A Thesis Entitled the Effects of Radial Core Decompression on Lunate

A Thesis entitled

The Eﬀects of Radial Core Decompression on Lunate and Scaphoid Kinematics

by Andrew E. Smith

Submitted to the Graduate Faculty as partial fulﬁllment of the requirements for the Master of Science in Mechanical Engineering

Dr. Mohamed Samir Hefzy, Committee Chair

Dr. Vijay Goel, Committee Member

Dr. Michael Dennis, Committee Member

Dr. Abdul-Azim Mustapha, Committee Member

Dr. Patricia R. Komuniecki, Dean College of Graduate Studies

This document is copyrighted material. Under copyright law, no parts of this document may be reproduced without the expressed permission of the author. An Abstract of The Eﬀects of Radial Core Decompression on Lunate and Scaphoid Kinematics by Andrew E. Smith

Submitted to the Graduate Faculty as partial fulﬁllment of the requirements for the Master of Science in Mechanical Engineering The University of Toledo May 2012

Kienbocks disease causes degeneration of the lunate bone in the wrist leading to pain and reduced function of the joint. Clinical studies have found a new technique, radial core decompression (RCD) to be clinically eﬀective in improving early stage

Kienbock’s disease. However, there have been no biomechanical studies characterizing the changes in wrist kinematics following the RCD procedure. The purpose of this study is to determine the changes in lunate and scaphoid motions following the RCD procedure.

This study employs an electromagnetic 3-dimensional tracking system, Polhemus

3-SPACE to measure the motions of the lunate, scaphoid, and third metacarpal in four cadaveric specimens. Specimens were partially dissected and sutures were attached to

ﬁve major tendons used for wrist motion. Motion sensors were installed on the lunate, scaphoid, and third metacarpal, and a source was installed on the radius. CT scans were taken of the specimens and digitally reconstructed to determine the relationships between bony coordinate systems and sensor coordinate systems. Wrist specimens were installed in a custom test rig and weights were attached to the sutured tendons to simulate muscle tone. The wrists were passively moved through Flexion/Extension and Radial/Ulnar Deviation motion cycles with motion data collected at various positions through the cycles.

iii After collecting motion data for intact wrist specimens, RCD procedures were performed and motion data was collected for the post-RCD wrists. Joint Coordinate

Systems were developed for each specimen and test results were calculated as ﬂexion, ulnar deviation, and pronation angles for each position of Flexion/Extension and Ra- dial/Ulnar Deviation motion. Results were normalized so that statistical comparisons could be performed.

Results shows statistically signiﬁcant diﬀerences in wrist motion following the

RCD technique. However, most of these diﬀerences were less than 4 degrees. This suggests there are minimal clinically-relevant changes in wrist kinematics following the RCD technique.

iv This work is dedicated to my late mother, Lynn Janet Fluster.

Thank You Acknowledgments

I extend my fullest gratitude to Dr. Mohamed Samir Hefzy. Thank you for your support, guidance, and patience throughout my master’s program. Thank you for the opportunities you gave me, for pushing me, and for providing me with the learning experiences that exceeded my expectations for graduate school.

This project would not have been possible without the help of many others. I would like to thank Dr. Philip Nowicki, Dr. Abdul-Azim Mustapha, Dr. Chad Smith, and the rest of the Department of Orthopaedic Surgery for coming forward with this project idea, and providing not only ﬁnancial support, but the skilled hands and minds to complete the study. I would like to thank my fellow lab mate, Amey Kelkar for helping me with testing. I would like to Dan Ingraham, Zach Nielsen, and Vasanth

Allampalli for broadening my MATLAB knowledge. I extend a great thank you to

Dr. Michael Dennis and the CT Scanner technicians who found the time to provide me with their expertise and assistance in scanning and processing the data for many specimens. I would also like to thank Dr. Vijay Goel and Mr. David Dick for sharing their knowledge and the use of equipment necessary to the success of the project.

Additionally, I would like to thank the faculty and staﬀ of the College of Engineering for their assistance with my work.

To my friends and family, thank you for you unending support and patience.

Carrie Cochran, thank you for waiting.

vi Contents

Abstract iii

Acknowledgments vi

Contents vii

List of Tables x

List of Figures xx

List of Abbreviations xxvi

1 Introduction 1

1.1 Wrist Anatomy ...... 1

1.1.1 Bony Anatomy ...... 2

1.1.1.1 Forearm ...... 2

1.1.1.2 Carpus and Metacarpals ...... 2

1.1.2 Ligamentous Anatomy ...... 3

1.1.3 Tendon Anatomy ...... 4

1.1.4 Wrist Motions ...... 4

1.2 Kienbocks Disease ...... 5

1.2.1 Core Decompression Surgery ...... 6

1.3 Previous Biomechanical Studies ...... 7

1.4 Scope of Study ...... 13

vii 2 Experimental Set-up 24

2.1 Motion Tracking ...... 24

2.2 Specimen Preparation ...... 25

2.3 Laser Tracker Attachment ...... 27

2.4 Test Apparatus ...... 27

2.5 Testing ...... 28

2.6 RCD Procedure ...... 29

3 Data Analysis 38

3.1 CT Reconstruction ...... 39

3.2 Coordinate Systems ...... 40

3.2.1 Radius ...... 40

3.2.2 Carpal Bones ...... 40

3.2.3 Third Metacarpal ...... 41

3.2.4 Source and Sensors ...... 41

3.3 Radial Bony Coordinate System Derivation ...... 41

3.4 Source Coordinate System Derivation ...... 43

3.5 Carpal (Lunate and Scaphoid) Bony Coordinate System Derivation . 45

3.6 Third Metacarpal Bony Coordinate System Derivation ...... 47

3.7 Sensor Coordinate System Derivation ...... 48

3.8 Source-Sensor Transformation Derivation ...... 50

3.9 Joint Coordinate Systems ...... 52

3.10 Data Processing ...... 55

4 Results 69

4.1 Flexion/Extension Results ...... 69

4.1.1 Intact Specimen Results ...... 70

4.1.2 Post-RCD Specimen Results ...... 72

viii 4.2 Radial/Ulnar Deviation Results ...... 73

4.2.1 Intact Specimen Results ...... 73

4.2.2 Post-RCD Specimen Results ...... 75

5 Discussion and Conclusions 131

5.1 In-plane motions during FEM testing ...... 132

5.2 Out-of-plane motions during FEM testing ...... 133

5.2.1 Pronation/Supination ...... 133

5.2.2 Radial/Ulnar Deviation ...... 135

5.3 In-plane motions during RUD testing ...... 136

5.4 Out-of-plane motions during RUD testing ...... 136

5.4.1 Flexion ...... 136

5.4.2 Pronation ...... 137

5.5 Eﬀects of RCD on Scaphoid and Lunate Kinematics ...... 138

5.5.1 FEM Testing ...... 139

5.5.2 RUD Testing ...... 142

5.6 Inﬂuence of Experimental Setup Factors ...... 144

5.7 Previous Biomechanical Studies on RCD ...... 146

5.8 Conclusions ...... 147

5.9 Limitations and Future Work ...... 147

References 178

A Normalized Specimen Data 183

B Transformation Matrix Program 240

C Data Normalization Program 253

D Results Comparison Program 267

ix List of Tables

2.1 Attributes of Tested Specimens ...... 25

4.1 Tendon Loads at Neutral Wrist Position ...... 76

4.2 Wrist Position during FEM Testing for Specimen 1 ...... 76

4.3 Wrist Position during FEM Testing for Specimen 2 ...... 77

4.4 Wrist Position during FEM Testing for Specimen 3 ...... 78

4.5 Wrist Position during FEM Testing for Specimen 4 ...... 79

4.6 Comparison of FEM ranges for Test Specimens ...... 79

4.7 Wrist Position during RUD Testing for Specimen 1 ...... 80

4.8 Wrist Position during RUD Testing for Specimen 2 ...... 80

4.9 Wrist Position during RUD Testing for Specimen 3 ...... 81

4.10 Wrist Position during RUD Testing for Specimen 4 ...... 82

4.11 Comparison of RUD ranges for Test Specimens ...... 82

5.1 Multiple study comparison of in-plane carpal motion during wrist FEM

movement. * Wrist motions measured by radiocapitate joint motions. . . 150

5.2 Multiple study comparison of in-plane carpal motion during wrist RUD

movement ...... 150

5.3 Kinematic Eﬀects of RCD during FEM cycle for Specimen 1 Metacarpal 151

5.4 Kinematic Eﬀects of RCD during FEM cycle for Specimen 2 Metacarpal 151

5.5 Kinematic Eﬀects of RCD during FEM cycle for Specimen 3 Metacarpal 151

5.6 Kinematic Eﬀects of RCD during FEM cycle for Specimen 4 Metacarpal 152

x 5.7 Kinematic Eﬀects of RCD during FEM cycle for Specimen 1 Lunate . . . 152

5.8 Kinematic Eﬀects of RCD during FEM cycle for Specimen 2 Lunate . . . 152

5.9 Kinematic Eﬀects of RCD during FEM cycle for Specimen 3 Lunate . . . 153

5.10 Kinematic Eﬀects of RCD during FEM cycle for Specimen 4 Lunate . . . 153

5.11 Kinematic Eﬀects of RCD during FEM cycle for Specimen 1 Scaphoid . . 153

5.12 Kinematic Eﬀects of RCD during FEM cycle for Specimen 2 Scaphoid . . 154

5.13 Kinematic Eﬀects of RCD during FEM cycle for Specimen 3 Scaphoid . . 154

5.14 Kinematic Eﬀects of RCD during FEM cycle for Specimen 4 Scaphoid . . 154

5.15 Comparison of Eﬀects of RCD during FEM cycle for Lunate Flexion . . . 155

5.16 Comparison of Eﬀects of RCD during FEM cycle for Lunate Ulnar Deviation155

5.17 Comparison of Eﬀects of RCD during FEM cycle for Lunate Pronation . 155

5.18 Comparison of Eﬀects of RCD during FEM cycle for Scaphoid Flexion . 156

5.19 Comparison of Eﬀects of RCD during FEM cycle for Scaphoid Ulnar De-

viation ...... 156

5.20 Comparison of Eﬀects of RCD during FEM cycle for Scaphoid Pronation 157

5.21 Comparison of Eﬀects of RCD on Metacarpal Flexion ...... 158

5.22 Comparison of Eﬀects of RCD on Metacarpal Ulnar Deviation ...... 159

5.23 Comparison of Eﬀects of RCD on Metacarpal Pronation ...... 160

5.24 Kinematic Eﬀects of RCD during RUD cycle for Specimen 1 Metacarpal 161

5.25 Kinematic Eﬀects of RCD during RUD cycle for Specimen 2 Metacarpal 161

5.26 Kinematic Eﬀects of RCD during RUD cycle for Specimen 3 Metacarpal 162

5.27 Kinematic Eﬀects of RCD during RUD cycle for Specimen 4 Metacarpal 162

5.28 Kinematic Eﬀects of RCD during RUD cycle for Specimen 1 Lunate . . . 162

5.29 Kinematic Eﬀects of RCD during RUD cycle for Specimen 2 Lunate . . 163

5.30 Kinematic Eﬀects of RCD during RUD cycle for Specimen 3 Lunate . . . 163

5.31 Kinematic Eﬀects of RCD during RUD cycle for Specimen 4 Lunate . . . 163

5.32 Kinematic Eﬀects of RCD during RUD cycle for Specimen 1 Scaphoid . . 164

xi 5.33 Kinematic Eﬀects of RCD during RUD cycle for Specimen 2 Scaphoid . . 164

5.34 Kinematic Eﬀects of RCD during RUD cycle for Specimen 3 Scaphoid . . 165

5.35 Kinematic Eﬀects of RCD during RUD cycle for Specimen 4 Scaphoid . . 165

5.36 Comparison of Eﬀects of RCD during RUD cycle for Lunate Flexion . . . 165

5.37 Comparison of Eﬀects of RCD during RUD cycle for Lunate Ulnar Deviation166

5.38 Comparison of Eﬀects of RCD during RUD cycle for Lunate Pronation . 166

5.39 Comparison of Eﬀects of RCD during RUD cycle for Scaphoid Flexion . 167

5.40 Comparison of Eﬀects of RCD during RUD cycle for Scaphoid Ulnar De-

viation ...... 167

5.41 Comparison of Eﬀects of RCD during RUD cycle for Scaphoid Pronation 168

5.42 Comparison of Eﬀects of RCD on Metacarpal Flexion during RUD . . . . 169

5.43 Comparison of Eﬀects of RCD on Metacarpal Ulnar Deviation during RUD170

5.44 Comparison of Eﬀects of RCD on Metacarpal Pronation during RUD . . 171

5.45 Kinematic Eﬀects of Specimen Removal and Reinstallation During FEM

Cycle for Specimen 4 Metacarpal ...... 172

5.46 Kinematic Eﬀects of Specimen Removal and Reinstallation During FEM

Cycle for Specimen 4 Lunate ...... 172

5.47 Kinematic Eﬀects of Specimen Removal and Reinstallation During FEM

Cycle for Specimen 4 Scaphoid ...... 173

5.48 Kinematic Eﬀects of Specimen Removal and Reinstallation During RUD

Cycle for Specimen 4 Metacarpal ...... 173

5.49 Kinematic Eﬀects of Specimen Removal and Reinstallation During RUD

Cycle for Specimen 4 Lunate ...... 173

5.50 Kinematic Eﬀects of Specimen Removal and Reinstallation During RUD

Cycle for Specimen 4 Scaphoid ...... 174

A.1 Calculated Global Wrist Flexion for Specimen 1 during FEM Cycle, intact 184

xii A.2 Calculated Global Wrist Pronation for Specimen 1 during FEM Cycle, intact184

A.3 Calculated Global Wrist Ulnar Deviation for Specimen 1 during FEM

Cycle, intact ...... 185

A.4 Calculated Lunate Flexion for Specimen 1 during FEM Cycle, intact . . 185

A.5 Calculated Lunate Pronation for Specimen 1 during FEM Cycle, intact . 185

A.6 Calculated Lunate Ulnar Deviation for Specimen 1 during FEM Cycle,

intact ...... 186

A.7 Calculated Scaphoid Flexion for Specimen 1 during FEM Cycle, intact . 186

A.8 Calculated Scaphoid Pronation for Specimen 1 during FEM Cycle, intact 186

A.9 Calculated Scaphoid Ulnar Deviation for Specimen 1 during FEM Cycle,

intact ...... 187

A.10 Calculated Global Wrist Flexion for Specimen 1 during FEM Cycle, RCD 187

A.11 Calculated Global Wrist Pronation for Specimen 1 during FEM Cycle, RCD187

A.12 Calculated Global Wrist Ulnar Deviation for Specimen 1 during FEM

Cycle, RCD ...... 188

A.13 Calculated Lunate Flexion for Specimen 1 during FEM Cycle, RCD . . . 188

A.14 Calculated Lunate Pronation for Specimen 1 during FEM Cycle, RCD . 188

A.15 Calculated Lunate Ulnar Deviation for Specimen 1 during FEM Cycle, RCD189

A.16 Calculated Scaphoid Flexion for Specimen 1 during FEM Cycle, RCD . . 189

A.17 Calculated Scaphoid Pronation for Specimen 1 during FEM Cycle, RCD 189

A.18 Calculated Scaphoid Ulnar Deviation for Specimen 1 during FEM Cycle,

RCD...... 190

A.19 Calculated Global Wrist Flexion for Specimen 2 during FEM Cycle, intact 191

A.20 Calculated Global Wrist Pronation for Specimen 2 during FEM Cycle, intact191

A.21 Calculated Global Wrist Ulnar Deviation for Specimen 2 during FEM

Cycle, intact ...... 192

A.22 Calculated Lunate Flexion for Specimen 2 during FEM Cycle, intact . . 192

xiii A.23 Calculated Lunate Pronation for Specimen 2 during FEM Cycle, intact . 192

A.24 Calculated Lunate Ulnar Deviation for Specimen 2 during FEM Cycle,

intact ...... 193

A.25 Calculated Scaphoid Flexion for Specimen 2 during FEM Cycle, intact . 193

A.26 Calculated Scaphoid Pronation for Specimen 2 during FEM Cycle, intact 193

A.27 Calculated Scaphoid Ulnar Deviation for Specimen 2 during FEM Cycle,

intact ...... 194

A.28 Calculated Global Wrist Flexion for Specimen 2 during FEM Cycle, RCD 194

A.29 Calculated Global Wrist Pronation for Specimen 2 during FEM Cycle, RCD194

A.30 Calculated Global Wrist Ulnar Deviation for Specimen 2 during FEM

Cycle, RCD ...... 195

A.31 Calculated Lunate Flexion for Specimen 2 during FEM Cycle, RCD . . . 195

A.32 Calculated Lunate Pronation for Specimen 2 during FEM Cycle, RCD . 195

A.33 Calculated Lunate Ulnar Deviation for Specimen 2 during FEM Cycle, RCD196

A.34 Calculated Scaphoid Flexion for Specimen 2 during FEM Cycle, RCD . . 196

A.35 Calculated Scaphoid Pronation for Specimen 2 during FEM Cycle, RCD 196

A.36 Calculated Scaphoid Ulnar Deviation for Specimen 2 during FEM Cycle,

RCD...... 197

A.37 Calculated Global Wrist Flexion for Specimen 3 during FEM Cycle, intact 198

A.38 Calculated Global Wrist Pronation for Specimen 3 during FEM Cycle, intact198

A.39 Calculated Global Wrist Ulnar Deviation for Specimen 3 during FEM

Cycle, intact ...... 199

A.40 Calculated Lunate Flexion for Specimen 3 during FEM Cycle, intact . . 199

A.41 Calculated Lunate Pronation for Specimen 3 during FEM Cycle, intact . 199

A.42 Calculated Lunate Ulnar Deviation for Specimen 3 during FEM Cycle,

intact ...... 200

A.43 Calculated Scaphoid Flexion for Specimen 3 during FEM Cycle, intact . 200

xiv A.44 Calculated Scaphoid Pronation for Specimen 3 during FEM Cycle, intact 200

A.45 Calculated Scaphoid Ulnar Deviation for Specimen 3 during FEM Cycle,

intact ...... 201

A.46 Calculated Global Wrist Flexion for Specimen 3 during FEM Cycle, RCD 201

A.47 Calculated Global Wrist Pronation for Specimen 3 during FEM Cycle, RCD201

A.48 Calculated Global Wrist Ulnar Deviation for Specimen 3 during FEM

Cycle, RCD ...... 202

A.49 Calculated Lunate Flexion for Specimen 3 during FEM Cycle, RCD . . . 202

A.50 Calculated Lunate Pronation for Specimen 3 during FEM Cycle, RCD . 202

A.51 Calculated Lunate Ulnar Deviation for Specimen 3 during FEM Cycle, RCD203

A.52 Calculated Scaphoid Flexion for Specimen 3 during FEM Cycle, RCD . . 203

A.53 Calculated Scaphoid Pronation for Specimen 3 during FEM Cycle, RCD 203

A.54 Calculated Scaphoid Ulnar Deviation for Specimen 3 during FEM Cycle,

RCD...... 204

A.55 Calculated Global Wrist Flexion for Specimen 4 during FEM Cycle, intact 205

A.56 Calculated Global Wrist Pronation for Specimen 4 during FEM Cycle, intact205

A.57 Calculated Global Wrist Ulnar Deviation for Specimen 4 during FEM

Cycle, intact ...... 206

A.58 Calculated Lunate Flexion for Specimen 4 during FEM Cycle, intact . . 206

A.59 Calculated Lunate Pronation for Specimen 4 during FEM Cycle, intact . 206

A.60 Calculated Lunate Ulnar Deviation for Specimen 4 during FEM Cycle,

intact ...... 207

A.61 Calculated Scaphoid Flexion for Specimen 4 during FEM Cycle, intact . 207

A.62 Calculated Scaphoid Pronation for Specimen 4 during FEM Cycle, intact 207

A.63 Calculated Scaphoid Ulnar Deviation for Specimen 4 during FEM Cycle,

intact ...... 208

A.64 Calculated Global Wrist Flexion for Specimen 4 during FEM Cycle, RCD 208

xv A.65 Calculated Global Wrist Pronation for Specimen 4 during FEM Cycle, RCD208

A.66 Calculated Global Wrist Ulnar Deviation for Specimen 4 during FEM

Cycle, RCD ...... 209

A.67 Calculated Lunate Flexion for Specimen 4 during FEM Cycle, RCD . . . 209

A.68 Calculated Lunate Pronation for Specimen 4 during FEM Cycle, RCD . 209

A.69 Calculated Lunate Ulnar Deviation for Specimen 4 during FEM Cycle, RCD210

A.70 Calculated Scaphoid Flexion for Specimen 4 during FEM Cycle, RCD . . 210

A.71 Calculated Scaphoid Pronation for Specimen 4 during FEM Cycle, RCD 210

A.72 Calculated Scaphoid Ulnar Deviation for Specimen 4 during FEM Cycle,

RCD...... 211

A.73 Calculated Global Wrist Flexion for Specimen 1 during RUD Cycle, intact 212

A.74 Calculated Global Wrist Pronation for Specimen 1 during RUD Cycle, intact212

A.75 Calculated Global Wrist Ulnar Deviation for Specimen 1 during RUD

Cycle, intact ...... 213

A.76 Calculated Lunate Flexion for Specimen 1 during RUD Cycle, intact . . 213

A.77 Calculated Lunate Pronation for Specimen 1 during RUD Cycle, intact . 213

A.78 Calculated Lunate Ulnar Deviation for Specimen 1 during RUD Cycle,

intact ...... 214

A.79 Calculated Scaphoid Flexion for Specimen 1 during RUD Cycle, intact . 214

A.80 Calculated Scaphoid Pronation for Specimen 1 during RUD Cycle, intact 214

A.81 Calculated Scaphoid Ulnar Deviation for Specimen 1 during RUD Cycle,

intact ...... 215

A.82 Calculated Global Wrist Flexion for Specimen 1 during RUD Cycle, RCD 215

A.83 Calculated Global Wrist Pronation for Specimen 1 during RUD Cycle, RCD215

A.84 Calculated Global Wrist Ulnar Deviation for Specimen 1 during RUD

Cycle, RCD ...... 216

A.85 Calculated Lunate Flexion for Specimen 1 during RUD Cycle, RCD . . . 216

xvi A.86 Calculated Lunate Pronation for Specimen 1 during RUD Cycle, RCD . 216

A.87 Calculated Lunate Ulnar Deviation for Specimen 1 during RUD Cycle, RCD217

A.88 Calculated Scaphoid Flexion for Specimen 1 during RUD Cycle, RCD . . 217

A.89 Calculated Scaphoid Pronation for Specimen 1 during RUD Cycle, RCD 217

A.90 Calculated Scaphoid Ulnar Deviation for Specimen 1 during RUD Cycle,

RCD...... 218

A.91 Calculated Global Wrist Flexion for Specimen 2 during RUD Cycle, intact 219

A.92 Calculated Global Wrist Pronation for Specimen 2 during RUD Cycle, intact219

A.93 Calculated Global Wrist Ulnar Deviation for Specimen 2 during RUD

Cycle, intact ...... 220

A.94 Calculated Lunate Flexion for Specimen 2 during RUD Cycle, intact . . 220

A.95 Calculated Lunate Pronation for Specimen 2 during RUD Cycle, intact . 220

A.96 Calculated Lunate Ulnar Deviation for Specimen 2 during RUD Cycle,

intact ...... 221

A.97 Calculated Scaphoid Flexion for Specimen 2 during RUD Cycle, intact . 221

A.98 Calculated Scaphoid Pronation for Specimen 2 during RUD Cycle, intact 221

A.99 Calculated Scaphoid Ulnar Deviation for Specimen 2 during RUD Cycle,

intact ...... 222

A.100Calculated Global Wrist Flexion for Specimen 2 during RUD Cycle, RCD 222

A.101Calculated Global Wrist Pronation for Specimen 2 during RUD Cycle, RCD222

A.102Calculated Global Wrist Ulnar Deviation for Specimen 2 during RUD

Cycle, RCD ...... 223

A.103Calculated Lunate Flexion for Specimen 2 during RUD Cycle, RCD . . . 223

A.104Calculated Lunate Pronation for Specimen 2 during RUD Cycle, RCD . 223

A.105CalculatedLunate Ulnar Deviation for Specimen 2 during RUD Cycle, RCD224

A.106Calculated Scaphoid Flexion for Specimen 2 during RUD Cycle, RCD . . 224

A.107Calculated Scaphoid Pronation for Specimen 2 during RUD Cycle, RCD 224

xvii A.108Calculated Scaphoid Ulnar Deviation for Specimen 2 during RUD Cycle,

RCD...... 225

A.109Calculated Global Wrist Flexion for Specimen 3 during RUD Cycle, intact 226

A.110CalculatedGlobal Wrist Pronation for Specimen 3 during RUD Cycle, intact226

A.111Calculated Global Wrist Ulnar Deviation for Specimen 3 during RUD

Cycle, intact ...... 227

A.112Calculated Lunate Flexion for Specimen 3 during RUD Cycle, intact . . 227

A.113Calculated Lunate Pronation for Specimen 3 during RUD Cycle, intact . 227

A.114Calculated Lunate Ulnar Deviation for Specimen 3 during RUD Cycle,

intact ...... 228

A.115Calculated Scaphoid Flexion for Specimen 3 during RUD Cycle, intact . 228

A.116Calculated Scaphoid Pronation for Specimen 3 during RUD Cycle, intact 228

A.117Calculated Scaphoid Ulnar Deviation for Specimen 3 during RUD Cycle,

intact ...... 229

A.118Calculated Global Wrist Flexion for Specimen 3 during RUD Cycle, RCD 229

A.119Calculated Global Wrist Pronation for Specimen 3 during RUD Cycle, RCD229

A.120Calculated Global Wrist Ulnar Deviation for Specimen 3 during RUD

Cycle, RCD ...... 230

A.121Calculated Lunate Flexion for Specimen 3 during RUD Cycle, RCD . . . 230

A.122Calculated Lunate Pronation for Specimen 3 during RUD Cycle, RCD . 230

A.123CalculatedLunate Ulnar Deviation for Specimen 3 during RUD Cycle, RCD231

A.124Calculated Scaphoid Flexion for Specimen 3 during RUD Cycle, RCD . . 231

A.125Calculated Scaphoid Pronation for Specimen 3 during RUD Cycle, RCD 231

A.126Calculated Scaphoid Ulnar Deviation for Specimen 3 during RUD Cycle,

RCD...... 232

A.127Calculated Global Wrist Flexion for Specimen 4 during RUD Cycle, intact 233

A.128CalculatedGlobal Wrist Pronation for Specimen 4 during RUD Cycle, intact233

xviii A.129Calculated Global Wrist Ulnar Deviation for Specimen 4 during RUD

Cycle, intact ...... 234

A.130Calculated Lunate Flexion for Specimen 4 during RUD Cycle, intact . . 234

A.131Calculated Lunate Pronation for Specimen 4 during RUD Cycle, intact . 234

A.132Calculated Lunate Ulnar Deviation for Specimen 4 during RUD Cycle,

intact ...... 235

A.133Calculated Scaphoid Flexion for Specimen 4 during RUD Cycle, intact . 235

A.134Calculated Scaphoid Pronation for Specimen 4 during RUD Cycle, intact 235

A.135Calculated Scaphoid Ulnar Deviation for Specimen 4 during RUD Cycle,

intact ...... 236

A.136Calculated Global Wrist Flexion for Specimen 4 during RUD Cycle, RCD 236

A.137Calculated Global Wrist Pronation for Specimen 4 during RUD Cycle, RCD236

A.138Calculated Global Wrist Ulnar Deviation for Specimen 4 during RUD

Cycle, RCD ...... 237

A.139Calculated Lunate Flexion for Specimen 4 during RUD Cycle, RCD . . . 237

A.140Calculated Lunate Pronation for Specimen 4 during RUD Cycle, RCD . 237

A.141CalculatedLunate Ulnar Deviation for Specimen 4 during RUD Cycle, RCD238

A.142Calculated Scaphoid Flexion for Specimen 4 during RUD Cycle, RCD . . 238

A.143Calculated Scaphoid Pronation for Specimen 4 during RUD Cycle, RCD 238

A.144Calculated Scaphoid Ulnar Deviation for Specimen 4 during RUD Cycle,

RCD...... 239

xix List of Figures

1-1 Anterior view of radius and ulna (right arm) [1] ...... 14

1-2 Left arm in standard anatomical position ...... 15

1-3 Distal articulating surfaces of the radius and ulna ...... 16

1-4 Posterior (a) and Anterior (b) aspects of the wrist ...... 16

1-5 Palmer aspect of wrist ligamenture (left arm)[2] ...... 17

1-6 Dorsal aspect of wrist ligamenture (left arm)[2] ...... 18

1-7 Attachment of ﬂexors on the palmar side of the forearm[3] ...... 19

1-8 Attachment of extensors on the dorsal side of the forearm[3] ...... 20

1-9 Range of motion for wrist ﬂexion/extension [4] ...... 21

1-10 Range of motion for wrist radial/ulnar deviation [4] ...... 21

1-11 Stages of Kienbock’s disease [5] ...... 22

1-12 Currettage and impaction of cancellous bone during core decompression [6] 23

2-1 Polhemus 3-SPACE Motion Tracking System ...... 30

2-2 Specimen with laser and sensors attached ...... 31

2-3 Prepared specimen with suture loops sewn into tendons (extensors not

visible) ...... 32

2-4 Test frame apparatus ...... 33

2-5 Wrist passively moving into extension during ﬂexion/extension testing . . 34

2-6 Wrist passively moving into radial deviation during ulnar/radial deviation

testing ...... 35

2-7 Approximate positions of the wrist during a ﬂexion/extension cycle . . . 36

xx 2-8 Approximate positions of the wrist during a radial/ulnar deviation cycle 37

3-1 Thresholding of CT slice ...... 56

3-2 Reconstructed CT scan solids imported into SolidWorks ...... 57

3-3 Palmar view of left forearm with radius bony coordinate system . . . . . 57

3-4 Palmar view of left forearm with lunate bony coordinate system . . . . . 58

3-5 Palmar view of left forearm with scaphoid bony coordinate system . . . . 58

3-6 Sagittal view of left ﬁnger illustrating metacarpal with bony system of axes 59

3-7 Source magnetic center and coordinate system ...... 60

3-8 Sensor magnetic center and coordinate system ...... 61

3-9 Construction of source and radius coordinate systems ...... 62

3-10 Construction of lunate sensor coordinate system ...... 63

3-11 Construction of scaphoid sensor coordinate system ...... 64

3-12 Construction of third metacarpal coordinate system ...... 65

3-13 Euler angle 3-2-1 rotation ...... 66

3-14 JCS for radiometacarpal joint ...... 67

3-15 JCS for radiolunate joint ...... 67

3-16 JCS for radioscaphoid joint ...... 68

4-1 Measured wrist bone ﬂexion/extension during FEM testing for intact Spec-

imen 1 ...... 83

4-2 Measured wrist bone ﬂexion/extension during FEM testing for intact Spec-

imen 2 ...... 84

4-3 Measured wrist bone ﬂexion/extension during FEM testing for intact Spec-

imen 3...... 85

4-4 Measured wrist bone ﬂexion/extension during FEM testing for intact Spec-

imen 4...... 86

xxi 4-5 Measured wrist bone pronation/supination during FEM testing for intact

Specimen 1 ...... 87

4-6 Measured wrist bone pronation/supination during FEM testing for intact

Specimen 2 ...... 88

4-7 Measured wrist bone pronation/supination during FEM testing for intact

Specimen 3...... 89

4-8 Measured wrist bone pronation/supination during FEM testing for intact

Specimen 4...... 90

4-9 Measured wrist bone radial/ulnar deviation during FEM testing for intact

Specimen 1 ...... 91

4-10 Measured wrist bone radial/ulnar deviation during FEM testing for intact

Specimen 2 ...... 92

4-11 Measured wrist bone radial/ulnar deviation during FEM testing for intact

Specimen 3...... 93

4-12 Measured wrist bone radial/ulnar deviation during FEM testing for intact

Specimen 4...... 94

4-13 Measured wrist bone ﬂexion/extension during FEM testing for Specimen

1 following RCD ...... 95

4-14 Measured wrist bone ﬂexion/extension during FEM testing for Specimen

2 following RCD ...... 96

4-15 Measured wrist bone ﬂexion/extension during FEM testing for Specimen

3 following RCD...... 97

4-16 Measured wrist bone ﬂexion/extension during FEM testing for Specimen

4 following RCD...... 98

4-17 Measured wrist bone pronation/supination during FEM testing for Spec-

imen 1 following RCD ...... 99

xxii 4-18 Measured wrist bone pronation/supination during FEM testing for Spec-

imen 2 following RCD ...... 100

4-19 Measured wrist bone pronation/supination during FEM testing for Spec-

imen 3 following RCD...... 101

4-20 Measured wrist bone pronation/supination during FEM testing for Spec-

imen 4 following RCD...... 102

4-21 Measured wrist bone radial/ulnar deviation during FEM testing for Spec-

imen 1 following RCD ...... 103

4-22 Measured wrist bone radial/ulnar deviation during FEM testing for Spec-

imen 2 following RCD ...... 104

4-23 Measured wrist bone radial/ulnar deviation during FEM testing for Spec-

imen 3 following RCD...... 105

4-24 Measured wrist bone radial/ulnar deviation during FEM testing for Spec-

imen 4 following RCD...... 106

4-25 Measured wrist bone radial/ulnar deviation during RUD testing for intact

Specimen 1 ...... 107

4-26 Measured wrist bone radial/ulnar deviation during RUD testing for intact

Specimen 2 ...... 108

4-27 Measured wrist bone radial/ulnar deviation during RUD testing for intact

Specimen 3...... 109

4-28 Measured wrist bone radial/ulnar deviation during RUD testing for intact

Specimen 4...... 110

4-29 Measured wrist bone ﬂexion/extension during RUD testing for intact Spec-

imen 1 ...... 111

4-30 Measured wrist bone ﬂexion/extension during RUD testing for intact Spec-

imen 2 ...... 112

xxiii 4-31 Measured wrist bone ﬂexion/extension during RUD testing for intact Spec-

imen 3...... 113

4-32 Measured wrist bone ﬂexion/extension during RUD testing for intact Spec-

imen 4...... 114

4-33 Measured wrist bone pronation/supination during RUD testing for intact

Specimen 1 ...... 115

4-34 Measured wrist bone pronation/supination during RUD testing for intact

Specimen 2 ...... 116

4-35 Measured wrist bone pronation/supination during RUD testing for intact

Specimen 3...... 117

4-36 Measured wrist bone pronation/supination during RUD testing for intact

Specimen 4...... 118

4-37 Measured wrist bone radial/ulnar deviation during RUD testing for Spec-

imen 1 following RCD ...... 119

4-38 Measured wrist bone radial/ulnar deviation during RUD testing for Spec-

imen 2 following RCD ...... 120

4-39 Measured wrist bone radial/ulnar deviation during RUD testing for Spec-

imen 3 following RCD...... 121

4-40 Measured wrist bone radial/ulnar deviation during RUD testing for Spec-

imen 4 following RCD...... 122

4-41 Measured wrist bone ﬂexion/extension during RUD testing for Specimen

1 following RCD ...... 123

4-42 Measured wrist bone ﬂexion/extension during RUD testing for Specimen

2 following RCD ...... 124

4-43 Measured wrist bone ﬂexion/extension during RUD testing for Specimen

3 following RCD...... 125

xxiv 4-44 Measured wrist bone ﬂexion/extension during RUD testing for Specimen

4 following RCD...... 126

4-45 Measured wrist bone pronation/supination during RUD testing for Spec-

imen 1 following RCD ...... 127

4-46 Measured wrist bone pronation/supination during RUD testing for Spec-

imen 2 following RCD ...... 128

4-47 Measured wrist bone pronation/supination during RUD testing for Spec-

imen 3 following RCD...... 129

4-48 Measured wrist bone pronation/supination during RUD testing for Spec-

imen 4 following RCD...... 130

5-1 Custom-modiﬁed Tekscan sensor ...... 174

5-2 Dorsal aspect of Specimen 1 with Tekscan sensor ...... 175

5-3 Palmar view of Specimen 1 with posts installed in distal cortex . . . . . 176

5-4 Palmar view of right wrist CT reconstruction ...... 177

xxv List of Abbreviations

CT ...... Computed Tomography CH ...... Capitohamate ligament DIC ...... Dorsal intercarpal ligament DICOM ...... Digital Imaging and Communications in Medicine DRC ...... Dorsal radiocarpal ligament ECRB/L ...... Extensor Carpi Radialis Brevis and Longus ECU ...... Extensor Carpi Ulnaris FEM ...... Flexion/Extension Motion FCR ...... Flexor Carpi Radialis Tendon FCU ...... Flexor Carpi Ulnaris ISB ...... International Society of Biomechanics JCS ...... Joint Coordinate System LRL ...... Long radiolunate ligament LT ...... Lunotriquetral ligament MCD ...... Metaphysial Core Decompression PVC ...... Polyvinyl Chloride RCD ...... Radial Core Decompression ROM ...... Range of Motion RSC ...... Radioscaphocapitate ligament RSL ...... Radioscapholunate ligament RUD ...... Radial/Ulnar Deviation Motion SC ...... Scaphocapitate ligament SL ...... Scapholunate ligament SLIL ...... Scapholunate Interosseous Ligament SRL ...... Short radiolunate ligament STL ...... Stereolithography STT ...... Scaphotrapeziotrapezoid ligament TC ...... Triquetrocapitate ligament TC2 ...... Trapeziocapitate ligament TH ...... Triquetrohamate ligament TT ...... Trapeziotrapezoid ligament

xxvi UC ...... Ulnocapitate ligament UL ...... Ulnolunate ligament UT ...... Ulnotriquetral ligament

xxvii Chapter 1

Introduction

Kienbocks disease is an uncommon, but not rare, aﬄiction in young people (20 to

40 years age). The disease causes degeneration of the lunate bone in the wrist leading to pain and reduced function of the joint. To date, the causes of the disease are still unclear and a variety of treatment methods exist. However, none of the treatments offer a clear, superior advantage. Additionally, some of the conventional treatments have potential side effects including arthritis. A new procedure, core decompression, shows promise to treat disease while minimizing side effects. In order to quantify the effects of the procedure, it is important study both physiological and biomechanical effects of core decompression. Clinical studies on core decompression have already been published, but there is limited documentation of the biomechanical effects. This study focuses on the kinematic effects of core decompression on the carpal bones. In the remainder of this chapter, a brief review of wrist anatomy and Kienbocks disease are discussed. Additionally, previous wrist kinematics studies are presented.

1.1 Wrist Anatomy

The features of the bones comprising the wrist joint are ﬁrst discussed, followed by the ligaments holding them together, and ﬁnally the major tendons/muscles applying motor forces to move the bones. 1 1.1.1 Bony Anatomy

1.1.1.1 Forearm

The forearm consists of two bones: the radius and the ulna [1], as shown in Figure

1.4. In standard anatomical position (elbow fully extended with wrist fully supinated so the thumb points laterally), the ulna is located on the medial side of the forearm as shown in Figure 1.4. The proximal end of the ulna is C-shaped and forms the elbow joint with the humerus. The larger, more proximal portion of the C-shape is the olecranon process. The smaller, slightly more distal portion of the C-shape forms the coronoid process. The curved surface contained within the two processes is the trochlear notch. The distal end of the ulna articulates with both the radius and carpal bones. This small distal head features a styloid process with ligamentous attachment to the wrist. The lateral bone of the forearm, the radius, features a cylindrically- shaped proximal head. The terminal face of this head is concave and articulates with the humerus. The cylindrical face of the head rotates against the radial notch of the ulna to form the proximal radioulnar joint. The distal portion of the radius forms a broad head which articulates with the distal ulna to form the distal radioulnar joint.

The distal surface of the radial head is concave with two distinct articulating areas separated by a ridge as seen in Figure 1-3. The lateral area articulates with the scaphoid, and the medial area articulates with the lunate. The distal radial head also features a small lateral styloid process.

1.1.1.2 Carpus and Metacarpals

The carpus is a complex structure consisting of eight carpal bones positioned in two rows: the proximal carpal row and the distal carpal row [1], as seen in Figures

1-4. From lateral to medial, the proximal carpal row consists of the scaphoid (A), lunate (B), triquetrum (C), and pisiform (D) bones. The scaphoid and lunate provide

2 the primary compressive load transfer to the forearm through contact with the radius

(1) as shown in Figure 1-4. While the scaphoid articulates with only the radius, the lunate articulates with both the radius and the ulna (2) as shown in Figure 1-4. The distal carpal row, from lateral to medial, consists of the trapezium (E), trapezoid (F), capitate (G), and hamate (H) bones. The distal carpal row articulates with the ﬁve metacarpal bones [7] which create the bony framework of the hand as shown in Figure

1-4. The metacarpals are long bones with concave proximal heads and convex distal heads. The largest carpal bone, the capitate, articulates proximally with the lunate and scaphoid, and distally with the third metacarpal. Since the motion between the capitate and third metacarpal is so small, global wrist motions are typically measured by tracking the position of the capitate or the third metacarpal relative to the radius

[8].

1.1.2 Ligamentous Anatomy

Wrist ligaments control and stabilize the complex motions of the carpal bones.

Wrist ligamenture is complex and can be characterized using various means. A common scheme is to assign names based on major attachment ordered from proximal to distal or radial to ulnar [7]. Additionally, ligaments can be further speciﬁed by indicating their size (short, long, etc.) or location (dorsal, palmar, etc.).

Starting with the palmar radiocarpal ligaments, major stabilizers include the radioscaphocapitate (RSC), long radiolunate (LRL), radioscapholunate (RSL), and short radiolunate (SRL) ligaments as shown in Figure 1.4. The dorsal aspect consists primarily of two ligaments: the dorsal radiocarpal (DRC) ligament, originating on the dorsal radial rim and inserting into the lunate and triquetrum; and the dorsal intercarpal (DIC) ligament, originating on the dorsal triquetrum and attaching to the dorsal scaphoid and trapezoid as shown in Figure 1.4. The three ulnocarpal ligaments include the ulnocapitate (UC), ulnolunate (UL), and ulnotriquetral (UT)

3 ligaments. The midcarpal ligaments, found on the palmar portion of the wrist, include the scaphotrapeziotrapezoid (STT), scaphocapitate (SC), triquetrocapitate (TC), and triquetrohamate (TH) ligaments. The interosseous ligaments, featuring both dorsal and palmar sections, include the scapholunate (SL), lunotriquetral (LT), trapeziotrapezoid (TT), trapeziocapitate(TC2), and capitohamate (CH) ligaments.

1.1.3 Tendon Anatomy

Wrist motion is controlled via tendons attached to muscles in the forearm [1].

The major muscles/tendons are Flexor Carpi Radialis (FCR), Flexor Carpi Ulnaris

(FCU), Extensor Carpi Radialis Brevis and Longus (ECRB/L), and Extensor Carpi

Ulnaris (ECU) [1] [8] [3]. Volarly, the FCR attaches to the bases of the second and third metacarpals and the FCU attaches to the pisiform, hamate, and base of the

fifth metacarpal as shown in Figure 1.4. Dorsally, the ECRB/L inserts on the bases of the second and third metacarpals and the ECU inserts on the base of the fifth metacarpal [1] as shown in Figure 1.4. Coordination of the various muscles/tendons allows the wrist to actively flex/extend, radial/ulnar deviate, or a combination of the two (circumduction). Other tendon/muscles can contribute to the aforementioned motions, but the five listed structures are the primary motors. [8]

1.1.4 Wrist Motions

The normal wrist can ﬂex from about 85 degrees extension to 85 degrees ﬂexion shown in Figure 1.4. The wrist can deviate from approximately 15 degrees radial deviation to 45 degrees ulnar deviation shown in Figure 1.4.

4 1.2 Kienbocks Disease

Lunatomalacia, or Kienbock’s disease, was ﬁrst described in 1910 by Robert Kien- bock [5] . The disease is characterized by avascular necrosis of the lunate bone in the wrist. The disease is commonly classiﬁed using Lichtman’s criteria [5] described below and shown in Figure 1.4:

Stage I: Normal Radiograph

Stage II: Deﬁnite changes in radiodensity of lunate; possible minimal ﬂattening and collapse in height of the radial side of the lunate

Stage IIIA: Collapse of entire lunate without scaphoid rotation

Stage IIIB: Collapse of entire lunate; scapholunate dissociation; gap increases between scaphoid and lunate; scaphoid rotates so that it does not sit congruent with its articulating surface on the radius

Stage IV: Stage III plus general degenerative changes in other bones in carpus

The causes of Kienbock’s disease are not precisely known. Disruption of the vas- cular supply to lunate may lead to Kienbock’s disease [5]. The lunate is typically fed by vessels on the palmar and dorsal sides. At least three predictable vessel patterns exist: a single palmar or dorsal vessel, multiple palmar and dorsal vessels, and multiple palmar and dorsal vessels with a central anastomosis [9]. Repeated compressive loading of the wrist joint or any trauma to the joint can reduce blood supply with the

ﬁrst vessel pattern being most vulnerable. In addition, negative ulnar variance may lead to higher loads carried through the radius and lunate in the radiocarpal joint thereby increasing risk towards the disease [5] [10].

Due to the lack of known etiology, a variety of procedures, both surgical and non- surgical, exist to treat the disease. Surgical joint-leveling techniques are popular, such as ulnar-lengthening and radial-shortening [10]. In addition, radial-wedge osteotomies may be used to change the contour of the radiocarpal joint. These surgeries work to

5 remove compressive load oﬀ of the lunate and encourage revascularization. However, joint-leveling and wedge osteotomies may change the biomechanics of the wrist joint, leading to longterm problems such as arthritis. In late stage Kienbock’s disease, the lunate may be excised and/or carpal bones may be fused.

1.2.1 Core Decompression Surgery

Because of known biomechanical problems associated with the other surgical procedures, an increasingly-popular surgical technique for treating the disease is metaphyseal core decompression (MCD), ﬁrst introduced by Illarramendi [11]. During the procedure, the distal radius is approached through approximately a 4cm longitudinal incision along the radial border of the metaphysis. Caution is taken when distracting the radial nerve bundles out of the way. The extensor tendons are also distracted to reveal a broad area of the radial metaphysis. The periosteum covering the radius is incised and distracted to expose the bone. A 2cm by 0.5cm cortical window is cut into the distal radius with a bone saw or drill and osteotome. An osteotome or other instrument is used to cause trauma to the cancellous tissue inside the distal metaphysis by curettage and impaction as shown in Figure 1.4. The impacted cancellous bone is not removed. The cortical shell of bone is left intact to support the wrist joint. The periosteum is left open, but the skin is closed. A similar procedure is performed on the distal ulna with care taken to protect the distal sensory branch of the ulnar nerve.

The trauma to the cancellous bone and periosteum triggers a healing response which revascularizes the region including the carpus. As a result of the improved blood supply to the lunate, Kienbock’s disease may be prevented from progressing, and the lunate may even heal to normal.

Clinically, the eﬃcacy of the procedure is similar to other procedures that are more invasive [11]. In a study of twenty two patients who underwent MCD, ap-

6 proximately 72% of patients reported no pain by final follow-up visit. Patients were documented having 75% average grip strengths compared to their unaffected wrists after MCD. Ranges of motion of patients affected wrists were improved to 77% of the unaffected wrists during final check-ups. Additionally, the MCD procedure was not associated with many postoperative complications of joint-leveling surgeries including: nonunions, distal radioulnar joint incongruence, and ulnocarpal impingement

[11]. More recently, equivalent clinical success was reported performing the core decompression on just the radius [6] . This implies that MCD of the radius alone is enough to trigger the bodys biological reaction to revascularize the lunate. Radial core decompression (RCD) may be preferable over MCD of both forearm bones because it is less invasive.

1.3 Previous Biomechanical Studies

There are several published experimental studies found in the literature that explore various aspects of wrist biomechanics including both studies on wrist kinematics and on wrist joint loading/contact areas. In order to understand the biomechanical eﬀects of disease and injury on the wrist, it is important to be able to characterize normal wrist biomechanics as well.

Kinematics studies of wrist were published as early as 1896 involving radiographic studies of living subjects [12] . Other early studies relied on measuring the motion of long pins inserted into the carpal bones [13] and analyzing anatomy through dissection and plaster mold replicas of the bones [14]. As radiographic technology advanced, so did the methods of studying wrist kinematics. Studies using cineradiography to dynamically capture carpal bone motion were published as early as 1966 [15], and have been used by other investigators up through present times [16] [17].

As technology and computing power increased, new techniques for studying three

7 dimensional wrist kinematics became more viable. Instrumented spatial linkages have been used to measure joint kinematics [18]. Multiple researchers have also utilized three dimensional sonic digitization in their work to examine wrist motion [19] [20].

However, optical and electromagnetic systems have become increasingly popular for three dimensional motion tracking.

Several wrist kinematic studies have used optical systems. Patterson, et al. used optical marker tracking with both passive and active wrist motion simulators to examine wrist kinematics [21]. The setup in the study used reflective markers arranged in triads. Triads were pinned to each bone to be motion-tracked. A four camera system was used to track the markers. Knowing the exact relative orientation between the cameras allowed the location of the markers to be determined relative to each other in three dimensional space. In the active simulation, loading was applied to the wrist through cables attached to major tendons in the forearm. The other ends of these cables were attached to a marionette-like control, with which a researcher actively loaded the wrist so that it moved in a desired motion. In the passive setup, the cables attached to the tendons were no longer attached to the marionette controls, but looped together and tensioned with a hanging weight and elastic band. This provided co-contraction forces physiologically seen in the joint. The motion of the wrist was then actuated by a researcher directly moving the third metacarpal. In both cases, repeatable motion was ensured by attaching a laser to the third metacarpal and making sure the laser beam projection follows a predetermined path. In the experiment directly comparing active and passive wrist motion, Patterson, et al. found no significant differences in motion. In addition, the passive motion was easier to control and thus more repeatable. In another study by Moritomo, et al., a similar passive motion setup was used to evaluate the kinematics of the scaphotrapezio-trapezoidal

(STT) joint [22]. Computed tomography (CT) scans were reconstructed to visualize the surfaces of the bones during motion. The study found that trapezium-trapezoid

8 and trapezoid-capitate joints were virtually immobile.

Electromagnetic tracking systems are also feasible for studying wrist kinematics.

As with optical tracking systems, electromagnetic systems, such as the 3-SPACE system, can track six degree-of-freedom motion. Jackson, Hefzy, and Guo used the

3-SPACE system to track and wrist kinematics under physiological loading conditions

[3] [23]. The magnetic sensors were attached to custom-made acrylic posts that were screwed to the carpal bones creating rigid links between the sensors and bones. Loads were applied to the major extensors and flexors of the wrist to cause it to flex and extend. The results show that the lunate and scaphoid motions during wrist flexion and extension are virtually pure rotations. Supination/pronation and radial/ulnar deviations of the carpal bones accompanied their primary flexion/extension motions during wrist flexion/extension. Additionally, digitization of the articular surfaces of the radioulnar and radiolunate joints allowed for visualization of the joint surfaces during motion. During wrist flexion in this study, points on the articular surface of the lunate in the radiolunate moved from palmar to dorsal and points on the articular surface of the scaphoid in the radioscaphoid joint remained virtually motionless.

In a study published in 1997, Ishikawa, et al. compared the diﬀerences in measuring wrist kinematics with a 3-SPACE system versus biplanar radiography [24] .

The magnetic sensors were attached to the bones using similar methods to Jackson, et al [23]. Spherical markers were imbedded in the bones for radiographic registra- tion. Specimens were placed in a special jig to ﬁx wrist angle in varying degrees of

flexion/extension and radial/ulnar deviation. Angle measurement using the magnetic tracking system was not significantly different from the radiographic method with average differences between 0.0 and 2.0 degrees. The advantage of the magnetic system is that it can take continuous measurements during motion.

In Werner, et al., a computer-controlled wrist motion simulator is discussed [25]

. The simulator has six servo-actuated hydraulic cylinders which are each attached

9 to a major tendon involved in wrist motion. Force transducers are connected in series with the cylinders and tendons in order to monitor tendon loads. A three degree-of-freedom electrogoniometer is attached between the radius and second and third metacarpals to measure global wrist angles. 3-SPACE sensors can be attached to the carpal bones to track their motion [26]. The simulator uses a hybrid force- feedback control system to adjust tendon tensions until the desired position of the electrogoniometer is achieved. The system is capable of cyclic motions for simple planar movements such as ﬂexion/extension and ulnar/radial deviation as well as complex motions such as circumduction.

In Short, et al., significant hysteresis effects in lunate and scaphoid motion were observed [26]. For example, in cyclic wrist flexion/extension, the position of the lunate depends not just on the global wrist angle, but the direction of motion (going from extension to flexion versus flexion to extension).

In addition, to kinematic studies of the wrist, there have been several studies regarding load transmission and joint contact in the wrist. To determine load transfer across an articular surface and gain insight into contact pressures and areas, many studies have incorporated the use of pressure sensitive ﬁlm such as Prescale Fujiﬁlm

[27] [28] [29]. The film consists of two layers that inserted between the articular surfaces of the joint. When pressure is applied to an area of the film, it darkens relative to the pressure applied. The film can be manually compared to a calibrated color chart or scanned and analyzed using imaging software. The Fujifilm is limited in that it can only collect data one instance at a time, its readings are affected by moisture, and it cannot accurately measure shear forces.

In 1992, Short, et al. examined the eﬀects of simulated STT fusion and simulated lunate collapse on forces and pressures in the wrist [30]. The fusions were performed with the scaphoid in varying degrees of ﬂexion relative to the lunate. Kienbocks disease was simulated by performing osteotomies to create lunate collapse. Pressure

10 sensitive film was inserted into the radiocarpal and ulnocarpal joints through dorsal capsulotomy. Loads were applied to the individual flexor and extensor tendons. The results showed that when the STT fusions were performed with the scaphoid in neutral or extension, the radiolunate joint was unloaded. However, when the scaphoid was fused in flexion, no radiolunate unloading occurred. [30]

In several studies, Tekscan pressure sensors are used instead of Fujiﬁlm. The

Tekscan pressure sensors are constructed from two sheets on Mylar film that sandwich a special pressure-sensitive, conductive ink and can measure pressure in a grid-like fashion. The sensors are connected to a personal computer via a data acquisition dongle. When pressure is applied to the sensor, results are outputted to the computer graphically in real time. The Tekscan system can record at up to 100 samples per second. The sensors are thin, mostly waterproof, and can measure dynamic pressure and contact in real time. However, the system is very temperature sensitive and subject to drift effects dependent on loading rate. Depending on the model, the sensors can also be difficult to cut to fit the irregular contours of joints.

In Short, et al., the Tekscan system is incorporated into the servohydraulic wrist simulator to evaluate biomechanical eﬀects of SLIL sectioning [26]. A transverse dorsal capsulotomy of the radiocarpal and ulnocarpal joints is made to insert the pressure sensor. The sensor is then secured in place by carefully suturing it through the volar capsule to posts drilled into the palmar cortices of the radius and ulna. The wrist is cycled through motion in the simulator and tendon loads, pressure readings, and carpal positions are recorded. The SLIL is then progressively sectioned and motion testing is repeated. Results show that after sectioning the SLIL, the lunate and scaphoid show increased rotation during wrist motion. Additionally, result show that the pressures are distributed diﬀerently in the radiocarpal and ulnocarpal joints following the sectioning.

In Teurlings, et al., the Tekscan system was used to determine the changes in ra-

11 diocarpal and ulnocarpal joint pressures resulting from ulnar lengthening and changes in wrist position [30]. In the in-vitro study, axial compressive loads were externally applied to the forearm and wrist with the wrist in dorsiﬂexion. A Tekscan sensor was inserted into the radiocarpal and ulnocarpal joints through a dorsal capsulotomy to measure articular surface pressures. A turnbuckle installed in the ulna was used to change ulnar variance. Results from the study show that ulnar lengthening increased peak pressures at the ulnolunate joint.

However, there is a drawback to using the Tekscan system in the wrist. In 2002,

Short, et al., used the Tekscan system with the wrist simulator again to examine the effects of dorsal radiocarpal ligament sectioning and sensor insertion on lunate and scaphoid kinematics [31] . Results show that both the ligament disruption and insertion of the sensor affect lunate and scaphoid kinematics during wrist motion. In order get radiocarpal pressure data using Tekscan, normal wrist kinematic data must be sacrificed.

While previous research extensively investigated other treatments for Kienbocks disease, at the time of writing only one study had looked at the biomechanical effects of RCD on the wrist joint. In 2008, Sherman, et al. examined the effects of RCD on radiocarpal contact and force transmission [23]. Neutrally-positioned cadaver wrists were loaded in a compressive loading machine. The study used Fujifilm inserted into the radiocarpal/ulnocarpal joint to measure the effects of RCD. Additionally, forearm stiffness was calculated using the transducer and load cell in the loading machine.

The study showed no changes in contact area or force transmission across the joints.

However, there was a signiﬁcant decrease in forearm stiﬀness ( 14%) following the

RCD.

12 1.4 Scope of Study

The purpose of this study is to determine the kinematic effects of RCD on a normal wrist to determine if there is a kinematic component in addition to the physiological effects of the surgery. With the scarcity of biomechanical studies for RCD effects, especially kinematic effects, the rationale behind performing this study is simply that there are currently no published studies of the kinematic effects of RCD. Due to the simplicity and repeatability of the system used in Patterson, et al., a similar passive setup was chosen for this research [21].

Passive ﬂexion/extension and radial/ulnar deviation testing is performed on four wrist specimens using a custom-made setup. The experimental setup is explained in detail in Chapter 2.

In Chapter 3, the methods of data analysis and processing results are explained.

The coordinate system transformations are derived and the joint coordinate systems

(JCS) for the radiocarpal joints are developed. Additionally, a method for displaying the motion of the wrist bones is presented. This method combines the kinematic data from testing with topographical data of the bones from CT scan reconstruction.

The results for the study are presented in Chapter 4, and in Chapter 5, the results are discussed and conclusions are drawn. In Chapter 5, the results are discussed and conclusions are drawn for the study.

13 Figure 1-1: Anterior view of radius and ulna (right arm) [1]

14 Figure 1-2: Left arm in standard anatomical position

15 Figure 1-3: Distal articulating surfaces of the radius and ulna

Figure 1-4: Posterior (a) and Anterior (b) aspects of the wrist

16 Figure 1-5: Palmer aspect of wrist ligamenture (left arm)[2]

17 Figure 1-6: Dorsal aspect of wrist ligamenture (left arm)[2]

18 Figure 1-7: Attachment of ﬂexors on the palmar side of the forearm[3]

19 Figure 1-8: Attachment of extensors on the dorsal side of the forearm[3]

20 Figure 1-9: Range of motion for wrist ﬂexion/extension [4]

Figure 1-10: Range of motion for wrist radial/ulnar deviation [4]

21 Figure 1-11: Stages of Kienbock’s disease [5]

22 Figure 1-12: Currettage and impaction of cancellous bone during core decompression [6]

23 Chapter 2

Experimental Set-up

2.1 Motion Tracking

Complete characterization of the motion of a rigid body can be deﬁned by three orthogonal translations and three orthogonal rotations with respect to a reference frame. To completely capture the motion of bones in an experimental setting, all six degrees of freedom must be measured. In this study, the Polhemus 3-SPACE

Motion Tracking System is used to measure the motions of the bones in the wrist.

The 3-SPACE system uses electromagnetic ﬁeld technology to measure the complete three-dimensional motion of three sensors with respect to a source coordinate system.

The tracking equipment is shown in Figure 2.6 and Figure 2.6. The system used in this project consists of a main electronics unit (Figure 2.6) , a source, and three sensors (Figure 2.6). The electronics unit performs multiple tasks; it generates an output to the source to produce electromagnetic ﬁelds, receives analog sensed signals from the three sensors, digitizes the analog sensor signals, and outputs digital signal data to an attached personal computer. The computer is installed with DOS-based companion software to control the 3-SPACE system and record data.

The magnetic ﬁelds of the 3-SPACE system are aﬀected by paramagnetic objects, therefore the amount of ferrous metal in the experimental setup must be minimized.

24 2.2 Specimen Preparation

Four cadaveric arms were obtained from the university, through the Department

of Orthopaedic Surgery, after being used previously for shoulder research. The spec-

imens came amputated at mid-humerus and were obtained from individuals with

normal, healthy arms. Before being dissected, the specimens were screened for de-

generative factors that could aﬀect wrist biomechanics such as presence of arthritis

and evidence of previous surgery. The details of the selected specimens are listed

below in Table 2.1.

Specimen # Age (years) Gender Side 1 94 Male Left 2 55 Female Left 3 81 Male Left 4 57 Male Right

Table 2.1: Attributes of Tested Specimens

Once cleared for use, the specimens were prepared by removing soft tissues and leaving the joint capsules, ligaments, and tendons intact. More speciﬁcally, the elbow joints and interosseous membranes were left intact to preserve relative ulnar and radial anatomy in the specimens. Careful dissection was used to identify and free the distal portions of the major extensor and ﬂexor tendons of the wrist including the

Extensor Carpi Ulnaris (ECU), Extensor Carpi Radialis Brevis/Longus (ECRBL),

Flexor Carpi Ulnaris (FCU), and Flexor Carpi Radialis (FCR). Loops of suture were sewn into the distal portions of the tendons to allow loads to be applied to them as shown in Figure 2.6. The ulnohumeral joint was ﬁxed in 90 degrees of ﬂexion by a driving pin through the ulna and the humerus at the joint. The radiocapitellar joint was left unrestrained allowing the radius to rotate about its longitudinal axes. The humeral portion of the specimen was potted in 7.6-cm-diameter polyvinyl chloride

(PVC) pipe using quick-setting epoxy as shown in Figure 2.6. 25 Sensors were then rigidly connected to the lunate, scaphoid, and third metacarpal of each specimen. Since the carpal bones are small and located very closely together, it is impossible to directly attach the 3-SPACE sensors to the lunate and scaphoid.

Custom fixtures manufactured from Plexiglas and carbon fiber were used to attach the sensors to the carpal bones as shown in Figure 2.6. Each fixture consisted of a

2.5mm diameter carbon ﬁber post cemented to a Plexiglas platform. The platforms featured two threaded holes to match the attachment hole patterns on the sensors.

Nylon fasteners were used to attach the sensors to the platforms. Holes were drilled into the carpal bones and the posts were inserted and cemented into place using super glue. The sensors were attached in a manner so that they would not interfere with each other or the normal motion of the wrists.

The source was attached to the radius by a Plexiglas ﬁxture as shown in Figure

2.6. The source features a three-hole attachment pattern. The radius is large enough that the source can directly attach using two of the three holes. However, in order to attach the source more securely, an intermediate platform was used that bolted through the three holes on the source and three additional bolts into the radius.

Computer tomography (CT) scans were then taken of the specimens with the 3-

SPACE sensors installed to relate the sensor and source positions to their respective bones. The CT scans were performed on a Toshiba Aquilion helical CT scanner using the following parameters:

Modality: CT, bone

Slice thickness: 0.5mm x 64

Power: 120 KV

Gantry/detector Tilt: +0.0

Convolution kernel: FC30

The ﬁeld of view (FOV) was kept large enough to scan the entire specimen and attached sensors. Care was taken to reduce the eﬀects of artifacts on scan quality by

26 moving the sensor wires away from the areas of interest. This prevented the metal wires from creating artifacts that could obscure the clarity of the scan near the wrist joint.

2.3 Laser Tracker Attachment

A small laser pointer was installed on the third metacarpal to assist in tracking the wrist motion during testing. The laser that was used was a small cylinder with a button on the curved face to activate the beam as shown in Figure 2.6. A carbon

ﬁber post was attached to the laser and inserted into a hole drilled through the third metacarpal, rigidly attaching the laser to the bone. The laser was additionally secured by plastic ties holding it to the proximal portion of the middle ﬁnger.

2.4 Test Apparatus

The test apparatus consists of a custom, aluminum housing rigidly ﬁxed to the top of a wooden frame, as shown in Figure 2.6. The frame was constructed from 4cm by 9cm cross wooden planks pegged together with wooden dowel rods. The pegging was used to reduce the amount of ferrous metal in the setup that might interfere with the 3-SPACE sensors. A wooden board was fastened to the top of the platform to serve as a base for the aluminum housing. An opening 33cm by 28cm was made in the top of the platform to allow suspended weights to directly load the tendons of the specimen.

The aluminum housing is attached to the top of the frame using four stainless steel bolts as shown in Figure 2.6. The housing features a 6.4cm diameter cylindrical bore which accepts the humeral portion of a specimen potted in PVC pipe. Three stainless steel setscrews on the top of the housing secure the potted specimen when

27 tightened.

2.5 Testing

The potted portion of the specimen is inserted into the aluminum housing. The specimen is positioned so that the forearm is vertical, with the hand at the top.

Once in position, stainless steel setscrews in the housing are tightened to secure the specimen in a ﬁxed position. The apparatus positions the elbow of the specimen approximately one meter above the ﬂoor. Ninety-newton spring scales are attached to the suture loops in each freed tendon on the specimen. Weights hung from the scales apply load to the tendons so that the wrist maintains a neutral position.

During testing, the laser is turned on and the wrist of the specimen is moved passively in either ﬂexion/extension cycles or radial/ulnar deviation cycles. This is accomplished by articulating the metacarpals as shown in Figure 2.6 and Figure 2.6.

The researcher grips the specimen with both his hands using his thumbs and index and middle ﬁngers to ﬁrmly hold the metacarpals, especially the third metacarpal.

Care is taken not to touch and interfere with the attached motion sensors. For

ﬂexion/extension testing, the wrist is moved through multiple cycles starting from neutral to full extension to full ﬂexion and back to neutral. For radial/ulnar deviation testing, the wrist is moved through cycles starting from neutral to full radial deviation to full ulnar deviation and back to neutral. During testing, the projection of the laser beam on the ceiling follows a predetermined path ensuring repeatable motion.

The motion is serial static, meaning that the wrist motion is positioned at diﬀerent

flexion angles during the flexion/extension cycles and at different ulnar deviation angles during the radial/ulnar deviation cycles. Figure 2.6 and Figure 2.6 show the approximate positions of the wrist during a flexion/extension cycle and a radial/ulnar deviation cycle, respectively. At each position the kinematic data are measured and

28 recorded with the 3-SPACE system.

2.6 RCD Procedure

The core decompression procedure used in this study deviates slightly from the method previously mentioned in the Introduction. Speciﬁcally, the cortical window is created along the radial border of the metaphysis of the radius by means of a 1cm diameter drill bit. An osteotome is used to cause trauma to the cancellous tissue inside the distal metaphysis by curettage and impaction. Some of the fragmented bone is removed and the rest is impacted and left in the radius. The periosteum is left open, and the skin is not closed as it was previously removed during intact specimen preparation.

29 Figure 2-1: Polhemus 3-SPACE Motion Tracking System

30 Figure 2-2: Specimen with laser and sensors attached

31 32

Figure 2-3: Prepared specimen with suture loops sewn into tendons (extensors not visible) Figure 2-4: Test frame apparatus

33 Figure 2-5: Wrist passively moving into extension during ﬂexion/extension testing

34 Figure 2-6: Wrist passively moving into radial deviation during ulnar/radial deviation testing

35 Figure 2-7: Approximate positions of the wrist during a ﬂexion/extension cycle

36 Figure 2-8: Approximate positions of the wrist during a radial/ulnar deviation cycle

37 Chapter 3

Data Analysis

In this chapter, the steps for processing raw data into pertinent results are described in detail. Motion data was collected and recorded for several different positions during flexion/extension and ulnar/radial deviation testing using the 3-SPACE system as described in the Methods section. 3-SPACE data for each sensor at each position is recorded as a set of three rotations and three translations. Several steps are required to link this motion data with the CT scan data and produce meaning- ful results. First the CT scan data is reconstructed. Coordinate systems for the bones of interest and their attached sensors are defined and recreated in the 3-D CT reconstruction. Transformations from individual coordinate systems to an intermediate one are developed to relate the motion of the bones and their attached sensors.

Transformations from the sensor coordinate systems to the source coordinate system are developed. Individual transformations are combined to describe all spatial data in a single global radial bony coordinate system. Finally, the method of Joint Coor- dinate Systems (JCS) is introduced and the JCS for the radiolunate, radioscaphoid, and radiometacarpal joints are deﬁned to provide clinically relevant results.

38 3.1 CT Reconstruction

In order to relate the sensors and source systems to their respective bony coordinate systems, the previously obtained CT scans are analyzed and reconstructed.

Each complete CT scan consists of a series of images in an industry standard format,

DICOM. Each DICOM image is a cross-section of the scanned object at a speciﬁc interval of the scan. The DICOM images are displayed in grayscale. The shade of gray of each pixel indicates the radiodensity of that point in the image. The ordered stack of images constitutes the volume of the scan.

The DICOM format CT scans are imported to AbleSoft 3D-Doctor reconstruction software. During the import process, the CT slices are arranged in correct stacked order in a 3D space. Algorithms in the software are used to detect borders of objects in each slice by comparing densities between neighboring pixels. Preconﬁgured thresholding levels for bone are used to automatically separate it out from the rest of the scan area. After analyzing each slice, the program interpolates and constructs surfaces between the bony borders on each layer. The surfaces are sewn together to create volumes representative of the shape of each bone.

Despite the quality of the scans, metal objects in the specimen create streak and star-patterned artifacts that interfere with the automatic thresholding. Additional manual correction is performed by the user to improve reconstruction quality as shown in Figure 3.10. The CT slice is automatically thresholded to outline the radius, but includes artifacts (A). The artifacts are manually selected (B) and deleted (C). The

ﬁnal result is a CT slice containing the cleanly thresholded radius (D).

For each specimen, the reconstructions of the lunate, scaphoid, third metacarpal, radius, ulna, and attached sensors are exported from 3D-Doctor as stereolithography

(STL) ﬁles.

The STL ﬁles are imported to SolidWorks software as solid bodies as shown in

39 Figure 3.10. This allows for geometric coordinates of points on the surfaces of the bones and sensors to be located relative to the ﬁxed origin in the software. Transfor- mations are developed to and from the intermediate SolidWorks coordinate system for the bones and sensors.

3.2 Coordinate Systems

3.2.1 Radius

The radial bony coordinate system is defined as follows. The y-axis is defined by a vector drawn between a proximal point and a distal point on the radius. The proximal point is located at the center of the concave surface on the proximal head of the radius. The distal point is located on the distal radial head in the middle of the ridge dividing the fossas that articulate with the scaphoid and lunate. The x-axis is perpendicular to the plane formed by the y-axis and a vector drawn from the distal point of the y-axis to the tip of the styloid on the distal ulnar head. The z-axis is defined by two successive cross products making it perpendicular to the x-axis and y-axis. The origin is defined as the center of the distal articulating surface defined by the same point that distally defines the z-axis vector. For the left radius, the positive x-axis is dorsal, the positive y-axis is distal, and the positive z-axis is from radius to ulna as shown in Figure 3.10. For the right radius, the positive x-axis is palmar, the positive y-axis is proximal, and the positive z-axis is from ulna to radius.

3.2.2 Carpal Bones

The lunate and scaphoid bony coordinate systems are defined as having parallel corresponding axes to the radial bony coordinate system when the wrist is in neutral position, elbow flexed 90 degrees with the wrist supinated so that the hand lays flat in

40 the same plane as the humerus and forearm. The origins for the lunate and scaphoid systems are located at their respective volumetric centroids automatically calculated by SolidWorks. The lunate bony coordinate system is shown in Figure 3.10 and the scaphoid system in Figure 3.10.

3.2.3 Third Metacarpal

The third metacarpal bony coordinate system has an origin located midway between the base and head of the bone at the center of the tubular section. The y-axis is deﬁned by a line parallel to the line passing from the center of the distal head to the midpoint of the base as shown in Figure 3.10. The x-axis forms a sagittal plane with the y-axis that splits the metacarpal into mirrored halves. The z-axis is the common perpendicular to the x-axis and y-axis. For the right hand metacarpal, the positive x-axis is palmar, the positive y-axis is proximal, and the positive z-axis is from ulna to radius. For the left hand metacarpal, the positive x-axis is dorsal, the positive y-axis is distal, and the positive z-axis is from radius to ulna.

3.2.4 Source and Sensors

The sensor and source coordinate systems are deﬁned as shown in Figure 3.10 and

Figure 3.10.

3.3 Radial Bony Coordinate System Derivation

The transformation between the radial coordinate system and the SolidWorks coordinate system is developed as follows. As shown in Figure 3.10, rF sw is the point at the center of the concavity of the proximal radial head with respect to the

SolidWorks coordinate system. The point at the center of the distal articulating surface on the distal radial head with respect to the SolidWorks coordinate system is

41 rDsw. The point at the tip of the styloid process on the distal ulnar head with respect

to the SolidWorks coordinate system is rEsw. Derivations are shown for the left arm. The unit vector for the y-axis of the radius with respect to the SolidWorks coordinate system, rY sw is deﬁned by:

rDsw − rF sw rY sw = |rDsw − rF sw|

An intermediate vector for determining the x-axis is found:

rEsw − rDsw r23sw = |rEsw − rDsw|

The x-axis is then calculated as:

rY sw × r23sw rXsw = |rY sw × r23sw|

Finally, the z-axis can be calculated as:

rXsw × rY sw rZsw = |rXsw × rY sw|

The rotation matrix from the SolidWorks coordinate system to the radial bony

coordinate system, Rswr, is calculated as:

  rXsw     [Rswr] = r   Y sw    rZsw

Likewise, the rotation matrix from the radial bony coordinate system to the Solid-

Works coordinate system, Rrsw, is calculated as:

−1 T [Rrsw] = [Rswr] = [Rswr]

42 The origin of the radial bony coordinate system, Orsw, is taken as rDsw.

Orsw = Drsw

The transformation matrix from radial bony coordinate system to SolidWorks coordinate system is therefore:

  1 {0} [Brsw] =    T  Orsw [Rrsw]

And, the transformation matrix from SolidWorks coordinate system to radial bony coordinate system, Bswr, is the inverse:

−1 [Bswr] = [Brsw]

3.4 Source Coordinate System Derivation

To reconstruct the source coordinate system from the scans, the magnetic center, or source origin, is found based on dimensions of the source shown in Figure 3.10.

The magnetic center is shown as rsBsw in Figure 3.10. The orientation of the source coordinate system is determined by constructing the x-y plane parallel to the top surface of the source and coincident with the magnetic center. A line segment is drawn from magnetic center through the center of the front bolt hole on the sensor.

The end of this segment is projected on to the x-y plane to create point rsCsw. The x-axis for the source is drawn from rsBsw to rsCsw. Next, an x-y coplanar line segment is constructed from rsAsw to rsBsw to be perpendicular to the x-axis to create the y- axis. The direction of this segment is chosen so that the cross product between the x-axis and y-axis yields a positive z-axis emerging from the top of the source.

The unit vector for the x-axis of the source with respect to the SolidWorks coor-

43 dinate system, rsXsw is deﬁned by:

rsCsw − rsBsw rsXsw = |rsCsw − rsBsw|

The y-axis is then calculated as:

rsBsw − rsAsw rsY sw = |rsBsw − rsAsw|

Finally, the z-axis can be calculated as:

rsXsw × rsY sw rsZsw = |rsXsw × rsY sw|

The rotation matrix from the SolidWorks coordinate system to the source coordinate system, RswRs, is calculated as:

  rsXsw     [RswRs] = r   sY sw    rsZsw

Likewise, the rotation matrix from the source coordinate system to the SolidWorks coordinate system, RRssw, is calculated as:

−1 T [RRssw] = [RswRs] = [RswRs]

The origin of the source coordinate system, ORssw, is taken as RsBsw.

ORssw = RsBsw

The transformation matrix from source coordinate system to SolidWorks coordi-

nate system is therefore:

44   1 {0} [BRssw] =    T  ORssw [RRssw]

And, the transformation matrix from SolidWorks coordinate system to source coordinate system, BswRs, is the inverse:

−1 [BswRs] = [BRssw]

Therefore, any point described in the source coordinate system can be described in the SolidWorks coordinate system using the following equation:

rsw = [BRssw] {rsource}

Likewise, any point described in the source coordinate system can be described in the radial bony coordinate system using the following equation:

{rr} = [Bswr][BRssw] {rsource}

3.5 Carpal (Lunate and Scaphoid) Bony Coordi-

nate System Derivation

As with the radius and source, the transformations between carpal bony coordinate systems and their respective sensor coordinate systems must be developed by intermediate transformations to the SolidWorks coordinate system. The bony coordinate systems for the carpal must be developed while the wrist is in neutral position during the CT scan. During neutral wrist position, the bony coordinate systems for the carpal bones and radius are parallel to each other. Therefore, the rotation matrix from the SolidWorks coordinate system to the lunate bony coordinate system, Rswl,

45 is the same as the radial bony coordinate system:

    rXsw lXsw         [Rswl] = [Rswr] = r  = l   Y sw   Y sw      rZsw lZsw

The rotation matrix from the lunate bony coordinate system to the SolidWorks coordinate system, Rlsw, is calculated as:

−1 T [Rlsw] = [Rswl] = [Rswl]

The origin of the lunate bony coordinate system, Olsw, is taken as the lunates volumetric centroid location automatically calculated in SolidWorks as shown in Figure

3.10.

In neutral wrist position, the transformation matrix from lunate bony coordinate system to SolidWorks coordinate system is therefore:

  1 {0} [Blsw] =    T  Olsw [Rlsw]

Likewise, during neutral wrist position, the transformation matrix from Solid-

Works coordinate system to lunate bony coordinate system, Bswl, is the inverse:

−1 [Bswl] = [Blsw]

The transformations for the scaphoid are derived similarly using its centroid found in Figure 3.10.

46 3.6 Third Metacarpal Bony Coordinate System Deriva-

tion

To complete the derivations for the third metacarpal, the bony coordinate is sys-

tem is constructed as shown in Figure 3.10. The origin of the third metacarpal is

described by rmBsw in SolidWorks. The y-axis, mY sw, is formed by a segment parallel to the long axis of the bone passing through the origin. The proximal endpoint is

speciﬁed as rmCsw.

rmBsw − rmCsw rmY sw = |rmBsw − rmCsw|

The x-axis of the third metacarpal with respect to the SolidWorks coordinate system, rmXsw is deﬁned by perpendicular segment to the y-axis which together for a plane to split the bone sagittally:

rmAsw − rmBsw rmXsw = |rmAsw − rmBsw|

Since the segments are perpendicular, no intermediate vectors are needed and the z-axis is then calculated as:

rmXsw × rmY sw rmZsw = |rmXsw × rmY sw|

The rotation matrix from the SolidWorks coordinate system to the radial bony coordinate system, Rswm, is calculated as:

  rmXsw     [Rswm] = r   mY sw    rmZsw

47 Likewise, the rotation matrix from the third metacarpal bony coordinate system to the SolidWorks coordinate system, Rmsw, is calculated as:

−1 T [Rmsw] = [Rswm] = [Rswm]

The transformation matrix from third metacarpal coordinate system to Solid-

Works coordinate system is therefore:

  1 {0} [Bmsw] =    T  Omsw [Rmsw]

And, the transformation matrix from SolidWorks coordinate system to third metacarpal coordinate system, Bswm, is the inverse:

−1 [Bswm] = [Bmsw]

3.7 Sensor Coordinate System Derivation

To reconstruct the lunate sensor coordinate system from the scans, the magnetic center, or sensor origin, is found based on dimensions of the sensor shown in Figure

3.10. For the lunate sensor the magnetic center is shown as rlsBsw in Figure 3.10. The orientation of the sensor coordinate system is determined by constructing the x-y plane parallel to the top surface of the sensor and coincident with the magnetic center. A line segment is drawn from magnetic center through the back of the sensor where the wire attaches to the unit. The end of this segment is projected on to the x-y plane to create point rlsAsw. The x-axis for the source is drawn from rlsAsw to rlsBsw. Next, an x-y coplanar line segment is constructed from rlsCsw to rlsBsw to be perpendicular to the x-axis to create the y-axis. The direction of this segment is chosen so that the cross product between the x-axis and y-axis yields a positive z-axis

48 emerging from bottom of the sensor.

The unit vector for the x-axis of the sensor with respect to the SolidWorks coordinate system, rlsXsw is deﬁned by:

rlsBsw − rlsAsw rlsXsw = |rlsBsw − rlsAsw|

The y-axis is then calculated as:

rlsBsw − rlsCsw rlsY sw = |rlsBsw − rlsCsw|

Finally, the z-axis can be calculated as:

rlsXsw × rlsY sw rlsZsw = |rlsXsw × rlsY sw|

The rotation matrix from the SolidWorks coordinate system to the lunate sensor coordinate system, Rswls, is calculated as:

  rlsXsw     [Rswls] = r   lsY sw    rlsZsw

Likewise, the rotation matrix from the lunate sensor coordinate system to the

SolidWorks coordinate system, Rlssw, is calculated as:

−1 T [Rlssw] = [Rswls] = [Rswls]

The origin of the lunate sensor coordinate system, Olssw, is taken as RlsBsw.

Olssw = RlsBsw

The transformation matrix from lunate source coordinate system to SolidWorks

49 coordinate system is therefore:

  1 {0} [Blssw] =    T  Olssw [Rlssw]

And, the transformation matrix from SolidWorks coordinate system to lunate sensor coordinate system, Bswls, is the inverse:

−1 [Bswls] = [Blssw]

Any point in the lunate bony coordinate system can now be described in the lunate sensor coordinate system using the following equation:

{rls} = [Bswls][Blsw] {rl}

While this transformation derivation requires the wrist in neutral during the CT scan, the transformation holds true for all wrist positions while the sensor is rigidly attached to the lunate.

The scaphoid and third metacarpal transformations derived similarly.

3.8 Source-Sensor Transformation Derivation

Each sensor position is recorded by the 3-SPACE system as a set of three translations and three Euler angles following the 3-2-1 axis rotation sequence from ﬁxed reference frame to moving body coordinate system as shown in Figure 3.10. X, Y, and Z are the axes of the source coordinate system. The sensor coordinate system consists of x, y, and z.

To transform from the ﬁxed source coordinate system to the moving sensor coordinate system, three rotations are performed as shown in Figure 3.10. First, the source

50 system is rotated about the Z axis by an angle, ψ (psi), to create a new intermediate

coordinate system consisting of X0, Y0, and Z. The next rotation is about the Y0 axis by an angle, θ (theta), to create an intermediate coordinate system consisting of x, Y0, and Z0. The ﬁnal rotation is taken about the x axis by an angle, φ (phi), to arrive at the sensor coordinate system of x, y, and z.

The translation vector from the lunate sensor coordinate system to source coordinate system Tsensorsourcelunate is obtained directly from the 3-SPACE sensor for each measurement recorded and shown below:

  x translation     [Tsensorsourcelunate] = y translation     z translation

Where x translation, y translation, and z translation are the coordinates of

the origin of the lunate sensor coordinate system with respect to the source coordinate

system.

The rotation matrix from the lunate sensor coordinate system to the source co-

ordinate system [Rsensorsourcelunate] is determined from the 3-2-1 Euler axis rotation matrix shown below:

  cos θ cos ψ cos ψ sin φ sin θ − cos φ sin ψ cos φ cos ψ sin θ + sin φ sin ψ     [Rsensorsourcelunate] = cos θ sin ψ cos φ cos ψ + sin φ sin θ sin ψ cos φ sin θ sin ψ − cos ψ sin φ     − sin θ cos θ sin φ cos φ cos θ

The transformation matrix from the lunate sensor coordinate system to the source

coordinate system [Bsensorsourcelunate] is then deﬁned as below:

51   1 {0}   [Bsensorsourcelunate] =   {Tsensorsourcelunate} [Rsensorsourcelunate]

Therefore, during motion testing, the coordinates of any point in the lunate sensor

coordinate system can be expressed in terms of the source coordinate system using

the following equation:

{rRs} = [Bsensorsourcelunate] {rls}

Finally, during motion, any point described in the lunate bony coordinate system can be described in the radial bony coordinate system using the following equation:

{rr} = [Bswr][BRssw][Bsensorsourcelunate][Bswls][Blsw] {rl}

Similar transformations are developed for the scaphoid and third metacarpal. For the scaphoid:

{rr} = [Bswr][BRssw][Bsensorsourcescaphoid][Bswscs][Bscsw] {rsc}

For the third metacarpal:

{rr} = [Bswr][BRssw][Bsensorsourcemetacarpal][Bswms][Bmsw] {rm}

3.9 Joint Coordinate Systems

There are several methods of reporting kinematic results. In order to present results in the most useful fashion, the researcher must consider how the results will be used. Engineers commonly report kinematic results using several methods including

Euler angles, instantaneous screw axes, and joint coordinate systems. When study-

52 ing biomechanics where both engineers and clinicians are interested in results, it is useful to present data in a way that is clinically relevant. Joint coordinate systems

(JCS) hold an advantage over the other reporting methods because they do this precisely. Joint coordinate systems report display results using axes that correspond to the clinically defined motions such as flexion/extension, supination/pronation, and lateral/medial deviations. This results in coordinate systems that are not necessar- ily orthogonal, but still complete in the description of motion. In general JCS have one axis fixed to each bone in the joint, and a third moving axis which is mutually perpendicular to the two body-fixed axes.

Using guidelines from ISB standards (1), joint coordinate systems were created between the radius and the third metacarpal, lunate, and scaphoid, respectively.

The JCS for the radius with the third metacarpal is defined as follows. The first axis, e1, is defined as the z-axis fixed to the radius in the radial bony coordinate system as shown in Figure 3.10. Rotations about the e1 axis correspond to flexion/extension of the joint, with flexion being positive. The next axis, e3, is defined as the y-axis of metacarpal bony coordinate system. Rotations about the e3 axis correspond to pronation/supination of the joint with pronation being positive. The final axis, e2, is the mutual perpendicular to e1 and e3 defined by the cross product of e3 and e1.

Rotations about the e2 axis correspond to ulnar/radial deviation of the joint with ulnar deviation being positive.

To calculate the clinical rotation angles, the JCS axes need to be described in the same global coordinate system.

For the radiometacarpal joint, the e1 axis is simply the radial bony z-axis, rrZ :

{e1} = {rrZ }

The e3 axis must be transformed from the third metacarpal bony coordinate

53 system:

{e3} = [Bswr][BRssw][Bsensorsourcemetacarpal][Bswms][Bmsw] {rmY }

Finally, the e2 axis is calculated as:

{e2} = {e3} × {e1}

To quantify rotation about the e1 axis (ﬂexion), the angle, α , between the e2 axis and the radial bony y-axis is calculated:

−1 α = sin ({e2}·{rrY })

To quantify rotation about the e2 axis (ulnar deviation), the angle, β, between the e1 axis and the e3 axis is calculated:

β = sin−1 ({e1}·{e3})

Where:

{rrmZ } = [Bswr][BRssw][Bsensorsourcemetacarpal][Bswms][Bmsw] {rmZ }

The JCS for the radius with the lunate and scaphoid, respectively, are formed similarly to the JCS for the radius and third metacarpal as shown in Figure 3.10 and

Figure 3.10. Calculations for clinical rotation angles are calculated similarly to those of the radiometacarpal JCS.

54 3.10 Data Processing

The 3-SPACE data for each trial was exported in the form of a text file. The files were manually checked for discrepancies. The files were formatted to remove errors and redundant data before being saved as spreadsheet files. A custom in-house code was written in MATLAB to process raw data from the 3-SPACE system and output results in the form of JCS data. This code is found in the Appendix.

55 Figure 3-1: Thresholding of CT slice: (A) automatic border detection with artifacts, (B) selection of artifacts, (C) manual removal of artifacts, (D) clean thresholding of radius bone

56 Figure 3-2: Reconstructed CT scan solids imported into SolidWorks, palmar view of left forearm

Figure 3-3: Palmar view of left forearm with radius bony coordinate system

57 Figure 3-4: Palmar view of left forearm with lunate bony coordinate system

Figure 3-5: Palmar view of left forearm with scaphoid bony coordinate system

58 Figure 3-6: Sagittal view of left ﬁnger illustrating metacarpal with bony system of axes

59 Figure 3-7: Source magnetic center and coordinate system with dimensions (inches) used to locate center

60 Figure 3-8: Sensor magnetic center and coordinate system with dimensions (inches) used to locate center

61 Figure 3-9: Construction of source and radius coordinate systems

62 Figure 3-10: Construction of lunate sensor coordinate system

63 Figure 3-11: Construction of scaphoid sensor coordinate system

64 Figure 3-12: Construction of third metacarpal coordinate system

65 Figure 3-13: Euler angle 3-2-1 rotation from source coordinate system (XYZ) to sensor coordinate system (xyz)

66 Figure 3-14: JCS for radiometacarpal joint

Figure 3-15: JCS for radiolunate joint

67 Figure 3-16: JCS for radioscaphoid joint

68 Chapter 4

Results

Test results are presented for four cadaveric arm specimens. The kinematic results are presented using the Joint Coordinate System (JCS) angles for the radiolunate, radioscaphoid, and radiometacarpal joints. A set of JCS angles for each joint consists of three angles: ﬂexion/extension, radial/ulnar deviation, and pronation/supination.

Rotation data for each JCS is graphed versus the in-plane global wrist motion. Global wrist motion is taken as the motion of the radiometacarpal joint.

In-plane wrist motion is defined by the axis of primary motion during a specific test. For flexion/extension (FEM) testing, in-plane motion is radiometacarpal flexion/extension. For ulnar/radial deviation (RUD) testing, the primary global wrist motion is radiometacarpal ulnar/radial deviation.

4.1 Flexion/Extension Results

During FEM testing, the tendons of the specimens were loaded to simulate muscle tension. The tendon loading arrangement to set each wrist in approximately neutral position is listed in Table 4.1. The largest tendon tension of 33N was applied to the Extensor Carpi Radialis Brevis /Longus. The Flexor Carpi Radialis received the second largest load of 22N. The Flexor Carpi Ulnaris and the Extensor Carpi Ulnaris were loaded with 11N each. 69 Each specimen moved through twenty-one to twenty-three sequential positions during a full cycle of FEM. Tables 4.2–4.5 list the speciﬁc radiometacarpal ﬂexion angles that each specimen cycled through during their respective FEM test cycles.

Overall, the specimens averaged a 116.2◦ Range of Motion (ROM) during FEM testing as shown in Table 4.6.

4.1.1 Intact Specimen Results

Figure 4-1 through Figure 4-4 show the in-plane motions of the lunate and scaphoid during FEM testing for Specimen 1 through Specimen 4, respectively, before the RCD procedure. Specimens demonstrated a common in-plane motion behavior during FEM testing. From a neutral position, as the wrist moves into flexion, both the lunate and scaphoid flex. As the wrist returns to neutral and moves into extension, both the lunate and scaphoid extend. Hysteresis is present in both scaphoid and lunate motion. Carpal flexion angles depend on both global wrist position and the direction of wrist motion. At a specific wrist position,the carpals will be more flexed during wrist extension motions versus wrist flexion motions.

It is important to note that while Specimen 2 through Specimen 4 were intact wrists during this testing, Specimen 1 had already undergone a dorsal capsulotomy.

Additionally, during testing of Specimen 1, the sensor attached to the scaphoid loosened which may have aﬀected accuracy of the scaphoid results for the specimen.

During testing of Specimen 2, the sensor attached to the lunate loosened, possibly aﬀecting lunate results. The results for the Specimen 1 scaphoid and Specimen 2 lunate are presented, but not included in group averages.

Excluding results from the Specimen 2 lunate, the average amount of lunate FEM was 48% of wrist FEM. Excluding results from the Specimen 1 scaphoid, the average amount of scaphoid FEM was 72% of wrist FEM.

Figure 4-5 through Figure 4-8 show the pronation motions of the lunate, scaphoid,and

70 metacarpal during FEM testing for Specimen 1 through Specimen 4, respectively, before the RCD procedure. During FEM testing, two pronation patterns are consistent for all specimens. First, the lunate pronation angle changes are minimal throughout the cycle. Second, scaphoid pronation follows a similar motion pattern to that of the third metacarpal for each specimen.

In Specimens 1, 2, and 4, the metacarpal supinates during wrist extension and pronates during wrist flexion. From a neutral position, as the wrist extends, the metacarpal supinates. As the wrist returns to neutral, the metacarpal pronates. As the wrist moves from neutral into flexion, the metacarpal supinates. The metacarpal pronates as the wrist returns from maximum flexion to a neutral position. Specimen

3 demonstrates the most hysteresis in metacarpal motion.

Figure 4-9 through Figure 4-12 show the deviation motions of the lunate and scaphoid during FEM testing for Specimen 1 through Specimen 4, respectively, before the RCD procedure. Deviation behaviors vary greatly between specimens during

FEM testing. However, scaphoid motion resembles metacarpal motion patterns in all specimens.

In Specimen 1, there is minimal change in lunate deviation as the wrist moves from neutral to maximum ﬂexion and as it returns to neutral. However, as the wrist moves from neutral to 50% maximum extension, the lunate radially deviates approximately

5 degrees. As the wrist reaches maximum extension the lunate ulnarly deviates back

5 degrees. As the wrist moves from maximum extension to a neutral position, the lunate deviation remains basically unchanged. In Specimen 2, both the scaphoid and metacarpal radially deviate during wrist extension motion and ulnarly deviate during wrist flexion motion. The scaphoid ulnarly deviates considerably more than the metacarpal. In Specimen 3, the lunate, scaphoid, and metacarpal ulnarly deviate as the wrist moves from neutral to maximum flexion. As the wrist returns to neutral from maximum flexion, the lunate, scaphoid, and metacarpal radially deviate back

71 to their neutral positions. As the wrist moves from neutral position to maximum extension, scaphoid and metacarpal continue to radially deviate, while the lunate’s deviation does not change. As the wrist returns to neutral position from maximum extension, the scaphoid and metacarpal ulnarly deviate back to their neutral positions.

There is approximately 5 degrees of hysteresis in scaphoid motion between neutral and maximum extension. The scaphoid exhibits approximately 5 degrees hysteresis during extension. In Specimen 4, as the wrist moves from neutral position to either maximum

ﬂexion or maximum extension, the lunate, scaphoid, and metacarpal ulnarly deviate.

As the wrist returns to neutral position, the carpal and metacarpal bones radially deviate back to their neutral positions.

4.1.2 Post-RCD Specimen Results

Figure 4-13 through Figure 4-16 show the in-plane motions of the lunate and scaphoid during FEM testing for Specimen 1 through Specimen 4, respectively, after the RCD procedure. The test results following the RCD procedure are similar to the results from intact specimen testing. Again, there is common in-plane motion during FEM testing with the lunate and scaphoid both ﬂexing during wrist ﬂexion, and extending during wrist extension. The average range of motion for the wrist in

ﬂexion and extension was 117 degrees. Excluding results from the Specimen 2 lunate, the average amount of lunate ﬂexion/extension was 47% of global wrist motion.

Excluding results from the Specimen 1 scaphoid, the average amount of scaphoid

ﬂexion/extension was 71% of global wrist motion.

Figure 4-17 through Figure 4-20 show the pronation motions of the lunate and scaphoid during FEM testing for Specimen 1 through Specimen 4, respectively, after the RCD procedure. As with the intact specimen testing, the post-RCD results show small pronation changes for the lunate and patterns where scaphoid motion closely follows third metacarpal motion. Metacarpal pronation after RCD is similar to intact

72 specimen results.

Figure 4-21 through Figure 4-24 show the deviation motions of the lunate and scaphoid during FEM testing for Specimen 1 through Specimen 4, respectively, after the RCD procedure. Like the pronation results, deviation motions for the scaphoid are similar to the third metacarpal. The deviation behaviors after RCD resemble the intact deviation behaviors for the respective specimens.

4.2 Radial/Ulnar Deviation Results

During RUD testing, the tendons of the specimens were loaded to simulate muscle tension. The tendon loading arrangement to set each wrist in approximately neutral position was the same as during FEM testing and is listed in Table 4.1.

Each specimen moved through thirteen to twenty-one sequential positions during a full cycle of RUD. Tables 4.7–4.10 list the speciﬁc radiometacarpal RUD angles that each specimen cycled through during their respective RUD test cycles. Overall, the specimens averaged a 37◦ ROM during RUD testing as shown in Table 4.11.

4.2.1 Intact Specimen Results

Figure 4-25 through Figure 4-28 show the in-plane motions of the lunate and scaphoid during RUD testing for Specimen 1 through Specimen 4, respectively, before the RCD procedure. These figures show that during RUD testing of the intact specimens, the in-plane motions of scaphoid and lunate follow those of the third metacarpal. Carpal motion paths differ among specimens, but all specimens show that as the third metacarpal radially deviates, the lunate and scaphoid radially deviate. Likewise, as the metacarpal ulnarly deviates, the carpals ulnarly deviate. As with FEM testing, the carpal bones motions paths depend not just on wrist position, but the direction of wrist motion. At a specific wrist position, the carpals will be more

73 radially deviated during wrist ulnar deviation motions versus wrist radial deviation motions.

Excluding results from the Specimen 2 lunate, the average amount of lunate RUD was 37% of wrist RUD. Excluding results from the Specimen 1 scaphoid, the average amount of scaphoid RUD was 41% of wrist RUD.

In addition to the in-plane RUD motions, the scaphoid and lunate exhibit large

flexion/extension motions during RUD testing. In all specimens, as the wrist ulnarly deviates, the scaphoid and lunate extend. However, movement patterns differ between specimens. Specimens 1 and 3 show a mostly linear relationship between lunate flexion and global wrist RUD. Specimen’s 1 lunate undergoes a large amount of hysteresis.

Between neutral and maximum ulnar deviation of the wrist, Specimens 2 and 4 show similar linear patterns of lunate motion to Specimens 1 and 3. However, as the wrist moves from neutral to maximum radial deviation, instead of seeing a continued increase in lunate ﬂexion, Specimens 2 and 4 show decreased ﬂexion of the lunate. In

Specimen 4, the scaphoid also decreases in ﬂexion as the wrist moves from neutral to maximum radial deviation. Figure 4-29 through Figure 4-32 show the ﬂexion motions of the lunate and scaphoid during RUD testing for Specimen 1 through Specimen 4, respectively, before the RCD procedure.

Figure 4-33 through Figure 4-36 show the pronation motions of the lunate and scaphoid during RUD testing for Specimen 1 through Specimen 4, respectively, before the RCD procedure. In Specimens 1 and 2, the lunate pronates as the wrist radially deviates and supinates as the wrist ulnarly deviates. In Specimens 2 , 3, and

4, the scaphoid pronates as the wrist radially deviates and supinates as the wrist ulnarly deviates. In Specimen 1, the scaphoid pronates minimally through wrist RUD.

In Specimens 3 and 4, the lunate pronates minimally. In Specimens 1 and 2, the metacarpal pronates as the wrist radially deviates and supinates as the wrist ulnarly deviates. In Specimen 3, the metacarpal supinates as the wrist radially deviates and

74 pronates as the wrist ulnarly deviates. In Specimen 4, the metacarpal pronation angle changes minimally during wrist RUD. All four specimens show some hysteresis in lunate, scaphoid, and metacarpal pronation up to approximately 3 degrees.

4.2.2 Post-RCD Specimen Results

Results for RUD testing following the RCD procedure are very similar to their intact counterparts. As with the intact RUD test results, in-plane motions of the scaphoid and lunate follow that of the third metacarpal. Figure 4-37 through Figure

4-40 show the in-plane motions of the lunate and scaphoid during RUD testing for

Specimen 1 through Specimen 4, respectively, after the RCD procedure.

Excluding results from the Specimen 2 lunate, the average amount of lunate RUD after the RCD procedure was 37% of wrist RUD. Excluding results from the Specimen

1 scaphoid, the average amount of scaphoid RUD after the RCD procedure was 40% of wrist RUD.

After the RCD procedure, both the scaphoid and lunate extend during wrist ulnar deviation in similar fashion to when the specimens were intact. Figure 4-41 through

Figure 4-44 show the ﬂexion motions of the lunate and scaphoid during RUD testing for Specimen 1 through Specimen 4, respectively, after the RCD procedure.

Figure 4-45 through Figure 4-48 show the pronation motions of the lunate and scaphoid during RUD testing for Specimen 1 through Specimen 4, respectively, after the RCD procedure. Following RCD, the lunates in Specimens 1, 2, and 3 supinate during wrist ulnar deviation. In Specimen 4, the lunate pronation remains virtually unchanged during wrist RUD. As with the intact test results, in all specimens, the scaphoid also supinates during wrist ulnar deviation.

75 Table 4.1: Tendon Loads at Neutral Wrist Position

Tendon Load (Newtons) Extensor Carpi Radialis Brevis / Longus 33 Extensor Carpi Ulnaris 11 Flexor Carpi Radialis 22 Flexor Carpi Ulnaris 11

Table 4.2: Wrist Position during FEM Testing for Specimen 1

Position # Wrist Flexion Angle (◦) Approx. Wrist Position 1 -1.2 Neutral 2 -13.0 3 -23.2 4 -32.6 5 -41.4 6 -51.4 Max. Ext. 7 -42.2 8 -33.7 9 -24.5 10 -15.7 11 -3.9 Neutral 12 25.5 13 39.9 14 48.5 15 56.1 16 69.2 17 72.4 Max. Flex. 18 69.1 19 56.1 20 48.8 21 40.6 22 26.4 23 -1.5 Neutral

76 Table 4.3: Wrist Position during FEM Testing for Specimen 2

Position # Wrist Flexion Angle (◦) Approx. Wrist Position 1 -9.6 Neutral 2 -19.2 3 -28.7 4 -34.7 5 -41.9 6 -51.8 Max. Ext. 7 -42.0 8 -34.4 9 -28.3 10 -19.1 11 -10.2 Neutral 12 5.4 13 20.7 14 31.2 15 44.0 16 55.9 Max. Flex. 17 45.0 18 31.9 19 20.6 20 6.4 21 -10.5 Neutral

77 Table 4.4: Wrist Position during FEM Testing for Specimen 3

Position # Wrist Flexion Angle (◦) Approx. Wrist Position 1 -4.1 Neutral 2 -18.6 3 -27.9 4 -37.2 5 -46.0 6 -52.3 Max. Ext. 7 -45.5 8 -37.3 9 -27.4 10 -16.8 11 -2.9 Neutral 12 14.8 13 31.9 14 45.3 15 56.9 16 64.9 Max. Flex. 17 57.0 18 45.1 19 31.7 20 14.2 21 -4.2 Neutral

78 Table 4.5: Wrist Position during FEM Testing for Specimen 4

Position # Wrist Flexion Angle (◦) Approx. Wrist Position 1 4.2 Neutral 2 -13.2 3 -29.1 4 -40.9 5 -50.8 6 -59.6 Max. Ext. 7 -50.5 8 -41.0 9 -29.0 10 -12.6 11 3.2 Neutral 12 15.8 13 26.1 14 35.2 15 48.6 16 56.3 Max. Flex. 17 48.7 18 35.5 19 26.8 20 16.9 21 4.3 Neutral

Table 4.6: Comparison of FEM ranges for Test Specimens

Specimen # Max. Ext. (◦) Max. Flex. (◦) Total range of FEM (◦) 1 51.4 72.4 123.8 2 51.8 55.9 107.7 3 52.3 64.9 117.2 4 59.6 56.3 115.9 Average 116.2

79 Table 4.7: Wrist Position during RUD Testing for Specimen 1

Position # Wrist Ulnar Deviation Angle (◦) Approx. Wrist Position 1 3.8 Neutral 2 -1.6 3 -7.6 4 -12.1 Max. Radial Dev. 5 -8.1 6 -3.1 7 2.3 Neutral 8 9.5 9 16.4 10 20.3 Max. Ulnar Dev. 11 16.9 12 10.8 13 3.8 Neutral

Table 4.8: Wrist Position during RUD Testing for Specimen 2

Position # Wrist Ulnar Deviation Angle (◦) Approx. Wrist Position 1 -2.5 Neutral 2 -3.9 3 -5.3 4 -7.7 5 -11.3 6 -14.8 Max. Radial Dev. 7 -11.4 8 -7.0 9 -4.9 10 -2.7 11 -1.2 Neutral 12 4.5 13 9.2 14 15.3 15 20.8 16 24.6 Max. Ulnar Dev. 17 20.2 18 15.2 19 9.5 20 3.7 21 -1.5 Neutral

80 Table 4.9: Wrist Position during RUD Testing for Specimen 3

Position # Wrist Ulnar Deviation Angle (◦) Approx. Wrist Position 1 -0.7 Neutral 2 -3.9 3 -7.8 4 -10.8 5 -14.4 Max. Radial Dev. 6 -10.9 7 -8.1 8 -4.0 9 -0.7 Neutral 10 4.4 11 10.9 12 16.7 13 24.0 14 30.3 Max. Ulnar Dev. 15 24.4 16 16.9 17 11.3 18 4.8 19 -0.6 Neutral

81 Table 4.10: Wrist Position during RUD Testing for Specimen 4

Position # Wrist Ulnar Deviation Angle (◦) Approx. Wrist Position 1 -8.9 Neutral 2 -0.9 3 5.2 4 11.0 5 16.3 Max. Ulnar Dev. 6 22.6 7 16.6 8 11.1 9 5.3 Neutral 10 -0.5 11 -9.1 12 -12.4 13 -14.5 14 -17.1 Max. Radial Dev. 15 -18.9 16 -17.2 17 -14.5 18 -12.3 19 -9.1 Neutral

Table 4.11: Comparison of RUD ranges for Test Specimens

Specimen # Max. Ulnar Dev. (◦) Max. Radial Dev. (◦) Total range of RUD (◦) 1 20.3 12.1 32.4 2 24.6 14.8 39.4 3 30.3 14.4 44.7 4 16.3 17.1 33.4 Average 37.5

82 83

Figure 4-1: Measured wrist bone ﬂexion/extension during FEM testing for intact Specimen 1. * Specimen 1 underwent a dorsal capsulotomy prior to intact testing. † Scaphoid sensor loosened from bone during testing. 84

Figure 4-2: Measured wrist bone ﬂexion/extension during FEM testing for intact Specimen 2. † Lunate sensor loosened from bone during testing. 85

Figure 4-3: Measured wrist bone ﬂexion/extension during FEM testing for intact Specimen 3. 86

Figure 4-4: Measured wrist bone ﬂexion/extension during FEM testing for intact Specimen 4. 87

Figure 4-5: Measured wrist bone pronation/supination during FEM testing for intact Specimen 1. * Specimen 1 underwent a dorsal capsulotomy prior to intact testing. † Scaphoid sensor loosened from bone during testing. 88

Figure 4-6: Measured wrist bone pronation/supination during FEM testing for intact Specimen 2. † Lunate sensor loosened from bone during testing. 89

Figure 4-7: Measured wrist bone pronation/supination during FEM testing for intact Specimen 3. 90

Figure 4-8: Measured wrist bone pronation/supination during FEM testing for intact Specimen 4. 91

Figure 4-9: Measured wrist bone radial/ulnar deviation during FEM testing for intact Specimen 1. * Specimen 1 underwent a dorsal capsulotomy prior to intact testing. † Scaphoid sensor loosened from bone during testing. 92

Figure 4-10: Measured wrist bone radial/ulnar deviation during FEM testing for intact Specimen 2. † Lunate sensor loosened from bone during testing. 93

Figure 4-11: Measured wrist bone radial/ulnar deviation during FEM testing for intact Specimen 3. 94

Figure 4-12: Measured wrist bone radial/ulnar deviation during FEM testing for intact Specimen 4. 95

Figure 4-13: Measured wrist bone ﬂexion/extension during FEM testing for Specimen 1 following RCD. * Specimen 1 underwent a dorsal capsulotomy prior to intact testing. † Scaphoid sensor loosened from bone during testing. 96

Figure 4-14: Measured wrist bone ﬂexion/extension during FEM testing for Specimen 2 following RCD. † Lunate sensor loosened from bone during testing. 97

Figure 4-15: Measured wrist bone ﬂexion/extension during FEM testing for Specimen 3 following RCD. 98

Figure 4-16: Measured wrist bone ﬂexion/extension during FEM testing for Specimen 4 following RCD. 99

Figure 4-17: Measured wrist bone pronation/supination during FEM testing for Specimen 1 following RCD. * Specimen 1 underwent a dorsal capsulotomy prior to intact testing. † Scaphoid sensor loosened from bone during testing. 100

Figure 4-18: Measured wrist bone pronation/supination during FEM testing for Specimen 2 following RCD. † Lunate sensor loosened from bone during testing. 101

Figure 4-19: Measured wrist bone pronation/supination during FEM testing for Specimen 3 following RCD. 102

Figure 4-20: Measured wrist bone pronation/supination during FEM testing for Specimen 4 following RCD. 103

Figure 4-21: Measured wrist bone radial/ulnar deviation during FEM testing for Specimen 1 following RCD. * Specimen 1 underwent a dorsal capsulotomy prior to intact testing. † Scaphoid sensor loosened from bone during testing. 104

Figure 4-22: Measured wrist bone radial/ulnar deviation during FEM testing for Specimen 2 following RCD. † Lunate sensor loosened from bone during testing. 105

Figure 4-23: Measured wrist bone radial/ulnar deviation during FEM testing for Specimen 3 following RCD. 106

Figure 4-24: Measured wrist bone radial/ulnar deviation during FEM testing for Specimen 4 following RCD. Figure 4-25: Measured wrist bone radial/ulnar deviation during RUD testing for intact Specimen 1. * Specimen 1 underwent a dorsal capsulotomy prior to intact testing. † Scaphoid sensor loosened from bone during testing.

107 Figure 4-26: Measured wrist bone radial/ulnar deviation during RUD testing for intact Specimen 2. † Lunate sensor loosened from bone during testing.

108 Figure 4-27: Measured wrist bone radial/ulnar deviation during RUD testing for intact Specimen 3.

109 Figure 4-28: Measured wrist bone radial/ulnar deviation during RUD testing for intact Specimen 4.

110 Figure 4-29: Measured wrist bone ﬂexion/extension during RUD testing for intact Specimen 1. * Specimen 1 underwent a dorsal capsulotomy prior to intact testing. † Scaphoid sensor loosened from bone during testing.

111 Figure 4-30: Measured wrist bone ﬂexion/extension during RUD testing for intact Specimen 2. † Lunate sensor loosened from bone during testing.

112 Figure 4-31: Measured wrist bone ﬂexion/extension during RUD testing for intact Specimen 3.

113 Figure 4-32: Measured wrist bone ﬂexion/extension during RUD testing for intact Specimen 4.

114 Figure 4-33: Measured wrist bone pronation/supination during RUD testing for intact Specimen 1. * Specimen 1 underwent a dorsal capsulotomy prior to intact testing. † Scaphoid sensor loosened from bone during testing.

115 Figure 4-34: Measured wrist bone pronation/supination during RUD testing for intact Specimen 2. † Lunate sensor loosened from bone during testing.

116 Figure 4-35: Measured wrist bone pronation/supination during RUD testing for intact Specimen 3.

117 Figure 4-36: Measured wrist bone pronation/supination during RUD testing for intact Specimen 4.

118 Figure 4-37: Measured wrist bone radial/ulnar deviation during RUD testing for Specimen 1 following RCD. * Specimen 1 underwent a dorsal capsulotomy prior to intact testing. † Scaphoid sensor loosened from bone during testing.

119 Figure 4-38: Measured wrist bone radial/ulnar deviation during RUD testing for Specimen 2 following RCD. † Lunate sensor loosened from bone during testing.

120 Figure 4-39: Measured wrist bone radial/ulnar deviation during RUD testing for Specimen 3 following RCD.

121 Figure 4-40: Measured wrist bone radial/ulnar deviation during RUD testing for Specimen 4 following RCD.

122 Figure 4-41: Measured wrist bone ﬂexion/extension during RUD testing for Specimen 1 following RCD. * Specimen 1 underwent a dorsal capsulotomy prior to intact testing. † Scaphoid sensor loosened from bone during testing.

123 Figure 4-42: Measured wrist bone ﬂexion/extension during RUD testing for Specimen 2 following RCD. † Lunate sensor loosened from bone during testing.

124 Figure 4-43: Measured wrist bone ﬂexion/extension during RUD testing for Specimen 3 following RCD.

125 Figure 4-44: Measured wrist bone ﬂexion/extension during RUD testing for Specimen 4 following RCD.

126 Figure 4-45: Measured wrist bone pronation/supination during RUD testing for Specimen 1 following RCD. * Specimen 1 underwent a dorsal capsulotomy prior to intact testing. † Scaphoid sensor loosened from bone during testing.

127 Figure 4-46: Measured wrist bone pronation/supination during RUD testing for Specimen 2 following RCD. † Lunate sensor loosened from bone during testing.

128 Figure 4-47: Measured wrist bone pronation/supination during RUD testing for Specimen 3 following RCD.

129 Figure 4-48: Measured wrist bone pronation/supination during RUD testing for Specimen 4 following RCD.

130 Chapter 5

Discussion and Conclusions

This study was performed to determine the three dimensional kinematic eﬀects of radial core decompression on lunate and scaphoid motions in the wrist joint. Wrist kinematics were determined using joint coordinate systems previous described in

Chapter 3.

In order to obtain useful results while studying wrist biomechanics, it is essential to recreate physiological conditions as close as possible. Maintaining the integrity of mechanically important structures such as tendons and ligaments as well as loading the joint under normal physiological conditions are particularly important as both factors may aﬀect results.

We were interested in analyzing the feasibility of directly acquiring interface pressures and force transmission across the radiocarpal joint. Thus, Specimen 1 was tested with Tekscan pressure sensors inserted into the radiocarpal joint to directly calculate joint pressures and contact areas at the interface. In order to insert the sensor, a dorsal capsulotomy on the wrist joint was performed to gain access to the joint. During testing, the sensor would continually move around in the joint and slide out through the capsulotomy. To minimize this, sutures were attached to the perimeter of the sensor as shown in Figure 5.9, passed through the joint capsule, and secured to rigid posts inserted in the distal cortex of the radius similar to Short et al.

131 [32]. The insertion of the sensor into the wrist joint is shown Figure 5.9. The posts in the distal cortex with sutures attached to them can be seen in Figure 5.9 This did not adequately immobilize the pressure sensor. The testing provided unrepeatable pressure and contact area results.

Additionally, the capsulotomy and insertion of the pressure sensor altered carpal kinematics. During ﬂexion/extension testing, large diﬀerences are found in lunate

flexion and RUD . During these same positions there are minimal changes in metacarpal motion. The kinematic effects of the insertion of the Tekscan sensor are especially apparent during lunate flexion/extension where the hysteresis motion of the lunate is greatly reduced. During RUD testing, differences in lunate motion due to Tekscan sensor insertion are not as evident. However, results for Specimen 1 fail to show the effects of the dorsal capsulotomy, which in itself, may have large effects on carpal kinematics. In Short et al., reported that dorsal capsulotomy and pressure sensor insertion significantly affected carpal kinematics [32].

As a result of these issues, the remaining specimens were tested without performing the capsulotomy and only kinematics data were collected. Results from Specimen

2 through Specimen 4 directly show the eﬀects of the isolated RCD procedure.

5.1 In-plane motions during FEM testing

Prior to the RCD procedure, the in-plane motion behaviors of the wrist bones during FEM testing tests were similar for all four specimens. As the wrist ﬂexed and extended, individual carpal bones followed the overall wrist. This is observed in other studies shown in Table 5.1. It should be noted that wrist range of motion (ROM) is taken as the capitate ROM in Moojen et al. [33] and Guo et al. [3]. Wrist ROM in the current study falls within range of previous studies. In-plane motions of the lunate and scaphoid as percentages of global wrist in-plane motion are near the lower

132 range of previous studies.

With the exception of Specimen 1, the lunate and scaphoid exhibited very little hysteresis in their in-plane motions. It may be possible that the large amount of hysteresis in the ﬁrst specimen can be attributed to the laxity of the specimen. This specimen underwent a dorsal capsulotomy prior to testing. As a result of the capsulotomy, the joint capsule became disrupted causing damage to ligaments that formerly acted to constrain movements of the lunate and scaphoid.

5.2 Out-of-plane motions during FEM testing

5.2.1 Pronation/Supination

The pronation motions for the metacarpals were similar in Specimens 1, 2, and 4, with the wrist supinating during extension and pronating during flexion. However, in Specimen 3, the metacarpal supinated as the wrist moved from neutral position to maximum flexion. The pronation motions of the scaphoids were similar to the motions of their respective metacarpals. Lunate pronation angles changed very little throughout the flexion/extension testing. Wrist motion was controlled during testing by grasping the metacarpals and actively manually moving the hand. While it was attempted to similarly grasp and move all specimens, small differences may have gone unnoticed during testing, only to be realized during analysis. In general, lunate pronation did not change during wrist flexion and extension and scaphoid pronation followed overall wrist pronation as measured by the third metacarpal.

Other studies report a variety of different pronation behaviors for the lunate and scaphoid during wrist flexion and extension. Moojen et al. reports that the lunate slightly pronates 3.8 degrees moving from extension to flexion [33]. Conversely,

Kobayashi et al. indicates that the lunate supinates 3.4 degrees moving from extension to ﬂexion [34]. Short et al. also reported that lunate supinated 6 degrees

133 during wrist ﬂexion. Moojen et al. reports slight scaphoid pronation moving from neutral to both extension and ﬂexion [33]. This range of pronation is on the order of

1 degree. Kobayashi et al. reports 4.5 degrees of scaphoid pronation while moving from extension to flexion [34]. Short et al. indicates 6 degrees of scaphoid supination during wrist flexion [32]. Patterson et al. did not report a specific supination/pronation behavior, but noted that lunate pronation/supination changed an average of 3.2 degrees throughout flexion/extension testing [21].

There are several factors that could influence the variation in out-of-plane motions reported among studies. First, results presented in other studies were averaged for multiple specimens. While the average motion may show a specific behavior for motion, the behaviors of individual specimens may differ from the average. A small standard deviation in pronation/supination values between specimens at various positions shows that the average behavior closely represents the behavior of individual specimens. However, a large standard deviation shows that the average may poorly represent the individual specimens. For example, Moojen et al. reported a 2.7 degree range of lunate pronation/supination during wrist flexion/extension [33]. However,

Moojen et al. also reported between 0.9 and 3.1 degrees for standard deviation. With the value of standard deviation being so large in comparison to the range of pronation/supination values, the reported average values in Moojen et al. indicated that large variations existed between specimens. Likewise, Kobayashi et al. reported a 2.8 degree standard deviation for lunate pronation/supination over a range of 3.4 degrees

[34].

In addition to the standard deviations, Kobayashi et al. [34] and Moojen et al.[33] reported carpal and metacarpal pronation/supination as a rotation about the long axis fixed to the radius. This study reports pronation/supination of the carpals and metacarpal as rotations about body-fixed axes of these bones, not a single external global axis. The projections of these rotations on a global fixed axis will change the

134 apparent magnitudes of the angles. This difference will increase as the angles between the body-fixed axes and the global axis increase, i.e. when the carpals and metacarpal undergo flexion/extension and ulnar/radial deviation.

5.2.2 Radial/Ulnar Deviation

During wrist ﬂexion, Specimens 2, 3, and 4 showed that the third metacarpals and scaphoids deviated ulnarly. Additionally, the lunates in Specimens 3 and 4 deviated ulnarly. Ulnar deviation from neutral to maximum wrist ﬂexion exceeded 20 degrees in Specimen 3. Whereas, ulnar deviation in Specimens 2 and 4 over the same wrist

ﬂexion range is under 10 degrees. In Specimen 1, lunate and third metacarpal deviation angles remained virtually unchanged during wrist ﬂexion. In wrist extension, the metacarpal and scaphoid radially deviated in Specimens 2 and 3 and ulnarly deviate in Specimen 4. Lunate deviation angle remained unchanged in Specimens 1 and 3 and ulnarly deviated in Specimen 4. Short et al. [32], Moojen et al. [33], and Kobayashi et al. [34] all reported that the lunate and scaphoid ulnarly deviated during wrist

flexion. During wrist extension, Kobayashi et al. reported ulnar deviation motion of the two carpals, but Moojen et al. reported slight radial deviation. This study is consistent with previous studies in that the carpals undergo ulnar deviation during wrist flexion. Scaphoid and lunate motion appear to be greatly affected by third metacarpal motion as the carpal motions show similar motion patterns to that of the third metacarpal.

In general, while lunate and scaphoid pronation did not follow any set behavior, the carpals consistently ulnarly deviated during wrist ﬂexion.

135 5.3 In-plane motions during RUD testing

Prior to the RCD procedure, the in-plane motions of the wrist bones during radial/ulnar deviation testing are similar for all four specimens. As the wrist deviates ulnarly and radially, individual carpal bones follow the motions as they contribute to the overall in-plane motion of the wrist. Similar results were obtained in other studies as shown in Table 5.2. In Moojen et al., wrist ROM is taken as the capitate

ROM [33]. Global wrist ROM and lunate ROM fall in range of previous studies.

The scaphoid ROM that was recorded in this study is slightly higher than previous studies. [33] [34] [32]

5.4 Out-of-plane motions during RUD testing

5.4.1 Flexion

The flexion/extension motions of the lunate and scaphoid were similar for all specimens during radial/ulnar deviation testing. As the wrist radially deviates, the scaphoid and lunate flex. As the wrist ulnarly deviates, the scaphoid and lunate extend. The ROM for lunate and scaphoid flexion/extension during wrist deviation ranges between 20 and 30 degrees, respectively. Previous studies report similar behaviors. Short et al. indicates that average flexion/extension ROM for the scaphoid during deviation is 23 degrees and lunate ROM is 18 degrees [32]. Moojen et al. reports 25 degrees of scaphoid flexion/extension and 37 degrees of lunate motion [33].

Kobayashi et al. notes that scaphoid and lunate ROM average 27 degrees and 30 degrees respectively [34]. As the wrist ulnarly deviates, the distance increases between the radius and metacarpals on the radial side of the hand. As a result, the scaphoid and lunate must extend to lengthen and ﬁll the increased height of the joint space on the radial side of the wrist. Figure 5.9 shows that as the wrist ulnarly deviates,

136 the height of the carpal row increases on the radial side of the wrist. In order to accommodate this change of height in the wrist, the scaphoid undergoes extension rotation so that a longer portion of the bone can ﬁll the space. Ligaments between the scaphoid and lunate cause the lunate to follow the scaphoid’s motion.

5.4.2 Pronation

During wrist ulnar/radial deviation, the scaphoids in the specimens pronated as the wrist radially deviated and supinated as the wrist ulnarly deviated. With the exception of Specimen 1, the lunates in the current study had minimal pronation angle changes during radial/ulnar deviation testing. In Specimen 1, the lunate pronated during radial deviation and supinated during ulnar deviation.

Previous studies report a mix of scaphoid and lunate pronation behaviors during

RUD. Short et al. reports minimal lunate and scaphoid supination during RUD [32].

Kobayashi et al. reports slight scaphoid and lunate pronation during ulnar deviation of 6.6 degrees and 3.9 degrees , respectively [34]. Moojen et al. reports 4.2 and

2.6 degrees of pronation for the scaphoid and lunate and 20 degrees of wrist ulnar deviation [33].

One factor that may cause a discrepancy between the results of the current study and previous ones has to do with the experimental setup. Moojen et al. and

Kobayashi et al. both report slight scaphoid and lunate pronation during ulnar deviation. Both of these studies utilize noninvasive methods of measuring carpal motion,

Moojen et al. uses CT scanning and Kobayashi et al., biplanar radiography. [33] [34]

Conversely, Short et al. and the current study utilize motion sensors attached to the carpal bones via posts passing through the joint capsule [32]. As the wrist ulnarly deviates and the scaphoid extends, the posts may interact with the joint capsule and cause the motion of the bone to diﬀer from its motion without a sensor attached.

Additionally, a dorsally-inserted sensor may cause a moment due gravity about the

137 scaphoid that may cause it to supinate during wrist ulnar deviation.

Overall, the pre-RCD results agree with previous studies. In-plane motions of the scaphoid and lunate are similar in behavior and magnitude to previous studies. Ad- ditionally, large out-of-plane motions such as carpal extension during ulnar deviation are consistent with other studies. Diﬀerences in motion between the current study and previous ones may be a result of many factors including testing conditions and methods of processing the data and reporting the results. Experimental setups vary greatly and hence the methods of loading and moving the joint.

5.5 Eﬀects of RCD on Scaphoid and Lunate Kine-

matics

There are two items to consider when comparing results before and after RCD.

First, it is important to examine statistically significant differences in motion resulting from RCD. Second, it is also important to consider the clinical relevance of these differences. While lunate and scaphoid kinematics may be statistically different following RCD, the difference may have minimal clinical importance.

To statistically evaluate the effects of RCD for the study, specimen results were normalized for both intact and RCD tests. Data normalization was performed by applying seventh-order polynomial curve fits to the flexion/extension, pronation/supination, and radial/ulnar deviation results for each trial for each specimen. Hysteresis effects caused bones to follow different motion paths depending on the direction of motion. To best accommodate this, separate curves were fit to the data for each direction of motion. For flexion/extension testing, normalized data was analyzed at nine positions during the motion cycle: Maximum Extension, 50% Extension, Neutral,

50% Flexion, Maximum Flexion, 50% Flexion, Neutral, 50% Extension, and Maxi- mum Extension. Similar normalization was performed for the radial/ulnar deviation

138 testing using ﬁfth-order polynomials and the following positions: Maximum Ulnar

Deviation, 50% Ulnar Deviation, Neutral, 50% Radial Deviation, Maximum Radial

Deviation, 50% Radial Deviation, Neutral, 50% Ulnar Deviation, Maximum Ulnar

Deviation. After the normalized data for each trial was calculated, it was averaged at each position for both intact and RCD testing for each specimen. Using t-tests, the eﬀects of RCD were determined at each normalized position for each specimen.

The normalization values for each trial for each specimen can be found in Appendix

A. After determining if any statistically significant differences existed, this study analyzed if any of the differences were also clinically significant. Other studies have defined clinically relevant differences in kinematics as being greater than 4 degrees

[32] or 5 degrees [21]. For comparison of results, this study assumes diﬀerences greater than 4 degrees as clinically relevant.

After examining the kinematic effects of RCD in individual specimens, the group was analyzed as a whole to determine the overall kinematic effects of the surgery. The average changes in motion for each specimen were compared at each position using t-tests to determine if there were any consistent statistically significant changes in motion due to RCD.

5.5.1 FEM Testing

Table 5.3 through Table 5.14 show the differences in flexion, pronation, and ulnar deviation angles following RCD for Specimen 1 through Specimen 4 during flexion/extension testing. The average values at each position of motion for intact and RCD testing are compared using two-sample t-tests. The tests are two-tailed and assume unequal variances between the compared populations. The probabilities of the differences being statistically insignificant (P-values) are listed next to the differences.

P-values below 0.05 are bolded and indicate at least a 95% chance that the differences are statistically significant. All four specimens showed statistically significant

139 diﬀerences motion following the RCD procedures.

Specimen 1 showed significant changes in motion following RCD. Significant differences in metacarpal pronation and ulnar deviation are to due differences in how the specimen was held during testing. Significant differences in lunate motion were noticed. Additionally, lunate ulnar deviation changed by 5 degrees at maximum wrist extension, indicating a clinically relevant difference. However, between intact testing and RCD testing, several tests were performed on the wrist with a pressure sensor inserted into the joint and then removed. The use of this pressure sensor may have permanently affected wrist kinematics. During the same wrist position that the lunate demonstrated clinically significant changes, the third metacarpal also showed a large change of 3.3 degrees which may have contributed to the large difference in lunate motion. Scaphoid motion showed very large changes when comparing intact and RCD test results. During testing, the scaphoid sensor loosened from the the bone. This is the suspected cause for large differences in motion. Specimen 1 shows that while there are statistically significant changes in lunate motion following RCD, they are not clinically significant under the previously established criteria. The capsulotomy procedure was performed prior to the ”intact” and RCD testing so it does not directly factor into these differences. The results for Specimen 1 demonstrate the kinematic effects of RCD on an injured wrist. The effects of RCD on an uninjured wrist may differ.

Specimen 2 showed statistically significant changes in lunate and scaphoid motion following RCD. For the lunate, these differences were 3 degrees or less. For the scaphoid, all changes in motion were less than 2 degrees. The scaphoid demonstrated the largest changes in motion at 50% and full wrist flexion. During these positions, metacarpal motion was significantly different which may have contributed significant changes in scaphoid motion. During testing the lunate sensor loosened from the bone which may have affected results. No clinically significant changes were observed in

140 lunate or scaphoid motion even though the metacarpal demonstrated an increase in maximum ﬂexion of nearly 8 degrees and a decrease in pronation of 5 degrees at this position.

Specimen 3 also showed statistically significant changes in lunate and scaphoid motion following RCD. The lunate extended between 3 to 4 degrees less during wrist extension following RCD. This change is considered clinically significant. Additionally, the lunate increased in pronation between 2.5 and 6.3 degrees throughout the entire wrist motion cycle, also a clinically significant change after RCD. Significant changes in scaphoid motion include a notable decrease in maximum flexion and increase in pronation during this part of the motion cycle. At 50% wrist flexion, scaphoid flexion is 4.4 degrees lower and scaphoid pronation is 4.2 degrees higher which are clinically significant.

Specimen 4 shows statistically significant differences in lunate and scaphoid motion following RCD. The lunate shows slightly increased flexion and ulnar deviation through the motion cycle. The scaphoid shows decreased flexion, increased, pronation, and increased ulnar deviation throughout the motion cycle. With the exception of scaphoid pronation, these differences are not clinically significant. Scaphoid pronation changes are all less than 4.4 degrees. Aside from the apparent shift in results, motion behaviors are similar between the intact and RCD results.

Table 5.15 through table 5.23 show the overall changes wrist motion for the group of specimens following RCD. In the group analysis, Specimen 1’s scaphoid and Spec- imen 2’s lunate have been excluded due to their sensors loosening during testing.

Lunate ulnar deviation experienced a statistically significant increase of 1.8 degrees at 50% wrist extension as the wrist moved from maximum extension to neutral. The data also suggests that lunate flexion increases about 2.5 degrees at neutral wrist position as the wrist moves from maximum flexion to maximum extension. The data suggests that scaphoid flexion may decrease approximately 2 degrees at 50% wrist

141 extension as the wrist moves from maximum extension to neutral. Results suggest that while RCD may cause statistically significant changes during wrist flexion and extension, the changes are small and not clinically significant.

5.5.2 RUD Testing

Table 5.24 through Table 5.35 show the differences in flexion, pronation, and ulnar deviation angles following RCD for Specimen 1 through Specimen 4 during ulnar/radial deviation testing. The average values at each position of motion for intact and RCD testing are compared using two-sample t-tests with the same parameters used to evaluate the flexion/extension test results. The probabilities of the differences being statistically insignificant are listed next to the differences. P-values below 0.05 are bolded and indicate at least a 95% chance that the differences are statistically significant. As with flexion/extension testing, all four specimens showed statistically significant differences motion following the RCD procedures, but limited clinically relevant differences.

Specimen 1 showed significant changes in motion following RCD. Significant differences in metacarpal flexion and pronation are to due differences in how the specimen was held during testing. Significant differences in lunate motion were calculated, but the changes were not clinically significant under our criteria. Additionally, the aforementioned pressure sensor insertion and removal may have contributed to these changes. Scaphoid motion showed very large changes when comparing intact and

RCD test results. During testing, the scaphoid sensor loosened from the bone. This is appears to have caused an approximately 7 degree shift in pronation and is con- sistant with the shift seen for FEM test results. Specimen 1 shows that while there are statistically signiﬁcant changes in lunate motion following RCD, they are not clinically signiﬁcant under the previously established criteria.

Specimen 2 showed statistically signiﬁcant changes in lunate and scaphoid mo-

142 tion following RCD. The scaphoid demonstrated the largest changes in motion at maximum wrist ulnar deviation and radial deviation. During maximum wrist radial deviation, scaphoid flexion decreased 3.5 degrees following RCD. However, overall wrist flexion measured 3.5 degrees less as well. At maximum wrist ulnar deviation, scapahoid flexion increased 3.8 degrees. While significant, this change was still less than our 4 degree threshold for significant clinical differences. Scaphoid pronation increased approximately 1 to 2 degrees across the entire motion cycle, but was not clinically significant. Statistically significant changes in scaphoid ulnar deviation were all under 1.5 degrees. Specimen 2’s lunate demonstrated statistically significant changes in motion including a clinically significant increase of 6 degrees flexion at maximum wrist ulnar deviation. However, because the lunate sensor loosened from the bone some time during testing, this result cannot be trusted. Overall, Specimen

2 did not demonstrate clinically signiﬁcant diﬀerences following RCD.

Specimen 3 demonstrated clinical differences in lunate flexion and pronation and scaphoid flexion. While the entire motion path for lunate flexion appears to have shifted approximately 3 degrees higher into flexion, the motion pattern is nearly identical to that of the intact specimen. Changes in lunate pronation following RCD are large and indicate significant clinical changes in motion. The clinically relevant decrease in scaphoid flexion occurs at maximum wrist ulnar deviation during which the metacarpal is also flexed significantly less by 3.4 degrees. Overall, Specimen 3 demonstrates that RCD may have significant effects on lunate kinematics.

Specimen 4 showed statistically significant changes in lunate and scaphoid motion following RCD. In the lunate, all statistically significant differences were under

2.5 degrees. The behaviors of the scaphoid before and after surgery are very similar. However, scaphoid pronation appears to have increased approximately 4 degrees throughout the wrist motion cycle, indicating clinically signiﬁcant changes.

Table 5.36 through table 5.44 show the overall changes wrist motion for the group

143 of specimens following RCD for RUD testing. In the group analysis, Specimen 1’s scaphoid and Specimen 2’s lunate have been excluded due to their sensors loosening during testing. Lunate flexion experienced a statistically significant increase in flexion of 1.9 degrees at 50% wrist radial deviation as the wrist moved from neutral to maximum radial deviation. A similar increase, although not statistically significant, is seen at this position as the wrist moves back to neutral from maximum radial deviation. Scaphoid flexion is statistically less at maximum wrist radial deviation by about 2.8 degrees following RCD. Additionally, as the wrist moves from maximum radial deviation to neutral, scaphoid flexion is statistically decreased by 1.8 degrees at

50% wrist radial deviation. As a group, the specimens show no clinically signiﬁcant changes in carpal kinematics following RCD.

5.6 Inﬂuence of Experimental Setup Factors

Small changes in kinematics that are not expected to occur may result from the failure to properly account for all variables in the study. In order to properly account for and control variables that may aﬀect results, a closer look is needed at the diﬀerences in testing of the intact and post-RCD specimens.

In addition to the RCD procedure, there are two other factors that may contribute to changes in the results. First, time may aﬀect the condition of the specimens. The specimens are fresh-frozen and not preserved. Over time, the specimens may start to decompose and dry out. The decomposition should not be signiﬁcant because post-

RCD testing was performed within 24 hours of the intact testing. However, over this

24-hour period, there could be signiﬁcant drying of the specimen, especially if placed back in the refrigerator between intact and post-RCD testing. To mitigate this, the specimens were covered in damp towels and sealed in bags when not in use. A spray bottle was also used to rehydrate the specimens if they appeared dry. As a result of

144 this, the post-RCD testing may have been performed on a more hydrated specimen than the intact testing .

In addition to the environmental factors, the specimens were sometimes removed from the test fixture and reinstalled between intact and post-RCD testing. This depended on how soon after intact testing the surgeon was able to come and perform the RCD procedure. To quantify effects of this, results were compared for two sets of testing on the intact Specimen 4. In between these two sets of testing, Specimen 4 was removed from the test fixture, covered, stored in the refrigerator, and reinstalled in the test fixture. Statistical differences are determined using the same method used to evaluate the effects of the RCD procedure.

Table 5.45 through Table 5.47 show the effects of removal and reinstallation of a specimen on wrist motion during FEM testing. Statistically significant differences are seen in lunate and scaphoid flexion. Changes in lunate motion due to reinstallation average less that 1 degree. Changes in scaphoid motion average about 2 degrees.

Changes in Specimen 4’s scaphoid motion after the RCD surgery were larger than the effects of removing and reinstalling the specimen. However, since the effects of removal and installation of the specimen were found to be statistically significant, the measured effects of the RCD surgery may not be as large as they appear. While the specimens still demonstrate statistically significant changes in motion following

RCD, these changes may not be clinically signiﬁcant.

Table 5.48 through Table 5.50 show the effects of removal and reinstallation of a specimen on wrist motion during RUD testing. During RUD testing, statistically and clinically significant differences are seen in lunate and scaphoid flexion. Changes in Specimen 4’s lunate and scaphoid flexion are clinically significant and exceed the changes seen in the carpals following RCD. Changes in Specimen 4’s scaphoid pronation after the RCD surgery were larger than the effects of removing and reinstalling the specimen during RUD testing. However, similar to the FEM testing, reinstalla-

145 tion eﬀects were statistically signiﬁcant and may contribute to the observed changes in motion seen after the RCD procedure.

5.7 Previous Biomechanical Studies on RCD

At the time of writing, Sherman et al. was the only other biomechanical study on the effects of RCD [29]. That study found that the RCD procedure created a significant decrease in distal forearm stiffness by about 13.4%. This appears to conflict with the results obtained from the current study which suggests minimal kinematics changes due to RCD. However, Sherman et al. also reported no significant changes in contact areas between carpals and radius and ulna and no significant change in force transmission across the joints. When inferring contact through kinematics, no change in kinematics infers no change in contact area. Therefore, the lack of change in contact and force transmission in Sherman et al. may support this study. Additionally, the changes in forearm stiffness cannot be pinpointed to the radiocarpal joint in Sherman et al.

Our research and Sherman et al. have starkly diﬀerent experiment setups. The setup in Sherman et al. externally loaded the wrist joint using a compressive testing machine. The specimens were loaded in only the neutral position. Dorsal capsu- lotomies were performed on the specimens to insert the pressure sensors for direct pressure measurement across the joint. Additionally, the RCD procedures are different; Sherman et al. drilled a dorsal hole in the radius versus the radial windows created in the current study. These diﬀerences do not allow for direct comparison of the studies. [29]

146 5.8 Conclusions

The results from Specimen 1 through Specimen 4 suggest that there are minimal changes in wrist kinematics following RCD. However, Illarramendi indicated that in- vivo subjects had significant decreases in the progression of disease, and even some improvement in condition [11]. This difference might be explained by the earlier literature that suggests that RCD exhibits a physiological healing response which increases the vascularity of the region. Different types of studies would need to be conducted in order to test this hypothesis.

5.9 Limitations and Future Work

As with any in-vitro study, there are limitations when the conclusions apply to living tissue. Although the experimental setup was designed to simulate the physiological cocontraction and tendon loading of a living subject, loading conditions were ultimately different. In this study, the four major tendon groups that control wrist motion were loaded. However, there are several other tendons in the area that may play a role in wrist motion. Additionally, the wrist motion was induced passively by articulating the third metacarpal. In reality, the wrist motion is generated by actively and dynamically loading the tendons. However, Patterson et al. reported that active and passive movement of the wrist does not result in significantly different carpal motions [21].

The data collection and motion was serial-static meaning the wrist was paused in motion for the collection of position data. Our equipment would sometimes produce errors if prompted to collect data too quickly. This prevented us from performing real-time continuous data collection. However, since the cyclic nature of the wrist motion was still captured and the results agree reasonably with real time studies, it is believed that this limitation had a minimal eﬀect on the conclusions of the study. 147 Another limitation was that the specimens had no evidence of Kienbocks disease.

The effects of RCD on subjects with Kienbocks disease may differ from those effects on healthy subjects. In absence of the availability of specimens with Kienbocks disease, researchers have little choice but choose healthy specimens in order to provide consistent results that can be related to Kienbocks disease treatment.

The method of data capture may have also limited the results of the study. While sensors were attached to the specimens in a minimally invasive manner, the method may have impacted wrist biomechanics. The posts attaching the sensors to the carpals passed through the wrist capsule and may have caused some disruption to the complex ligamenture of the wrist. In addition, the small amount of added mass from the sensors created nonphysiological moments about the scaphoid and lunate resulting in undesired motion. However, this small loading was consistent for specimens before and after RCD so it should not have an eﬀect on determining the kinematic eﬀects of the procedure.

Additionally, the motion capture system limited the number of sensors available to track motion. It would be desirable to track the motion of additional carpal bones such as the capitate. The capitate forms articulations with both the lunate and scaphoid, and the third metacarpal. However, due to the limited number of sensors available for the system used in testing, we felt it was more important to measure third metacarpal motion directly since this was the bone that was directly moved to create wrist motion.

The number of specimens in the current study also represents a limitation to the conclusions obtained from this study. Increasing the number of specimens in future studies will statistically strengthen the results.

While this study examines the kinematic eﬀects of RCD, it does not explore the changes in contact areas or pressures in the radiocarpal joint. In order to completely describe the biomechanics of the joint, contact data is needed in addition to kinematic

148 data. Attempts were made to directly measure the contact areas and pressures. How- ever, the method that was used to measure contact interfered with carpal kinematics.

It was more important for this study to capture normal wrist kinematics than to compromise this by trying to collect direct contact data as well. As a result of cap- turing normal kinematic data and having access to the bone surface topography for the lunate, scaphoid, and radius, indirect contact can be inferred using computer simulation. This provides data for future research in wrist biomechanics.

In closing, it can be concluded that while there may be statistically significant differences in lunate and scaphoid kinematics following RCD, these differences may not be clinically significant.

149 Table 5.1: Multiple study comparison of in-plane carpal motion during wrist FEM movement. * Wrist motions measured by radiocapitate joint motions. Study ROM (◦) Lunate (% of total ROM) Scaphoid (% of total ROM) This Study 116 48 72 Patterson [21] - 62 83 Short [32] 80 50 84 Moojen [33] 120* 48 74 Kobayashi [34] 120 44 77 Guo (Spec 1) [3] 74* 51 95 Guo (Spec 2) [3] 82* 50 -

Table 5.2: Multiple study comparison of in-plane carpal motion during wrist RUD movement. * Wrist motions measured by radiocapitate joint motions. Study ROM (◦) Lunate (% of total ROM) Scaphoid (% of total ROM) This Study 39 37 41 Short [32] 26 35 38 Moojen [33] 40* 40 38 Kobayashi [34] 45 46 40

150 Table 5.3: Kinematic Eﬀects of RCD during FEM cycle for Specimen 1 Metacarpal

Wrist Flexion Flexion p-value Pronation p-value Ulnar deviation p-value ∆ (◦) ∆ (◦) ∆ (◦) Maximum Extension -1.2 0.16 1.96 0.14 3.3 0.0003 50% Extension -0.6 0.16 -0.29 0.36 1.3 0.05 Neutral 0.0 NaN -0.99 0.07 0.7 0.31 50% Flexion -0.6 0.09 -1.78 0.02 -2.1 0.03 Maximum Flexion -1.2 0.09 -0.85 0.05 -2.1 0.01 50% Flexion -0.6 0.09 -0.16 0.75 -1.5 0.12 Neutral 0.0 NaN -0.65 0.03 -1.2 0.12 50% Extension -0.6 0.16 -0.44 0.64 0.1 0.82 Maximum Extension -1.2 0.16 2.06 0.13 3.2 0.001

Table 5.4: Kinematic Eﬀects of RCD during FEM cycle for Specimen 2 Metacarpal

Wrist Flexion Flexion p-value Pronation p-value Ulnar deviation p-value ∆ (◦) ∆ (◦) ∆ (◦) Maximum Extension -0.7 0.20 1.8 0.004 0.2 0.29 50% Extension -0.3 0.20 0.2 0.66 -1.0 0.04 Neutral 0.0 NaN -0.6 0.28 -0.9 0.00002 50% Flexion 3.9 0.0002 -2.0 0.01 1.4 0.02 Maximum Flexion 7.7 0.0002 -5.2 0.001 2.6 0.001 50% Flexion 3.9 0.0002 -1.7 0.01 1.9 0.001 Neutral 0.0 NaN -0.5 0.24 -1.1 0.0001 50% Extension -0.3 0.20 0.0 0.91 -1.3 0.002 Maximum Extension -0.7 0.20 1.8 0.003 0.2 0.28

Table 5.5: Kinematic Eﬀects of RCD during FEM cycle for Specimen 3 Metacarpal

Wrist Flexion Flexion p-value Pronation p-value Ulnar deviation p-value ∆ (◦) ∆ (◦) ∆ (◦) Maximum Extension 1.8 0.004 -1.2 0.12 -3.5 0.00004 50% Extension 0.9 0.004 -1.2 0.26 -1.7 0.000002 Neutral 0.0 NaN 3.4 0.08 0.6 0.003 50% Flexion -0.7 0.0001 3.2 0.001 1.4 0.001 Maximum Flexion -1.5 0.0001 1.3 0.03 1.8 0.005 50% Flexion -0.7 0.0001 1.9 0.001 0.8 0.02 Neutral 0.0 NaN 2.2 0.03 0.5 0.004 50% Extension 0.9 0.004 -1.8 0.02 -1.7 0.0001 Maximum Extension 1.8 0.004 -1.2 0.14 -3.5 0.00004

151 Table 5.6: Kinematic Eﬀects of RCD during FEM cycle for Specimen 4 Metacarpal

Wrist Flexion Flexion p-value Pronation p-value Ulnar deviation p-value ∆ (◦) ∆ (◦) ∆ (◦) Maximum Extension 0.6 0.003 0.4 0.57 -0.1 0.81 50% Extension 0.3 0.003 -1.0 0.0004 0.0 0.99 Neutral 0.0 NaN -1.2 0.01 -0.1 0.32 50% Flexion 0.4 0.003 -1.6 0.001 -0.8 0.03 Maximum Flexion 0.8 0.003 -1.6 0.0003 -1.8 0.001 50% Flexion 0.4 0.003 -1.7 0.0003 -0.6 0.08 Neutral 0.0 NaN -1.3 0.002 0.0 0.84 50% Extension 0.3 0.003 -0.1 0.70 0.6 0.09 Maximum Extension 0.6 0.003 0.4 0.56 -0.1 0.80

Table 5.7: Kinematic Eﬀects of RCD during FEM cycle for Specimen 1 Lu- nate Wrist Flexion Flexion p-value Pronation p-value Ulnar deviation p-value ∆ (◦) ∆ (◦) ∆ (◦) Maximum Extension -0.1 0.85 0.52 0.59 5.0 0.05 50% Extension -3.5 0.001 -1.29 0.01 1.8 0.09 Neutral -0.7 0.28 -1.88 0.004 0.4 0.41 50% Flexion -0.2 0.53 -2.28 0.002 -1.7 0.004 Maximum Flexion -0.5 0.14 -0.39 0.01 -1.5 0.02 50% Flexion 1.4 0.33 -0.66 0.05 -2.1 0.001 Neutral 1.1 0.36 -0.50 0.15 -2.0 0.01 50% Extension -0.7 0.42 -1.37 0.13 1.0 0.52 Maximum Extension -0.1 0.73 0.51 0.60 5.0 0.05

Table 5.8: Kinematic Eﬀects of RCD during FEM cycle for Specimen 2 Lunate* Wrist Flexion Flexion p-value Pronation p-value Ulnar deviation p-value ∆ (◦) ∆ (◦) ∆ (◦) Maximum Extension -2.6 0.002 -0.6 0.29 -0.3 0.56 50% Extension -3.0 0.00001 -1.7 0.003 -1.0 0.003 Neutral -0.8 0.105 -2.2 0.002 -1.0 0.00001 50% Flexion 0.7 0.01 -1.4 0.02 1.1 0.04 Maximum Flexion -0.8 0.01 -2.6 0.0002 2.5 0.01 50% Flexion 0.1 0.69 -0.9 0.04 1.7 0.03 Neutral 1.0 0.04 0.2 0.69 0.7 0.04 50% Extension 0.3 0.38 0.9 0.16 0.6 0.17 Maximum Extension -2.6 0.002 -0.6 0.27 -0.3 0.53 * Specimen 2 Lunate data is excluded from the averages and statistics shown in Tables 5.15 through 5.17

152 Table 5.9: Kinematic Eﬀects of RCD during FEM cycle for Specimen 3 Lu- nate Wrist Flexion Flexion p-value Pronation p-value Ulnar deviation p-value ∆ (◦) ∆ (◦) ∆ (◦) Maximum Extension 4.0 0.000003 3.6 0.01 -0.2 0.13 50% Extension 3.6 0.0002 2.5 0.03 1.4 0.0001 Neutral 3.5 0.01 5.8 0.01 0.6 0.30 50% Flexion 0.6 0.67 4.4 0.003 1.9 0.0001 Maximum Flexion 0.8 0.31 2.9 0.002 1.5 0.001 50% Flexion 2.1 0.05 5.0 0.001 -0.5 0.04 Neutral 4.1 0.0004 6.3 0.001 -0.5 0.06 50% Extension 3.3 0.0001 2.8 0.02 1.2 0.002 Maximum Extension 4.0 0.000002 3.6 0.01 -0.2 0.11

Table 5.10: Kinematic Eﬀects of RCD during FEM cycle for Specimen 4 Lunate Wrist Flexion Flexion p-value Pronation p-value Ulnar deviation p-value ∆ (◦) ∆ (◦) ∆ (◦) Maximum Extension 1.5 0.000001 0.0 0.57 1.7 0.0003 50% Extension 1.6 0.001 0.0 0.92 2.1 2.6E-11 Neutral 1.0 0.001 0.0 0.65 1.3 0.000005 50% Flexion 1.0 0.00002 -0.1 0.03 0.5 0.0004 Maximum Flexion 0.4 0.13 -0.5 0.0000004 -0.2 0.05 50% Flexion 1.0 0.00002 0.0 0.52 0.9 0.0000003 Neutral 1.5 0.0002 0.1 0.18 2.0 0.00001 50% Extension 2.3 0.00002 0.3 0.01 3.4 1.1E-10 Maximum Extension 1.5 0.000002 0.0 0.60 1.7 0.0003

Table 5.11: Kinematic Eﬀects of RCD during FEM cycle for Specimen 1 Scaphoid*

Wrist Flexion Flexion p-value Pronation p-value Ulnar deviation p-value ∆ (◦) ∆ (◦) ∆ (◦) Maximum Extension -7.9 0.001 -11.58 0.0004 -2.9 0.03 50% Extension -4.5 0.02 -10.85 0.001 -0.9 0.21 Neutral -4.4 0.07 -9.88 0.001 0.9 0.29 50% Flexion -6.3 0.004 -9.38 0.0002 0.8 0.01 Maximum Flexion -10.4 0.0002 -14.60 0.000003 0.6 0.26 50% Flexion -5.2 0.003 -9.94 0.0005 1.3 0.08 Neutral -1.6 0.06 -7.71 0.001 0.8 0.25 50% Extension -4.2 0.03 -9.38 0.01 0.5 0.42 Maximum Extension -8.0 0.001 -11.64 0.0004 -2.9 0.03 * Specimen 1 Scaphoid data is excluded from the averages and statistics shown in Tables 5.18 through 5.20

153 Table 5.12: Kinematic Eﬀects of RCD during FEM cycle for Specimen 2 Scaphoid

Wrist Flexion Flexion p-value Pronation p-value Ulnar deviation p-value ∆ (◦) ∆ (◦) ∆ (◦) Maximum Extension -0.5 0.06 0.6 0.02 -0.1 0.62 50% Extension -0.8 0.11 0.7 0.0002 -0.9 0.01 Neutral 0.2 0.75 0.2 0.57 -0.6 0.15 50% Flexion 1.4 0.02 -1.5 0.01 -0.7 0.01 Maximum Flexion 1.6 0.002 -1.5 0.02 -0.2 0.26 50% Flexion 0.3 0.63 -1.1 0.02 -0.4 0.34 Neutral 0.0 0.99 0.6 0.04 -0.8 0.08 50% Extension -0.4 0.41 1.3 0.000001 -0.3 0.43 Maximum Extension -0.5 0.07 0.6 0.02 -0.1 0.50

Table 5.13: Kinematic Eﬀects of RCD during FEM cycle for Specimen 3 Scaphoid

Wrist Flexion Flexion p-value Pronation p-value Ulnar deviation p-value ∆ (◦) ∆ (◦) ∆ (◦) Maximum Extension 0.5 0.18 -0.4 0.46 -1.0 0.01 50% Extension -2.5 0.0003 -1.4 0.04 0.0 0.92 Neutral -2.9 0.0002 2.9 0.05 -1.4 0.0000001 50% Flexion -4.4 0.00001 4.2 0.0002 -0.7 0.23 Maximum Flexion -3.4 0.0000002 2.4 0.0002 1.4 0.03 50% Flexion -3.3 0.0000003 2.8 0.00004 0.2 0.47 Neutral -2.3 0.0001 1.5 0.01 -0.2 0.45 50% Extension -1.6 0.001 -2.3 0.0004 -0.8 0.001 Maximum Extension 0.5 0.19 -0.4 0.49 -1.0 0.01

Table 5.14: Kinematic Eﬀects of RCD during FEM cycle for Specimen 4 Scaphoid

Wrist Flexion Flexion p-value Pronation p-value Ulnar deviation p-value ∆ (◦) ∆ (◦) ∆ (◦) Maximum Extension -2.0 0.0002 4.4 0.00000001 3.9 0.00001 50% Extension -2.5 0.0000001 3.4 0.00000001 3.6 0.000003 Neutral -3.1 0.0000003 3.8 0.000001 3.4 0.00000004 50% Flexion -2.5 0.0001 4.2 0.000000002 3.1 0.000001 Maximum Flexion -0.4 0.15 3.1 0.00000001 1.8 0.00001 50% Flexion -2.4 0.0001 3.8 0.00000001 2.7 0.000001 Neutral -3.3 0.000004 4.1 0.000000001 3.7 0.000000002 50% Extension -2.6 0.00000001 4.1 0.0000001 4.1 0.0000001 Maximum Extension -2.0 0.0002 4.4 0.00000001 3.9 0.00001

154 Table 5.15: Comparison of Eﬀects of RCD during FEM cycle for Lunate Flexion Specimen 1 Specimen 3 Specimen 4 Average Std. Dev. p-value ∆ (◦) ∆ (◦) ∆ (◦) ∆ (◦)(◦) Maximum Extension -0.1 4.0 1.5 1.8 2.0 0.27 50% Extension -3.5 3.6 1.6 0.6 3.7 0.82 Neutral -0.7 3.5 1.0 1.3 2.1 0.41 50% Flexion -0.2 0.6 1.0 0.5 0.6 0.31 Maximum Flexion -0.5 0.8 0.4 0.2 0.7 0.60 50% Flexion 1.4 2.1 1.0 1.5 0.6 0.05 Neutral 1.1 4.1 1.5 2.2 1.6 0.14 50% Extension -0.7 3.3 2.3 1.6 2.1 0.31 Maximum Extension -0.1 4.0 1.5 1.8 2.1 0.27

Table 5.16: Comparison of Eﬀects of RCD during FEM cycle for Lunate Ulnar Deviation Specimen 1 Specimen 3 Specimen 4 Average Std. Dev. p-value ∆ (◦) ∆ (◦) ∆ (◦) ∆ (◦)(◦) Maximum Extension 5.0 -0.2 1.7 2.2 2.6 0.29 50% Extension 1.8 1.4 2.1 1.8 0.4 0.02 Neutral 0.4 0.6 1.3 0.8 0.5 0.11 50% Flexion -1.7 1.9 0.5 0.2 1.8 0.84 Maximum Flexion -1.5 1.5 -0.2 -0.1 1.5 0.93 50% Flexion -2.1 -0.5 0.9 -0.6 1.5 0.59 Neutral -2.0 -0.5 2.0 -0.1 2.0 0.91 50% Extension 1.0 1.2 3.4 1.8 1.4 0.14 Maximum Extension 5.0 -0.2 1.7 2.2 2.7 0.29

Table 5.17: Comparison of Eﬀects of RCD during FEM cycle for Lunate Pronation Specimen 1 Specimen 3 Specimen 4 Average Std. Dev. p-value ∆ (◦) ∆ (◦) ∆ (◦) ∆ (◦)(◦) Maximum Extension 0.5 3.6 0.0 1.4 2.0 0.35 50% Extension -1.3 2.5 0.0 0.4 1.9 0.76 Neutral -1.9 5.8 0.0 1.3 4.0 0.62 50% Flexion -2.3 4.4 -0.1 0.7 3.4 0.76 Maximum Flexion -0.4 2.9 -0.5 0.7 1.9 0.62 50% Flexion -0.7 5.0 0.0 1.5 3.1 0.50 Neutral -0.5 6.3 0.1 2.0 3.7 0.46 50% Extension -1.4 2.8 0.3 0.6 2.1 0.68 Maximum Extension 0.5 3.6 0.0 1.4 2.0 0.35

155 Table 5.18: Comparison of Eﬀects of RCD during FEM cycle for Scaphoid Flexion Specimen 2 Specimen 3 Specimen 4 Average Std. Dev. p-value ∆ (◦) ∆ (◦) ∆ (◦) ∆ (◦)(◦) Maximum Extension -0.5 0.5 -2.0 -0.7 1.3 0.46 50% Extension -0.8 -2.5 -2.5 -1.9 1.0 0.08 Neutral 0.2 -2.9 -3.1 -1.9 1.9 0.21 50% Flexion 1.4 -4.4 -2.5 -1.8 3.0 0.40 Maximum Flexion 1.6 -3.4 -0.4 -0.7 2.5 0.66 50% Flexion 0.3 -3.3 -2.4 -1.8 1.9 0.24 Neutral 0.0 -2.3 -3.3 -1.9 1.7 0.20 50% Extension -0.4 -1.6 -2.6 -1.5 1.1 0.14 Maximum Extension -0.5 0.5 -2.0 -0.7 1.3 0.47

Table 5.19: Comparison of Eﬀects of RCD during FEM cycle for Scaphoid Ulnar Deviation Specimen 2 Specimen 3 Specimen 4 Average Std. Dev. p-value ∆ (◦) ∆ (◦) ∆ (◦) ∆ (◦)(◦) Maximum Extension -0.1 -1.0 3.9 1.0 2.6 0.59 50% Extension -0.9 0.0 3.6 0.9 2.4 0.58 Neutral -0.6 -1.4 3.4 0.5 2.6 0.78 50% Flexion -0.7 -0.7 3.1 0.6 2.2 0.70 Maximum Flexion -0.2 1.4 1.8 1.0 1.1 0.25 50% Flexion -0.4 0.2 2.7 0.9 1.6 0.45 Neutral -0.8 -0.2 3.7 0.9 2.5 0.59 50% Extension -0.3 -0.8 4.1 1.0 2.7 0.59 Maximum Extension -0.1 -1.0 3.9 0.9 2.6 0.59

156 Table 5.20: Comparison of Eﬀects of RCD during FEM cycle for Scaphoid Pronation Specimen 2 Specimen 3 Specimen 4 Average Std. Dev. p-value ∆ (◦) ∆ (◦) ∆ (◦) ∆ (◦)(◦) Maximum Extension 0.6 -0.4 4.4 1.5 2.5 0.40 50% Extension 0.7 -1.4 3.4 0.9 2.4 0.59 Neutral 0.2 2.9 3.8 2.3 1.9 0.16 50% Flexion -1.5 4.2 4.2 2.3 3.3 0.34 Maximum Flexion -1.5 2.4 3.1 1.4 2.5 0.44 50% Flexion -1.1 2.8 3.8 1.8 2.6 0.34 Neutral 0.6 1.5 4.1 2.1 1.8 0.18 50% Extension 1.3 -2.3 4.1 1.0 3.2 0.63 Maximum Extension 0.6 -0.4 4.4 1.5 2.5 0.40

157 Table 5.21: Comparison of Eﬀects of RCD on Metacarpal Flexion

Specimen 1 Specimen 2 Specimen 3 Specimen 4 Average Std. Dev. p-value ∆ (◦) ∆ (◦) ∆ (◦) ∆ (◦) ∆ (◦)(◦) Maximum Extension -1.2 -0.7 1.8 0.6 0.1 1.4 0.86 50% Extension -0.6 -0.3 0.9 0.3 0.1 0.7 0.86 Neutral 0.0 0.0 0.0 0.0 0.0 0.0 NaN 50% Flexion -0.6 3.9 -0.7 0.4 0.7 2.1 0.55 Maximum Flexion -1.2 7.7 -1.5 0.8 1.5 4.3 0.55 50% Flexion -0.6 3.9 -0.7 0.4 0.7 2.1 0.55 Neutral 0.0 0.0 0.0 0.0 0.0 0.0 NaN 50% Extension -0.6 -0.3 0.9 0.3 0.1 0.7 0.86 Maximum Extension -1.2 -0.7 1.8 0.6 0.1 1.4 0.86 158 Table 5.22: Comparison of Eﬀects of RCD on Metacarpal Ulnar Deviation

Specimen 1 Specimen 2 Specimen 3 Specimen 4 Average Std. Dev. p-value ∆ (◦) ∆ (◦) ∆ (◦) ∆ (◦) ∆ (◦)(◦) Maximum Extension 3.3 0.2 -3.5 -0.1 0.0 2.8 0.99

159 50% Extension 1.3 -1.0 -1.7 0.0 -0.4 1.3 0.61 Neutral 0.7 -0.9 0.6 -0.1 0.1 0.7 0.88 50% Flexion -2.1 1.4 1.4 -0.8 0.0 1.7 0.98 Maximum Flexion -2.1 2.6 1.8 -1.8 0.1 2.4 0.92 50% Flexion -1.5 1.9 0.8 -0.6 0.2 1.5 0.84 Neutral -1.2 -1.1 0.5 0.0 -0.5 0.8 0.35 50% Extension 0.1 -1.3 -1.7 0.6 -0.6 1.1 0.36 Maximum Extension 3.2 0.2 -3.5 -0.1 0.0 2.7 0.98 Table 5.23: Comparison of Eﬀects of RCD on Metacarpal Pronation

Specimen 1 Specimen 2 Specimen 3 Specimen 4 Average Std. Dev. p-value ∆ (◦) ∆ (◦) ∆ (◦) ∆ (◦) ∆ (◦)(◦) Maximum Extension 2.0 1.8 -1.2 0.4 0.7 1.5 0.40 50% Extension -0.3 0.2 -1.2 -1.0 -0.6 0.6 0.17 Neutral -1.0 -0.6 3.4 -1.2 0.1 2.2 0.92 50% Flexion -1.8 -2.0 3.2 -1.6 -0.6 2.5 0.69 Maximum Flexion -0.9 -5.2 1.3 -1.6 -1.6 2.7 0.32 50% Flexion -0.2 -1.7 1.9 -1.7 -0.4 1.7 0.67 Neutral -0.6 -0.5 2.2 -1.3 -0.1 1.5 0.93 50% Extension -0.4 0.0 -1.8 -0.1 -0.6 0.8 0.26 Maximum Extension 2.1 1.8 -1.2 0.4 0.8 1.5 0.38 160 Table 5.24: Kinematic Eﬀects of RCD during RUD cycle for Specimen 1 Metacarpal

Wrist Ulnar Deviation Flexion p-value Pronation p-value Ulnar deviation p-value ∆ (◦) ∆ (◦) ∆ (◦) Maximum Radial Deviation -1.2 0.003 -0.71 0.60 -0.6 0.42 50% Radial Deviation -1.7 0.005 1.70 0.02 -0.3 0.42 Neutral -1.3 0.03 3.47 0.05 0.0 NaN 50% Ulnar Deviation -0.1 0.8 4.27 0.12 0.4 0.21 Maximum Ulnar Deviation 4.3 0.002 0.88 0.15 0.9 0.21 50% Ulnar Deviation -0.5 0.09 3.22 0.24 0.4 0.21 Neutral -1.7 0.01 0.44 0.43 0.0 NaN 50% Radial Deviation -1.8 0.02 -1.47 0.11 -0.3 0.42 Maximum Radial Deviation -1.2 0.003 -0.74 0.56 -0.6 0.42

Table 5.25: Kinematic Eﬀects of RCD during RUD cycle for Specimen 2 Metacarpal

Wrist Ulnar Deviation Flexion p-value Pronation p-value Ulnar deviation p-value ∆ (◦) ∆ (◦) ∆ (◦) Maximum Radial Deviation -3.4 0.03 1.2 0.001 0.4 0.03 50% Radial Deviation -1.8 0.06 0.3 0.37 0.2 0.03 Neutral -1.1 0.30 0.4 0.40 0.0 NaN 50% Ulnar Deviation -0.1 0.91 0.5 0.51 0.1 0.58 Maximum Ulnar Deviation -0.2 0.86 1.5 0.11 0.2 0.58 50% Ulnar Deviation 0.1 0.89 0.9 0.25 0.1 0.58 Neutral 0.2 0.80 0.8 0.15 0.0 NaN 50% Radial Deviation 0.0 0.99 0.8 0.06 0.2 0.03 Maximum Radial Deviation -3.5 0.03 1.2 0.001 0.4 0.03

161 Table 5.26: Kinematic Eﬀects of RCD during RUD cycle for Specimen 3 Metacarpal

Wrist Ulnar Deviation Flexion p-value Pronation p-value Ulnar deviation p-value ∆ (◦) ∆ (◦) ∆ (◦) Maximum Radial Deviation -3.4 0.01 4.5 0.00003 -1.2 0.10 50% Radial Deviation -1.1 0.21 2.9 0.001 -0.6 0.10 Neutral -0.2 0.81 2.3 0.01 0.0 NaN 50% Ulnar Deviation -0.4 0.44 2.5 0.01 -0.6 0.03 Maximum Ulnar Deviation -3.4 0.01 1.9 0.10 -1.3 0.03 50% Ulnar Deviation 0.0 0.94 3.0 0.001 -0.6 0.03 Neutral -0.6 0.60 3.5 0.0001 0.0 NaN 50% Radial Deviation -2.1 0.15 3.5 0.0001 -0.6 0.10 Maximum Radial Deviation -3.3 0.01 4.4 0.00003 -1.2 0.10

Table 5.27: Kinematic Eﬀects of RCD during RUD cycle for Specimen 4 Metacarpal

Wrist Ulnar Deviation Flexion p-value Pronation p-value Ulnar deviation p-value ∆ (◦) ∆ (◦) ∆ (◦) Maximum Radial Deviation 1.7 0.19 -1.0 0.11 -0.2 0.32 50% Radial Deviation 1.0 0.03 -1.7 0.05 -0.1 0.32 Neutral 1.0 0.00003 -1.6 0.08 0.0 NaN 50% Ulnar Deviation 0.9 0.0002 -1.7 0.06 -0.4 0.04 Maximum Ulnar Deviation 1.4 0.01 -2.2 0.03 -0.7 0.04 50% Ulnar Deviation 0.9 0.001 -1.7 0.07 -0.4 0.04 Neutral 0.8 0.02 -1.3 0.15 0.0 NaN 50% Radial Deviation 0.9 0.11 -1.3 0.08 -0.1 0.32 Maximum Radial Deviation 1.7 0.19 -1.0 0.13 -0.2 0.32

Table 5.28: Kinematic Eﬀects of RCD during RUD cycle for Specimen 1 Lunate Wrist Ulnar Deviation Flexion p-value Pronation p-value Ulnar deviation p-value ∆ (◦) ∆ (◦) ∆ (◦) Maximum Radial Deviation 0.3 0.26 1.7 0.07 -0.6 0.20 50% Radial Deviation 1.4 0.03 1.8 0.005 0.0 0.94 Neutral 0.7 0.04 1.2 0.10 -0.3 0.30 50% Ulnar Deviation -3.4 0.003 1.9 0.04 1.0 0.06 Maximum Ulnar Deviation -1.7 0.001 1.4 0.004 1.2 0.06 50% Ulnar Deviation -2.3 0.01 2.1 0.08 1.6 0.01 Neutral -0.4 0.66 0.8 0.03 0.7 0.23 50% Radial Deviation 1.6 0.10 0.8 0.10 0.5 0.21 Maximum Radial Deviation 0.2 0.27 1.7 0.06 -0.6 0.19

162 Table 5.29: Kinematic Eﬀects of RCD during RUD cycle for Specimen 2 Lunate* Wrist Ulnar Deviation Flexion p-value Pronation p-value Ulnar deviation p-value ∆ (◦) ∆ (◦) ∆ (◦) Maximum Radial Deviation -1.2 0.12 0.7 0.32 1.1 0.005 50% Radial Deviation 0.8 0.06 0.5 0.40 0.8 0.003 Neutral 0.9 0.02 0.4 0.52 0.7 0.05 50% Ulnar Deviation 2.1 0.01 0.5 0.46 0.9 0.04 Maximum Ulnar Deviation 5.9 0.000002 1.9 0.01 2.6 0.00003 50% Ulnar Deviation 3.3 0.0001 0.5 0.54 1.5 0.001 Neutral 1.3 0.01 0.3 0.66 0.8 0.03 50% Radial Deviation 1.3 0.01 0.5 0.51 0.7 0.03 Maximum Radial Deviation -1.1 0.138 0.7 0.32 1.1 0.004 * Specimen 2 Lunate data is excluded from the averages and statistics shown in Tables 5.36 through 5.38

Table 5.30: Kinematic Eﬀects of RCD during RUD cycle for Specimen 3 Lunate Wrist Ulnar Deviation Flexion p-value Pronation p-value Ulnar deviation p-value ∆ (◦) ∆ (◦) ∆ (◦) Maximum Radial Deviation 2.6 0.02 7.8 0.00004 -0.6 0.40 50% Radial Deviation 3.7 0.001 6.3 0.0001 0.3 0.45 Neutral 4.0 0.001 5.2 0.0004 0.5 0.09 50% Ulnar Deviation 4.0 0.001 2.8 0.002 -0.9 0.07 Maximum Ulnar Deviation 2.6 0.00002 1.8 0.03 -0.3 0.81 50% Ulnar Deviation 4.1 0.001 4.8 0.0001 -2.3 0.002 Neutral 4.1 0.003 5.1 0.00001 -0.4 0.41 50% Radial Deviation 2.8 0.01 6.3 0.00001 -0.5 0.38 Maximum Radial Deviation 2.7 0.01 7.6 0.00004 -0.5 0.47

Table 5.31: Kinematic Eﬀects of RCD during RUD cycle for Specimen 4 Lunate Wrist Ulnar Deviation Flexion p-value Pronation p-value Ulnar deviation p-value ∆ (◦) ∆ (◦) ∆ (◦) Maximum Radial Deviation 2.0 0.02 0.0 0.99 1.9 0.0000004 50% Radial Deviation 1.8 0.003 -0.2 0.34 0.9 0.00001 Neutral 2.1 0.01 -0.2 0.41 1.4 0.000000005 50% Ulnar Deviation 1.5 0.151 -0.3 0.44 2.1 0.00001 Maximum Ulnar Deviation 2.2 0.02 -0.5 0.26 2.4 0.001 50% Ulnar Deviation 0.5 0.580 0.0 1.00 2.1 0.0001 Neutral 0.9 0.097 -0.1 0.57 1.1 0.00002 50% Radial Deviation 1.4 0.02 -0.1 0.49 0.9 0.00001 Maximum Radial Deviation 2.1 0.02 0.0 0.98 2.0 0.0000003

163 Table 5.32: Kinematic Eﬀects of RCD during RUD cycle for Specimen 1 Scaphoid*

Wrist Ulnar Deviation Flexion p-value Pronation p-value Ulnar deviation p-value ∆ (◦) ∆ (◦) ∆ (◦) Maximum Radial Deviation -4.2 0.08 -7.62 0.01 1.4 0.05 50% Radial Deviation -3.3 0.154 -5.94 0.01 1.3 0.01 Neutral -2.6 0.32 -5.35 0.02 1.4 0.01 50% Ulnar Deviation -0.7 0.78 -5.58 0.02 -0.5 0.54 Maximum Ulnar Deviation -1.1 0.61 -9.43 0.00 -4.3 0.01 50% Ulnar Deviation -2.2 0.48 -7.74 0.01 -1.2 0.30 Neutral -3.4 0.29 -7.59 0.001 0.8 0.34 50% Radial Deviation -4.2 0.15 -7.54 0.01 1.0 0.06 Maximum Radial Deviation -4.2 0.08 -7.64 0.01 1.4 0.05 * Specimen 1 Scaphoid data is excluded from the averages and statistics shown in Tables 5.39 through 5.41

Table 5.33: Kinematic Eﬀects of RCD during RUD cycle for Specimen 2 Scaphoid

Wrist Ulnar Deviation Flexion p-value Pronation p-value Ulnar deviation p-value ∆ (◦) ∆ (◦) ∆ (◦) Maximum Extension -3.4 0.03 1.0 0.0001 0.1 0.50 50% Extension -1.3 0.14 1.0 0.00005 0.5 0.05 Neutral -0.4 0.62 1.3 0.0002 0.4 0.10 50% Flexion 0.8 0.41 1.7 0.002 0.2 0.50 Maximum Flexion 3.8 0.001 2.3 0.0001 1.4 0.02 50% Flexion 1.6 0.10 1.6 0.001 0.5 0.01 Neutral 0.6 0.49 1.4 0.0001 0.7 0.0001 50% Extension 0.0 0.99 1.0 0.0001 0.7 0.007 Maximum Extension -3.4 0.04 1.0 0.0001 0.1 0.560

164 Table 5.34: Kinematic Eﬀects of RCD during RUD cycle for Specimen 3 Scaphoid

Wrist Ulnar Deviation Flexion p-value Pronation p-value Ulnar deviation p-value ∆ (◦) ∆ (◦) ∆ (◦) Maximum Radial Deviation -3.6 0.002 1.3 0.02 -0.4 0.35 50% Radial Deviation -1.7 0.02 0.5 0.14 0.3 0.31 Neutral -1.4 0.04 0.1 0.90 0.5 0.19 50% Ulnar Deviation -2.8 0.002 -0.1 0.83 -2.2 0.00001 Maximum Ulnar Deviation -6.0 0.003 -0.7 0.41 -3.7 0.000002 50% Ulnar Deviation -1.7 0.02 1.1 0.02 -1.1 0.0003 Neutral -1.2 0.13 0.5 0.09 0.0 0.88 50% Radial Deviation -2.5 0.05 0.7 0.08 -0.1 0.68 Maximum Radial Deviation -3.5 0.002 1.1 0.02 -0.4 0.29

Table 5.35: Kinematic Eﬀects of RCD during RUD cycle for Specimen 4 Scaphoid

Wrist Ulnar Deviation Flexion p-value Pronation p-value Ulnar deviation p-value ∆ (◦) ∆ (◦) ∆ (◦) Maximum Radial Deviation -1.5 0.14 3.7 0.0000001 3.4 4.3E-11 50% Radial Deviation -2.3 0.001 4.0 0.000001 3.3 4.0E-10 Neutral -2.7 0.0001 4.2 0.000004 2.8 0.00000003 50% Ulnar Deviation -3.2 0.001 4.8 0.00001 2.9 0.0000001 Maximum Ulnar Deviation -3.9 0.0001 5.5 0.0001 3.3 0.001 50% Ulnar Deviation -3.4 0.0004 5.1 0.00001 3.0 0.0000001 Neutral -3.1 0.0002 4.4 0.00001 3.0 0.00000001 50% Radial Deviation -2.5 0.001 4.1 0.00001 3.4 3.5E-09 Maximum Radial Deviation -1.4 0.18 3.7 0.0000001 3.4 2.2E-10

Table 5.36: Comparison of Eﬀects of RCD during RUD cycle for Lunate Flex- ion Specimen 1 Specimen 3 Specimen 4 Average Std. Dev. p-value ∆ (◦) ∆ (◦) ∆ (◦) ∆ (◦)(◦) Maximum Radial Deviation 0.3 2.6 2.0 1.6 1.2 0.14 50% Radial Deviation 1.4 3.7 1.8 2.3 1.2 0.08 Neutral 0.7 4.0 2.1 2.2 1.7 0.15 50% Ulnar Deviation -3.4 4.0 1.5 0.7 3.7 0.79 Maximum Ulnar Deviation -1.7 2.6 2.2 1.0 2.4 0.53 50% Ulnar Deviation -2.3 4.1 0.5 0.8 3.2 0.72 Neutral -0.4 4.1 0.9 1.5 2.3 0.37 50% Radial Deviation 1.6 2.8 1.4 1.9 0.8 0.05 Maximum Radial Deviation 0.2 2.7 2.1 1.7 1.3 0.15

165 Table 5.37: Comparison of Eﬀects of RCD during RUD cycle for Lunate Ul- nar Deviation Specimen 1 Specimen 3 Specimen 4 Average Std. Dev. p-value ∆ (◦) ∆ (◦) ∆ (◦) ∆ (◦)(◦) Maximum Radial Deviation -0.6 -0.6 1.9 0.2 1.5 0.81 50% Radial Deviation 0.0 0.3 0.9 0.4 0.4 0.26 Neutral -0.3 0.5 1.4 0.5 0.9 0.40 50% Ulnar Deviation 1.0 -0.9 2.1 0.8 1.5 0.47 Maximum Ulnar Deviation 1.2 -0.3 2.4 1.1 1.4 0.30 50% Ulnar Deviation 1.6 -2.3 2.1 0.4 2.4 0.78 Neutral 0.7 -0.4 1.1 0.5 0.8 0.39 50% Radial Deviation 0.5 -0.5 0.9 0.3 0.7 0.53 Maximum Radial Deviation -0.6 -0.5 2.0 0.3 1.5 0.77

Table 5.38: Comparison of Eﬀects of RCD during RUD cycle for Lunate Pronation Specimen 1 Specimen 3 Specimen 4 Average Std. Dev. p-value ∆ (◦) ∆ (◦) ∆ (◦) ∆ (◦)(◦) Maximum Radial Deviation 1.7 7.8 0.0 3.1 4.1 0.31 50% Radial Deviation 1.8 6.3 -0.2 2.7 3.3 0.30 Neutral 1.2 5.2 -0.2 2.1 2.8 0.33 50% Ulnar Deviation 1.9 2.8 -0.3 1.5 1.6 0.26 Maximum Ulnar Deviation 1.4 1.8 -0.5 0.9 1.2 0.32 50% Ulnar Deviation 2.1 4.8 0.0 2.3 2.4 0.24 Neutral 0.8 5.1 -0.1 1.9 2.8 0.35 50% Radial Deviation 0.8 6.3 -0.1 2.3 3.5 0.36 Maximum Radial Deviation 1.7 7.6 0.0 3.1 4.0 0.31

166 Table 5.39: Comparison of Eﬀects of RCD during RUD cycle for Scaphoid Flexion Specimen 2 Specimen 3 Specimen 4 Average Std. Dev. p-value ∆ (◦) ∆ (◦) ∆ (◦) ∆ (◦)(◦) Maximum Radial Deviation -3.4 -3.6 -1.5 -2.8 1.2 0.05 50% Radial Deviation -1.3 -1.7 -2.3 -1.8 0.5 0.03 Neutral -0.4 -1.4 -2.7 -1.5 1.2 0.16 50% Ulnar Deviation 0.8 -2.8 -3.2 -1.7 2.2 0.31 Maximum Ulnar Deviation 3.8 -6.0 -3.9 -2.1 5.1 0.56 50% Ulnar Deviation 1.6 -1.7 -3.4 -1.2 2.5 0.50 Neutral 0.6 -1.2 -3.1 -1.2 1.9 0.37 50% Radial Deviation 0.0 -2.5 -2.5 -1.7 1.4 0.18 Maximum Radial Deviation -3.4 -3.5 -1.4 -2.8 1.1 0.05

Table 5.40: Comparison of Eﬀects of RCD during RUD cycle for Scaphoid Ulnar Deviation Specimen 2 Specimen 3 Specimen 4 Average Std. Dev. p-value ∆ (◦) ∆ (◦) ∆ (◦) ∆ (◦)(◦) Maximum Radial Deviation 0.1 -0.4 3.4 1.0 2.0 0.48 50% Radial Deviation 0.5 0.3 3.3 1.4 1.7 0.30 Neutral 0.4 0.5 2.8 1.2 1.3 0.25 50% Ulnar Deviation 0.2 -2.2 2.9 0.3 2.6 0.86 Maximum Ulnar Deviation 1.4 -3.7 3.3 0.4 3.6 0.88 50% Ulnar Deviation 0.5 -1.1 3.0 0.8 2.1 0.58 Neutral 0.7 0.0 3.0 1.2 1.6 0.31 50% Radial Deviation 0.7 -0.1 3.4 1.3 1.9 0.35 Maximum Radial Deviation 0.1 -0.4 3.4 1.0 2.1 0.49

167 Table 5.41: Comparison of Eﬀects of RCD during RUD cycle for Scaphoid Pronation Specimen 2 Specimen 3 Specimen 4 Average Std. Dev. p-value ∆ (◦) ∆ (◦) ∆ (◦) ∆ (◦)(◦) Maximum Radial Deviation 1.0 1.3 3.7 2.0 1.5 0.14 50% Radial Deviation 1.0 0.5 4.0 1.8 1.9 0.24 Neutral 1.3 0.1 4.2 1.9 2.1 0.27 50% Ulnar Deviation 1.7 -0.1 4.8 2.1 2.5 0.28 Maximum Ulnar Deviation 2.3 -0.7 5.5 2.4 3.1 0.32 50% Ulnar Deviation 1.6 1.1 5.1 2.6 2.1 0.17 Neutral 1.4 0.5 4.4 2.1 2.1 0.22 50% Radial Deviation 1.0 0.7 4.1 2.0 1.9 0.21 Maximum Radial Deviation 1.0 1.1 3.7 2.0 1.5 0.16

168 Table 5.42: Comparison of Eﬀects of RCD on Metacarpal Flexion during RUD Specimen 1 Specimen 2 Specimen 3 Specimen 4 Average Std. Dev. p-value ∆ (◦) ∆ (◦) ∆ (◦) ∆ (◦) ∆ (◦)(◦) Maximum Radial Deviation -1.2 -3.4 -3.4 1.7 -1.6 2.4 0.27 50% Radial Deviation -1.7 -1.8 -1.1 1.0 -0.9 1.3 0.25 Neutral -1.3 -1.1 -0.2 1.0 -0.4 1.0 0.50 50% Ulnar Deviation -0.1 -0.1 -0.4 0.9 0.1 0.5 0.84 Maximum Ulnar Deviation 4.3 -0.2 -3.4 1.4 0.5 3.2 0.76 50% Ulnar Deviation -0.5 0.1 0.0 0.9 0.1 0.6 0.68 Neutral -1.7 0.2 -0.6 0.8 -0.3 1.1 0.61 50% Radial Deviation -1.8 0.0 -2.1 0.9 -0.8 1.4 0.36 Maximum Radial Deviation -1.2 -3.5 -3.3 1.7 -1.6 2.4 0.28 169 Table 5.43: Comparison of Eﬀects of RCD on Metacarpal Ulnar Deviation during RUD

Specimen 1 Specimen 2 Specimen 3 Specimen 4 Average Std. Dev. p-value ∆ (◦) ∆ (◦) ∆ (◦) ∆ (◦) ∆ (◦)(◦) Maximum Radial Deviation -0.6 0.4 -1.2 -0.2 -0.4 0.7 0.31 50% Radial Deviation -0.3 0.2 -0.6 -0.1 -0.2 0.3 0.31 Neutral 0.0 0.0 0.0 0.0 0.0 0.0 NaN 50% Ulnar Deviation 0.4 0.1 -0.6 -0.4 -0.1 0.5 0.65 Maximum Ulnar Deviation 0.9 0.2 -1.3 -0.7 -0.2 1.0 0.65 50% Ulnar Deviation 0.4 0.1 -0.6 -0.4 -0.1 0.5 0.65 Neutral 0.0 0.0 0.0 0.0 0.0 0.0 NaN 50% Radial Deviation -0.3 0.2 -0.6 -0.1 -0.2 0.3 0.31 Maximum Radial Deviation -0.6 0.4 -1.2 -0.2 -0.4 0.7 0.31 170 Table 5.44: Comparison of Eﬀects of RCD on Metacarpal Pronation during RUD Specimen 1 Specimen 2 Specimen 3 Specimen 4 Average Std. Dev. p-value ∆ (◦) ∆ (◦) ∆ (◦) ∆ (◦) ∆ (◦)(◦) Maximum Radial Deviation -0.7 1.2 4.5 -1.0 1.0 2.5 0.49 50% Radial Deviation 1.7 0.3 2.9 -1.7 0.8 2.0 0.47 Neutral 3.5 0.4 2.3 -1.6 1.1 2.2 0.38 50% Ulnar Deviation 4.3 0.5 2.5 -1.7 1.4 2.6 0.35 Maximum Ulnar Deviation 0.9 1.5 1.9 -2.2 0.5 1.8 0.61 50% Ulnar Deviation 3.2 0.9 3.0 -1.7 1.4 2.3 0.32 Neutral 0.4 0.8 3.5 -1.3 0.9 2.0 0.44 50% Radial Deviation -1.5 0.8 3.5 -1.3 0.4 2.3 0.77 Maximum Radial Deviation -0.7 1.2 4.4 -1.0 1.0 2.5 0.50 171 Table 5.45: Kinematic Eﬀects of Specimen Removal and Reinstallation Dur- ing FEM Cycle for Specimen 4 Metacarpal

Flexion p-value Pronation p-value Ulnar deviation p-value ∆ (◦) ∆ (◦) ∆ (◦) Maximum Extension -1.6 3.4E-10 -0.5 0.43 1.0 0.05 50% Extension -0.8 3.4E-10 0.2 0.57 1.1 0.01 Neutral 0.0 NaN 0.4 0.34 1.2 0.0000003 50% Flexion -1.2 4.4E-11 -0.1 0.86 -1.2 0.0005 Maximum Flexion -2.3 4.4E-11 1.7 0.00002 -2.1 0.000002 50% Flexion -1.2 4.4E-11 -0.2 0.49 -1.3 0.0001 Neutral 0.0 NaN -0.6 0.07 0.7 0.000001 50% Extension -0.8 3.4E-10 -0.6 0.07 0.8 0.005 Maximum Extension -1.6 3.4E-10 -0.5 0.44 1.0 0.05

Table 5.46: Kinematic Eﬀects of Specimen Removal and Reinstallation Dur- ing FEM Cycle for Specimen 4 Lunate

Flexion p-value Pronation p-value Ulnar deviation p-value ∆ (◦) ∆ (◦) ∆ (◦) Maximum Extension 0.2 0.14 -0.1 0.27 1.0 0.001 50% Extension -1.2 0.003 0.2 0.17 1.1 0.0001 Neutral -1.6 0.0001 0.5 0.02 0.2 0.14 50% Flexion -1.1 0.01 0.4 0.004 0.3 0.001 Maximum Flexion 0.0 0.91 0.5 5.7E-09 0.6 0.0002 50% Flexion -0.8 0.04 0.3 0.003 0.4 0.0001 Neutral -1.4 0.0002 0.2 0.08 0.3 0.05 50% Extension -1.2 0.001 0.0 1.00 0.1 0.45 Maximum Extension 0.2 0.210 -0.1 0.27 0.9 0.001

172 Table 5.47: Kinematic Eﬀects of Specimen Removal and Reinstallation Dur- ing FEM Cycle for Specimen 4 Scaphoid

Flexion p-value Pronation p-value Ulnar deviation p-value ∆ (◦) ∆ (◦) ∆ (◦) Maximum Extension -2.0 0.000002 0.8 0.002 1.2 0.004 50% Extension -1.9 0.00003 1.4 0.00002 2.5 0.000002 Neutral -2.5 0.00002 2.1 8.2E-09 2.4 3.4E-09 50% Flexion -2.4 0.00002 2.6 2.5E-10 2.4 1.9E-08 Maximum Flexion -1.6 0.000002 2.8 1.3E-11 2.7 8.9E-10 50% Flexion -3.0 7.8E-08 3.2 5.3E-12 2.7 2.3E-09 Neutral -2.7 4.7E-11 2.2 1.5E-08 2.3 1.5E-09 50% Extension -2.5 1.9E-09 1.0 0.003 2.3 8.2E-08 Maximum Extension -2.0 0.000002 0.8 0.002 1.2 0.004

Table 5.48: Kinematic Eﬀects of Specimen Removal and Reinstallation Dur- ing RUD Cycle for Specimen 4 Metacarpal

Flexion p-value Pronation p-value Ulnar deviation p-value ∆ (◦) ∆ (◦) ∆ (◦) Maximum Radial Deviation -3.7 0.00002 -1.0 0.04 0.7 0.0002 50% Radial Deviation -2.6 1.8E-07 -0.4 0.40 0.4 0.0002 Neutral -2.3 7.1E-09 0.3 0.62 0.0 NaN 50% Ulnar Deviation -1.8 3.6E-07 0.4 0.50 0.1 0.54 Maximum Ulnar Deviation -1.2 0.006 0.6 0.37 0.2 0.54 50% Ulnar Deviation -1.9 1.9E-08 -0.2 0.67 0.1 0.54 Neutral -2.0 3.00E-08 0.0 0.92 0.0 NaN 50% Radial Deviation -2.2 0.00001 -0.6 0.13 0.4 0.0002 Maximum Radial Deviation -3.7 0.00002 -0.9 0.08 0.7 0.0002

Table 5.49: Kinematic Eﬀects of Specimen Removal and Reinstallation Dur- ing RUD Cycle for Specimen 4 Lunate

Flexion p-value Pronation p-value Ulnar deviation p-value ∆ (◦) ∆ (◦) ∆ (◦) Maximum Radial Deviation -2.7 0.00001 0.1 0.81 0.5 0.0004 50% Radial Deviation -3.4 1.8E-09 0.2 0.19 0.8 6.4E-07 Neutral -4.6 2.8E-09 0.2 0.31 0.5 0.002 50% Ulnar Deviation -6.0 8.8E-07 0.6 0.03 0.8 0.001 Maximum Ulnar Deviation -2.5 0.01 0.2 0.51 0.4 0.39 50% Ulnar Deviation -5.5 0.00001 0.1 0.75 1.7 0.00001 Neutral -5.3 5.4E-13 0.1 0.65 1.1 3.6E-07 50% Radial Deviation -3.1 1.8E-09 0.0 0.91 0.7 0.00003 Maximum Radial Deviation -2.7 0.00002 0.0 0.91 0.4 0.003

173 Table 5.50: Kinematic Eﬀects of Specimen Removal and Reinstallation Dur- ing RUD Cycle for Specimen 4 Scaphoid

Flexion p-value Pronation p-value Ulnar deviation p-value ∆ (◦) ∆ (◦) ∆ (◦) Maximum Radial Deviation -5.8 2.9E-09 0.7 0.01 1.4 1.3E-07 50% Radial Deviation -5.1 2.3E-11 1.5 0.00001 1.6 2.8E-12 Neutral -5.7 4.2E-11 2.3 2.5E-07 1.8 4.1E-07 50% Ulnar Deviation -5.9 3.6E-08 2.5 2.3E-07 1.6 0.00001 Maximum Ulnar Deviation -3.4 0.0003 2.3 0.00001 2.7 0.0004 50% Ulnar Deviation -5.8 1.2E-07 2.0 0.000001 1.4 2.3E-08 Neutral -6.4 2.4E-14 2.5 7.0E-09 0.9 0.0002 50% Radial Deviation -5.2 2.1E-12 1.6 2.0E-07 1.3 5.5E-08 Maximum Radial Deviation -5.9 4.8E-09 0.6 0.02 1.4 7.1E-07

Figure 5-1: Custom-modiﬁed Tekscan sensor with sutures attached to perimeter to aid with securing sensor to wrist of specimen.

174 Figure 5-2: Dorsal aspect of Specimen 1 with Tekscan sensor inserted in wrist joint through dorsal capsulotomy.

175 Figure 5-3: Palmar view of Specimen 1 with posts installed in distal cortex. Sutures attached to the Tekscan sensor are passed through the capsule and secured to the posts to hold the sensor in place.

176 Figure 5-4: Palmar view of right wrist showing scaphoid (in blue) and lunate (in orange) (A) extending during wrist ulnar deviation, (B) in neutral position, (C) ﬂexing during wrist radial deviation.)

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182 Appendix A

Normalized Specimen Data

Table A.1 through Table A.9 show the individual trial and average values of ﬂex- ion, pronation, and ulnar deviation, respectively, for Specimen 1 before RCD for

ﬂexion/extension testing. Table A.10 through Table A.18 show the same information for Specimen 1 following RCD. Similar data for Specimens 2 through 4 are shown in

Table A.19 through Table A.72. The number of trials for each specimen before and after RCD varied between 2 and 6 trials.

Table A.73 through Table A.81 show the individual trial and average values of

ﬂexion, pronation, and ulnar deviation, respectively, for Specimen 1 before RCD for ulnar/radial deviation testing. Table A.82 through Table A.90 show the same information for Specimen 1 following RCD. Similar data for Specimens 2 through 4 are shown in Table A.91 through Table A.144. The number of trials for each specimen before and after RCD varied between 2 and 6 trials.

183 Table A.1: Calculated Global Wrist Flexion for Specimen 1 during FEM Cy- cle, intact

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Average (◦)(◦)(◦)(◦) (◦) Maximum Extension -49.6 -51.3 -52.1 -52.6 -51.4 50% Extension -24.8 -25.7 -26.1 -26.3 -25.7 Neutral 0.0 0.0 0.0 0.0 0.0 50% Flexion 36.8 36.5 35.8 35.8 36.2 Maximum Flexion 73.5 73.0 71.5 71.5 72.4 50% Flexion 36.8 36.5 35.8 35.8 36.2 Neutral 0.0 0.0 0.0 0.0 0.0 50% Extension -24.8 -25.7 -26.1 -26.3 -25.7 Maximum Extension -49.6 -51.3 -52.1 -52.6 -51.4

Table A.2: Calculated Global Wrist Pronation for Specimen 1 during FEM Cycle, intact

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Average (◦)(◦)(◦)(◦) (◦) Maximum Extension -12.3 -11.6 -9.6 -8.1 -10.4 50% Extension -11.9 -11.8 -11.8 -12.0 -11.9 Neutral -9.3 -8.2 -8.9 -9.8 -9.1 50% Flexion -7.5 -7.9 -6.1 -7.2 -7.2 Maximum Flexion -4.6 -4.4 -4.0 -3.4 -4.1 50% Flexion -4.1 -5.3 -4.4 -5.1 -4.7 Neutral -6.8 -7.2 -6.4 -6.7 -6.8 50% Extension -14.2 -14.1 -13.1 -12.4 -13.4 Maximum Extension -12.4 -11.7 -9.6 -8.1 -10.4

184 Table A.3: Calculated Global Wrist Ulnar Deviation for Specimen 1 during FEM Cycle, intact

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Average (◦)(◦)(◦)(◦) (◦) Maximum Extension 14.2 14.6 13.6 13.8 14.0 50% Extension 5.2 6.0 4.3 4.2 4.9 Neutral 6.0 6.1 4.5 4.8 5.3 50% Flexion 7.9 7.2 5.7 5.8 6.6 Maximum Flexion 3.9 3.5 3.2 3.2 3.4 50% Flexion 8.0 7.6 6.4 7.6 7.4 Neutral 5.9 6.2 4.0 4.3 5.1 50% Extension 4.1 5.8 5.7 5.9 5.4 Maximum Extension 14.4 14.8 13.6 13.8 14.1

Table A.4: Calculated Lunate Flexion for Specimen 1 during FEM Cycle, intact Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Average (◦)(◦)(◦)(◦) (◦) Maximum Extension -21.9 -22.8 -22.0 -22.0 -22.2 50% Extension -5.0 -5.8 -6.5 -6.4 -5.9 Neutral 0.2 0.5 -0.8 -1.1 -0.3 50% Flexion 13.7 13.6 14.5 13.1 13.7 Maximum Flexion 43.1 42.9 43.4 43.6 43.3 50% Flexion 19.9 19.5 21.2 20.6 20.3 Neutral 19.9 20.9 22.3 21.7 21.2 50% Extension 4.0 0.5 2.8 2.9 2.6 Maximum Extension -21.9 -22.8 -22.0 -21.9 -22.2

Table A.5: Calculated Lunate Pronation for Specimen 1 during FEM Cycle, intact Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Average (◦)(◦)(◦)(◦) (◦) Maximum Extension -3.0 -1.8 -0.0 0.8 -1.0 50% Extension -1.1 -0.7 -0.4 -0.3 -0.6 Neutral -0.1 1.0 0.6 0.2 0.4 50% Flexion -0.3 -0.2 0.6 -0.2 -0.0 Maximum Flexion 3.4 3.6 3.3 3.5 3.4 50% Flexion 1.3 1.1 1.6 1.4 1.3 Neutral 2.8 2.5 3.4 3.1 3.0 50% Extension -0.1 0.0 1.3 1.3 0.6 Maximum Extension -3.0 -1.8 0.1 0.8 -1.0

185 Table A.6: Calculated Lunate Ulnar Deviation for Specimen 1 during FEM Cycle, intact

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Average (◦)(◦)(◦)(◦) (◦) Maximum Extension -9.2 -6.7 -3.1 -2.7 -5.4 50% Extension -7.1 -5.5 -4.1 -3.9 -5.1 Neutral -6.5 -5.7 -5.1 -4.7 -5.5 50% Flexion -4.1 -3.8 -3.6 -3.4 -3.7 Maximum Flexion -5.2 -5.4 -6.4 -6.6 -5.9 50% Flexion -4.6 -4.9 -5.1 -4.3 -4.7 Neutral -6.8 -8.3 -6.8 -6.6 -7.1 50% Extension -14.2 -11.0 -9.6 -8.7 -10.9 Maximum Extension -9.2 -6.7 -3.1 -2.7 -5.4

Table A.7: Calculated Scaphoid Flexion for Specimen 1 during FEM Cycle, intact Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Average (◦)(◦)(◦)(◦) (◦) Maximum Extension -26.4 -23.6 -24.5 -24.4 -24.7 50% Extension -14.1 -12.1 -16.1 -16.3 -14.7 Neutral -6.3 -5.0 -10.9 -11.4 -8.4 50% Flexion 3.6 4.7 1.8 0.6 2.7 Maximum Flexion 24.4 24.0 22.2 21.8 23.1 50% Flexion 6.7 6.8 4.4 4.2 5.5 Neutral 1.9 1.9 4.0 3.3 2.8 50% Extension -11.1 -10.5 -14.4 -14.5 -12.6 Maximum Extension -26.4 -23.6 -24.5 -24.4 -24.7

Table A.8: Calculated Scaphoid Pronation for Specimen 1 during FEM Cy- cle, intact

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Average (◦)(◦)(◦)(◦) (◦) Maximum Extension -21.6 -22.3 -20.3 -19.3 -20.9 50% Extension -21.8 -21.5 -21.5 -21.6 -21.6 Neutral -20.8 -21.2 -22.9 -23.5 -22.1 50% Flexion -18.6 -17.9 -16.8 -17.4 -17.7 Maximum Flexion -12.4 -11.3 -12.3 -12.6 -12.2 50% Flexion -15.4 -15.6 -16.9 -16.7 -16.2 Neutral -16.5 -17.2 -15.9 -16.2 -16.4 50% Extension -21.5 -22.1 -23.8 -23.1 -22.6 Maximum Extension -21.5 -22.3 -20.2 -19.2 -20.8

186 Table A.9: Calculated Scaphoid Ulnar Deviation for Specimen 1 during FEM Cycle, intact

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Average (◦)(◦)(◦)(◦) (◦) Maximum Extension -4.9 -2.4 -1.8 -1.4 -2.6 50% Extension -13.4 -10.7 -11.3 -11.2 -11.6 Neutral -14.1 -14.7 -16.8 -16.8 -15.6 50% Flexion -13.6 -13.5 -13.0 -13.1 -13.3 Maximum Flexion -14.5 -13.3 -14.8 -15.5 -14.5 50% Flexion -14.2 -13.4 -15.2 -15.3 -14.5 Neutral -16.7 -15.5 -14.2 -14.5 -15.2 50% Extension -13.3 -11.0 -12.9 -12.4 -12.4 Maximum Extension -4.8 -2.3 -1.7 -1.3 -2.5

Table A.10: Calculated Global Wrist Flexion for Specimen 1 during FEM Cycle, RCD

Wrist Position Trial 1 Trial 2 Average (◦)(◦) (◦) Maximum Extension -52.8 -52.5 -52.6 50% Extension -26.4 -26.2 -26.3 Neutral 0.0 0.0 0.0 50% Flexion 35.5 35.6 35.6 Maximum Flexion 71.1 71.2 71.2 50% Flexion 35.5 35.6 35.6 Neutral 0.0 0.0 0.0 50% Extension -26.4 -26.2 -26.3 Maximum Extension -52.8 -52.5 -52.6

Table A.11: Calculated Global Wrist Pronation for Specimen 1 during FEM Cycle, RCD

Wrist Position Trial 1 Trial 2 Average (◦)(◦) (◦) Maximum Extension -8.8 -8.0 -8.4 50% Extension -12.0 -12.3 -12.2 Neutral -10.3 -9.8 -10.0 50% Flexion -8.9 -9.0 -9.0 Maximum Flexion -4.8 -5.1 -4.9 50% Flexion -4.6 -5.3 -4.9 Neutral -7.5 -7.4 -7.5 50% Extension -13.2 -14.5 -13.9 Maximum Extension -8.8 -8.0 -8.4

187 Table A.12: Calculated Global Wrist Ulnar Deviation for Specimen 1 during FEM Cycle, RCD

Wrist Position Trial 1 Trial 2 Average (◦)(◦) (◦) Maximum Extension 17.4 17.2 17.3 50% Extension 6.4 6.0 6.2 Neutral 5.6 6.4 6.0 50% Flexion 4.4 4.7 4.5 Maximum Flexion 1.1 1.5 1.3 50% Flexion 6.4 5.5 6.0 Neutral 3.9 4.0 3.9 50% Extension 5.7 5.3 5.5 Maximum Extension 17.5 17.2 17.4

Table A.13: Calculated Lunate Flexion for Specimen 1 during FEM Cycle, RCD Wrist Position Trial 1 Trial 2 Average (◦)(◦) (◦) Maximum Extension -22.5 -22.0 -22.2 50% Extension -9.7 -9.2 -9.4 Neutral -0.6 -1.4 -1.0 50% Flexion 13.5 13.5 13.5 Maximum Flexion 42.9 42.6 42.8 50% Flexion 22.5 20.8 21.6 Neutral 23.0 21.6 22.3 50% Extension 2.2 1.5 1.8 Maximum Extension -22.5 -22.1 -22.3

Table A.14: Calculated Lunate Pronation for Specimen 1 during FEM Cycle, RCD Wrist Position Trial 1 Trial 2 Average (◦)(◦) (◦) Maximum Extension -0.7 -0.3 -0.5 50% Extension -1.9 -1.9 -1.9 Neutral -1.4 -1.5 -1.4 50% Flexion -2.3 -2.3 -2.3 Maximum Flexion 3.1 3.0 3.1 50% Flexion 0.8 0.5 0.7 Neutral 2.6 2.3 2.5 50% Extension -0.3 -1.2 -0.7 Maximum Extension -0.6 -0.3 -0.5

188 Table A.15: Calculated Lunate Ulnar Deviation for Specimen 1 during FEM Cycle, RCD

Wrist Position Trial 1 Trial 2 Average (◦)(◦) (◦) Maximum Extension -0.3 -0.5 -0.4 50% Extension -3.2 -3.4 -3.3 Neutral -5.3 -4.9 -5.1 50% Flexion -5.6 -5.2 -5.4 Maximum Flexion -7.5 -7.3 -7.4 50% Flexion -6.7 -7.0 -6.8 Neutral -9.3 -8.9 -9.1 50% Extension -10.5 -9.3 -9.9 Maximum Extension -0.3 -0.5 -0.4

Table A.16: Calculated Scaphoid Flexion for Specimen 1 during FEM Cycle, RCD Wrist Position Trial 1 Trial 2 Average (◦)(◦) (◦) Maximum Extension -32.6 -32.6 -32.6 50% Extension -19.2 -19.2 -19.2 Neutral -12.9 -12.6 -12.8 50% Flexion -3.2 -4.0 -3.6 Maximum Flexion 13.1 12.2 12.7 50% Flexion 0.6 -0.0 0.3 Neutral 1.5 0.8 1.1 50% Extension -16.8 -16.8 -16.8 Maximum Extension -32.8 -32.7 -32.7

Table A.17: Calculated Scaphoid Pronation for Specimen 1 during FEM Cy- cle, RCD

Wrist Position Trial 1 Trial 2 Average (◦)(◦) (◦) Maximum Extension -32.5 -32.4 -32.4 50% Extension -32.3 -32.6 -32.5 Neutral -32.0 -32.0 -32.0 50% Flexion -27.0 -27.1 -27.0 Maximum Flexion -26.6 -26.9 -26.7 50% Flexion -25.7 -26.5 -26.1 Neutral -23.8 -24.5 -24.1 50% Extension -31.3 -32.7 -32.0 Maximum Extension -32.5 -32.4 -32.5

189 Table A.18: Calculated Scaphoid Ulnar Deviation for Specimen 1 during FEM Cycle, RCD

Wrist Position Trial 1 Trial 2 Average (◦)(◦) (◦) Maximum Extension -5.5 -5.5 -5.5 50% Extension -12.6 -12.5 -12.6 Neutral -14.8 -14.6 -14.7 50% Flexion -12.4 -12.5 -12.5 Maximum Flexion -13.8 -14.0 -13.9 50% Flexion -13.5 -12.9 -13.2 Neutral -14.6 -14.3 -14.4 50% Extension -12.0 -11.8 -11.9 Maximum Extension -5.5 -5.5 -5.5

190 Table A.19: Calculated Global Wrist Flexion for Specimen 2 during FEM Cycle, intact

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Extension -51.9 -51.1 -51.3 -50.5 -53.1 -52.9 -51.8 50% Extension -26.0 -25.6 -25.6 -25.2 -26.5 -26.5 -25.9 Neutral 0.0 0.0 0.0 0.0 0.0 0.0 0.0 50% Flexion 29.9 27.9 28.0 28.5 26.3 27.1 28.0 Maximum Flexion 59.9 55.8 56.0 57.0 52.7 54.2 55.9 50% Flexion 29.9 27.9 28.0 28.5 26.3 27.1 28.0 Neutral 0.0 0.0 0.0 0.0 0.0 0.0 0.0 50% Extension -26.0 -25.6 -25.6 -25.2 -26.5 -26.5 -25.9 Maximum Extension -51.9 -51.1 -51.3 -50.5 -53.1 -52.9 -51.8

Table A.20: Calculated Global Wrist Pronation for Specimen 2 during FEM Cycle, intact

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Extension -15.4 -16.1 -15.5 -15.7 -14.5 -13.7 -15.1 50% Extension -15.0 -14.8 -14.8 -14.1 -13.6 -13.7 -14.3 Neutral -10.6 -11.2 -10.8 -10.1 -8.5 -9.1 -10.1 50% Flexion -6.6 -5.6 -6.2 -5.3 -3.6 -4.5 -5.3 Maximum Flexion -8.0 -4.9 -5.0 -5.5 -2.0 -2.7 -4.7 50% Flexion -4.4 -4.1 -4.9 -4.7 -3.2 -3.5 -4.1 Neutral -10.7 -9.7 -10.3 -10.3 -9.1 -8.4 -9.7 50% Extension -14.4 -14.1 -13.5 -13.9 -13.1 -12.7 -13.6 Maximum Extension -15.4 -16.1 -15.6 -15.7 -14.5 -13.7 -15.1

191 Table A.21: Calculated Global Wrist Ulnar Deviation for Specimen 2 during FEM Cycle, intact

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Extension -4.5 -4.9 -3.9 -4.1 -4.0 -4.3 -4.3 50% Extension -5.7 -5.1 -5.1 -3.7 -3.8 -3.5 -4.5 Neutral -2.2 -2.1 -2.0 -1.8 -2.4 -2.1 -2.1 50% Flexion -0.1 -0.9 -1.3 -1.1 -3.2 -1.8 -1.4 Maximum Flexion 4.6 3.0 3.3 3.6 1.5 2.5 3.1 50% Flexion -0.0 -0.4 -0.6 -0.8 -1.1 -1.4 -0.7 Neutral -2.4 -2.1 -1.7 -1.6 -1.8 -1.9 -1.9 50% Extension -5.3 -4.9 -3.9 -4.1 -4.3 -3.7 -4.4 Maximum Extension -4.5 -4.9 -3.9 -4.1 -4.0 -4.3 -4.3

Table A.22: Calculated Lunate Flexion for Specimen 2 during FEM Cycle, intact Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Extension -6.1 -5.6 -6.2 -6.1 -8.3 -8.4 -6.8 50% Extension 11.2 11.5 11.2 12.7 10.6 11.9 11.5 Neutral 20.8 20.9 22.4 22.4 22.6 23.2 22.0 50% Flexion 15.7 15.5 16.4 15.7 15.8 16.4 15.9 Maximum Flexion 13.5 13.8 14.1 13.9 14.6 14.1 14.0 50% Flexion 11.7 11.5 12.3 12.4 12.7 13.0 12.3 Neutral 15.0 14.3 16.0 16.1 16.6 16.2 15.7 50% Extension 8.1 7.8 7.9 8.2 6.7 6.8 7.6 Maximum Extension -6.1 -5.6 -6.2 -6.0 -8.3 -8.4 -6.7

Table A.23: Calculated Lunate Pronation for Specimen 2 during FEM Cycle, intact Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Extension 0.0 -0.6 -1.5 -1.8 -1.7 -1.4 -1.2 50% Extension -1.4 -1.8 -2.7 -2.4 -2.8 -2.5 -2.3 Neutral -3.6 -4.2 -4.4 -4.5 -4.3 -4.3 -4.2 50% Flexion -7.0 -7.4 -8.5 -8.8 -9.5 -8.7 -8.3 Maximum Flexion -18.0 -16.6 -17.0 -17.3 -15.9 -15.9 -16.8 50% Flexion -9.2 -9.2 -10.7 -10.6 -10.3 -10.2 -10.0 Neutral -6.6 -7.2 -8.2 -8.4 -8.8 -8.7 -8.0 50% Extension -4.3 -5.4 -6.3 -6.7 -7.0 -7.0 -6.1 Maximum Extension 0.1 -0.6 -1.4 -1.8 -1.7 -1.4 -1.1

192 Table A.24: Calculated Lunate Ulnar Deviation for Specimen 2 during FEM Cycle, intact

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Extension -19.0 -19.8 -20.6 -20.9 -20.7 -20.7 -20.3 50% Extension -21.6 -21.6 -22.3 -21.8 -22.4 -22.0 -21.9 Neutral -21.4 -21.6 -21.2 -21.1 -21.5 -21.0 -21.3 50% Flexion -25.9 -26.7 -27.2 -27.6 -28.4 -27.8 -27.3 Maximum Flexion -20.0 -22.3 -22.5 -22.1 -24.5 -24.0 -22.6 50% Flexion -26.7 -27.6 -28.1 -28.3 -28.8 -28.8 -28.1 Neutral -24.9 -25.4 -25.4 -25.3 -25.4 -25.7 -25.3 50% Extension -22.8 -23.4 -24.2 -24.6 -24.6 -24.9 -24.1 Maximum Extension -19.0 -19.8 -20.5 -20.9 -20.7 -20.7 -20.3

Table A.25: Calculated Scaphoid Flexion for Specimen 2 during FEM Cycle, intact Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Extension -5.8 -5.2 -5.4 -4.9 -6.1 -6.1 -5.6 50% Extension 12.4 12.6 13.2 13.7 12.1 12.5 12.7 Neutral 32.9 33.1 34.5 34.7 35.5 35.3 34.3 50% Flexion 50.3 49.8 51.6 51.5 51.7 51.4 51.0 Maximum Flexion 68.0 66.6 67.0 67.0 66.1 65.9 66.7 50% Flexion 49.6 48.6 50.7 50.7 49.9 50.5 50.0 Neutral 31.6 31.7 33.5 33.6 34.3 34.2 33.1 50% Extension 11.6 12.2 12.8 13.6 11.7 11.7 12.3 Maximum Extension -5.8 -5.2 -5.4 -4.9 -6.1 -6.1 -5.6

Table A.26: Calculated Scaphoid Pronation for Specimen 2 during FEM Cy- cle, intact

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Extension 2.3 2.7 2.9 2.9 2.6 2.7 2.7 50% Extension 5.0 4.7 5.1 5.0 5.0 4.7 4.9 Neutral 7.7 7.4 8.1 8.6 9.8 9.0 8.4 50% Flexion 8.5 9.2 9.4 9.7 11.3 10.4 9.8 Maximum Flexion 4.8 6.2 6.2 6.2 7.9 7.4 6.4 50% Flexion 8.9 9.3 9.0 9.2 10.1 10.0 9.4 Neutral 7.8 8.2 8.4 8.2 8.8 9.4 8.4 50% Extension 6.4 6.3 6.6 6.6 6.9 6.6 6.6 Maximum Extension 2.3 2.7 2.9 2.9 2.6 2.7 2.7

193 Table A.27: Calculated Scaphoid Ulnar Deviation for Specimen 2 during FEM Cycle, intact

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Extension -5.2 -5.3 -5.0 -5.4 -4.8 -4.9 -5.1 50% Extension -5.6 -5.2 -5.0 -4.3 -4.4 -4.4 -4.8 Neutral -2.3 -2.0 -1.1 -0.6 -0.1 -0.4 -1.1 50% Flexion 2.8 2.5 2.9 3.2 2.9 2.8 2.8 Maximum Flexion 11.5 10.9 11.4 11.6 10.7 11.2 11.2 50% Flexion 3.6 2.8 3.4 3.4 3.0 3.1 3.2 Neutral -2.2 -1.9 -0.8 -0.6 -0.3 -0.4 -1.0 50% Extension -3.5 -3.4 -2.6 -2.6 -2.3 -2.4 -2.8 Maximum Extension -5.2 -5.4 -5.0 -5.4 -4.8 -5.0 -5.1

Table A.28: Calculated Global Wrist Flexion for Specimen 2 during FEM Cycle, RCD

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Extension -52.0 -52.4 -51.8 -52.6 -53.2 -52.7 -52.5 50% Extension -26.0 -26.2 -25.9 -26.3 -26.6 -26.3 -26.2 Neutral 0.0 0.0 0.0 0.0 0.0 0.0 0.0 50% Flexion 33.1 32.5 31.1 30.9 32.2 31.0 31.8 Maximum Flexion 66.2 65.0 62.2 61.8 64.5 62.1 63.6 50% Flexion 33.1 32.5 31.1 30.9 32.2 31.0 31.8 Neutral 0.0 0.0 0.0 0.0 0.0 0.0 0.0 50% Extension -26.0 -26.2 -25.9 -26.3 -26.6 -26.3 -26.2 Maximum Extension -52.0 -52.4 -51.8 -52.6 -53.2 -52.7 -52.5

Table A.29: Calculated Global Wrist Pronation for Specimen 2 during FEM Cycle, RCD

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Extension -13.0 -13.5 -13.4 -13.0 -13.6 -13.6 -13.3 50% Extension -13.4 -13.4 -14.3 -13.9 -14.5 -15.3 -14.1 Neutral -10.3 -9.1 -11.1 -10.7 -11.3 -11.8 -10.7 50% Flexion -7.6 -5.7 -7.5 -7.3 -7.9 -7.6 -7.3 Maximum Flexion -12.3 -10.8 -7.9 -8.4 -11.2 -8.6 -9.9 50% Flexion -7.3 -6.5 -5.4 -5.8 -6.0 -3.9 -5.8 Neutral -10.0 -9.6 -10.6 -10.4 -11.0 -10.0 -10.3 50% Extension -13.3 -13.6 -13.6 -13.4 -13.7 -14.0 -13.6 Maximum Extension -13.0 -13.5 -13.4 -13.0 -13.6 -13.6 -13.4

194 Table A.30: Calculated Global Wrist Ulnar Deviation for Specimen 2 during FEM Cycle, RCD

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Extension -4.6 -4.1 -4.2 -4.1 -3.5 -3.7 -4.0 50% Extension -5.4 -5.4 -5.7 -5.2 -5.1 -6.4 -5.5 Neutral -2.9 -3.0 -3.0 -2.8 -3.0 -3.2 -3.0 50% Flexion 0.7 0.6 -0.1 -0.4 0.1 -0.6 0.1 Maximum Flexion 6.0 6.2 5.6 5.5 5.8 5.2 5.7 50% Flexion 2.1 1.9 0.6 0.8 1.1 0.4 1.2 Neutral -3.4 -3.4 -2.8 -3.1 -2.8 -2.8 -3.0 50% Extension -6.2 -6.3 -5.5 -5.4 -5.5 -5.3 -5.7 Maximum Extension -4.6 -4.1 -4.2 -4.1 -3.5 -3.7 -4.0

Table A.31: Calculated Lunate Flexion for Specimen 2 during FEM Cycle, RCD Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Extension -8.9 -8.8 -8.9 -9.6 -10.2 -9.9 -9.4 50% Extension 8.3 7.9 8.7 8.7 9.2 8.5 8.5 Neutral 20.8 20.5 20.9 21.3 22.0 21.6 21.2 50% Flexion 16.5 15.9 17.0 16.8 17.0 16.7 16.7 Maximum Flexion 13.3 13.1 13.6 13.6 12.9 12.6 13.2 50% Flexion 11.6 12.0 13.1 13.1 12.8 12.0 12.4 Neutral 16.3 16.3 17.2 17.0 17.1 16.3 16.7 50% Extension 7.4 7.3 8.6 8.2 8.1 7.9 7.9 Maximum Extension -8.9 -8.8 -8.9 -9.6 -10.2 -9.9 -9.4

Table A.32: Calculated Lunate Pronation for Specimen 2 during FEM Cycle, RCD Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Extension -0.4 -0.7 -2.2 -1.8 -2.8 -2.5 -1.7 50% Extension -2.9 -2.9 -4.3 -4.1 -4.7 -4.7 -3.9 Neutral -5.4 -5.1 -7.0 -6.7 -7.1 -7.2 -6.4 50% Flexion -9.1 -8.7 -9.7 -9.8 -10.6 -10.5 -9.7 Maximum Flexion -19.6 -19.5 -18.6 -18.5 -20.1 -20.0 -19.4 50% Flexion -10.9 -10.2 -10.5 -10.5 -11.7 -11.6 -10.9 Neutral -6.5 -6.2 -8.0 -8.1 -8.9 -8.7 -7.7 50% Extension -3.9 -4.0 -5.4 -5.4 -5.9 -6.5 -5.2 Maximum Extension -0.4 -0.6 -2.2 -1.8 -2.8 -2.5 -1.7

195 Table A.33: Calculated Lunate Ulnar Deviation for Specimen 2 during FEM Cycle, RCD

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Extension -19.8 -19.6 -20.9 -20.6 -21.2 -21.2 -20.6 50% Extension -22.4 -22.4 -23.2 -22.9 -23.2 -23.7 -23.0 Neutral -22.3 -22.3 -22.4 -22.3 -22.1 -22.5 -22.3 50% Flexion -25.0 -25.4 -26.3 -26.4 -26.5 -27.0 -26.1 Maximum Flexion -18.4 -18.9 -20.9 -20.9 -20.1 -21.5 -20.1 50% Flexion -24.6 -24.9 -27.0 -26.9 -27.1 -27.9 -26.4 Neutral -24.2 -24.0 -24.5 -24.8 -25.1 -25.6 -24.7 50% Extension -23.0 -22.8 -23.6 -23.5 -23.9 -24.2 -23.5 Maximum Extension -19.8 -19.6 -20.9 -20.6 -21.2 -21.2 -20.5

Table A.34: Calculated Scaphoid Flexion for Specimen 2 during FEM Cycle, RCD Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Extension -6.5 -6.1 -5.6 -6.0 -6.2 -6.0 -6.1 50% Extension 10.9 10.7 12.3 12.0 12.7 13.0 11.9 Neutral 33.3 33.3 34.3 34.9 35.8 35.7 34.5 50% Flexion 51.4 51.3 52.4 52.4 54.0 53.3 52.5 Maximum Flexion 68.5 68.5 67.9 67.7 68.7 68.7 68.4 50% Flexion 48.8 48.6 50.6 50.4 51.9 51.5 50.3 Neutral 32.0 31.8 33.4 33.6 34.2 33.9 33.1 50% Extension 11.2 11.0 12.6 12.0 12.2 12.5 11.9 Maximum Extension -6.5 -6.1 -5.6 -6.0 -6.2 -6.0 -6.1

Table A.35: Calculated Scaphoid Pronation for Specimen 2 during FEM Cy- cle, RCD

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Extension 4.0 2.9 3.7 3.2 2.9 3.0 3.3 50% Extension 5.9 5.7 5.7 5.4 5.3 5.8 5.6 Neutral 8.7 9.3 8.3 8.6 8.6 8.4 8.7 50% Flexion 7.7 8.5 8.4 8.4 8.3 8.5 8.3 Maximum Flexion 4.1 4.6 5.3 5.3 5.0 5.4 5.0 50% Flexion 7.2 7.7 8.5 8.5 8.6 9.3 8.3 Neutral 8.9 9.1 8.8 9.0 9.0 9.5 9.1 50% Extension 8.2 8.0 7.8 7.7 8.0 7.6 7.9 Maximum Extension 4.0 2.9 3.7 3.2 2.9 3.0 3.3

196 Table A.36: Calculated Scaphoid Ulnar Deviation for Specimen 2 during FEM Cycle, RCD

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Extension -4.8 -5.4 -5.1 -5.3 -5.1 -5.3 -5.2 50% Extension -5.7 -6.0 -5.7 -5.6 -5.4 -6.0 -5.7 Neutral -1.9 -1.7 -1.8 -1.6 -1.3 -1.8 -1.7 50% Flexion 1.5 2.0 2.1 2.0 2.8 2.4 2.1 Maximum Flexion 10.7 10.8 10.8 10.8 11.4 11.3 11.0 50% Flexion 2.0 2.2 2.7 2.7 3.7 3.8 2.9 Neutral -2.7 -2.5 -1.6 -1.9 -1.3 -1.2 -1.9 50% Extension -3.7 -3.7 -2.9 -2.7 -2.7 -2.5 -3.0 Maximum Extension -4.8 -5.4 -5.1 -5.3 -5.1 -5.3 -5.2

197 Table A.37: Calculated Global Wrist Flexion for Specimen 3 during FEM Cycle, intact

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Extension -52.9 -53.2 -51.8 -52.3 -51.8 -51.6 -52.3 50% Extension -26.5 -26.6 -25.9 -26.1 -25.9 -25.8 -26.1 Neutral 0.0 0.0 0.0 0.0 0.0 0.0 0.0 50% Flexion 32.5 32.3 32.6 32.5 32.4 32.4 32.5 Maximum Flexion 65.0 64.7 65.2 65.1 64.8 64.8 64.9 50% Flexion 32.5 32.3 32.6 32.5 32.4 32.4 32.5 Neutral 0.0 0.0 0.0 0.0 0.0 0.0 0.0 50% Extension -26.5 -26.6 -25.9 -26.1 -25.9 -25.8 -26.1 Maximum Extension -52.9 -53.2 -51.8 -52.3 -51.8 -51.6 -52.3

Table A.38: Calculated Global Wrist Pronation for Specimen 3 during FEM Cycle, intact

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Extension 5.6 6.4 6.2 6.4 6.5 6.0 6.2 50% Extension 12.4 14.2 14.5 15.5 14.1 15.2 14.3 Neutral 17.8 21.6 21.4 21.3 19.0 23.0 20.7 50% Flexion 19.7 21.5 21.9 22.3 19.9 22.5 21.3 Maximum Flexion 12.5 12.1 11.5 12.7 11.0 11.9 12.0 50% Flexion 24.1 24.8 24.7 25.2 24.9 25.3 24.8 Neutral 25.1 24.8 25.0 25.9 26.2 25.6 25.4 50% Extension 16.9 17.4 17.6 18.0 17.8 18.2 17.7 Maximum Extension 5.4 6.3 6.2 6.4 6.5 6.0 6.2

198 Table A.39: Calculated Global Wrist Ulnar Deviation for Specimen 3 during FEM Cycle, intact

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Extension -13.8 -13.8 -14.9 -14.9 -15.4 -15.5 -14.7 50% Extension -11.6 -11.1 -11.9 -11.7 -11.9 -11.4 -11.6 Neutral -3.0 -2.4 -2.3 -2.4 -2.6 -2.2 -2.5 50% Flexion 12.5 12.1 12.6 12.7 12.9 12.7 12.6 Maximum Flexion 23.2 23.4 24.2 24.6 24.4 24.6 24.1 50% Flexion 11.8 12.2 12.3 12.4 12.6 12.6 12.3 Neutral -2.0 -1.7 -1.9 -1.6 -1.7 -1.8 -1.8 50% Extension -10.9 -10.4 -11.6 -11.4 -11.9 -11.5 -11.3 Maximum Extension -13.8 -13.8 -14.9 -14.9 -15.5 -15.5 -14.7

Table A.40: Calculated Lunate Flexion for Specimen 3 during FEM Cycle, intact Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Extension -20.0 -19.9 -19.2 -19.0 -18.6 -18.3 -19.1 50% Extension -16.7 -16.8 -16.2 -16.0 -15.3 -15.1 -16.0 Neutral -13.0 -12.4 -12.1 -11.2 -10.8 -9.8 -11.6 50% Flexion 5.1 8.6 8.6 10.3 9.0 11.1 8.8 Maximum Flexion 28.0 28.7 30.1 30.9 30.9 31.4 30.0 50% Flexion 7.3 7.7 9.1 9.4 9.9 9.7 8.8 Neutral -13.7 -13.2 -13.0 -12.6 -11.9 -11.8 -12.7 50% Extension -17.3 -17.8 -17.2 -17.1 -16.6 -16.5 -17.1 Maximum Extension -19.9 -19.9 -19.2 -19.0 -18.6 -18.3 -19.2

Table A.41: Calculated Lunate Pronation for Specimen 3 during FEM Cycle, intact Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Extension 17.8 18.0 18.6 18.7 18.7 18.5 18.4 50% Extension 17.8 18.6 18.7 19.3 18.7 19.3 18.7 Neutral 18.3 20.8 20.7 20.9 19.7 22.6 20.5 50% Flexion 19.0 21.1 21.0 21.7 20.1 21.9 20.8 Maximum Flexion 17.4 17.5 17.2 17.7 17.2 17.6 17.4 50% Flexion 18.9 20.1 20.2 20.5 20.6 20.9 20.2 Neutral 20.5 20.9 21.5 21.9 22.6 22.3 21.6 50% Extension 20.9 20.4 20.4 20.4 20.3 20.7 20.5 Maximum Extension 17.8 18.1 18.6 18.8 18.7 18.5 18.4

199 Table A.42: Calculated Lunate Ulnar Deviation for Specimen 3 during FEM Cycle, intact

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Extension -16.4 -16.4 -16.2 -16.2 -15.9 -15.7 -16.1 50% Extension -17.8 -18.2 -17.7 -18.0 -17.3 -17.5 -17.8 Neutral -17.0 -18.3 -17.7 -17.7 -16.6 -18.0 -17.5 50% Flexion -12.8 -12.5 -12.7 -12.4 -11.7 -11.5 -12.3 Maximum Flexion -3.5 -3.1 -3.1 -2.7 -2.2 -1.9 -2.7 50% Flexion -11.0 -11.2 -11.3 -11.4 -11.1 -11.0 -11.2 Neutral -17.3 -17.3 -17.6 -17.7 -18.0 -17.5 -17.6 50% Extension -18.6 -18.2 -17.7 -17.6 -17.3 -17.3 -17.8 Maximum Extension -16.4 -16.4 -16.3 -16.2 -15.9 -15.7 -16.1

Table A.43: Calculated Scaphoid Flexion for Specimen 3 during FEM Cycle, intact Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Extension -28.9 -29.8 -29.6 -29.7 -30.3 -30.4 -29.8 50% Extension -9.9 -10.3 -10.4 -10.4 -11.0 -10.6 -10.4 Neutral 7.3 7.4 5.7 6.0 5.0 5.6 6.2 50% Flexion 26.6 28.9 27.3 28.2 26.3 27.9 27.5 Maximum Flexion 52.5 52.7 52.4 52.8 51.8 52.4 52.4 50% Flexion 28.0 28.1 27.5 27.6 26.9 27.0 27.5 Neutral 2.7 2.9 1.7 1.7 1.2 1.3 1.9 50% Extension -13.9 -15.5 -14.7 -15.1 -15.6 -15.5 -15.1 Maximum Extension -28.8 -29.9 -29.6 -29.8 -30.4 -30.5 -29.8

Table A.44: Calculated Scaphoid Pronation for Specimen 3 during FEM Cy- cle, intact

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Extension 20.9 20.9 21.1 21.3 21.1 20.7 21.0 50% Extension 26.2 27.2 27.7 28.4 27.3 27.6 27.4 Neutral 32.8 35.2 35.6 35.5 33.5 36.4 34.8 50% Flexion 36.8 38.0 39.1 39.2 37.7 39.3 38.4 Maximum Flexion 31.3 31.3 31.7 32.0 31.8 32.0 31.7 50% Flexion 39.6 40.7 41.1 41.2 41.4 41.4 40.9 Neutral 40.4 40.6 41.1 41.5 41.8 41.0 41.1 50% Extension 31.8 31.6 32.4 32.4 32.2 32.3 32.1 Maximum Extension 20.8 20.9 21.0 21.3 21.1 20.7 21.0

200 Table A.45: Calculated Scaphoid Ulnar Deviation for Specimen 3 during FEM Cycle, intact

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Extension -8.7 -8.3 -8.5 -8.4 -8.1 -8.0 -8.3 50% Extension -6.3 -6.3 -5.6 -5.8 -5.6 -5.6 -5.9 Neutral -2.5 -2.1 -2.4 -2.5 -2.7 -2.5 -2.4 50% Flexion 6.2 8.0 7.5 8.3 7.3 8.6 7.6 Maximum Flexion 18.0 18.4 19.0 19.7 19.4 20.0 19.1 50% Flexion 6.2 6.6 7.1 7.3 7.0 7.2 6.9 Neutral -5.1 -5.0 -5.3 -5.3 -5.3 -5.3 -5.2 50% Extension -9.9 -10.5 -9.5 -9.8 -9.8 -9.7 -9.9 Maximum Extension -8.7 -8.3 -8.5 -8.4 -8.2 -8.1 -8.4

Table A.46: Calculated Global Wrist Flexion for Specimen 3 during FEM Cycle, RCD

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Extension -51.3 -51.5 -49.4 -49.4 -51.0 -50.2 -50.5 50% Extension -25.6 -25.8 -24.7 -24.7 -25.5 -25.1 -25.2 Neutral 0.0 0.0 0.0 0.0 0.0 0.0 0.0 50% Flexion 31.6 31.4 31.8 31.6 31.8 32.0 31.7 Maximum Flexion 63.3 62.9 63.6 63.2 63.6 64.1 63.4 50% Flexion 31.6 31.4 31.8 31.6 31.8 32.0 31.7 Neutral 0.0 0.0 0.0 0.0 0.0 0.0 0.0 50% Extension -25.6 -25.8 -24.7 -24.7 -25.5 -25.1 -25.2 Maximum Extension -51.3 -51.5 -49.4 -49.4 -51.0 -50.2 -50.5

Table A.47: Calculated Global Wrist Pronation for Specimen 3 during FEM Cycle, RCD

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Extension 2.8 3.6 6.6 6.7 5.1 5.0 5.0 50% Extension 10.3 11.1 13.5 16.2 14.2 13.3 13.1 Neutral 18.8 21.5 25.2 28.8 26.3 23.7 24.1 50% Flexion 22.6 23.8 25.5 26.0 24.9 24.0 24.5 Maximum Flexion 13.2 12.9 14.0 14.9 12.5 11.9 13.2 50% Flexion 25.9 26.8 27.1 25.8 28.0 27.0 26.8 Neutral 25.3 26.8 28.1 26.1 28.9 30.2 27.6 50% Extension 14.7 14.2 17.2 16.1 17.2 16.2 15.9 Maximum Extension 2.8 3.6 6.6 6.7 5.2 5.1 5.0

201 Table A.48: Calculated Global Wrist Ulnar Deviation for Specimen 3 during FEM Cycle, RCD

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Extension -17.1 -17.1 -19.1 -19.1 -18.2 -18.6 -18.2 50% Extension -13.2 -13.2 -13.8 -13.0 -13.2 -13.5 -13.3 Neutral -1.8 -2.0 -2.0 -2.0 -1.8 -1.8 -1.9 50% Flexion 13.6 13.3 14.0 13.7 14.4 14.7 14.0 Maximum Flexion 24.8 24.6 26.1 26.0 26.6 27.1 25.9 50% Flexion 12.4 12.8 13.1 13.0 13.5 14.1 13.1 Neutral -1.0 -1.2 -1.7 -1.2 -1.5 -1.4 -1.3 50% Extension -12.4 -12.6 -13.0 -13.2 -13.4 -13.4 -13.0 Maximum Extension -17.1 -17.1 -19.1 -19.1 -18.2 -18.6 -18.2

Table A.49: Calculated Lunate Flexion for Specimen 3 during FEM Cycle, RCD Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Extension -16.2 -16.0 -14.9 -14.9 -14.7 -14.3 -15.2 50% Extension -13.6 -13.8 -12.4 -12.5 -11.3 -10.9 -12.4 Neutral -11.1 -10.7 -7.9 -6.4 -5.7 -6.6 -8.1 50% Flexion 4.8 6.7 10.5 11.6 12.5 10.6 9.4 Maximum Flexion 29.0 29.3 31.2 31.6 32.0 31.9 30.8 50% Flexion 8.4 8.8 11.7 11.2 13.2 12.4 11.0 Neutral -10.6 -9.8 -8.5 -8.8 -7.1 -6.9 -8.6 50% Extension -14.8 -14.7 -13.9 -13.7 -13.0 -12.7 -13.8 Maximum Extension -16.2 -16.0 -15.0 -14.9 -14.7 -14.3 -15.2

Table A.50: Calculated Lunate Pronation for Specimen 3 during FEM Cycle, RCD Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Extension 19.3 19.6 22.8 22.9 23.5 23.7 22.0 50% Extension 18.4 19.2 21.2 22.4 23.3 22.7 21.2 Neutral 21.0 23.3 26.8 30.2 29.6 27.2 26.3 50% Flexion 21.7 23.1 26.0 26.9 27.4 26.1 25.2 Maximum Flexion 18.7 19.0 20.3 20.8 21.7 21.3 20.3 50% Flexion 22.8 23.5 25.5 25.1 27.8 26.8 25.2 Neutral 25.2 26.0 28.2 26.9 30.3 30.7 27.9 50% Extension 21.2 20.8 23.6 23.6 25.7 25.1 23.3 Maximum Extension 19.3 19.6 22.9 23.0 23.6 23.7 22.0

202 Table A.51: Calculated Lunate Ulnar Deviation for Specimen 3 during FEM Cycle, RCD

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Extension -16.3 -16.3 -16.4 -16.4 -16.5 -16.2 -16.3 50% Extension -15.8 -16.4 -16.3 -16.8 -16.7 -16.2 -16.4 Neutral -15.3 -16.4 -17.4 -18.7 -17.6 -16.1 -16.9 50% Flexion -10.9 -11.0 -10.7 -9.7 -10.0 -9.6 -10.3 Maximum Flexion -1.3 -1.3 -1.2 -1.1 -1.3 -1.0 -1.2 50% Flexion -11.0 -11.4 -11.7 -11.7 -12.4 -11.9 -11.7 Neutral -17.5 -17.7 -18.4 -17.7 -18.5 -18.7 -18.1 50% Extension -16.6 -16.1 -16.6 -16.5 -17.2 -16.7 -16.6 Maximum Extension -16.3 -16.2 -16.5 -16.4 -16.5 -16.3 -16.4

Table A.52: Calculated Scaphoid Flexion for Specimen 3 during FEM Cycle, RCD Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Extension -29.6 -29.3 -28.4 -28.6 -30.0 -29.9 -29.3 50% Extension -12.1 -12.1 -12.5 -12.9 -13.9 -13.8 -12.9 Neutral 4.0 3.6 3.4 3.4 2.9 2.1 3.2 50% Flexion 22.2 23.0 23.5 23.9 23.7 22.2 23.1 Maximum Flexion 49.2 49.0 49.2 49.6 49.0 48.1 49.0 50% Flexion 24.2 24.2 24.5 24.2 24.8 23.6 24.3 Neutral -1.0 -0.4 -0.3 -0.8 0.0 -0.1 -0.4 50% Extension -17.0 -16.8 -15.5 -16.8 -17.2 -17.1 -16.7 Maximum Extension -29.5 -29.2 -28.5 -28.6 -30.1 -30.0 -29.3

Table A.53: Calculated Scaphoid Pronation for Specimen 3 during FEM Cy- cle, RCD

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Extension 19.6 20.0 22.2 22.0 19.8 19.8 20.6 50% Extension 24.7 25.6 27.1 27.9 25.5 25.0 26.0 Neutral 34.2 36.5 39.1 42.0 38.9 36.0 37.8 50% Flexion 41.3 42.4 43.8 44.4 42.5 40.7 42.5 Maximum Flexion 34.2 34.3 34.8 35.0 33.5 33.0 34.1 50% Flexion 43.9 44.1 44.6 43.5 43.4 42.6 43.7 Neutral 41.8 42.6 43.5 41.3 43.3 43.4 42.6 50% Extension 29.9 28.9 31.0 30.1 30.1 29.0 29.8 Maximum Extension 19.6 19.9 22.3 22.1 19.9 19.7 20.6

203 Table A.54: Calculated Scaphoid Ulnar Deviation for Specimen 3 during FEM Cycle, RCD

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Extension -9.0 -8.9 -10.3 -9.8 -8.7 -9.1 -9.3 50% Extension -5.8 -5.8 -6.2 -6.0 -5.6 -5.6 -5.8 Neutral -3.7 -3.9 -3.9 -4.0 -3.7 -3.7 -3.8 50% Flexion 5.3 6.1 7.0 7.9 8.1 7.1 6.9 Maximum Flexion 18.9 19.3 20.7 21.0 21.2 21.3 20.4 50% Flexion 6.3 6.6 7.2 7.2 8.2 7.5 7.2 Neutral -5.9 -5.8 -5.6 -5.3 -4.9 -4.7 -5.4 50% Extension -10.6 -10.5 -11.0 -10.5 -10.9 -10.7 -10.7 Maximum Extension -9.1 -8.9 -10.4 -9.8 -8.8 -9.1 -9.3

204 Table A.55: Calculated Global Wrist Flexion for Specimen 4 during FEM Cycle, intact

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Extension -59.6 -59.8 -59.7 -59.6 -59.5 -59.5 -59.6 50% Extension -29.8 -29.9 -29.9 -29.8 -29.8 -29.8 -29.8 Neutral 0.0 0.0 0.0 0.0 0.0 0.0 0.0 50% Flexion 28.2 27.9 28.1 27.9 28.4 28.3 28.1 Maximum Flexion 56.4 55.8 56.2 55.9 56.8 56.7 56.3 50% Flexion 28.2 27.9 28.1 27.9 28.4 28.3 28.1 Neutral 0.0 0.0 0.0 0.0 0.0 0.0 0.0 50% Extension -29.8 -29.9 -29.9 -29.8 -29.8 -29.8 -29.8 Maximum Extension -59.6 -59.8 -59.7 -59.6 -59.5 -59.5 -59.6

Table A.56: Calculated Global Wrist Pronation for Specimen 4 during FEM Cycle, intact

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Extension -12.1 -12.6 -13.6 -14.0 -15.8 -14.9 -13.8 50% Extension -16.0 -15.2 -15.6 -15.2 -15.5 -15.9 -15.6 Neutral -9.2 -9.7 -8.4 -7.9 -7.6 -8.6 -8.6 50% Flexion -4.2 -4.3 -2.8 -3.1 -2.7 -2.8 -3.3 Maximum Flexion -5.1 -5.3 -4.2 -4.0 -4.8 -4.8 -4.7 50% Flexion -4.1 -4.6 -3.6 -3.2 -3.1 -3.3 -3.6 Neutral -8.8 -9.1 -9.0 -8.8 -7.6 -8.2 -8.6 50% Extension -13.1 -14.1 -14.5 -14.6 -14.1 -14.0 -14.1 Maximum Extension -12.1 -12.6 -13.6 -14.0 -15.8 -14.9 -13.8

205 Table A.57: Calculated Global Wrist Ulnar Deviation for Specimen 4 during FEM Cycle, intact

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Extension 0.8 0.5 -0.4 -0.6 -2.0 -1.9 -0.6 50% Extension -8.7 -8.5 -9.1 -9.2 -9.8 -10.1 -9.2 Neutral -10.8 -10.9 -11.1 -11.0 -10.8 -10.8 -10.9 50% Flexion -8.1 -7.2 -7.9 -8.6 -7.6 -7.0 -7.8 Maximum Flexion -1.0 -1.1 -1.0 -2.0 -0.2 -0.2 -0.9 50% Flexion -6.7 -6.8 -7.2 -7.5 -6.1 -6.4 -6.8 Neutral -10.4 -10.6 -10.8 -10.8 -10.4 -10.5 -10.6 50% Extension -7.6 -8.0 -8.6 -8.5 -9.2 -9.1 -8.5 Maximum Extension 0.8 0.5 -0.4 -0.6 -2.0 -1.9 -0.6

Table A.58: Calculated Lunate Flexion for Specimen 4 during FEM Cycle, intact Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Extension -18.6 -18.7 -18.2 -18.2 -18.1 -18.2 -18.3 50% Extension -1.7 -2.3 -1.1 -1.2 -0.6 -0.6 -1.3 Neutral 21.0 20.8 21.0 20.8 21.0 21.2 21.0 50% Flexion 31.9 31.5 31.6 32.1 31.8 31.6 31.7 Maximum Flexion 37.7 37.5 38.1 38.5 37.8 37.7 37.9 50% Flexion 31.4 31.3 31.8 31.8 31.5 31.6 31.6 Neutral 21.4 21.6 21.8 21.7 21.6 21.7 21.6 50% Extension -2.1 -1.8 -1.0 -1.1 -0.7 -1.0 -1.3 Maximum Extension -18.7 -18.7 -18.2 -18.2 -18.1 -18.2 -18.3

Table A.59: Calculated Lunate Pronation for Specimen 4 during FEM Cycle, intact Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Extension 2.1 2.0 1.8 1.8 1.7 1.8 1.9 50% Extension 1.4 1.6 1.3 1.3 1.5 1.3 1.4 Neutral 3.3 3.1 3.3 3.5 3.6 3.2 3.3 50% Flexion 3.2 3.2 3.3 3.3 3.4 3.3 3.3 Maximum Flexion 1.8 1.8 1.7 1.7 1.8 1.7 1.8 50% Flexion 3.0 3.0 3.0 3.1 3.2 3.1 3.1 Neutral 3.1 3.0 3.0 3.0 3.5 3.3 3.2 50% Extension 1.7 1.3 1.1 1.3 1.5 1.4 1.4 Maximum Extension 2.1 2.0 1.8 1.8 1.7 1.8 1.9

206 Table A.60: Calculated Lunate Ulnar Deviation for Specimen 4 during FEM Cycle, intact

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Extension 6.4 6.1 5.7 5.6 5.1 5.2 5.7 50% Extension -0.7 -0.6 -0.6 -0.9 -0.7 -0.8 -0.7 Neutral -3.2 -2.9 -3.4 -3.5 -2.9 -3.1 -3.1 50% Flexion -1.2 -1.2 -1.1 -1.2 -0.9 -0.9 -1.1 Maximum Flexion 3.7 3.5 3.7 3.6 4.0 4.0 3.7 50% Flexion -1.4 -1.4 -1.4 -1.3 -1.2 -1.2 -1.3 Neutral -4.2 -4.1 -3.8 -3.8 -3.4 -3.5 -3.8 50% Extension -1.5 -2.1 -1.9 -1.7 -1.5 -1.7 -1.7 Maximum Extension 6.4 6.1 5.7 5.6 5.1 5.2 5.7

Table A.61: Calculated Scaphoid Flexion for Specimen 4 during FEM Cycle, intact Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Extension -42.1 -42.5 -42.7 -43.0 -43.5 -43.3 -42.8 50% Extension -15.2 -15.4 -15.1 -15.3 -15.0 -15.5 -15.3 Neutral 15.3 14.6 15.3 15.3 14.7 14.6 15.0 50% Flexion 33.3 32.6 32.8 33.3 32.1 31.9 32.7 Maximum Flexion 47.9 47.6 48.6 48.7 48.2 47.8 48.1 50% Flexion 35.2 34.8 35.1 35.2 34.4 33.8 34.7 Neutral 17.6 17.5 17.5 17.4 17.4 17.2 17.4 50% Extension -13.3 -13.8 -13.7 -14.0 -13.9 -14.0 -13.8 Maximum Extension -42.1 -42.4 -42.7 -43.0 -43.4 -43.3 -42.8

Table A.62: Calculated Scaphoid Pronation for Specimen 4 during FEM Cy- cle, intact

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Extension -3.3 -3.3 -4.0 -4.0 -4.2 -3.9 -3.8 50% Extension -0.6 -0.2 -1.1 -0.8 -0.6 -0.7 -0.7 Neutral 6.1 6.0 5.9 6.1 6.3 6.0 6.1 50% Flexion 8.4 8.1 8.0 8.2 8.6 8.4 8.3 Maximum Flexion 9.2 8.7 8.4 8.5 8.5 8.8 8.7 50% Flexion 7.5 7.2 7.1 7.3 7.2 8.0 7.4 Neutral 5.4 5.3 4.6 4.9 5.2 5.2 5.1 50% Extension -0.1 -0.6 -1.6 -1.3 -1.0 -0.8 -0.9 Maximum Extension -3.3 -3.3 -4.0 -4.0 -4.2 -3.8 -3.8

207 Table A.63: Calculated Scaphoid Ulnar Deviation for Specimen 4 during FEM Cycle, intact

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Extension -1.4 -1.6 -2.4 -2.2 -3.2 -3.0 -2.3 50% Extension -7.9 -7.8 -8.7 -8.6 -9.0 -9.1 -8.5 Neutral -8.4 -8.3 -9.1 -9.0 -8.9 -8.9 -8.8 50% Flexion -3.5 -3.6 -4.3 -4.3 -4.5 -4.3 -4.1 Maximum Flexion 2.2 1.6 1.2 1.3 1.1 1.2 1.4 50% Flexion -3.4 -3.6 -4.3 -4.1 -4.6 -4.0 -4.0 Neutral -8.7 -8.9 -9.6 -9.5 -9.3 -9.2 -9.2 50% Extension -8.6 -8.9 -9.8 -9.4 -9.8 -9.7 -9.4 Maximum Extension -1.4 -1.6 -2.5 -2.2 -3.2 -3.0 -2.3

Table A.64: Calculated Global Wrist Flexion for Specimen 4 during FEM Cycle, RCD

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Extension -59.5 -59.2 -58.9 -58.9 -58.6 -59.0 -59.0 50% Extension -29.7 -29.6 -29.4 -29.4 -29.3 -29.5 -29.5 Neutral 0.0 0.0 0.0 0.0 0.0 0.0 0.0 50% Flexion 28.5 28.6 28.6 28.6 28.6 28.6 28.6 Maximum Flexion 56.9 57.1 57.2 57.2 57.2 57.1 57.1 50% Flexion 28.5 28.6 28.6 28.6 28.6 28.6 28.6 Neutral 0.0 0.0 0.0 0.0 0.0 0.0 0.0 50% Extension -29.7 -29.6 -29.4 -29.4 -29.3 -29.5 -29.5 Maximum Extension -59.5 -59.2 -58.9 -58.9 -58.6 -59.0 -59.0

Table A.65: Calculated Global Wrist Pronation for Specimen 4 during FEM Cycle, RCD

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Extension -13.2 -12.8 -13.9 -13.7 -14.1 -13.2 -13.5 50% Extension -16.0 -16.8 -16.9 -17.0 -16.4 -16.6 -16.6 Neutral -10.2 -10.3 -9.1 -9.4 -9.5 -10.3 -9.8 50% Flexion -5.2 -5.0 -4.5 -4.6 -4.9 -5.6 -5.0 Maximum Flexion -6.6 -6.0 -5.7 -5.9 -6.9 -6.8 -6.3 50% Flexion -5.7 -5.6 -4.6 -4.8 -5.7 -5.7 -5.3 Neutral -10.2 -10.0 -10.0 -9.4 -9.9 -9.7 -9.9 50% Extension -14.7 -14.2 -14.2 -13.9 -14.0 -14.0 -14.2 Maximum Extension -13.2 -12.8 -13.8 -13.7 -14.1 -13.1 -13.5

208 Table A.66: Calculated Global Wrist Ulnar Deviation for Specimen 4 during FEM Cycle, RCD

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Extension -0.2 0.3 -1.3 -0.9 -1.5 -0.9 -0.8 50% Extension -8.5 -8.9 -9.5 -9.3 -10.1 -9.0 -9.2 Neutral -11.0 -11.3 -11.0 -11.2 -10.9 -10.6 -11.0 50% Flexion -8.7 -9.3 -8.9 -8.5 -8.0 -8.0 -8.6 Maximum Flexion -3.0 -2.5 -2.8 -2.7 -2.4 -2.9 -2.7 50% Flexion -8.3 -7.4 -7.6 -7.3 -6.9 -6.8 -7.4 Neutral -10.6 -10.7 -10.7 -10.5 -10.5 -10.4 -10.6 50% Extension -8.1 -7.6 -8.0 -7.9 -8.2 -7.7 -7.9 Maximum Extension -0.2 0.3 -1.3 -0.9 -1.5 -0.9 -0.8

Table A.67: Calculated Lunate Flexion for Specimen 4 during FEM Cycle, RCD Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Extension -16.9 -17.2 -16.8 -16.8 -16.7 -16.8 -16.9 50% Extension 0.3 0.3 0.5 0.3 0.0 0.5 0.3 Neutral 22.5 22.0 22.2 21.8 21.5 21.6 21.9 50% Flexion 32.5 33.0 33.1 32.8 32.5 32.7 32.8 Maximum Flexion 37.7 37.8 38.6 38.4 38.5 38.6 38.3 50% Flexion 32.6 32.3 32.9 32.6 32.6 32.2 32.5 Neutral 23.7 23.3 23.4 23.0 22.7 22.6 23.1 50% Extension 1.5 1.1 1.3 0.8 0.9 0.6 1.0 Maximum Extension -16.9 -17.2 -16.8 -16.8 -16.7 -16.8 -16.9

Table A.68: Calculated Lunate Pronation for Specimen 4 during FEM Cycle, RCD Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Extension 1.9 2.0 1.7 1.8 1.7 1.8 1.8 50% Extension 1.7 1.5 1.4 1.2 1.3 1.3 1.4 Neutral 3.4 3.4 3.6 3.5 3.4 3.1 3.4 50% Flexion 3.2 3.2 3.2 3.2 3.2 3.1 3.2 Maximum Flexion 1.2 1.2 1.3 1.4 1.2 1.1 1.2 50% Flexion 3.1 3.0 3.2 3.1 3.1 3.0 3.1 Neutral 3.3 3.4 3.3 3.4 3.1 3.3 3.3 50% Extension 1.5 1.8 1.7 1.8 1.6 1.8 1.7 Maximum Extension 1.9 2.0 1.7 1.8 1.7 1.8 1.8

209 Table A.69: Calculated Lunate Ulnar Deviation for Specimen 4 during FEM Cycle, RCD

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Extension 7.3 7.6 7.3 7.3 7.2 7.5 7.4 50% Extension 1.6 1.5 1.4 1.4 1.3 1.4 1.4 Neutral -2.0 -2.0 -1.7 -1.7 -1.7 -1.8 -1.8 50% Flexion -0.7 -0.6 -0.6 -0.6 -0.6 -0.6 -0.6 Maximum Flexion 3.6 3.7 3.4 3.4 3.5 3.3 3.5 50% Flexion -0.4 -0.3 -0.4 -0.3 -0.4 -0.4 -0.4 Neutral -1.9 -1.8 -1.7 -1.7 -1.8 -1.7 -1.7 50% Extension 1.3 1.7 1.8 1.7 1.6 1.9 1.7 Maximum Extension 7.3 7.6 7.3 7.3 7.2 7.5 7.4

Table A.70: Calculated Scaphoid Flexion for Specimen 4 during FEM Cycle, RCD Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Extension -44.7 -45.0 -44.8 -44.8 -44.9 -44.8 -44.8 50% Extension -17.3 -17.7 -17.7 -18.0 -18.1 -17.8 -17.8 Neutral 12.5 12.1 12.2 11.5 11.6 11.3 11.9 50% Flexion 30.8 31.0 30.6 29.8 29.2 29.4 30.1 Maximum Flexion 47.4 47.2 48.7 47.9 47.4 47.6 47.7 50% Flexion 33.2 32.8 32.5 32.4 32.2 31.1 32.4 Neutral 14.8 14.6 14.3 13.9 13.7 13.7 14.2 50% Extension -16.2 -16.2 -16.2 -16.6 -16.4 -16.7 -16.4 Maximum Extension -44.7 -45.0 -44.8 -44.8 -44.9 -44.8 -44.8

Table A.71: Calculated Scaphoid Pronation for Specimen 4 during FEM Cy- cle, RCD

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Extension 0.5 0.9 0.3 0.7 0.5 0.7 0.6 50% Extension 2.8 2.7 2.7 2.6 3.0 2.8 2.8 Neutral 9.4 9.8 10.1 10.7 9.8 9.5 9.9 50% Flexion 12.0 12.6 12.7 12.9 12.6 12.3 12.5 Maximum Flexion 11.8 12.1 11.6 11.8 12.1 11.7 11.8 50% Flexion 11.0 10.7 11.8 11.2 10.9 11.5 11.2 Neutral 8.8 9.0 9.1 9.7 9.1 9.4 9.2 50% Extension 2.6 3.2 3.1 3.5 3.3 3.5 3.2 Maximum Extension 0.5 0.9 0.3 0.7 0.5 0.7 0.6

210 Table A.72: Calculated Scaphoid Ulnar Deviation for Specimen 4 during FEM Cycle, RCD

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Extension 1.7 2.2 1.3 1.5 1.3 1.7 1.6 50% Extension -4.8 -4.8 -5.1 -4.9 -5.2 -4.6 -4.9 Neutral -5.5 -5.3 -5.4 -4.9 -5.5 -5.4 -5.3 50% Flexion -0.9 -0.7 -1.0 -0.9 -1.1 -1.1 -1.0 Maximum Flexion 3.5 3.3 3.1 2.9 3.4 3.0 3.2 50% Flexion -1.0 -1.6 -1.0 -1.5 -1.5 -1.1 -1.3 Neutral -5.8 -5.7 -5.5 -5.1 -5.5 -5.1 -5.5 50% Extension -5.7 -5.0 -5.4 -5.1 -5.5 -5.0 -5.3 Maximum Extension 1.7 2.1 1.3 1.5 1.3 1.6 1.6

211 Table A.73: Calculated Global Wrist Flexion for Specimen 1 during RUD Cycle, intact

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Average (◦)(◦)(◦)(◦) (◦) Maximum Radial Deviation -4.7 -5.4 -5.0 -5.1 -5.0 50% Radial Deviation -3.8 -3.9 -4.3 -4.3 -4.1 Neutral -4.2 -4.5 -5.0 -4.5 -4.5 50% Ulnar Deviation -3.7 -4.1 -5.1 -4.9 -4.4 Maximum Deviation -9.2 -7.8 -8.1 -9.6 -8.7 50% Deviationt -3.9 -3.9 -4.5 -4.5 -4.2 Neutral -3.7 -3.8 -5.0 -4.9 -4.4 50% Radial Deviation -3.3 -2.8 -4.1 -4.2 -3.6 Maximum Radial Deviation -4.7 -5.4 -5.0 -5.2 -5.1

Table A.74: Calculated Global Wrist Pronation for Specimen 1 during RUD Cycle, intact

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Average (◦)(◦)(◦)(◦) (◦) Maximum Radial Deviation -4.1 -5.5 -6.2 -7.3 -5.8 50% Radial Deviation -7.0 -8.2 -8.7 -8.8 -8.2 Neutral -7.3 -8.1 -9.1 -9.3 -8.5 50% Ulnar Deviation -9.9 -10.2 -11.6 -11.1 -10.7 Maximum Deviation -8.7 -8.2 -9.3 -10.2 -9.1 50% Deviationt -9.4 -6.6 -8.7 -10.2 -8.7 Neutral -7.7 -8.7 -7.0 -7.0 -7.6 50% Radial Deviation -7.0 -9.5 -7.9 -6.9 -7.8 Maximum Radial Deviation -4.1 -5.6 -6.2 -7.3 -5.8

212 Table A.75: Calculated Global Wrist Ulnar Deviation for Specimen 1 during RUD Cycle, intact

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Average (◦)(◦)(◦)(◦) (◦) Maximum Radial Deviation -11.9 -11.9 -14.3 -14.3 -13.1 50% Radial Deviation -6.0 -6.0 -7.2 -7.1 -6.6 Neutral 0.0 0.0 0.0 0.0 0.0 50% Ulnar Deviation 13.5 13.4 12.5 12.5 13.0 Maximum Deviation 27.1 26.8 25.0 25.1 26.0 50% Deviationt 13.5 13.4 12.5 12.5 13.0 Neutral 0.0 0.0 0.0 0.0 0.0 50% Radial Deviation -6.0 -6.0 -7.2 -7.1 -6.6 Maximum Radial Deviation -11.9 -11.9 -14.3 -14.3 -13.1

Table A.76: Calculated Lunate Flexion for Specimen 1 during RUD Cycle, intact Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Average (◦)(◦)(◦)(◦) (◦) Maximum Radial Deviation 12.6 12.6 12.9 13.1 12.8 50% Radial Deviation 12.1 12.7 12.9 12.3 12.5 Neutral 11.7 12.3 12.4 11.8 12.1 50% Ulnar Deviation 1.8 3.4 3.3 2.1 2.7 Maximum Deviation -9.1 -9.4 -9.2 -9.9 -9.4 50% Deviationt -2.8 -2.8 -3.3 -4.3 -3.3 Neutral 6.2 5.9 7.8 4.0 6.0 50% Radial Deviation 10.6 10.7 11.2 9.7 10.6 Maximum Radial Deviation 12.5 12.5 12.9 13.0 12.7

Table A.77: Calculated Lunate Pronation for Specimen 1 during RUD Cycle, intact Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Average (◦)(◦)(◦)(◦) (◦) Maximum Radial Deviation 6.4 5.4 4.9 4.9 5.4 50% Radial Deviation 4.5 3.9 3.4 3.8 3.9 Neutral 4.1 3.8 3.2 3.3 3.6 50% Ulnar Deviation -1.0 -1.7 -1.9 -2.0 -1.6 Maximum Deviation -4.2 -4.4 -4.2 -5.1 -4.5 50% Deviationt 0.4 1.1 0.4 -1.0 0.2 Neutral 3.4 2.4 3.3 2.9 3.0 50% Radial Deviation 4.5 2.9 3.6 4.0 3.8 Maximum Radial Deviation 6.4 5.3 4.9 4.8 5.4

213 Table A.78: Calculated Lunate Ulnar Deviation for Specimen 1 during RUD Cycle, intact

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Average (◦)(◦)(◦)(◦) (◦) Maximum Radial Deviation -7.3 -7.7 -9.1 -8.4 -8.1 50% Radial Deviation -6.8 -7.6 -8.1 -7.7 -7.6 Neutral -6.6 -7.1 -7.8 -7.1 -7.2 50% Ulnar Deviation -4.6 -5.0 -4.1 -3.4 -4.2 Maximum Deviation 5.0 3.9 4.9 6.0 5.0 50% Deviationt -1.7 -2.8 -2.1 -1.3 -2.0 Neutral -4.9 -4.9 -7.0 -5.6 -5.6 50% Radial Deviation -6.3 -7.0 -7.9 -7.0 -7.0 Maximum Radial Deviation -7.3 -7.7 -9.1 -8.5 -8.1

Table A.79: Calculated Scaphoid Flexion for Specimen 1 during RUD Cycle, intact Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Average (◦)(◦)(◦)(◦) (◦) Maximum Radial Deviation 2.9 1.8 -3.1 -3.5 -0.5 50% Radial Deviation 0.9 1.2 -4.8 -5.1 -2.0 Neutral 0.6 1.2 -6.3 -6.8 -2.8 50% Ulnar Deviation -6.3 -4.5 -13.7 -13.6 -9.5 Maximum Deviation -13.7 -12.8 -19.4 -20.2 -16.5 50% Deviationt -5.4 -4.8 -14.0 -14.7 -9.7 Neutral 0.1 0.5 -8.6 -9.0 -4.3 50% Radial Deviation 1.8 2.5 -5.3 -5.4 -1.6 Maximum Radial Deviation 2.9 1.7 -3.1 -3.4 -0.5

Table A.80: Calculated Scaphoid Pronation for Specimen 1 during RUD Cy- cle, intact

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Average (◦)(◦)(◦)(◦) (◦) Maximum Radial Deviation -16.7 -18.7 -18.0 -18.5 -18.0 50% Radial Deviation -19.8 -20.6 -20.2 -20.6 -20.3 Neutral -19.6 -19.5 -20.5 -21.0 -20.1 50% Ulnar Deviation -19.4 -19.3 -24.3 -24.3 -21.8 Maximum Deviation -17.9 -18.3 -20.3 -20.6 -19.3 50% Deviationt -17.2 -17.1 -21.4 -22.4 -19.5 Neutral -18.6 -19.1 -20.5 -20.7 -19.7 50% Radial Deviation -19.5 -20.3 -19.9 -19.7 -19.9 Maximum Radial Deviation -16.7 -18.7 -18.0 -18.5 -18.0

214 Table A.81: Calculated Scaphoid Ulnar Deviation for Specimen 1 during RUD Cycle, intact

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Average (◦)(◦)(◦)(◦) (◦) Maximum Radial Deviation -17.0 -15.7 -15.0 -15.1 -15.7 50% Radial Deviation -16.2 -15.6 -15.2 -15.2 -15.6 Neutral -16.6 -16.1 -15.6 -15.6 -16.0 50% Ulnar Deviation -13.2 -13.5 -15.9 -16.1 -14.7 Maximum Deviation -6.4 -6.1 -9.3 -8.9 -7.7 50% Deviationt -12.9 -13.7 -16.5 -16.6 -14.9 Neutral -15.0 -14.1 -16.8 -16.8 -15.7 50% Radial Deviation -15.4 -14.7 -15.6 -15.7 -15.3 Maximum Radial Deviation -17.0 -15.7 -15.0 -15.1 -15.7

Table A.82: Calculated Global Wrist Flexion for Specimen 1 during RUD Cycle, RCD

Wrist Position Trial 1 Trial 2 Average (◦)(◦) (◦) Maximum Radial Deviation -6.3 -6.3 -6.3 50% Radial Deviation -5.6 -5.9 -5.7 Neutral -5.6 -6.0 -5.8 50% Ulnar Deviation -4.5 -4.5 -4.5 Maximum Deviation -4.3 -4.4 -4.3 50% Deviationt -4.8 -4.6 -4.7 Neutral -5.9 -6.2 -6.1 50% Radial Deviation -5.1 -5.6 -5.4 Maximum Radial Deviation -6.3 -6.2 -6.3

Table A.83: Calculated Global Wrist Pronation for Specimen 1 during RUD Cycle, RCD

Wrist Position Trial 1 Trial 2 Average (◦)(◦) (◦) Maximum Radial Deviation -5.6 -7.4 -6.5 50% Radial Deviation -6.3 -6.7 -6.5 Neutral -4.3 -5.7 -5.0 50% Ulnar Deviation -5.4 -7.5 -6.4 Maximum Deviation -8.0 -8.5 -8.2 50% Deviationt -4.0 -7.0 -5.5 Neutral -6.9 -7.4 -7.1 50% Radial Deviation -8.9 -9.7 -9.3 Maximum Radial Deviation -5.7 -7.4 -6.5

215 Table A.84: Calculated Global Wrist Ulnar Deviation for Specimen 1 during RUD Cycle, RCD

Wrist Position Trial 1 Trial 2 Average (◦)(◦) (◦) Maximum Radial Deviation -13.8 -13.7 -13.8 50% Radial Deviation -6.9 -6.8 -6.9 Neutral 0.0 0.0 0.0 50% Ulnar Deviation 13.5 13.4 13.4 Maximum Deviation 27.0 26.7 26.9 50% Deviationt 13.5 13.4 13.4 Neutral 0.0 0.0 0.0 50% Radial Deviation -6.9 -6.8 -6.9 Maximum Radial Deviation -13.8 -13.7 -13.8

Table A.85: Calculated Lunate Flexion for Specimen 1 during RUD Cycle, RCD Wrist Position Trial 1 Trial 2 Average (◦)(◦) (◦) Maximum Radial Deviation 12.9 13.2 13.1 50% Radial Deviation 14.2 13.7 13.9 Neutral 12.6 12.8 12.7 50% Ulnar Deviation -0.5 -1.0 -0.7 Maximum Deviation -11.0 -11.2 -11.1 50% Deviationt -5.5 -5.7 -5.6 Neutral 6.0 5.2 5.6 50% Radial Deviation 12.6 11.7 12.2 Maximum Radial Deviation 12.9 13.1 13.0

Table A.86: Calculated Lunate Pronation for Specimen 1 during RUD Cycle, RCD Wrist Position Trial 1 Trial 2 Average (◦)(◦) (◦) Maximum Radial Deviation 7.5 6.6 7.0 50% Radial Deviation 5.9 5.5 5.7 Neutral 5.1 4.5 4.8 50% Ulnar Deviation 0.6 -0.1 0.3 Maximum Deviation -3.0 -3.2 -3.1 50% Deviationt 2.9 1.8 2.3 Neutral 3.9 3.8 3.8 50% Radial Deviation 4.8 4.4 4.6 Maximum Radial Deviation 7.4 6.6 7.0

216 Table A.87: Calculated Lunate Ulnar Deviation for Specimen 1 during RUD Cycle, RCD

Wrist Position Trial 1 Trial 2 Average (◦)(◦) (◦) Maximum Radial Deviation -8.7 -8.9 -8.8 50% Radial Deviation -7.4 -7.7 -7.5 Neutral -7.4 -7.6 -7.5 50% Ulnar Deviation -3.3 -3.2 -3.2 Maximum Deviation 6.1 6.3 6.2 50% Deviationt -0.5 -0.3 -0.4 Neutral -4.8 -4.9 -4.8 50% Radial Deviation -6.4 -6.6 -6.5 Maximum Radial Deviation -8.7 -8.9 -8.8

Table A.88: Calculated Scaphoid Flexion for Specimen 1 during RUD Cycle, RCD Wrist Position Trial 1 Trial 2 Average (◦)(◦) (◦) Maximum Radial Deviation -4.1 -5.2 -4.7 50% Radial Deviation -4.7 -5.7 -5.2 Neutral -4.8 -6.0 -5.4 50% Ulnar Deviation -9.8 -10.7 -10.3 Maximum Deviation -17.3 -17.9 -17.6 50% Deviationt -11.5 -12.3 -11.9 Neutral -7.2 -8.1 -7.6 50% Radial Deviation -5.1 -6.4 -5.7 Maximum Radial Deviation -4.2 -5.3 -4.7

Table A.89: Calculated Scaphoid Pronation for Specimen 1 during RUD Cy- cle, RCD

Wrist Position Trial 1 Trial 2 Average (◦)(◦) (◦) Maximum Radial Deviation -24.9 -26.3 -25.6 50% Radial Deviation -25.9 -26.6 -26.3 Neutral -24.9 -26.1 -25.5 50% Ulnar Deviation -26.8 -28.0 -27.4 Maximum Deviation -28.4 -29.1 -28.7 50% Deviationt -26.6 -27.9 -27.3 Neutral -27.0 -27.6 -27.3 50% Radial Deviation -27.1 -27.8 -27.4 Maximum Radial Deviation -25.0 -26.3 -25.6

217 Table A.90: Calculated Scaphoid Ulnar Deviation for Specimen 1 during RUD Cycle, RCD

Wrist Position Trial 1 Trial 2 Average (◦)(◦) (◦) Maximum Radial Deviation -14.1 -14.4 -14.2 50% Radial Deviation -14.1 -14.4 -14.2 Neutral -14.4 -14.7 -14.5 50% Ulnar Deviation -15.1 -15.4 -15.2 Maximum Deviation -11.9 -12.0 -11.9 50% Deviationt -16.2 -16.1 -16.1 Neutral -14.6 -15.2 -14.9 50% Radial Deviation -14.0 -14.5 -14.3 Maximum Radial Deviation -14.1 -14.4 -14.2

218 Table A.91: Calculated Global Wrist Flexion for Specimen 2 during RUD Cycle, intact

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Radial Deviation -6.9 -7.4 -9.7 -9.2 -9.7 -9.0 -8.6 50% Radial Deviation -5.5 -5.8 -8.3 -8.6 -8.1 -8.0 -7.4 Neutral -6.7 -6.0 -8.2 -9.3 -9.7 -11.0 -8.5 50% Ulnar Deviation -5.2 -4.1 -7.5 -8.1 -7.5 -8.5 -6.8 Maximum Deviation -5.7 -5.5 -8.4 -8.4 -8.7 -9.0 -7.6 50% Deviationt -4.9 -4.9 -6.1 -6.9 -8.0 -8.8 -6.6 Neutral -6.1 -6.1 -7.9 -8.3 -7.3 -9.2 -7.4 50% Radial Deviation -3.8 -4.5 -6.0 -5.8 -5.7 -6.3 -5.3 Maximum Radial Deviation -6.8 -7.4 -9.6 -9.2 -9.6 -8.8 -8.6

Table A.92: Calculated Global Wrist Pronation for Specimen 2 during RUD Cycle, intact

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Radial Deviation -11.8 -11.3 -10.4 -11.1 -10.8 -11.3 -11.1 50% Radial Deviation -12.7 -12.5 -11.7 -11.8 -12.2 -12.1 -12.2 Neutral -13.8 -13.8 -12.8 -12.4 -13.1 -12.5 -13.1 50% Ulnar Deviation -14.8 -15.4 -13.0 -12.7 -14.2 -12.7 -13.8 Maximum Deviation -17.8 -17.8 -14.9 -15.5 -16.5 -15.2 -16.3 50% Deviationt -13.5 -13.6 -12.3 -12.3 -12.4 -11.3 -12.6 Neutral -12.4 -12.4 -11.4 -11.7 -12.5 -11.5 -12.0 50% Radial Deviation -11.7 -11.5 -10.9 -11.2 -11.9 -11.6 -11.5 Maximum Radial Deviation -11.8 -11.4 -10.4 -11.0 -10.8 -11.3 -11.1

219 Table A.93: Calculated Global Wrist Ulnar Deviation for Specimen 2 during RUD Cycle, intact

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Radial Deviation -15.2 -15.2 -14.8 -14.8 -14.7 -14.8 -14.9 50% Radial Deviation -7.6 -7.6 -7.4 -7.4 -7.3 -7.4 -7.5 Neutral 0.0 0.0 0.0 0.0 0.0 0.0 0.0 50% Ulnar Deviation 12.0 11.9 12.3 12.3 12.0 12.3 12.1 Maximum Deviation 24.1 23.8 24.6 24.5 24.0 24.6 24.2 50% Deviationt 12.0 11.9 12.3 12.3 12.0 12.3 12.1 Neutral 0.0 0.0 0.0 0.0 0.0 0.0 0.0 50% Radial Deviation -7.6 -7.6 -7.4 -7.4 -7.3 -7.4 -7.5 Maximum Radial Deviation -15.2 -15.2 -14.8 -14.8 -14.7 -14.8 -14.9

Table A.94: Calculated Lunate Flexion for Specimen 2 during RUD Cycle, intact Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Radial Deviation 12.3 12.1 9.3 10.2 10.4 11.1 10.9 50% Radial Deviation 16.9 17.1 15.7 15.9 17.1 17.6 16.7 Neutral 20.1 20.2 18.9 19.0 19.8 19.6 19.6 50% Ulnar Deviation 18.5 19.4 17.3 17.2 18.3 17.4 18.0 Maximum Deviation 9.9 10.0 8.5 10.0 9.8 9.1 9.6 50% Deviationt 16.7 17.3 16.4 16.6 16.9 16.0 16.7 Neutral 19.6 19.7 18.6 19.1 20.3 19.5 19.5 50% Radial Deviation 17.5 17.4 16.6 16.9 18.3 18.3 17.5 Maximum Radial Deviation 12.2 12.1 9.2 10.1 10.3 11.1 10.8

Table A.95: Calculated Lunate Pronation for Specimen 2 during RUD Cycle, intact Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Radial Deviation -5.5 -5.2 -7.7 -7.4 -7.6 -7.5 -6.8 50% Radial Deviation -5.9 -5.7 -8.0 -7.6 -7.8 -7.7 -7.1 Neutral -5.4 -5.4 -7.6 -7.2 -7.3 -6.9 -6.6 50% Ulnar Deviation -6.4 -6.5 -9.0 -8.7 -9.6 -9.3 -8.2 Maximum Deviation -12.7 -12.8 -14.8 -14.3 -15.6 -15.4 -14.3 50% Deviationt -5.9 -5.9 -8.6 -8.6 -8.9 -8.7 -7.8 Neutral -5.6 -5.6 -7.6 -7.5 -7.9 -7.3 -6.9 50% Radial Deviation -6.2 -6.1 -8.3 -8.3 -8.4 -8.0 -7.5 Maximum Radial Deviation -5.6 -5.3 -7.8 -7.5 -7.7 -7.5 -6.9

220 Table A.96: Calculated Lunate Ulnar Deviation for Specimen 2 during RUD Cycle, intact

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Radial Deviation -27.5 -26.9 -28.0 -28.1 -27.8 -27.9 -27.7 50% Radial Deviation -24.2 -23.9 -24.9 -24.7 -24.5 -24.4 -24.4 Neutral -20.7 -20.7 -22.2 -21.9 -21.8 -21.7 -21.5 50% Ulnar Deviation -17.1 -17.1 -18.8 -18.5 -18.7 -18.5 -18.1 Maximum Deviation -12.0 -12.3 -13.5 -13.2 -13.6 -13.2 -13.0 50% Deviationt -18.3 -18.2 -19.5 -19.2 -19.3 -19.2 -18.9 Neutral -21.0 -20.8 -22.4 -22.1 -22.0 -22.0 -21.7 50% Radial Deviation -23.2 -23.1 -24.4 -24.2 -24.0 -23.8 -23.8 Maximum Radial Deviation -27.5 -26.9 -28.0 -28.1 -27.8 -27.9 -27.7

Table A.97: Calculated Scaphoid Flexion for Specimen 2 during RUD Cycle, intact Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Radial Deviation 30.9 30.5 29.1 29.8 29.5 30.1 30.0 50% Radial Deviation 30.9 30.8 29.7 29.5 30.3 30.8 30.3 Neutral 27.4 28.0 27.5 26.8 26.9 26.1 27.1 50% Ulnar Deviation 20.0 21.4 20.1 19.6 20.8 19.4 20.2 Maximum Deviation 8.4 8.2 8.4 9.5 9.9 9.1 8.9 50% Deviationt 20.2 20.7 20.7 20.1 19.8 18.6 20.0 Neutral 28.0 28.1 27.7 27.6 28.9 27.1 27.9 50% Radial Deviation 32.2 31.7 31.4 31.8 32.3 31.9 31.9 Maximum Radial Deviation 30.9 30.6 29.2 29.8 29.5 30.1 30.0

Table A.98: Calculated Scaphoid Pronation for Specimen 2 during RUD Cy- cle, intact

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Radial Deviation 13.8 14.1 14.7 14.5 14.4 14.3 14.3 50% Radial Deviation 10.0 10.1 10.4 10.5 9.9 10.2 10.2 Neutral 4.7 4.8 5.5 5.8 5.1 5.5 5.2 50% Ulnar Deviation -1.1 -1.2 0.1 0.6 -0.8 0.1 -0.4 Maximum Deviation -5.1 -4.8 -3.6 -3.8 -5.3 -4.6 -4.5 50% Deviationt 0.6 0.7 1.2 1.0 0.7 1.3 0.9 Neutral 6.5 6.5 6.8 6.7 6.0 6.6 6.5 50% Radial Deviation 10.9 11.1 11.1 11.2 10.4 10.8 10.9 Maximum Radial Deviation 13.8 14.1 14.8 14.5 14.4 14.3 14.3

221 Table A.99: Calculated Scaphoid Ulnar Deviation for Specimen 2 during RUD Cycle, intact

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Radial Deviation -5.2 -5.1 -4.8 -4.8 -4.8 -5.0 -5.0 50% Radial Deviation -3.5 -3.3 -2.6 -2.5 -2.6 -2.4 -2.8 Neutral -0.6 -0.6 0.1 0.4 0.2 0.5 0.0 50% Ulnar Deviation 3.2 3.0 3.6 3.8 3.4 3.6 3.4 Maximum Deviation 7.1 6.5 7.3 7.7 7.6 7.8 7.3 50% Deviationt 4.0 3.9 4.1 4.0 3.8 4.1 4.0 Neutral 0.6 0.8 1.0 1.0 0.9 1.1 0.9 50% Radial Deviation -3.0 -2.8 -2.2 -2.1 -2.2 -2.1 -2.4 Maximum Radial Deviation -5.2 -5.1 -4.7 -4.8 -4.8 -4.9 -4.9

Table A.100: Calculated Global Wrist Flexion for Specimen 2 during RUD Cycle, RCD

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Radial Deviation -12.1 -15.2 -14.3 -13.3 -7.6 -10.0 -12.1 50% Radial Deviation -9.4 -10.7 -10.8 -9.6 -7.2 -7.5 -9.2 Neutral -9.0 -10.3 -12.3 -10.3 -8.1 -7.7 -9.6 50% Ulnar Deviation -5.7 -6.9 -11.3 -6.7 -5.5 -5.5 -6.9 Maximum Deviation -5.9 -7.1 -11.1 -7.3 -7.6 -7.7 -7.8 50% Deviationt -4.9 -7.3 -9.2 -7.5 -3.9 -5.9 -6.4 Neutral -8.1 -8.9 -8.0 -8.9 -4.5 -4.8 -7.2 50% Radial Deviation -8.1 -6.2 -5.0 -7.9 -4.1 -0.8 -5.4 Maximum Radial Deviation -11.8 -15.4 -14.4 -13.0 -7.3 -10.2 -12.0

Table A.101: Calculated Global Wrist Pronation for Specimen 2 during RUD Cycle, RCD

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Radial Deviation -10.0 -9.5 -9.6 -9.9 -10.6 -10.2 -9.9 50% Radial Deviation -11.3 -11.0 -11.9 -11.5 -12.8 -12.6 -11.9 Neutral -12.5 -12.1 -11.8 -12.2 -13.5 -13.9 -12.7 50% Ulnar Deviation -13.9 -12.6 -10.6 -13.1 -14.8 -14.7 -13.3 Maximum Deviation -16.4 -14.6 -11.7 -15.0 -15.6 -15.4 -14.8 50% Deviationt -12.2 -10.7 -10.1 -10.7 -14.0 -12.4 -11.7 Neutral -10.4 -10.3 -10.5 -10.4 -12.6 -12.6 -11.1 50% Radial Deviation -9.8 -10.1 -10.6 -10.0 -11.3 -12.0 -10.6 Maximum Radial Deviation -10.0 -9.4 -9.6 -9.9 -10.7 -10.0 -9.9

222 Table A.102: Calculated Global Wrist Ulnar Deviation for Specimen 2 during RUD Cycle, RCD

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Radial Deviation -14.4 -14.1 -14.2 -14.4 -14.9 -14.9 -14.5 50% Radial Deviation -7.2 -7.0 -7.1 -7.2 -7.4 -7.5 -7.2 Neutral 0.0 0.0 0.0 0.0 0.0 0.0 0.0 50% Ulnar Deviation 11.7 12.2 12.9 12.1 12.2 12.3 12.2 Maximum Deviation 23.4 24.4 25.7 24.2 24.4 24.5 24.4 50% Deviationt 11.7 12.2 12.9 12.1 12.2 12.3 12.2 Neutral 0.0 0.0 0.0 0.0 0.0 0.0 0.0 50% Radial Deviation -7.2 -7.0 -7.1 -7.2 -7.4 -7.5 -7.2 Maximum Radial Deviation -14.4 -14.1 -14.2 -14.4 -14.9 -14.9 -14.5

Table A.103: Calculated Lunate Flexion for Specimen 2 during RUD Cycle, RCD Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Radial Deviation 10.0 8.3 8.3 9.7 11.6 10.1 9.7 50% Radial Deviation 16.9 17.1 17.2 17.8 18.1 18.0 17.5 Neutral 20.1 20.2 19.8 20.4 21.3 21.4 20.5 50% Ulnar Deviation 20.4 20.1 17.7 20.2 20.7 21.4 20.1 Maximum Deviation 15.8 15.5 13.5 15.4 15.9 16.6 15.4 50% Deviationt 20.2 19.5 18.5 19.7 21.0 21.1 20.0 Neutral 20.6 20.1 20.2 20.4 21.5 21.8 20.8 50% Radial Deviation 18.4 18.6 18.4 18.3 19.3 19.7 18.8 Maximum Radial Deviation 10.0 8.3 8.3 9.8 11.7 10.1 9.7

Table A.104: Calculated Lunate Pronation for Specimen 2 during RUD Cy- cle, RCD

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Radial Deviation -5.3 -4.9 -6.1 -6.0 -7.7 -7.0 -6.2 50% Radial Deviation -5.9 -5.4 -6.5 -6.5 -7.9 -7.6 -6.6 Neutral -5.6 -5.4 -6.0 -6.2 -7.3 -7.3 -6.3 50% Ulnar Deviation -6.6 -6.5 -7.9 -7.8 -8.7 -8.7 -7.7 Maximum Deviation -11.4 -11.3 -12.6 -12.7 -13.0 -13.2 -12.4 50% Deviationt -6.5 -6.0 -7.2 -7.2 -8.6 -8.2 -7.3 Neutral -5.3 -5.6 -6.6 -6.3 -8.0 -7.9 -6.6 50% Radial Deviation -5.0 -6.2 -7.6 -6.4 -8.0 -9.1 -7.0 Maximum Radial Deviation -5.5 -4.8 -6.1 -6.0 -7.8 -6.9 -6.2

223 Table A.105: Calculated Lunate Ulnar Deviation for Specimen 2 during RUD Cycle, RCD

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Radial Deviation -26.5 -25.8 -26.6 -26.5 -27.1 -27.3 -26.6 50% Radial Deviation -23.7 -23.1 -23.6 -23.4 -24.0 -24.0 -23.6 Neutral -20.8 -20.5 -20.9 -20.8 -21.1 -21.0 -20.9 50% Ulnar Deviation -17.2 -16.7 -17.0 -17.4 -17.7 -17.5 -17.3 Maximum Deviation -11.0 -10.2 -9.4 -11.0 -10.3 -10.2 -10.3 50% Deviationt -17.8 -17.0 -17.2 -17.5 -17.9 -17.4 -17.5 Neutral -20.5 -20.7 -21.1 -20.9 -21.3 -21.0 -20.9 50% Radial Deviation -22.4 -22.8 -23.4 -22.9 -23.3 -23.5 -23.0 Maximum Radial Deviation -26.6 -25.8 -26.6 -26.5 -27.1 -27.2 -26.6

Table A.106: Calculated Scaphoid Flexion for Specimen 2 during RUD Cy- cle, RCD

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Radial Deviation 25.8 23.0 24.7 26.1 31.0 28.8 26.6 50% Radial Deviation 27.8 26.9 27.8 29.0 31.4 31.0 29.0 Neutral 25.9 25.6 24.9 26.3 28.7 28.9 26.7 50% Ulnar Deviation 21.4 20.4 17.2 21.3 22.7 23.2 21.0 Maximum Deviation 12.7 12.0 10.4 12.6 13.9 14.3 12.7 50% Deviationt 22.6 20.3 18.9 21.0 23.8 22.9 21.6 Neutral 27.0 26.7 27.9 27.4 31.1 31.1 28.5 50% Radial Deviation 28.7 30.6 32.1 30.2 33.5 36.1 31.9 Maximum Radial Deviation 26.0 22.9 24.7 26.3 31.2 28.7 26.6

Table A.107: Calculated Scaphoid Pronation for Specimen 2 during RUD Cycle, RCD

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Radial Deviation 15.5 15.5 15.4 15.4 15.0 15.3 15.3 50% Radial Deviation 11.2 11.3 11.1 11.2 11.0 11.2 11.2 Neutral 6.4 6.7 7.0 6.6 6.4 6.2 6.5 50% Ulnar Deviation 1.0 1.7 2.3 1.1 0.7 0.9 1.3 Maximum Deviation -2.5 -1.6 -1.4 -2.4 -2.6 -2.5 -2.2 50% Deviationt 2.6 3.1 2.9 2.8 1.4 2.3 2.5 Neutral 8.1 8.3 8.1 8.1 7.3 7.4 7.9 50% Radial Deviation 12.1 12.1 11.9 12.2 11.9 11.6 11.9 Maximum Radial Deviation 15.5 15.5 15.4 15.4 15.0 15.4 15.3

224 Table A.108: Calculated Scaphoid Ulnar Deviation for Specimen 2 during RUD Cycle, RCD

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Radial Deviation -4.9 -4.8 -5.0 -5.1 -4.7 -4.8 -4.9 50% Radial Deviation -2.5 -2.2 -2.2 -2.3 -2.4 -2.4 -2.3 Neutral 0.0 0.4 0.7 0.4 0.8 0.4 0.5 50% Ulnar Deviation 2.8 3.5 4.2 3.3 3.9 3.9 3.6 Maximum Deviation 7.3 8.1 9.5 8.1 9.8 9.7 8.8 50% Deviationt 4.0 4.5 4.5 4.5 4.4 5.0 4.5 Neutral 1.7 1.7 1.7 1.6 1.4 1.6 1.6 50% Radial Deviation -1.7 -1.6 -1.7 -1.6 -1.6 -2.0 -1.7 Maximum Radial Deviation -4.8 -4.8 -5.0 -5.1 -4.7 -4.7 -4.9

225 Table A.109: Calculated Global Wrist Flexion for Specimen 3 during RUD Cycle, intact

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Radial Deviation 7.7 7.5 10.7 6.1 5.6 9.0 7.7 50% Radial Deviation 6.5 6.4 7.3 6.2 4.6 6.5 6.3 Neutral 4.6 4.4 5.5 4.0 3.0 4.1 4.3 50% Ulnar Deviation -0.9 -0.9 -0.8 -2.0 -2.5 -2.1 -1.5 Maximum Deviation -8.5 -8.2 -9.6 -8.4 -9.6 -10.2 -9.1 50% Deviationt -0.9 -1.5 -1.1 -2.0 -2.6 -1.9 -1.7 Neutral 4.4 4.6 6.5 4.4 1.6 3.0 4.1 50% Radial Deviation 5.6 6.6 10.0 6.4 2.2 4.0 5.8 Maximum Radial Deviation 7.8 7.3 10.6 6.1 5.6 8.3 7.6

Table A.110: Calculated Global Wrist Pronation for Specimen 3 during RUD Cycle, intact

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Radial Deviation 15.8 17.1 17.5 16.4 18.4 17.9 17.2 50% Radial Deviation 16.8 17.9 18.5 17.8 18.8 19.4 18.2 Neutral 17.5 18.6 19.2 18.6 19.1 20.0 18.8 50% Ulnar Deviation 20.0 21.5 23.4 23.8 22.7 22.5 22.3 Maximum Deviation 25.3 25.2 29.9 30.3 28.1 26.5 27.5 50% Deviationt 23.4 23.1 25.7 25.4 25.2 25.6 24.7 Neutral 19.4 19.1 19.7 20.3 20.7 21.1 20.1 50% Radial Deviation 18.8 18.3 18.6 19.5 19.7 19.9 19.1 Maximum Radial Deviation 15.7 17.1 17.5 16.2 18.4 18.3 17.2

226 Table A.111: Calculated Global Wrist Ulnar Deviation for Specimen 3 during RUD Cycle, intact

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Radial Deviation -15.3 -14.6 -12.9 -15.1 -15.1 -13.3 -14.4 50% Radial Deviation -7.7 -7.3 -6.5 -7.6 -7.5 -6.7 -7.2 Neutral 0.0 0.0 0.0 0.0 0.0 0.0 0.0 50% Ulnar Deviation 14.7 15.1 14.9 15.2 15.5 15.4 15.1 Maximum Deviation 29.4 30.1 29.9 30.5 31.1 30.8 30.3 50% Deviationt 14.7 15.1 14.9 15.2 15.5 15.4 15.1 Neutral 0.0 0.0 0.0 0.0 0.0 0.0 0.0 50% Radial Deviation -7.7 -7.3 -6.5 -7.6 -7.5 -6.7 -7.2 Maximum Radial Deviation -15.3 -14.6 -12.9 -15.1 -15.1 -13.3 -14.4

Table A.112: Calculated Lunate Flexion for Specimen 3 during RUD Cycle, intact Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Radial Deviation -2.4 -2.5 -0.1 -2.5 -1.0 1.0 -1.3 50% Radial Deviation -7.0 -6.9 -6.6 -6.3 -6.1 -5.0 -6.3 Neutral -12.9 -12.8 -11.7 -12.2 -11.7 -11.0 -12.1 50% Ulnar Deviation -21.2 -21.3 -20.9 -21.2 -20.8 -20.7 -21.0 Maximum Deviation -24.9 -24.6 -25.1 -24.7 -24.2 -25.5 -24.8 50% Deviationt -22.1 -22.5 -21.8 -22.3 -22.3 -22.0 -22.2 Neutral -13.6 -13.8 -11.5 -12.9 -13.5 -12.3 -12.9 50% Radial Deviation -7.9 -7.2 -4.2 -6.4 -8.1 -7.7 -6.9 Maximum Radial Deviation -2.5 -2.7 -0.2 -2.6 -1.0 0.5 -1.4

Table A.113: Calculated Lunate Pronation for Specimen 3 during RUD Cy- cle, intact

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Radial Deviation 18.7 18.9 18.7 19.8 20.9 19.1 19.4 50% Radial Deviation 18.0 18.5 19.1 19.1 20.2 19.2 19.0 Neutral 17.1 17.7 18.4 18.4 18.7 18.4 18.1 50% Ulnar Deviation 16.2 17.3 18.4 18.7 18.2 18.1 17.8 Maximum Deviation 16.5 17.6 19.7 20.5 19.9 19.6 19.0 50% Deviationt 17.9 18.3 19.7 20.0 20.7 21.3 19.7 Neutral 18.0 18.0 18.6 19.3 20.1 20.2 19.0 50% Radial Deviation 18.6 18.5 18.5 19.6 20.9 20.4 19.4 Maximum Radial Deviation 18.8 19.0 18.8 19.8 20.9 19.4 19.5

227 Table A.114: Calculated Lunate Ulnar Deviation for Specimen 3 during RUD Cycle, intact

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Radial Deviation -17.6 -17.8 -15.7 -17.7 -16.5 -15.2 -16.7 50% Radial Deviation -16.0 -16.3 -15.6 -16.0 -15.8 -15.2 -15.8 Neutral -14.8 -15.1 -14.2 -14.7 -14.2 -13.9 -14.5 50% Ulnar Deviation -9.8 -10.5 -10.7 -10.8 -9.3 -10.1 -10.2 Maximum Deviation -8.6 -8.9 -4.1 -4.6 -2.3 -2.3 -5.1 50% Deviationt -10.2 -10.0 -9.1 -8.9 -7.8 -8.5 -9.1 Neutral -14.4 -14.2 -13.0 -13.6 -14.0 -13.8 -13.8 50% Radial Deviation -16.3 -16.3 -14.3 -16.0 -16.5 -15.5 -15.8 Maximum Radial Deviation -17.6 -17.8 -15.7 -17.7 -16.4 -15.6 -16.8

Table A.115: Calculated Scaphoid Flexion for Specimen 3 during RUD Cy- cle, intact

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Radial Deviation 10.0 10.2 11.5 7.8 7.5 10.6 9.6 50% Radial Deviation 8.1 8.3 7.5 6.9 5.7 7.2 7.3 Neutral 5.1 5.0 4.8 3.8 2.8 3.8 4.2 50% Ulnar Deviation -1.0 -1.4 -1.6 -2.7 -3.8 -3.9 -2.4 Maximum Deviation -6.7 -6.2 -8.0 -6.5 -8.6 -10.4 -7.7 50% Deviationt -1.6 -2.1 -2.4 -3.3 -4.7 -4.4 -3.1 Neutral 4.1 3.7 4.7 3.0 0.7 1.8 3.0 50% Radial Deviation 7.3 7.7 9.6 6.7 3.3 4.3 6.5 Maximum Radial Deviation 10.0 10.0 11.4 7.8 7.4 10.1 9.5

Table A.116: Calculated Scaphoid Pronation for Specimen 3 during RUD Cycle, intact

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Radial Deviation 42.0 42.5 42.0 42.1 41.7 41.0 41.9 50% Radial Deviation 40.5 41.5 41.5 40.8 40.0 40.0 40.7 Neutral 37.9 39.1 39.5 38.6 37.3 38.0 38.4 50% Ulnar Deviation 32.7 34.5 35.5 35.7 33.0 33.5 34.2 Maximum Deviation 33.9 34.9 37.5 38.3 35.7 35.2 35.9 50% Deviationt 35.1 35.4 36.7 36.9 36.0 37.1 36.2 Neutral 38.4 38.5 38.8 39.2 38.2 39.0 38.7 50% Radial Deviation 40.5 40.7 40.6 41.1 39.9 40.0 40.5 Maximum Radial Deviation 42.0 42.6 42.0 42.2 41.7 41.2 42.0

228 Table A.117: Calculated Scaphoid Ulnar Deviation for Specimen 3 during RUD Cycle, intact

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Radial Deviation -5.8 -5.6 -4.3 -5.7 -5.4 -4.5 -5.2 50% Radial Deviation -4.6 -4.4 -3.8 -4.2 -4.4 -4.1 -4.2 Neutral -3.9 -3.8 -3.0 -3.3 -3.5 -3.4 -3.5 50% Ulnar Deviation 2.2 1.5 2.5 2.2 2.8 1.9 2.2 Maximum Deviation 14.1 14.0 15.5 14.9 15.2 14.6 14.7 50% Deviationt 2.4 2.4 3.2 3.1 3.1 2.5 2.8 Neutral -3.7 -3.7 -2.7 -3.1 -3.6 -3.3 -3.3 50% Radial Deviation -4.9 -4.8 -3.5 -4.3 -5.0 -4.6 -4.5 Maximum Radial Deviation -5.7 -5.6 -4.3 -5.8 -5.4 -4.6 -5.3

Table A.118: Calculated Global Wrist Flexion for Specimen 3 during RUD Cycle, RCD

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Radial Deviation 0.6 4.4 6.5 6.2 4.0 4.2 4.3 50% Radial Deviation 1.9 5.4 7.2 6.3 4.9 5.0 5.1 Neutral 1.2 3.8 6.6 4.5 4.0 4.3 4.1 50% Ulnar Deviation -2.7 -3.4 -1.0 -1.8 -1.6 -1.1 -1.9 Maximum Deviation -9.1 -10.9 -13.2 -13.4 -14.1 -14.4 -12.5 50% Deviationt -3.0 -3.0 -1.9 -1.3 -1.3 0.2 -1.7 Neutral 0.1 2.6 3.8 3.6 4.7 6.1 3.5 50% Radial Deviation -0.3 4.1 5.4 4.3 3.8 4.7 3.7 Maximum Radial Deviation 0.7 4.4 6.2 6.2 4.1 4.4 4.3

Table A.119: Calculated Global Wrist Pronation for Specimen 3 during RUD Cycle, RCD

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Radial Deviation 21.0 21.1 20.9 20.6 23.2 22.9 21.6 50% Radial Deviation 19.9 20.7 20.6 20.3 22.3 22.7 21.1 Neutral 19.3 21.0 20.6 20.6 22.8 22.4 21.1 50% Ulnar Deviation 23.7 26.5 23.1 24.4 25.7 25.4 24.8 Maximum Deviation 28.0 30.6 29.8 29.3 28.8 30.0 29.4 50% Deviationt 26.7 28.4 26.7 27.3 28.6 28.6 27.7 Neutral 23.0 23.6 22.3 22.9 24.5 25.0 23.6 50% Radial Deviation 23.0 21.7 21.3 22.1 23.5 24.0 22.6 Maximum Radial Deviation 20.9 21.2 21.0 20.6 23.1 22.8 21.6

229 Table A.120: Calculated Global Wrist Ulnar Deviation for Specimen 3 during RUD Cycle, RCD

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Radial Deviation -17.5 -15.3 -14.3 -14.5 -16.1 -15.5 -15.5 50% Radial Deviation -8.8 -7.7 -7.1 -7.3 -8.1 -7.8 -7.8 Neutral 0.0 0.0 0.0 0.0 0.0 0.0 0.0 50% Ulnar Deviation 15.0 15.3 14.4 14.2 14.0 14.1 14.5 Maximum Deviation 30.1 30.5 28.8 28.4 27.9 28.2 29.0 50% Deviationt 15.0 15.3 14.4 14.2 14.0 14.1 14.5 Neutral 0.0 0.0 0.0 0.0 0.0 0.0 0.0 50% Radial Deviation -8.8 -7.7 -7.1 -7.3 -8.1 -7.8 -7.8 Maximum Radial Deviation -17.5 -15.3 -14.3 -14.5 -16.1 -15.5 -15.5

Table A.121: Calculated Lunate Flexion for Specimen 3 during RUD Cycle, RCD Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Radial Deviation -1.4 -0.2 2.2 2.5 2.5 2.1 1.3 50% Radial Deviation -5.2 -3.8 -1.3 -2.0 -1.6 -2.1 -2.6 Neutral -10.7 -9.2 -6.4 -8.1 -7.1 -7.2 -8.1 50% Ulnar Deviation -18.7 -18.8 -16.8 -16.7 -15.8 -15.6 -17.1 Maximum Deviation -22.4 -23.4 -21.9 -22.1 -21.7 -21.9 -22.2 50% Deviationt -19.8 -20.0 -18.3 -17.6 -16.9 -16.2 -18.1 Neutral -12.1 -10.3 -8.4 -8.5 -7.3 -6.4 -8.8 50% Radial Deviation -7.2 -5.1 -3.0 -3.6 -3.0 -2.5 -4.1 Maximum Radial Deviation -1.3 -0.2 2.1 2.5 2.5 2.3 1.3

Table A.122: Calculated Lunate Pronation for Specimen 3 during RUD Cy- cle, RCD

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Radial Deviation 27.6 25.0 25.5 26.1 29.5 29.2 27.1 50% Radial Deviation 24.5 23.5 24.4 24.9 27.4 27.5 25.4 Neutral 21.2 21.9 22.6 23.2 25.4 25.4 23.3 50% Ulnar Deviation 18.9 20.7 19.5 20.5 22.4 21.9 20.6 Maximum Deviation 20.0 21.7 20.8 20.0 20.8 21.7 20.8 50% Deviationt 22.6 24.4 24.0 24.1 25.8 25.8 24.4 Neutral 23.4 23.1 23.5 23.7 25.6 25.6 24.1 50% Radial Deviation 26.1 23.6 24.6 25.5 27.3 27.3 25.7 Maximum Radial Deviation 27.5 25.0 25.6 26.0 29.4 29.0 27.1

230 Table A.123: Calculated Lunate Ulnar Deviation for Specimen 3 during RUD Cycle, RCD

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Radial Deviation -19.3 -17.1 -16.2 -16.1 -17.9 -17.3 -17.3 50% Radial Deviation -17.0 -15.4 -14.7 -15.0 -15.7 -15.4 -15.5 Neutral -14.7 -14.4 -13.4 -14.1 -13.9 -13.6 -14.0 50% Ulnar Deviation -11.6 -12.3 -10.4 -10.8 -11.0 -10.1 -11.0 Maximum Deviation -6.7 -7.5 -5.6 -4.2 -4.0 -4.7 -5.4 50% Deviationt -12.1 -12.7 -11.8 -10.9 -10.9 -9.9 -11.4 Neutral -15.6 -14.9 -14.3 -13.9 -13.7 -12.8 -14.2 50% Radial Deviation -18.4 -15.9 -15.8 -16.1 -16.2 -15.5 -16.3 Maximum Radial Deviation -19.2 -17.2 -16.3 -16.0 -17.9 -17.2 -17.3

Table A.124: Calculated Scaphoid Flexion for Specimen 3 during RUD Cy- cle, RCD

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Radial Deviation 4.2 7.5 7.0 6.8 5.5 5.0 6.0 50% Radial Deviation 4.5 7.0 6.7 5.7 5.2 4.5 5.6 Neutral 1.9 4.1 4.3 2.0 2.5 1.8 2.8 50% Ulnar Deviation -4.5 -4.2 -5.8 -5.8 -5.3 -5.5 -5.2 Maximum Deviation -9.3 -10.5 -14.5 -15.1 -16.4 -16.7 -13.8 50% Deviationt -4.0 -4.0 -5.8 -5.2 -5.3 -4.4 -4.8 Neutral 0.9 2.8 1.2 0.9 2.2 2.8 1.8 50% Radial Deviation 2.4 5.8 4.6 3.7 3.7 3.9 4.0 Maximum Radial Deviation 4.3 7.4 6.8 6.9 5.5 5.2 6.0

Table A.125: Calculated Scaphoid Pronation for Specimen 3 during RUD Cycle, RCD

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Radial Deviation 44.7 43.5 42.4 42.5 43.2 42.8 43.2 50% Radial Deviation 41.2 41.8 41.1 41.0 41.0 41.1 41.2 Neutral 36.9 39.2 38.9 38.6 38.5 38.5 38.4 50% Ulnar Deviation 33.1 35.6 33.5 34.1 34.0 33.8 34.0 Maximum Deviation 34.8 36.7 36.3 35.2 33.8 34.5 35.2 50% Deviationt 36.9 38.4 37.1 37.5 37.0 37.0 37.3 Neutral 39.4 39.9 38.7 38.8 38.7 39.3 39.1 50% Radial Deviation 42.6 41.4 40.6 41.0 40.5 41.0 41.2 Maximum Radial Deviation 44.6 43.5 42.3 42.4 43.1 42.6 43.1

231 Table A.126: Calculated Scaphoid Ulnar Deviation for Specimen 3 during RUD Cycle, RCD

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Radial Deviation -6.9 -5.6 -5.1 -5.1 -5.4 -5.6 -5.6 50% Radial Deviation -5.0 -4.2 -3.4 -3.8 -3.6 -3.6 -3.9 Neutral -4.3 -3.4 -2.5 -2.9 -2.5 -2.5 -3.0 50% Ulnar Deviation -0.0 -0.4 0.1 0.1 -0.0 0.2 -0.0 Maximum Deviation 12.1 11.6 10.6 10.7 10.6 10.6 11.1 50% Deviationt 1.5 1.3 1.5 1.6 1.9 2.0 1.6 Neutral -4.1 -4.0 -3.3 -3.5 -2.7 -2.8 -3.4 50% Radial Deviation -5.6 -4.7 -4.3 -4.5 -4.3 -4.4 -4.6 Maximum Radial Deviation -6.9 -5.7 -5.2 -5.1 -5.5 -5.7 -5.7

232 Table A.127: Calculated Global Wrist Flexion for Specimen 4 during RUD Cycle, intact

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Radial Deviation -3.6 -2.2 -5.1 -6.6 -5.1 -6.1 -4.8 50% Radial Deviation 5.0 5.4 3.7 3.7 4.1 4.5 4.4 Neutral 8.9 8.8 8.6 8.9 8.5 9.2 8.8 50% Ulnar Deviation 11.6 11.8 12.1 12.0 12.1 12.1 11.9 Maximum Deviation 13.3 13.8 14.6 14.4 14.2 14.0 14.1 50% Deviationt 11.3 11.6 11.5 11.6 12.4 11.9 11.7 Neutral 9.5 8.7 8.3 8.7 9.6 8.9 9.0 50% Radial Deviation 5.4 4.1 3.5 3.9 5.1 3.7 4.3 Maximum Radial Deviation -3.4 -2.2 -5.0 -6.6 -5.4 -6.3 -4.8

Table A.128: Calculated Global Wrist Pronation for Specimen 4 during RUD Cycle, intact

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Radial Deviation -9.3 -10.1 -8.6 -7.7 -7.6 -7.3 -8.4 50% Radial Deviation -9.3 -8.9 -7.8 -7.6 -6.5 -6.2 -7.7 Neutral -8.7 -7.7 -7.0 -6.8 -5.5 -5.3 -6.8 50% Ulnar Deviation -8.8 -7.4 -6.1 -6.5 -6.2 -5.9 -6.8 Maximum Deviation -10.2 -8.7 -6.3 -7.5 -8.5 -7.3 -8.1 50% Deviationt -7.9 -6.9 -5.3 -5.4 -6.8 -5.2 -6.2 Neutral -7.2 -6.5 -5.5 -5.6 -5.9 -4.4 -5.9 50% Radial Deviation -8.4 -7.9 -7.1 -6.8 -6.8 -5.8 -7.1 Maximum Radial Deviation -9.1 -10.2 -8.7 -7.5 -7.4 -7.1 -8.3

233 Table A.129: Calculated Global Wrist Ulnar Deviation for Specimen 4 during RUD Cycle, intact

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Radial Deviation -19.2 -19.3 -19.0 -18.3 -19.2 -18.6 -18.9 50% Radial Deviation -9.6 -9.7 -9.5 -9.2 -9.6 -9.3 -9.5 Neutral 0.0 0.0 0.0 0.0 0.0 0.0 0.0 50% Ulnar Deviation 11.6 11.4 11.0 11.1 11.4 11.4 11.3 Maximum Deviation 23.3 22.7 21.9 22.2 22.8 22.8 22.6 50% Deviationt 11.6 11.4 11.0 11.1 11.4 11.4 11.3 Neutral 0.0 0.0 0.0 0.0 0.0 0.0 0.0 50% Radial Deviation -9.6 -9.7 -9.5 -9.2 -9.6 -9.3 -9.5 Maximum Radial Deviation -19.2 -19.3 -19.0 -18.3 -19.2 -18.6 -18.9

Table A.130: Calculated Lunate Flexion for Specimen 4 during RUD Cycle, intact Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Radial Deviation 19.5 20.6 18.5 17.4 18.5 17.8 18.7 50% Radial Deviation 24.5 24.4 23.7 23.1 23.1 23.0 23.6 Neutral 22.4 21.6 22.0 21.8 21.2 20.5 21.6 50% Ulnar Deviation 8.5 8.7 11.3 10.5 9.8 8.0 9.5 Maximum Deviation -8.5 -7.3 -4.2 -5.3 -6.6 -7.1 -6.5 50% Deviationt 2.4 4.6 7.4 6.1 3.9 4.6 4.8 Neutral 19.0 19.7 20.4 20.0 19.0 18.9 19.5 50% Radial Deviation 24.5 23.7 23.4 23.4 24.1 22.8 23.6 Maximum Radial Deviation 20.0 20.9 18.7 17.6 18.6 17.9 18.9

Table A.131: Calculated Lunate Pronation for Specimen 4 during RUD Cy- cle, intact

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Radial Deviation 2.5 2.2 2.9 3.5 3.4 3.6 3.0 50% Radial Deviation 3.1 3.0 3.4 3.6 3.7 3.7 3.4 Neutral 2.7 2.9 3.1 3.3 3.5 3.4 3.2 50% Ulnar Deviation 1.5 2.1 2.5 2.5 2.7 2.9 2.4 Maximum Deviation 3.5 3.9 4.2 3.9 3.8 4.2 3.9 50% Deviationt 2.8 2.9 3.5 3.5 3.3 3.7 3.3 Neutral 3.1 3.3 3.7 3.7 3.5 3.9 3.5 50% Radial Deviation 3.1 3.3 3.7 3.7 3.6 3.9 3.6 Maximum Radial Deviation 2.5 2.2 2.9 3.5 3.4 3.6 3.0

234 Table A.132: Calculated Lunate Ulnar Deviation for Specimen 4 during RUD Cycle, intact

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Radial Deviation -5.2 -4.6 -5.3 -5.2 -5.3 -5.0 -5.1 50% Radial Deviation -2.6 -2.6 -2.7 -2.4 -2.4 -2.4 -2.5 Neutral -1.2 -1.3 -1.1 -1.1 -0.9 -1.0 -1.1 50% Ulnar Deviation 4.4 4.2 3.5 3.8 4.3 4.5 4.1 Maximum Deviation 14.9 14.0 12.2 13.0 14.2 13.9 13.7 50% Deviationt 6.6 5.8 5.1 5.4 6.5 6.0 5.9 Neutral -0.0 -0.4 -0.4 -0.2 0.2 0.0 -0.1 50% Radial Deviation -2.4 -2.6 -2.5 -2.5 -2.2 -2.2 -2.4 Maximum Radial Deviation -5.4 -4.7 -5.3 -5.3 -5.5 -5.2 -5.2

Table A.133: Calculated Scaphoid Flexion for Specimen 4 during RUD Cy- cle, intact

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Radial Deviation 11.7 12.6 10.4 9.1 10.4 9.5 10.6 50% Radial Deviation 19.9 19.9 18.8 18.3 18.4 18.4 19.0 Neutral 17.1 16.7 16.9 16.8 16.1 15.8 16.6 50% Ulnar Deviation 4.9 5.6 7.7 6.9 6.0 5.0 6.0 Maximum Deviation -3.7 -2.6 -0.5 -1.9 -2.9 -3.3 -2.5 50% Deviationt 3.3 4.9 6.8 6.0 4.2 4.7 5.0 Neutral 16.9 17.3 17.5 17.1 16.5 16.4 16.9 50% Radial Deviation 21.0 20.2 19.6 19.7 20.5 19.1 20.0 Maximum Radial Deviation 12.2 12.8 10.6 9.3 10.3 9.5 10.8

Table A.134: Calculated Scaphoid Pronation for Specimen 4 during RUD Cycle, intact

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Radial Deviation 5.2 4.9 5.3 5.7 6.2 6.1 5.6 50% Radial Deviation 3.9 4.0 4.5 4.5 5.2 5.1 4.5 Neutral 1.1 1.2 1.8 1.9 2.4 2.5 1.8 50% Ulnar Deviation -0.8 -0.3 0.4 0.5 0.9 1.0 0.3 Maximum Deviation -0.6 -0.2 0.8 0.4 0.3 0.7 0.2 50% Deviationt 0.0 0.1 1.1 1.2 1.4 1.4 0.9 Neutral 1.6 1.5 2.2 2.3 2.6 2.6 2.1 50% Radial Deviation 3.9 3.9 4.5 4.4 4.8 4.7 4.3 Maximum Radial Deviation 5.2 4.9 5.3 5.7 6.2 6.0 5.5

235 Table A.135: Calculated Scaphoid Ulnar Deviation for Specimen 4 during RUD Cycle, intact

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Radial Deviation -14.7 -14.4 -15.0 -14.8 -15.0 -14.8 -14.8 50% Radial Deviation -8.0 -8.1 -8.4 -8.4 -8.4 -8.3 -8.3 Neutral -4.1 -4.5 -4.6 -4.7 -4.7 -5.0 -4.6 50% Ulnar Deviation -0.8 -1.2 -1.6 -1.5 -1.5 -1.6 -1.3 Maximum Deviation 6.1 4.8 2.2 3.0 4.8 4.4 4.2 50% Deviationt -2.3 -2.6 -3.0 -2.9 -2.8 -3.0 -2.8 Neutral -4.7 -5.0 -5.2 -5.2 -4.9 -5.5 -5.1 50% Radial Deviation -8.0 -8.4 -8.6 -8.3 -7.9 -8.3 -8.3 Maximum Radial Deviation -14.6 -14.4 -15.0 -14.8 -15.0 -14.8 -14.8

Table A.136: Calculated Global Wrist Flexion for Specimen 4 during RUD Cycle, RCD

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Radial Deviation -1.8 -1.0 -0.6 -3.8 -5.9 -5.7 -3.1 50% Radial Deviation 5.0 6.4 5.8 5.1 4.8 5.1 5.4 Neutral 9.6 9.5 10.2 9.8 9.9 9.8 9.8 50% Ulnar Deviation 13.0 12.7 12.4 12.6 13.1 13.1 12.8 Maximum Deviation 15.7 15.7 13.8 15.5 16.2 16.2 15.5 50% Deviationt 12.6 12.6 12.3 12.6 12.9 13.0 12.7 Neutral 9.3 10.3 10.3 9.8 9.1 9.7 9.8 50% Radial Deviation 5.2 6.4 5.5 4.9 3.7 5.1 5.1 Maximum Radial Deviation -2.0 -0.8 -0.6 -3.8 -6.0 -5.7 -3.1

Table A.137: Calculated Global Wrist Pronation for Specimen 4 during RUD Cycle, RCD

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Radial Deviation -10.0 -10.2 -10.1 -9.3 -8.6 -8.3 -9.4 50% Radial Deviation -9.8 -10.8 -10.4 -9.9 -7.4 -8.0 -9.4 Neutral -8.4 -9.1 -10.5 -9.1 -6.2 -7.1 -8.4 50% Ulnar Deviation -8.3 -8.6 -10.7 -9.5 -7.1 -6.7 -8.5 Maximum Deviation -9.7 -10.5 -12.6 -11.7 -8.5 -8.5 -10.3 50% Deviationt -7.8 -9.5 -9.5 -8.7 -5.8 -6.2 -7.9 Neutral -7.9 -9.0 -7.7 -8.1 -4.9 -5.1 -7.1 50% Radial Deviation -9.1 -9.9 -8.9 -9.5 -6.7 -6.8 -8.5 Maximum Radial Deviation -9.9 -10.3 -10.0 -9.3 -8.5 -8.1 -9.4

236 Table A.138: Calculated Global Wrist Ulnar Deviation for Specimen 4 during RUD Cycle, RCD

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Radial Deviation -19.6 -19.6 -19.3 -18.8 -19.0 -18.7 -19.2 50% Radial Deviation -9.8 -9.8 -9.7 -9.4 -9.5 -9.4 -9.6 Neutral 0.0 0.0 0.0 0.0 0.0 0.0 0.0 50% Ulnar Deviation 10.7 10.8 11.5 10.9 10.7 11.1 10.9 Maximum Deviation 21.4 21.7 23.0 21.8 21.5 22.1 21.9 50% Deviationt 10.7 10.8 11.5 10.9 10.7 11.1 10.9 Neutral 0.0 0.0 0.0 0.0 0.0 0.0 0.0 50% Radial Deviation -9.8 -9.8 -9.7 -9.4 -9.5 -9.4 -9.6 Maximum Radial Deviation -19.6 -19.6 -19.3 -18.8 -19.0 -18.7 -19.2

Table A.139: Calculated Lunate Flexion for Specimen 4 during RUD Cycle, RCD Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Radial Deviation 21.4 22.2 22.4 20.3 19.0 19.3 20.8 50% Radial Deviation 25.6 26.4 26.4 25.6 24.2 24.6 25.5 Neutral 24.4 24.4 24.6 24.3 22.1 22.1 23.6 50% Ulnar Deviation 12.9 13.1 9.1 11.7 9.7 9.0 10.9 Maximum Deviation -3.4 -3.0 -6.5 -4.6 -3.9 -4.6 -4.3 50% Deviationt 7.0 6.0 2.9 5.4 5.9 4.8 5.3 Neutral 21.2 21.1 20.4 21.3 19.1 19.2 20.4 50% Radial Deviation 25.3 26.2 25.4 25.5 23.5 24.2 25.0 Maximum Radial Deviation 21.6 22.6 22.6 20.8 19.2 19.5 21.1

Table A.140: Calculated Lunate Pronation for Specimen 4 during RUD Cy- cle, RCD

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Radial Deviation 2.8 2.6 2.4 3.0 3.6 3.7 3.0 50% Radial Deviation 3.3 2.8 3.0 3.2 3.6 3.4 3.2 Neutral 3.2 2.9 2.4 2.8 3.4 3.2 3.0 50% Ulnar Deviation 2.1 1.7 1.0 1.6 2.8 3.1 2.1 Maximum Deviation 3.8 3.1 2.2 2.8 4.3 4.4 3.4 50% Deviationt 3.3 2.4 2.9 3.0 4.0 4.1 3.3 Neutral 3.3 2.9 3.2 3.2 3.9 3.9 3.4 50% Radial Deviation 3.4 3.1 3.2 3.2 4.0 3.7 3.4 Maximum Radial Deviation 2.8 2.6 2.4 3.0 3.7 3.8 3.0

237 Table A.141: Calculated Lunate Ulnar Deviation for Specimen 4 during RUD Cycle, RCD

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Radial Deviation -3.3 -3.3 -3.3 -3.2 -3.0 -3.0 -3.2 50% Radial Deviation -1.8 -1.9 -1.7 -1.6 -1.4 -1.4 -1.6 Neutral 0.3 0.3 0.3 0.1 0.5 0.4 0.3 50% Ulnar Deviation 5.8 5.8 7.0 6.0 6.3 6.4 6.2 Maximum Deviation 15.5 15.6 17.8 16.3 15.4 15.7 16.1 50% Deviationt 7.5 7.8 9.1 8.0 7.5 8.1 8.0 Neutral 0.8 0.9 1.0 0.7 1.3 1.3 1.0 50% Radial Deviation -1.5 -1.7 -1.6 -1.6 -1.2 -1.3 -1.5 Maximum Radial Deviation -3.4 -3.4 -3.4 -3.3 -3.0 -3.1 -3.3

Table A.142: Calculated Scaphoid Flexion for Specimen 4 during RUD Cy- cle, RCD

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Radial Deviation 9.9 10.7 11.3 9.1 6.8 7.0 9.1 50% Radial Deviation 16.6 17.7 17.6 16.9 15.4 15.6 16.6 Neutral 14.3 14.2 14.5 14.5 12.7 12.8 13.8 50% Ulnar Deviation 4.4 3.9 0.9 3.1 2.2 2.4 2.8 Maximum Deviation -5.3 -5.7 -8.4 -6.9 -5.9 -6.1 -6.4 50% Deviationt 2.9 1.4 -0.1 1.5 2.1 1.4 1.5 Neutral 14.1 14.3 14.7 14.6 12.4 12.8 13.8 50% Radial Deviation 17.6 18.7 18.3 18.0 15.8 16.6 17.5 Maximum Radial Deviation 10.0 11.1 11.5 9.3 6.9 7.2 9.3

Table A.143: Calculated Scaphoid Pronation for Specimen 4 during RUD Cycle, RCD

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Radial Deviation 9.3 9.4 8.7 8.9 9.5 9.7 9.2 50% Radial Deviation 8.9 8.2 7.9 7.9 9.5 9.2 8.6 Neutral 6.2 5.7 5.0 5.3 7.1 6.9 6.0 50% Ulnar Deviation 5.0 4.7 4.0 4.0 6.2 6.5 5.1 Maximum Deviation 6.3 5.6 3.5 4.7 6.9 7.3 5.7 50% Deviationt 6.2 5.2 4.5 5.2 7.1 7.4 5.9 Neutral 6.7 6.1 5.5 5.6 7.5 7.8 6.5 50% Radial Deviation 8.9 8.3 7.5 7.5 9.2 9.3 8.5 Maximum Radial Deviation 9.3 9.3 8.7 8.8 9.5 9.8 9.3

238 Table A.144: Calculated Scaphoid Ulnar Deviation for Specimen 4 during RUD Cycle, RCD

Wrist Position Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Average (◦)(◦)(◦)(◦)(◦)(◦) (◦) Maximum Radial Deviation -11.4 -11.1 -11.4 -11.6 -11.5 -11.3 -11.4 50% Radial Deviation -4.8 -4.9 -5.1 -5.4 -4.7 -4.8 -4.9 Neutral -1.6 -1.8 -1.3 -2.1 -1.9 -2.2 -1.8 50% Ulnar Deviation 1.9 1.7 2.1 1.4 1.3 1.1 1.6 Maximum Deviation 7.3 7.4 9.1 7.3 7.0 7.1 7.6 50% Deviationt 0.8 0.7 -0.0 -0.2 0.1 0.2 0.3 Neutral -1.7 -1.8 -2.4 -2.2 -2.2 -2.4 -2.1 50% Radial Deviation -4.7 -4.7 -5.2 -5.2 -4.6 -4.5 -4.8 Maximum Radial Deviation -11.4 -11.1 -11.3 -11.4 -11.5 -11.3 -11.3

239 Appendix B

Transformation Matrix Program

%Coordinate transformation calculations Andrew Smith August 21, 2009 %updated September 8, 2010 c l c c l e a r a l l format compact

%These calculations are based off formulae found in the MS thesis for %Huqing Guo, entitled , ”Kinematics of the Human Wrist Joint using the %Polhemus 3−SPACE Tracker and Digitizer System.”

%Radial Coordinate System

%z−axis defined by line drawn between a proximal and a distal point on the %radius/forearm: proximally −center of concave surfaces of head of radius, %d i s t a l l y −center of distal articulating surface defined by middle of ridge %dividing fossas for scaphoid and lunate.

%y−axis perpendicular to plane formed by z−axis and line defined as %follows: line drawn from center of distal articulating surface on radius %to center of flat distal surface of small distal end of ulnar head.

%x−axis defined by two successive cross products making it perpendicular to %the z−a x i s and y−a x i s .

%p o s i t i v e z−axis: always distal positive x−axis: always directed from %radius to ulna positive y−axis: dorsal to palmar for right hands, % palmartodorsal for left hands

240 %Origin: center of distal articulating surface of radius

%Radial coordinate system rFsw=[27.90, 9.75, −148.37]; %F, position vector of center of radius at %elbow wrt SW rDsw=[3.52, 4.79, 106.80]; %D, position vector of center of radius at %wrist wrt SW rEsw=[34.58, −0.51, 105.97]; %E, position vector of distal ulna wrt SW

rZsw=(rDsw−rFsw)/norm(rDsw−rFsw); %unit vector for Z wrt sw r23sw=(rEsw−rDsw)/norm(rEsw−rDsw ) ; rYsw=(cross(rZsw,r23sw))/norm(cross(rZsw,r23sw)); %unit vector for Y wrt sw rXsw=cross(rYsw,rZsw)/norm(cross(rYsw,rZsw)); %unit vector for X wrt sw

Rswr=[rXsw; rYsw; rZsw]; %rotation matrix from sw coords to radial coords Rrsw=inv(Rswr); %rotation matrix from radial coords to sw coords

Orsw=rDsw; %position of radial coord system wrt sw origin/coord system Brsw=[1 0 0 0;Orsw’, Rrsw]; %transformation matrix from radial coords to %sw coords Bswr=inv(Brsw); %transformation matrix from sw coords to radial coords

%Source coordinate system RsBsw=[ −1.38 , −18.84 , −73.39]; %B, position vector of center of platform %wrt SW RsCsw=[ −1.07 , −33.96, 8.62]; %C, distal edge of platform wrt SW RsAsw=[53.55 , −50.83 , −79.51]; %A, lateral edge of platform wrt SW

RsXsw=(RsCsw−RsBsw)/norm(RsCsw−RsBsw); %unit vector for source X wrt SW Rs13sw=(RsAsw−RsBsw)/ norm (RsAsw−RsBsw); %unit vector from B to A RsZsw=(cross(Rs13sw,RsXsw))/norm(cross(Rs13sw,RsXsw)); %unit vector for %source Z wrt SW RsYsw=(cross(RsZsw,RsXsw))/norm(cross(RsZsw,RsXsw)); %unit vector for %source Y wrt SW

RswRs=[RsXsw; RsYsw; RsZsw]; %rotation matrix from sw coords to source coords RRssw=inv(RswRs); %rotation matrix from source coords to sw coords

ORssw=RsBsw; %position of source coord system wrt sw origin/coord system BRssw=[1 0 0 0;ORssw’, RRssw]; %transformation matrix from source coords

241 %to sw coords BswRs=inv(BRssw); %transformation matrix from sw coords to source coords

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %Lunate Sensor Coordinate System

LsAsw=[27.95 , −56.64, 95.21]; %point A, Lunate Sensor LsBsw=[22.96, −51.61, 124.36]; %point B, Lunate Sensor LsCsw=[ −5.47 , −60.58, 121.03]; %point C, Lunate Sensor

LsXsw=(LsBsw−LsAsw)/norm(LsBsw−LsAsw ) ; %unit vector for Lunate sensor X wrt SW LsYsw=(LsBsw−LsCsw)/norm(LsBsw−LsCsw ) ; %unit vector for Lunate sensor Y wrt SW LsZsw=(cross (LsXsw,LsYsw))/norm( cross (LsXsw,LsYsw)); % unit vector for Lunate sensor Z wrt SW

%no intermediate cross product needed because line segments BD and AC are %chosen orthogonal in solidworks

RswLs=[LsXsw; LsYsw; LsZsw]; %rotation matrix from sw coords to Lunate sensor coords RLssw=inv (RswLs); %rotation matrix from lunate sensor coords to sw coords

OLssw=LsBsw ; %position of lunate sensor coord system wrt sw origin/coord system BLssw=[1 0 0 0;OLssw’, RLssw]; %transformation matrix from lunate sensor coords to sw coords BswLs=inv (BLssw ); %transformation matrix from sw coords to lunate sensor coords

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %Scaphoid Sensor Coordinate System

SsAsw=[ −59.03 , −51.71, 142.80]; %point A, Scaphoid Sensor SsBsw=[ −46.25 , −38.04, 166.25]; %point B, Scaphoid Sensor SsCsw=[ −67.94 , −17.31, 165.98]; %point C, Scaphoid Sensor

SsXsw=(SsBsw−SsAsw)/norm(SsBsw−SsAsw ) ; %unit vector for Scaphoid sensor X wrt SW

242 SsYsw=(SsBsw−SsCsw)/norm(SsBsw−SsCsw ) ; %unit vector for Scaphoid sensor Y wrt SW SsZsw=(cross (SsXsw,SsYsw))/norm( cross (SsXsw,SsYsw)); % unit vector for Scaphoid sensor Z wrt SW

%no intermediate cross product needed because line segments BD and AC are %chosen orthogonal in solidworks

RswSs=[SsXsw; SsYsw; SsZsw]; %rotation matrix from sw coords to Scaphoid sensor coords RSssw=inv (RswSs ); %rotation matrix from Scaphoid sensor coords to sw coords

OSssw=SsBsw ; %position of Scaphoid sensor coord system wrt sw origin/coord system BSssw=[1 0 0 0;OSssw’, RSssw]; %transformation matrix from Scaphoid sensor coords to sw coords BswSs=inv (BSssw ); %transformation matrix from sw coords to Scaphoid sensor coords

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %3rd Metacarpal Sensor Coordinate System

MsAsw=[10.81 , −18.58, 219.79]; %point A, 3M Sensor MsBsw=[10.86 , −18.76, 189.79]; %point B, 3M Sensor MsCsw=[ −18.72 , −23.77, 189.77]; %point C, 3M Sensor

MsXsw=(MsBsw−MsCsw)/ norm (MsBsw−MsCsw); %unit vector for 3M sensor X wrt SW MsYsw=(MsBsw−MsAsw)/ norm (MsBsw−MsAsw); %unit vector for 3M sensor Y wrt SW MsZsw=( c r o s s (MsXsw, MsYsw) ) / norm ( c r o s s (MsXsw, MsYsw ) ) ; % unit vector for 3M sensor Z wrt SW

%no intermediate cross product needed because line segments BD and AC are %chosen orthogonal in solidworks

RswMs=[MsXsw ; MsYsw ; MsZsw ] ; %rotation matrix from sw coords to 3M sensor coords RMssw=inv (RswMs ) ; %rotation matrix from 3M sensor coords to sw coords

OMssw=MsBsw; %position of 3M sensor coord system wrt sw origin/coord system

243 BMssw=[1 0 0 0 ;OMssw’ , RMssw ] ; %transformation matrix from 3M sensor coords to sw coords BswMs=inv(BMssw); %transformation matrix from sw coords to 3M sensor coords

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %3rd Metacarpal Bony Coordinate System

%Origin− midway between the base and head of the 3rd metacarpal at the %center of the tubular bone

%Y−a x i s − parallel to the line from the center of the distal head to the %midpoint of the base

%X−a x i s − Xm and Ym form a sagittal plane that splits the metacarpal into %mirroed halves. This is done through visual inspection

%Z−a x i s − the common perpendicular to X and Y

%p o s i t i v e z−axis: always to the right positive x−axis: volar for the right %hand % dorsalforthelefthand %p o s i t i v e y−axis: proximal for right hands, % distalforlefthands

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %Metacarpal bony coordinate system mAsw=[7.86 , −35.75, 180.74]; %point A, 3M mBsw=[6.32 , −5.83, 179.38]; %point B, 3M mCsw=[5.19 , −7.24, 149.43]; %point C, 3M mXsw=(mBsw−mAsw)/ norm (mBsw−mAsw); %unit vector for 3MX wrt SW mYsw=(mCsw−mBsw)/ norm (mCsw−mBsw); %unit vector for 3MY wrt SW mZsw=( c r o s s (mXsw,mYsw) ) / norm ( c r o s s (mXsw,mYsw ) ) ; % unit vector for 3MZ wrt SW

%no intermediate cross product needed because line segments BD and AC are %chosen orthogonal in solidworks

Rswm=[mXsw; mYsw; mZsw]; %rotation matrix from sw coords to 3M coords Rmsw=inv(Rswm); %rotation matrix from 3M coords to sw coords

244 Omsw=mBsw; %position of 3M sensor system wrt sw origin/coord system Bmsw=[1 0 0 0 ;Omsw’ , Rmsw ] ; %transformation matrix from 3M sensor to sw coords Bswm=inv(Bmsw); %transformation matrix from sw coords to 3M coords

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %Lunate bony coordinate system

Olsw=[13.50, 4.91, 112.26]; %origin located at volumetric centroid of lunate

lXsw=(rXsw)/norm(rXsw); %unit vector for lunate X wrt SW lYsw=(rYsw)/norm(rYsw); %unit vector for lunate Y wrt SW lZsw=(rZsw)/norm(rZsw); %unit vector for lunate Z wrt SW

Rswl=[lXsw; lYsw; lZsw]; %rotation matrix from sw coords to lunate coords Rlsw=inv(Rswl); %rotation matrix from lunate coords to sw coords

Blsw=[1 0 0 0;Olsw’, Rlsw]; %transformation matrix from lunate to sw coords Bswl=inv(Blsw); %transformation matrix from sw coords to lunate coords

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %Scaphoid bony coordinate system

Ossw=[ −2.71, 7.10, 119.95]; %origin located at volumetric centroid of scaphoid

sXsw=(rXsw)/norm(rXsw); %unit vector for scaphoid X wrt SW sYsw=(rYsw)/norm(rYsw); %unit vector for scaphoid Y wrt SW sZsw=(rZsw)/norm(rZsw); %unit vector for scaphoid Z wrt SW

Rsws=[sXsw; sYsw; sZsw]; %rotation matrix from sw coords to scaphoid coords Rssw=inv(Rsws); %rotation matrix from scaphoid coords to sw coords

Bssw=[1 0 0 0;Ossw’, Rssw]; %transformation matrix from scaphoid coords to sw coords Bsws=inv(Bssw); %transformation matrix from sw coords to scaphoid coords

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %Load motion data

245 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%Prompt for motion data file selection [datafilename]=uigetfile (’ ∗ .csv’,’Select ∗ .csv motion data file for processing ’)

data=load(datafilename); %load csv file data and assign it to proper bone scaphoiddata=data(: ,1:6); metacarpaldata=data(: ,7:12); lunatedata=data(: ,13:18);

disp(’motion data loaded ’)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %Lunate Sensor %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%Sensor source transformation (3−2−1 r o t a t i o n ) for n=1:size(lunatedata ,1) %for each position define translations and rotations recorded by the 3space Txlun=lunatedata(n,1) ∗ 1 0 ; Tylun=lunatedata(n,2) ∗ 1 0 ; Tzlun=lunatedata(n,3) ∗ 1 0 ; psilun=lunatedata(n,4) ∗ p i /180; thetalun=lunatedata(n,5) ∗ p i /180; philun=lunatedata(n,6) ∗ p i /180;

Tsourcesensorlunate=[Txlun; Tylun; Tzlun]; %create translation matrix

Rsensorsourcelunate=[cos(psilun)∗ cos(thetalun) cos(psilun)∗ sin(philun)∗ sin(thetalun)− cos(philun)∗ sin(psilun) sin(philun)∗ sin(psilun)+cos(philun)∗ cos(psilun)∗ sin(thetalun); cos(thetalun)∗ sin(psilun) cos(philun)∗ cos(psilun)+sin(philun)∗ sin(psilun)∗ sin(thetalun) cos(philun)∗ sin(psilun)∗ sin(thetalun)−1∗ cos(psilun)∗ sin(philun); −1∗ sin(thetalun) cos(thetalun)∗ sin(philun) cos(philun)∗ cos(thetalun )]; %3−2−1 rotation matrix from sensor to source

Bsensorsourcelunate=[1 0 0 0; Tsourcesensorlunate Rsensorsourcelunate ]; % transformation from sensor coords to source coords

246 %Joint Coordinate System (JCS) for the radiolunate joint

%e1 axis defined by x−axis fixed to radius (flexion negative for right %hand, positive for left hand) e3 axis defined by z−axis fixed to lunate %(pronation negative for right hand, positive for left hand) e2 axis is %common perpendicular to e1 and e3 (ulnar deviation positive) e1RLsw=rXsw ; e3RLsw=lZsw ; e2RLsw=(cross (e3RLsw,e1RLsw))/norm( cross (e3RLsw,e1RLsw));

%Lunate coordinate system unit vector z axis coverted to radial bony %coordinate system originlunate4=[1, 0, 0, 0]’; e3lunate=[1, 0, 0, 1]’; %ez for lunate e3JCSlunate4=Bswr∗BRssw∗ Bsensorsourcelunate ∗BswLs∗Blsw∗ e 3 l u n a t e −Bswr∗BRssw∗ Bsensorsourcelunate ∗BswLs∗Blsw∗ originlunate4 ; e3JCSlunate=[e3JCSlunate4(2) ,e3JCSlunate4(3) ,e3JCSlunate4 (4)]; e1JCSlunate=[1, 0, 0]; %ex for radius e2JCSlunate=(cross(e3JCSlunate ,e1JCSlunate))/norm(cross(e3JCSlunate ,e1JCSlunate ));

%f l e x i o n K=[0 , 0 , 1 ] ; alphalun=asind(dot(e2JCSlunate ,K)); flexionlun=−alphalun; %positive values are flexion

%pronation ilunate=[1, 1, 0, 0]’; i 4 l u n=Bswr∗BRssw∗ Bsensorsourcelunate ∗BswLs∗Blsw∗ i l u n a t e −Bswr∗BRssw∗ Bsensorsourcelunate ∗BswLs∗Blsw∗ originlunate4 ; ilun=[i4lun(2), i4lun(3), i4lun(4)]; gammalun=asind(dot(e2JCSlunate , ilun )); pronationlun=−gammalun; %positive values are pronation

%ulnar deviation betalun=acosd(dot(e1JCSlunate ,e3JCSlunate )); ulnardeviationlun=(90− betalun); %positive values are ulnar deviation

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% H4lun=Bswr∗BRssw∗ Bsensorsourcelunate ∗BswLs∗Blsw∗ originlunate4 ; Hlun=[H4lun(2), H4lun(3), H4lun(4)]; q1lun=dot(Hlun, e1JCSlunate );

247 q2lun=dot(Hlun, e2JCSlunate ); q3lun=dot(Hlun, e3JCSlunate );

resultslun(n,1)=q1lun; resultslun(n,2)=q2lun; resultslun(n,3)=q3lun; resultslun(n,4)=flexionlun ; resultslun(n,5)=pronationlun; resultslun(n,6)=ulnardeviationlun ; end resultslun;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %Scaphoid Sensor %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%Sensor source transformation (3−2−1 r o t a t i o n ) for n=1:size(scaphoiddata ,1) Txscap=scaphoiddata(n,1) ∗ 1 0 ; Tyscap=scaphoiddata(n,2) ∗ 1 0 ; Tzscap=scaphoiddata(n,3) ∗ 1 0 ; psiscap=scaphoiddata(n,4) ∗ p i /180; thetascap=scaphoiddata(n,5) ∗ p i /180; phiscap=scaphoiddata(n,6) ∗ p i /180;

Tsourcesensorscaphoid=[Txscap; Tyscap; Tzscap ];

Rsensorsourcescaphoid=[cos(psiscap)∗ cos(thetascap) cos(psiscap)∗ sin(phiscap)∗ sin(thetascap)− cos(phiscap)∗ sin(psiscap) sin(phiscap)∗ sin(psiscap)+cos(phiscap)∗ cos(psiscap)∗ sin(thetascap); cos(thetascap)∗ sin(psiscap) cos(phiscap)∗ cos(psiscap)+sin(phiscap)∗ sin(psiscap)∗ sin(thetascap) cos(phiscap)∗ sin(psiscap)∗ sin(thetascap)−1∗ cos(psiscap)∗ sin(phiscap); −1∗ sin(thetascap) cos(thetascap)∗ sin(phiscap) cos(phiscap)∗ cos(thetascap )];

Bsensorsourcescaphoid=[1 0 0 0; Tsourcesensorscaphoid Rsensorsourcescaphoid ]; % transformation from sensor coords to source coords

%Joint Coordinate System (JCS) for the radioscaphoid joint

248 %e1 axis defined by x−axis fixed to radius (flexion negative for right %hand, positive for left hand) e3 axis defined by z−axis fixed to scaphoid %(pronation negative for right hand, positive for left hand) e2 axis is %common perpendicular to e1 and e3 (ulnar deviation positive) e1RSsw=rXsw ; e3RSsw=sZsw ; e2RSsw=(cross (e3RSsw,e1RSsw))/norm( cross (e3RSsw,e1RSsw));

%Scaphoid coordinate system unit vector z axis coverted to radial bony %coordinate system originscaphoid4=[1, 0, 0, 0]’; e3scaphoid=[1, 0, 0, 1]’; %ez for scaphoid e3JCSscaphoid4=Bswr∗BRssw∗ Bsensorsourcescaphoid ∗BswSs∗Bssw∗ e3scaphoid −Bswr∗BRssw∗ Bsensorsourcescaphoid ∗BswSs∗Bssw∗ originscaphoid4 ; e3JCSscaphoid=[e3JCSscaphoid4(2) ,e3JCSscaphoid4(3) ,e3JCSscaphoid4 (4)]; e1JCSscaphoid=[1, 0, 0]; %ex for radius e2JCSscaphoid=(cross (e3JCSscaphoid , e1JCSscaphoid)) /norm(cross(e3JCSscaphoid ,e1JCSscaphoid ));

%f l e x i o n K=[0 , 0 , 1 ] ; alphascap=asind(dot(e2JCSscaphoid ,K)); flexionscap=−alphascap;%positive values are flexion

%pronation iscaphoid=[1, 1, 0, 0]’; i4scap=Bswr∗BRssw∗ Bsensorsourcescaphoid ∗BswSs∗Bssw∗ i s c a p h o i d −Bswr∗BRssw∗ Bsensorsourcescaphoid ∗BswSs∗Bssw∗ originscaphoid4 ; iscap=[i4scap(2), i4scap(3), i4scap(4)]; gammascap=asind(dot(e2JCSscaphoid , iscap )); pronationscap=−gammascap;%positive values are pronation

%ulnar deviation betascap=acosd(dot(e1JCSscaphoid ,e3JCSscaphoid )); ulnardeviationscap=(90−betascap); %positive values are ulnar deviation

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% H4scap=Bswr∗BRssw∗ Bsensorsourcescaphoid ∗BswSs∗Bssw∗ originscaphoid4 ; Hscap=[H4scap(2), H4scap(3), H4scap(4)]; q1scap=dot(Hscap , e1JCSscaphoid );

249 q2scap=dot(Hscap , e2JCSscaphoid ); q3scap=dot(Hscap , e3JCSscaphoid );

resultsscap(n,1)=q1scap; resultsscap(n,2)=q2scap; resultsscap(n,3)=q3scap; resultsscap(n,4)=flexionscap ; resultsscap(n,5)=pronationscap; resultsscap(n,6)=ulnardeviationscap ; end resultsscap;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %Metacarpal Sensor %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%Sensor source transformation (3−2−1 r o t a t i o n ) for n=1:size(metacarpaldata ,1) Txmeta=metacarpaldata(n,1) ∗ 1 0 ; Tymeta=metacarpaldata(n,2) ∗ 1 0 ; Tzmeta=metacarpaldata(n,3) ∗ 1 0 ; psimeta=metacarpaldata(n,4) ∗ p i /180; thetameta=metacarpaldata(n,5) ∗ p i /180; phimeta=metacarpaldata(n,6) ∗ p i /180;

Tsourcesensormetacarpal=[Txmeta; Tymeta; Tzmeta];

Rsensorsourcemetacarpal=[cos(psimeta)∗ cos(thetameta) cos(psimeta)∗ sin(phimeta)∗ sin(thetameta)− cos(phimeta)∗ sin(psimeta) sin(phimeta)∗ sin(psimeta)+cos(phimeta)∗ cos(psimeta)∗ sin(thetameta); cos(thetameta)∗ sin(psimeta) cos(phimeta)∗ cos(psimeta)+sin(phimeta)∗ sin(psimeta)∗ sin(thetameta) cos(phimeta)∗ sin(psimeta)∗ sin(thetameta)−1∗ cos(psimeta)∗ sin(phimeta); −1∗ sin(thetameta) cos(thetameta)∗ sin(phimeta) cos(phimeta)∗ cos(thetameta )];

Bsensorsourcemetacarpal=[1 0 0 0; Tsourcesensormetacarpal Rsensorsourcemetacarpal ]; % transformation from sensor coords to source coords

%Joint Coordinate System (JCS) for the radiometacarpal joint

250 %e1 axis defined by x−axis fixed to radius (flexion negative for right %hand, positive for left) e3 axis defined by y−axis fixed to metacarpal %(pronation positive) e2 axis is common perpendicular to e1 and e3 (ulnar %deviation negative for right hand, positive for left) e1RMsw=rXsw ; e3RMsw=mYsw; e2RMsw=( c r o s s (e3RMsw , e1RMsw) ) / norm ( c r o s s (e3RMsw , e1RMsw ) ) ;

%metacarpal coordinate system unit vector z axis coverted to radial bony %coordinate system originmetacarpal4=[1, 0, 0, 0]’; e3metacarpal=[1, 0, 1, 0]’; %ey for metacarpal e3JCSmetacarpal4=Bswr∗BRssw∗ Bsensorsourcemetacarpal ∗BswMs∗Bmsw∗ e3metacarpal −Bswr∗BRssw∗ Bsensorsourcemetacarpal ∗BswMs∗Bmsw∗ originmetacarpal4 ; e3JCSmetacarpal=[e3JCSmetacarpal4(2) ,e3JCSmetacarpal4(3) ,e3JCSmetacarpal4 (4)]; e1JCSmetacarpal=[1, 0, 0]; %ex for radius e2JCSmetacarpal=(cross (e3JCSmetacarpal , e1JCSmetacarpal)) /norm(cross(e3JCSmetacarpal ,e1JCSmetacarpal ));

%f l e x i o n K=[0 , 0 , 1 ] ; alphameta=asind(dot(e2JCSmetacarpal ,K)); flexionmeta=alphameta; %positive value is flexion

%pronation kmetacarpal=[1, 0, 0, 1]’; k4meta=Bswr∗BRssw∗ Bsensorsourcemetacarpal ∗BswMs∗Bmsw∗ kmetacarpal −Bswr∗BRssw∗ Bsensorsourcemetacarpal ∗BswMs∗Bmsw∗ originmetacarpal4 ; kmeta=[k4meta(2), k4meta(3), k4meta(4)]; gammameta=asind(dot(e2JCSmetacarpal ,kmeta )); pronationmeta=−gammameta; %positive value is pronation

%ulnar deviation betameta=acosd(dot(e1JCSmetacarpal , e3JCSmetacarpal )); ulnardeviationmeta=−(90−betameta); %positive value is ulnar deviation

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% H4meta=Bswr∗BRssw∗ Bsensorsourcemetacarpal ∗BswMs∗Bmsw∗ originmetacarpal4 ; Hmeta=[H4meta(2) , H4meta(3) , H4meta(4)];

251 q1meta=dot(Hmeta, e1JCSmetacarpal ); q2meta=dot(Hmeta, e2JCSmetacarpal ); q3meta=dot(Hmeta, e3JCSmetacarpal );

resultsmeta(n,1)=q1meta; resultsmeta(n,2)=q2meta; resultsmeta(n,3)=q3meta; resultsmeta(n,4)=flexionmeta ; resultsmeta(n,5)=pronationmeta; resultsmeta(n,6)=ulnardeviationmeta ; end resultsmeta ;

%use input filename to create an output filename [path,inputfilename ,extension]=fileparts(datafilename); resultsfilename=sprintf(’%s’, inputfilename , ’results ’ , ’.xls ’);

l a b e l ={’q1’ ’q2’ ’q3’ ’flexion ’ ’pronation’ ’ulnar deviation’ } xlswrite(resultsfilename ,label ,’metacarpal results ’) xlswrite(resultsfilename ,resultsmeta ,’metacarpal results ’,’A2’) xlswrite(resultsfilename ,label ,’lunate results ’) xlswrite(resultsfilename ,resultslun ,’lunate results ’,’A2’) xlswrite(resultsfilename ,label ,’scaphoid results ’) xlswrite(resultsfilename ,resultsscap ,’scaphoid results ’,’A2’)

252 Appendix C

Data Normalization Program

function [metaflex , metapro, metadev, lunateflex , lunatepro , lunatedev , scaphoidflex , scaphoidpro , scaphoiddev]=datanormalization(datafilename) %Results Normalization and Processing %Andrew Smith %June 16, 2011 %c l c %c l e a r a l l format compact

%Input: motion data for each trial for individual specimens% %Normalization is performed by performing separating the motion into two %sets: max extension to max flexion and max flexion to max extension. Input %data is entered in this format: % % max extension % n e u t r a l % max flexion % neutral (averaged) % max extension % %This provides uninterrupted ranges on which to perform polynomial fits to %both the ext−to−flex and flex −to−ext parts of the motion cycle. % %A nth−order polynomial fit is performed on each motion range for each type %of data measurement besides metacarpal flexion (or ulnar deviation for %deviation testing). % %Normalized data positions are defined for metacarpal flexion and the

253 %appropriate polynomial fit is used to evaluate these points for the other %data measurements.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %Import Data

data=load(datafilename); %loads data from file designated by user

%data is imported from a CSV file versus a MS Excel file format because %”CSV import” is significantly faster than ”Excel import”

%data is formatted columns listing metacarpal flexion for each trial , then %metacarpal pronation for each trial ,then metacarpal ulnar deviation for %each trial. This is repeated for lunate and scaphoid.

%The number of trials for a specimen is automatically calculated by %dividing the number of columns by 3 [inputrows ,inputcolumns]=size(data); numtrials=inputcolumns/9;

metaflexion=data(: ,1: numtrials ); metapronation=data (: , numtrials+1:2∗ numtrials ); metadeviation=data(: ,2 ∗ numtrials+1:3∗ numtrials );

lunateflexion=data(: ,3 ∗ numtrials+1:4∗ numtrials ); lunatepronation=data(: ,4 ∗ numtrials+1:5∗ numtrials ); lunatedeviation=data(: ,5 ∗ numtrials+1:6∗ numtrials );

scaphoidflexion=data(: ,6 ∗ numtrials+1:7∗ numtrials ); scaphoidpronation=data(: ,7 ∗ numtrials+1:8∗ numtrials ); scaphoiddeviation=data(: ,8 ∗ numtrials+1:9∗ numtrials );

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %polynomial fit equation calculation

%create empty matrices for data metaflex=[] metapro=[]; metadev=[];

254 lunateflex=[]; lunatepro=[]; lunatedev=[]; scaphoidflex=[]; scaphoidpro=[]; scaphoiddev=[]; power=7 %set polynomial power

Rsqmin=1; %initiate Rsquared min value Rsqadjustedmin=1; %initiate Rsquared adjusted min value for trial=1:numtrials; % loop for each trial [maxflexangle , maxflexposition] = max(metaflexion(:, trial ) ,[] ,1); %calculate maximum flexion index [maxextangle, maxextposition] = min(metaflexion(: , trial ) ,[] ,1); %calculate maximum extension index midflexangle=maxflexangle/2; %calculate midflexion midextangle=maxextangle/2; %calculate midextension normflex=[maxextangle %define normalized flexion positions midextangle 0 midflexangle maxflexangle ]; normext=[midflexangle %define normalized extension positions 0 midextangle maxextangle ]; lastposition=length(metaflexion(: ,1)); %determine ending max ext position x=(maxextangle: 1: maxflexangle);

metaflex(1:5,trial)=normflex(1:5); %define flexion portion of cycle metaflex(6:9,trial)=normext(1:4); % define extension portion of cycle [flexfitmetapro ,s1 ,mu1]=polyfit(metaflexion(1:maxflexposition , trial ), metapronation(1:maxflexposition , trial ),power); %calculate best fit curve for flexion path of cycle metapro(1:5 , trial)=polyval(flexfitmetapro ,(normflex−mu1(1))/mu1(2)); %calculate normalized metacarpal pronation values for during flexion [ extfitmetapro ,s2 ,mu2]= polyfit(metaflexion(maxflexposition:lastposition , trial ),

255 metapronation(maxflexposition: lastposition , trial ),power); %calculate best fit curve for extension path of cycle metapro(6:9 , trial)=polyval(extfitmetapro ,(normext−mu2(1))/mu2(2)); %calculate normalized metacarpal pronation values for during extension

%calculate how well polynomial fit correlates with test data Flex testflex=metapronation(1:maxflexposition , trial ); %load actual test values for UD range inputflex=metaflexion(1:maxflexposition , trial ); %input values used with fit fitflex=polyval(flexfitmetapro ,( inputflex −mu1(1))/mu1(2)); %calculate fit values to compare with actual data trialcorrelationflex=corrcoef(testflex , fitflex ); %calculate Rsquared correlations between fit and test data Rsqflex=trialcorrelationflex (1,2); %pull correct Rsquared value from corrcoef function n1=length(metaflexion(1:maxflexposition , trial )); %calculate number of points used to calculate fit Rsqadjustedflex=1−(1− trialcorrelationflex(1,2)) ∗ ( n1 −1)/(n1−power −1); %calculate adjusted Rsquared value %check if local minimum Rsquared values exceed global values i f Rsqflex<=Rsqmin ; Rsqmin=Rsqflex ; end if Rsqadjustedflex <=Rsqadjustedmin ; Rsqadjustedmin=Rsqadjustedflex ; end

%calculate how well polynomial fit correlates with test data Ext testext=metapronation(maxflexposition: lastposition , trial ); %load actual test values for ext range inputext=metaflexion(maxflexposition: lastposition , trial ); %input values used with fit fitext=polyval(extfitmetapro ,(inputext −mu1(1))/mu1(2)); %calculate fit values to compare with actual data trialcorrelationext=corrcoef(testext , fitext ); %calculate Rsquared correlations between fit and test data Rsqext=trialcorrelationext (1 ,2); %pull correct Rsquared value from corrcoef function n1=length(metaflexion(maxflexposition: lastposition , trial )); %calculate number of points used to calculate fit Rsqadjustedext=1−(1− trialcorrelationext(1,2)) ∗ ( n1 −1)/(n1−power −1);

256 %calculate adjusted Rsquared value %check if local minimum Rsquared values exceed global values i f Rsqext<=Rsqmin ; Rsqmin=Rsqext ; end if Rsqadjustedext<=Rsqadjustedmin ; Rsqadjustedmin=Rsqadjustedext ; end

%metacarpal ulnar deviation normalization [flexfitmetadev ,s1 ,mu1]=polyfit(metaflexion(1:maxflexposition , trial ), metadeviation(1:maxflexposition , trial ),power); metadev(1:5 , trial)=polyval(flexfitmetadev ,(normflex−mu1(1))/mu1(2)); [ extfitmetadev ,s2 ,mu2]= polyfit(metaflexion(maxflexposition:lastposition , trial ), metadeviation(maxflexposition: lastposition , trial ),power); metadev(6:9 , trial)=polyval(extfitmetadev ,(normext−mu2(1))/mu2(2));

%calculate how well polynomial fit correlates with test data Flex testflex=metadeviation(1:maxflexposition , trial ); %load actual test values for UD range inputflex=metaflexion(1:maxflexposition , trial ); %input values used with fit fitflex=polyval(flexfitmetadev ,( inputflex −mu1(1))/mu1(2)); %calculate fit values to compare with actual data trialcorrelationflex=corrcoef(testflex , fitflex ); %calculate Rsquared correlations between fit and test data Rsqflex=trialcorrelationflex (1,2); %pull correct Rsquared value from corrcoef function n1=length(metaflexion(1:maxflexposition , trial )); %calculate number of points used to calculate fit Rsqadjustedflex=1−(1− trialcorrelationflex(1,2)) ∗ ( n1 −1)/(n1−power −1); %calculate adjusted Rsquared value %check if local minimum Rsquared values exceed global values i f Rsqflex<=Rsqmin ; Rsqmin=Rsqflex ; end if Rsqadjustedflex <=Rsqadjustedmin ; Rsqadjustedmin=Rsqadjustedflex ; end

%calculate how well polynomial fit correlates with test data Ext

257 testext=metadeviation(maxflexposition: lastposition , trial ); %load actual test values for ext range inputext=metaflexion(maxflexposition: lastposition , trial ); %input values used with fit fitext=polyval(extfitmetadev ,(inputext −mu1(1))/mu1(2)); %calculate fit values to compare with actual data trialcorrelationext=corrcoef(testext , fitext ); %calculate Rsquared correlations between fit and test data Rsqext=trialcorrelationext (1 ,2); %pull correct Rsquared value from corrcoef function n1=length(metaflexion(maxflexposition: lastposition , trial )); %calculate number of points used to calculate fit Rsqadjustedext=1−(1− trialcorrelationext(1,2)) ∗ ( n1 −1)/(n1−power −1); %calculate adjusted Rsquared value %check if local minimum Rsquared values exceed global values i f Rsqext<=Rsqmin ; Rsqmin=Rsqext ; end if Rsqadjustedext<=Rsqadjustedmin ; Rsqadjustedmin=Rsqadjustedext ; end

%lunate flexion normalization [ flexfitlunateflex ,s1,mu1]=polyfit(metaflexion(1:maxflexposition , trial ), lunateflexion(1:maxflexposition , trial ),power); lunateflex(1:5, trial)=polyval(flexfitlunateflex ,(normflex−mu1(1))/mu1(2)); [ extfitlunateflex ,s2 ,mu2]= polyfit(metaflexion(maxflexposition:lastposition , trial ), lunateflexion(maxflexposition:lastposition , trial ),power); lunateflex(6:9, trial)=polyval(extfitlunateflex ,(normext−mu2(1))/mu2(2));

%calculate how well polynomial fit correlates with test data Flex testflex=lunateflexion(1:maxflexposition , trial ); %load actual test values for UD range inputflex=metaflexion(1:maxflexposition , trial ); %input values used with fit fitflex=polyval(flexfitlunateflex ,(inputflex −mu1(1))/mu1(2)); %calculate fit values to compare with actual data trialcorrelationflex=corrcoef(testflex , fitflex ); %calculate Rsquared correlations between fit and test data Rsqflex=trialcorrelationflex (1,2);

258 %pull correct Rsquared value from corrcoef function n1=length(metaflexion(1:maxflexposition , trial )); %calculate number of points used to calculate fit Rsqadjustedflex=1−(1− trialcorrelationflex(1,2)) ∗ ( n1 −1)/(n1−power −1); %calculate adjusted Rsquared value %check if local minimum Rsquared values exceed global values i f Rsqflex<=Rsqmin ; Rsqmin=Rsqflex ; end if Rsqadjustedflex <=Rsqadjustedmin ; Rsqadjustedmin=Rsqadjustedflex ; end

%calculate how well polynomial fit correlates with test data Ext testext=lunateflexion(maxflexposition:lastposition , trial ); %load actual test values for ext range inputext=metaflexion(maxflexposition: lastposition , trial ); %input values used with fit fitext=polyval(extfitlunateflex ,(inputext −mu1(1))/mu1(2)); %calculate fit values to compare with actual data trialcorrelationext=corrcoef(testext , fitext ); %calculate Rsquared correlations between fit and test data Rsqext=trialcorrelationext (1 ,2); %pull correct Rsquared value from corrcoef function n1=length(metaflexion(maxflexposition: lastposition , trial )); %calculate number of points used to calculate fit Rsqadjustedext=1−(1− trialcorrelationext(1,2)) ∗ ( n1 −1)/(n1−power −1); %calculate adjusted Rsquared value %check if local minimum Rsquared values exceed global values i f Rsqext<=Rsqmin ; Rsqmin=Rsqext ; end if Rsqadjustedext<=Rsqadjustedmin ; Rsqadjustedmin=Rsqadjustedext ; end

%lunate pronation normalization [ flexfitlunatepro ,s1,mu1]=polyfit(metaflexion(1:maxflexposition , trial ), lunatepronation(1:maxflexposition , trial ),power); lunatepro(1:5, trial)=polyval(flexfitlunatepro ,(normflex−mu1(1))/mu1(2)); [ extfitlunatepro ,s2 ,mu2]=

259 polyfit(metaflexion(maxflexposition:lastposition , trial ), lunatepronation(maxflexposition: lastposition , trial ),power); lunatepro(6:9 , trial)=polyval(extfitlunatepro ,(normext−mu2(1))/mu2(2));

%calculate how well polynomial fit correlates with test data Flex testflex=lunatepronation(1:maxflexposition , trial ); %load actual test values for UD range inputflex=metaflexion(1:maxflexposition , trial ); %input values used with fit fitflex=polyval(flexfitlunatepro ,(inputflex −mu1(1))/mu1(2)); %calculate fit values to compare with actual data trialcorrelationflex=corrcoef(testflex , fitflex ); %calculate Rsquared correlations between fit and test data Rsqflex=trialcorrelationflex (1,2); %pull correct Rsquared value from corrcoef function n1=length(metaflexion(1:maxflexposition , trial )); %calculate number of points used to calculate fit Rsqadjustedflex=1−(1− trialcorrelationflex(1,2)) ∗ ( n1 −1)/(n1−power −1); %calculate adjusted Rsquared value %check if local minimum Rsquared values exceed global values i f Rsqflex<=Rsqmin ; Rsqmin=Rsqflex ; end if Rsqadjustedflex <=Rsqadjustedmin ; Rsqadjustedmin=Rsqadjustedflex ; end

%calculate how well polynomial fit correlates with test data Ext testext=lunatepronation(maxflexposition: lastposition , trial ); %load actual test values for ext range inputext=metaflexion(maxflexposition: lastposition , trial ); %input values used with fit fitext=polyval(extfitlunatepro ,(inputext −mu1(1))/mu1(2)); %calculate fit values to compare with actual data trialcorrelationext=corrcoef(testext , fitext ); %calculate Rsquared correlations between fit and test data Rsqext=trialcorrelationext (1 ,2); %pull correct Rsquared value from corrcoef function n1=length(metaflexion(maxflexposition: lastposition , trial )); %calculate number of points used to calculate fit Rsqadjustedext=1−(1− trialcorrelationext(1,2)) ∗ ( n1 −1)/(n1−power −1); %calculate adjusted Rsquared value

260 %check if local minimum Rsquared values exceed global values i f Rsqext<=Rsqmin ; Rsqmin=Rsqext ; end if Rsqadjustedext<=Rsqadjustedmin ; Rsqadjustedmin=Rsqadjustedext ; end

%lunate ulnar deviation normalization [ flexfitlunatedev ,s1,mu1]=polyfit(metaflexion(1:maxflexposition , trial ), lunatedeviation(1:maxflexposition , trial ),power); lunatedev(1:5, trial)=polyval(flexfitlunatedev ,(normflex−mu1(1))/mu1(2)); [ extfitlunatedev ,s2 ,mu2]= polyfit(metaflexion(maxflexposition:lastposition , trial ), lunatedeviation(maxflexposition: lastposition , trial ),power); lunatedev(6:9 , trial)=polyval(extfitlunatedev ,(normext−mu2(1))/mu2(2));

%calculate how well polynomial fit correlates with test data Flex testflex=lunatedeviation(1:maxflexposition , trial ); %load actual test values for UD range inputflex=metaflexion(1:maxflexposition , trial ); %input used with fit fitflex=polyval(flexfitlunatedev ,(inputflex −mu1(1))/mu1(2)); %calculate fit values to compare with actual data trialcorrelationflex=corrcoef(testflex , fitflex ); %calculate Rsquared correlations between fit and test data Rsqflex=trialcorrelationflex (1,2); %pull correct Rsquared value from corrcoef function n1=length(metaflexion(1:maxflexposition , trial )); %calculate number of points used to calculate fit Rsqadjustedflex=1−(1− trialcorrelationflex(1,2)) ∗ ( n1 −1)/(n1−power −1); %calculate adjusted Rsquared value %check if local minimum Rsquared values exceed global values i f Rsqflex<=Rsqmin ; Rsqmin=Rsqflex ; end if Rsqadjustedflex <=Rsqadjustedmin ; Rsqadjustedmin=Rsqadjustedflex ; end

%calculate how well polynomial fit correlates with test data Ext testext=lunatedeviation(maxflexposition: lastposition , trial );

261 %load actual test values for ext range inputext=metaflexion(maxflexposition: lastposition , trial ); %input values used with fit fitext=polyval(extfitlunatedev ,(inputext −mu1(1))/mu1(2)); %calculate fit values to compare with actual data trialcorrelationext=corrcoef(testext , fitext ); %calculate Rsquared correlations between fit and test data Rsqext=trialcorrelationext (1 ,2); %pull correct Rsquared value from corrcoef function n1=length(metaflexion(maxflexposition: lastposition , trial )); %calculate number of points used to calculate fit Rsqadjustedext=1−(1− trialcorrelationext(1,2)) ∗ ( n1 −1)/(n1−power −1); %calculate adjusted Rsquared value %check if local minimum Rsquared values exceed global values i f Rsqext<=Rsqmin ; Rsqmin=Rsqext ; end if Rsqadjustedext<=Rsqadjustedmin ; Rsqadjustedmin=Rsqadjustedext ; end

%scaphoid flexion normalization [ flexfitscaphoidflex ,s1,mu1]=polyfit(metaflexion(1:maxflexposition , trial ), scaphoidflexion(1:maxflexposition , trial ),power); scaphoidflex(1:5, trial)=polyval(flexfitscaphoidflex ,(normflex−mu1(1))/mu1(2)); [ extfitscaphoidflex ,s2 ,mu2]= polyfit(metaflexion(maxflexposition:lastposition , trial ), scaphoidflexion(maxflexposition: lastposition , trial ),power); scaphoidflex(6:9, trial)=polyval(extfitscaphoidflex ,(normext−mu2(1))/mu2(2));

%calculate how well polynomial fit correlates with test data Flex testflex=scaphoidflexion(1:maxflexposition , trial ); %load actual test values for UD range inputflex=metaflexion(1:maxflexposition , trial ); %input values used with fit fitflex=polyval(flexfitscaphoidflex ,(inputflex −mu1(1))/mu1(2)); %calculate fit values to compare with actual data trialcorrelationflex=corrcoef(testflex , fitflex ); %calculate Rsquared correlations between fit and test data Rsqflex=trialcorrelationflex (1,2); %pull correct Rsquared value from corrcoef function n1=length(metaflexion(1:maxflexposition , trial ));

262 %calculate number of points used to calculate fit Rsqadjustedflex=1−(1− trialcorrelationflex(1,2)) ∗ ( n1 −1)/(n1−power −1); %calculate adjusted Rsquared value %check if local minimum Rsquared values exceed global values i f Rsqflex<=Rsqmin ; Rsqmin=Rsqflex ; end if Rsqadjustedflex <=Rsqadjustedmin ; Rsqadjustedmin=Rsqadjustedflex ; end

%calculate how well polynomial fit correlates with test data Ext testext=scaphoidflexion(maxflexposition: lastposition , trial ); %load actual test values for ext range inputext=metaflexion(maxflexposition: lastposition , trial ); %input values used with fit fitext=polyval(extfitscaphoidflex ,(inputext −mu1(1))/mu1(2)); %calculate fit values to compare with actual data trialcorrelationext=corrcoef(testext , fitext ); %calculate Rsquared correlations between fit and test data Rsqext=trialcorrelationext (1 ,2); %pull correct Rsquared value from corrcoef function n1=length(metaflexion(maxflexposition: lastposition , trial )); %calculate number of points used to calculate fit Rsqadjustedext=1−(1− trialcorrelationext(1,2)) ∗ ( n1 −1)/(n1−power −1); %calculate adjusted Rsquared value %check if local minimum Rsquared values exceed global values i f Rsqext<=Rsqmin ; Rsqmin=Rsqext ; end if Rsqadjustedext<=Rsqadjustedmin ; Rsqadjustedmin=Rsqadjustedext ; end

%scaphoid pronation normalization [flexfitscaphoidpro ,s1,mu1]=polyfit(metaflexion(1:maxflexposition , trial ), scaphoidpronation(1:maxflexposition , trial ),power); scaphoidpro(1:5, trial)=polyval(flexfitscaphoidpro ,(normflex−mu1(1))/mu1(2)); [ extfitscaphoidpro ,s2 ,mu2]= polyfit(metaflexion(maxflexposition:lastposition , trial ), scaphoidpronation(maxflexposition: lastposition , trial ),power);

263 scaphoidpro(6:9 , trial)=polyval(extfitscaphoidpro ,(normext−mu2(1))/mu2(2));

%calculate how well polynomial fit correlates with test data Flex testflex=scaphoidpronation(1:maxflexposition , trial ); %load actual test values for UD range inputflex=metaflexion(1:maxflexposition , trial ); %input values used for fit fitflex=polyval(flexfitscaphoidpro ,( inputflex −mu1(1))/mu1(2)); %calculate fit values to compare with actual data trialcorrelationflex=corrcoef(testflex , fitflex ); %calculate Rsquared correlations between fit and test data Rsqflex=trialcorrelationflex (1,2); %pull correct Rsquared value from corrcoef function n1=length(metaflexion(1:maxflexposition , trial )); %calculate number of points used to calculate fit Rsqadjustedflex=1−(1− trialcorrelationflex(1,2)) ∗ ( n1 −1)/(n1−power −1); %calculate adjusted Rsquared value %check if local minimum Rsquared values exceed global values i f Rsqflex<=Rsqmin ; Rsqmin=Rsqflex ; end if Rsqadjustedflex <=Rsqadjustedmin ; Rsqadjustedmin=Rsqadjustedflex ; end

%calculate how well polynomial fit correlates with test data Ext testext=scaphoidpronation(maxflexposition: lastposition , trial ); %load actual test values for ext range inputext=metaflexion(maxflexposition: lastposition , trial ); %input values used with fit fitext=polyval(extfitscaphoidpro ,(inputext −mu1(1))/mu1(2)); %calculate fit values to compare with actual data trialcorrelationext=corrcoef(testext , fitext ); %calculate Rsquared correlations between fit and test data Rsqext=trialcorrelationext (1 ,2); %pull correct Rsquared value from corrcoef function n1=length(metaflexion(maxflexposition: lastposition , trial )); %calculate number of points used to calculate fit Rsqadjustedext=1−(1− trialcorrelationext(1,2)) ∗ ( n1 −1)/(n1−power −1); %calculate adjusted Rsquared value %check if local minimum Rsquared values exceed global values i f Rsqext<=Rsqmin ;

264 Rsqmin=Rsqext ; end if Rsqadjustedext<=Rsqadjustedmin ; Rsqadjustedmin=Rsqadjustedext ; end

%scaphoid ulnar deviation normalization [flexfitscaphoiddev ,s1 ,mu1]=polyfit(metaflexion(1:maxflexposition , trial ), scaphoiddeviation(1:maxflexposition , trial ),power); scaphoiddev(1:5 , trial)=polyval(flexfitscaphoiddev ,(normflex−mu1(1))/mu1(2)); [ extfitscaphoiddev ,s2 ,mu2]= polyfit(metaflexion(maxflexposition:lastposition , trial ), scaphoiddeviation(maxflexposition: lastposition , trial ),power); scaphoiddev(6:9 , trial)=polyval(extfitscaphoiddev ,(normext−mu2(1))/mu2(2));

%calculate how well polynomial fit correlates with test data Flex testflex=scaphoiddeviation(1:maxflexposition , trial ); %load actual test values for UD range inputflex=metaflexion(1:maxflexposition , trial ); %input values used with fit fitflex=polyval(flexfitscaphoiddev ,( inputflex −mu1(1))/mu1(2)); %calculate fit values to compare with actual data trialcorrelationflex=corrcoef(testflex , fitflex ); %calculate Rsquared correlations between fit and test data Rsqflex=trialcorrelationflex (1,2); %pull correct Rsquared value from corrcoef function n1=length(metaflexion(1:maxflexposition , trial )); %calculate number of points used to calculate fit Rsqadjustedflex=1−(1− trialcorrelationflex(1,2)) ∗ ( n1 −1)/(n1−power −1); %calculate adjusted Rsquared value %check if local minimum Rsquared values exceed global values i f Rsqflex<=Rsqmin ; Rsqmin=Rsqflex ; end if Rsqadjustedflex <=Rsqadjustedmin ; Rsqadjustedmin=Rsqadjustedflex ; end

%calculate how well polynomial fit correlates with test data Ext testext=scaphoiddeviation(maxflexposition: lastposition , trial ); %load actual test values for ext range inputext=metaflexion(maxflexposition: lastposition , trial );

265 %input values used with fit fitext=polyval(extfitscaphoiddev ,(inputext −mu1(1))/mu1(2)); %calculate fit values to compare with actual data trialcorrelationext=corrcoef(testext , fitext ); %calculate Rsquared correlations between fit and test data Rsqext=trialcorrelationext (1 ,2); %pull correct Rsquared value from corrcoef function n1=length(metaflexion(maxflexposition: lastposition , trial )); %calculate number of points used to calculate fit Rsqadjustedext=1−(1− trialcorrelationext(1,2)) ∗ ( n1 −1)/(n1−power −1); %calculate adjusted Rsquared value %check if local minimum Rsquared values exceed global values i f Rsqext<=Rsqmin ; Rsqmin=Rsqext ; end if Rsqadjustedext<=Rsqadjustedmin ; Rsqadjustedmin=Rsqadjustedext ; end end Rsqmin %displays lowest R−squared value Rsqadjustedmin % displays lowest weighted r−square value

266 Appendix D

Results Comparison Program

%Statistical comparison of intact and RCD results %Andrew Smith %June 20, 2011 c l c c l e a r a l l format compact

%This program does statistical comparison between the normalized data for %intact and RCD results. The program calls up the data−normalization %function/program to normalize the data for both intact and RCD results.

%normalize intact data filename=’FEM’; %type of test resultsfilename=sprintf(’%s’, filename , ’stats ’,’.xls ’); %display file name positionlist={’Maximum Extension ’ ’50% Extension ’ ’Neutral ’ ’50% Flexion ’ ’Maximum Flexion ’ ’50% Flexion ’ ’Neutral ’ ’50% Extension ’ ’Maximum Extension ’ } % ordered list of normalized positions for FEM motion i t e m l i s t ={’Position ’; ’Delta (degrees)’;’p−value ’; ’Std. Dev. Intact ’; ’Std. Dev. RCD’ } %column headings

for specs=1:4 %initiates loop to run through 4 specimens %pull in and normalize data for each specimen for both intact and RCD intactfilename=strcat(’s’,num2str(specs),’flex ’,’intact ’,’prenormal.csv ’) %create file name for use with normalization sub−code [imetaflex , imetapro, imetadev, ilunateflex , ilunatepro , ilunatedev , iscaphoidflex , iscaphoidpro , iscaphoiddev]=datanormalization(intactfilename ); %call up and run normalization sub−code for intact test data rcdfilename=strcat(’s’ ,num2str(specs),’flex ’ , ’RCD’ , ’prenormal.csv ’)

267 [rmetaflex , rmetapro, rmetadev, rlunateflex , rlunatepro , rlunatedev , rscaphoidflex , rscaphoidpro , rscaphoiddev]=datanormalization(rcdfilename ); %call up and run normalization sub−code for post RCD test data

bone={’meta’ ’lunate ’ ’scaphoid’ } %list of labels for looping through the three bones meastype ={’flex ’ ’pro’ ’dev’ } %list of labels for looping through three types of motion

for n=1:length(bone); %initiates loop to cycle through the three bones bonestring=bone(n); %assigns proper label to bonestring for k=1:length(meastype); %for each type of measurement(flexion , pronation , deviation) meastypestring=meastype(k); %grab string name for measurement type variablename=strcat(bonestring , meastypestring ); %name variable based on bone and measurement type rvalues=eval(char(strcat(’r’,variablename))) ’; %add r to variable %name to reference specific RCD array from normalization function rmean=mean(rvalues); %calculate mean values for RCD data ivalues=eval(char(strcat(’i ’,variablename))) ’; %add i to variable %name to reference specific intact array from normalization function imean=mean(ivalues); %calculate mean values for Intact data delta=rmean−imean; % calculate difference between RCD and Intact means [h,p] = ttest2(ivalues ,rvalues ,0.05,’both’,’unequal ’); %performs two−sample t−test with 95% confidence level , %two−tailed with unequal variances stdi=std(ivalues); %calculate standard deviation for intact values stdr=std(rvalues); %calculate standard deviation for RCD values M=[delta;p;stdi;stdr;h]; %create matrix for stats data for specific %measurement (metaflex , etc) with following format in columns: %difference in angle, p−value, intact standard deviation , RCD %standard deviation , and logic values for significant %difference , H=1 indicates that the null hypothesis can be %rejected at the 5% level. assignin(’base ’ ,char(strcat(’s’ ,num2str(specs),variablename , ’data ’)) ,M); %give unique name to measurement data matrix end end end

%create array to compare rcd effects among specimens for each type of

268 %measurement for n=1:length(bone); %initiates loop to cycle through the three bones bonestring=bone(n); %assigns proper label to bonestring for k=1:length(meastype); %for each type of measurement %(flexion , pronation , deviation) meastypestring=meastype(k); %grab string name for measurement type variablename=strcat(bonestring , meastypestring ); %name variable based on bone and measurement type for pos=1:9; %iniatiates loop to cycle through each normalized position for specs=1:4; %initiates loop to cycle through each specimen values=eval(char(strcat(’s’ ,num2str(specs),variablename , ’data ’))); %creates matrix of RCD effects for all specimens for %a given bone and motion and normalized position MM(pos , specs)=values(1,pos); %assigns in proper values for each position end [hh,pp]=ttest(MM(pos ,1:4)); %performs one−sample paired t−t e s t %on changes for each specimen at a given position. %null hypothesis assumes that there is no change. MM(pos,5)=mean(MM(pos ,1:4)); % adds to matrix a column with %average change for specimens for a given position MM(pos,6)=std(MM(pos ,1:4)); % adds to matrix a column with %standard deviation for change in angle for a given position MM(pos,7)=pp; %adds to matrix a column with p−value for the t−t e s t MM(pos,8)=hh; %adds to matrix a column with the logical value %indicate result of t−t e s t end assignin(’base ’ ,char(strcat(variablename , ’comparison ’)) ,MM); %give unique name to comparison matrix c l e a r MM end end

%create arrays for individual specimens %d e l t a f l e x | p−value | delta pronation | pvalue | delta deviation | pvalue | bone={’meta’ ’lunate ’ ’scaphoid’ } for specs=1:4; %for 4 specimens for n=1:length(bone); %for each type of bone bonestring=bone(n); %assign in correct type of bone flexvalues=eval(char(strcat(’s’ ,num2str(specs),bonestring , ’flexdata ’))); %pull in flexion values

269 provalues=eval(char(strcat(’s’ ,num2str(specs),bonestring , ’prodata ’))); %pull in pronation values devvalues=eval(char(strcat(’s’ ,num2str(specs),bonestring , ’devdata ’))); %pull in deviation values MMM=[flexvalues (1:2 ,:) ’ ,provalues(1:2 ,:) ’ ,devvalues(1:2 ,:) ’]; %pulls delta and p−values from matrices assignin(’base ’ ,char(strcat(’s’ ,num2str(specs),bonestring , ’values ’)) ,MMM); %give unique name to specimen matrix end end

270