakest. The coupling of INV-EV to IR-ER and vice versa was considerably stronger. The results of the study by Valderrabano et al. agree with  these findings [52]. Although, they didn’t look at PF-DF coupling to other directions, the results  presented here show that PF-DF had a stronger coupling relationship to INV-EV and IR-ER loading than in the reverse direction. This can be explained by the fact that maximum inversion and 134  internal rotation occur in supination, and maximum eversion and external rotation occur in  pronation, whereas maximum PF/DF occurs independently of these motions.  Only two studies have been performed that have examined the phenomenon of motion coupling in  total ankle replacements that provide a basis for comparison. The one by Michelson et al. only  reported IR-ER motion coupled to PF-DF loading, which applied manual angular rotation to the PFDF axis with the other axes unconstrained while under a 300 N axial load with the foot upside-  down [53]. The one by Valderrabano et al. looked at the INV-EV and IR-ER coupled to PF-DF and INV-EV coupled to IR-ER and vice versa, which manually applied rotation about each of the three  axes with the others unconstrained under a 200 N axial compression with the foot right side up [52].  The coupling patterns differed slightly, with the Agility matching the intact motion better in some instances and the STAR matching it better in others. The consequence of the exact motion patterns  is unknown, but it is assumed that the closer a TAA design matches the intact ankle the better. In this respect, neither implant proved to be convincingly superior over the other.  In PF-DF, the amount of IR-ER motion coupling for the intact ankle in the current study (MC ratio =  0.136 ± 0.065) agreed quite well with the findings of Michelson et al. (MC ratio ≈ 0.13), but Valderrabano et al. found a smaller amount of coupling (MC ratio ≈ 0.08). This makes sense because  the testing methodologies of this study and that of Michelson et al. were quite similar. However, when looking at unconstrained TARs (STAR in this and Valderrabano’s study and the Irvine Ankle Arthroplasty in Michelson’s study), the results of these two studies were closer to each other (MC  ratio ≈ 0.04) than they were to the results of the current study (MC ratio = 0.147 ± 0.101). The  explanation for the disagreement between the coupling found here and in Michelson’s study could be due to the different TAR design examined.  135  Comparing the other three coupling patterns (PF-DFINV-EV, INV-EVIR-ER, and IR-ERINVEV) to those found by Valderrabano, a consistent trend of larger coupling ratios in the current study  emerges across all ankle conditions. This difference is likely due to differences between the loading apparatuses. The presence of friction within Valderrabano’s loading device could prevent some  motion in the secondary axes. The orientation of the foot may also have a small effect on the ankle motion because the forces of gravity would interact with the foot in different ways.  If we look at the relative differences between the intact and implanted ankles, there is some  agreement and some disagreement. The motion coupling ratio for INV-EV due to PF-DF was lowest  in the Agility for both studies, but the STAR had a higher mean ratio than the intact ankle in this  study. The IR-ER motion caused by INV-EV was highest in the intact ankles and lowest in the ankles  with the STAR, which agreed with the prior results. There was little difference in INV-EV caused by  IR-ER between implants in compressed loading, but the uncompressed loading found the intact to be highest, followed by the Agility and the STAR in agreement with Valderrabano.  4.5.3  JOINT ORIGIN TRANSLATION  Joint translation in the M/L direction was the largest when the applied moment was about the INVEV axis. This makes sense because mediolateral direction is approximately parallel to the plane of induced rotation. The STAR caused a slightly larger increase in M/L motion than the Agility, but the  difference was not significant. This result also makes sense because the talus is free to slide in the  M/L direction with respect to the tibia in both implants, but it is slightly less constrained in the STAR. When loaded about the PF-DF axis, compression was found to increase the amount of M/L  translation in the intact ankles but not the implanted ones, and it increased from a magnitude which wasn’t significantly different from the implanted ankles to one that was larger.  136  The main effects in A/P translation were those of compression in PF-DF and IR-ER loading, both of which are easily explained. When the ankle dorsiflexes and plantarflexes, a proportion of the  applied compressive load acts as a shear force in the A/P direction instead of in axial compression because of the design of the loading apparatus. Because the talar component is free to translate in the A/P direction with respect to the tibia in the STAR, it is expected that increased joint laxity in  this direction would be present, and this was confirmed by Watanabe et al. [71]. The decrease in translation due to compression in IR-ER loading was likely due to the significant decrease in ROM  (decrease of approximately 69% averaged across all ankle conditions).  Similarly to A/P translation, the STAR produced an increase in C/D translation in PF-DF and  compression caused a decrease for all conditions in IR-ER. One might intuitively think that there  should be very little C/D translation occurring in TARs because the materials are not very compliant compared to cartilage, and the compressive load applied is relatively low. However, the  C/D axis is fixed to the calcaneus and as such is not always oriented parallel to the long axis of the tibia. This provides a logical explanation for the correlation with the A/P translation in PF-DF, since the A/P translation with respect to the tibia can be decomposed to components in both C/D and  A/P directions in the calcaneus reference frame. The compression effect in IR-ER loading is also likely due to the large decrease in IR-ER ROM from compression.  No other studies have examined this exact quantity, so there is no ideal reference material to  compare to. The third part of Valderrabano’s study reported mediolateral talar translation during PF-DF [18], which isn’t directly comparable to the M/L translation reported in this study, but it is  worth discussing. They found that the intact ankles and the ones with the STAR had similar magnitudes at around 5 mm, but the ankles replaced with the Agility had much less translation at closer to 1.5 mm. The translation magnitudes were close to the average values found in the present  investigation, but a large decrease in M/L translation was not observed in the Agility. Reasons for 137  the disparity are not likely due to the different M/L translation definition, but could be due to differences in the loading mechanism.  4.6 MOTION DEPENDENCE ON LOADING DIRECTION  The motion patterns of the implants with respect to the bone were quite dependent on the loading  direction. This was expected because applying moments about different axes will in turn transfer  different loads to the implants. This illustrates the need to apply a number of different loading conditions to the ankle joint in order to obtain a representative sample of micromotion. This idea is  also backed up by results from the FEA simulations by Chong et al. [114] where a number of different activities were approximated by the applied loading conditions and found considerably  different relative displacements along the surface of the implant. Depending on how the implant interface geometry is designed, one type of loading or another may create more micromotion.  The tibial component would be expected to show less micromotion than the talar component because it has a larger contact area and is supported on the medial and lateral sides in addition to  the flat, finned surface. It would be expected to show the most motion when loaded in PF-DF based on increased A/P shear force because it is semi-constrained and the loading device induces shear  loading in PF-DF. Because of the orientation of the fin, one would expect the Agility’s talar component to be more prone to motion when loaded about the PF-DF and INV-EV axes than the IR-  ER axis. In PF-DF, it would be susceptible to A/P sliding along the talar fin groove. When loaded in  INV-EV, the implant would be expected to rocker about the fin’s long axis.  138  The tibial component of the STAR would be expected to show very low levels of micromotion because the bearing is not constrained to it and therefore the only forces transferred to the implant  are compressive forces normal to the implant and shear forces from due to friction. The A/P direction would be most susceptible to motion since it is parallel to the barrel orientation, hence PF-DF loading would be expected to show the highest micromotion. One might expect even lower  levels of micromotion for IR-ER loading because there are no rotational constraints on the bearing in that direction, resulting in minimal force transfer. For the talar component, we would expect  much higher interfacial strains in PF-DF and INV-EV. PF-DF would have larger micromotion because the majority of force is being directed parallel to its stability fin. Larger motions would be expected in INV-EV because rotation in frontal plane is constrained by the device geometry. The loading would induce a large stresses in the edge of the PE causing the implant to rocker about this axis.  These predictions based on geometry were quite accurate for the most part. The differences found in the micromotion between loading directions for the Agility’s tibial component was quite minimal, but it did have less motion than the talar component as expected. The micromotion at its talar  component agreed with the theoretical predictions as well, showing the smallest micromotion magnitudes in the IR-ER loading direction. The PF-DF direction had more micromotion than the INV-EV direction, which was not necessarily expected, and this was attributable to the large  motions observed during component lift-off during the uncompressed loading. During compressed loading where no lift-off occurred, the talar component had comparable micromotion magnitudes  in both PF-DF and INV-EV, which were still higher than IR-ER. For the STAR’s tibial component, the  most amount of micromotion occurred during PF-DF loading in accordance with expectation,  especially when loaded with compression since it increases the friction force between the bearing  and tibial component and hence the A/P shear force. The talar component’s micromotion also lived up to the expectation, since it exhibited larger magnitudes in PF-DF and INV-EV than IR-ER.  139  4.7 LARGE INTER-SPECIMEN VARIANCE  It is normally expected that there will be noticeable differences between the kinematic behaviour of different specimens, especially when they are from people of varying body types and sizes. It is also expected that there would be quite significant changes to the kinematics of an ankle that has had  any operation performed on it, especially a total joint replacement. It was surprising to find that the  variation in the kinematic parameters measured (ROM, MC, and JT) was sometimes larger between  specimens (even different limbs from the same donor) than the changes caused by replacing the  joint. Typically, there were more similarities between an intact limb and the same limb with a joint replacement than there were between two intact ankles or two ankles with the same implant.  Large inter-specimen variance made it difficult to find significant differences in the kinematic  parameters between the STAR and Agility. However, taking advantage of the paired analysis  between the intact and implanted conditions of the same ankle enabled us to find some significant changes. In order to extract differences between the implants, a larger sample size would be  required or implanting the same ankle with two different implants sequentially to allow for a paired analysis between the implants as well.  4.8 OPTOTRAK MEASUREMENTS  To my knowledge, no other studies have been performed that measure implant micromotion for total ankle replacements. As such, a discussion of measurement device options in light of the unique  challenges of this joint is necessary to understand the trade-offs being made. Doing this type of analysis on a cadaveric ankle joint has some unique challenges that aren’t present in the hip or 140  knee; hence, techniques utilized in these studies were not necessarily transferrable. The measurement methods that were considered included: linear variable differential transformer  (LVDT) arrays, extensometers, radiostereometric analysis (RSA), and optoelectronic.  LVDT arrays have great accuracy (2 µm – mean error 1.6µm [108]) but can only measure relative  movement and would not be useful to analyze the kinematics of the ankle. Even if we weren’t  concerned about the kinematics, these arrays are very heavy, bulky, and would not fit in the small confines of the ankle joint without restricting its motion. Similarly to LVDTs, extensometers have very high accuracy but are only capable of measuring linear relative displacements. Systems of  extensometers have not been created that can measure 3-dimensional motions to my knowledge. Additionally, they require a relatively large amount of space.  The accuracy of RSA is lower than the previously mentioned measurement option (under optimal conditions can be as low as 6µm [131], but typically on the order of 20µm), but it comes with  considerable advantages in other areas. It doesn’t require any massive devices to be physically attached to what is being measured. At most it would require tantalum beads or some other type of  small fiducial to be inserted into the bones and implants. Because it uses x-rays, tissues obstructing the view would not be a concern, and reattaching the anterior capsule would be possible; however, obstruction of the x-rays by the footplate and mounting jig would be an issue when setting up the system if they weren’t constructed with radiolucent materials.  RSA has been used for migration and micromotion measurements for joint replacements numerous  times in the past and has proven to be effective. For this particular application RSA was the only option other than optoelectronic measurements that could reliably measure the relative motion of both tibial and talar implant components as well as the 3d tibiocalcaneal kinematics. The major  drawbacks of RSA are that it is quite complex to set up including fiducial bead insertion and their  arrangement, it requires a large amount of radiation which limits the ability to monitor visually 141  from up close, and data analysis is quite complex. Therefore, this method was the runner-up to optoelectronic measurement.  There are a number of different optoelectronic measurement methods, including both custom made and commercially available systems. A custom CCD camera measurement system has been used for  micromotion measurement of radial head arthroplasty implants and was capable of just slightly  lower accuracy/resolution than the LVDT at 7 µm [105]. However, this custom measurement setup  is specifically useful for relative displacement measurements with respect to a relatively stationary reference, but the talus and talar component would be moving a substantial amount. Its  effectiveness at measuring 3-dimensional kinematics and relative displacements between two objects moving relatively large amounts is unverified. It is also unlikely that a camera could be  positioned in such a way that the target area would be optimally located and visible throughout the  various motions of the ankle. On the other hand, commercially available optoelectronic systems are  capable of measuring 3-dimensional motion.  The method of measurement chosen to track the motion of the individual bones and implant  components was optoelectronic, and more specifically the Optotrak Certus. This method of  measurement was desirable because it was minimally invasive and was feasible to implement within the confines of the ankle joint. It required only K-wire pins extending out from the bones and  similar extensions from the implants. This permitted full range of motion in all directions with a few exceptions limiting the dorsiflexion of implanted ankles. It did require considerable effort in the  strategic placement and adjustment of markers to ensure each was free from obstructions and  optimally located throughout the entire range of motion for all three axes. Another benefit of using this method was that data collection issues would be minimized because previous work with this equipment meant that data acquisition systems and programs were already set up and debugged.  142  While convenient from the initial setup and data collection point of view, this approach did have its limitations.  Optoelectronic methods are typically considered to be too inaccurate for micromotion measurement and thus have not been used for this application. Since the equipment was readily available, it was worth investigating as a possible option nonetheless. The technical specifications  of the Optotrak Certus state that it has a 3-D spatial accuracy of 0.1 mm with a resolution of 0.01mm, which would not be accurate enough for micromotion measurements since they are  typically less than 0.2mm. However, this claim is too modest. The accuracy validation test  performed on our particular Optotrak Certus system (Appendix F) showed that for the ranges of  measurements performed in this experiment, the accuracy was better than 10µm with a resolution of around 5µm. Another accuracy test that mimicked the relative displacement measurements came  up with an average error of around 30µm. Pilot testing confirmed this level of accuracy to be sufficient for discerning differences between the micromotion patterns of different implants.  The challenge of ensuring that all markers remained unobstructed required some of the marker sets to be projected out a significant distance away from the bone or implant to which they were  attached. The increased marker attachment length had two negative consequences: increased susceptibility to vibrational noise and larger loads/moments exerted by the marker on their target.  143  4.9 LIMITATIONS  4.9.1  PF-DF ANGULAR LIMITS  It was discovered that while testing the implanted ankles in the PF-DF direction with torque limits  that the range of motion in plantar-flexion became exceedingly high. The ROM was so far beyond  the normal range that the polyethylene insert in the STAR was getting dislocated. Even though the anterior capsule of the ankle doesn’t govern the kinematics and guide the ankle to the same degree  as the ligaments, it still plays a major role in controlling its range of motion limit in plantar-flexion. The anterior capsule could not be sewn back up because Optotrak measurements were dependent on the components being exposed. Therefore, angular displacement limits were imposed on the  implanted PF-DF tests instead of torque limits. These limits were determined by considering their  range of motion in the intact PF-DF test as well as other limits imposed by the particular case, such  as marker attachment interference, bearing liftoff, etc. This unfortunately restricted us from being able to take any range of motion measurements for the implants in PF-DF. Angular limits were also used on one specimen in INV-EV because the ankle turned out to be slightly unstable with excess  ligament laxity on the lateral side.  4.9.2  FOOT ALIGNMENT  The main challenge accompanying potting the proximal tibia/fibula in dental stone was the alignment of the limb within the mounting rig. The goal was to have the foot plate aligned square  with the mounting rig while the foot is in its neutral position (the natural pose of the foot while standing). This would entail having the long axis of the tibia normal to the plane of the ground, with the long axis of the foot (posterior most point of the calcaneus along the second metatarsal) normal  to the frontal plane of the mounting jig, and the foot plate parallel to the ground. Obtaining this  144  ideal alignment is quite difficult because the definition of tibial long axis and frontal plane depend  on landmarks on the proximal tibia (which was unavailable), but it is not technically necessary.  However, it is necessary for the alignment technique to be consistent for proper inter-specimen kinematics comparisons. The most important axis to keep consistent is the flexion axis because neutral position, as defined by the static shot during test setup, was when the foot plate was level to  the ground about the flexion axis. The other axes were close to level because of how the limb was  potted; however, they were not constrained by the torque applicator like the flexion axis and thus  would fall into the foot’s natural alignment as a self-correcting mechanism. The neutral orientation  of the foot about the flexion axis could not be obtained in a similar manner because the foot would naturally fall into dorsiflexion because of the weight distribution of the foot. Therefore, slight deviations in the alignment of the tibia about the flexion axis within the potting would reproduce that same deviation in PF-DF angle measurements.  The rotational alignment is the most difficult and critical component, but the translational placement also has some requirements. Axially, we need the bone to be submerged deep enough to  ensure the dental stone would create a strong, rigid bond to the bone. In the transverse plane, the  most important consideration is that the two malleoli were somewhat centered between the cable guide posts in the A/P direction to allow for proper configuration of the cable guides to coincide  with the flexion axis. Also, the ankle had to be positioned within the confines of the posts in the M/L direction to ensure clearance for the foot.  4.9.3  PURE MOMENT ASSUMPTION  The torque applicator was verified to produce an isolated moment about the specified axis with  negligible forces and moments about the other axes for a range of motion of the spine when set up with proper counter-balances. The magnitude of the off-axis moments increased with the amount of  145  angular displacement deviating from the initial position. For small angles such as those seen in a  single functional spinal unit, which is what it was designed for, this is a great approximation.  However, the ankle has a much larger range of motion (over 80° of total motion in one specific case  of PF-DF), and while the off-axis moments are still very small with respect to the applied moment, their precise magnitude was not measured.  4.9.4  SAMPLE SIZE  The number of limb pairs tested and compared was only 6, which is quite low but typical in cadaveric testing. In many cases the low sample size does not hinder the effectiveness of these tests  because the differences observed for a given treatment are very large in comparison to the  standard deviation within a group. However, the low sample size does limit the power of the study and the ability to detect small differences. In the present study, several comparisons were found to  have low p values that were not below 0.05. This shows that there could possibly be a relation between these, but that it is still within possibility that the difference could just be due to random variation. If a larger number of specimens were tested, we would probably find that these relations with a low p value are indeed significant.  146  4.10 FUTURE WORK 4.10.1 MICROMOTION  Since this is the first micromotion study for total ankle replacements, there is a lot of room to build on and expand this body of research. For this specific comparison of implants, it would be useful to  test a larger sample size in order to support these findings and tease out some of the relations that were nearly found to be significant. It would also be of benefit to the TAA community to know  where other implants on the market stand in this area. With a more comprehensive catalogue of the  micromotion characteristics of each implant, it would be possible to determine which implants will provide the highest probability of complete osseointegration and to infer which design components and geometries contribute to creating strong initial fixation.  The testing methodology has room for improvements to be made as implied previously. While the  accuracy of the Optotrak was sufficient to compare the micromotion of these two implants, it may not be capable of discerning differences in other implants with lower micromotion magnitudes. The objective of this research is to reduce the micromotion and achieve higher long-term success rates,  comparable to hip/knee arthroplasty. Consequently, we expect that eventually the micromotion magnitudes will be reduced to comparable levels as well (lower than 200µm), and the differences  to be found between implants will be too small for the Optotrak to accurately detect. As mentioned  earlier, RSA is a very promising alternative measurement method because it offers better accuracy with proven efficacy in micromotion measurement [117] and is even less intrusive, and it has been  used in dynamic applications [132] but not yet verified in total joint replacements.  The loading profiles chosen for this experiment were intentionally very general and not necessarily  representative of any specific tasks. Loading versatility was desirable in this specific application, but it can also be of interest to determine more detailed information about the micromotion  147  patterns for specific activities. The applied loads could be refined to closer replicate precise loading  patterns and include fluctuations in compression and varying angular velocities over the course of the loading. One might be interested in the gait because it is a very repetitive motion that all  patients will be performing, or one might be interested in determining which activities the patient should not take part in during this initial healing phase. A more complex loading simulator must be  used to carry out experiments for this purpose, such as gait simulators with muscle actuation [54,61].  In vivo analysis can also be useful for analyzing specific tasks with a greater degree of biofidelity.  Doing in vivo tests would limit the measurement method to RSA and require the prosthesis in question to be approved to clinical testing at a minimum. In vivo testing wouldn’t be as effective for comparing between implant types because patient variability would come in to play and it would be  very difficult to control for applied loading. However, it would be quite effective at comparing within patient activities.  Another possible avenue of work in this area would be to refine the testing protocol to a format that is practical for standardized testing. All new implant designs must satisfy certain requirements  before they can be approved for clinical testing, and ideally this would include a micromotion analysis to ensure adequate initial fixation. It would likely be much further into the future, but if we  can establish the importance of a test like this in reducing the risk of aseptic loosening failure, it would be required to create a testing protocol that would be appropriate for all implant testing at a national level.  148  4.10.2 KINEMATICS  In this particular study where we were analyzing micromotion and kinematics with the same measurement system, our investigation of kinematics was incomplete because of the limitations  imposed by having to measure the implant motion. Switching the motion measurement system to  RSA would eliminate these limitations and allow a complete kinematic analysis. However, this is only an improvement if both need to be measured simultaneously.  In order to properly compare kinematic differences between implants and specimens for the  compressed configurations, modifications need to be made to the compressive load application.  Either a more accurate and repeatable way of setting the cable guides to the joint axis of rotation needs to be established, or a different method of applying the compressive load that doesn’t  influence the kinematic behaviour as strongly needs to be used. Otherwise, analyzing the compressed kinematic patterns will be pointless because one would not be able to distinguish between differences caused by variables of interest and those cause by loading variations.  Another interesting and possibly more relevant kinematic analysis would be one comparing different joint replacements in gait simulation. An experiment along these lines would give us an idea of how different ankle replacements affect the ankle kinematics in a more practical setting with better transference into real world application.  149  4.11 CONTRIBUTIONS  This is the first study to date that has analyzed the relative bone-implant motion for TAA. An  effective testing methodology has been developed for this end, providing future researchers with detailed information on this procedure and several considerations for future work and improvements to this technique.  The micromotion data from this experiment provides evidence supporting the hypothesis that higher initial post-operative micromotion magnitudes correlate with higher aseptic loosening rates. The implications of this are:  1. We need to know the initial fixation micromotion magnitudes for all implants on the market. Use ones with lower values to reduce probability of aseptic loosening failure.  2. Shows the importance of micromotion metric in predicting aseptic loosening. We should be  testing for micromotion magnitudes post implantation in pre-clinical analysis to determine relative loosening risks and design/modify devices with features to minimize this value.  This also shows that the initial fixation of these two devices is insufficient to facilitate proper osseointegration even when subjected loads much lower than experienced in vivo. This emphasizes  the need to eliminate all unnecessary weight bearing and loading within the first few weeks to enable continuous bone ingrowth to occur and fortify the bone-implant bond before using it.  While kinematic analysis of the STAR and Agility is not novel, the data produced by this experiment supplements the data already published with look at several different kinematic variables from a new ankle loading simulator.  150  5 CONCLUSION  The Agility was determined to exhibit a greater amount of micromotion between the bone and prosthesis than the STAR for the tibial component in INV-EV, and for the talar component in PF-DF and IR-ER. Aside from the previously noted tests, the differences found between the two implants  were insignificant, despite the Agility having higher mean micromotion magnitudes than the STAR in all but one test. This agrees with the hypothesis of this study that higher clinically observed  aseptic loosening rates are correlated with larger micromotion values immediately postoperatively.  Micromotion magnitudes were found to be affected by loading direction and compression, which  confirms the need to apply a variety of loading conditions to obtain a comprehensive micromotion analysis.  Kinematic changes were observed after replacement of the ankle joint in a few comparisons, but  due to large interspecimen variability the majority of differences were found insignificant. Consequently, no meaningful conclusions were able to be drawn from these analyses.  This is the first time micromotion has been studied in total ankle replacements, and a novel method for this analysis was developed for this experiment. Results from this study suggest the importance of this line of testing. Improving this methodology and adapting it for the analysis of other implants  in use, and for the pre-clinical analysis of new implant designs would be beneficial in addressing the aseptic loosening issues in TAA.  151  REFERENCES  1. . Arthroscope: The Arthritis Society, 2004. 2. Cushnaghan J, Dieppe P. Study of 500 patients with limb joint osteoarthritis. I. Analysis by age, sex, and distribution of symptomatic joint sites. Ann Rheum Dis 1991;50(1):8-13. 3. Extremity Reconstruction: Procedural Volumes: © 2010 PearlDiver Technologies, Inc:Source: PearlDiver Patient Records Database and Center for Medicare & Medicaid Services Databases. 4. Saltzman CL, Mann RA, Ahrens JE, Amendola A, Anderson RB, Berlet GC, et al. 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Comparison of the model-based and marker-based roentgen stereophotogrammetry methods in a typical clinical setting. J Arthroplasty 2009;24(4):594-606. 117. Trozzi C, Kaptein BL, Garling EH, Shelyakova T, Russo A, Bragonzoni L, et al. Precision assessment of model-based RSA for a total knee prosthesis in a biplanar set-up. Knee 2008;15(5):396-402. 118. Atkins GJ, Haynes DR, Howie DW, Findlay DM. Role of polyethylene particles in peri-prosthetic osteolysis: A review. World J Orthop 2011;2(10):93-101. 119. Grewal R, Rimmer MG, Freeman MA. Early migration of prostheses related to long-term survivorship. Comparison of tibial components in knee replacement. J Bone Joint Surg Br 1992;74(2):239-42. 120. Ryd L, Albrektsson BE, Carlsson L, Dansgard F, Herberts P, Lindstrand A, et al. Roentgen stereophotogrammetric analysis as a predictor of mechanical loosening of knee prostheses. J Bone Joint Surg Br 1995;77(3):377-83. 121. Goertzen DJ, Lane C, Oxland TR. Neutral zone and range of motion in the spine are greater with stepwise loading than with a continuous loading protocol. An in vitro porcine investigation. J Biomech 2004;37(2):257-61. 122. Veldpaus FE, Woltring HJ, Dortmans LJ. A least-squares algorithm for the equiform transformation from spatial marker co-ordinates. J Biomech 1988;21(1):45-54. 123. Grood ES, Suntay WJ. A joint coordinate system for the clinical description of three-dimensional motions: application to the knee. J Biomech Eng 1983;105(2):136-44. 124. Wu G, Siegler S, Allard P, Kirtley C, Leardini A, Rosenbaum D, et al. ISB recommendation on definitions of joint coordinate system of various joints for the reporting of human joint motion-part I: ankle, hip, and spine. International Society of Biomechanics. J Biomech 2002;35(4):543-8. 125. Siegler S, Udupa JK, Ringleb SI, Imhauser CW, Hirsch BE, Odhner D, et al. Mechanics of the ankle and subtalar joints revealed through a 3D quasi-static stress MRI technique. J Biomech 2005;38(3):567-78. 126. Kassi JP, Heller MO, Stoeckle U, Perka C, Duda GN. Stair climbing is more critical than walking in pre-clinical assessment of primary stability in cementless THA in vitro. J Biomech 2005;38(5):1143-54. 157  127. Pancanti A, Bernakiewicz M, Viceconti M. The primary stability of a cementless stem varies between subjects as much as between activities. J Biomech 2003;36(6):777-85. 128. Cripton PA, Bruehlmann SB, Orr TE, Oxland TR, Nolte LP. In vitro axial preload application during spine flexibility testing: towards reduced apparatus-related artefacts. J Biomech 2000;33(12):1559-68. 129. Haskell A, Mann RA. Perioperative complication rate of total ankle replacement is reduced by surgeon experience. Foot Ankle Int 2004;25(5):283-9. 130. Kienapfel H, Sprey C, Wilke A, Griss P. Implant fixation by bone ingrowth. J Arthroplasty 1999;14(3):355-68. 131. Madanat R, Makinen TJ, Moritz N, Mattila KT, Aro HT. Accuracy and precision of radiostereometric analysis in the measurement of three-dimensional micromotion in a fracture model of the distal radius. J Orthop Res 2005;23(2):481-8. 132. Koning OH, Kaptein BL, van der Vijver R, Dias NV, Malina M, Schalij MJ, et al. Fluoroscopic Roentgen stereophotogrammetric analysis (FRSA) to study three-dimensional stent graft dynamics. J Vasc Surg 2009;50(2):407-12.  158  APPENDIX A: TAA FAILURES AND THEIR CAUSES  159  APPENDIX B: INDICATIONS FOR TAA Author  Year  Implant  Total  PTOA  POA  RA  Other  Claridge  2009  agility  28  14  10  4  0  Anderson Karantana Wood  Fevang Henricson  2003 2009 2008 2007 2007  Hosman  2007  Knecht  2004  Criswell  2012  Spirt  Hurowitz Kopp  Valderrabano Buechel  San Giovanni Naal  Valderrabano Bonnin Total  Percentage  2004  star star star star tpr  star bp  aes  other  agility star  mobility ramses agility agility agility agility agility star bp bp  bp & mobility hintegra salto  51 50  200 216 32  303 92  10 12 25 57  13 24 56 53  28 14  119 129  0 0 0 9  175  119  216  21  34  144  24  0  132  61  38  31  2  41  25  2  5  9  69 67  117 45 29 11  306 62 40 68 75 31  101 152 98  2416  199 37 24 48 55 0  47  115 43  981  40.60  77 12 8 9 8 0  35 21 22  651  26.95  13 10 8  11 9  31 19 16 29  716  29.64  17 3 0 0 3 0 0 0 4  68  2.81  160  APPENDIX C: MOUNTING RIG  161  162  163  164  165  166  167  168  169  170  APPENDIX D: AGILITY SURGICAL PROCEDURE  1. Open joint and separate the syndesmosis  2. Align and secure jig to the tibia  171  3. Make flat cuts to tibia and talus  4. Make tibial fin cut  172  5. Clean up cuts and remove bone fragments  6. Insert trial tibial component to help align jig for talar fin cut  173  7. Drill and rasp out talar fin slot  8. Install final components (no image)  9. Fuse the syndesmosis with a plate and screws  174  APPENDIX E: STAR SURGICAL PROCEDURE  1. Secure and align the jig on the tibia  2. Select the appropriate size guide and make the flat tibial cut  3. Remove the bone from the tibial cut  175  4. Make flat talar cut  5. Select proper size talar component and align/secure jig for side cuts  6. Remove bone fragments and clean up cuts  176  7. Fasten jig for diagonal A/P cuts  8. Make diagonal A/P cuts  9. Attach jig and drill out fin slot  177  10. Clean out slot and install talar component  11. Drill out barrel holes and install tibial component  12. Select appropriate size meniscal component and insert (no image)  178  APPENDIX F: OPTOTRAK ACCURACY STUDY F.1 SETUP  The accuracy study was performed using a linear translation platform (A25 graduated knob 3.5”  UniSlide®, Velmex Inc., Bloomfield, NY) and a high precision rotation mount (PR01, Thorlabs Inc.,  Newton, NJ). The translational accuracy, the rotational accuracy, the combined accuracy when translations and rotations are applied, and the accuracy of measuring the relative displacement when using digitized points (as was employed in my experiment) were calculated.  The A25 Unislide is a screw-drive linear translation platform with a resolution of one thousandth of  an inch and a travel of 3.5 inches. Its lead screw is calibrated to have a lead error of less than .0015  in/10 in length (0.015%). For the range being operated at (0 - .394 in), the resultant measurement error was less than 8 µm.  Figure 87: Velmex A25 Unislide  The PR01 is a high precision rotation mount with coarse rotation divisions of 1° and a vernier scale  resolution of 5 arcmin, and fine rotation adjustment via micrometer with divisions of 2.4 arcmin, which has a resolution of 1 arcmin across a ±5° range and an accuracy of better than 1%.  179  Figure 88: Thorlabs PR01  The PR01 was mounted to an L-bracket, which in turn was mounted to the Unislide. A marker  carrier was attached to the PR01 by a wire fixed to a ¼-20 machine screw by a nut, and the screw was threaded into one of the holes in the PR01.  X Y  Z  Figure 89: Optotrak accuracy test setup  180  F.2 PROTOCOL  The accuracy protocol was performed with the Optotrak at 3 separate distances away from the  target markers: 1.5m, 2.0m, and 2.5m. Measurements were taken at several increments  along/about each of the 3 axes to calculate the directional error over a range of translations and rotations (see tables 7-10).  The coordinate frame was designated to mimic that of the Optotrak: with positive X vertically up, Y horizontally to the right, and Z toward the camera.  Firstly, the whole assembly was clamped to the test bed such that the direction of the Unislide  and/or PR01 was aligned with the axis of interest. As aligning it exactly with the Optotrak was  impossible, specific points on the PR01 and/or Unislide were digitized in order to set up local axes for the measurements. The arrangement of digitized points varied depending on which test was being performed, and for the pure translation measurement the magnitude of the displacement was used rather than the projection onto the local reference frame.  The translational and angular displacements were determined using the transformation matrix (as  previously described) between the initial and incremental target shots. Measurements were taken for 10 seconds at each increment, and the accuracy and precision were calculated.  The relative displacement test (fig. 90) was intended to mimic the micromotion measurement being  done during the live tests. An aluminum bar with a tab was attached to the PR01 rotational platform, which was fixed to the table by the previously used L-bracket. An aluminum block with a  tab was clamped to the table. The two tabs were aligned and set to flush in the zero degree position on the PR01. The tips of the tabs were digitized and the distance between them was determined  with the Optotrak and Matlab program, as well as being mechanically measured with a micrometer for the gold standard.  181  Figure 90: Relative displacement accuracy test setup  Table 7: Translation accuracy test increments  Displ.  mm in  0.0254 0.001  deg min  0.04 2.4  mm in deg min  0.1016 0.004 0.16 9.6  deg min  0  0.1016 0.004  Table 8: Rotation accuracy test increments  Angle  0.16 9.6  0.508 0.02  0.48 28.8  1  1.016 0.04 5  2.032 0.08  10  5.0038 0.197  20  10.0076 0.394  40  Table 9: Combined translation and rotation accuracy test increments  Displ.  Angle  0.1016 0.004 1  0.1016 0.004 10  2.032 0.08 0.16 9.6  2.032 0.08 1  2.032 0.08 10  Table 10: Relative displacement accuracy test increments  Angle  0.04 2.4  0.16 9.6  0.32 19.2  0.68 40.8  1  2  4  10.0076 0.394 0.16 9.6  10.0076 0.394 1  10.0076 0.394 10  6 182  Displacements and angle errors were determined for all three axes. The test combining translations  and rotations were performed only once at each Optotrak distance with translation along the Y-axis  and rotation about the X-axis. This was done to see whether the translational and rotational errors  would be compounding or independent. The relative displacement test was performed twice, using rotations about the Y and Z axes.  F.3 RESULTS  The results from this accuracy test show that the setup used in this study were actually much better  than the 0.1 mm stated in its specifications (table 11). The translational accuracy was closer to 10 µm with a resolution of 5 µm. The rotational accuracy was better than 0.1 degree. The accuracy of  measuring relative displacements of digitized points was found to be approximately 30 µm, which  is a manageable error considering the magnitudes of relative displacements were typically 0.1 mm  or greater. However, the error estimates in this test were likely an overestimation due to the uncertainty and human error in the micrometer measurements.  Table 11: Results of the Optotrak accuracy study. Values are the average of the 1.5m and 2.0m tests. Repeatability and precision are given as one standard deviation, and accuracies are given as mean error ± 95% confidence interval.  Dir. X Y Z  Repeatability (mm)  Precision (mm)  Trans Acc (mm)  Ang. Acc (deg)  Rel. Displ. (mm)  .0013  .0026  0.0036 ± 0.0070  0.0222 ± 0.0629  -  .0022  .0052  0.0035 ± 0.0029  -0.0141 ± 0.0309  .0016  .0025  -0.0077 ± 0.0044  0.0064 ± 0.0321  0.0306 ± 0.0181  -0.0078 ± 0.0081  183  F.4 ACCURACY STUDY DATA Table 12: Repeatability (mm)  Direction X Y Z  1.5 0.000795 0.001021 0.001953  Optotrak Distance 2.0 .001822 .002093 .002357  2.5 0.009622 0.016139 0.014485  Table 13: Precision (mm) – standard deviation of 500 frames (10 sec x 50 Hz) averaged over 5 trials randomly selected  Direction X Y Z  1.5 0.002198 0.002636 0.004698  Optotrak Distance 2.0 0.002918 0.002271 0.005641  2.5 0.003336 0.003178 0.008302  Table 14: Displacement error measurements (mm) Opto dist. (m) 1.5  Dir X  1.5  Y  1.5  Z  2.0  X  2.0  Y  2.0  Z  2.5  X  2.5  Y  2.5  Z  2.032  5.0038  10.0076  Average Bias  0.0122  -0.0105  0.0119  0.0149  0.0127 ± 0.0114  -0.0008  -0.0021  -0.0013  -0.0033  -0.0039  0.0027 ± 0.0021  0.0037  -0.0007  0.0019  0.0005  -0.0057  0.0025 ± 0.0020  0.0073  0.0080  0.0143  0.0077 ± 0.0052  -0.0237  0.0146 ± 0.0056  -0.0012  0.0069 ± 0.0055  0.0141  0.0069 ± 0.0046  0.0254  0.1016  0.0039  0.0000  -0.0358  0.0067  -0.0011  0.0041  -0.0008  0.0001  0.0022  0.0293 0.0321 0.0295 0.0255 0.0134  0.1016 0.1005 0.1008 0.1038 0.0881  0.508  0.4722 0.5072 0.5117 0.5153 0.4987  1.016  1.0282 1.0139 1.0153 1.0240 1.0049  2.0215 2.0307 2.0339 2.0411 0.0091 2.0206  5.0157 5.0005  10.0037  5.0043  10.0019  5.0168  10.0219  4.9824  9.9839  0.0130  -0.0120  -0.0135  -0.0093  -0.0111  -0.0114  -0.0214  0.0030  0.0134  0.0113  0.0027  0.0034  0.0132  0.0284 0.0307  0.1150 0.1011  0.5193 0.5057  1.0187 1.0239  2.0417  10.0064  5.0122  10.0217  4.9793  9.9762  -0.0005  -0.0023  -0.0073  -0.0182  -0.0221  -0.0263  -0.0182  -0.0245  -0.0314  0.0211 ± 0.0077  -0.0102  -0.0097  -0.0060  -0.0050  -0.0144  -0.0082  -0.0108  0.0092 ± 0.0032  0.0152  0.0834 0.0919  0.4859 0.5020  0.9897 1.0110  0.0097  5.0170  0.0053 0.0181  0.0079  2.0354  10.0225  2.0138 2.0176  0.0084 4.9956  9.9968  184  Table 15: Rotation error measurements (deg) Opto dist. (m)  Axis  1.5  Y  1.5  0.04  X  1.5  2.0  0.0423  0.1757  0.1628 0.0028 0.0157  0.0181  0.1344  -0.0219  -0.0256  0.0362  0.1557  -0.0038  -0.0043  0.0391  0.1524  -0.0009  -0.0076  0.0037  Y  2.5  0.0001  0.1553  0.0023  X  2.5  -0.0047  0.0031  Z  2.5  -0.0052  0.0008  0.0431  Y  2.0  0.4824  0.0348  X  0.1201  -0.0363  -0.0399  0.0438  Z  0.48  0.1608  -0.0017  Z  2.0  0.16  0.0383  0.1595  1  5  0.9944  10  4.9917  20.0794  -0.0685  0.0328  0.0024  -0.0056  -0.0083  -0.0215  0.4872  0.9851  4.9570  9.9943  0.4801 0.0072 0.4823 0.0023 0.4582  -0.0218 0.4700  -0.0100 0.4508  -0.0292 0.4344  -0.0456 0.4801  0.9901  4.9604  -0.0099  9.9315  -0.0396  -0.0149  -0.0430  0.9977  -0.0057  5.0035  -0.0023  9.9732  0.0035  0.9890  -0.0110  -0.0268  4.9650  10.1222  -0.0374  -0.0620  4.9041  9.9907  -0.0350  0.9850  0.1222  4.9626  -0.0150 0.9749  9.9380  4.9751  -0.0251  9.9990  -0.0249  0.9562  -0.0438  -0.0010  -0.0959  0.9852  -0.0093  4.9589  20*  9.9785  9.9268  40*  40.4069  0.0794  0.4069  20.0328  39.9791  -0.0209  20.0555  40.1141  0.0555  0.1141  20.0425  39.8656  0.0425  -0.1344  20.1279  40.0828  0.1279  0.0828  19.9210  39.8671  -0.0790  -0.1329  19.9896  39.6905  -0.0104  -0.3095  20.1364  40.1338  0.1364  0.1338  19.9537  39.9585  Average Bias  0.0067 ± 0.0078 0.0213 ± 0.0271 0.0128 ± 0.0154 0.0088 ± 0.0103 0.0396 ± 0.0412 0.0221 ± 0.0231  0.0148 ± 0.0130 0.0451 ± 0.0282  0.0038 -0.0005 0.0001 -0.0148 -0.0411 -0.0732 -0.0463 -0.0415 0.0223 ± 0.0294 * 20 and 40 degree measurements were not used in calculating the average errors because they were taken using the coarse adjustment on the PR01  Table 16: Relative displacement error measurements (mm) Opto Dist. (m) 1.5  2.0  Rot. Axis Y Z Y Z  Meas. Calc. Err.  Meas. Calc. Err.  Meas. Calc. Err.  Meas. Calc. Err.  0  6.18 6.245 6.19 6.21  Rotation (deg)  0.04  0.16  0.32  0.68  6.221  6.463  6.806  7.570  8.248  10.375  14.606  18.858  6.291  6.525  6.837  7.585  8.247  10.356  14.593  18.855  6.21  0.011  6.46  6.81  7.54  8.19  10.32  14.52  18.77  -0.025  -0.003  6.230  6.481  6.817  7.578  8.229  10.347  14.559  18.781  6.273  6.494  6.828  7.570  8.235  10.336  14.546  18.780  6.24  -0.010  6.26  0.013  6.45  0.031 6.505  -0.011  6.81  0.007 6.855  -0.027  7.585 0.000  7.51  0.068 7.585  -0.015  8.235 0.012  8.16  0.069  8.22  0.015  10.34 0.016 10.31 0.037 10.36  -0.024  0.086  6  0.011  6.84  0.055  4  -0.004  6.55  0.058  2  0.003  6.28  0.030  1  14.61  -0.017 14.57  -0.011 14.57  -0.024  Average Bias  0.088  0.0419 ± 0.0349  -0.025  0.0136 ± 0.0091  18.88 18.81  -0.029  0.0328 ± 0.0246  -0.020  0.0186 ± 0.0059  18.80  185  Table 17: Combined translation and rotation error measurements (mm & deg)  Opto dist. (m) 1.5  Angle  .1016  Error (mm;deg)  0.1589  -0.0011  .16  0.0944  1.5  1  0.1078  1.5  10  2.0  .16  2.0  1  2.0  10  2.5  .16  2.5  1  2.5  10  2.0246  -0.0074  0.0062  2.0351  0.0031  -0.0039  9.9805  -0.0195  0.1634  0.0034  0.0867  0.0771  -0.0149  0.0893  -0.0123  0.0258  -0.0758  0.9832 9.9818 0.1251  -0.0168 -0.0182 0.0235  0.1412  -0.0188  0.9764  -0.0236  9.5323  -0.4677  0.4157 3.8869  2.032  -0.0072  0.9961 0.1787  Displacement (mm)  0.3141 3.7853  0.1609 1.0006 2.1002  9.9968  -0.0108  9.9978  -0.0098  0.0682  10.0723  0.0647  -0.0256  9.9700  0.0009 0.0006  9.9766  -0.0234  0.1578  -0.0022  2.0064 2.0060 0.9900 1.9111 9.9869 2.0134 0.1762 2.0499 1.0087 4.2973 9.9755  10.0076  -0.0260 -0.0100 -0.1209  0.1614 0.9863  -0.0137 -0.0260  0.1601  0.0001  -0.0376  9.9765  -0.0311  9.8566  -0.1510  -0.0131  10.0199  0.0162  0.1668  -0.0186  0.0014  9.9740  0.9837  -0.0163 0.0199  10.0045  -0.0031  0.0179  10.0013  -0.0063  2.2653  10.4299  0.4223  0.0087 -0.0245  1.0094 9.9744  Average Bias  0.0068 0.0094  -0.0256  186  APPENDIX G: MATLAB DATA ANALYSIS PROGRAMS G.1 OPT_ANKLE_ANGLES.M  % opt_ankle_angles.m % Modified Sept 12, 2011 by Kurt McInnes % opt_pfj_angles_Ankle_Version.m % Modified August 9, 2005 by Craig Davidson % This file has been modified to analyze the optotrak ankle data % Make sure to check that the path directory is correct and no other ankle % sample's directories are open as well as this can give erroneous data. % Make sure Matlab directory is set to desired output directory % opt_pfj_angles.m % June 10 2003 by Dave Wilson % written to analyze pfj and tfj kinematics from Optotrak data % % % % % % %  modified from: all_pfj_angles.m modified January 10, 2000 to do patellar kinematics should only be used from within masterpfj modified from pli3.m June 8, 1999 by Dave Wilson for determining flexion angles for patellofemoral studies  %% clear all clf NAME = 'C004'; % data file name - used for input (e.g. C006) SAMPLE = 'H1352R'; % specimen id # - used for output name (e.g. H1347L) NUM = '7'; % Digitized point file # associated with specific run. LOAD = 'PF-DF 15N -18-40'; % loading configurations - used for output name side = 'r'; % r/l changes direction conventions imp = 2; % none = 1; star = 2; agility = 3 % for implants - make sure correct dimension file is referenced on Line 225 name_of_output = [SAMPLE '_' LOAD]; opto_freq = 20; %optotrak data collection frequency[Hz] 187  errthresh = 1; % see below maxthresh = 1; % see below % errthresh: error level at which markers are rejected in trs % maxthresh: error level at which angle results are rejected assigned the value "NaN"  and  % This path is the directory of each test you are doing % e.g. 'X:\Oxland\Ortho_Eng\Kurt\H1119R\MATLAB Input' path(path,['H:\WORKING DIR\MATLAB Input\' SAMPLE]) %% Markers associated with rigid bodies % baseframe = [1 2 3 4]; tibia_m = [5 6 7 8]; calca_m = [9 10 11 12]; if imp > 1 talus_m = [13 14 15 16]; tib_implant_m = [17 18 19 20]; tal_implant_m = [21 22 23 24]; SUFF = ['S_TIBIA'; 'S_CALCA'; 'S_TALUS'; 'S_TIBIM'; 'S_TALIM'; 'DIGITIZ']; %static shot marker and digitize point files % Use con_digi.m and con_static.m - make sure converted files are moved into the working directory else SUFF = ['S_TIBIA'; 'S_CALCA'; 'DIGITIZ']; end %% DEFINING COORDINATE SYSTEMS disp('WORKING OUT REFERENCE AXES') for q = 1:size(SUFF,1) filename = [SUFF(q,:),NUM,'.csv']; filesuff = [SUFF(q,:),NUM]; filesave = SUFF(q,:); eval([ 'load -ascii ', filename,';']); eval([ filesave, ' = ', filesuff,';']); end % This loop loads up the files so you dont need to use the file numbers % convention: this assigns axes as follows: % e1: Rotations ? - Dorsiflexion +ve, Plantarflexion -ve; displacement q1 - lateral +ve, medial -ve % e2: Rotations ? - Inversion +ve, Eversion -ve; displacement q2 anterior +ve, posterior -ve % e3: Rotations ? - Internal +ve, External -ve; displacement q3 compression +ve, distraction -ve 188  % as per Wu et al. J. Biomech 35 (2002) % ANATOMICAL REFERENCE POINTS %1=MM(medial maleolus);2=LM(lateral maleolus);3,4,5=prox tib; %PT = centroid of prox tib points PT = (DIGITIZ(3,:) + DIGITIZ(4,:) + DIGITIZ(5,:))/3; IM = (DIGITIZ(1,:) + DIGITIZ(2,:))/2; % AXES ltib = ftib = ttib =  for kinematics analysis according to JCS convention unitv(PT' - IM')'; unitv(DIGITIZ(2,:)' - DIGITIZ(1,:)')'; ucross(ltib,ftib);  lcal = ltib; fcal = ftib; tcal = ttib; % ORIGIN for kinematics analysis according to JCS convention tibrefpt = IM; calrefpt = IM; if imp==2 %2=STAR % AXES for implant coordinate frames derived from digitized pts ftibimp = unitv(DIGITIZ(7,:)' - DIGITIZ(6,:)')'; %e1 ltibimp = ucross((DIGITIZ(10,:)'DIGITIZ(9,:)')',(DIGITIZ(8,:)'-DIGITIZ(9,:)')'); %e3 ttibimp = ucross(ltibimp,ftibimp); %e2 ftibimp = ucross(ttibimp,ltibimp); %ensure e1 is orthogonal to e3 and e2 ftalimp ltalimp ttalimp ltalimp  = = = =  unitv(DIGITIZ(12,:)' - DIGITIZ(11,:)')'; ltibimp; ucross(ltalimp,ftalimp); ucross(ftalimp,ttalimp);  % ORIGINS for tibial and talar implant coordinate frames tibimprefpt = ((DIGITIZ(6,:)'+DIGITIZ(7,:)')/2)'; tib2refpt = tibimprefpt; talimprefpt = ((DIGITIZ(11,:)'+DIGITIZ(12,:)')/2)'; tal2refpt = talimprefpt; elseif imp==3 %3=Agility ftibimp = unitv(DIGITIZ(7,:)' - DIGITIZ(6,:)')'; ttibimp = ucross(ftibimp,(DIGITIZ(8,:)' DIGITIZ(6,:)')'); ltibimp = ucross(ftibimp,ttibimp); ttibimp = ucross(ltibimp,ftibimp);  -  ftalimp = unitv(DIGITIZ(10,:)' - DIGITIZ(9,:)')'; ltalimp = ltibimp; ttalimp = ucross(ltalimp,ftalimp); 189  ltalimp = ucross(ftalimp,ttalimp); tibimprefpt tib2refpt = talimprefpt tal2refpt =  = ((DIGITIZ(6,:)'+DIGITIZ(7,:)')/2)'; tibimprefpt; = ((DIGITIZ(9,:)'+DIGITIZ(10,:)')/2)'; talimprefpt;  end % note that the longitudinal axes will always be oriented proximally, flexion axes will be oriented laterally, and third axes will be oriented anteriorly % Making axes fit convention for the left foot if side == 'l' ttib = -ttib; tcal = -tcal; if imp==2 ltibimp = -ltibimp; ttalimp = -ttalimp; ltib2 = ltibimp; ftib2 = ftibimp; ttib2 = ttibimp; %duplicate tibial implant coordinate frame - to be attached to tibia ltal = ltalimp; ftal = ftalimp; ttal = ttalimp; %duplicate talar implant coordinate frame - to be attached to talus elseif imp==3 ttalimp = -ttalimp; ttibimp = -ttibimp; ltib2 = ltibimp;ftib2 = ftibimp;ttib2 = ttibimp; ltal = ltalimp;ftal = ftalimp;ttal = ttalimp; end elseif imp > 1 ltib2 = ltibimp;ftib2 = ftibimp;ttib2 = ttibimp; ltal = ltalimp;ftal = ftalimp;ttal = ttalimp; end  %% plot the systems and the reference markers (check to make sure they are oriented properly) clf hold on plot_marks(S_TIBIA) plot_marks(S_CALCA) if imp > 1 plot_marks(S_TALUS) plot_marks(S_TIBIM) plot_marks(S_TALIM) end plot_sys(calrefpt,fcal,lcal,tcal,80) plot_sys(tibrefpt,ftib,ltib,ttib,80) 190  if imp > 1 plot_sys(tal2refpt,ftal,ltal,ttal,80) plot_sys(tibimprefpt,ftibimp,ltibimp,ttibimp,80) plot_sys(talimprefpt,ftalimp,ltalimp,ttalimp,80) end axis('equal') view(ftib) hold off disp('Axis systems in the ankle ') %pause keyboard  %% DETERMINE JOINT ANGLES AND RELATIVE DISPLACEMENTS % load the continuous files disp('CONTINUOUS DATA') % load data % must convert C# dat file to csv first. filename = [NAME,'.csv']; filesuff = NAME; workstr = [ 'load -ascii ', filename]; failstr = [filesuff, ' = NaN;']; filesuff %eval(workstr) eval(workstr,failstr) %eval([ filesave, ' = ', filesuff,';']) % analyze continuous data eval(['A =', NAME,';']) %this sets A equal to the optotrak motion file A = A(2:size(A,1),:); if imp > 1 % Define 4 corner global(optotrak) frame  vectors  from  origin(static  refpt)  in  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% dim_STAR_MtibStal; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  191  c1a c2a c3a c4a  = = = =  x1a*ftibimp x2a*ftibimp x3a*ftibimp x4a*ftibimp  + + + +  y1a*ttibimp y2a*ttibimp y3a*ttibimp y4a*ttibimp  + + + +  z1a*ltibimp; z2a*ltibimp; z3a*ltibimp; z4a*ltibimp;  c1b c2b c3b c4b  = = = =  x1b*ftalimp x2b*ftalimp x3b*ftalimp x4b*ftalimp  + + + +  y1b*ttalimp y2b*ttalimp y3b*ttalimp y4b*ttalimp  + + + +  z1b*ltalimp; z2b*ltalimp; z3b*ltalimp; z4b*ltalimp;  end if size(A,2) > 1 % initialize error matrix, which summarizes the transformation errors ERR = ones(size(A,1),3); %initialize displacement and angle matrices DISPL = ones(size(A,1),3); ANGLE = ones(size(A,1),3); if imp > 1 ERR = ones(size(A,1),6); %initialize corner coordinate arrays C1tibb = ones(size(A,1),3); C2tibb = ones(size(A,1),3); C3tibb = ones(size(A,1),3); C4tibb = ones(size(A,1),3);  % % % % %  C1tibi C2tibi C3tibi C4tibi  = = = =  ones(size(A,1),3); ones(size(A,1),3); ones(size(A,1),3); ones(size(A,1),3);  C1talb C2talb C3talb C4talb  = = = =  ones(size(A,1),3); ones(size(A,1),3); ones(size(A,1),3); ones(size(A,1),3);  C1tali C2tali C3tali C4tali  = = = =  ones(size(A,1),3); ones(size(A,1),3); ones(size(A,1),3); ones(size(A,1),3);  %initialize transform arrays TR_tal = ones(4,4,size(A,1)); TR_talimp = ones(4,4,size(A,1)); TR_tib = ones(4,4,size(A,1)); TR_tibimp = ones(4,4,size(A,1)); %initialize relative displacement magnitude arrays 192  TIB_CORNERS = ones(size(A,1),4); TAL_CORNERS = ones(size(A,1),4); end for k = 1:(size(A,1)) %BASE = mark_mat(A(k,:), baseframe); CAL = mark_mat(A(k,:), calca_m); TIB = mark_mat(A(k,:), tibia_m); if imp > 1 TAL = mark_mat(A(k,:), talus_m); TIBIMP = mark_mat(A(k,:), tib_implant_m); TALIMP = mark_mat(A(k,:), tal_implant_m); end if size(CAL,1) > 2 && size(TIB,1) > 2 % Calculating Calcaneus Position/Orientation with respect to Tibia [calpt, Trcal, trs(calrefpt,CAL,S_CALCA,errthresh,2); [tibpt, Trtib, trs(tibrefpt,TIB,S_TIBIA,errthresh,2);  Errcal]  =  Errtib]  =  if Errcal > maxthresh || Errtib > maxthresh caltibang = [NaN NaN NaN]; tibpt = [NaN NaN NaN]; calpt = [NaN NaN NaN]; else caltibang = ankle_angles(Trtib,Trcal,ftib,ltib,ttib,fcal,lcal,tcal); %here tib is the reference and cal is the target segment end ANGLE(k,:) = caltibang; defined angles (alpha, beta, gamma)  %ANGLE is an array of the JCS  caltibvec = calpt - tibpt; %  rotate  vectors  from  tibial  and  calcaneal  coordinate  systems % to the current position according to JCS convention f_jcs = rot(Trtib,ftib'); l_jcs = rot(Trcal,lcal'); t_jcs = ucross(l_jcs,f_jcs); % determining components of caltibvec along the axes of the JCS (ie. q1 - lateral, q2 - anterior, q3 - compression/superior translation) DISPL(k,1) = dot(caltibvec',f_jcs); DISPL(k,2) = dot(caltibvec',t_jcs); DISPL(k,3) = dot(caltibvec',l_jcs); 193  if imp > 1 if k ==1 %translate the reference point for the tibia/talus to the starting point of the implant to eliminate previous migration/subsidence effects [tib2refpt, N1, Errn1] = trs(tibimprefpt,TIBIMP,S_TIBIM,errthresh,2); tibimprefpt = tib2refpt; S_TIBIM = TIBIMP; S_TIBIA2 = TIB; [tal2refpt, N2, trs(talimprefpt,TALIMP,S_TALIM,errthresh,2); talimprefpt = tal2refpt; S_TALIM = TALIMP; S_TALUS = TAL; end  Errn2]  =  %TIBIAL IMPLANT if size(TIB,1) > 2 && size(TIBIMP,1) > 2 [tib2pt, Trtib, trs(tib2refpt,TIB,S_TIBIA2,errthresh,2); [tibimppt, Trtibimp, trs(tibimprefpt,TIBIMP,S_TIBIM,errthresh,2);  Errtib]  =  Errtibimp]  =  if Errtib > maxthresh || Errtibimp > maxthresh tibpt = [NaN NaN NaN]; tibimppt = [NaN NaN NaN]; else % %  TR_tib(:,:,k) = Trtib; TR_tibimp(:,:,k) = Trtibimp; % determining C1tibb(k,:) C1tibi(k,:) C2tibb(k,:) C2tibi(k,:) C3tibb(k,:) C3tibi(k,:) C4tibb(k,:) C4tibi(k,:)  corner position in current frame = rot(Trtib,c1a') + tib2pt'; = rot(Trtibimp,c1a') + tibimppt'; = rot(Trtib,c2a') + tib2pt'; = rot(Trtibimp,c2a') + tibimppt'; = rot(Trtib,c3a') + tib2pt'; = rot(Trtibimp,c3a') + tibimppt'; = rot(Trtib,c4a') + tib2pt'; = rot(Trtibimp,c4a') + tibimppt';  % calculating relative displacement between tibial implant and bone for each corner 194  TIB_CORNERS(k,1) = tibimppt') - (rot(Trtib,c1a') + tib2pt')); TIB_CORNERS(k,2) = tibimppt') - (rot(Trtib,c2a') + tib2pt')); TIB_CORNERS(k,3) = tibimppt') - (rot(Trtib,c3a') + tib2pt')); TIB_CORNERS(k,4) = tibimppt') - (rot(Trtib,c4a') + tib2pt'));  norm((rot(Trtibimp,c1a')  +  norm((rot(Trtibimp,c2a')  +  norm((rot(Trtibimp,c3a')  +  norm((rot(Trtibimp,c4a')  +  end end % TALAR IMPLANT if size(TAL,1) > 2 && size(TALIMP,1) > 2 [talpt, Trtal, trs(tal2refpt,TAL,S_TALUS,errthresh,2); [talimppt, Trtalimp, trs(talimprefpt,TALIMP,S_TALIM,errthresh,2);  Errtal]  =  Errtalimp]  =  if Errtal > maxthresh || Errtalimp > maxthresh talpt = [NaN NaN NaN]; talimppt = [NaN NaN NaN]; else % %  TR_tal(:,:,k) = Trtal; TR_talimp(:,:,k) = Trtalimp; % determining C1talb(k,:) = C1tali(k,:) = C2talb(k,:) = C2tali(k,:) = C3talb(k,:) = C3tali(k,:) = C4talb(k,:) = C4tali(k,:) =  corner position in current frame rot(Trtal,c1b') + talpt'; rot(Trtalimp,c1b') + talimppt'; rot(Trtal,c2b') + talpt'; rot(Trtalimp,c2b') + talimppt'; rot(Trtal,c3b') + talpt'; rot(Trtalimp,c3b') + talimppt'; rot(Trtal,c4b') + talpt'; rot(Trtalimp,c4b') + talimppt';  % calculating relative displacement between talar implant and bone for each corner TAL_CORNERS(k,1) = norm((rot(Trtalimp,c1b') + talimppt') - (rot(Trtal,c1b') + talpt')); TAL_CORNERS(k,2) = norm((rot(Trtalimp,c2b') + talimppt') - (rot(Trtal,c2b') + talpt')); TAL_CORNERS(k,3) = norm((rot(Trtalimp,c3b') + talimppt') - (rot(Trtal,c3b') + talpt')); TAL_CORNERS(k,4) = norm((rot(Trtalimp,c4b') + talimppt') - (rot(Trtal,c4b') + talpt')); end 195  end ERR(k,:) = [k Errtib Errcal Errtal Errtibimp Errtalimp]; else ERR(k,:) = [k Errtib Errcal]; end  else caltibang = [NaN NaN NaN]; calpt = [NaN NaN NaN]; tibpt = [NaN NaN NaN];  end end else disp('No data at this position') Errcal = NaN; Errtib = NaN; end %fixing angle rotation direction for right foot if side == 'r' ANGLE(:,1) = -ANGLE(:,1); %ANGLE(:,2) = -ANGLE(:,2); ANGLE(:,3) = -ANGLE(:,3); end %% Plotting JCS displacements and angles and the 4 corner relative displacement magnitudes x = size(DISPL,1)/opto_freq; if imp == 1 Proper_Output = [DISPL, ANGLE, ERR]; clf; hold on plot((1/opto_freq):(1/opto_freq):x,DISPL(:,1),'k','linewidth',2) plot((1/opto_freq):(1/opto_freq):x,DISPL(:,2),'b','linewidth',2) plot((1/opto_freq):(1/opto_freq):x,DISPL(:,3),'r','linewidth',2) xlabel('Time (s)','fontsize',12) ylabel('Displacement (mm)','fontsize',12) leg = legend('q1 (flexion axis - lateral +ve)', 'q2 (floating axis anterior +ve)', 'q3 (long axis compression +ve)','Location','Best'); set(leg,'FontSize',9); title(['Intact ' LOAD ': Translation of JCS Origin'],'fontsize',14) 196  set(gca, 'ygrid','on','box','on','fontsize', 12) saveas(gcf,['IntactJCSdispl' LOAD],'emf') clf; hold on plot((1/opto_freq):(1/opto_freq):x,ANGLE(:,1),'k','linewidth',2) plot((1/opto_freq):(1/opto_freq):x,ANGLE(:,2),'b','linewidth',2) plot((1/opto_freq):(1/opto_freq):x,ANGLE(:,3),'r','linewidth',2) xlabel('Time (s)','fontsize',12) ylabel('Angle (deg)','fontsize',12) leg = legend('\alpha (flexion axis - DF +ve)', '\beta (third axis - INV +ve)', '\gamma (long axis - IR +ve)','Location','Best'); set(leg,'FontSize',9); title(['Intact - ' LOAD ': Joint Rotation Angles'],'fontsize',14) set(gca, 'ygrid','on','box','on','fontsize', 12) saveas(gcf,['IntactJCSangles' LOAD],'emf') elseif imp == 2 % 1-3 4-6 7-10 11-14 15-17 18-20 21-23 24-26 27-29 30-32 33-35 36-38 39-41 42-44 45-47 48-50 51-53 54-56 57-59 60-62 63-68 Proper_Output = [DISPL, ANGLE, TIB_CORNERS, TAL_CORNERS, C1tibb, C1tibi, C2tibb, C2tibi, C3tibb, C3tibi, C4tibb, C4tibi, C1talb, C1tali, C2talb, C2tali, C3talb, C3tali, C4talb, C4tali, ERR]; clf; hold on plot((1/opto_freq):(1/opto_freq):x,DISPL(:,1),'k','linewidth',2) plot((1/opto_freq):(1/opto_freq):x,DISPL(:,2),'b','linewidth',2) plot((1/opto_freq):(1/opto_freq):x,DISPL(:,3),'r','linewidth',2) xlabel('Time (s)','fontsize',12) ylabel('Displacement (mm)','fontsize',12) leg = legend('q1 (flexion axis - lateral +ve)', 'q2 (floating axis anterior +ve)', 'q3 (long axis compression +ve)','Location','Best'); set(leg,'FontSize',9); title(['STAR - ' LOAD ': Translation of JCS Origin'],'fontsize', 14) set(gca, 'ygrid','on','box','on','fontsize', 12) saveas(gcf,['STAR-JCSdispl' LOAD],'emf') clf; hold on plot((1/opto_freq):(1/opto_freq):x,ANGLE(:,1),'k','linewidth',2) plot((1/opto_freq):(1/opto_freq):x,ANGLE(:,2),'b','linewidth',2) plot((1/opto_freq):(1/opto_freq):x,ANGLE(:,3),'r','linewidth',2) xlabel('Time (s)','fontsize',12) ylabel('Angle (deg)','fontsize',12) leg = legend('\alpha (flexion axis - DF +ve)', '\beta (third axis - INV +ve)', '\gamma (long axis - IR +ve)','Location','Best'); set(leg,'FontSize',9); title(['STAR - ' LOAD ': Joint Rotation Angles'],'fontsize',14) set(gca, 'ygrid','on','box','on','fontsize', 12) saveas(gcf,['STAR-JCSangles' LOAD],'emf') clf; hold on 197  plot((1/opto_freq):(1/opto_freq):x,TIB_CORNERS(:,1),'k','linewidth',2) plot((1/opto_freq):(1/opto_freq):x,TIB_CORNERS(:,2),'b','linewidth',2) plot((1/opto_freq):(1/opto_freq):x,TIB_CORNERS(:,3),'r','linewidth',2) plot((1/opto_freq):(1/opto_freq):x,TIB_CORNERS(:,4),'g','linewidth',2) xlabel('Time (s)','fontsize',12) ylabel('Displacement Magnitude (mm)','fontsize',12) leg = legend('Corner 1 (anterolateral)', 'Corner 2 (anteromedial)', 'Corner 3 (posterolateral)', 'Corner 4 (posteromedial)','Location','Best'); set(leg,'FontSize',9); title(['STAR - ' LOAD ': Implant Relative Displacements Tibia'],'fontsize',14) set(gca, 'ygrid','on','box','on','fontsize', 12) saveas(gcf,['STAR-TibRelDispl' LOAD],'emf') clf; hold on plot((1/opto_freq):(1/opto_freq):x,TAL_CORNERS(:,1),'k','linewidth',2) plot((1/opto_freq):(1/opto_freq):x,TAL_CORNERS(:,2),'b','linewidth',2) plot((1/opto_freq):(1/opto_freq):x,TAL_CORNERS(:,3),'r','linewidth',2) plot((1/opto_freq):(1/opto_freq):x,TAL_CORNERS(:,4),'g','linewidth',2) xlabel('Time (s)','fontsize',12) ylabel('Displacement Magnitude (mm)','fontsize',12) leg = legend('Corner 1 (anterolateral)', 'Corner 2 (anteromedial)', 'Corner 3 (posterolateral)', 'Corner 4 (posteromedial)','Location','Best'); set(leg,'FontSize',9); title(['STAR - ' LOAD ': Implant Relative Displacements Talus'],'fontsize',14) set(gca, 'ygrid','on','box','on','fontsize', 12) saveas(gcf,['STAR-TalRelDispl' LOAD],'emf') else Proper_Output = [DISPL, ANGLE, TIB_CORNERS, TAL_CORNERS, C1tibb, C1tibi, C2tibb, C2tibi, C3tibb, C3tibi, C4tibb, C4tibi, C1talb, C1tali, C2talb, C2tali, C3talb, C3tali, C4talb, C4tali, ERR]; clf; hold on plot((1/opto_freq):(1/opto_freq):x,DISPL(:,1),'k','linewidth',2) plot((1/opto_freq):(1/opto_freq):x,DISPL(:,2),'b','linewidth',2) plot((1/opto_freq):(1/opto_freq):x,DISPL(:,3),'r','linewidth',2) xlabel('Time (s)','fontsize',12) ylabel('Displacement (mm)','fontsize',12) leg = legend('q1 (flexion axis - lateral +ve)', 'q2 (floating axis anterior +ve)', 'q3 (long axis compression +ve)','Location','Best'); 198  set(leg,'FontSize',9); title(['Agility ' LOAD ': Translation Origin'],'fontsize',14) set(gca, 'ygrid','on','box','on','fontsize', 12) saveas(gcf,['Agility-JCSdispl' LOAD],'emf')  of  JCS  clf; hold on plot((1/opto_freq):(1/opto_freq):x,ANGLE(:,1),'k','linewidth',2) plot((1/opto_freq):(1/opto_freq):x,ANGLE(:,2),'b','linewidth',2) plot((1/opto_freq):(1/opto_freq):x,ANGLE(:,3),'r','linewidth',2) xlabel('Time (s)','fontsize',12) ylabel('Angle (deg)','fontsize',12) leg = legend('\alpha (flexion axis - DF +ve)', '\beta (third axis - INV +ve)', '\gamma (long axis - IR +ve)','Location','Best'); set(leg,'FontSize',9); title(['Agility - ' LOAD ': Joint Rotation Angles'],'fontsize',14) set(gca, 'ygrid','on','box','on','fontsize', 12) saveas(gcf,['Agility-JCSangles' LOAD],'emf') clf; hold on plot((1/opto_freq):(1/opto_freq):x,TIB_CORNERS(:,1),'k','linewidth',2) plot((1/opto_freq):(1/opto_freq):x,TIB_CORNERS(:,2),'b','linewidth',2) plot((1/opto_freq):(1/opto_freq):x,TIB_CORNERS(:,3),'r','linewidth',2) plot((1/opto_freq):(1/opto_freq):x,TIB_CORNERS(:,4),'g','linewidth',2) xlabel('Time (s)','fontsize',12) ylabel('Displacement Magnitude (mm)','fontsize',12) leg = legend('Corner 1 (anterolateral)', 'Corner 2 (anteromedial)', 'Corner 3 (posterolateral)', 'Corner 4 (posteromedial)','Location','Best'); set(leg,'FontSize',9); title(['Agility - ' LOAD ': Implant Relative Displacements Tibia'],'fontsize',14) set(gca, 'ygrid','on','box','on','fontsize', 12) saveas(gcf,['Agility-TibRelDispl' LOAD],'emf') clf; hold on plot((1/opto_freq):(1/opto_freq):x,TAL_CORNERS(:,1),'k','linewidth',2) plot((1/opto_freq):(1/opto_freq):x,TAL_CORNERS(:,2),'b','linewidth',2) plot((1/opto_freq):(1/opto_freq):x,TAL_CORNERS(:,3),'r','linewidth',2) plot((1/opto_freq):(1/opto_freq):x,TAL_CORNERS(:,4),'g','linewidth',2) xlabel('Time (s)','fontsize',12) ylabel('Displacement Magnitude (mm)','fontsize',12)  199  leg = legend('Corner 1 (anterolateral)', 'Corner (anteromedial)', 'Corner 3 (posterolateral)', 'Corner (posteromedial)','Location','Best'); set(leg,'FontSize',9); title(['Agility - ' LOAD ': Implant Relative Displacements Talus'],'fontsize',14) set(gca, 'ygrid','on','box','on','fontsize', 12) saveas(gcf,['Agility-TalRelDispl' LOAD],'emf') end  2 4  -  eval('ERRF = ERR;') dlmwrite '.csv'],Proper_Output,'delimiter',',','precision',16)  ([name_of_output  200  G.2 ANKLE_ANGLES.M  function [JCS]=ankle_angles(Trf,Trt,ff,lf,tf,ft,lt,tt) % Modified Sept 12, 2011 by Kurt McInnes % function spine_angles.m % modified from find_angles.m, Oct. 21, 1997 % by David Wilson % this function finds the Cardan agles of flexion, ad/adduction and % axial rotation of the spine as defined by the standardization proposal % of Cole et al, J. Biomech Eng. 115:344-349, Nov. 1993 % Input: t % Output: the matrix CA: column 1: flexion; column 2: inv/ev; % column 3: int/ext rot i = 1; % Determine the orientations of these axes in the reference and target segments % fi,li,ti refer to the axes in the reference segment: tibia % fj,lj,tj refer to the axes in the target segment: calcaneus fj = Trt(2:4,2:4)*ft'; lj = Trt(2:4,2:4)*lt'; tj = Trt(2:4,2:4)*tt'; fi = Trf(2:4,2:4)*ff'; li = Trf(2:4,2:4)*lf'; ti = Trf(2:4,2:4)*tf'; % Normalize these vectors fi = fi/norm(fi); li = li/norm(li); ti = ti/norm(ti); fj = fj/norm(fj); lj = lj/norm(lj); tj = tj/norm(tj); % Determine the unit vectors e1,e2 and e3 e1 = fi; e3 = lj; e2 = cross(e3,e1)/norm(cross(e1,e3));  201  %  Calculate the magnitude and direction of the Cardan angles  %plantarflexion/dorsiflexion v1 = (e3 - (e3'*e1)*e1)/norm(e3 - (e3'*e1)*e1); %projecting e3 and initial e3 position (li) onto plane normal to flexion axis and normalizing v2 = (li - (li'*e1)*e1)/norm(li - (li'*e1)*e1); JCS(i,1) = 180/pi*acos(v1'*v2); if e2'*li > 0 convention  %DF is +ve according to Wu 2002 JCS  JCS(i,1) = -JCS(i,1); end %inversion/eversion v3 = (li - (li'*e2)*e2)/norm(li - (li'*e2)*e2); %projecting initial e3 (li) onto plane normal to inv/ev axis - by definition e3 belongs to this plane already JCS(i,2) = 180/pi*acos(e3'*v3); if cross(e2,e3)'*v3 > 0  %INV is +ve  JCS(i,2) = -JCS(i,2); end %internal/external rotation v4 = (e1 - (e1'*e3)*e3)/norm(e1 - (e1'*e3)*e3); v5 = (fj - (fj'*e3)*e3)/norm(fj - (fj'*e3)*e3); JCS(i,3) = 180/pi*acos(v5'*v4);  if v5'*e2 > 0 JCS(i,3) = -JCS(i,3);  %IR is +ve  end % remove complex parts of angles JCS = real(JCS);  202  G.3 TRS.M  function [NOW, T, Err] = trs(THEN,REFNOW,REFTHEN,errthresh,option) % trs.m % [NOW, T, Err] = trs(THEN,REFNOW,REFTHEN,errthresh) % this function transforms the coordinates of the % points in the matrix THEN to the coordinate % system defined by the reference points REFNOW % that were in the system REFTHEN % % modified March 30, 2000: if option 2 is selected, % then the points are considered to match exactly [1 2 3 4] in refthen % corresponds to [1 2 3 4] in refnow if size(REFNOW,1) < 3 | size(REFTHEN,1) < 3 NOW = [NaN NaN NaN]; Err = NaN; T = NaN .* eye(4); return end % determine order of points if nargin < 4, errthresh = 1.5, end [Or,Err,For] = best_order4(REFTHEN,REFNOW,errthresh); % option 2 allows the order to be prescribed if points are % known to correspond if nargin > 4 if option == 2 minsize = min([size(REFNOW,1) size(REFTHEN,1)]) ; For = 1:minsize; Or = 1:minsize; end end % determine transformation matrix [T,Err] = vwd(REFTHEN(For,:),REFNOW(Or,:));  % transform NOW = transform(T,THEN);  203  G.4 VWD.M  function [T, err] = vwd(A,Q) % vwd.m % started June 30, 1995 by Dave Wilson % % based on the algorithm developed by Veldpaus, Woltring, Dortmans, J. Biomechanics, % V. 21, 1988, pp 45-54 % This takes as input the original positions of the reference markers % and the final positions of the reference markers, and generates % the rotation matrix R and the translation vector v between them % % The rows of A are the initial positions % The rows of Q are the final positions  % n is the number of points defining the reference system n = size(A,1); G = zeros(3,3); % a and p are the average vectors: row vectors a = (1/n)*sum(A); p = (1/n)*sum(Q); % G is the average matrix for i = 1:n g = (Q(i,:)-p)'*(A(i,:)-a); G = G+g; end G = 1/n*G; ad = adj(G); detg = det(G); P = G'*G; j1 = P(1,1) + P(2,2) + P(3,3); pad = adj(P); j2 = pad(1,1) + pad(2,2) + pad(3,3); 204  j3 = detg*detg; % find beta1, beta2, beta3 eps = 10E-10; x=1; y=1; h1 = sqrt(j2)/j1; h2 = detg*sqrt(j1)/j2; test = 1000; while test > eps Det = x*y - h1*h2; help1 = 0.5*(1-x*x+2*h1*y); help2 = 0.5*(1 - y*y + 2*h2*x); dx = (y*help1 + h1*help2)/Det; dy = (h2*help1 + x*help2)/Det; test = (dx*dx/x*x + dy*dy/y*y); x = x+dx; y = y+dy; end x = x+dx; y = y+dy; beta1 = x*sqrt(j1); beta2 = y*sqrt(j2); beta3 = detg; R = (beta1*G + ad)*inv(P + beta2*eye(3)); % v is the translation vector v = p - (R*a')'; % compute final transformation  position  of  the  points  predicted  by  calculated  for i = 1:size(A,1) F(i,:) = [v + (R*(A(i,:))')']; end % determine position  the  error  in  the  predicted  position  and  the  actual 205  point_error = F-Q; total_error = 0; max_error = 0.0000000001; for j = 1:size(A,1) total_error = total_error+norm(point_error(j,:)); if norm(point_error(j,:)) > max_error max_error = norm(point_error(j,:)); end end % error can be the total position (total_error) % or the maximum error  difference  between  predicted  and  actual  err = total_error; %err = max_error; % set up a 4X4 transformation matrix containing v and R T(1,:) = [1 0 0 0]; T(2:4,1) = v'; T(2:4,2:4) = R;  206  APPENDIX H: JCS ANGLE PLOTS  207  208  209  210  211  212  213  214  215  216  217  218  APPENDIX I: APPLIED LOADING: MOMENT-ANGLE PLOTS  219  220  221  222  223  224  225  226  227  228  229  230  APPENDIX J: DATA TABLES  Table 18: Peak tibial micromotion magnitudes. Data given as mean values ± standard deviation (in mm).  Uncompressed Compressed  Agility STAR Agility STAR  PF-DF 0.436 ± 0.619 0.214 ± 0.183 0.222 ± 0.070 0.484 ± 0.358  INV-EV 0.257 ± 0.172 0.098 ± 0.025 0.240 ± 0.115 0.152 ± 0.049  IR-ER 0.344 ± 0.149 0.200 ± 0.046 0.240 ± 0.163 0.129 ± 0.075  Table 19: Peak talar micromotion magnitudes. Data given as mean values ± standard deviation (in mm).  Uncompressed Compressed  Agility STAR Agility STAR  PF-DF 2.772 ± 1.363 0.728 ± 0.269 1.214 ± 0.505 0.789 ± 0.328  INV-EV 1.460 ± 0.889 0.643 ± 0.176 1.020 ± 0.815 0.633 ± 0.310  IR-ER 0.904 ± 0.322 0.396 ± 0.188 0.237 ± 0.145 0.206 ± 0.130  Table 20: Motion Coupling Ratios for PF-DF loading direction. Ratios are shown as mean ± SD  INV-EV IR-ER  Compression 15 300 15 300  Intact 0.175 ± 0.055 0.138 ± 0.054 0.132 ± 0.051 0.136 ± 0.065  Agility 0.159 ± 0.075 0.088 ± 0.027 0.155 ± 0.045 0.145 ± 0.010  STAR 0.158 ± 0.086 0.161 ± 0.090 0.130 ± 0.060 0.147 ± 0.101  Table 21: Motion coupling ratios for INV-EV loading direction. Ratios are shown as mean ± SD  PF-DF IR-ER  Compression 15 75 15 75  Intact 1.867 ± 0.730 1.866 ± 0.696 0.756 ± 0.280 0.815 ± 0.248  Table 22: Motion coupling ratios for IR-ER loading direction  PF-DF INV-EV  Compression 15 300 15 300  Intact 0.704 ± 0.112 0.629 ± 0.217 0.584 ± 0.141 0.686 ± 0.298  Agility 1.170 ± 0.367 0.843 ± 0.412 0.687 ± 0.123 0.522 ± 0.150  STAR 1.365 ± 0.418 1.101 ± 0.318 0.498 ± 0.305 0.453 ± 0.227  Agility 0.505 ± 0.129 0.200 ± 0.150 0.441 ± 0.127 0.618 ± 0.293  STAR 0.444 ± 0.174 0.352 ± 0.158 0.374 ± 0.245 0.672 ± 0.213  231  Table 23: Peak medial/lateral (q1) joint translations (mean ± SD in millimeters)  PF-DF INV-EV IR-ER  Compression 15 N 300 N 15 N 75 N 15 N 300 N  Intact 3.29 ± 1.77 6.34 ± 2.85 8.92 ± 6.19 9.25 ± 6.26 5.19 ± 4.90 5.10 ± 5.35  Agility 4.03 ± 1.84 4.15 ± 1.35 13.65 ± 4.39 14.25 ± 5.59 6.88 ± 3.26 5.45 ± 4.13  STAR 1.78 ± 0.84 3.29 ± 1.23 11.39 ± 6.36 10.91 ± 6.51 4.74 ± 1.39 4.68 ± 2.66  Compression 15 N 300 N 15 N 75 N 15 N 300 N  Intact 4.12 ± 1.58 2.84 ± 1.40 5.75 ± 2.01 6.53 ± 2.16 5.02 ± 2.60 3.20 ± 3.01  Agility 2.72 ± 0.99 2.99 ± 1.95 5.43 ± 1.50 5.27 ± 2.64 6.66 ± 3.16 2.74 ± 1.83  STAR 4.35 ± 1.17 7.25 ± 2.25 6.71 ± 2.45 5.74 ± 2.91 4.61 ± 2.65 3.46 ± 2.72  Table 24: Peak anterior/posterior (q2) joint translations (mean ± SD in millimeters)  PF-DF INV-EV IR-ER  Table 25: Peak compression/distraction (q3) joint translations (mean ± SD in millimeters)  PF-DF INV-EV IR-ER  Compression 15 N 300 N 15 N 75 N 15 N 300 N  Intact 6.09 ± 2.28 6.24 ± 3.12 5.33 ± 2.82 5.54 ± 2.46 2.68 ± 1.76 0.73 ± 0.45  Agility 5.94 ± 1.65 6.27 ± 2.50 5.02 ± 1.26 3.96 ± 2.18 3.00 ± 1.72 1.01 ± 0.50  STAR 8.27 ± 4.13 11.60 ± 5.69 7.36 ± 3.34 5.87 ± 3.77 2.46 ± 1.77 0.32 ± 0.23  232  

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