List of Contributors xv
Preface xvii
Acknowledgments xix
About the Companion Website xxi
1 Biomechanics as an Interdiscipline 1
Stephen J. Thomas Joseph A. Zeni and David A. Winters
1.0 Introduction 1
1.0.1 Importance of Human Movement Analysis 1
1.0.2 The Interprofessional Team 2
1.1 Measurement Description Analysis and Assessment 2
1.1.1 Measurement Description and Monitoring 3
1.1.2 Analysis 4
1.1.3 Assessment and Interpretation 5
1.2 Biomechanics and its Relationship with Physiology and Anatomy 6
1.3 References 7
2 Signal Processing 8
Joseph A. Zeni Stephen J. Thomas and David A. Winters
2.0 Introduction 8
2.1 Auto- and Cross-Correlation Analyses 8
2.1.1 Similarity to the Pearson Correlation 9
2.1.2 Formulae for Auto- and Cross-Correlation Coefficients 10
2.1.3 Four Properties of the Autocorrelation Function 11
2.1.4 Three Properties of the Cross-Correlation Function 14
2.1.5 Importance in Removing the Mean Bias from the Signal 15
2.1.6 Digital Implementation of Auto- and Cross-Correlation Functions 15
2.1.7 Application of Autocorrelations 16
2.1.8 Applications of Cross-Correlations 17
2.2 Frequency Analysis 19
2.2.1 Introduction – Time Domain vs. Frequency Domain 19
2.2.2 Discrete Fourier (Harmonic) Analysis 19
2.2.3 Fast Fourier Transform (FFT) 21
2.2.4 Applications of Spectrum Analyses 22
2.3 Ensemble Averaging of Repetitive Waveforms 29
2.3.1 Examples of Ensemble-Averaged Profiles 31
2.3.2 Normalization of Time Bases to 100% 31
2.3.3 Measure of Average Variability about the Mean Waveform 32
2.4 References 32
3 Kinematics 34
Amy L. Lenz
3.0 Historical Development and Complexity of Problem 34
3.1 Kinematic Conventions 35
3.1.1 Absolute Spatial Reference System 35
3.1.2 Total Description of a Body Segment in Space 36
3.2 Direct Measurement Techniques 36
3.2.1 Goniometers 36
3.2.2 Accelerometers 38
3.2.3 Inertial Sensors 39
3.2.4 Special Joint Angle Measuring Systems 40
3.2.5 Electromagnetic Systems 41
3.3 Imaging Measurement Techniques 42
3.3.1 Review of Basic Lens Optics 42
3.3.2 f-Stop Setting and Field of Focus 43
3.3.3 Television Imaging Camera Historical Development 43
3.3.4 Optical Motion Capture 44
3.3.5 Optoelectric Techniques 47
3.3.6 Biplane Fluoroscopy 48
3.3.7 Markerless Systems 51
3.3.8 Summary of Various Kinematic Systems 51
3.4 Clinical Measures of Kinematics 52
3.4.1 2-D Kinematic Apps/Sensors 52
3.4.2 Sensor-Based Systems 52
3.5 Processing of Raw Kinematic Data 52
3.5.1 Nature of Unprocessed Image Data 52
3.5.2 Signal Versus Noise in Kinematic Data 53
3.5.3 Problems of Calculating Velocities and Accelerations 54
3.5.4 Smoothing and Curve Fitting of Data 54
3.5.5 Comparison of Some Smoothing Techniques 60
3.6 Calculation of Other Kinematic Variables 62
3.6.1 Limb-Segment Angles 62
3.6.2 Joint Angles 63
3.6.3 Velocities – Linear and Angular 63
3.6.4 Accelerations – Linear and Angular 63
3.7 Problems Based on Kinematic Data 64
3.8 References 65
4 Anthropometry 67
Joseph A. Zeni Stephen J. Thomas and David A. Winters
4.0 Scope of Anthropometry in Movement Biomechanics 67
4.0.1 Segment Dimensions 67
4.1 Density Mass and Inertial Properties 68
4.1.1 Whole-Body Density 68
4.1.2 Segment Densities 69
4.1.3 Segment Mass and Center of Mass 69
4.1.4 Center of Mass of a Multisegment System 72
4.1.5 Mass Moment of Inertia and Radius of Gyration 73
4.1.6 Parallel Axis Theorem 74
4.1.7 Use of Anthropometric Tables and Kinematic Data 75
4.2 Direct Experimental Measures 78
4.2.1 Location of the Anatomical Center of Mass of the Body 79
4.2.2 Calculation of the Mass of a Distal Segment 79
4.2.3 Moment of Inertia of a Distal Segment 80
4.2.4 Joint Axes of Rotation 81
4.3 Muscle Anthropometry 82
4.3.1 Cross-Sectional Area of Muscles 82
4.3.2 Change in Muscle Length During Movement 83
4.3.3 Force per Unit Cross-Sectional Area (Stress) 84
4.3.4 Mechanical Advantage of Muscle 84
4.3.5 Multijoint Muscles 85
4.4 Problems Based on Anthropometric Data 86
4.5 References 87
5 Kinetics: Forces and Moments of Force 89
Stephen J. Thomas Joseph A. Zeni and David A. Winters
5.0 Biomechanical Models 89
5.0.1 Link-Segment Model Development 89
5.0.2 Forces Acting on the Link-Segment Model 90
5.0.3 Joint Reaction Forces and Bone-on-Bone Forces 91
5.1 Basic Link-Segment Equations – The Free-Body Diagram 93
5.2 Force Transducers and Force Plates 98
5.2.1 Multidirectional Force Transducers 98
5.2.2 Force Plates 99
5.2.3 Combined Force Plate and Kinematic Data 104
5.2.4 Interpretation of Moment-of-Force Curves 105
5.2.5 Differences Between Center of Mass and Center of Pressure 107
5.2.6 Kinematics and Kinetics of the Inverted Pendulum Model 108
5.3 Bone-on-bone Forces During Dynamic Conditions 110
5.3.1 Indeterminacy in Muscle Force Estimates 110
5.3.2 Example Problem 111
5.4 References 114
6 Mechanical Work Energy and Power 115
Joseph A. Zeni Stephen J. Thomas and David A. Winters
6.0 Introduction 115
6.0.1 Mechanical Energy and Work 115
6.0.2 Law of Conservation of Energy 116
6.0.3 Internal Versus External Work 116
6.0.4 Positive Work of Muscles 118
6.0.5 Negative Work of Muscles 118
6.0.6 Muscle Mechanical Power 119
6.0.7 Mechanical Work of Muscles 119
6.0.8 Mechanical Work Done on an External Load 120
6.0.9 Mechanical Energy Transfer Between Segments 122
6.1 Efficiency 123
6.1.1 Causes of Inefficient Movement 124
6.1.2 Summary of Energy Flows 127
6.2 Forms of Energy Storage 128
6.2.1 Energy of a Body Segment and Exchanges of Energy Within the Segment 129
6.2.2 Total Energy of a Multisegment System 132
6.3 Calculation of Internal and External Work 133
6.3.1 Internal Work Calculation 133
6.3.2 External Work Calculation 136
6.4 Power Balances at Joints and Within Segments 136
6.4.1 Energy Transfer via Muscles 137
6.4.2 Power Balance Within Segments 138
6.5 Problems Based on Kinetic and Kinematic Data 141
6.6 References 143
7 Understanding 3D Kinematic and Kinetic Variables 145
Thomas Hulcher
7.0 Introduction 145
7.1 Axes Systems 145
7.1.1 Global Reference System 145
7.1.2 Local Reference Systems and Rotation of Axes 146
7.1.3 Other Possible Rotation Sequences 147
7.1.4 Dot and Cross Products 148
7.2 Marker and Anatomical Axes Systems 148
7.2.1 Markerset Design 150
7.2.2 Event Detection Methods for Gait 152
7.2.3 Event Detection Methods for Other Activities 153
7.2.4 Considerations for Applications with Implements 153
7.2.5 Example of a Kinematic Data Set 154
7.3 Determination of Segment Angular Velocities and Accelerations 158
7.4 Kinetic Analysis of Reaction Forces and Moments 162
7.4.1 Newtonian Three-Dimensional Equations of Motion for a Segment 162
7.4.2 Euler’s Three-Dimensional Equations of Motion for a Segment 163
7.4.3 Example of a Kinetic Data Set 164
7.4.4 Joint Mechanical Powers 167
7.4.5 Induced Acceleration Analysis 167
7.4.6 Sample Moment and Power Curves 168
7.5 Suggested Further Reading 170
7.6 References 170
8 Muscle Mechanics 171
Stephen J. Thomas Joseph A. Zeni and David A. Winters
8.0 Introduction 171
8.0.1 The Motor Unit 171
8.0.2 Recruitment of Motor Units 172
8.0.3 Size Principle 173
8.0.4 Types of Motor Units – Fast- and Slow-Twitch Classification 174
8.0.5 The Muscle Twitch 175
8.0.6 Shape of Graded Contractions 176
8.1 Force–Length Characteristics of Muscles 177
8.1.1 Force–Length Curve of the Contractile Element 177
8.1.2 Influence of Parallel Connective Tissue 178
8.1.3 Series Elastic Tissue 178
8.1.4 In Vivo Force–Length Measures 180
8.2 Force–Velocity Characteristics 181
8.2.1 Concentric Contractions 181
8.2.2 Eccentric Contractions 183
8.2.3 Combination of Length and Velocity Versus Force 183
8.2.4 Combining Muscle Characteristics with Load Characteristics: Equilibrium 184
8.3 Technique to Measure in Vivo Tendon Mechanical Properties 186
8.3.1 Ankle Joint Moment 186
8.3.2 Tendon Mechanical Properties 187
8.4 References 187
9 Kinesiological Electromyography 189
Joseph A. Zeni Stephen J. Thomas and David A. Winters
9.0 Introduction 189
9.1 Electrophysiology of Muscle Contraction 189
9.1.1 Motor End Plate 189
9.1.2 Sequence of Chemical Events Leading to a Twitch 190
9.1.3 Generation of a Muscle Action Potential 190
9.1.4 Duration of the Motor Unit Action Potential 192
9.1.5 Detection of Motor Unit Action Potentials from Electromyogram During Graded Contractions 194
9.2 Recording of the Electromyogram 195
9.2.1 Amplifier Gain 196
9.2.2 Input Impedance 196
9.2.3 Frequency Response 197
9.2.4 Common-Mode Rejection 199
9.2.5 Cross-Talk in Surface Electromyograms 202
9.2.6 Recommendations for Surface Electromyogram Reporting and Electrode Placement Procedures 205
9.3 Processing of the Electromyogram 205
9.3.1 Full-Wave Rectification 206
9.3.2 Linear Envelope 207
9.3.3 True Mathematical Integrators 208
9.4 Relationship Between Electromyogram and Biomechanical Variables 208
9.4.1 Electromyogram Versus Isometric Tension 209
9.4.2 Electromyogram During Muscle Shortening and Lengthening 210
9.4.3 Electromyogram Changes During Fatigue 211
9.5 References 212
10 Modeling of Human Movement 215
Brian A. Knarr Todd J. Leutzinger and Namwoong Kim
10.0 Introduction 215
10.1 Review of Forward Solution Models 216
10.1.1 Assumptions and Constraints of Forward Solution Models 217
10.1.2 Potential of Forward Solution Simulations 217
10.2 Muscle-Actuated Simulation of Movement 218
10.2.1 Musculoskeletal Modeling 218
10.2.2 Control 221
10.2.3 OpenSim 223
10.2.4 EMG-Driven Modeling 227
10.3 Model Validation 230
10.4 References 231
11 Static and Dynamic Balance 235
Stephen J. Thomas Joseph A. Zeni and David A. Winters
11.0 Introduction 235
11.1 The Support Moment Synergy 236
11.1.1 Relationship Between Ms and the Vertical Ground Reaction Force 237
11.2 Medial/Lateral and Anterior/Posterior Balance in Standing 239
11.2.1 Quiet Standing 239
11.2.2 Medial Lateral Balance Control During Workplace Tasks 240
11.3 Dynamic Balance During Walking 241
11.3.1 The Human Inverted Pendulum in Steady State Walking 241
11.3.2 Initiation of Gait 242
11.3.3 Gait Termination 244
11.4 References 246
12 Central Nervous System’s Role in Biomechanics 247
Alan R. Needle and Christopher J. Burcal
12.0 Introduction 247
12.1 Central Nervous System and Volitional Control of Movement 247
12.1.1 Key Structures for Movement 247
12.1.2 Synapses and Neurotransmitters 249
12.1.3 CNS Adaptations 249
12.2 Peripheral Nervous System and Reflexive Control of Movement 250
12.2.1 Sensory Receptors and Motor Units 252
12.3 Methodologies to Understand Central Nervous System Function 253
12.3.1 Functional Magnetic Resonance Imaging (fMRI) 253
12.3.2 Electroencephalography (EEG) 257
12.3.3 Neural Excitability 265
12.4 Peripheral Nervous System Measurement Techniques 269
12.4.1 Nerve Conduction Studies 269
12.4.2 Microneurography 271
12.5 Methodologies to Understand Central Nervous System Behavior and Environmental Interactions 271
12.5.1 Virtual Reality 271
12.6 Nervous System Role in Muscle Synergies 274
12.6.1 Measurement Techniques and Experimental Setup 274
12.6.2 Analysis Techniques 275
12.7 The Central Nervous System and Learning and Injury 276
12.7.1 Translation of Synaptic Plasticity to Motor Learning 276
12.7.2 Role of Pathology on the Central Nervous System 276
12.8 References 278
13 A Case-Based Approach to Interpreting Biomechanical Data 281
Ankur Padhye John D. Willson Joseph A. Zeni Kristen F. Nicholson and Garrett S. Bullock
13.0 Patellofemoral Pain 281
13.0.1 Introduction 281
13.0.2 Case Description 281
13.0.3 Patient Examination 282
13.0.4 Gait Analysis 282
13.0.5 Interpretations and Intervention 282
13.0.6 Patient Outcomes and Discussion 283
13.0.7 Conclusion 284
13.0.8 References 284
13.1 Biomechanical Approach to Manage Knee Osteoarthritis 284
13.1.1 Osteoarthritis and Biomechanics 284
13.1.2 Patient History 286
13.1.3 Biomechanical Assessment 286
13.1.4 References 288
13.2 Ulnar Collateral Ligament Reconstruction 288
13.2.1 Player History 289
13.2.2 References 293
APPENDICES
A. Kinematic Kinetic and Energy Data 295
Figure A.1 Walking Trial – Marker Locations and Mass and Frame Rate Information 295
Table A.1 Raw Coordinate Data (cm) 296
Table A.2(a) Filtered Marker Kinematics – Rib Cage and Greater Trochanter (Hip) 300
Table A.2(b) Filtered Marker Kinematics – Femoral Lateral Epicondyle (Knee) and Head of Fibula 304
Table A.2(c) Filtered Marker Kinematics – Lateral Malleolus (Ankle) and Heel 308
Table A.2(d) Filtered Marker Kinematics – Fifth Metatarsal and Toe 312
Table A.3(a) Linear and Angular Kinematics – Foot 316
Table A.3(b) Linear and Angular Kinematics – Leg 320
Table A.3(c) Linear and Angular Kinematics – Thigh 324
Table A.3(d) Linear and Angular Kinematics – ½ HAT 328
Table A.4 Relative Joint Angular Kinematics – Ankle Knee and Hip 332
Table A.5(a) Reaction Forces and Moments of Force – Ankle and Knee 336
Table A.5(b) Reaction Forces and Moments of Force – Hip 340
Table A.6 Segment Potential Kinetic and Total Energies – Foot Leg Thigh and ½ HAT 344
Table A.7 Power Generation/Absorption and Transfer – Ankle Knee and Hip 348
B. Units and Definitions Related to Biomechanical and Electromyographical Measurements 351
Table B.1 Base SI Units 351
Table B.2 Derived SI Units 352
Index 355
