Biomechanical Characterization of the Human Upper Thoracic Spine – Pectoral Girdle (UTS-PG) System: Anthropometry, Dynamic

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Biomechanical Characterization of the Human Upper Thoracic Spine – Pectoral Girdle (UTS-PG) System: Anthropometry, Dynamic Properties, and Kinematic Response Criteria for Adult and Child ATDs

DISSERTATION

Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University

Jason Anthony Stammen

Graduate Program in Mechanical Engineering

The Ohio State University

2012

Dissertation Committee:

Professor Rebecca Dupaix, Advisor

Professor John Bolte

Professor Dennis Guenther

Professor Ahmet Kahraman

Jason Anthony Stammen

2012

Abstract

The dynamic response of the human thoracic spine is not well understood in the field of injury biomechanics, largely because of experimental challenges in isolating the properties of the upper thoracic spine segment from the rest of the thorax. Even though research has indicated that increased compliance in the anthropomorphic test device

(ATD) posterior thorax improves the biofidelity of head and spine kinematics, the majority of ATDs designed for frontal crash regulatory testing have a rigid thoracic spine component. The Hybrid III family of ATDs, which possesses a rigid steel thoracic “spine box”, has been the standard tool for many years for improving restraint designs and crash injury prevention. Thoracic spine rigidity simplifies chest instrumentation and maintains a stable reaction surface for the ribs. However, there are reasons to incorporate a flexible thoracic spine. Advances in material science, computer-aided manufacturing, and electronics make it possible to implement compliant yet durable components into ATDs.

Restraint systems are more sophisticated, requiring ATD tools to discern higher resolution performance differences, which is more feasibly achieved with sensitive and more compliant ATDs. Head injuries continue to occur in restrained occupant situations, indicating that assessment of head and spine kinematics has room to improve. Finally, and most relevant to this study, is the question of whether ATDs simulating the population of booster-seat aged children can accurately depict human head and spine

ii kinematics or provide useful head or neck injury assessment without some sort of flexible thoracic spine component.

The objectives of this study were to (a) characterize the dynamic response of the intact human upper thoracic spine while considering the effects of pectoral girdle restraint configuration, speed, and anthropometry, (b) quantify the link between upper thoracic spine – pectoral girdle (UTS-PG) system dynamics and whole-body spinal kinematics in crash simulation (sled) testing, and (c) develop a methodology to estimate large child

UTS-PG properties using anthropometry, kinematics, and adult UTS-PG material properties.

A novel approach, Isolated Segment Manipulation (ISM), was developed and used to quantify the intact upper thoracic spine – pectoral girdle (UTS-PG) dynamic response of nine adult post-mortem human subjects (PMHS). A system identification technique was employed to obtain the non-parametric, dynamic response. Mechanical parameters of the upper thoracic system were determined from a second-order model and statistically analyzed in each speed/restraint configuration. These properties were confirmed to be applicable in more realistic crash conditions by applying them in a sled model with an input acceleration applied directly to the mid-thoracic spine. This was achieved by coupling the PMHS to the sled via a seat fixture designed for both ISM and sled tests. Thoracic spine displacements were measured in twelve HYGE sled tests conducted on three of the nine PMHS at various speeds (ΔV = 3.8 – 7.0 m/s) indicative of spine velocities observed in typical belted sled tests. Using two different models, it was determined that the dynamic properties from ISM testing could be used to accurately

iii reflect T3 spine displacements for multiple sizes of PMHS and various combinations of restraint and speed. Head, shoulder, and spine kinematics were calculated through three- dimensional kinematic measurement (3aω and 6aω instrumentation schemes), and T3 displacement vs. T6 force relationships were presented as preliminary ATD response targets.

Anatomic and kinematic statistical analyses were then completed to aide in translating the adult UTS-PG data to the child population. Structural anatomy measurements were taken from radiology data of both adult PMHS and pediatric patients, and statistically significant age-dependent measures were identified for scaling purposes.

Head displacements of both children and adults were estimated through calculation of occupant available space (OAS) in 71 real-world crash cases, where face/head contact with the front row seatback was used as a doubly-censored binary response surrogate for head displacement. Differences between real world estimates for children (age 6-13) and adults were consistent with experimental sled data from the literature. A distributed parameter analysis was employed to estimate the elastic modulus of the adult UTS-PG to be 7.5 – 16.5 MPa using anthropometric, ISM test, and kinematic data from this study.

Extension of this methodology to the large child using anatomic and kinematic age- dependent scale factors from this study, along with information from the literature, resulted in normalized mode shape differences consistent with kinematic differences.

Using the techniques, findings, and tools from this study, it is believed that biofidelity response corridors and a test method can be developed for the upper thoracic region of large child ATDs used to evaluate booster seat designs.

Dedication

To Liz and our children

Acknowledgments

I would like to extend my sincerest gratitude to my dissertation committee for lending their expertise and feedback to my project: Dr. Rebecca Dupaix, my advisor, for her understanding and guidance in helping me to pull this thesis together; Dr. John Bolte, who provided the opportunity to use his laboratory at will and encouraged me to take the leap back into school; Dr. Dennis Guenther and Dr. Ahmet Kahraman, who both provided helpful and constructive feedback to this work.

I thank my colleagues at the NHTSA Vehicle Research & Test Center for keeping my projects going while I was in school. I especially credit Dr. Bruce Donnelly for re- starting the academic study pilot program at NHTSA so that I could have the opportunity to pursue my degree. I thank Dr. Kevin Moorhouse for taking the time to teach me about system identification. I am grateful to Mike Monk and Dr. Roger Saul for their support.

Rod Herriott provided invaluable assistance in conducting the extensive amount of fabrication and hands-on tasks required for this study. Dr. Yun Seok Kang lent his considerable expertise to nearly every portion of this research. I am grateful also to Kyle

Icke for exhibiting extreme patience while I used and modified his TAPPER device.

Finally, I thank my family for their support. I am indebted to my wife Liz especially, for keeping me positive throughout this journey. My children Kasey, Henry, and Nick remind me every day why I chose this topic.

Vita

July 24, 1974 ...... Born: Coldwater, OH

1998...... B.S. Mechanical Engineering, University of

Cincinnati, Cincinnati, OH

2000...... M.S. Mechanical Engineering, Georgia

Institute of Technology, Atlanta, GA

2000-2001 ...... Research Engineer, Transportation Research

Center, Inc., East Liberty, OH

2001-present ...... Mechanical Engineer, Applied

Biomechanics Division, NHTSA Vehicle

Research & Test Center, East Liberty, OH

Selected Publications

Ott K, Wiechel J, Guenther D, Stammen J, Mallory A. “Assessment of the Simulated

Injury Monitor (SIMon) in Analyzing Head Injuries in Pedestrian Crashes,” SAE

World Congress Technical Paper 2012-01-0569 (2012).

Stammen J, Bolte J, Shaw J. “Biomechanical Impact Response of the Human Chin and

Manubrium.” Annals of Biomedical Engineering. 39(11): 1-13 (2011).

vii Kremer, M, Gustafson, H, Stammen, J, Donnelly, B, Herriott, R, Bolte IV, JH. "Pressure

-Based Abdominal Injury Criteria Using Isolated Liver and Fill-Body Post-

Mortem Human Subject Impact Tests." Stapp Car Crash Journal. Vol. 55: 317-

350 (2011).

Sparks, J.L., Stammen, J., Herriott, R., Jones, K. “Development of a Fluid-Filled Catheter

System for Dynamic Pressure Measurement in Soft Tissue Trauma.” International

Journal of Crashworthiness 13(3):255-264 (2008).

Sparks, J.L., Dupaix, R.B., Jones, K.H., Steinberg, S.M., Herriott, R.G., Stammen, J,

Donnelly, B., Bolte IV, J.H. "Using Pressure to Predict Liver Injury Risk From

Blunt Impact." Stapp Car Crash Journal. Vol. 51st. (2007).

Stammen J, „„Technical Evaluation of the Hybrid III Ten Year Old Dummy (HIII–10C),‟‟

Docket # NHTSA-2005-21247 (2004).

Stammen, J., Ko, S., Guenther, D., and Heydinger, G., "A Demographic Analysis and

Reconstruction of Selected Cases from the Pedestrian Crash Data Study," SAE

World Congress Technical Paper 2002-01-0560 (2002).

Stammen J, Williams S, Ku D, Guldberg R. “Mechanical properties of a novel PVA

hydrogel in shear and unconfined compression.” Biomaterials. 22(8): 799-806

(2001).

Fields of Study

Major Field: Mechanical Engineering

viii

Table of Contents

Abstract ...... ii

Dedication ...... v

Acknowledgments ...... vi

Vita ...... vii

List of Tables ...... xv

List of Figures ...... xvii

Abbreviations & Symbols ...... xxiixvii

Chapter 1 . Background & Motivation ...... 1

1.1. ATD vs. Human Structural Characteristics ...... 2

1.2. The Thoracic Spine and ATD Injury Assessment ...... 4

1.3. Thoracic Spine Anatomy ...... 8

1.4. Pectoral Girdle Anatomy ...... 15

1.5. Anatomy Summary ...... 19

1.6. Project Objectives ...... 20

ix Chapter 2 . Sequential Biomechanics of the Human Upper Thoracic Spine and Pectoral

Girdle (UTS-PG) System ...... 26

2.1. Introduction ...... 26

2.2. Methods ...... 30

2.2.1. Experimental Setup...... 31

2.2.2. Data Acquisition ...... 35

2.2.3. Subject Characteristics ...... 36

2.2.4. Data Analysis ...... 37

2.2.4.1. Rigid Body Correction...... 37

2.2.4.2. System Identification ...... 41

2.2.4.3. Modeling the IRF ...... 42

2.2.5. Statistical Methods ...... 43

2.3. Results ...... 44

2.4. Discussion ...... 51

2.4.1. IRF Derivation and Modeling...... 51

2.4.2. Effect of Speed, Constraint, and Anthropometry ...... 52

2.4.3. Directional Characteristics ...... 55

2.4.4. Thoracic Spine Kinematics ...... 56

2.4.5. Limitations ...... 57

x 2.4.6. Future Work ...... 58

2.5. Conclusions ...... 59

Chapter 3 . Dynamic Properties of the Upper Thoracic Spine-Pectoral Girdle (UTS-PG)

System and Corresponding Kinematics in PMHS Sled Tests ...... 61

3.1. Introduction ...... 61

3.2. Methods ...... 68

3.2.1. Subject Characteristics ...... 68

3.2.2. ISM Testing ...... 69

3.2.3. Sled Testing ...... 78

3.2.3.1. PMHS Instrumentation ...... 80

3.2.3.2. PMHS Positioning & Coordinate System Definition ...... 83

3.2.3.3. UTS-PG Model Formulation & Sled Pulse Derivation ...... 84

3.2.3.4. Test Matrix ...... 90

3.2.3.5. Data Processing ...... 91

3.2.3.6. Rigid Body Kinematics ...... 92

3.2.3.7. Statistical Analysis ...... 92

3.2.3.8. Injury Assessment...... 93

3.3. Results ...... 94

3.3.1. ISM Testing ...... 94

xi 3.3.2. Sled Testing ...... 97

3.3.2.1. Effect of Anthropometry ...... 98

3.3.2.2. Effect of Speed ...... 99

3.3.2.3. Effect of Restraint ...... 101

3.3.2.4. UTS-PG Model vs. Experimental Spine Displacements ...... 102

3.3.2.5. Relative Head/T1 Motion ...... 106

3.3.2.6. Statistical Analysis ...... 107

3.3.2.7. Injuries ...... 107

3.4. Discussion ...... 108

3.4.1. Effect of Anthropometry, Speed, and Restraint ...... 108

3.4.2. Comparison with Previous Data ...... 110

3.4.3. Experimental vs. Model-Predicted Displacements ...... 111

3.4.4. Effect of Cervical Spine Injuries ...... 114

3.4.5. Relative Influence of Shoulder and Manubrium ...... 115

3.4.6. Limitations ...... 115

3.4.7. Applicability of the Methods & Data ...... 116

3.5. Conclusions ...... 118

Chapter 4 . Age-Dependent Anthropometry and Kinematics for Translating Adult Upper

Thoracic Spine – Pectoral Girdle (UTS-PG) Data to the Large Child Population ...... 121

xii 4.1. Introduction ...... 121

4.2. Methods ...... 126

4.2.1. Structural Anatomy...... 127

4.2.2. Head Kinematics: Child vs. Adult ...... 131

4.2.3. Estimation of 10 Year Old UTS-PG Mechanical Properties ...... 134

4.2.3.1. Distributed Parameter Model for Small Displacements/Negligible

Damping ...... 135

4.3. Results ...... 139

4.3.1. Structural Anatomy (Children vs. Adults) ...... 139

4.3.2. Head Kinematics (Children vs. Adults) ...... 146

4.3.3. Estimation of Adult UTS-PG Elastic Modulus ...... 149

4.4. Discussion ...... 153

4.4.1. Anthropometry & Anatomy ...... 153

4.4.2. Kinematics ...... 154

4.4.3. Adult UTS-PG Elastic Modulus Calculation...... 154

4.4.4. A Methodology for Estimating 10 Year Old UTS-PG Properties ...... 155

4.5. Conclusions ...... 157

Chapter 5 . Conclusions & Recommendations ...... 158

5.1. Biofidelity Test Method ...... 159

xiii 5.2. Response Corridor Development ...... 161

5.2.1. Head Displacement Criteria ...... 162

5.2.2. Thoracic Spine Response Criteria ...... 163

5.3. Evaluating the UTS-PG of the Large Omni-Directional Child (LODC) ATD .... 164

References ...... 166

Appendix A: Head-Neck Assembly CG Location ...... 177

Appendix B: Linear Proportionality Verification ...... 179

Appendix C: Derivation of Impulse Response Function using Correlation Functions 180

Appendix D: IRF Model Parameters ...... 181

Appendix E: Impulse Response Functions & Model Fits ...... 188

Appendix F: PMHS Anthropometry ...... 219

Appendix G: UTS Model Solution for X Axis Displacement ...... 221

Appendix H: 3D Kinematic Processing of Sled Data ...... 227

Appendix I: PMHS 7, 8 , and 9 Sled Test Time Histories ...... 233

Appendix J: Distribution of ISM Dynamic Properties ...... 239

Appendix K: Student T-tests on Anthropometry Data (Child vs. Adult)...... 242

Appendix L: NASS-CDS Data ...... 244

Appendix M: Statistical Analysis of Experimental Head Displacements ...... 247

Appendix N: Radiology Plots ...... 254

xiv

List of Tables

Table 2.1. ISM test matrix per PMHS ...... 36

Table 2.2. Subject characteristics...... 36

Table 2.3. P-values from ANOVA (p < 0.05 indicates significance in regression model)

...... 46

Table 2.4. UTS-PG data summary ...... 50

Table 3.1. Subject characteristics...... 69

Table 3.2. ISM test matrix per PMHS ...... 74

Table 3.3. Estimated accelerations to obtain typical spine velocities in sled tests ...... 88

Table 3.4. Sled test input summary ...... 90

Table 3.5. UTS-PG model parameters (0.5 m/s, X axis) to predict T3 X displacements . 95

Table 3.6. UTS-PG model parameters for full set of 9 PMHS (mean values for 0.5 m/s,

MNB/RS constraint, X-axis) ...... 96

Table 3.7. Experimental vs. model-predicted T3 X displacements & properties ...... 104

Table 3.8. Comparative statistics for model fits to experimental T3 X displacement .... 105

Table 3.9. Correlation coefficients for peak measurements ...... 107

Table 4.1. List of skeletal measurements from radiology ...... 129

Table 4.2. Subject anthropometry ...... 130

Table 4.3. Summary of UTS-PG skeletal measurements ...... 144

xv Table 4.4. Correlation coefficients for UTS-PG skeletal measurements (n = 48) ...... 145

Table 4.5. Uncoupled ISM properties (mean values) from UTS-PG testing ...... 149

Table 4.6. Scale factors from radiology data ...... 149

Table 4.7. Summary of large child and adult UTS-PG distributed model parameters ... 152

Table 5.1. Model-predicted head displacements required for a large child ATD ...... 163

Table D.1. X axis IRF model fit results ...... 182

Table D.2. Z axis IRF model fit results ...... 184

Table D.3. Rotation about Y IRF model fit results ...... 186

Table F.1. PMHS anthropometry summary ...... 219

Table K.1. Student t-tests comparing means for child (n=39) and adult (n=9) geometry ...... 243

Table L.1. NASS-CDS case data summary ...... 245

Table M.1. Child & adult PMHS head displacements & occupant characteristics ...... 247

Table M.2. Child & adult volunteer head displacements (from Arbogast et al 2009) .....248

Table M.3. Statistical comparison to determine best normalization factor ...... 252

xvi

List of Figures

Figure 1.1. Superior view comparison of human and ATD pectoral girdle ...... 3

Figure 1.2. Hybrid III 10 year old ATD chin contact and typical head acceleration ...... 5

Figure.1.3. Vertebral column and thoracic vertebra characteristics ...... 10

Figure 1.4. Ligaments of the vertebral column (lateral view) ...... 12

Figure 1.5. Ligaments of the vertebral column (anterior & posterior views) ...... 13

Figure 1.6. Superficial and intermediate muscles of the thoracic spine ...... 14

Figure 1.7. Deep muscles of the thoracic spine ...... 15

Figure 1.8. Superior view of the pectoral girdle ...... 16

Figure 1.9. Ligaments of the pectoral girdle (anterior view) ...... 17

Figure 1.10. Muscles supporting the pectoral girdle (posterior) ...... 18

Figure 1.11. Muscles supporting the pectoral girdle (anterior) ...... 19

Figure 1.12. Strategy to develop large child ATD UTS-PG criteria ...... 20

Figure 2.1. Sagittal 3DOF model of the intact upper thoracic structure including the thoracic spine and pectoral girdle ...... 30

Figure 2.2. Anterior and posterior views of manubrium, shoulder, T1, and T6 mounts .. 32

Figure 2.3. ISM test setup – lateral view ...... 33

Figure 2.4. TAPPER setup & perturbation example...... 34

xvii Figure 2.5. Relative T1-T6 displacements ...... 35

Figure 2.6. Free body diagram of UTS-PG...... 38

Figure 2.7. Displacement response to a unit impulse force (IRF) and second order model fit with mechanical parameters ...... 44

Figure 2.8. IRF at 0.5, 1.5, and 2.5 m/s (MNB/LS/RS Fixed) ...... 44

Figure 2.9. IRF in X axis for PMHS #4 in five constraint conditions (0.5 m/s) ...... 45

Figure 2.10. IRF in Z axis for each PMHS at 0.5 m/s, MNB/LS/RS Fixed ...... 45

Figure 2.11. Actual vs. IRF-Predicted Displacement (0.5 m/s, MNB/LS/RS Fixed) ...... 46

Figure 2.12. ωnat and ζ (X axis) ...... 47

Figure 2.13. ωnat and ζ (Z axis) ...... 48

Figure 2.14. ωnat and ζ (Rotation about Y) ...... 49

Figure.3.1. UTS sagittal plane model (n=6 PMHS) from Stammen et al (2012) ...... 66

Figure 3.2. Anterior and posterior views of manubrium, shoulder, and spine mounts ..... 70

Figure 3.3. Use of three toggle bolts to secure T6-T8 ...... 70

Figure 3.4. ISM setup...... 72

Figure 3.5. Test setup & loading profile for ISM configurations ...... 73

Figure 3.6. (Top) T1/T6 data corrected to T3 location; (bottom) impulse response function with 2nd order M-C-K model fit ...... 77

Figure 3.7. Attachment of seat with PMHS to sled interface ...... 78

Figure 3.8. Cable cutter used to release head ...... 79

Figure 3.9. Restraint geometry in belted and unbelted condition ...... 80

Figure 3.10. 6aω Tetrahedron to measure 6DOF kinematics of the head ...... 80

xviii Figure 3.11. Right shoulder 3aω with modified mount to prevent belt interference ...... 81

Figure 3.12. T1 and T3 instrumentation ...... 82

Figure 3.13. Instrumentation at T6-T8, T1, T3, and right shoulder ...... 82

Figure 3.14. Skeletal landmarks for estimating PMHS head CG ...... 83

Figure 3.15. UTS-PG mechanical model in both ISM and sled configurations ...... 84

Figure 3.16. UTS-PG mechanical model ...... 85

Figure 3.17. Representation of UTS-PG segment in sled test ...... 87

Figure 3.18. Using impulse to obtain a normalized force input profile across tests ...... 89

Figure 3.19. Sled accelerations ...... 91

Figure 3.20. Sled velocities ...... 91

Figure 3.21. IRF and UTS-PG model fit for 3 PMHS (0.5 m/s, MNB/RS Fixed) ...... 94

Figure 3.22. (Top) PMHS 7, (Center) PMHS 8, (Bottom) PMHS 9 at 4.7 – 5.0 m/s ...... 97

Figure 3.23. High speed video vs. 3aω displacements ...... 98

Figure 3.24. T1 and T3 displacement vs. T6 force ...... 99

Figure 3.25. T1 and T3 rotation vs. T6 moment ...... 99

Figure 3.26. T1 and T3 trajectories relative to T6 at increasing velocities ...... 100

Figure 3.27. Lack of speed sensitivity and linearity of PMHS 8 thoracic spine response

...... 100

Figure 3.28. Effect of belt presence on T1 and T3 kinematics/kinetics ...... 101

Figure 3.29. Experimental vs. model-predicted T3 X displacements (PMHS7/8) ...... 102

Figure 3.30. Experimental vs. model-predicted T3 X displacements (PMHS9) ...... 103

Figure 3.31. Head/T1 trajectories ...... 106

xix Figure 3.32. Modeled vs. measured shoulder belt force ...... 114

Figure 4.1. Measurements taken from adult PMHS and pediatric patient radiology ..... 128

Figure 4.2. Calculation of occupant available space (OAS) in NASS-CDS cases ...... 132

Figure 4.3. Distributed parameter representation of UTS-PG ...... 135

Figure 4.4. Overall height ...... 139

Figure 4.5. Clavicle length ...... 140

Figure 4.6. T1 depth in transverse plane ...... 140

Figure 4.7. T1 width in transverse plane...... 141

Figure 4.8. T6 depth in transverse plane ...... 141

Figure 4.9. T6 width in transverse plane...... 142

Figure 4.10. T1-T6 anterior height in transverse plane ...... 142

Figure 4.11. T1-T6 posterior height ...... 143

Figure 4.12. Calculated head displacement using OAS ...... 146

Figure 4.13. Experimental statistical model vs. NASS-CDS head displacement estimates

(Age 6-13) ...... 147

Figure 4.14. Experimental statistical model vs. NASS-CDS head displacement estimates

(Age > 13) ...... 147

Figure 4.15. Eigenvalue solution for lumped mass/fixed distributed parameter model . 150

Figure 4.16. Elastic modulus vs. adult natural frequency ...... 151

Figure 4.17. Natural modes of adult and child UTS-PG...... 151

Figure 5.1. Modified pendulum test with simulated belt input (shoulders removed) ..... 161

Figure 5.2. The large omni-directional child (LODC) and Hybrid III 10 year old ATD 165

xx Figure A.1. Locating the estimated center of gravity for the assembly ...... 161

Figure A.2. Measuring the x and z moment arms between the HdT1 assembly CG and T1

...... 161

Figure B.1. T3 motion is proportional to T1 applied motion...... 161

Figure H.1. Rigid body transformation vectors for the head ...... 227

Figure I.1. Data from PMHS 7 sled test (set 1) ...... 234

Figure I.2. Data from PMHS 7 sled test (set 2) ...... 235

Figure I.3. Data from PMHS 8 sled test (set 1) ...... 236

Figure I.4. Data from PMHS 8 sled test (set 2) ...... 237

Figure I.5. Data from PMHS 9 sled test...... 238

Figure J.1. UTS-PG natural frequency (X axis, all speeds & constraints) ...... 239

Figure J.2. UTS-PG damping ratio (X axis, all speeds & constraints) ...... 239

Figure J.3. UTS-PG natural frequency (Z axis, all speeds & constraints) ...... 240

Figure J.4. UTS-PG damping ratio (Z axis, all speeds & constraints)...... 240

Figure J.5. UTS-PG natural frequency (rotation about Y, all speeds & constraints) ..... 241

Figure J.6. UTS-PG damping ratio (rotation about Y, all speeds & constraints) ...... 241

Figure M.1. Head displacement normalized by occupant height, by age group ...... 249

Figure M.2. Head displacement normalized by occupant height, by age group ...... 250

Figure M.3. Head displacement normalized by occupant body mass index (in kg / m2), by age group ...... 250

Figure M.4. Adults & children head displacements converge at higher deltaV ...... 253

xxi

Abbreviations & Symbols

θ1 Clavicle angle

θ2 Manubrium angle

θ3 Rib 1 angle in sagittal plane

θ4 Rib 6 angle in sagittal plane

θ5 T1 vertebral body angle

θ6 T6 vertebral body angle

θ7 Relative T1/T6 angle

θ, θ θ Angular displacement, velocity, and acceleration about y axis

A Amplitude for IRF model or area for T1-T6 cross-section

Ar Beam height normalization term a Depth of sternal notch to anterior body T1 (transverse plane)

ALL Anterior Longitudinal Ligament

ANOVA Analysis of Variance

ATD Anthropomorphic Test Device

βL Eigenvalue bθ Rotational damping coefficient about the y (lateral) axis

xxii bT1 Width of T1 vertebra (between transverse process ends) bT6 Width of T6 vertebra (between transverse process ends)

BMD Bone Mineral Density

BMI Body Mass Index

CG Center of Gravity cx, cz, cUTS-PG Damping coefficient in x axis, z axis, and corrected to T3 cneck Damping coefficient of neck alone in x axis cT1 Depth of T1 vertebra (between transverse process ends) cT6 Depth of T6 vertebra (between transverse process ends) cxx Autocorrelation matrix cxy Cross-correlation matrix d Clavicle length

δHead, normalized Normalized head displacement from experimental sled survey

DOF Degrees of Freedom

E Elastic modulus ep Height of T1-T6 vertebral column (posterior between spinous processes) ea Height of T1-T6 vertebral column (anterior)

F Frequency (in Hertz) in IRF parametric model f Superior-inferior distance from T1 body top to sternal notch

Fbelt, FShoulderBelt Shoulder belt tension force in time

Fx, Fz Forces measured in time

FMVSS Federal Motor Vehicle Safety Standard

xxiii

Fsled Force applied by the sled to the PMHS

Fexternal Sum of the applied forces to the UTS-PG

Fo Amplitude of sinusoidal force input

FSU Functional Spine Unit g Acceleration of gravity, m/s2, or sum of T1-T6 vertebral heights (Chap. 4) g(t) Parametric IRF model displacement for unit impulse force

H Impulse response function h Skeletal fraction of T1-T6 height

(HdT1) Head-neck assembly with associated connection hardware

IRF Impulse Response Function

I Area moment of inertia (in Chapter 4)

Iθ Mass moment of inertia about the y axis

ISM Isolated Segment Manipulation jθ Rotational stiffness about the y (lateral) axis kx, kz, kUTS-PG Stiffness in the x (forward) axis, z (vertical) axis, and corrected to T3 kneck Stiffness of neck alone in x axis meffective Effective mass of the UTS-PG mHdT1 Mass of the head, neck, and coupling hardware combined mx, mz Mass in the x (forward) and z (vertical) axes mhead-neck, mHN Mass of the head and neck combined

My Moment measured in time about y axis

N, n Number of data points

xxiv

NHTSA National Highway Traffic Safety Administration

NASS-CDS National Automotive Sampling System – Crashworthiness Data Study

HIC Head Injury Criterion

LODC Large Omni-Directional Child ATD

LS Left Shoulder

LSE Least Square Error

MNB Manubrium

MSE Mean Square Error

NIOI Normalized Impulse/Optimized ISM

NRMSD Normalized Root Mean Square Deviation

OAS Occupant Available Space

ρo Beam mass per unit length

P Phase (in rad) in IRF parametric model

PDOF Principal Direction of Force

PLL Posterior Longitudinal Ligament

PMHS Post-Mortem Human Subject

QLV Quasi-Linear Viscoelastic

RMSD Root Mean Square Deviation

RS Right Shoulder

SAE Society of Automotive Engineers

TAPPER Thoracic Apparatus for Producing Perturbations

(T1) Inertially compensated forces and moments at T1

xxv

(T3) T3 location (assumed to be consistent with UTS-PG center of gravity)

T1-T6 Upper thoracic segment of vertebral column (1st - 6th vertebral level)

(T6HW) Hardware attachment to T6 location, including instrumentation

(T6, UTS-PG) Inertially compensated forces and moments at T6 u Forward displacement of beam

UTS-PG Upper Thoracic Spine - Pectoral Girdle

V Damping exponent in IRF parametric model

VAF Variance Accounted For

ωn Natural frequency

ωsled Sled excitation frequency x, Displacement, velocity, and acceleration in x axis

Applied Acceleration applied directly to the T3 location

HN Acceleration in x axis of head + neck together

(X,total) X axis assignment for natural frequency and viscous damping factor

Xi ith data point of the experimental displacement at T3

Xi' ith data point of the model-predicted displacement at T3

Xmin Minimum value of the experimental displacement at T3

Xmax Maximum value of the experimental displacement at T3

X1 SAE dimension for front row - rear row H-point

X2 Documented seat track position for front row seat

X3 Hip point to Head CG x distance

X4 Head CG to seatback x distance

xxvi

U Mode shape employing eigenvalues

YA Young Adult (baseline level for T-Score in DEXA scan) z, Displacement, velocity, and acceleration in z axis

ζ Viscous damping factor

xxvii

Chapter 1 . Background & Motivation

Research has demonstrated that thoracic spine flexibility significantly affects head motion in motor vehicle occupants [Ash et al. 2009; Lopez-Valdes et al. 2009, 2010;

Seacrist et al. 2010; Sherwood et al. 2002]. Head injury continues to be the leading cause of death and disability in motor vehicle occupants [Adekoya et al. 1998]. The control of occupant head kinematics by motor vehicle restraint systems is critical for the prevention of head contacts to the vehicle interior, the most common injury source in crashes

[NHTSA, 2010]. The motion of the head and spine is dictated by how a belt or airbag distributes loading to the body [Alem et al. 1978]. Because of the role of the thoracic spine in transferring restraint loads from the pectoral girdle and ribcage to the neck and ultimately the head, it is important to understand the relationship between the dynamic properties of the thoracic spine, the structural interactions between the thoracic spine and the pectoral girdle, and resulting spine and head kinematics.

In developing anthropomorphic test devices (ATDs) and computer models to represent occupants in vehicle restraint evaluations, it is important to consider the effect of a dynamic input to one component on the response of another component (“sequential biofidelity”). Without understanding the dynamic behavior of the connections between commonly injured body components such as the head and thorax, it is difficult to know if the loading input characteristics to an injured component are realistic in the dummy/model. Without knowing the inputs, both internal (from restraint loading of

1 another connecting body component) and external (contact from vehicle interior), it is difficult to characterize injury mechanisms for that component in the occupant model.

The upper thoracic spine is a key area in need of sequential biofidelity because of its integration with the shoulder and ribcage in dictating the kinematics of the occupant‟s head and neck in a crash. The thoracic segment of the spine, like the cervical and lumbar segments, is controlled largely by muscles, but this portion is much more integrated with other skeletal structures, namely the thoracic cage and pectoral girdle. The location of the shoulder belt restraint on the pectoral girdle, relative to the clavicle and sternum in particular, alters the overall upper body kinematics of the occupant. This condition is important not only for assuring appropriate belt fit in a vehicle, but also for assuring that the ATD is sensitive to incremental differences in the restraint design.

1.1.ATD vs. Human Structural Characteristics

The Hybrid III family of ATDs has a completely rigid steel thoracic spine “box” that contains chest instrumentation. All spinal motion occurs in the cervical and lumbar segments. This rigidity is a practical necessity for the most part, as relative motion between the individual ribs is simplified considerably, as is measurement of chest kinematics. These considerations, in addition to the fact that thoracic flexibility is substantially less than the cervical or lumbar spine segments due to the stability afforded by the ribcage, have comprised the standard design philosophy in ATDs for many years.

In addition, unlike in the human body, the ribs and shoulder are rigidly and separately fixed directly to the spine box in frontal dummies (Figure 1.1), with no clavicle to couple

2 them into a single mechanism [NHTSA, 2011]. Therefore restraint loads can be transmitted independently via the shoulder and ribs.

Shoulder-Spine Joint

Shoulder

Ribcage Sternum

Figure 1.1. Superior view comparison of human and ATD pectoral girdle

The junction between the soft neck and rigid thoracic spine is an area of high stress concentration in Hybrid III ATDs. This structural discontinuity has caused problems with measuring neck loads in addition to causing severe rotation of the head in some circumstances for the Hybrid III ten year old child ATD, in particular. This kinematic condition has made it difficult to develop and justify head and neck injury criteria in ATDs, especially for large child ATDs in evaluating the performance of belt- positioning booster seats [NHTSA, 2003; NHTSA, 2010; Stammen et al. 2007].

Some recently developed ATDs, such as the THOR and BioRID, have much more complex spinal structures with joints built into the simulated vertebral segments. Side- by-side comparisons between these ATDs and the Hybrid III family have indicated that these newer ATDs possess more biofidelic kinematics in frontal and rear impacts [Vezin et al. 2009], but it is not clear whether this improvement is primarily due to the presence

3 of a thoracic joint or because of other features such as the shoulder, neck, or ribcage. The

Q series of child ATDs has a more realistic shoulder structure than Hybrid III child

ATDs, but it is unclear whether this change results in a significant improvement in kinematics without a more biofidelic thoracic spine component.

Upon review of the current state of ATD thoracic spine components, there are four elements in need of investigation. First, an ATD spine should be as continuous as possible to optimize kinematic similarity to humans. The spine should act as a single unit in transferring restraint loads. Second, there is not an established correlation between thoracic spine dynamic properties and resulting upper body kinematics. Third, because of the integration of the thoracic spine with so many other load-bearing structures in a crash, any modification to such an ATD spine component should account for interactions with the shoulder, pectoral girdle, and ribcage. Finally, it has become apparent that the design concepts used successfully for many years in simulating adult occupants with

ATDs are becoming less sufficient for evaluating booster seats with large child ATDs.

1.2.The Thoracic Spine and ATD Injury Assessment

Head injuries occur frequently in motor vehicle crashes, and often are associated with a high risk of morbidity and mortality [Hu et al. 1996]. This statistic is true for adults and children, front and rear seated occupants, and all impact directions [Arbogast et al. 2004, 2005]. The majority of these injuries occur from contact to some part of the vehicle interior. A search of National Automotive Sampling System – Crashworthiness

Data Study (NASS-CDS) data from 1998-2007 revealed that, for rear-seated occupants,

4 the seatback, console, B-pillar, and door were the most frequent sources of head injury

[NHTSA, 2011]. Differences have been observed between field data and laboratory ATD measurements with respect to head injury. There were no head injuries attributed to same-occupant contact in the NASS-CDS data. However, in Federal Motor Vehicle

Safety Standard (FMVSS) No. 213-type sled tests with the Hybrid III ten year old ATD

(HIII-10C), head injury criterion (HIC) values due to chin-chest contact routinely exceeded 1000, which is associated with a moderate risk of skull fracture (Figure 1.2).

As noted in Stammen et al. (2011), there are three possible reasons for this discrepancy:

(1) chin-chest contacts are occurring in real occupants but are much softer than in the

ATD, (2) the velocity of the occupant head is much lower than the ATD head prior to contact, or (3) this type of contact simply does not occur in occupants due to kinematic differences. The stiffness of the thoracic spine has been determined to be a primary reason for velocity or kinematic differences between the ATD and human.

100 90 HeadskinTest 1 A, HIC=730

80 HeadskinTest 2 B, HIC=800 70 60 50 40 30 Spike due to 20 chin-to-chest

HeadResultant Acceleration . (g) 10 contact 0 0 20 40 60 80 100 120 Time (msec)

Figure 1.2. Hybrid III 10 year old ATD chin contact and typical head acceleration

It is important for an ATD to replicate both occupant head translation and rotation so that head injury potential can be more fully assessed in a crash simulation. The result of inconsistency between elevated HIC outcomes with the HIII-10C and the paucity of this type of head injury in field data was the suspension of HIC as an injury criterion for the HIII-10C in FMVSS No. 213 booster seat testing until “the biofidelity of the ATD” is improved [NHTSA, 2011]. The only current performance criterion for head protection in

FMVSS No. 213 is excursion, which is perhaps more important than HIC in this test scenario given the lack of vehicle interior structures. Excursion is becoming even more critical because vehicle designs are trending toward decreasing occupant compartment space. A survey of rear row clearances in 2010 model year vehicles showed that current vehicles have less space than the vehicles used to create excursion limits for FMVSS No.

213 [Aram et al. 2011]. Safety systems are more advanced to offset this decrease in space, but nonetheless, an ATD should accurately interact with those systems for evaluation purposes. In addition, belt-positioning booster seats are becoming more common in the market for older children. This effectively moves the occupant forward, resulting in even less room for the head to move freely. Given the frequency and severity of head injury as well as decreasing occupant space, an accurate measure of head injury potential is necessary and would be most accurate with revision of the spine.

It has been shown that even in crashes documented as “frontal”, there is some oblique component of occupant motion prior to head contact due to a “narrow offset” crash configuration (also known as “FREE” or “FLEE”) where the corner of the struck vehicle‟s front end is contacted by the corner of the striking vehicle causing a lateral component of force. This condition has been shown to be present in reconstructions of

6 child occupant injury scenarios where head contacts in frontal cases occur to the B-pillar or door [Bohman et al. 2011]. To date, all regulatory-standard ATDs in the United States are designed to be biofidelic in either pure frontal or pure lateral loading. Because of the oblique nature of actual crashes, ATD thoracic spine and pectoral girdle kinematics should be sensitive enough to capture the omni-directional load distributions provided by the restraint regardless of impact direction.

Neck injuries, while much lower in frequency than head injuries, are often as severe in motor vehicle crashes. It has been shown that head and neck injury often occur together [Bohman et al. 2011], and the vertebral level of spine injuries tends to move lower with age/size [Reddy et al. 2003]. This has been attributed to the relative size of the head and under-developed neck muscles in younger occupants. In addition, younger children do not fit into vehicle restraints designed for adult occupants, and therefore have a greater propensity for “submarining” under the belt when not optimally restrained in a belt-positioning booster [Arbogast et al. 2002]. In this condition, the shoulder belt is loading the lower neck rather than the clavicle and sternum, leading to excessive head rotational velocity and high loads at the junction of the cervical and thoracic spine segments [Stammen et al. 2007]. Because the belt load location can vary significantly in a crash, an ATD thoracic spine component should be sensitive to these differences.

The lack of neck injury criteria in occupant protection standards using Hybrid III

ATDs is also due in part to the rigid thoracic spine. After the Nij calculation was proposed by NHTSA [NHTSA, 2003], public comments opposed its inclusion because the relationship between the Nij measurement and real world injuries was not well- founded. The neck loads observed in the child ATDs were very high while neck injuries

7 due to inertial loads appeared to be infrequent in crash data. These high neck loads are attributed to high stress concentration between the soft neck and completely rigid thoracic spine. It has been demonstrated that these neck loads are reduced considerably by increasing flexibility of the thoracic spine of a 6YO dummy model [Sherwood et al.

2002]. Implementation of a neck injury measure would become more feasible if the ATD thoracic spine were more compliant to decrease neck loads to more humanlike levels.

The most noticeable differences between the human and ATD spine/pectoral girdle are (1) the human spine is a continuous structure with different articulations along its length, while the ATD spine exhibits an abrupt change between the thoracic and cervical spine segments and (2) the ATD shoulder and sternum are not coupled together through a clavicle-like element. As a result the shoulder and sternum experience completely separate load paths to the rigid thoracic spine. By understanding how the shoulder, sternum, and thoracic spine work together in the human body, ATD upper thoracic kinematics can be made more sensitive to restraint conditions, and, as a result, injury assessment can be more accurate. By developing these relationships in adult human experiments, the tools and mechanisms can then be feasibly applied to the larger child population of ATDs.

1.3.Thoracic Spine Anatomy

In an automotive impact, the spine is arguably the most important structure in the body because it plays some role in the response of so many other structures. It is a very complex structure connecting the upper half to the lower half of the body. The cervical

8 spine provides support and mobility for the head and dictates the kinematics of the head by articulating in response to the restraint in a crash event. The spine also protects the spinal cord, which is a vital organ for motor and sensory function. While the cervical spine provides mobility and the lumbar spine provides load bearing function, the thoracic segment provides stability for the thoracic cage [Moore et al. 2000]. Without a spine, the ribs would “float” and there would be no reaction surface to resist compression and protect the organs within the thorax and abdomen. The spine is unique in that it provides both protection, like the skull does for the brain, and flexibility, like a joint does for two neighboring bones.

The thoracic spine consists of twelve vertebrae, each of which articulates with a rib (Figure 1.3). Adjacent thoracic vertebra have vertically oriented articular facets that engage one another in the anterior-posterior direction to limit shear motion and overlapping spinous processes limit to flexion and extension. The facets form an arc centered in the intervertebral (IV) disc to allow 3-5 degrees of rotation per motion segment [Mow & Hayes, 1997]. Ribs articulate with the vertebrae at two locations. The rib end interfaces between vertebrae at the inferior/superior costal facets, which are located at the junction between the pedicle and the vertebral body. The rib is further stabilized by a facet located on the transverse process of the vertebral body.

Spinous process Lamina

Transverse st 1 thoracic vertebra (T1) process

Vertebral Pedicle Spinous process canal Superior Vertebral costal facet body Inferior articular SUPERIOR VIEW process Superior articular Superior process articular process Zygopophyseal joint

Transverse Spinous process process Inferior costal facet ANTERIOR VIEW Superior Costal facet costal facet Costal facet on transverse Inferior on transverse process costal facet process

Vertebral body

Inferior vertebral notch Intervertebral Intervertebral disc foramen LATERAL VIEW

Figure.1.3. Vertebral column and thoracic vertebra characteristics

The stability provided by the ribcage on the thoracic spine has been investigated quasistatically [Watkins et al. 2005; Brasiliense et al. 2011; Oda et al. 2002], and the results from those studies illustrate the importance of the costovertebral joints on thoracic spine stiffness. The vertebral column is further stabilized by a series of ligaments. The

10 posterior longitudinal and anterior longitudinal ligaments resist flexion and extension, respectively (Figures 1.4 and 1.5). The ligamentum flava help to maintain normal curvature of the spine by preventing separation of vertebra and abrupt flexion, and the intervertebral discs resist compression. The posterior portions of the vertebrae are stabilized by a series of other ligaments. The supraspinous ligament runs continuously along the posterior border of the vertebral column. The interspinous ligaments hold together the spinous processes of adjacent vertebrae. Panjabi et al. (2004) compared the spinal ligament strains in intact flexibility testing with strains in frontal head impact simulations with muscle substitutes. They found that the strains in the intraspinous ligaments and ligamentum flavum exceeded the strains indicative of injury, and the strains were highest at C3-C4 in the whole adult cadaveric cervical spine. The viscoelastic properties of the cervical spine ligaments (anterior longitudinal ligament

(ALL), posterior longitudinal ligament (PLL), and ligamentum flavum (LF)) have been studied to determine how they would respond in high rate loading. A number of studies have examined the viscoelastic properties of the spinal ligaments. Lucas et al. (2008) examined the viscoelastic properties of adult cervical spine ligaments by testing the ligaments in stress relaxation and using Fung‟s Quasilinear Viscoelastic theory (QLV) to model the response. They found that the ligaments exhibited a linear relationship between the instantaneous elastic force and applied displacement. They found that the anterior and posterior longitudinal ligaments were nearly twice as stiff as the ligamentum flavum. They attributed this difference to both the structure (elastic/collagen ratio) and function (mobility vs. stability) of the respective ligaments. They also found that gender, vertebral level, and ligament type have an effect on the time-dependent relaxation

11 modulus. In a companion paper, Bass et al. (2007) found no difference in failure force or failure stress for gender or spinal level, but did find a statistically significant difference in failure force between the longitudinal ligaments and ligamentum flavum. The intertransverse ligaments provide lateral stability by connecting the transverse processes of adjacent vertebrae. All of these ligaments have been found to exhibit viscoelastic properties that are strongly associated with their relative composition of elastin and collagen, fibril size, and cross-linking density, all of which change with age [Barros et al.

2002; Lucas et al. 2008].

Vertebral canal Vertebral Ligamenta body flava Intervertebral disc Supraspinous ligament Anterior longitudinal Spinous ligament process Interspinous ligaments

Posterior longitudinal Intertransverse ligament ligaments

LATERAL CROSS - SECTION

Figure 1.4. Ligaments of the vertebral column (lateral view)

Intervertebral Vertebral disc body Ligamenta Transverse flava process

Intertransverse ligaments Posterior longitudinal ligament

Anterior longitudinal ligament

ANTERIOR CROSS-SECTION POSTERIOR CROSS-SECTION

Figure 1.5. Ligaments of the vertebral column (anterior & posterior views)

A large number of muscles produce movement of the thoracic intervertebral joints, including the splenius (rotation), rhomboids (lateral flexion), erector spinae

(extension), and rectus abdominis (flexion). Superficial, intermediate, and deep layers of musculature provide a large amount of passive resistance to thoracic spine motion.

Figure 1.6 illustrates the superficial and intermediate muscle groups. The splenius muscles span the cervical to the mid-thoracic vertebrae and cover the deeper intrinsic muscles of the vertebral column. The splenius capitis connects the mastoid process of the skull with the upper thoracic vertebrae, while the splenius cervicis connects the upper cervical vertebrae to the mid thoracic vertebrae. The erector spinae muscles are the primary extensors of the vertebral column and occupy the groove between the rib angles laterally and spinous processes of the vertebrae along the sagittal midline. These long

13 muscles consist of the iliocostalis, longissimus, and spinalis columns which form the lateral, intermediate, and medial portions of the erector spinae muscles, respectively.

Mastoid Process

Splenius Capitis Spinalis Cervicis Splenius Cervicis

Longissimus Posterior Serratus Superior

Iliocostalis

Spinalis Thoracis

Figure 1.6. Superficial and intermediate muscles of the thoracic spine

While the superficial and intermediate layer muscles span large multi-segment portions of the vertebral column, the deep layer of muscles, known as the transversospinales muscles, are short and function at the intervertebral level (Figure 1.7).

They consist of the semispinales group (superficial), multifidus (intermediate), and rotatores (deep). The semispinales muscles extend the head and both cervical and thoracic segments of the vertebral column while rotating contralaterally. The multifidus and rotatores muscles stabilize the vertebrae and assist with localized motion. Deep

14 segmental muscles function to provide peripheral support for the other muscles. The levatores muscles connect the transverse processes and costal angles of adjacent vertebral/costal levels, while the interspinales muscles connect adjacent spinous processes.

Interspinalis Semispinalis

Rotatores (Breves & Longi)

Levatores (Breves & Longi)

Multifidus

Figure 1.7. Deep muscles of the thoracic spine

1.4.Pectoral Girdle Anatomy

The pectoral girdle, which consists skeletally of the clavicle and scapula, articulates with both the thoracic spine (through muscular attachments with the scapula) and sternum (through the sternoclavicular (SC) joint and pectoral muscles), to support the upper extremities as shown in Figure 1.8.

Figure 1.8. Superior view of the pectoral girdle

There are a number of ligaments that stabilize and hold together the skeletal components of the pectoral girdle (Figure 1.9). On the medial side of the pectoral girdle, the sternoclavicular (SC) ligament provides a very strong attachment between the clavicle and sternum, and is one of the least dislocated joints in the body because of this strength

[Renfree et al. 2003]. Despite this strength, it has been found to be quite mobile with approximately 30-35 degrees of elevation/flexion/extension. The costoclavicular ligament provides additional stabilization for the medial end of the clavicle by connecting with the first rib. On the lateral end of the pectoral girdle, the acromioclavicular (AC) ligament attaches the scapula to the clavicle. The coracoclavicular ligament maintains stability between the coracoid process, which is on the superior-anterior border of the scapula and the attachment point for the biceps muscle, and the clavicle. The coracoacromial (CA) ligament holds together the acromion and coracoid processes. Koh et al. (2004) evaluated the dynamic properties of the shoulder ligaments using tensile tests. They noted differences in failure mode at each shoulder joint, with ligament ruptures more prevalent in the acromioclavicular and coracoclavicular joints and bone

16 fractures occurring more commonly at the bone. Interestingly, this variation in the failure mode and strength of each ligament did not vary with age, height, or weight of the specimen donor.

Sternoclavicular Clavicle Coracoclavicular Ligament Acromioclavicular Ligaments Ligament

Acromion Process

Coracoid Process Coraco-Acromial Costoclavicular Ligament Ligament Manubrium

Figure 1.9. Ligaments of the pectoral girdle (anterior view)

The clavicle serves as a strut to support the upper extremity to the upper torso, and is moved by the pectoralis major and subclavius muscles, as well as trapezius

(Figures 1.10 and 1.11). Pectoralis major couples the upper half of the humerus with the sternum and medial part of the clavicle. Subclavius connects the clavicle to the sternum.

Trapezius elevates, depresses, and retracts the scapula and also couples together the distal third of the clavicle with the acromion and spine of the scapula. The scapulothoracic

(ST) connection has been characterized as a “sliding” joint as the scapula moves relative to the posterior ribcage [Culham et al. 1993]. The rhomboid muscles in the intermediate layer retract and rotate the scapula with respect to the lower cervical and thoracic vertebral columns (C7 through T5). The ST and SC joints work in unison to move the pectoral girdle, with less relative motion in the acromioclavicular joint and little passive

17 resistance in the muscles. Because the shoulder and ribcage are the primary load-bearing structures resisting the crash restraint, the joints connecting the pectoral girdle to the spine and sternum should be replicated in an ATD as closely as possible.

Levator Scapulae

Rhomboid Minor Trapezius Rhomboid Major

Scapula

Figure 1.10. Muscles supporting the pectoral girdle (posterior)

Trapezius Sternocleidomastoid Serratus Subclavian Deltoid Anterior

Biceps Brachii

Pectoralis Pectoralis Major Minor

Figure 1.11. Muscles supporting the pectoral girdle (anterior)

1.5.Anatomy Summary

The structural complexity of the thoracic spine and pectoral girdle provides a glimpse into how much the two mechanisms are integrated within the upper thorax. In a typical occupant restraint scenario, the shoulder belt recruits both the sternum/ribcage and clavicle, both of which are intimately tied into the thoracic spine. To truly quantify the dynamic response of the thoracic spine in a manner representative of how an ATD should respond, the entire upper thoracic structure should be maintained in an experimental setup.

1.6.Project Objectives

This study was structured as shown in Figure 1.12, with a technical paper written to address three primary objectives. The abstracts for each paper are listed below.

Structural Anatomy Adult UTS-PG Adult Head & Spine

& Development of Dynamic Properties Kinematics from Adult UTS-PG from ISM Testing Real World/Sled (Paper #1) Testing Paper #2

Pediatric Distributed NASS Paper #3 Parameter Estimates vs. Adult Patient Modeling of T1- &Sled Radiology T6 Segment Data Survey Structural Anatomy Estimate 10 Year 10 Year Old Head & Development of Old UTS-PG & Spine Kinematics 10 Year Old UTS- Dynamic Properties from Real PG World/Sled Testing

Construction (How UTS Component Response to fit together UTS Properties Corridors with shoulders & (Biofidelity & ribcage) Large Child ATD Certification)

Figure 1.12. Strategy to develop large child ATD UTS-PG criteria

Objective #1: Characterize the dynamic response of the intact human upper thoracic spine while considering the effects of pectoral girdle restraint configuration, speed, and anthropometry

Chapter 2 addresses the first objective of this study with journal manuscript #1,

“Sequential Biomechanics of the Human Upper Thoracic Spine & Pectoral Girdle”. As stated earlier in this chapter, very little is known about the biomechanics of the thoracic spine in crash-level scenarios, and this is largely due to the difficulty of isolating the spine‟s response from the ribcage and shoulders. An original experimental/analytical approach, Isolated Segment Manipulation (ISM), was introduced to quantify the intact upper thoracic spine-pectoral girdle (UTS-PG) dynamic response of six adult post- mortem human subjects (PMHS). A continuous series of small displacement, frontal perturbations were applied to the human UTS-PG using fifteen combinations of speed and constraint per PMHS. The non-parametric response of the T1-T6 lumped mass segment was obtained using a system identification technique. A parametric mass- damper-spring model was used to fit the non-parametric system response. Mechanical parameters of the upper thoracic spine were determined from the experimental model and analyzed in each speed/constraint configuration. The natural frequencies of the UTS-PG were 22.9 ± 7.1 rad/sec (shear, n=58), 32.1 ± 7.4 rad/sec (axial, n=58), and 27.8 ± 7.7 rad/sec (rotation, n=65). The damping ratios were 0.25 ± 0.20 (shear), 0.42 ± 0.24

(axial), and 0.58 ± 0.32 (rotation). N-way analysis of variance (Type III constrained sum of squares, no interaction effects) revealed that the relative effects of test speed, pectoral girdle constraint, and PMHS anthropometry on the UTS-PG dynamic properties varied per property and direction.

Objective #2: Establish a mechanical link between thoracic spine system dynamics and whole-body spinal kinematics in crash simulations

Chapter 3 extends the applicability of ISM-derived dynamic properties to a higher energy, more crash-like environment in journal manuscript #2, “Dynamic Properties of the Upper Thoracic Spine-Pectoral Girdle (UTS-PG) System and Corresponding

Kinematics in PMHS Sled Tests”. Because head injury continues to be the primary cause of fatality in motor vehicle crashes, anthropomorphic test devices (ATDs) should accurately depict head kinematics in crash tests. Literature has demonstrated that thoracic spine rigidity affects head displacements and neck loads to some degree; however, it is not known how flexible an ATD thoracic spine component should be when integrated with the shoulders and thorax, in order to match human kinematics in a frontal, belted, non-airbag situation. To investigate the relationships between thoracic spine properties and resulting kinematics, three adult PMHS (n=3) were tested in both ISM and sled configurations. The ISM data were combined with previous ISM data to update the total set of UTS-PG data (n=9 PMHS). In the frontal sled tests, the PMHS was coupled through the T6-T8 vertebrae to a rigid seat fixed directly to the sled buck to provide direct measurement of UTS-PG system input as in ISM testing. Mid-thoracic spine and belt loads along with head, spine, and pectoral girdle (PG) displacements were measured in 12 sub-injurious sled tests across three PMHS (3-pt belted/unbelted at velocities from

3.8 – 7.0 m/s applied directly through T6-T8). The sled pulse, ISM-derived parameters, and external forces due to the head-neck and shoulder belt were used to predict kinematic time histories of T3 displacement. Normalized root mean square deviation (NRMSD) was used to compare experimental vs. modeled UTS-PG displacement-time histories.

Correlation analysis was used to compare the contributions of the shoulder and manubrium restraint on UTS-PG response.

The mean X-axis natural frequency for all nine PMHS (six ISM only and three in both ISM and sled) in the MNB/RS fixed, 0.5 m/s ISM condition was 23.4 ± 5.1 rad/sec, with effective stiffness of 21.0 ± 11.5 kN/m. Speed, anthropometry, and restraint condition had varying effects on the sled spine kinematics. The slope of the T6 force vs.

T3 displacement curve was quite linear and did not change significantly with increasing speed. The presence of a shoulder belt affected only rotation of the head, T1, and T3.

Over the duration of 150 ms, two UTS-PG models (Normalized Impulse/Optimized ISM and Critical Damping) replicated the experimental T3 displacement quite well (NRMSD of 10.4% and 4.8%, respectively), considering a very simple, single degree of freedom model was used. Differences between experimental and model properties were attributed to the absence of coupled Z axis and rotation effects, as well as the recruitment of viscous thoracic components in the higher energy, higher displacement sled environment. The optimized natural frequency for the NIOI model was very consistent with the ISM natural frequency across the three PMHS (29.9 ± 10.5 vs. 21.9 rad/s), while the damping ratio was considerably higher in the NIOI model optimized case (0.57 ± 0.45 vs. 0.12).

Objective #3: Develop a method for estimating the dynamic properties of a 10 year old

UTS-PG by considering age-related correlations in anthropometry and kinematics, adult

UTS-PG elastic modulus, and literature related to skeletal development of the spine.

Chapter 4 contains a third manuscript, “Age-Dependent Anthropometry and

Kinematics for Translating Adult Upper Thoracic Spine – Pectoral Girdle (UTS-PG)

Data to the Large Child Population”. The development of child anthropomorphic test devices (ATDs) is a challenge because of the absence of crash-level pediatric spine data, gaps in anatomic and kinematic comparisons of children vs. adults, and shifts in spinal injury location. There is an immediate need to better define the dynamic characteristics of the upper thoracic spine in large/older children (age 8-12) so that booster seats can be evaluated more comprehensively in crash simulations. To build on the new data generated in the first two papers, the objectives of this study were to (1) quantify structural anatomy & developmental differences between the adult and child upper thoracic spine – pectoral girdle (UTS-PG) mechanism using radiology, (2) assess the kinematic differences between adults and children using real world crash and sled test data, and (3) calculate the adult UTS-PG effective elastic modulus and develop a methodology that uses material property, anthropometry, and kinematic information from this study to estimate large child UTS-PG dynamic properties.

Anatomic and kinematic statistical analyses were completed to aide in translating the adult UTS-PG data to the child population. Structural anatomy measurements were taken from radiology data of both adult PMHS and pediatric patients, and statistically significant age-dependent measures were identified for scaling purposes. Head displacements of both children and adults were estimated through calculation of occupant available space (OAS) in 71 real-world crash cases, where face/head contact with the front row seatback was used as a doubly-censored binary response surrogate for head displacement. Differences between real world estimates for children (age 6-13) and

24 adults were consistent with experimental sled data from the literature. Using distributed parameter analysis, a range of adult UTS-PG elastic modulus was calculated using ISM natural frequency and anthropometry/mass data from radiology.

For the set of 39 pediatric patients, stature was strongly correlated (r2 = 0.91) with age, indicating that the sample was representative of a healthy child population. Clavicle length (r2 = 0.85), T1-T6 height (r2 = 0.77), T1 width (r2 = 0.77), and T6 width (r2 = 0.84) were strongly correlated with age in the pediatric dataset. Statistically significant differences (p<0.05, Student t-test) in skeletal fraction, sternal angle, clavicle angle, T1-

T6 anterior depth, and both T1 and T6 vertebral depths were observed between the pediatric and adult PMHS (n=9) datasets. The estimated displacement distributions from

OAS calculation in NASS-CDS cases showed consistency with literature experimental data from adults and children. Children in the 6-13 age range on average experienced

1.46 times the normalized head displacement as adults. A distributed parameter analysis was used to estimate the elastic modulus of the adult UTS-PG to be 7.5 – 16.5 MPa using anthropometric and ISM-derived dynamic properties from this study. Scale factors were then applied to develop a large child UTS-PG model. The large child normalized displacements reflected real world observations for adult vs. large child head displacement, indicating that the scale factors employed from radiology, kinematics, and elastic modulus along with ISM natural frequency resulted in accurate spine motions.

Taken together, these three investigations provide new biomechanical information on the anthropometry, dynamic properties, and kinematic response of the human upper thorax in belt loading during frontal loading scenarios.

Chapter 2 .Sequential Biomechanics of the Human Upper Thoracic Spine

and Pectoral Girdle (UTS-PG) System

2.1. Introduction

Thoracic spine flexibility significantly affects head motion in pediatric motor vehicle occupants [Sherwood et al., 2002], and the location of the shoulder belt restraint on the pectoral girdle (relative to the clavicle and sternum, in particular) alters the overall upper body kinematics of the occupant. Head injury continues to be the leading cause of death and disability in motor vehicle occupants [Adekoya et al., 2002]. The control of occupant head kinematics by motor vehicle restraint systems is critical for the prevention of head contacts to the vehicle interior, the most common injury source in crashes for both adults and children [Arbogast et al., 2002, 2004, 2005, Bohman et al., 2011, NHTSA

2010]. Because of the role of the thoracic spine in transferring restraint loads from the pectoral girdle and ribcage to the neck and ultimately the head, it is important to characterize the correlations between the dynamic properties of the thoracic spine, the connections between the thoracic spine and the pectoral girdle, and resulting head kinematics. If these relationships can be experimentally and analytically deduced for the adult population, those mechanistic correlations could be applied with the growing number of adult vs. child biomechanical comparisons to the pediatric population.

The upper thoracic spine and pectoral girdle are important areas in the anthropomorphic test device (ATD) because of their integrated function of producing the kinematics of the occupant‟s head and neck in a crash. Many ATDs used in research and regulatory testing have very rigid thoracic spine components where all spinal motion occurs in the cervical and lumbar segments. This structural discontinuity can cause high neck loads and severe chin-to-chest contacts in some circumstances, making it difficult to justify head and neck injury criteria in ATDs, especially some child ATDs in evaluating the performance of belt-positioning booster seats [NHTSA 2003, NHTSA 2010,

Stammen et al., 2008]. The human pectoral girdle and thoracic spine are structured as a continuous mechanism unlike in most ATDs. Therefore, any modification of an ATD thoracic spine component should also consider the interactive properties of the shoulder and ribcage.

It has been shown that ATD and human spinal kinematics are different, and this difference affects head motion. Humans tend to experience larger T1 displacements but less severe head rotations than ATDs in similar conditions. The head and spine motions of the Hybrid III 6YO ATD were compared with a child-sized PMHS and marked differences in T1 trajectory were found [Lopez-Valdes et al., 2009]. In a study by Ash et al. (2009), head excursion was found to be similar for a scaled human response compared to the Hybrid III 10YO and 5th percentile female ATDs, even with significant differences in T1 displacement, indicating the neck itself could be too flexible. Differences between spinal kinematics of child volunteers and the Hybrid III 6YO ATD were demonstrated in low speed frontal tests [Seacrist et al., 2010]. In another study, inverse dynamics were applied to experimental kinematics to estimate upper neck forces and moments within

27 adult PMHS and Hybrid III 50th percentile male ATD in both low and high speed tests

[Lopez-Valdes et al., 2010 & 2011b]. The PMHS spine showed different behavior at low and high speed, while the ATD did not exhibit this rate-dependent behavior. The ATD forward displacements were consistently less than the human, and the thoracic spine stiffness appears to be a major contributor to this discrepancy in child ATDs, and, to a lesser extent, adult ATDs. A rigid thoracic spine contributes to more extreme head rotations, higher loads in the cervicothoracic area, and underestimated head translation in the ATD, all of which appear to occur in practice with child ATDs.

While many studies have provided valuable information on the lower speed response and injury tolerance of thoracic functional spine units or multi-vertebra segments [Panjabi et al., 1976a, 1976b, 1981, Lopez-Valdes et al., 2011a, Andriacchi et al., 1974, Edmonston et al., 1999, Oda et al., 2002] and higher speed vertical or lateral response of the entire spine [Cramer et al., 1976, Lindbeck et al., 1987, Orne et al., 1971,

Terry et al., 1968, Begeman et al., 1973], few studies have investigated the frontal, sagittal dynamic properties of the intact thoracic spine-pectoral girdle mechanism in motor vehicle crash-level situations.

The objective of this study is to characterize the dynamic response of the intact human upper thoracic spine-pectoral girdle (UTS-PG) and investigate how constraint loading of the shoulder and sternum influences this response. An original experimental and analytical approach, Isolated Segment Manipulation, is introduced and used to obtain dynamic data from post-mortem human subjects (PMHS) at motor vehicle crash-level thoracic spine velocities. System identification was used to derive UTS-PG dynamic

28 parameters with sensitivity to rate, constraint of the shoulder and manubrium, and PMHS anthropometry.

2.2. Methods

To describe the behavior of the UTS-PG, a sagittal plane (XZ) mechanical model is shown in Figure 2.1.

Figure 2.1. Sagittal 3DOF model of the intact upper thoracic structure including the thoracic spine and pectoral girdle

Isolated segment manipulation consists of three primary steps to obtain the UTS-

PG dynamic properties:

1) Experimental testing of human specimens in various pectoral girdle conditions

2) System identification and modeling to obtain UTS-PG physical parameters

3) Statistical analysis to assess the relative effects of speed, constraint, and anthropometry on UTS-PG response

2.2.1. Experimental Setup

T-shaped body mounts were attached to thoracic vertebra 1, thoracic vertebra 6-8, manubrium, and left and right shoulder/acromioclavicular (AC) joints (Figure 2.2). Only superficial tissue was removed to allow entry and the neck was accessed through the muscles using the technique developed to non-destructively instrument the cervical vertebrae [Kang 2011a]. Each mount had a socket to receive a rigid welded bar link to the instrumentation, locations for skeletal mounting screws, and holes to attach a 3aω block [Kang et al. 2011b] consisting of three accelerometers (model 7264, Endevco) and three angular rate sensors (model ARS-8K, Diversified Technical Systems) when the location was free to move. The manubrium mount was vertically oriented on the sternum so that the sternoclavicular (SC) joint was free to articulate. The same vertical configuration was used for T6, with screws mounted to the T6 and T8 vertebral bodies and the socket located at approximately T7. The shoulder T-mount spanned the AC joint to simplify the complex range of motion at the shoulder joint. The T1 mount was secured by routing strong wire ties between ribs 1 and 2 through the trapezius muscle, between the muscles of the neck around the anterior side of the T1 vertebral body, and back through the mount on the opposite side. After tightening the wire ties, screws were put into the posterior aspect of the T1 vertebral body to provide additional stability.

Figure 2.2. Anterior and posterior views of manubrium, shoulder, T1, and T6 mounts

Instrumentation assemblies consisting of a six-axis ATD femur load cell (model

2667, R.A. Denton) and 3aω block were attached to adjustable reaction plates anterior and posterior to the test subject (Figure 2.3). Adaptor links were welded between the 3aω block housing and the body mounts to provide a customized, rigid attachment between the instrumentation and skeleton so that external measurements could be transferred to the body location using rigid body mechanics. The coupled head-neck support plate was attached rigidly to the Thoracic Apparatus for Producing PERturbations (TAPPER) loading source, which applied dynamic, pseudo-step displacement perturbations. To assure lateral rigidity, the head-neck support plate was secured against the head via

32 clamps screwed into the skull above the ear. The PMHS lower body was supported by both an extrication jacket harnessed to the frame and anterior/posterior reaction plates to prevent motion below the T6/sternum level.

Figure 2.3. ISM test setup – lateral view

The TAPPER is capable of a continuous speed range using a motor, flywheel, shaft, and cam arrangement (Figure 2,4). The cam was designed to provide a repeated nominal stroke of 9.5 mm measured by a linear potentiometer (model MLT, Honeywell) connected between the frame and extender arm, which was rigidly attached to a plate coupling together the head and neck (HdT1). Compression springs positioned between the moving extender and rigid frame provided sufficient return force to move the

33 assembly back to the cam for a repeatable, full length stroke following the cam tooth profile. Vertical motion was restricted, and resulting Z-axis and angular Y displacements were small (Figure 2.5).

Unloading (spring Steady state (follower returns riding on cam tooth) follower to cam)

Displacement(mm) Time (s)

Figure 2.4. TAPPER setup & perturbation example

Figure 2.5. Relative T1-T6 displacements

2.2.2. Data Acquisition

A test series was conducted on each PMHS (Table 2.1). Linear speeds of 0.5, 1.5, and 2.5 m/s were applied. Five constraint configurations simulated typical occupant scenarios. In each test, the coupled head-neck assembly underwent the same 9.5 mm nominal displacement and T6 remained fixed. Following attachment of the PMHS to the TAPPER, subject positioning was documented and static preload data was acquired.

A clutch disengaging the follower from the cam was set in place. The motor was then programmed to the correct revolutions per minute (RPM) associated with the desired linear speed. After the appropriate RPM was reached, the clutch was manually disengaged to initiate PMHS loading. Perturbation data was collected for five seconds at a sampling rate of 4 kHz. SAE J211 polarities were applied to all channels.

Table 2.1. ISM test matrix per PMHS Fixed 0.5 m/s 1.5 m/s 2.5 m/s MNB/LS/RS X X X LS/RS X X X MNB/RS X X X MNB X X X All Free X X X *MNB-Manubrium, LS-Left Shoulder, RS-Right Shoulder

2.2.3. Subject Characteristics

Six adult post-mortem human subjects (PMHS)1 were tested (Table 2.2).

Specimens were excluded from testing if they were found to be osteoporotic (DEXA lumbar spine T-score < -2.4 assuming same reference population for all PMHS), were obese (>30 kg/m2) or emaciated (<18.5 kg/m2) based on body mass index, or had evidence of substantial spine or shoulder surgery/deformity. A full set of anthropometry is found in Appendix F.

Table 2.2. Subject characteristics Test Age Ht Wt YA T- BMD ID Sex (yrs) (cm) (kg) score (g/cm2) 1 F 70 168 60.9 -2.1 0.951 2 M 68 170 86.4 -0.7 1.158 3 F 89 157 58.2 -1.3 1.042 4 M 72 159 72.3 2.4 1.523 5 * M 74 178 84 4.1 1.729 6 F 86 165 59.1 -1.3 1.043

AVG 76.5 166.2 70.2 0.2 1.2 STD 8.8 7.7 12.7 2.5 0.3

*PMHS 5 had cancer with metastases in the abdominal/lumbar region, which may explain high BMD.

1 Research was reviewed and approved by The Ohio State University Institutional Review Board (IRB) and was conducted in accordance with the practice of the IRB.

Following the series of tests, necropsy was performed. The spine was dissected from the second cervical vertebra to the ninth thoracic vertebra, and the entire thoracic structure was examined for injury.

2.2.4. Data Analysis

2.2.4.1. Rigid Body Correction

Because the experimental data was collected external to the body, the kinetic measurements were transferred to the PMHS skeletal locations using rigid body mechanics. Fast Fourier transform analysis was conducted on both moving (signal) and non-moving (noise) acceleration signals to determine that the appropriate low-pass filter to apply to all channels was CFC 180 (300 Hz). This was possible because the custom- welded adaptor links connecting the instrumentation to the skeleton were rigid. To calculate the motion equations to transfer the data to the skeleton, a free body diagrams was derived for the UTS-PG system (Figure 2.6).

m UTS-PG

Figure 2.6. Free body diagram of UTS-PG

Assuming the externally applied pectoral girdle constraint loads were encompassed by the deformable UTS-PG properties, the resulting motion equations are developed at each point in time:

(2.1)

(2.2)

b+e x HdT1+ f (z HdT1-g) (2.3)

(2.4)

(2.5)

–

θ (2.6)

where FX(HdT1), FZ(HdT1), MY(HdT1), FX(T6HW), FZ(T6HW), and MY(T6HW) were measured by the load cells, and FX(T1), FZ(T1), MY(T1), FX(T6,UTS-PG), FZ(T6,UTS-PG), and MY(T6,UTS-PG) were calculated. Linear accelerations ( , , , ) were measured by

accelerometers. Angular accelerations and were differentiated from angular

rate sensors, and the products and were found to be negligible with respect to the other terms given that rotation of the head-neck (HdT1) assembly was limited and T6 was held fixed.

The mass and center of gravity location for the HdT1 and T6HW hardware assemblies were calculated following the ISM test series on each PMHS. The head-neck was transected from the upper torso with the coupling fixture still attached via the adaptor links. To locate the HdT1 center of gravity, a method for the head and neck [Walker et al., 1973] was used with the modification that the HdT1 coupling hardware remained attached and thus was included in the calculation (see Appendix A). The HdT1 assembly mass was measured with a scale and this mass was confirmed to be consistent with the

39 average effective mass calculated using conservation of momentum and the experimental data:

FX(HdT1)-FX(T1) dt m(HdT1) = meff = x HdT1 dt

(2.7)

Accuracy of the CFC 180 filter class and geometric correction was confirmed by testing a Hybrid III ATD head-neck and verifying that the upper neck forces/moments matched the corrected external forces/moments applied to the head. After transferring the data to the T1 and T6 skeletal mount attachments, the UTS-PG segment could be further discretized into a point mass at the geometric center of the UTS-PG segment.

Because the displacement was small, the UTS-PG could be assumed as linear (negligible curvature & stretch) with the applied T1 and T6 skeletal displacements and loads adjusted to the point mass location using dimensional proportionality relations (see

Appendix B for verification data):

1 x = (x - x ) (2.8a) - 2 T1 T6

1 z = (z -z ) (2.8b) - 2 T1 T6

FX( - ) = FX(T1) +FX(T6) (2.8c)

FZ( - ) = FZ(T1) +FZ(T6) (2.8d)

MY( - ) = MY(T1) -MY(T6) +

FX( - ) z - +FZ( - ) (x - ) (2.8e)

2.2.4.2. System Identification

The UTS-PG dynamic response was determined using a system identification technique. Because of the small displacement and nearly-constant velocity in the ISM tests, the UTS-PG was assumed to be a linear system that is both scalable and time- invariant [Oppenheim et al., 1997]. The linear dynamic system response was found by convolving the input signal x(t) with the impulse response function (IRF) h(t) to obtain the output signal y(t).

y t = x h t- d =x t *h(t) (2.9) -

This convolution integral could be algebraically manipulated to express it in terms of well-known autocorrelation and cross-correlation functions [Hunter et al., 1982]:

c t = x x t+ d (2.10) xx -

c t = x y t+ d (2.11) xy -

This approach has been used previously in biomechanical tests to reduce measurement noise [Moorhouse et al., 2005]. The following equation is obtained through manipulation of the convolution integral:

x r y t+r dr = h t- ( x r x t+r dr)d (2.12) - - -

It can be seen that the left side of the equation is in the form of the cross- correlation function and the right side is the convolution of the IRF with the autocorrelation function. For a real system with discrete time points, this integral could be solved numerically and written in matrix form as

1 H= C-1 C (2.13) t xx xy

where Cxx is the autocorrelation matrix, Cxy is the cross-correlation matrix, and Δt is the time step. This procedure gave the impulse response function, H, of the UTS-PG system given the entire time history of the input and output signals at T1 and T6 for a given set of perturbations. This method can be applied in each of the three axes.

2.2.4.3. Modeling the IRF

The IRF could be modeled as shown in Figure 2.1 to provide meaningful physical parameters for the upper thoracic structure. The IRF of the UTS-PG resembles the response of a second order mass-spring-damper system:

m - x - +c - x - +k - x - =FX - (2.14)

Alternatively,

F 2 X( - ) x - +2ζ - ω - x - +ω - x - = (2.15) m -

The displacement response for this system was

x(t) = A e-Vt sin(2πFt + P) (2.16)

where

-1 mUTS-PG = (A*2πF) (2.17a)

-1 cUTS-PG = -2V*(A*2πF) (2.17b)

2 2 -1 kUTS-PG = ((2πF) + V )*(A*2πF) (2.17c)

2 2 1/2 1/2 ωUTS-PG = ((2πF) + V ) = (kUTS-PG/mUTS-PG) (2.17d)

2 2 1/2 ζUTS-PG = (V/((2πF) + V ) ) = (cUTS-PG/2ωUTS-PG) (2.17e)

The phase term P accounted for time delays present between the input and output.

The A, F, V, and P terms were optimized over the first 0.3 seconds to encompass the first

2-3 cycles of the experimental IRF using a least squared error (LSE) fit algorithm separately in the X, Z, and Y rotation axes using the experimental IRF obtained in each test.

2.2.5. Statistical Methods

Analysis of variance (ANOVA) using Type III constrained sum of squares was used to assess the effects of test speed, constraint, and PMHS anthropometry on the UTS-

PG dynamic properties.

2.3. Results

Figure 2.7 gives an example of an IRF (output displacement to a unit impulse force input) and second order model fit of the IRF for a single test.

Figure 2.7. Displacement response to a unit impulse force (IRF) and second order model fit with mechanical parameters

Figure 2.8 shows impulse response functions at three speeds for a single PMHS

(MNB/RS/LS fixed).

Figure 2.8. IRF at 0.5, 1.5, and 2.5 m/s (MNB/LS/RS Fixed)

Figure 2.9 illustrates the IRF differences obtained in the five constraint conditions for one PMHS, each at a speed of 0.5 m/s.

Figure 2.9. IRF in X axis for PMHS #4 in five constraint conditions (0.5 m/s)

Figure 2.10 displays the impulse response functions from the six PMHS for the

MNB/LS/RS Fixed condition at 0.5 m/s.

Figure 2.10. IRF in Z axis for each PMHS at 0.5 m/s, MNB/LS/RS Fixed

Figure 2.11 compares the experimental displacement with the displacement predicted using the IRF convolved with the experimentally measured force.

0 0.5 1.0 1.5 2.0 Time (sec)

Figure 2.11. Actual vs. IRF-Predicted Displacement (0.5 m/s, MNB/LS/RS Fixed)

Table 2.3 shows the p-values from ANOVA for test speed, constraint condition, and PMHS body mass index with no interaction terms between these variables included.

Table 2.3. P-values from ANOVA (p < 0.05 indicates significance in regression model)

Figures 2.12 – 2.14 break the data into BMI and constraint, with standard deviations from test speed variation.

Figure 2.12. ωnat and ζ (X axis)

Figure 2.13. ωnat and ζ (Z axis)

Figure 2.14. ωnat and ζ (Rotation about Y)

Table 2.4 summarizes the dynamic properties.

Table 2.4. UTS-PG data summary

2.4. Discussion

The frontal dynamic response of the human upper thoracic region was investigated in this study by conducting experiments using iterative constraint and speed variations, employing system identification to generate the non-parametric IRF relationship between T1-T6 displacements and loads, and modeling the IRF as a second- order system to determine the dynamic parameters and their sensitivity to test conditions.

2.4.1. IRF Derivation and Modeling

There was more variation in the individual mass, stiffness, and damping parameters than in the normalized natural frequency and damping ratio parameters. It appears that this could be a function of manually searching for a global minimum least square error (LSE) by iteratively adjusting the starting points of the A, F, V, and P parameters in the data processing algorithm. Therefore, natural frequency and damping ratio were the focus of this study. If both are known, then selection of appropriate mass, mass moment of inertia, stiffness, and damping coefficient for a given ATD or human size can be specified.

Because the UTS-PG system is underdamped (ζ < 1), there was often some oscillation of the measured force response at the beginning of the steady-state phase.

Especially in the 2.5 m/s tests, non-system behavior due to vibration began to appear in the force measurement even after filtering removed high frequency components of the measurement. The IRF captures this low level of error, and when the measured force is convolved with the IRF, the predicted displacement shows some oscillatory behavior

51 with respect to the actual displacement (Figure 2.11). If the variance accounted for, or

VAF [Oppenheim et al., 1997], between the predicted and actual displacement was below

60%, that data point was removed. This typically occurred in situations where the instrumentation hardware became loose during the test. There were 270 possible IRF and model fits in this study (6 PMHS x 15 constraint/speed combinations x 3 axes), but only

181 were used to derive the dynamic properties. In early testing, the links between the instrumentation and T-mounts were not as stable as in later tests, and consequently either the higher speed tests were not completed or the resulting IRF exhibited an unusual shape because non-skeletal elements were present in either the input or output signal. If the mount was found to be loose following a test, it was removed from the dataset. Even with these experimental anomalies, the advantages of this test method are that there is ample data to assess the dynamic response of the system, and it was evident quantitatively from either the IRF or sensor data itself when the system was not behaving appropriately.

2.4.2. Effect of Speed, Constraint, and Anthropometry

The relative effects of rate, constraint, and anthropometry on the dynamic properties of the upper thoracic structure consisting of the thoracic spine, pectoral girdle, and ribcage varied considerably (Figures 2.8 - 2.14 and Table 2.3). Overall, it appeared that constraint was somewhat less significant than body mass index or test speed on the resulting natural frequency and damping ratio. From the data collected in this study, it appears that the mechanics of the upper thorax is sensitive to constraint, test speed, and

52 anthropometry and do in fact need to be considered when assessing ATD design for robustness under multiple input conditions in practice.

To the knowledge of the authors, this is the first study to examine the system dynamic interactions of pectoral girdle, ribcage, and thoracic spine response under varying degrees of constraint. Specific attention was given to the T1-T6 segment because of documented discrepancies between ATD and human thoracic spine properties. Several quasi-static studies have examined the effect of ribcage presence on thoracic spine stiffness, but no known studies have investigated the relationship between ribcage/shoulder constraint and dynamic upper thoracic response in loading severities indicative of automotive crashes. A three-dimensional human thorax model was used to isolate the effects of various ribcage elements on thoracic spine flexion [Andriacchi et al.,

1974]. It was found that the ribcage stiffened the thoracic motion segments, and the presence of the sternum had the greatest effect on the spinal column bending response.

However, the material properties employed for the model were based on static material tests, so the extent of the sternum‟s presence could not be extended to the dynamic case.

In static testing of patient volunteers, the ribcage stiffness was estimated to contribute roughly 33% of the measured stiffness of the thoracic spine [Edmonston et al., 1999]. In an in vitro cadaveric study, the rib head joints were shown to serve as stabilizing structures for the thoracic spine in the sagittal, coronal, and transverse planes [Oda et al.,

2002]. The results from this study (Tables 2.3 and 2.4) indicate that the nature of the boundary condition applied to the sternum and shoulder influences the UTS-PG response dynamically. Perhaps ATD designs should be evaluated under various shoulder belt geometries to assure the upper thorax and belt are interacting in a humanlike manner.

While test speed was not found to be important for natural frequency and damping ratio of the UTS-PG in all cases, the damping coefficient was required in all cases to best model the IRF, indicating that the UTS-PG response is linear viscoelastic.

A number of studies have examined the response of the entire spine in vertical acceleration events or lateral loading [Cramer et al., 1976, Lindbeck et al., 1987, Orne et al., 1971, Terry et al., 1968]. These studies along with the current study all suggest that adding a viscous component to a spine model provides better agreement with experimental results than does a purely elastic system. However, the average damping ratio in all 3 axes was well below 1, indicating that the elastic response dominated the viscous response in this series of PMHS tests.

Body mass index, bone mineral density, and age all had very similar effects in preliminary ANOVA. Because BMD is normally considered vital only in injurious situations, superficial tissue and musculature are included in the response, and the age range was relatively narrow, BMI was selected as the most appropriate anthropometric measure to include in the statistical analysis. BMI significantly affected the natural frequency and damping ratio in all comparisons except damping ratio in the Z axis (Table

2.3). It is not clear whether the change in natural frequency with BMI is more affected by mass or by stiffness, but it does appear that the time-invariant properties of the upper thorax are influenced by the BMI. While this appears to be true for the age range in this study, it would be interesting to investigate whether this relationship between BMI and natural frequency holds true for younger specimens.

2.4.3. Directional Characteristics

In comparing the UTS-PG dynamic properties in the X, Z, and Y rotation axes, it appears the upper thoracic structure is most stiff axially and most viscous in rotation

(Figures 2.12 – 2.14 and Table 2.4). Recall that the X axis was the only direction where natural frequency was affected by constraint. This may be due to the orientation of the instrumentation links, which were almost purely horizontal. Also, the X axis results typically had the highest VAF and best model fit, indicating that the results in that axis are more stable than in rotation or the Z axis. The UTS-PG structure is somewhat less stiff in X (shear) and rotation about Y than in the Z axis. Injuries did not play a role in this behavior, as no vertebral column injuries were discovered in the spinal structure during post-test dissection. There was some laxity present in the sternoclavicular joint of

PMHS 1, which may have affected the relationship between constraint and UTS-PG properties to some extent in that test series. The moments and rotations experienced in the testing were significantly lower than the failure thresholds reported by Lopez-Valdes et al. (2011a).

While only sagittal plane properties were examined in this study, previous work has demonstrated that the thoracic spine experiences combined loading patterns due primarily to its integration with the ribcage as well as the complex anatomical orientation of adjacent vertebral bodies. In tests of functional spine units (FSU) from the thoracic spine, it was shown that the thoracic spine is a complex, three-dimensional structure with coupled motion characteristics [Panjabi et al., 1976a, 1976b, 1981]. Begeman et al.

(1973) found that substantial seat pan vertical loads were generated in frontal loading

55 scenarios. Axially applied forces resulted in significant shear displacements indicating intrinsic combined loading, and the spine was more flexible in flexion than in extension.

Therefore, it is not surprising that almost pure forward/shear perturbations resulted in relatively large axial forces and moments within the upper thoracic structure.

2.4.4. Thoracic Spine Kinematics

In sled test studies examining thoracic spine kinematics, some combination of T1,

T4, T8, and T12 is typically tracked during the event. T6 was chosen as the lower boundary in this testing largely because of ATD practicability purposes. T6-T8 represents roughly ½ the height of the ribcage and a load cell with sufficient measurement capacity would span multiple vertebral levels, especially in a large child

ATD. A rigid segment at this location would also allow measurement of chest acceleration in the typical vicinity for current ATDs.

The speed range applied in the ISM tests was based upon estimated spine velocities in previously conducted sled tests by Lopez-Valdes et al. (2010). Assuming a typical logistic shape for displacement-time at both T1 and T8 locations, the peak T1-T8 displacements along with their respective peak times (time zero was taken as the time where initial relative displacement commenced) were differentiated to estimate relative

T1-T8 velocity. A range of 0.9 – 2 m/s was calculated for relative T1-T8 velocity for a

40 km/hr adult PMHS sled test. Therefore, while the results presented here have yet to be proven in higher displacement crash simulations, the rates applied in this testing are consistent with high speed conditions for sled tests with adult PMHS.

The relative T1-T8 displacement trajectories reported in high speed tests of adult

PMHS by Lopez-Valdes et al. (2011b) indicate very little Z displacement and rotation about Y with respect to forward X translation. This displacement pattern was captured with the ISM test configuration by limiting vertical motion and rotation to the extent possible. In that same study, it was shown that while absolute PMHS T1 and T8 displacements increased significantly from 9 km/h to 40 km/h, the relative T1-T8 displacements did not increase nearly as much. This may be because the UTS-PG natural frequency and damping ratio do not change appreciably with increasing spinal input.

2.4.5. Limitations

While the intended loading direction was purely in the x-direction, there was a very small amount of Z axis deformation (5 – 10% of X axis displacement) in the system due to the PMHS resistance. Because the UTS-PG was not oriented perfectly vertical, there was some Z force resulting from this nearly pure X axis motion. As a result of the very small Z axis displacement, there is likely some small amount of error in both the X and Z axis impulse response functions. As a result, a coupled model of the UTS-PG response may be more appropriate than separating the individual axis responses and assuming superposition will hold at higher displacements.

The implications of this work so far should be considered with discretion, as the dynamic properties may only be valid for small displacements and should not yet be extrapolated to higher displacement, longer duration transient conditions such as crash simulations until the model parameters are verified in full system tests. Additionally, as

57 with most PMHS test series, the mean age is relatively high at 76.5 years old (Table 2.2).

Without some relationship between UTS-PG properties and spine/head displacements, it is difficult to establish the applicability of these results to younger individuals. It is encouraging that the T-score average from the subjects is close to zero, which indicates that the average bone mineral density is similar to that of a young adult. However, as mentioned earlier, this testing is in the sub-injurious range so mineral density is likely less important than soft tissue properties for structural response.

2.4.6. Future Work

The next steps of this research will extend the development of the model by comparing model-predicted with experimentally measured spine displacements in frontal sled tests, quantifying the relative effects of the shoulder and manubrium individually on upper thoracic response, and finally combining the UTS-PG model with anatomic and kinematic information in an attempt to develop preliminary thoracic spine response corridors for both adult and large child-sized ATDs.

2.5. Conclusions

 The UTS-PG response was accurately captured at crash-level PMHS spine velocities using Isolated Segment Manipulation. Dynamic properties were obtained using a second-order mass/spring/damper mechanical model of the impulse response function with T1 and T6 measurements in the sagittal plane.

 In the X direction (global horizontal), the natural frequency of the adult upper thoracic spine-pectoral girdle structure (UTS-PG) was 22.9 ± 7.1 rad/sec and damping ratio was 0.25 ± 0.20 (n=58). In the Z direction (global vertical), the natural frequency was 32.1 ± 7.4 rad/sec and damping ratio was 0.42 ± 0.24 (n=58). In the rotation about Y direction (flexion in the sagittal plane), the natural frequency was 27.8 ± 7.7 rad/sec and damping ratio was 0.58 ± 0.32 (n=65).

 A damping coefficient was required to best capture the UTS-PG response, illustrating that the upper thorax has some degree of viscoelasticity. However, the relatively low damping ratio in all 3 axes indicates that the elastic response dominated the viscous response in this series of PMHS tests.

 Body mass index (BMI) influenced the time-invariant dynamic response of the

UTS-PG, but it is unclear if the natural frequency variation is due more to stiffness or mass.

 Constraint significantly affected the natural frequency in the forward direction, indicating that dynamic, sequential interactions between the upper thoracic spine, pectoral girdle, and ribcage should be considered in evaluating the sensitivity of an ATD upper thorax.

Chapter 3 . Dynamic Properties of the Upper Thoracic Spine-Pectoral Girdle

(UTS-PG) System and Corresponding Kinematics in PMHS Sled Tests

3.1. Introduction

Detailed posterior thorax data, specifically thoracic spine flexion, is typically limited to accelerations obtained at a given vertebral level in frontal crash investigations.

61 adult population, those mechanistic correlations could be applied with the growing number of adult vs. child biomechanical comparisons to the pediatric population.

The upper thoracic spine and pectoral girdle are important areas in the anthropomorphic test device (ATD) because of their integrated function of producing the kinematics of the occupant‟s head and neck in a crash. Hybrid III ATDs used in research and regulatory testing have very rigid thoracic spine components where all spinal motion occurs in the cervical and lumbar segments. This structural discontinuity can cause high lower neck loads and severe chin-to-chest contacts in some circumstances, making it difficult to justify head and neck injury criteria in ATDs, especially in the Hybrid III 10 year old (HIII-10C), which is used in evaluating the performance of belt-positioning booster seats [NHTSA 2003, NHTSA 2010, Stammen et al., 2008]. Whereas the HIII-

10C has separate load paths for belt loading of the ribcage and shoulder, the human ribcage and shoulder are coupled together by the clavicle for a distributed belt load path to the thoracic spine through a series of muscles, ligaments, and rib compression. Any modification of an ATD thoracic spine component should also consider these boundary conditions developed by the shoulder and ribcage. Information on dynamic flexion of the human thoracic spine with respect to these constraining interactions at crash-level speeds will be useful for ATD enhancements in the future.

Characterization of thoracic spine – pectoral girdle interactions could also aide in improving finite element models, which are constructed using material property data for the individual, dissected segments of the human body, with validation of the full body model using sled test kinematic evaluation. “Sequential” biofidelity information to pull together individual component mechanical properties with the corresponding full body,

62 crash-level kinematics would greatly advance the injury-predictive capability of these models for simulating motor vehicle occupants. This would be especially beneficial for the large child population, where there is paucity of both component mechanical property and high-speed kinematic data.

While some studies have provided information on the lower speed response and injury tolerance of thoracic functional spine units or multi-vertebra segments [Panjabi et al., 1976a, 1976b, 1981, Lopez-Valdes et al., 2011a, Andriacchi et al., 1974, Edmonston et al., 1999, Oda et al., 2002] and higher speed vertical or lateral response of the entire spine [Cramer et al., 1976, Lindbeck et al., 1987, Orne et al., 1971, Terry et al., 1968,

Begeman et al., 1973], numerous recent studies have investigated the frontal dynamic properties of the intact thoracic spine-pectoral girdle mechanism in motor vehicle crash- level situations. These studies have investigated the whole-body kinematics of the thorax in belted adult PMHS, in the context of anterior ribcage (sternum) loading relative to the thoracic spine. Vezin et al. (2002) reported T1, T8, and T12 accelerations in belt loading scenarios from 30 – 50 km/hr. They reported thoracic spine accelerations in the range of

15 – 20 G when the shoulder belt force was 2.8 -4 kN. Forman et al. (2006a, 2006b) reported T1 accelerations of 8 – 20 G and T8 accelerations of 20 – 23 G in frontal PMHS sled tests conducted at 29 and 38 km/hr. These accelerations corresponded to between 7

– 19% chest compression. They presented slight vertical (upward, Z) displacements of

T1 and a peak head X displacement of approximately 320 mm at 125-130 msec.

Michaelson et al. (2008) conducted rear-seated PMHS sled tests at 48 km/hr and observed significant rib fractures (avg age 55 years) and lower cervical spine injuries.

Shaw et al. (2009) observed very little forward displacement below the mid-thoracic

63 spine with respect to the seat/sled in 12 G pulse, belted adult PMHS tests. Shoulder belt tensions were 5 – 7.5 kN, and peak head displacement occurred near 140 msec. These studies provide valuable kinematic data for full-body ATD biofidelity assessments. For evaluating a thoracic spine ATD component, however, it is necessary to quantify the relationships between loads and displacements in the context of the surrounding skeletal attachments (ribcage and pectoral girdle). The sensitivity of full body kinematics to the dynamic properties of a given component is typically accomplished through modeling approaches, such as finite element analysis. However, if an experimental approach could be devised to provide the necessary mass, stiffness, and damping values for the physical component, both FE model accuracy and subsequent ATD design biofidelity could be improved considerably.

It has been shown that ATD and human spinal kinematics are different [Shaw et al. 2001], and this difference affects head motion, especially in children. Humans appear to experience larger T1 displacements but less severe head rotations than ATDs in similar conditions for both volunteer and PMHS testing. In a recent study [Lopez-Valdes et al.,

2010 & 2011b], inverse dynamics were applied to experimental kinematics to estimate upper neck forces and moments within adult PMHS and Hybrid III 50th percentile male

ATD in both low and high speed tests. The PMHS spine exhibited different kinematic profiles at low and high speed, while the ATD did not exhibit this rate-dependent behavior. The ATD forward displacements were consistently less than the human. This behavior also appears to be true for the child occupant as well, when head and spine motions of the Hybrid III 6YO ATD were compared with a child-sized PMHS and marked differences in T1 trajectory were found [Lopez-Valdes et al., 2009]. In a study

64 by Ash et al. (2009), head excursion was found to be similar for a scaled human response compared to the Hybrid III 10YO and 5th percentile female ATDs, even with significant differences in T1 displacement, indicating the neck itself could be compromising for the lack of thoracic spine compliance. Differences between spinal kinematics of child volunteers and the Hybrid III 6YO ATD were demonstrated in low speed frontal tests

[Seacrist et al., 2010]. These studies indicate that thoracic spine stiffness appears to be a major contributor to kinematic differences between both child and adult human and their corresponding ATDs. A rigid thoracic spine appears to lead to more extreme head rotations, higher loads in the cervicothoracic area, and underestimated head translation in the ATD, all of which appear to occur in practice with child ATDs.

Pintar et al. (2010) applied inverse dynamics techniques with head and neck properties and head/spine kinematics to estimate lower cervical spine loads in frontal sled tests with adult PMHS. The data from that study provides an important step toward developing lower neck criteria in ATDs, and provides a top-down approach for estimating loads in the upper thoracic spine region. While inverse dynamics has been shown to be successfully applied to body regions with well-defined physical characteristics, it would appear difficult to apply this same methodology to an integrated skeletal structure such as the thoracic spine.

In order to estimate the dynamic properties of the child thoracic spine, it is first necessary to derive these properties for an adult through experiments with PMHS.

Arbogast et al. (2006) examined cardiopulmonary resuscitation (CPR) data on adult

PMHS and reported an average spring stiffness of 588 N at 40 mm of compression

(approximately 14.7 kN/m) at a loading speed of 0.25 m/s. Salzar et al. (2009) examined

65 the viscoelastic response of the PMHS thorax with belt ramp-hold tests at rates of 0.5 –

1.2 m/s. They noted that the thorax exhibited linear behavior and that an elastic model of the thorax would be reasonable at the displacements obtained. The intrinsic relationship between upper thoracic spine compliance and the interfacing structures (pectoral girdle) were investigated in Chapter 2. Six PMHS were tested in the Isolated Segment

Manipulation (ISM) configuration. A series of small displacement perturbations were applied at various combinations of speed and pectoral girdle constraint, and system identification was employed with forces and displacements measured at T1 and T6, and the impulse response functions (IRF) were modeled as a second order mass-spring- damper system to obtain natural frequencies & damping ratios for the upper thoracic spine – pectoral girdle (UTS-PG) system in three degrees of freedom. Figure 3.1 shows the model form of the UTS-PG.

Figure 3.1. UTS sagittal plane model (n=6 PMHS)

The objective of this study is to provide new data on the dynamics of the intact human upper thoracic region of the body, by introducing the measurement of forces and moments into the thoracic spine. A sled test environment was used to confirm the applicability of the previously-developed UTS-PG model properties at higher energies than previously used in ISM tests. By testing a set of three PMHS in both ISM and sled scenarios, model-predicted and experimental spine (third thoracic vertebra) displacements with respect to T6-T8 are compared. Using statistical methods, the relative effects of anthropometry, speed, and restraint are compared, and relationships are drawn between UTS-PG dynamic properties and overall spine kinematics on the sled.

Preliminary load vs. displacement ATD targets and T1/T3 trajectory information are presented for the T1-T6 segment at crash-level speeds (3.8 – 7 m/s). Finally, the potential applications of this data are discussed in the context of previous work, including the use of this sled configuration for more accurately calculating cervicothoracic loads in full-body PMHS sled tests.

3.2. Methods

Three PMHS were tested in both ISM and sled configurations. The UTS dynamic properties were derived from the ISM testing described in Chapter 2. Single degree-of- freedom models using ISM properties from that specific PMHS were used to predict spine displacements near the geometric center of the UTS segment at the third thoracic vertebra (T3). These displacements were then compared with the experimentally measured displacements in the sled test for a given acceleration input. The two test configurations applied to the same PMHS were used to investigate whether (1) the UTS dynamic properties from ISM testing accurately predict the thoracic spine response in sled testing and (2) the UTS model can be more broadly applied to realistic crash simulation tests. Additionally, relationships between shoulder belt forces, T6-T8 input forces (directly applied via the sled pulse), and spinal/shoulder/head kinematics were examined.

3.2.1. Subject Characteristics

Three adult post-mortem human subjects (PMHS)1 were tested experimentally

(Table 3.1). Specimens were excluded from testing if they were found to be osteoporotic

(DEXA lumbar spine T-score < -2.4 assuming same population), were obese or emaciated (body mass index (BMI) > 18.5 and < 30), or had evidence of substantial spine or shoulder surgery. A full anthropometry summary can be found in Appendix F.

1 Research was reviewed and approved by The Ohio State University Institutional Review Board (IRB) and was conducted in accordance with the practice of the IRB.

Table 3.1. Subject characteristics Bone Mineral Density ID Age Sex Ht (cm) Wt (kg) T-Score (g/cm3) 7 72 F 155 54 -1.2 1.03 8 88 M 168 58 1.0 1.30 9 86 M 178 73 1.0 1.30

3.2.2. ISM Testing

3.2.2.1. Experimental Setup

T-shaped body mounts were attached to thoracic vertebra 1, thoracic vertebra 6-8, manubrium, and left and right shoulder/acromioclavicular (AC) joints (Figure 3.2). Only superficial tissue was removed to allow entry and the neck was accessed through the muscles using the technique developed to non-destructively instrument the cervical vertebrae [Kang 2011a]. Each mount had a socket to receive a rigid welded bar link to the instrumentation, locations for skeletal mounting screws, and holes to attach a 3aω block [Kang et al. 2011b] consisting of three accelerometers (model 7264, Endevco) and three angular rate sensors (model ARS-8K, Diversified Technical Systems) when the location was free to move. The manubrium mount was vertically oriented on the sternum so that the sternoclavicular (SC) joint was free to articulate. The shoulder T-mount spanned the AC joint to simplify the complex range of motion at the shoulder joint. The

T1 mount was secured by routing strong wire ties between ribs 1 and 2 through the trapezius muscle, between the muscles of the posterior/lateral/anterior neck around the anterior side of the T1 vertebral body, and back through the mount on the opposite side.

After tightening the wire ties, screws were put into the posterior aspect of the T1

69 vertebral body to provide additional stability. The T3 mount was attached by truncating the spinous process and inserting a single wood screw posterior-to-anterior through the vertebral body. For the T6-T8 location, 1/8” toggle bolts were inserted into the T6, T7, and T8 vertebral bodies with the socket located at approximately T7 (Figure 3.3). The toggle bolts provided added support for the higher energy sled test scenario.

Figure 3.2. Anterior and posterior views of manubrium, shoulder, and spine mounts

Posterior Anterior

aA T6 T7

Figure 3.3. Use of three toggle bolts to secure T6-T8

Instrumentation assemblies consisting of a six-axis ATD femur load cell (model

2667, R.A. Denton) and 3aω block were attached to adjustable reaction plates anterior and posterior to the test subject (Figure 3.4). Adaptor links were welded between the 3aω block housing and the body mounts to provide a customized, rigid attachment between the instrumentation and skeleton so that external measurements could be transferred to the body location using rigid body mechanics. The coupled head-neck support plate was attached rigidly to the Thoracic Apparatus for Producing PERturbations (TAPPER) loading source, which applied dynamic, pseudo-step displacement perturbations. To assure lateral rigidity, the head-neck support plate was secured against the head via clamps fastened to the skull above the ear. The PMHS lower body was supported by both an extrication jacket harnessed to the frame and anterior/posterior reaction plates to prevent motion below the T6/sternum level.

As presented in Chapter 2, 3aω blocks were rigidly fixed to skeletal landmarks

T6, left/right shoulder, and manubrium via custom welded steel bar links to measure

6DOF motion. A 3aω block was also affixed to the plate coupling the head and neck together, with T1 as the lower boundary, as well as T3. ATD femur load cells were used to measure kinetics at the skeletal locations where kinematics were also obtained.

To allow for transfer of the same PMHS between the ISM and sled configurations, a seat was designed and fabricated to attach to each setup. Figure 3.4 shows the experimental setup. The main difference from the previous configuration was that the T6 instrumentation hardware was now integrated into the stand-alone seat. This change was not expected to alter the overall input conditions for the PMHS.

Custom Welded Bar Links

6DOF Load Cells TAPPER

3aω Motion Blocks

Experimental Seat

Figure 3.4. ISM setup

3.2.2.2. Test Procedure

Each PMHS was loaded using the thoracic apparatus for producing perturbations

(TAPPER). The TAPPER (shown in Figure 3.5) applied repeated 9.5 mm perturbations to the coupled head-neck of the PMHS over a five second data acquisition period.

Steady state (follower riding

on cam tooth)

Unloading (spring returns Loading follower to cam)

Displacement(mm) Time (s)

Figure 3.5. Test setup & loading profile for ISM configurations

Twelve tests were applied to each PMHS, with three speeds (0.5, 1.5, and 2.5 m/s nominal linear velocity) and four constraint configurations: manubrium/left shoulder/right shoulder fixed (MNB/LS/RS), left shoulder/right shoulder fixed (LS/RS), manubrium/right shoulder fixed (MNB/RS), and manubrium fixed (MNB) (Table 3.2).

Table 3.2. ISM test matrix per PMHS Constraint 0.5 m/s 1.5 m/s 2.5 m/s MNB/LS/RS Fixed X X X LS/RS Fixed X X X MNB/RS Fixed X X X MNB Fixed X X X

3.2.2.3. Data Processing and Analysis

Data was acquired at 4 kHz and filtered using CFC 180, which was deemed an appropriate low-pass filter level by conducting a Fast Fourier transform analysis of frequency content of moving/stationary acceleration signals as described in Chapter 2.

After performing a rigid body correction of external force and moment data from the load cells to the skeletal locations at T1 and T6, the displacements and loads were corrected to the mid-segment (~T3). Confirmation of this correction using linear proportionality is shown in Appendix B. System identification was then used to relate the inputs and outputs through convolution, and the impulse response function (IRF) of the system was calculated. This IRF was then modeled as a second order mass-spring-damper mechanical system to derive the natural frequency and damping ratio of the T1-T6 system, with variations due to constraint configuration, PMHS anthropometry, and speed incorporated into the response.

The UTS-PG dynamic response was determined using a non-parametric system identification technique. This approach has proven to provide accurate characterization of viscoelastic and biological structures [Moorhouse et al. 2005]. Because of the small

74 displacement and nearly-constant velocity in the ISM tests, the UTS-PG was assumed to be a linear system that is both scalable and time-invariant [Oppenheim et al., 1997]. The linear dynamic system response was found by convolving the input signal x(t) with the impulse response function (IRF) h(t) to obtain the output signal y(t).

(3.1)

y t = x h t- d =x t *h(t) -

This convolution integral could be algebraically manipulated to express it in terms of well-known autocorrelation and cross-correlation functions [Hunter et al., 1982]:

(3.2) cxx t = x x t+ d -

(3.3) cxy t = x y t+ d -

(3.4) x r y t+r dr = h t- ( x r x t+r dr)d - - -

It can be seen that the left side of the equation is in the form of the cross-correlation function and the right side is the convolution of the IRF with the autocorrelation function.

For a real system with discrete time points, this integral could be solved numerically and written in matrix form as

1 H= C-1 C (3.5) t xx xy

Each IRF was modeled as shown in Figure 3.1 to provide meaningful physical parameters for the upper thoracic structure. The IRF of the UTS-PG resembles the response of a second order mass-spring-damper system (Figure 3.6).

2 (3.6) X +2ζ ω X +ω X =Y

Where Y is the input (Fx(t), Fz(t), or My(t)) and X is the output (x(t), z(t), or θ(t)). The displacement response to a unit impulse load for this system in each direction is

X(t) = A e-Vt sin(2πFt + P) (3.7) where

-1 mUTS-PG = (A*2πF) (3.8a)

-1 (3.8b) cUTS-PG = -2V*(A*2πF)

2 2 -1 (3.8c) kUTS-PG = ((2πF) + V )*(A*2πF)

2 2 1/2 1/2 ωUTS-PG = ((2πF) + V ) = (kUTS-PG/mUTS-PG) (3.8d)

2 2 1/2 ζUTS-PG = (V/((2πF) + V ) ) = (cUTS-PG/2ωUTS-PG) (3.8e)

Figure 3.6. (Top) T1/T6 data corrected to T3 location; (bottom) impulse response function with 2nd order M-C-K model fit

The phase term P accounts for time delays present between the input and output.

The A, F, V, and P terms were optimized over the first 0.3 seconds to encompass the first

2-3 cycles of the experimental IRF using a least squared error (LSE) fit algorithm using the nine experimental IRF obtained in each test.

3.2.3. Sled Testing

After completing the ISM series of tests on a PMHS to obtain its unique UTS-PG dynamic properties, the seat with PMHS still installed was transported to the sled, where it was attached as shown in Figure 3.7.

Figure 3.7. Attachment of seat with PMHS to sled interface

The seating configuration was designed to support the head prior to the test, immobilize the lower body, preserve the PMHS for repeated testing, and provide adjustability for belt geometry and subject positioning. The head was fitted with a harness that was supported by a bar attached to the top of the seat. A cartridge-actuated cable cutter (Roberts Research Laboratory, Torrance, CA) configured as shown in Figure

8 was triggered in sync with the sled event to release the head.

Figure 3.8. Cable cutter used to release head

The lower body (everything below T6-T8) was immobilized by an adjustable- depth bar situated to span the left and right iliac crests of the PMHS. A foot rest was installed on the sled floor board to resist inertial motion of the legs. A padded head rest protected the head upon rebound, and foam was also added to the armrests to preserve the

PMHS in repeated testing.

In the belted configuration, a shoulder belt was installed on the seat to provide a realistic upper body restraint for the PMHS (Figure 3.9). The upper end had an adjustable anchor position in the Y-axis, while the lower end was buckled to the seat. A pre-tension of 5 lb was applied before the test, and a belt tension load cell was installed to measure shoulder belt force during the test. In the unbelted configuration, a shoulder belt was attached horizontally below the xyphoid process without initial tension to prevent jackknifing and preserve the lower ribcage for repeated testing.

Figure 3.9. Restraint geometry in (left) belted and (right) unbelted condition

3.2.3.1. PMHS Instrumentation

Head. An aluminum tetrahedron block [Yoganandan et al, 2006] was installed on the PMHS head and used to measure 6-degree of freedom kinematics as described by

Kang (2011) in both the body-fixed and global coordinate system (Figure 3.10).

Figure 3.10. 6aω Tetrahedron to measure 6DOF kinematics of the head

Shoulders. Mounts with 3aω instrumentation were installed on the left and right shoulders to prevent possible shoulder belt interference (Figure 3.11). Consistent with the ISM tests, the mount spanned the acromion process and clavicle distal end.

Belt

Post

erio

r Right Shoulder

Figure 3.11. Right shoulder 3aω with modified mount to prevent belt interference

Spine. T1 and T3 were both configured with 3aω blocks using the same mounts as the ISM setup (Figure 3.12). The mid-thoracic spine (T6-T8) was coupled to the sled via the T6 6DOF load cell rigidly attached to the seat fixture (Figure 3.13). The moment at the T6-T8 location was determined by correcting the load cell-measured moment by the Z force multiplied by the X distance between the load cell and skeletal attachment.

Figure 3.12. T1 and T3 instrumentation

T6 Load T3 Cell & 3aω Block Right Shoulder

Figure 3.13. Instrumentation at T6-T8, T1, T3, and right shoulder

3.2.3.2. PMHS Positioning & Coordinate System Definition

Orientations and polarities of all sensors were defined per SAE J211. To orient the 3aω block with respect to the PMHS, the tetrahedron and each 3aω block were digitized with a FARO arm (Faro Arm Technologies, Lake Mary, FL) so that signals obtained during the test could be transformed to SAE J211 convention. The FARO arm was also used to measure the position of the sternal notch, xyphoid process, top of head

(mid-sagittal), mandible (mid-sagittal), nasion, occiput, L/R tragion, and L/R greater trochanter. The landmarks on the head were used to define the Frankfort plane for transformation of the tetrahedron kinematic data to the head CG for comparison with

ATDs (Figure 3.14). The head CG is estimated to be at the mid-point of the line connecting the left and right tragion locations.

Nasion Tragion

Orbit Frankfort Plane

Figure 3.14. Skeletal landmarks for estimating PMHS head CG

3.2.3.3. UTS-PG Model Formulation & Sled Pulse Derivation

It is not physically possible to apply a pseudo-square wave impulse to the sled in the same way as ISM tests due to the large mass of the sled. To validate and evaluate the

UTS-PG model parameters identified in ISM tests, the PMHS mid-spine (T6-T8) was coupled directly to the sled to replicate the ISM configuration but in a higher energy, more realistic crash setup. Experimental spine displacements were compared to displacements predicted by a model constructed with ISM properties and the applied input to the UTS-PG. Because this is not a typical sled test where the ATD is restrained by the belt alone, the sled pulse should be derived to result in spine velocities consistent with both those applied in ISM tests and with measurements made in traditional sled testing from the literature.

We begin by considering the same PMHS spine system in both ISM and sled test scenarios (Figure 3.15):

TAPPER SLED

ISM Sled

Figure 3.15. UTS-PG mechanical model in both ISM and sled configurations

Unlike the ISM setup where the head and neck are coupled as a rigid body, the sled setup allows free motion of the head and neck. Therefore, the force at T1 should be included in the input to the UTS-PG system. This is done by constructing a two-degree of freedom system (Figure 3.16) and solving for the applied force on the UTS-PG body:

1. UTS-PG Representation: 2. Equivalent Mechanical System:

Fbelt

kUTS-PG kNeck

FT6(X) mUTS-PG mHeadNeck

cUTS-PG cNeck

xUTS-PG xHN UTS-PG 3. Free Body Diagrams:

4. Motion Equation Matrix:

mHN 0 + 0 mUTS-PG - - - -

5. Rearranging and substituting to solve for the input to the mUTS-PG:

F - m x - F T HN HN Belt x UTS-PG + 2ζ UTS-PG+ xUTS-PG = mUTS-PG

Figure 3.16. UTS-PG mechanical model

In the ISM test, the TAPPER applies the input force to the system with a rigid reaction surface on the other side (T6-T8 is held fixed). The displacement of the UTS mass is prescribed in this case, with resulting forces and moments measured by the instrumentation. In the sled test, the system is loaded by the sled itself through T6-T8, and the displacement of the UTS mass is dictated by the characteristics of the system.

For this analysis, it is assumed that the constraint was consistent with “MNB/RS

Fixed” in the belted cases and “LS/RS Fixed” in the unbelted case since this condition had consistent ISM properties as the “All Free” condition in Chapter 2. In ISM testing, the natural frequency and damping ratio are obtained in a particular constraint situation, so the appropriate values are applied for the same condition in the sled test. The focus of the data analysis will be on x-direction, as there is no z-motion of the sled and published data on relative T1-T8 spine displacements indicate that the motion is almost purely in the x-direction.

The differential equation using the ISM-derived properties along with the sled acceleration (equation 3.10) was solved as a single degree of freedom system using the method of undetermined coefficients with homogeneous/steady state and particular/transient portions of the response (full derivation is found in Appendix G).

x T3 + 2ζ ω + ω xT3 = Fexternal / meffective = x applied (3.10)

Literature data indicates that typical thoracic spine velocities (T1 relative to T8) are in the range of 0.9 – 2 m/s. Lopez-Valdes et al. (2011) reported relative T1-T8 forward displacements of 81.7 mm in 40 km/h sled tests with adult PMHS. The time

86 from initial rise in belt forces to time of peak forward displacement was in the range of

90 msec based on the data reported in their paper. While T1-T8 relative velocity was not reported, an estimated slope of 0.0817 m displacement change over 0.090 sec gives a relative T1-T8 velocity of 0.97 m/s. The sled pulse acceleration required at T6 should result in a peak T3 velocity in the range of 0.39 – 0.86 m/s, or roughly 42.8% of that of the relative T1-T8 velocity, given that the T3-T6 length is 3/7 that of the T1-T8 length.

Because the mid-thoracic spine is coupled to the sled, the pulse applied to the

PMHS should be derived to reflect typical spine velocities in normal sled testing scenarios. A simple, single degree of freedom system of the PMHS is considered as shown in Figure 3.17:

mUTS-PG sled

= 0.39 – 0.86 m/s

Figure 3.17. Representation of UTS-PG segment in sled test

Equating the external and internal forces, the governing motion equation (3.10) in the X-axis is manipulated to calculate the required input acceleration. The average ISM properties from the initial six PMHS in Chapter 2 are inserted, as well as the integrated

(displacement) and differentiated (acceleration) target T3 velocity time history assuming

87 a sinusoidal output shape. Table 3.3 summarizes the estimated sled pulses for each of the three PMHS to generate the required spine velocity.

Table 3.3. Estimated accelerations to obtain typical spine velocities in sled tests

Sled Sled Avg. Natural Effective Mass Avg. Damping Acceleration Acceleration Frequency PMHS ID (kg) = ½ Ratio from Peak Magnitude Peak Magnitude (rad/sec) from PMHS mass ISM Tests (G) for 0.39 m/s (G) for 0.86 m/s ISM Tests T3 Velocity T3 Velocity 7 (330) 27.0 24.5 0.24 4.04 8.88 8 (423) 29.0 24.5 0.24 5.12 11.30 9 (521) 36.5 24.5 0.24 5.02 11.06 Average 30.8 24.5 0.24 4.7 10.4

Based on this analysis, the range of acceleration peak pulses applied directly at T6-T8 should range between 4.7 G and 10.4 G to replicate T3 velocities from typical belted occupant sled tests.

Two UTS-PG model configurations were used to predict the T3 displacement in the sled test. Each model was of the form shown in equation 3.10 and Figure 3.16. The first model, which is referred to as the critical damping model, assumes that the large displacement case is critically damped. The effective mass and natural frequency from

ISM testing on that PMHS are maintained, the viscous damping factor zeta is set to

0.999, and the peak external force, with period reflecting the sled acceleration pulse, is optimized such that the resulting model displacement has a minimum least square error with respect to the experimental T3 displacement time history from 0 – 150 msec. The second model, referred to as the Normalized Impulse/Optimized ISM (NIOI) model, is

88 constructed by normalizing the time scale of the input force to the UTS-PG by (1) calculating the impulse by integrating the experimental force input over the first 150 milliseconds, (2) assuming a sinusoidal profile for the force with a half-cycle duration of

150 msec, which corresponds to a frequency of 20.94 rad/sec, (3) solving for the peak force FO, and (4) using the resulting normalized force profile as the input to the single degree of freedom UTS-PG model (Figure 3.18). Normalization by impulse calculation allows for time- and PMHS-related variations in head-neck effective mass and shoulder belt placement, and it was found to provide a more accurate T3 displacement shape.

0.150 sec 0.150 sec

Fosinωt dt = FT6(t) FT1(t) FShoulderBelt(t) dt 0 0

Figure 3.18. Using impulse to obtain a normalized force input profile across tests

Then, the natural frequency and viscous damping factor zeta are optimized to minimize the least square error between the modeled and experimental T3 X

89 displacement-time history. The ratio between the NIOI model and ISM natural frequency as well as the ratio between the critical damping model and actual experimental external force were both calculated to quantify the relationship between the linear-assumed ISM response and nonlinear-assumed sled response from the same PMHS. Differences in the dynamic properties between the ISM and sled case to best reflect the experimental spine displacement would be associated with the input energy.

3.2.3.4. Test Matrix

A series of twelve sled tests were conducted using different sled pulses and restraint configurations on a set of three PMHS as shown in Table 3.4 and Figures 3.19-

20. Note that the sled inputs are directly applied to T6-T8.

Table 3.4. Sled test input summary

Sled (T6-T8) Peak Sled (T6-T8) Peak PMHS # (Test) Shoulder Belt Deceleration (g) DeltaV (m/s) 7 (330-1) Yes 7.0 5.0

8 (423-1) Yes 5.1 3.7 8 (423-2) Yes 6.5 4.7 8 (423-3) Yes 7.4 5.1 8 (423-4) Yes 8.7 5.8 8 (423-5) Yes 10.7 7.0 9 (521-1) Yes 5.2 3.8 9 (521-2) Yes 6.6 4.8 9 (521-3) Yes 7.4 5.1 9 (521-4) No 5.1 3.7 9 (521-5) No 6.5 4.7 9 (521-6) No 7.5 5.2

Figure 3.19. Sled accelerations

Figure 3.20. Sled velocities

3.2.3.5. Data Processing

All instrumentation signals were sampled at 20 kHz and filtered per SAE J211 filter class (SAE, 2007). High speed video (1000 frames/second) was also acquired to allow for comparison of global PMHS landmarks with instrumentation-acquired kinematics.

3.2.3.6. Rigid Body Kinematics

To calculate the three-dimensional global motion of the head, spine, and shoulders, a method using 3aω data presented by Kang et al. (2011) was applied. The displacements, velocities, and accelerations of each skeletal landmark in the global coordinate system was found at each time point using data from the FARO arm, angular rate sensors, and accelerometers. The full processing method is shown in Appendix H.

3.2.3.7. Statistical Analysis

The kinematic time histories were quantitatively compared using normalized root mean squared deviation (NRMSD). To provide a quantitative measure of the difference between model-predicted and experimental sled data, the mean square error (MSE) was calculated between the model-predicted and experimentally measured T3 X displacements:

(3.11)

where:

Xi and Xi' are the ith data point of the experimental displacement and model- predicted displacement, respectively.

n is the number of data points.

The square root of the MSE was then taken to obtain the root mean square deviation

(RMSD):

(3.12)

The RMSD was then divided by the range of the observed values (i.e., data obtained from the video analysis) to obtain the normalized root mean squared deviation (NRMSD):

(3.13)

The NRMSD effectively provides an average percent error over time between the model- predicted and experimental sled kinematic data.

Correlation coefficients were calculated to assess relative relationships between anthropometry, speed, and restraint on PMHS head and spine kinematics and kinetics.

3.2.3.8. Injury Assessment

Following sled testing, dissection was performed to identify both skeletal and soft tissue injuries sustained in the test series. The cervical and thoracic segments of the spine were examined, along with the pectoral girdle and ribcage. Musculature was visually examined, and the intervertebral, glenohumeral, acromioclavicular, and sternoclavicular joints were checked for evidence of subluxation, fracture, or dislocation.

3.3. Results

3.3.1. ISM Testing

Figure 3.21 shows the ISM results for the MNB/RS fixed case at 0.5 m/s.

PMHS7

PMHS8

PMHS9

Figure 3.21. IRF and UTS-PG model fit for 3 PMHS (0.5 m/s, MNB/RS Fixed)

Table 3.5 summarizes the ISM results and UTS-PG model parameters for the set of three PMHS. Note that for each PMHS, the natural frequency was highest in the

MNB/LS/RS Fixed condition and lowest in the LS/RS Fixed constraint condition. The damping ratio did not follow the same trend.

Table 3.5. UTS-PG model parameters (0.5 m/s, X axis) to predict T3 X displacements

PMHS 7 PMHS 8 PMHS 9 Constraint Condition ω K C ω K C ω K C n ζ kN/ n ζ n ζ rad/s Ns/m rad/s kN/m Ns/m rad/s kN/m Ns/m m

MNB/LS/RS 20.0 0.12 14.2 174 24.6 0.10 24.4 189 24.1 0.07 25.6 143

LS/RS 14.3 0.21 5.59 161 11.6 0.23 7.64 306 10.1 0.05 9.2 90.4

MNB/RS 19.2 0.16 14.2 230 22.0 0.06 21.9 136 22.4 0.10 22.4 199

MNB 18.0 0.16 10.5 185 20.4 0.09 18.8 163 20.5 0.13 18.0 236

Table 3.6 summarizes the UTS-PG model parameters for the full set of nine

PMHS (six PMHS from Chapter 2 and three additional PMHS in this chapter). Detailed

ISM data, including impulse response functions, model fit parameters, and distributions of dynamic properties are in shown in Appendices D, E, and J.

Table 3.6. UTS-PG model parameters for full set of 9 PMHS (mean values for 0.5 m/s, MNB/RS constraint, X-axis)

ω Effective Effective PMHS Age Ht Wt BMD n ζ Sex (rad/s) Stiffness, K Damping, C ID (yrs) (cm) (kg) (g/cm2) (kN/m) (Ns/m)

1 F 70 168 60.9 0.951 20.1 0.23 15.7 366 2 M 68 170 86.4 1.158 34.1 0.06 45.6 171 3 F 89 157 58.2 1.042 26.7 0.06 12.9 60.5 4 M 72 159 72.3 1.523 19.3 0.21 6.5 143 5 M 74 178 84 1.729 19.2 0.48 19.0 956 6 F 86 165 59.1 1.043 27.3 0.40 30.4 898 7 F 72 155 54 1.030 19.2 0.16 14.2 230 8 M 88 168 58 1.300 22.0 0.06 21.9 136 9 M 86 178 73 1.302 22.4 0.10 22.4 199 AVG 78.3 166 67.3 1.231 23.4 0.20 21.0 351 SD 8.7 8.4 12.0 0.26 5.1 0.15 11.5 337

3.3.2. Sled Testing

Figure 3.22 shows screen captures of the 3 PMHS when subjected to a similar pulse (4.7 – 5.0 m/s).

Figure 3.22. (Top) PMHS 7, (Center) PMHS 8, (Bottom) PMHS 9 at 4.7 – 5.0 m/s

Figure 3.23 illustrates the accuracy of using gravity-compensated 3aω block displacements for head, spine, and shoulder global kinematics.

3aω 3aω (gravity compensated) High speed video tracking

Figure 3.23. High speed video vs. 3aω displacements

3.3.2.1. Effect of Anthropometry

Figures 3.24 and 3.25 show plots of T6 kinetics vs. T1 and T3 displacements in the T6-T8 pulse range of 6.54 – 7.43 g (deltaV = 4.7 – 5.1 m/s) for the 3 PMHS. Note the differences in relative T1/T3 motion for the three PMHS.

Figure 3.24. T1 and T3 displacement vs. T6 force

Figure 3.25. T1 and T3 rotation vs. T6 moment

3.3.2.2. Effect of Speed

Figure 3.26 illustrates the change in total T1/T3 spinal trajectory with input severity applied at T6 for the same PMHS. Both T3 and T1 exhibited upward motion as they displaced forward. Note also the change in length of the T3-T6 segment in each case.

423-1 423-3 423-5 5.11 g 7.43 g 10.7 g 3.8 m/s 5.1 m/s 6.4 m/s

Figure 3.26. T1 and T3 trajectories relative to T6 at increasing velocities

Figure 3.27 shows a lack of speed sensitivity for the UTS-PG of PMHS 8. The

slopes of the T6 force vs. T3 displacement curves show no significant trend with

increasing pulse severity and are also quite linear in shape.

Figure 3.27. Lack of speed sensitivity and linearity of PMHS 8 thoracic spine response

100

3.3.2.3. Effect of Restraint

Figure 3.28 shows differences in thoracic spine kinematics in PMHS 9 in the belt vs. unbelted condition. The data shows consistency in the sled accelerations between the restraint conditions at each speed. It is likely that a larger difference would be present in a normal sled test, with a larger amount of anterior ribcage compression.

Figure 3.28. Effect of belt presence on T1 and T3 kinematics/kinetics

101

3.3.2.4. UTS-PG Model vs. Experimental Spine Displacements

Figure 3.29 & 3.30 show the UTS-PG model-predicted and experimental thoracic spine (T3) displacements with respect to T6 in the X direction for all 12 sled tests.

330-1 423-1

423-2 423-3

423-4 423-5

Figure 3.29. Experimental vs. model-predicted T3 X displacements (PMHS7/8)

102

521-1 521-2

521-3 521-4

521-5 521-6

Figure 3.30. Experimental vs. model-predicted T3 X displacements (PMHS9)

Table 3.7 summarizes the differences between model-predicted and sled T3 displacements, and Table 3.8 contains the corresponding statistics.

103

Table 3.7. Experimental vs. model-predicted T3 X displacements & properties

UTS-PG NIOI Model UTS-PG Critical Damping Model Sled Test

Peak Peak Peak T3 ω ∑Fx(ext) m ω ∑Fx(ext) m ∑Fx(ext) Test ID n ζ eff T3 Disp n ζ eff T3 Disp Disp (rad/s) (N)** (kg) (rad/s) (N) (kg) (N) (mm) (mm) (mm) 330-1 10.0 0.001 522.5 38.4 64.7 19.2 0.999 1827 38.4 55.3 1178 59.7 423-1 45.7 0.29 1002.0 45.1 13.3 22 0.999 625 45.1 13.7 1634 12.6 423-2 37.5 0.33 1109.8 45.1 21.2 22 0.999 965 45.1 21.2 2211 21.8 423-3 39.8 0.16 1114.0 45.1 22.3 22 0.999 1029 45.1 22.6 2517 22.4 423-4 21.4 0.88 1234.4 45.1 30.4 22 0.999 1383 45.1 30.3 2808 30.4

104 423-5 25.0 0.001 1085.7 45.1 54.2 22 0.999 2323 45.1 52.9 2992 55

521-1 37.0 0.999 1569.5 44.7 17.2 22.4 0.999 784 44.7 17.1 2080 17.7 521-2 24.1 0.999 1523.4 44.7 30.0 22.4 0.999 1370 44.7 30.7 2171 30.6 521-3* 10.0 0.001 473.2 44.7 7.6 22.4 0.999 2121 44.7 18.8 1424 17.4 521-4 29.7 0.999 1256.4 44.7 18.8 22.4 0.999 831 44.7 18.8 1673 19.1 521-5 28.8 0.999 1838.5 44.7 28.8 22.4 0.999 1318 44.7 29.1 2565 29.3 521-6* 10.0 0.001 993.6 44.7 15.9 22.4 0.999 2354 44.7 20.9 2398 18.8 AVG*** 29.9 0.57 1226 44.3 30.1 21.9 0.999 1246 44.3 29.2 2183 29.9 STDev 10.5 0.45 361 2.1 16.7 1.0 0.000 520 2.1 14.3 566 15.7 *Toggle bolts pulled out at 75 msec, as indicated by the T6-T8 force drop. Peak for 0 – 75 ms shown but data not included in avg/stdev. **Determined by normalizing the impulse calculated from T6-T1-SBLC time history to a sinusoidal force with period 3.33 Hz (20.94 rad/sec)

104

Table 3.8. Comparative statistics for model fits to experimental T3 X displacement

Peak Pct Ratio of Peak Peak Pct NRMSD Difference NRMSD External Forces Difference (Critical Ratio of Natural (Critical (NIOI Model (Critical Damping Test ID (NIOI Model Damping Frequency (NIOI Damping vs. Model vs. vs. Model vs. Model vs. ISM) Model vs. Experimental) Experimental Peak Experimental) Experimental) Experimental) Force)

330-1 8.4% -7.3% 18.0% 3.5% 0.521 1.55 423-1 6.0% 8.9% 5.8% 9.3% 2.077 0.38 423-2 -2.6% -2.9% 6.8% 6.1% 1.705 0.44 423-3 -0.5% 0.7% 9.3% 8.7% 1.809 0.41

5 423-4 0.0% -0.1% 6.8% 4.4% 0.973 0.49

423-5 -0.5% -7.3% 5.0% 5.0% 1.136 0.78 521-1 -2.7% -4.0% 13.2% 3.5% 1.652 0.38 521-2 -1.7% -3.0% 5.6% 4.3% 1.076 0.63 521-3* -56.4% 8.1% 25.0% 2.1% 0.446 1.49 521-4 -1.4% -5.7% 7.5% 3.8% 1.326 0.50 521-5 -1.7% -2.5% 8.1% 3.5% 1.286 0.51 521-6* -15.5% 10.8% 13.1% 3.2% 0.446 0.98 AVERAGE -5.7% -0.4% 10.4% 4.8% 1.36 0.71

*Toggle bolts pulled out at 75 msec, as indicated by the T6-T8 force drop. Statistics only reflect up until 75 ms for these tests.

105 3.3.2.5. Relative Head/T1 Motion

Figure 3.31 shows the head kinematics relative to T1 for the 12 tests. Tests 521-3 and 521-6 are truncated at 75 msec, and note the three distinct sets of trajectories grouped together for each PMHS.

0.05

0 0 0.05 0.1 0.15 0.2 0.25 0.3

-0.05

-0.1

330-1 423-1 -0.15 423-2 423-3 -0.2 423-4 423-5

-0.25 521-1 521-2 521-3

Head/T1 Z Displacement Head/T1 Z (m) -0.3 521-4 521-5

-0.35 521-6

-0.4

-0.45

-0.5 Head/T1 X Displacement (m)

Figure 3.31. Head/T1 trajectories

106 3.3.2.6. Statistical Analysis

Table 3.9 summarizes the correlation results relating PMHS kinematics to anthropometry, speed, and restraint. For anthropometry, tests 330-1, 423-2, 423-3, and

521-2 were included (belted PMHS 7, 8, and 9 at 4.7 – 5 m/s). For speed, all tests for

PMHS 8 (423-1 through 423-5) were included (3.8 – 7 m/s belted). For restraint, tests

521-1, 521-2, 521-4, and 521-5 were included (two speeds belted vs. unbelted).

Table 3.9. Correlation coefficients for peak measurements

Anthropometry Speed Restraint Parameter (Body Mass Index) (n=5) (n=4) (n=4) T3 X displacement 0.61 0.97 -0.01 T3 Y rotation -0.22 0.98 -0.64 T1 X displacement 0.83 0.92 0.63 T1 Y rotation 0.70 0.95 -0.58 Head X displacement -0.72 0.95 0.35 Head Y rotation 0.78 1.00 -0.33 T6 X force 0.19 0.96 0.27 T6 Y moment 0.47 0.97 0.66 *Data does not include cases where toggle bolts pulled away from spine

3.3.2.7. Injuries

No thoracic spinal column or thorax injuries were observed for any of the three

PMHS. There were mid-low cervical spine injuries that presented at the highest speed pulse for PMHS 8 and PMHS 9. Facet joint dislocation and ligamentum flavum disruption occurred in both PMHS 8 (C5 level) and PMHS 9 (C6 level).

107 3.4. Discussion

Information on the posterior dynamic properties (load vs. displacement), curvature, and kinematics of the human upper thoracic spine is scarce. This study (1) provides human upper thoracic kinematic/kinetic data in frontal, belted sled tests, (2) evaluates the effects of anthropometry, speed, and restraint on spinal displacements & rotations, (3) relates dynamic properties from ISM testing to spine kinematics for the same PMHS using an experimentally-based mechanical model, and (4) contributes preliminary T6 force/moment vs. T1/T3 displacement and rotation corridors for ATD design at relevant crash velocities.

3.4.1. Effect of Anthropometry, Speed, and Restraint

Figure 3.27 illustrates how little speed sensitivity exists in the upper thoracic spine for the range of velocities applied. This linear behavior suggests that the structure is not viscoelastic, and the skeletal facet joints between the vertebral bodies and between the transverse costal facets and ribs are the primary locations of deformation. The damping ratios from the IRF model were quite low (avg = 0.108), indicating that the response of the UTS-PG is nearly linearly elastic in this displacement range. This finding is consistent with Salzar et al. (2009) who reported very little viscous contribution at 0.5

– 1.2 m/s for the PMHS thorax. This linearity also was exhibited in PMHS8/423 in this study (Figure 3.27) when the T3 displacements ranged from 12.6 – 55 mm (peak velocities 0.22 – 0.7 m/s). This behavior is likely affected by advanced age of the PMHS.

It has been shown that the intervertebral space closes with age along with increasing

108 kyphosis [O‟Gorman et al. 1987], which would both lead to increased resistance to flexion. Collagen content becomes the more dominant with age in the spinal ligaments

[Barros et al. 2002], which limits the ability of the tissue to absorb and hold viscous elements.

The size of the PMHS did not appear to significantly affect the head and spine kinematics. The exception was T1 X displacement, which appeared to increase with BMI

(Table 3.9). This lack of kinematic relationship with applied sled speed at T6-T8 could be attributed to the small dataset, limited range of BMI in the three PMHS, or the variation of speed (4.7 – 5 m/s). It could also be because the majority of difference in body mass is inferior to the T6-T8 level, and restriction of mid-thoracic spine motion and curvature could prevent the normal effect of increasing kyphosis in a standard sled test scenario. It should be noted that the ISM principal dynamic properties were quite similar between the 3 PMHS, which may contribute to the similarity in spine kinematics.

Preliminary T6 load vs. T1/T3 displacement ATD targets were presented in Figures 3.24 and 3.25. Even though this is for a very small sample set of 3 PMHS of advanced age, it is felt that this information could provide much-needed information for ATD design because the specimens possessed normal BMI and BMD as well as the tests being conducted in a crash speed range.

PMHS 9 was tested at three speeds in unbelted and belted configurations at each speed. There was a minimal effect of restraint on T6 resultant force (Figure 3.28) and spine displacements (Table 3.9), but the Y rotations of T1 and T3 as well as moment about Y increased in the unbelted scenario. It was decided to apply a 3-pt lap shoulder belt or no belt to encompass the most likely restraint scenario as well as the extreme case

109 of no added resistance to motion of the upper thoracic area. It was somewhat surprising that spine displacements weren‟t decreased by the shoulder belt, and it would be interesting to determine whether rotations are likely to be mitigated more than x displacements in a standard sled test when a 3 pt belt is applied. This observation may also indicate that the shoulder and ribcage are not as intrinsically coupled with the behavior of the thoracic spine as previously reported.

3.4.2. Comparison with Previous Data

It must be noted that all kinematics in this study are reported with respect to T6-T8, which is held fixed in both the ISM (static reaction) and sled (acceleration applied directly to spine). This step required the derivation of appropriate severity sled pulses to obtain spinal velocities reported in the literature. In addition, the modeled T3 displacements were in the global coordinate system when using the sled acceleration as the input to the system.

The X-axis stiffnesses calculated from modeling the impulse response functions

(Figure 3.21 and Table 3.5) for the three PMHS were 14.2, 21.9, and 22.4 kN/m.

Arbogast et al. (2006) reported anterior-posterior mid-sternum stiffness of 588 N at 40 mm (~14.7 kN/m) of compression on PMHS. This indicates accuracy of the impulse response function in characterizing the response and consistency between mid-sternum

(0.25 m/s) and T1-T6 forward motion while fixing the anterior chest (0.5 m/s).

The head and T1 trajectories from this study (see Figure 3.31 & Appendix I) were consistent with those presented by Forman et al. (2006a, 2006b), who reported slight

110 vertical (upward, Z) displacements of T1 and a peak head X displacement of approximately 320 mm at 125-130 msec. These measurements occurred with between 7

– 19% of chest compression. Figure 3.23 displays similar T1 trajectory characteristics.

The peak head displacement was typically 240 – 300 mm at around 150 msec (Figure

3.23), with the amplitude depending on the pulse severity, restraint condition, and PMHS.

Chest compression, when estimated by T3 displacement normalized by chest depth assuming the belt remains rigid with respect to the sled, ranged from 6.5% to 28.4%.

Michaelson et al. (2008) observed significant rib injuries, and both that study and

Pintar et al (2010) reported lower cervical spine injuries when testing PMHS at speeds similar to those applied in this study. It was believed that rib fractures would possibly confound the spinal flexion measurements if the chest were to sustain too much compression. This was one of the reasons for tethering T6-T8. Thoracic spine forward excursion with respect to the anterior ribcage would minimize the localized stresses associated with the shoulder belt tension while providing comparable chest compression with typical sled test scenarios. In Shaw et al. (2009), they observed very little forward displacement below the mid-thoracic spine with respect to the seat/sled in 12 G pulse, belted adult PMHS tests. This provided some justification for selecting T6-T8 as the baseline for attachment to the seat.

3.4.3. Experimental vs. Model-Predicted Displacements

IRFs were calculated from ISM testing on the three PMHS, and the dynamic properties were used to create a UTS-PG model for each PMHS. Figures 3.29 and 3.30

111 showed that two models, critically damped and normalized impulse/optimized ISM

(NIOI), using different combinations of ISM dynamic properties and externally applied forces matched the sled spine (T3) displacements reasonably well over 150 milliseconds.

Differences between model-predicted and experimental T3 displacements were likely due to the contributions in the Z axis and rotation about Y. The T3 location experienced between 10 and 20 mm of vertical/upward (Z) displacement and between 10 and 24 degrees of flexion over the 150 ms event duration. To improve the model fit, it would be appropriate to couple these contributions in a cantilever beam model experiencing transverse bending. Nonetheless, using only X axis properties in a single degree of freedom model proved to be a reasonable representation of the T3 motion given that X displacement is the dominant component. The average peak external force optimized for the critically damped model (1246 N) across all 12 tests was very close to the average normalized impulse peak force (1226 N) calculated from the combination of T6 force

(directly measured), T1 force (head-neck mass multiplied by the head X acceleration), and shoulder belt tension. This similarity indicates consistency between the NIOI and critical damping models. The critically damped model reduced both the peak percent error in T3 X displacement (-0.4% from -5.7%) and the NRMSD (4.8% from 10.4%), as shown in Table 3.8. The average, optimized natural frequencies for the NIOI model was

29.9 ± 10.5 rad/sec, which encompassed the average ISM-obtained value of 21.1 rad/sec.

The average damping ratio (0.57 ± 0.45) was considerably higher than the ISM-obtained average of 0.12 and varied widely. This is attributed to the possibility that the viscous component of the response overtakes the elastic portion as the viscous organs within the ribcage are recruited during the sled event. It should be noted the T3 velocities (Figure

112 3.27) experienced in sled testing were well within the range of the velocities employed in

ISM testing. The ratio of average NIOI model to ISM natural frequency (1.36) was found to be roughly the reciprocal of the ratio of optimized to experimentally measured peak external force (0.71) (Table 3.8). The differences between the sled model properties and ISM characteristics indicate the nonlinearity of the UTS-PG system in response to a higher energy, more sustained input than in the ISM tests as well as the lack of other degrees of freedom in the models.

Another cause of these discrepancies in damping ratio could be the angular momentum of the head and neck moving forward during the sled test, which results in time-based variation in the effective mass of the head and neck for the experimental impulse calculation. The models assume that the sternum does not move (a reaction surface), but in fact the anterior portion of the ribcage does have mass and does move as the belt stretches. This can be observed by comparing the measured belt tension with the calculated belt force using the ISM properties and T3 displacement/velocity (Figure

3.32). There are slight differences between the curves than can be attributed to the boundary condition assumption for the sternum. In ISM testing, the stroke of the coupled head and neck was controlled and rigid body mechanics could be employed to calculate the forces at T1. In the sled test, calculation of T1 loading is more difficult as the cervicothoracic junction is not a discontinuous point because the neck stretches. The effective mass of the head and neck changes with time, especially late in the event when the neck elongates and the head rotates. However, given that the T6 force is measured directly, as well as the belt tension, a reasonable estimate of T1 shear force is more feasible than if those vertebral column forces are not measured.

113 SBFX(Model) = c +kxT3

Figure 3.32. Modeled vs. measured shoulder belt force

3.4.4. Effect of Cervical Spine Injuries

The major injuries occurred in the lower cervical spine. It is likely that increasing levels of subluxation were present with additional testing, but this was difficult to tell from palpation and range of motion check between tests. As shown in Figure 3.30, there was a noticeable change in relative head/T1 rotation from test 423-4 to 423-5 as well as from test 521-5 to 521-6. Because the C7-T1 joint remained intact, it is believed that none of the cervical spine injuries significantly altered the T3 kinematics. The lower cervical spine injuries were consistent with both Lopez-Valdes et al (2010) and

Michaelson et al. (2008), where C4 – C6 facet joint dislocations were observed. These injuries indicate that the input severity range was sufficient for simulating sled tests where the occupant (ATD or PMHS) is uncoupled from the sled. On the other hand, because of these injuries, less focus was put on head kinematics in this study than would have been preferred.

114 3.4.5. Relative Influence of Shoulder and Manubrium

Removing the manubrium constraint had a much larger effect on the UTS-PG properties than did removing the shoulder constraints (Table 3.5). The LS/RS Fixed condition where the manubrium was free resulted in 30 – 35% of the effective stiffness for the MNB/LS/RS Fixed condition. This illustrates the importance of restraining the sternum with the shoulder belt in frontal crashes; the flexion of the thoracic spine is reduced when the belt is appropriately positioned on the occupant. It is important to replicate the relative contribution of the manubrium and shoulders in an ATD to assure that the thoracic spine is integrated with those structures in a humanlike manner.

3.4.6. Limitations

In order to stably hold the mid-thoracic spine to the sled, it was necessary to use three toggle bolts. This arrangement required the drilling of 3/8” holes through the vertebral bodies at T6, T7, and T8. Obviously, this compromised not only the strength of the bodies but also disrupted the anterior/posterior longitudinal ligaments. However, the ligamentum flavum at each level was maintained, as were the interspinous and intertransverse ligaments. The ALL/PLL and musculature were kept intact beginning with T6 and moving superior. Limited importance was given to head kinematics given the C5/C6 fractures that occurred at higher speeds.

A more comprehensive approach of determining the input acceleration at T3 is required to fully validate that the ISM properties provide a predictive link to crash-level spine kinematics. The coupled effects of rotation and axial stretch within the T1-T6

115 segment contribute to the forward displacement, especially later in the event. However, despite this simplification, a single degree of freedom model provided a reasonable approximation of T3 displacement given a posterior thoracic input.

The statistical analysis of this study is too limited to make firm conclusions on the effect of test conditions (anthropometry, speed, and restraint) on spine kinematics, but there appears to be some consistency between previous analysis of ISM dynamic properties and sled-induced PMHS kinematics.

3.4.7. Applicability of the Methods & Data

The primary purpose of using the sled was not necessarily to simulate a belted occupant sled test, but rather to apply larger displacement flexion to the thoracic spine at energies approaching crash levels. While the applied pulses (5 – 10 G) were considerably lower than typical regulatory/research type sled tests (15 – 25 G), recall that all motions are relative to the mid-thoracic spine, not relative to the ground. Coupling the spine to the sled minimized the chances of rib fractures confounding the spinal motion, and the setup was more controllable and repeatable than a typical PMHS sled test, allowing the measurement of forces/moments so that this setup could potentially be adapted to a biofidelity or certification test for upper thorax ATD components. Finally, it was desired to maintain consistency with the ISM setup, so that the ISM properties could be properly validated.

This study provides detailed relationships between T1-T6 mechanical properties and resulting kinematics at speeds reflective of standard sled tests. Criteria for the mass,

116 stiffness, and damping of an adult ATD thoracic spine component are presented, along with the effects of anthropometry, constraint, and speed. The information can be used also to determine how to integrate the shoulders, ribcage, and thoracic spine into an ATD upper thorax so that these structures work in conjunction with one another to transfer restraint loads to the head and neck.

Another possible use of this data is a method to calculate T1 loads in a PMHS sled test for quantifying neck properties and evaluating biofidelity of ATD lower neck load cell measurements. Perhaps the findings from this study can be used to corroborate the cervicothoracic loads reported by Pintar et al (2010) in an effort to validate the upper thoracic spine response targets for ATD or finite element development. Using the calculated T1 X force in the UTS-PG analysis along with the head mass and head X acceleration, the shear properties of the PMHS neck could conceivably be estimated, assuming that the head acts as a rigid body with respect to the neck. Inverse dynamics could be used to estimate the atlanto-occipital shear forces, and the relative head/T1 displacement is known, as 6-DOF motion is measured during the sled test.

The ISM test setup may be adaptable to volunteer tests in the future, assuming that the speeds/displacements are non-destructive and the skeletal attachments can be modified to externally restrict motion. It has the advantage of large amounts of data obtained from a single specimen. By quantifying the effects of anthropometry (affecting mass), speed (affecting damping), and restraint (affecting stiffness) on spinal trajectories and loads, this data could apply to existing child vs. adult kinematic studies to parametrically derive improved scaling techniques and eventually biomechanical response targets for large child ATDs.

117 3.5. Conclusions

 System dynamic properties of the UTS-PG are presented from ISM testing conducted on 9 adult PMHS. The mean X-axis natural frequency for a standard 3-pt belt scenario (MNB/RS fixed, 0.5 m/s) was 23.4 ± 5.1 rad/sec, while the mean damping ratio was 0.20 ± 0.15. The average effective stiffness (21.0 ± 11.5 kN/m) was relatively consistent with cardiopulmonary resuscitation results from the mid-sternum level conducted at comparable speeds.

 A novel technique is introduced to obtain thoracic spine curvatures, trajectories, displacements, and kinetic vs. kinematic data by coupling T6-T8 directly to the sled in a test environment approaching crash speeds. A series of 12 sled tests were conducted on 3 adult PMHS to assess the effects of anthropometry, speed, and restraint on thoracic spine kinematics and loading. This method of direct measurement of forces and moments along the vertebral skeleton could provide quantitative data for the calculation of cervicothoracic loads in intact PMHS sled tests.

 Increasing speed did increase head and spine displacements, but speed sensitivity was not significant, as the slopes of T6 force/moment vs. T3 displacement/rotation were quite constant in PMHS 8 when T6-T8 was subjected to increasing speeds (3.8 – 10.7 m/s). The linear viscoelastic behavior of the UTS-PG is consistent with previous viscoelastic assessments of the full thorax.

118  Anthropometry and mass only appeared to influence T1 X displacement, likely because the range of PMHS size and ISM dynamic properties was small.

 T6 load vs. T1/T3 displacement data were presented as preliminary response criteria for an ATD upper thoracic spine component under known belt loads applied anteriorly to the thoracic cage and shoulder.

 The presence of a restraint had a negligible effect on thoracic spine translational displacements and T6 force, but the presence of a shoulder belt did decrease head, T1, and T3 rotations as well as T6 Y moment. It is likely that a more realistic anterior chest boundary condition (without coupling T6-T8) would result in a more significant difference due to the restraint.

 A UTS-PG mechanical model using ISM properties from the same PMHS, T6-T8 forces, and sled input acceleration was used to predict T3 forward displacements. Over the duration of 150 ms, the ISM model-predicted displacement matched the experimental displacement reasonably well using two models, considering only a single degree of freedom system was used in each case. Discrepancies between model-predicted and experimentally measured X motion could be attributed to the coupled effects of Z displacement (10 – 20 mm) and Y rotation (10 – 24 degrees of flexion) observed at the

T3 location. These coupled effects appeared as increased damping ratio in the optimized models (both critical damping and NIOI models) with respect to the ISM-developed properties. The natural frequencies of the ISM-derived and optimized NIOI model were

119 relatively consistent (21.1 rad/sec vs. 29.9 ± 10.5 rad/sec). The critically damped model

(NRMSD = 4.8%) provided a better fit to the T3 experimental displacement than did the

NIOI model (NRMSD = 10.4%).

120

Chapter 4 . Age-Dependent Anthropometry and Kinematics for Translating

Adult Upper Thoracic Spine – Pectoral Girdle (UTS-PG) Data to the Large

Child Population

4.1. Introduction

The dynamic response of the pediatric thoracic spine is not well understood, and this lack of understanding results in significant challenges for designing a child-sized

ATD. This is mainly due to the paucity of pediatric tissue for biomechanical studies, but this lack of information is also due to the large variation in development in the pediatric population. Children change so rapidly that it makes it difficult to converge on a response requirement for a particular age or size. Developmental differences have been observed in vertebral ossification, spinal ligament composition, muscular girth, and spinal injury levels.

The structure and composition of spinal tissue is much different in young people than in older people. Pediatric ligaments have been shown to have a less dense collagen network, which also provides more mobility and less resistance to motion [Barros et al.

2002]. Osakabe et al. (2001) found that the mineral components of lumbar spine ligaments increase with age, while the matrix components (elastin and collagen) decrease with age for the age range 21 to 76. While the mineral and elastic content increases

121 during skeletal maturation, the collagen content increases in density during adolescence.

Therefore, collagen is the primary microstructural factor in ligaments that changes during adolescence. A number of studies have shown that this shift in composition results in changes in ligament failure strength and stiffness [Takahiro et al. 2002; Ivancic et al.

2007; Nuckley et al. 2005].

Pediatric bone tissue is less ossified than older bone, and therefore also more ductile than adult bone [Kumaresan et al. 1997; Luck et al. 2008; Nuckley et al. 2004;

Nuckley et al. 2006; Yoganandan et al. 2000]. The disk space between vertebrae decreases with age, and the orientation of the vertebrae change with age as well. These differences appear to affect the location of spine injuries moving from C1-C2 in infants, to C5-C6 in young children, to C7-T1 in older children, and finally to the thoracic and even lumbar vertebrae in adults [Reddy et al. 2003; Bilston et al. 2007; Birney et al.

1989; Hadley et al. 1988; Hill et al. 1984; Fesmire et al. 1989]. In addition to underdeveloped vertebral bone leading to differences in spine injury location, weaker musculature, a larger relative head mass, and less spinal curvature have also been shown to affect response in younger specimens [Bohn et al. 1990; Dickman et al. 1989; Oi et al.

2004].

Studies have included a variety of methods to measure age-dependent spine range of motion and curvature [Arbogast et al. 2007; Greaves et al. 2007; O‟Gorman et al.

1987; Sforza et al. 2002; Willems et al. 1996]. These studies showed that static range of motion decreases with age, the helical axis of motion is more anterior in flexion- extension in younger subjects due to relative head mass and less spinal curvature, axial rotation and lateral flexion of the thoracic spine are strongly coupled, and thoracic

122 kyphosis increases significantly with age. These age-related variations in geometry, mass distribution, and range of motion have been discussed as factors contributing to differences in injury patterns and also dynamic response.

Very few studies have been done on full-body, pediatric post-mortem specimens at crash speeds. A review of the literature shows that only 11 pediatric post-mortem human subjects (PMHS) have been tested in vehicle restraint conditions [Kallieris et al.

1976, 1978; Brun-Cassan et al. 1993; Dejeammes et al. 1984; Wismans et al. 1979;

Mattern et al. 2002]. Because of ethical concerns about full-scale evaluations of pediatric cadaver response, four typical approaches are taken: (1) animal surrogate testing, (2) pediatric tissue studies, (3) scaling using known mass and length relationships with age, and (4) low speed volunteer studies.

A number of research studies have included animal surrogate testing to develop spine response criteria for child anthropometric test devices (ATDs). Several dynamic studies have been done with anesthetized animal surrogates to examine the response of the neck and spine. These studies conducted on caprine and baboon specimens have demonstrated increased tensile/compressive stiffness and failure load with increasing developmental age [Clarke et al. 2007; Ching et al. 2001; Nuckley et al. 2006; Nuckley et al. 2004; Pintar et al. 2000].

Recently, there have been studies that have investigated human pediatric spine tissue. Luck et al. (2008) showed that the tensile properties of the human osteoligamentous pediatric spine were consistent with other studies using developmentally-matched animal surrogates. Ouyang et al. (2005) conducted quasistatic testing of pediatric cadaver specimens from donors age 2 – 12 years and found that the

123 rotational stiffness of the skull-C2 motion segment was 10 times that of the C2-T2 motion segment. The ultimate distraction force for specimens in the 2 – 4 age group was significantly lower than that for specimens aged 6 – 12.

Two approaches are typically used for scaling adult responses to child response.

Mertz et al. (1989) and Eppinger et al. (1984) proposed methodologies using some combination of mass, length, and stiffness scale factors to develop ATD segments, injury tolerance, and response criteria. More recently, Lopez-Valdes et al. (2011) proposed an energy-based approach that utilized relative mass, belt tension, and trajectory/path lengths of a given anatomic structure. While this approach improved upon the predictions provided by earlier methods, it still did not fully predict the pediatric spine response of volunteers at low speed.

Two recent approaches for developing spine or upper thorax biofidelity criteria have been introduced recently. Arbogast et al. (2009) used a low speed pulse developed from bumper car impacts at amusement parks to compare the response of adult and pediatric volunteers. This study showed distinctive differences in spinal displacement and rotation with age. Maltese et al. (2010) examined cardiopulmonary resuscitation force vs. displacement data on patients of all ages to characterize the stiffness and damping properties of the thorax. These studies exemplify the need to develop novel techniques for obtaining intact pediatric data for direct comparison with adult information.

In summary, these studies emphasize the absence of crash-level pediatric human thoracic spine data, gaps in anatomic and kinematic comparisons of children vs. adults, and shifts in spinal injury location due to a combination of factors including kyphosis,

124 range of motion, soft tissue viscoelasticity, and size. The consensus throughout all of these studies is that age 6 – 12 seems to be the transition range between pediatric and adult spine behavior. The pediatric spine is more elastic, flexible, and less stable than the adult spine. A number of studies have attempted to devise age-based scaling approaches that use existing data to predict child response, but none of these approaches have been shown to accurately predict the motion of a child‟s spine. The first two phases of this study (Chapters 2 and 3) have defined thoracic spine dynamics of adult PMHS through novel experimental approaches in both bench-top (Isolated Segment Manipulation) and

HYGE sled (coupled mid-spine to measure input loads). The objectives of this study are build on that new data by (1) examining structural anatomy & developmental differences between the adult and child upper thoracic spine – pectoral girdle (UTS-PG) mechanism using radiology, (2) quantifying real world and experimental kinematic differences between adults and children, and (3) using distributed parameter analytical techniques to estimate adult UTS-PG elastic modulus, and (4) applying this methodology to determine whether kinematic differences between large children and adults from real world observations are reflected using large child-based parameters in the UTS-PG model.

125 4.2. Methods

Four steps were taken in this study in an effort to derive a methodology to estimate large child upper thoracic spine – pectoral girdle (UTS-PG) dynamic properties:

(1) Quantify geometry and mass of large (10 year old) child and adult specimens

using radiological/anthropometry information from both pediatric patients and

adult PMHS.

(2) Estimate real-world differences in head displacements for adults and children

using geometric calculations from NASS-CDS crash cases.

(3) Employ distributed parameter analysis to estimate the elastic modulus of the

adult UTS-PG using results from (1) combined with adult ISM/sled data.

(4) Estimate the characteristics of a large child UTS-PG model using information

from steps (1) – (3).

To develop structural anatomy relationships between the UTS-PG of adults and children, relative skeletal landmarks from both adult (PMHS tested experimentally with

ISM and sled) and child (patient data from Nationwide Children‟s Hospital) radiology data were measured. To compare head kinematic relationships between children and adults, experimental sled tests with child and adult occupants (both volunteers and

PMHS) were surveyed from the literature and previous sled tests conducted in the current study. In addition, head displacements in 71 actual crashes were estimated by calculating occupant available space (OAS) in the rear seat from National Automotive Sampling

126 System – Crashworthiness Data System (NASS-CDS) case information. Using the presence of head/face contact with the front row seat back as a threshold, head displacements were greater than/equal to (right-censored) or less than (left-censored) the calculated OAS. This data was used as a real world supportive comparison of the experimental head displacements. The anthropometric and kinematic data from this study, along with ISM dynamic properties, were used to estimate the adult UTS-PG elastic modulus and properties for a large child UTS-PG.

4.2.1. Structural Anatomy

Nine adult PMHS were tested in Isolated Segment Manipulation experiments to derive system dynamic properties of the upper thoracic spine-pectoral girdle (UTS-PG) mechanism (see Chapters 2 and 3). In addition to radiological data from those specimens, pediatric radiology data2 was collected for 39 patients age 4 – 15 from

Nationwide Children‟s Hospital (Columbus, OH). Measurements were taken on the total of 48 human specimens lying in the supine position using Osirix imaging software

(Figure 4.1 and Table 4.1). The error associated with a given measurement was dictated by resolution of the image, orientation of the structure, and human repeatability. The average error for a given measurement was typically 2 – 5% of the magnitude in both adult PMHS and pediatric patient data, when accounting for these three sources.

2 Institutional Review Board (IRB) approval was obtained from Nationwide Children‟s Hospital (Columbus, OH) to use anonymized thorax radiology data from pediatric patients age 4 – 15.

127 cT1, cT6

bT1, bT6

θ1

θ 5 θ 3

θ 2 f

ep ea

θ 4 θ 6

Figure 4.1. Measurements taken from adult PMHS and pediatric patient radiology

128 Table 4.1. List of skeletal measurements from radiology

Symbol Description

a Depth of sternal notch to anterior body T1 (transverse plane)

bT1 Width of T1 vertebra (between transverse process ends)

bT6 Width of T6 vertebra (between transverse process ends)

cT1 Depth of T1 vertebra (anterior body to spinous process end)

cT6 Depth of T6 vertebra (anterior body to spinous process end)

d Clavicle length

ep Height of T1-T6 vertebral column (posterior between spinous processes) Height of T1-T6 vertebral column (anterior: top of T1 body to bottom of e a T6 body) f Superior-inferior distance from T1 body top to sternal notch

g Sum of T1 – T6 vertebral heights

h = g / ea Skeletal fraction of T1-T6 height (h – g is sum of intervertebral spaces) θ 1 Clavicle angle

θ 2 Manubrium angle

θ 3 Rib 1 angle in sagittal plane (middle third of anterior-posterior length)

θ 4 Rib 6 angle in sagittal plane (middle third of anterior-posterior length)

θ5 T1 vertebral body angle (sagittal plane, mid-anterior body to spinous process) θ6 T6 vertebral body angle (sagittal plane, mid-anterior body to spinous process) θ = θ – θ 7 5 6 Relative T1/T6 angle

129 Table 4.2 summarizes the anthropometry information from the 48 specimens.

Table 4.2. Subject anthropometry

The radiological measurements were combined and statistically analyzed for correlations with age. Mean anthropometry values were obtained for a 10 year old and adult PMHS to obtain scale values for the geometry of the UTS-PG.

130 4.2.2. Head Kinematics: Child vs. Adult

Due to the paucity of experimental data on pediatric subjects, head displacements for rear-seated, lap/shoulder belted occupants in frontal impacts (11 to 1 o‟clock PDOF) contained in the NASS-CDS database were estimated using available data from the given case. If consistency is observed between real-world crash estimates and experimental data in the literature for adults vs. children, the head displacement vs. age relationship can be used to help estimate 10 year old UTS-PG properties. It was hypothesized that if the available space between the occupant‟s head and the seatback in front were calculated for each case where the occupant‟s head or face made contact with the seatback, then the occupant‟s head displacement could be said to have been at least as much as the available space. This available space would then serve as a “right-censored” surrogate measure for the occupant‟s head displacement in the crash. To offset the conservative surrogate value for head displacement, occupants in those same cases who were restrained the same way

(lap/shoulder belt) in the rear seat, but who did not experience head/face contact with the seatback in front, were also included as “left-censored” data. Given that the impact speed, occupant characteristics (age, height, and weight), and vehicle compartment geometry were reported in each such case, relationships could be derived from this data to estimate variations in head displacement with age, size, and delta V. The occupant available space (OAS) was calculated as shown in Figure 4.2.

131

OAS = X1 ± X2 + X3 – X4 If Head/Face Contact with X4 = HeadCG OAS = Occupant Seatback, then Head to Seatback Available Space Displacement ≥ OAS If No Head/Face Contact with Seatback, then Head Displacement < OAS

X2 = Documented Seat +X2 -X2 Track Position X3 = Hip Point to Head CG (from X1 = SAE Dimension for Vehicle Model Reed 2005) (SAE J1100: Vehicle Dimensions)

Figure 4.2. Calculation of occupant available space (OAS) in NASS-CDS cases

A total of 71 occupants were included in the overall NASS-CDS sample, with the criteria for inclusion being that (a) a head/face injury due to front seat back contact occurred for at least one of the rear seated occupants in the vehicle, (b) the occupant was coded as being restrained in lap/shoulder belt with no misuse in the rear seat, (c) the crash principal direction of force (PDOF) was frontal (between 11 and 1 o‟clock), (d) the vehicle make/model was included in the NHTSA database of SAE dimensions, and (e) all relevant vehicle and occupant characteristics were reported in the NASS-CDS case documentation. The “X1” dimension is the L50 horizontal distance from front seat H- point to rear seat H-point, as described in SAE J1100: Vehicle Dimensions. This measurement was found in the NHTSA database for each of the case vehicles. The “X2” dimension is a case-specific portion of the L17 front seat track travel dimension in SAE

132 J1100. The NASS-CDS case documentation specified the position of the front seat during the crash event as forward, forward-mid, mid, rear-mid, and rear. For example, if

L17 is 200 mm and the documented track location in the case is forward, the X2 value would be +100 mm. If the position is rear for the same L17 value, the X2 value would be

-100 mm. A mid position gives X2 = 0 because L50 is based upon the mid position of the front seat track. All included cases had reported non-adjustable rear seats, so no adjustment on its position was necessary. The “X3” dimension is based on a survey of seated postures made by Reed et al. (2005). The algorithm for the rearward horizontal distance of the head CG relative to the H-point is

X3 = -890+0.0807*(Height)+1356*(Erect Seated Height/Standing

Height)+7.31*(Seatback Angle) (4.1)

The erect seated height was not reported for the NASS-CDS occupants. A study by Snyder et al. (1977) examined anthropometry of seated occupants and derived a relationship between standing height and erect seated height, given the occupant age.

The mean ratio of erect seated height to standing height was used along with the occupant‟s age for the case to estimate the erect seated height for the NASS-CDS occupants. For simplicity, the seatback angle was set constant to be 25 degrees. Finally, for the “X4” dimension of horizontal distance from head CG to back of seat, the x component was calculated from the triangle formed by the UMTRI-estimated erect seated height for the occupant (y component), seatback horizontal width (also set constant at

152.4 mm or 6 inches), and 25 degree seatback angle:

133 X4 = =-(Erect Seated Height*tan(Seatback Angle))+0.5*Seatback Horizontal

Width*cos(Seatback Angle) (4.2)

The occupant available space calculation is shown in Appendix L, along with vehicle & crash information, occupant age, deltaV, occupant height, occupant weight, and occupant body mass index (BMI) for all 71 cases.

4.2.3. Estimation of 10 Year Old UTS-PG Mechanical Properties

Adult upper thoracic spine – pectoral girdle (UTS-PG) dynamic properties were determined using Isolated Segment Manipulation in three individual sagittal plane axes

(X, Z, rotation), as described in Chapters 2 and 3. Subsequently, these properties were shown to provide a reasonable approximation of T3 displacement in the higher energy application of sled testing. However, there was some rotation (10 – 24 degrees of flexion) and Z (longitudinal) axis displacement (10 – 20 mm) over the span of 15 – 60 mm of forward displacement. It is likely that the error in predicted vs. measurement thoracic spine displacements is due to the absence of the coupled longitudinal and rotational degrees of freedom. In addition, for estimating child UTS-PG properties, the full set of system response parameters should be considered.

A more accurate model of the UTS-PG structure can be constructed using three steps: (1) distributed parameter model construction using a lumped mass/fixed cantilever beam to derive eigenvalues of the adult UTS-PG, (2) employing those eigenvalues with

ISM natural frequency and anthropometry/mass information to obtain a range of effective

134 elastic modulus values for the adult UTS-PG, and (3) discussing a process to extend this method to estimate large child dynamic properties by applying scale factors from anthropometric and kinematic assessments from this study, adult UTS-PG data, and literature information on material properties.

4.2.3.1. Distributed Parameter Model for Small Displacements/Negligible Damping

An appropriate representation of the UTS-PG is a uniform (ρo(z) = ρo, EI(z) = EI) cantilever beam that is fixed on one end (at T6-T8) and has a lumped mass on the other end (head and neck at T1) as shown in Figure 4.3:

Mhead+neck

u(z,t)

X ρo, E, I

Figure 4.3. Distributed parameter representation of UTS-PG

135 Because the input to the model is in the X-direction in both the sled and ISM configurations, we will develop the characteristic equation for the UTS-PG as a beam in transverse bending. The differential equation for such a system is

4 d U(z) 4 4 ω2 m -β U z =0, 0 < z < L, β = (4.3) d 4 EI

The boundary conditions at T6 (z=0) and T1 (z=L) are

dU(z) U(z) = 0, = 0 z = 0 (4.4a) dz

2 3 dU (z) d U(z) 4 = 0, - β U z =0 z = L (4.4b) dz2 dz3

Assuming a solution of the form

U(z) = Asinβz + Bcosβz + Csinhβz + Dcoshβz (4.5)

Then enforcing the boundary conditions above to solve for the coefficients, the characteristic equation (z=L) is found to be:

136 β β β – β β β β β β

β β β β β β β β β

(4.6)

This is a transcendental equation and therefore must be solved numerically for the eigenvalues, which occur at the intersection of the right and left sides of the equation manipulated as follows:

β β β β β β β β β β β β β β β β β

For x = L. Simplifying through algebraic manipulation:

β β β β β β β

(4.7)

The natural frequencies are then

ω β (4.8)

The corresponding natural mode shapes are

137

β β Ur (z) = β β β β (4.9) β β

We then insert appropriate values of m, M, and L into the characteristic equations to determine the natural frequencies and natural mode shapes. The next step is to rearrange the natural frequency equation and solve for E:

(4.10)

(4.11)

A range of elastic modulus values can be determined by substituting ISM natural frequency, eigenvalue, and geometric/mass parameters for the system. The area moment of inertia and area were calculated by orienting the cross-sectional area of the vertebral bodies from the radiology data and quantifying the surface using ImageJ software.

The final step was to incorporate scale factors for anthropometry, mass, and elastic modulus (from a literature survey) of a large child into the beam transverse displacement natural mode equation (4.9) and determine whether the height-normalized displacement expected for a large child reflects the same increase in stature-normalized head displacement determined in the head kinematic comparison described in section

4.2.2.

138 4.3. Results

4.3.1. Structural Anatomy (Children vs. Adults)

Figures 4.4 through 4.11 show the thoracic spine and pectoral dimensional measurements with respect to specimen age, with mean values for the adult PMHS (n=9) and 10 year old noted on each plot. The mean age of the 39 pediatric data points was 9.9.

Table 4.3 summarizes the mean and standard deviations of the geometric parameters for each age range. Table 4.4 provides a correlation analysis of the respective variables.

Appendix N contains plots for all parameters with respect to age.

Figure 4.4. Overall height

139

Figure 4.5. Clavicle length

Age (years)

Figure 4.6. T1 depth in transverse plane

140 Age (years)

Figure 4.7. T1 width in transverse plane

Age (years)

Figure 4.8. T6 depth in transverse plane

141 Age (years)

Figure 4.9. T6 width in transverse plane

Age (years)

Figure 4.10. T1-T6 anterior height in transverse plane

142 Age (years)

Figure 4.11. T1-T6 posterior height

143

Table 4.3. Summary of UTS-PG skeletal measurements

Pediatric Patients Adult PMHS 10YO/Adult Parameter (n=39) (n=9) Avg Std Dev Avg Std Dev Ratio Age (years) 9.9 3.4 78.3 8.7 0.13

Mass (kg) 41.0 21.5 67.3 12.0 0.61

Overall Height (cm) 140.9 23.5 166.4 8.4 0.85

Clavicle Length (cm) 11.1 1.8 14.8 1.6 0.75

Clavicle Angle (deg) 44.4 7.5 30.0 5.0 1.48

Sternal Angle (deg) 60.7 8.1 73.0 7.8 0.83

Rib 1 Angle (deg) 28.0 8.4 40.0 10.5 0.70

Rib 6 Angle (deg) 30.0 8.3 40.4 10.3 0.74

Sternal Notch-T1 Depth (cm) 3.7 0.8 2.9 0.8 1.27

Sternal Notch-T1 Height (cm) 2.4 1.1 3.2 1.1 0.75

T1 Vertebral Body Angle (deg) 8.7 4.5 13.1 5.5 0.67

T6 Vertebral Body Angle (deg) -15.8 6.8 -15.4 5.4 1.03*

T1-T6 Vertebral Body Angle (deg) 24.6 7.2 28.5 7.9 0.86*

T1-T6 Posterior Height (cm) 9.8 1.8 12.5 0.7 0.78

T1-T6 Anterior Height (cm) 9.1 1.7 11.6 0.9 0.78

T1 Vertebral Body Depth (cm) 5.2 0.8 6.4 0.7 0.81

T1 Vertebral Body Width (cm) 6.1 1.0 7.9 0.4 0.77

T6 Vertebral Body Depth (cm) 5.2 0.8 6.0 0.4 0.87

T6 Vertebral Body Width (cm) 5.2 0.9 6.8 0.7 0.75

Skeletal Fraction 0.82 0.05 0.92 0.02 0.89

T1-T6 Anterior Body Depth (cm) 1.8 0.6 4.4 1.2 0.41 *Indicates that pediatric and adult PMHS sets are NOT significantly different (p>0.05, Students t-test)

144

Table 4.4. Correlation coefficients for UTS-PG skeletal measurements (n = 48)

145 4.3.2. Head Kinematics (Children vs. Adults)

Figure 4.12 compares the OAS calculations of head displacement for children age

6 – 13 and adults. For the 71 cases evaluated in all, the child occupants tended to exhibit larger head displacements with respect to their documented stature.

0.70 NASS Contact (Age > 13) 0.60 NASS Non-Contact (Age > 13) NASS Contact (Age 6-13) NASS Non-Contact (Age 6-13) 0.50

0.40

0.30 OAS/Ht

0.20

0.10

0.00 0 10 20 30 40 50 60 DV Total (km/hr)

Figure 4.12. Calculated head displacement using OAS

Figures 4.13 and 4.14 compare OAS calculations of head displacement with literature values of experimental head displacements (see Appendix M for derivation of experimental data statistics and regression curves). These plots indicate consistency for the relative age groups.

146 Fit on Volunteer & PMHS Only with Comparison to NASS Estimates

0.70 y = 0.0359Ln(x) + 0.1588 2 0.60 R = 0.8112

0.50

0.40

0.30

Displacement / Displacement Ht 0.20 Volunteer/PMHS (Age 6-13) 0.10 NASS Contact (Age 6-13) Available Space (NASS) or Head or Head Available (NASS) Space NASS Non-Contact (Age 6-13) Log. (Volunteer/PMHS (Age 6-13)) 0.00 0 10 20 30 40 50 60 DV Total (km/hr)

Figure 4.13. Experimental statistical model vs. NASS-CDS head displacement estimates (Age 6-13)

Fit on Volunteer & PMHS Only with Comparison to NASS Estimates

0.70 Volunteer/PMHS (Age > 13) 0.60 NASS Contact (Age > 13) NASS Non-Contact (Age > 13) Log. (Volunteer/PMHS (Age > 13)) 0.50

0.40

0.30

0.20

Displacement / Displacement Ht 0.10 y = 0.0261Ln(x) + 0.1046 R2 = 0.7954 0.00 Available Space (NASS) or Head or Head Available (NASS) Space 0 10 20 30 40 50 60 DV Total (km/hr)

Figure 4.14. Experimental statistical model vs. NASS-CDS head displacement estimates (Age > 13)

147 When the ratio of experimental regression fits for a 10 year old child to adult is taken, the average ratio over the entire range of deltaV is 1.457. That is, for any deltaV, a child in the 6-13 age range (mean 9.5 yrs) would have 1.457 times the normalized head displacement as an adult:

 Head, normalized (10YO) 1.457  Head, normalized (adult) (4.35)

Given the uncertainty due to the censored nature of the NASS-CDS head displacement estimates, it was decided to (a) first develop statistical models using experimental data and (b) second, qualitatively confirm that the experimentally-based statistical models are representative of the child vs. adult estimated head displacements from actual crashes. Figures 4.16 – 4.17 show that the experimental head displacement models of children and adults follow the lower edge of their respective estimated NASS-

CDS data distributions. Both the mean and standard deviation of normalized head displacement for the child (age 6-13) group were larger than those same statistical measures for the adult (age > 13) group. It makes sense that there would be more variation in the child age group, given that the lap/shoulder restraint is typically designed for the adult population and the variability in restraint/occupant interaction during the crash would be greater. The higher mean NASS-CDS data for children versus adults is consistent with the higher experimental values.

148 4.3.3. Estimation of Adult UTS-PG Elastic Modulus

The uncoupled ISM properties (all speeds + all constraints) obtained in each axis from Chapters 2 and 3 are summarized in Table 4.5 and Appendix J.

Table 4.5. Uncoupled ISM properties (mean values) from UTS-PG testing

Effective Natural Mass/Mass Damping Ratio Axis Effective Stiffness Frequency Moment of (zeta) (rad/s) Inertia

X 63.0 kg 28,381 N/m 21.7 0.23

Z 92.4 kg 82,924 N/m 30.8 0.40

θ 0.825 kg-m2 500 Nm/deg 31.7 0.54

Table 4.6 summarizes the mean values for adult and 10 year old child from radiology data.

Table 4.6. Scale factors from radiology data

Parameter Adult 10 year old Scale Factor

Length 12.1 cm 9.45 cm 0.78

Mass 67.3 kg 41.0 kg 0.61

-7 4 -7 4 Area Moment of Inertia 5.63 x 10 m 2.35 x 10 m 0.417

2 2 Area 0.00177 m 0.00115 m 0.646

149 Eigenvalues for the distributed parameter system were found as shown in Figure

4.15 using mL = meff (from ISM) and M = mheadneck (from post-test dissection). The first mode eigenvalue was βL = 1.665.

Figure 4.15. Eigenvalue solution for lumped mass/fixed distributed parameter model

Next, the elastic modulus was calculated as a function of natural frequency

(Figure 4.16) using the eigenvalue and geometric/mass factors from Table 4.6. The range of elastic modulus was found to be 7.5 – 16.5 MPa for the natural frequency range of

21.7 – 31.7 rad/sec obtained from ISM testing (from Table 4.5).

150

Figure 4.16. Adult UTS-PG elastic modulus vs. ISM natural frequency range

In both bone bending and spinal ligament axial studies in the literature (Currey et al. 1980; Yoganandan et al. 2001; Ching et al. 2001; Luck et al. 2008), the elastic modulus and/or tensile stiffness of a 10 year old averages to roughly 75% that of an adult.

When a scale factor of 0.75 is applied to the mean adult UTS-PG elastic modulus

(0.75*12 MPa=9 MPa), along with scaled head-neck mass (large child/small female head is about 85% of adult per Yoganandan et al. 2009), and properties from Table 4.6, the large child eigenvalue was calculated to be βL = 1.605. Per equation (4.9), the normal modes for both adult and child were calculated and compared in Figure 4.17 as surrogates for forward displacement normalized by height of the UTS-PG.

151

Figure 4.17. Natural modes of adult and child UTS-PG

Table 4.7 shows that the difference in UTS-PG height-normalized displacement for a large child and adult for T1 (0.095 m), T3 (1/2 large child height = 0.0475 m), and average over the full large child height from 0 – 0.095 m closely approximates the 1.457 ratio calculated from the head kinematics analysis.

Table 4.7. Summary of large child and adult UTS-PG distributed model parameters

Displacement normalized by height of UTS-PG

m m E ω Avg over Model HN βL nat A T1 T3 (kg) (kg/m) (MPa) (rad/s) Height

Adult 6 331 12 1.665 27.1 0.45 0.696 0.214 0.273 Large Child 5.1 253 9 1.605 26.1 0.48 1.000 0.326 0.404 LC/A Ratio 0.85 0.76 0.75 0.96 0.96 1.07 1.436 1.526 1.50 OAS/Kinematics: 1.457

152 4.4. Discussion

This study presents steps for scaling adult UTS-PG data to the 10 year old child.

Radiology of both pediatric patients and adult PMHS were evaluated to derive geometry and mass scale factors. Crash data and experimental data from the literature were examined to derive a scale factor for normalized displacement. Finally, distributed parameter analysis was used to estimate the effective elastic modulus for the adult UTS-

PG and evaluate differences between adult and large child UTS-PG displacements.

4.4.1. Anthropometry & Anatomy

A strong correlation was found between age and height (Table 4.4), indicating that the pediatric dataset is representative of the population and not skewed by deformities or weight loss due to illness. Table 4.4 also shows that clavicle length is a better surrogate for thoracic spine development and size than age. O‟Gorman et al.

(1997) reported spine differences with age similar to those found in this study (Table

4.3), with increasing kyphosis and decreasing intervertebral space with age.

The cumulative error associated with manual human measurement is a limitation but is not expected to alter the age-related correlations significantly, as both the adult

PMHS and pediatric patient datasets were subjected to the same method and the images were obtained using the same scanning resolution. An automated, more reproducible technique that characterizes three-dimensional profiles [Reed et al. 2010] would be more precise.

153 4.4.2. Kinematics

The calculation of occupant available space (OAS) on a case by case basis provided a similar trend in normalized head displacement to that reported in experimental data from the literature. However, there were some limitations to this approach. Some assumptions were that pre-crash manuevers did not influence occupant position prior to impact, the case details had limited uncertainty, and the occupant was not misusing the restraint. In additon, an artificial (0,0) anchor point was applied to provide a third independent variable in the experimental data, and only a single high speed child cadaver test was included.

The age-dependent ratio of 1.457 for normalized head displacement data was assumed to be applicable to all anatomic body regions and therefore was applied to the thoracic spine displacements in the finite element analysis. It was assumed that all anatomic structures develop consistently in head and spine, and that any inconsistencies are minimized between a 10 year old and adult because primary ossification is generally completed by age 6 [Fesmire et al, 1989].

4.4.3. Adult UTS-PG Elastic Modulus Calculation

The approach of using a distributed parameter model to determine eigenvalues and calculating an elastic modulus range using the natural frequency mode equation, ISM properties, and adult UTS-PG geometric/mass information resulting in a realistic range of elastic modulus (7.5 – 16.5 MPa) as shown in Figure 4.16, which is mechanically

154 consistent with a polyurethane or rubber element. These materials are common in ATD designs. The effective mass, length, moment of inertia, and area values from the radiology information for the thoracic spine appeared to be appropriate, which is encouraging for the development of large child ATD properties.

4.4.4. A Methodology for Estimating 10 Year Old UTS-PG Properties

Scaling adult biomechanical data to a child has always been a challenge for ATD designers. Lopez-Valdes et al. (2011b) recently surveyed existing techniques and presented a new energy-based method that improved prediction accuracy for head and spine displacement but did not fully replicate the kinematics. To address the need for 10 year old UTS-PG properties, the distributed parameter model analysis used to obtain adult UTS-PG elastic modulus was deemed appropriate for this study as it lends itself to parametric evaluation of eigenvalues given displacement, geometric, and mass information.

Subject mass, length, and elastic moduli are historically the most common ways to scale adult data to a child for ATD component design purposes. In this study, the average mass ratio for 10 year old patient to adult PMHS was 0.61 based on full body mass. This is consistent with the 0.60 value obtained by Zanchetta et al. (1995). In both bone bending and spinal ligament axial studies in the literature, the elastic modulus and/or tensile stiffness of a 10 year old is roughly 75% that of an adult. Currey et al.

(1980) noted that femur bending modulus of elasticity increased from 116 GPa (age 10) to 153 GPa (age 50), which corresponds to a 76% ratio. For ligament stiffness,

155 Yoganandan et al. (2001) noted that the posterior longitudinal ligament stiffness of a 6 year old sheep spine was 89% of that of an adult sheep spine (17 N/mm vs. 19 N/mm).

Ching et al. (2001) evaluated maturing baboon C7-T1 functional spine units and noted that a 6-12 year old exhibited about 75% the tensile stiffness of an adult specimen (150

N/mm vs. 200 N/mm). Luck et al. (2008) noted that occipital condyle – C2 osteoligamentous spine stiffness of a 10 year old human specimen was approximately

70% that of an adult specimen (130 N/mm vs. 190 N/mm). They also noted good consistency of human data with earlier animal surrogate studies of spine tensile stiffness.

While actual displacements can be determined by applying external forces to the boundaries of the lumped mass/fixed cantilever beam using unconstrained modal analysis

(Meirovitch, 2001; Park et al. 2000; Ghaith et al. 2011), the difference between adult and large child UTS-PG normalized displacements (normal modes) by calculating eigenvalues and natural frequencies using ISM, anthropometric, and material property data presented in this study and elsewhere resulted in ratios closely approximating the

1.457 value observed in the head kinematics analysis (Figure 4.17 and Table 4.7). One limitation to this approach could be that an Euler-Bernoulli beam formula was assumed, which neglects the effects of rotary inertia and shear displacement. In the sled test, there is fairly substantial rotation of the head and neck, especially late in the event. Therefore, it may be more appropriate to use a Timoshenko beam with a larger thickness-to-length ratio to model the sled displacements so that the inertial/shear effects are included.

While improvements to large child ATD thoracic spine design could be realized by applying the adult UTS-PG data from both this and previous chapters directly, it is

156 encouraging that combining ISM natural frequencies with anthropometry/mass/material property scale factors results in spine kinematics consistent with real world observations.

It appears likely that further development of this methodology will result in viable response targets for a large child ATD in the future.

4.5. Conclusions

 Significant differences in thoracic spine and pectoral girdle anthropometry were

determined between adult and 10YO, and correlations between geometry and age

were found.

 Calculation of occupant available space (OAS) resulted in head displacement

estimates consistent with child vs. adult ratios observed in an experimental survey

of head displacement.

 Distributed parameter analysis incorporating ISM natural frequency along with

anthropometric/mass information for the UTS-PG, resulted in an estimated adult

UTS-PG elastic modulus in the range of 7.5 – 16.5 MPa.

 Application of the anthropometric and kinematic scale factors determined in this

study, along with age-dependent elastic modulus ratios found in the literature,

resulted in a large child UTS-PG distributed parameter model with normalized

forward displacements reflective of kinematic observations relative to those of

adult occupants.

157

Chapter 5 . Conclusions & Recommendations

This study provides a comprehensive assessment of the biomechanics of the upper thoracic spine and pectoral girdle, including investigations of anthropometry, system dynamics, and kinematics for both adult and child occupants. The following list summarizes the new technical contributions from this study:

(1) A novel experimental & analytical technique, Isolated Segment Manipulation, to

non-destructively and parametrically determine dynamic properties of an intact

biomechanical segment through iterative adjustment of boundary conditions.

(2) Dynamic properties for the upper thoracic spine – pectoral girdle (UTS-PG)

biomechanical system using ISM tests on nine adult post-mortem human subjects

(PMHS).

(3) An original method to couple a PMHS directly to the HYGE sled in order to

measure input loads to the thoracic spine while restricting motion below T8.

(4) Detailed human kinematic and kinetic data for the thoracic spine, shoulder, and head

from sled testing at crash-level speeds (3.8 – 7.0 m/s).

(5) Relative effects of anthropometry, rate, and constraint/restraint of the pectoral girdle

on adult UTS-PG dynamics.

158 (6) Optimized single-degree of freedom mechanical models to predict T3 forward

displacements given ISM dynamic properties, sled acceleration, and external loading

measured at T6, T1, and shoulder belt.

(7) Anthropometric data & statistical analyses of the UTS-PG for both adult and

pediatric patients.

(8) An approach for estimating head displacements in real crashes by calculating

occupant available space and noting whether head contact occurred for an occupant

of known age and size. It was found that this approach resulted in consistency with

experimentally measured head displacements of adults vs. children from the

literature.

(9) Estimation of the elastic modulus of the adult and large child UTS-PG for use in

distributed parameter or finite element models, using a methodology incorporating

ISM natural frequencies, anthropometry/mass information from radiology, and

kinematic scale factors from real world crash observations.

Applied together, it is hoped that these findings can lead to improved upper thoracic designs in both child and adult-sized future ATDs. The following outlines the next steps envisioned to accomplish this objective.

5.1. Biofidelity Test Method

The next step is to develop a laboratory test to check the ATD head, T1, and T6 displacements and rotations versus these estimated UTS-PG model criteria using the

159 finite element formulation for the 10 year old. For the low-to-medium speeds, a modified neck pendulum test seems appropriate. Given that the head displacement is a function of not only the neck properties, but also the combined shoulder and upper thorax response, it is proposed that the chest potentiometer adaptor plate be used as the interfacing attachment to the neck pendulum (Figure 5.1), with a load cell between the pendulum and the spine at T6-T8 level. Some type of a reaction surface that simulates a belt restraint input can be designed to provide a realistic interface for the shoulder and ribcage. The total head displacement is taken as the difference between the initial top of head position at initial contact with the simulated restraint and the maximum horizontal head displacement. Video analysis or application of 6-degree of freedom measurement with

3aω blocks can be used to measure the head, T1, and T3 displacement. Accelerometers on the sternum and spine would be useful for measuring simulated belt forces and chest compression. An IR-TRACC or chest potentiometer could also measure that compression.

160 Load cell @ T6-T8

Pendulum Foam simulating belt

Target Head Displacement

Figure 5.1. Modified pendulum test with simulated belt input (shoulders removed)

While many details would have to be worked out with a setup such as the one shown in Figure 5.1, it seems a setup such as this one would provide a platform for iterative design evaluations for the dummy. Once the dummy‟s design provides the necessary head and thoracic spine displacement behavior at the low-to-medium speed range, more comprehensive evaluations can then be done on the sled.

5.2. Response Corridor Development

The data generated in this research study resulted in force vs. displacement and moment vs. rotation criteria for the large child ATD thoracic spine, as well as head displacement criteria from both experimental literature and crash data estimates. The

161 steps below show suggested strategies for employing these findings to develop preliminary response targets for ATDs in the biofidelity test.

5.2.1. Head Displacement Criteria

In Appendix M, a statistical model for head displacement given the deltaV and occupant characteristics was derived. We can calculate the required horizontal head displacement using the statistical model with continuous age, deltaV, occupant height, and interaction term of the product of age and deltaV:

Log(Head Displacement / Height) = -1.38 - 0.0258*(Age) + 0.01056*(DeltaV) +

0.00083*((Age-19.2)*(DeltaV-12.4571))

For a large child or 10 year old sized ATD, we can input the theoretical age (10 years),

ATD height (1308 mm), and deltaV (25 km/hr) and calculate the requirement for head displacement:

Log(Head Displacement / Height) = -1.38 - 0.0258*(10 yrs) + 0.01056*(25 km/h) +

0.00083*((10-19.2)*(25-12.4571)))

Log(Head Displacement / Height) = -1.4698

Head Displacement / Height = exp(-1.4698) = 0.230

Head Displacement = (1308 mm) * 0.230 = 300.8 mm

162

When this same calculation is made for multiple deltaV values, we get the values shown in Table 5.1.

Table 5.1. Model-predicted head displacements required for a large child ATD

DeltaV Pendulum Drop DeltaV (m/s) Head Displacement (mm) (km/hr) Height (m) 5 1.39 0.098 283.7 10 2.78 0.393 287.9 15 4.17 0.885 292.1 20 5.56 1.573 296.4 25 6.94 2.458 300.8 30 8.33 3.539 305.2 35 9.72 4.818 309.7 40 11.11 6.292 314.3

5.2.2. Thoracic Spine Response Criteria

The primary objective and result of this research study was force vs. displacement dynamic response for the 10 year old upper thoracic spine – pectoral girdle mechanism.

The biofidelity test shown in Figure 5.1 reflects the Isolated Segment Manipulation and sled test setups used in this study to obtain human response data. It is adaptable to the conventional neck pendulum setup used by many laboratories to certify that ATDs meet

163 performance specifications before their use in crash and sled evaluations of automotive safety systems.

Because the 10 year old-sized UTS-PG dynamic properties are known and implemented into a finite element model, the model can be exercised with any number of applied pulses at T6-T8 to develop force vs. displacement corridors for the biofidelity test. The corridors can be changed slightly given the particular belt restraint configuration applied on the pendulum (i.e., manubrium and one shoulder).

5.3. Evaluating the UTS-PG of the Large Omni-Directional Child (LODC) ATD

A conceptual dummy has been developed at VRTC that is in the same size category as the Hybrid III 10 year old ATD. The large omni-directional child (LODC)

ATD (Figure 5.2) possesses thoracic anthropometry using data from real children seated in booster seats (Reed et al 2010). It also possesses a flexible, continuous thoracic and cervical spine structure that can be tuned to match available response corridors. Finally, the shoulder contains clavicle and scapular structures that mimic the human anatomy.

164

Figure 5.2. The large omni-directional child (LODC) and Hybrid III 10 year old ATD

Further development of the LODC thorax is an immediate, direct application of the results obtained from this research study.

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176

Appendix A: Head-Neck Assembly CG Location

Following each PMHS test series, the head and neck were transected from the rest of the body for locating the assembly center of gravity. This was necessary so that rigid body correction of the measured moment to the T1 location could be done, in addition to measuring the head-neck mass. On the anterior side just superior to the clavicle, the neck superficial tissue and muscles were dissected until the anterior vertebral column and rib 1 were visible. On the posterior side, the intervertebral space between T1 and T2 was found and the neck was dissected along the superior border of rib 1. The interface between the T1 transverse processes and rib 1 was found and distracted on both sides.

Then, on the anterior side, the T1-T2 intervertebral disc was cut and the facet joints were dislodged, resulting in complete separation of the head and neck.

With the head-neck coupled plate still attached, the assembly was hung by a string. A vertical laser level was used to line up with the strings (perpendicular to the sagittal plane) when the assembly was no longer oscillating. A straight edge marked the laser line, and the assembly was then hung again from the other end. The intersection of the two vertical laser lines represented the estimated center of gravity of the assembly in the sagittal plane (Figure A.1).

Once the estimated CG was located, the assembly was placed on a flat surface.

Using a corner of the coupling plate as a reference, the x and z distances between the

177 assembly CG and T1 were measured (Figure A.2). These values were used as the moment arms to help calculated the moment applied at T1 in the ISM experiments.

Figure A.1. Locating the estimated center of gravity for the assembly

Support

Reference Flat Table

Figure A.2. Measuring the x and z moment arms between the HdT1 assembly CG and T1

178

Appendix B: Linear Proportionality Verification

The following plots demonstrate that linear proportionality using T1 and T6 measurements can be used to determine displacement of T3 (~UTS-PG center of gravity).

Applied @ T1 = 0.47 m/s

T3 ~ 0.5(T1) = 0.23 m/s Velocity (m/s) Velocity

(m)

Applied @ T1 = 0.0093 m

T3 ~ 0.5(T1) = 0.0046 m Displacement

Applied @ T1 = 2.6 deg deg)

( T3 ~ T1 = 2.6 deg Rotation

Figure B.1. T3 motion is proportional to T1 applied motion

179

Appendix C: Impulse Response Function using Correlation Functions

Applying the time-invariance property to the convolution integral, both the input x(t) and output y(t) can be shifted by r:

y t = x h t- d -

(C.1)

Each side is then multiplied by x(r):

y t = x h t- d -

(C.2)

Finally, each side is integrated with respect to r to obtain

x y t+ d = h t- ( x x t+ d )d - - -

(C.3)

It can be seen that the left side of the equation is in the form of the cross-correlation function and the right side is the convolution of the IRF with the autocorrelation function.

180

Appendix D: IRF Model Parameters

181

Table D.1. X axis IRF model fit results

Test # PMHS Age Sex Ht Wt BMI BMD BC Speed (m/s) M (kg) K (N/m) C (Ns/m) Wn (rad/s) Zeta 1003 1 70 F 168 60.9 21.6 0.951 MNB/LS/RS 0.5 41.3 22034 138 23.1 0.07 1004 1 70 F 168 60.9 21.6 0.951 MNB/LS/RS 1.5 61.9 27288 296 21.0 0.11 1005 1 70 F 168 60.9 21.6 0.951 MNB/LS/RS 2.5 95.8 68140 347 26.7 0.07 1006 1 70 F 168 60.9 21.6 0.951 LS/RS 0.5 61.9 7510 174 11.0 0.13 1007 1 70 F 168 60.9 21.6 0.951 LS/RS 1.5 55.8 11605 394 14.4 0.24 1009 1 70 F 168 60.9 21.6 0.951 MNB/RS 0.5 38.8 15707 366 20.1 0.23 1010 1 70 F 168 60.9 21.6 0.951 MNB/RS 1.5 68.6 23499 64 18.5 0.03 1012 1 70 F 168 60.9 21.6 0.951 MNB 0.5 40.2 15966 479 19.9 0.30 1013 1 70 F 168 60.9 21.6 0.951 MNB 1.5 44.3 26606 577 24.5 0.27 1014 1 70 F 168 60.9 21.6 0.951 MNB 2.5 69.9 33644 1393 21.9 0.45 2003 2 68 M 170 86.4 29.9 1.158 MNB/LS/RS 0.5 52.2 79872 228 39.1 0.06 2004 2 68 M 170 86.4 29.9 1.158 MNB/LS/RS 1.5 61.6 62147 1339 31.8 0.34 2005 2 68 M 170 86.4 29.9 1.158 MNB/LS/RS 2.5 91.2 92774 1005 31.9 0.17 2006 2 68 M 170 86.4 29.9 1.158 LS/RS 0.5 29.5 10538 243 18.9 0.22 2007 2 68 M 170 86.4 29.9 1.158 LS/RS 1.5 105 44723 172 20.6 0.04 2008 2 68 M 170 86.4 29.9 1.158 MNB/RS 0.5 39.1 45596 171 34.1 0.06 2009 2 68 M 170 86.4 29.9 1.158 MNB/RS 1.5 31.4 37046 860 34.3 0.40 2010 2 68 M 170 86.4 29.9 1.158 MNB 0.5 38.4 39971 161 32.3 0.06 3003 3 89 F 157 58.2 23.6 1.042 MNB/LS/RS 0.5 41.8 20967 239 22.4 0.13 3004 3 89 F 157 58.2 23.6 1.042 MNB/LS/RS 1.5 95.4 35682 173 19.3 0.05 3006 3 89 F 157 58.2 23.6 1.042 LS/RS 0.5 45.6 61863 2185 36.8 0.65 182 3008 3 89 F 157 58.2 23.6 1.042 LS/RS 2.5 17.1 5844 233 18.5 0.37 3009 3 89 F 157 58.2 23.6 1.042 MNB/RS 0.5 18.1 12917 61 26.7 0.06

3010 3 89 F 157 58.2 23.6 1.042 MNB/RS 1.5 10.7 7198 140 25.9 0.25 3011 3 89 F 157 58.2 23.6 1.042 MNB/RS 2.5 12 4651 229 19.7 0.48 3012 3 89 F 157 58.2 23.6 1.042 MNB 0.5 18.9 10124 65 23.1 0.07 3013 3 89 F 157 58.2 23.6 1.042 MNB 1.5 51.3 18058 129 18.8 0.07 3014 3 89 F 157 58.2 23.6 1.042 MNB 2.5 20.7 11590 179 23.7 0.18 3016 3 89 F 157 58.2 23.6 1.042 All Free 1.5 32 22695 337 26.6 0.20 3017 3 89 F 157 58.2 23.6 1.042 All Free 2.5 26.9 7143 419 16.3 0.48 4003 4 72 M 159 72.3 28.6 1.523 MNB/LS/RS 0.5 17.4 6043 158 18.6 0.24 4004 4 72 M 159 72.3 28.6 1.523 MNB/LS/RS 1.5 80.3 33314 67 20.4 0.02 4005 4 72 M 159 72.3 28.6 1.523 MNB/LS/RS 2.5 31.6 15404 46 22.1 0.03 4006 4 72 M 159 72.3 28.6 1.523 LS/RS 0.5 93.8 8588 101 9.6 0.06 4007 4 72 M 159 72.3 28.6 1.523 LS/RS 1.5 52.3 8049 135 12.4 0.10 4009 4 72 M 159 72.3 28.6 1.523 MNB/RS 0.5 17.5 6530 143 19.3 0.21 4010 4 72 M 159 72.3 28.6 1.523 MNB/RS 1.5 12.5 3853 139 17.6 0.32 4011 4 72 M 159 72.3 28.6 1.523 MNB/RS 2.5 37.7 19944 161 23.0 0.09 4012 4 72 M 159 72.3 28.6 1.523 MNB 0.5 25.8 6752 163 16.2 0.19 4013 4 72 M 159 72.3 28.6 1.523 MNB 1.5 67.4 21686 50 17.9 0.02 4016 4 72 M 159 72.3 28.6 1.523 All Free 1.5 67.4 21686 50 17.9 0.02 5003 5 74 M 178 84 26.5 1.729 MNB/LS/RS 0.5 43.5 31767 920 27.0 0.39 5004 5 74 M 178 84 26.5 1.729 MNB/LS/RS 1.5 41.9 21992 289 22.9 0.15 5006 5 74 M 178 84 26.5 1.729 LS/RS 0.5 60.9 9490 836 12.5 0.55 5009 5 74 M 178 84 26.5 1.729 MNB/RS 0.5 51.8 19017 956 19.2 0.48 5010 5 74 M 178 84 26.5 1.729 MNB/RS 1.5 82 27763 248 18.4 0.08 5012 5 74 M 178 84 26.5 1.729 MNB 0.5 45.7 16778 1239 19.2 0.71

182

Table D.1. X axis IRF model fit results (continued)

Test # PMHS Age Sex Ht Wt BMI BMD BC Speed (m/s) M (kg) K (N/m) C (Ns/m) Wn (rad/s) Zeta 5016 5 74 M 178 84 26.5 1.729 All Free 1.5 64.7 17599 1074 16.5 0.50 6003 6 86 F 165 59.1 21.7 1.043 MNB/LS/RS 0.5 38.2 41143 824 32.8 0.33 6004 6 86 F 165 59.1 21.7 1.043 MNB/LS/RS 1.5 53.7 40781 932 27.6 0.31 6005 6 86 F 165 59.1 21.7 1.043 MNB/LS/RS 1.5 35.6 30486 1044 29.3 0.50 6006 6 86 F 165 59.1 21.7 1.043 LS/RS 0.5 19.3 11589 931 24.5 0.98 6007 6 86 F 165 59.1 21.7 1.043 LS/RS 1.5 76 13033 570 13.1 0.29 6008 6 86 F 165 59.1 21.7 1.043 LS/RS 2.5 63.5 119002 2371 43.3 0.43 6009 6 86 F 165 59.1 21.7 1.043 MNB/RS 0.5 40.9 30436 898 27.3 0.40 6010 6 86 F 165 59.1 21.7 1.043 MNB/RS 1.5 67.1 36671 545 23.4 0.17 6012 6 86 F 165 59.1 21.7 1.043 MNB 0.5 51 25544 979 22.4 0.43 6013 6 86 F 165 59.1 21.7 1.043 MNB 1.5 30.9 34626 486 33.5 0.23 7003 7 72 F 155 54 22.5 1.03 MNB/LS/RS 0.5 35.6 14243 174 20.0 0.12 7004 7 72 F 155 54 22.5 1.03 MNB/LS/RS 1.5 48.2 9797 499 14.3 0.36 7005 7 72 F 155 54 22.5 1.03 MNB/LS/RS 2.5 84.4 39057 1625 21.5 0.45 7006 7 72 F 155 54 22.5 1.03 LS/RS 0.5 27.2 5589 161 14.3 0.21 7008 7 72 F 155 54 22.5 1.03 LS/RS 2.5 92 34725 1770 19.4 0.50 7009 7 72 F 155 54 22.5 1.03 MNB/RS 0.5 38.4 14228 230 19.2 0.16 7010 7 72 F 155 54 22.5 1.03 MNB/RS 1.5 87.5 15788 357 13.4 0.15 7012 7 72 F 155 54 22.5 1.03 MNB 0.5 32.4 10506 185 18.0 0.16 7014 7 72 F 155 54 22.5 1.03 MNB 2.5 124 87965 928 26.6 0.14 7016 7 72 F 155 54 22.5 1.03 All Free 1.5 91.3 8233 137 9.5 0.08 183 7017 7 72 F 155 54 22.5 1.03 All Free 2.5 99.1 31301 11 17.8 0.00 8003 8 88 M 168 58 20.5 1.3 MNB/LS/RS 0.5 35.5 23232 205 25.6 0.11

8004 8 88 M 168 58 20.5 1.3 MNB/LS/RS 1.5 64.4 29615 381 21.4 0.14 8005 8 88 M 168 58 20.5 1.3 MNB/LS/RS 2.5 56.8 21635 993 19.5 0.45 8006 8 88 M 168 58 20.5 1.3 LS/RS 0.5 56.4 7640 306 11.6 0.23 8007 8 88 M 168 58 20.5 1.3 LS/RS 1.5 140 25983 301 13.6 0.08 8008 8 88 M 168 58 20.5 1.3 LS/RS 2.5 130 61344 2058 21.7 0.36 8009 8 88 M 168 58 20.5 1.3 MNB/RS 0.5 41.7 19442 186 21.6 0.10 8010 8 88 M 168 58 20.5 1.3 MNB/RS 1.5 68.7 24127 100 18.7 0.04 8011 8 88 M 168 58 20.5 1.3 MNB/RS 2.5 81.8 48915 561 24.5 0.14 8012 8 88 M 168 58 20.5 1.3 MNB 0.5 45.1 18770 163 20.4 0.09 8013 8 88 M 168 58 20.5 1.3 MNB 1.5 55.9 18818 19 18.3 0.01 8016 8 88 M 168 58 20.5 1.3 All Free 1.5 158 30195 247 13.8 0.06 8017 8 88 M 168 58 20.5 1.3 All Free 2.5 83.8 35440 1769 20.6 0.51 9003 9 86 M 178 73 23.0 1.3 MNB/LS/RS 0.5 44 25609 143 24.1 0.07 9004 9 86 M 178 73 23.0 4.3 MNB/LS/RS 1.5 37 24408 461 25.7 0.24 9005 9 86 M 178 73 23.0 7.3 MNB/LS/RS 2.5 56.7 21612 992 19.5 0.45 9006 9 86 M 178 73 23.0 10.3 LS/RS 0.5 90.4 9162 90 10.1 0.05 9007 9 86 M 178 73 23.0 13.3 LS/RS 1.5 186 24645 132 11.5 0.03 9008 9 86 M 178 73 23.0 15.3 LS/RS 2.5 82.6 110961 1581 36.7 0.26 9009 9 86 M 178 73 23.0 19.3 MNB/RS 0.5 44.7 22375 199 22.4 0.10 9010 9 86 M 178 73 23.0 22.3 MNB/RS 1.5 85.2 34803 117 20.2 0.03 9012 9 86 M 178 73 23.0 28.3 MNB 0.5 42.7 17995 236 20.5 0.13 9013 9 86 M 178 73 23.0 31.3 MNB 1.5 75.5 28088 112 19.3 0.04 9014 9 86 M 178 73 23.0 33.3 MNB 2.5 140 31997 1395 15.1 0.33 9015 9 86 M 178 73 23.0 37.3 All Free 0.5 518 21602 3409 6.5 0.51 9016 9 86 M 178 73 23.0 40.3 All Free 1.5 60.4 68889 1201 33.8 0.29 9017 9 86 M 178 73 23.0 40.3 All Free 2.5 47.4 82879 1755 41.8 0.44

183

Table D.2. Z axis IRF model fit results

Test # PMHS Age Sex Ht Wt BMI BMD BC Speed (m/s) M (kg) K (N/m) C (Ns/m) Wn (rad/s) Zeta 1003 1 70 F 168 60.9 21.6 0.951 MNB/LS/RS 0.5 26.3 50904 1020 44.0 0.44 1005 1 70 F 168 60.9 21.6 0.951 MNB/LS/RS 2.5 44.6 54891 1272 35.1 0.41 1006 1 70 F 168 60.9 21.6 0.951 LS/RS 0.5 15.6 23359 351 38.7 0.29 1007 1 70 F 168 60.9 21.6 0.951 LS/RS 1.5 179.0 180890 2498 31.8 0.22 1008 1 70 F 168 60.9 21.6 0.951 LS/RS 2.5 31.6 34668 638 33.1 0.30 1009 1 70 F 168 60.9 21.6 0.951 MNB/RS 0.5 526.0 524053 7955 31.6 0.24 1012 1 70 F 168 60.9 21.6 0.951 MNB 0.5 38.0 56685 1084 38.6 0.37 1014 1 70 F 168 60.9 21.6 0.951 MNB 2.5 31.3 42221 1086 36.7 0.47 2003 2 68 M 170 86.4 29.9 1.158 MNB/LS/RS 0.5 15.1 40720 977 51.9 0.62 2004 2 68 M 170 86.4 29.9 1.158 MNB/LS/RS 1.5 254.0 246265 4295 31.1 0.27 2005 2 68 M 170 86.4 29.9 1.158 MNB/LS/RS 2.5 26.5 23692 454 29.9 0.29 2006 2 68 M 170 86.4 29.9 1.158 LS/RS 0.5 8.2 20186 404 49.7 0.50 2009 2 68 M 170 86.4 29.9 1.158 MNB/RS 1.5 539.0 464168 5950 29.3 0.19 2010 2 68 M 170 86.4 29.9 1.158 MNB 0.5 45.5 52218 1958 33.9 0.64 3003 3 89 F 157 58.2 23.6 1.042 MNB/LS/RS 0.5 78.0 58658 3434 27.4 0.80 3004 3 89 F 157 58.2 23.6 1.042 MNB/LS/RS 1.5 353.0 352021 4966 31.6 0.22 3005 3 89 F 157 58.2 23.6 1.042 MNB/LS/RS 2.5 115.8 186665 2894 40.1 0.31 3006 3 89 F 157 58.2 23.6 1.042 LS/RS 0.5 21.5 25138 983 34.2 0.67 3007 3 89 F 157 58.2 23.6 1.042 LS/RS 1.5 361.0 306821 4288 29.2 0.20

1 3010 3 89 F 157 58.2 23.6 1.042 MNB/RS 1.5 169.0 109417 3280 25.4 0.38 84 3012 3 89 F 157 58.2 23.6 1.042 MNB 0.5 52.8 33741 2100 25.3 0.79

3013 3 89 F 157 58.2 23.6 1.042 MNB 1.5 143.0 78676 2777 23.5 0.41 3014 3 89 F 157 58.2 23.6 1.042 MNB 2.5 52.2 106286 1231 45.1 0.26 3015 3 89 F 157 58.2 23.6 1.042 All Free 0.5 112.0 121058 3025 32.9 0.41 3016 3 89 F 157 58.2 23.6 1.042 All Free 1.5 291.0 233737 3299 28.3 0.20 3017 3 89 F 157 58.2 23.6 1.042 All Free 2.5 10.6 11942 123 33.6 0.17 4003 4 72 M 159 72.3 28.6 1.523 MNB/LS/RS 0.5 59.1 28413 1913 21.9 0.74 4004 4 72 M 159 72.3 28.6 1.523 MNB/LS/RS 1.5 518.0 399168 7734 27.8 0.27 4005 4 72 M 159 72.3 28.6 1.523 MNB/LS/RS 2.5 18.2 4511 212 15.7 0.37 4006 4 72 M 159 72.3 28.6 1.523 LS/RS 0.5 7.2 11784 530 40.3 0.91 4007 4 72 M 159 72.3 28.6 1.523 LS/RS 1.5 185.7 147703 1748 28.2 0.17 4008 4 72 M 159 72.3 28.6 1.523 LS/RS 2.5 14.5 17402 187.8 34.6 0.19 4009 4 72 M 159 72.3 28.6 1.523 MNB/RS 0.5 98.7 111153 2431 33.6 0.37 4011 4 72 M 159 72.3 28.6 1.523 MNB/RS 2.5 10.3 12118 109.5 34.3 0.15 4012 4 72 M 159 72.3 28.6 1.523 MNB 0.5 38.1 16834 1022 21.0 0.64 4017 4 72 M 159 72.3 28.6 1.523 All Free 2.5 6.8 11845 256 41.8 0.45 5003 5 74 M 178 84 26.5 1.729 MNB/LS/RS 0.5 52.8 22208 1436 20.5 0.66 5004 5 74 M 178 84 26.5 1.729 MNB/LS/RS 1.5 66.2 60543 687 30.2 0.17 5005 5 74 M 178 84 26.5 1.729 MNB/LS/RS 2.5 9.7 7919 57.9 28.6 0.10 5006 5 74 M 178 84 26.5 1.729 LS/RS 0.5 23.2 16193 908 26.4 0.74 5008 5 74 M 178 84 26.5 1.729 LS/RS 2.5 39.2 26504 1802 26.0 0.88

184

Table D.2. Z axis IRF model fit results (continued)

Test # PMHS Age Sex Ht Wt BMI BMD BC Speed (m/s) M (kg) K (N/m) C (Ns/m) Wn (rad/s) Zeta 5009 5 74 M 178 84 26.5 1.729 MNB/RS 0.5 64.1 36667 1398 23.9 0.46 5011 5 74 M 178 84 26.5 1.729 MNB/RS 2.5 4.3 3510 70.2 28.7 0.29 5012 5 74 M 178 84 26.5 1.729 MNB 0.5 30.6 32439 296 32.6 0.15 5015 5 74 M 178 84 26.5 1.729 All Free 0.5 159.0 157904 4358 31.5 0.43 5016 5 74 M 178 84 26.5 1.729 All Free 1.5 242.0 240386 2189 31.5 0.14 5017 5 74 M 178 84 26.5 1.729 All Free 2.5 5.2 2961 153 23.9 0.62 6003 6 86 F 165 59.1 21.7 1.043 MNB/LS/RS 0.5 31.6 48712 551 39.3 0.22 6004 6 86 F 165 59.1 21.7 1.043 MNB/LS/RS 1.5 43.8 67357 1865 39.2 0.54 6005 6 86 F 165 59.1 21.7 1.043 MNB/LS/RS 1.5 837.0 779989 9885 30.5 0.19 6008 6 86 F 165 59.1 21.7 1.043 LS/RS 2.5 22.6 11377 856 22.4 0.84 6009 6 86 F 165 59.1 21.7 1.043 MNB/RS 0.5 31.9 64262 849 44.9 0.30 6010 6 86 F 165 59.1 21.7 1.043 MNB/RS 1.5 219.0 138079 7704 25.1 0.70 6012 6 86 F 165 59.1 21.7 1.043 MNB 0.5 35.7 56586 1052 39.8 0.37 6013 6 86 F 165 59.1 21.7 1.043 MNB 1.5 95.4 59525 3648 25.0 0.77 6014 6 86 F 165 59.1 21.7 1.043 MNB 2.5 12.5 9731 210 27.9 0.30 6015 6 86 F 165 59.1 21.7 1.043 All Free 0.5 153.0 261640 12594 41.4 1.00 6017 6 86 F 165 59.1 21.7 1.043 All Free 2.5 60.9 51015 132 28.9 0.04 7003 7 72 F 155 54 22.5 1.03 MNB/LS/RS 0.5 15.2 21962 160 38.0 0.14 7004 7 72 F 155 54 22.5 1.03 MNB/LS/RS 1.5 6.9 5568 175 28.4 0.45 7006 7 72 F 155 54 22.5 1.03 LS/RS 0.5 38.1 38106 1556 31.6 0.65

1 7009 7 72 F 155 54 22.5 1.03 MNB/RS 0.5 13.9 17516 153 35.5 0.16

85 7010 7 72 F 155 54 22.5 1.03 MNB/RS 1.5 13.6 10282 231 27.5 0.31 7012 7 72 F 155 54 22.5 1.03 MNB 0.5 47.8 61216 847 35.8 0.25

7016 7 72 F 155 54 22.5 1.03 All Free 1.5 1.7 5983 11.09 59.3 0.05 7017 7 72 F 155 54 22.5 1.03 All Free 2.5 0.5 317 11.4 24.2 0.44 8003 8 88 M 168 58 20.5 1.3 MNB/LS/RS 0.5 91.9 20181 690 14.8 0.25 8004 8 88 M 168 58 20.5 1.3 MNB/LS/RS 1.5 1.9 243 10.1 11.2 0.23 8005 8 88 M 168 58 20.5 1.3 MNB/LS/RS 2.5 0.1 201.6 9.094 44.2 1.00 8006 8 88 M 168 58 20.5 1.3 LS/RS 0.5 289.0 176276 8480 24.7 0.59 8008 8 88 M 168 58 20.5 1.3 LS/RS 2.5 1.3 448 15.8 18.8 0.33 8009 8 88 M 168 58 20.5 1.3 MNB/RS 0.5 268.0 42507 1689 12.6 0.25 8010 8 88 M 168 58 20.5 1.3 MNB/RS 1.5 11.2 1380 82.2 11.1 0.33 8013 8 88 M 168 58 20.5 1.3 MNB 1.5 6.7 2413 38.4 19.0 0.15 8016 8 88 M 168 58 20.5 1.3 All Free 1.5 1.7 830 13.7 22.1 0.18 8017 8 88 M 168 58 20.5 1.3 All Free 2.5 0.8 215 13.5 16.4 0.51 9003 9 86 M 178 73 23.0 2.3 MNB/LS/RS 0.5 73.7 85130 1998 34.0 0.40 9005 9 86 M 178 73 23.0 7.3 MNB/LS/RS 2.5 0.1 203 9.12 44.4 1.00 9006 9 86 M 178 73 23.0 11.3 LS/RS 0.5 6.6 8052 34.5 34.9 0.07 9007 9 86 M 178 73 23.0 14.3 LS/RS 1.5 24.7 20120 360 28.5 0.26 9008 9 86 M 178 73 23.0 15.3 LS/RS 2.5 5.1 4490 53.8 29.6 0.18 9015 9 86 M 178 73 23.0 38.3 All Free 0.5 40.6 13269 745 18.1 0.51 9016 9 86 M 178 73 23.0 40.3 All Free 1.5 42.8 43693 1237 32.0 0.45 9017 9 86 M 178 73 23.0 40.3 All Free 2.5 27.3 29529 186 32.9 0.10

185

Table D.3. Rotation about Y IRF model fit results

Test # PMHS Age Sex Ht Wt BMI BMD BC Speed (m/s) M (kg) K (N/m) C (Ns/m) Wn (rad/s) Zeta 1003 1 70 F 168 60.9 21.6 0.951 MNB/LS/RS 0.5 0.005 4.52 0.06 29.6 0.19 1004 1 70 F 168 60.9 21.6 0.951 MNB/LS/RS 1.5 0.004 3.576 0.08 31.8 0.36 1006 1 70 F 168 60.9 21.6 0.951 LS/RS 0.5 0.009 4.17 0.06 21.3 0.16 1007 1 70 F 168 60.9 21.6 0.951 LS/RS 1.5 0.005 2.957 0.04 23.8 0.15 1009 1 70 F 168 60.9 21.6 0.951 MNB/RS 0.5 0.004 3.082 0.05 28.5 0.21 1010 1 70 F 168 60.9 21.6 0.951 MNB/RS 1.5 0.004 2.218 0.04 24.0 0.23 1012 1 70 F 168 60.9 21.6 0.951 MNB 0.5 0.006 3.828 0.11 24.8 0.37 1014 1 70 F 168 60.9 21.6 0.951 MNB 2.5 0.050 18.67 0.58 19.3 0.30 2003 2 68 M 170 86.4 29.9 1.158 MNB/LS/RS 0.5 55.300 30892 2614 23.6 1.00 2004 2 68 M 170 86.4 29.9 1.158 MNB/LS/RS 1.5 0.007 7.3 0.23 31.4 0.49 2006 2 68 M 170 86.4 29.9 1.158 LS/RS 0.5 0.069 28.3 0.74 20.3 0.27 2007 2 68 M 170 86.4 29.9 1.158 LS/RS 1.5 0.020 6.02 0.07 17.3 0.10 2008 2 68 M 170 86.4 29.9 1.158 MNB/RS 0.5 0.019 1.11 0.02 7.6 0.06 2009 2 68 M 170 86.4 29.9 1.158 MNB/RS 1.5 0.006 4.68 0.15 27.3 0.43 3003 3 89 F 157 58.2 23.6 1.042 MNB/LS/RS 0.5 0.093 27.3 3.19 17.1 1.00 3004 3 89 F 157 58.2 23.6 1.042 MNB/LS/RS 1.5 0.011 11.5 0.24 32.3 0.34 3005 3 89 F 157 58.2 23.6 1.042 MNB/LS/RS 2.5 0.011 19.5 0.33 41.9 0.36 3006 3 89 F 157 58.2 23.6 1.042 LS/RS 0.5 0.197 103.5 1.57 22.9 0.17 3008 3 89 F 157 58.2 23.6 1.042 LS/RS 2.5 0.002 3.627 0.11 38.9 0.58 3011 3 89 F 157 58.2 23.6 1.042 MNB/RS 2.5 0.012 9.21 0.27 27.7 0.40

1 3013 3 89 F 157 58.2 23.6 1.042 MNB 1.5 0.011 4.59 0.21 20.4 0.46

86 3014 3 89 F 157 58.2 23.6 1.042 MNB 2.5 0.007 5.23 0.17 28.2 0.46

3016 3 89 F 157 58.2 23.6 1.042 All Free 1.5 0.008 3.786 0.18 21.9 0.52 3017 3 89 F 157 58.2 23.6 1.042 All Free 2.5 0.007 6.01 0.21 29.3 0.50 4003 4 72 M 159 72.3 28.6 1.523 MNB/LS/RS 0.5 0.015 10.86 0.80 27.2 1.00 4004 4 72 M 159 72.3 28.6 1.523 MNB/LS/RS 1.5 0.029 3.02 0.41 10.2 0.69 4005 4 72 M 159 72.3 28.6 1.523 MNB/LS/RS 2.5 0.004 3.95 0.14 33.1 0.57 4006 4 72 M 159 72.3 28.6 1.523 LS/RS 0.5 0.005 8.46 0.40 42.4 1.00 4007 4 72 M 159 72.3 28.6 1.523 LS/RS 1.5 0.003 2.28 0.11 25.9 0.61 4008 4 72 M 159 72.3 28.6 1.523 LS/RS 2.5 0.004 3.35 0.07 30.5 0.30 4009 4 72 M 159 72.3 28.6 1.523 MNB/RS 0.5 0.014 5.42 0.54 20.0 1.00 4010 4 72 M 159 72.3 28.6 1.523 MNB/RS 1.5 0.006 3.24 0.09 23.6 0.33 4011 4 72 M 159 72.3 28.6 1.523 MNB/RS 2.5 0.005 3.787 0.09 27.8 0.32 4012 4 72 M 159 72.3 28.6 1.523 MNB 0.5 0.012 5.21 0.50 20.7 1.00 4013 4 72 M 159 72.3 28.6 1.523 MNB 1.5 0.009 2.976 0.33 17.9 1.00 4014 4 72 M 159 72.3 28.6 1.523 MNB 2.5 0.006 5.155 0.13 28.4 0.35 4015 4 72 M 159 72.3 28.6 1.523 All Free 0.5 0.016 8.37 0.74 22.9 1.01 4016 4 72 M 159 72.3 28.6 1.523 All Free 1.5 0.009 2.976 0.33 17.9 1.00 4017 4 72 M 159 72.3 28.6 1.523 All Free 2.5 0.006 4.68 0.09 28.7 0.27 5003 5 74 M 178 84 26.5 1.729 MNB/LS/RS 0.5 0.029 23.3 1.65 28.3 1.00 5004 5 74 M 178 84 26.5 1.729 MNB/LS/RS 1.5 0.014 10.4 0.46 27.3 0.61 5005 5 74 M 178 84 26.5 1.729 MNB/LS/RS 2.5 0.056 77.6 1.27 37.2 0.30 5006 5 74 M 178 84 26.5 1.729 LS/RS 0.5 0.067 40 3.28 24.4 1.00 5007 5 74 M 178 84 26.5 1.729 LS/RS 1.5 0.016 12.1 0.21 27.5 0.24 5008 5 74 M 178 84 26.5 1.729 LS/RS 2.5 0.018 11.8 0.81 25.6 0.87 5009 5 74 M 178 84 26.5 1.729 MNB/RS 0.5 0.270 185 14.20 26.2 1.00 5010 5 74 M 178 84 26.5 1.729 MNB/RS 1.5 0.010 8.06 0.19 28.4 0.34

186

Table D.3. Rotation about Y IRF model fit results (continued)

Test # PMHS Age Sex Ht Wt BMI BMD BC Speed (m/s) M (kg) K (N/m) C (Ns/m) Wn (rad/s) Zeta 5012 5 74 M 178 84 26.5 1.729 MNB 0.5 11.400 7867 600 26.3 1.00 5013 5 74 M 178 84 26.5 1.729 MNB 1.5 0.007 6.57 0.19 30.9 0.45 5014 5 74 M 178 84 26.5 1.729 MNB 2.5 0.004 5.35 0.27 39.1 1.00 5015 5 74 M 178 84 26.5 1.729 All Free 0.5 0.026 25.1 1.61 31.1 1.00 5016 5 74 M 178 84 26.5 1.729 All Free 1.5 0.010 10.5 0.20 32.4 0.31 5017 5 74 M 178 84 26.5 1.729 All Free 2.5 0.004 5.77 0.12 39.5 0.42 6003 6 86 F 165 59.1 21.7 1.043 MNB/LS/RS 0.5 0.067 207 7.43 55.6 1.00 6004 6 86 F 165 59.1 21.7 1.043 MNB/LS/RS 1.5 0.035 26.5 1.08 27.5 0.56 6005 6 86 F 165 59.1 21.7 1.043 MNB/LS/RS 1.5 0.017 13.7 0.39 28.4 0.40 6006 6 86 F 165 59.1 21.7 1.043 LS/RS 0.5 0.160 124 8.92 27.8 1.00 6007 6 86 F 165 59.1 21.7 1.043 LS/RS 1.5 0.083 55.3 3.49 25.8 0.81 6008 6 86 F 165 59.1 21.7 1.043 LS/RS 2.5 0.021 21.3 1.10 31.8 0.82 6010 6 86 F 165 59.1 21.7 1.043 MNB/RS 1.5 0.010 8.39 0.25 29.0 0.44 6011 6 86 F 165 59.1 21.7 1.043 MNB/RS 2.5 0.032 30.5 0.63 30.9 0.32 6012 6 86 F 165 59.1 21.7 1.043 MNB 0.5 0.059 115 5.20 44.1 1.00 6013 6 86 F 165 59.1 21.7 1.043 MNB 1.5 0.037 26.5 0.66 26.8 0.33 6015 6 86 F 165 59.1 21.7 1.043 All Free 0.5 1.180 1272 77.5 32.8 1.00 6016 6 86 F 165 59.1 21.7 1.043 All Free 1.5 0.067 66.86 4.22 31.7 1.00 7004 7 72 F 155 54 22.5 1.03 MNB/LS/RS 1.5 0.027 16.6 0.49 24.8 0.37 7006 7 72 F 155 54 22.5 1.03 LS/RS 0.5 8.350 5866 443 26.5 1.00 7009 7 72 F 155 54 22.5 1.03 MNB/RS 0.5 0.002 23 0.18 100.0 0.39 1 7010 7 72 F 155 54 22.5 1.03 MNB/RS 1.5 0.011 6.99 0.16 25.1 0.29 87 7012 7 72 F 155 54 22.5 1.03 MNB 0.5 0.002 22.7 0.30 104.0 0.69

7013 7 72 F 155 54 22.5 1.03 MNB 1.5 0.011 4.83 0.09 21.2 0.20 7015 7 72 F 155 54 22.5 1.03 All Free 0.5 0.001 8.08 0.10 116.0 0.70 7016 7 72 F 155 54 22.5 1.03 All Free 1.5 0.014 7.92 0.17 23.8 0.26 8003 8 88 M 168 58 20.5 1.3 MNB/LS/RS 0.5 0.014 9.54 0.72 26.1 0.98 8004 8 88 M 168 58 20.5 1.3 MNB/LS/RS 1.5 0.001 0.782 0.02 23.6 0.24 8005 8 88 M 168 58 20.5 1.3 MNB/LS/RS 2.5 0.004 2.89 0.05 27.6 0.23 8006 8 88 M 168 58 20.5 1.3 LS/RS 0.5 0.869 294.5 32.0 18.4 1.00 8007 8 88 M 168 58 20.5 1.3 LS/RS 1.5 0.001 0.941 0.01 28.9 0.16 8010 8 88 M 168 58 20.5 1.3 MNB/RS 1.5 0.004 1.27 0.02 17.0 0.15 8011 8 88 M 168 58 20.5 1.3 MNB/RS 2.5 0.005 2.45 0.07 22.1 0.32 8015 8 88 M 168 58 20.5 1.3 All Free 0.5 0.038 9.19 1.09 15.6 0.92 8016 8 88 M 168 58 20.5 1.3 All Free 1.5 0.002 1.71 0.10 27.9 0.83 8017 8 88 M 168 58 20.5 1.3 All Free 2.5 0.007 1.13 0.10 13.1 0.55 9003 9 86 M 178 73 23.0 3.3 MNB/LS/RS 0.5 0.002 4.2 0.08 49.7 0.48 9004 9 86 M 178 73 23.0 6.3 MNB/LS/RS 1.5 0.006 4.97 0.08 30.1 0.24 9005 9 86 M 178 73 23.0 9.3 MNB/LS/RS 2.5 0.004 3.67 0.06 29.6 0.23 9006 9 86 M 178 73 23.0 12.3 LS/RS 0.5 0.005 92.3 0.88 133.2 0.63 9007 9 86 M 178 73 23.0 15.3 LS/RS 1.5 0.024 21.9 0.18 30.2 0.13 9008 9 86 M 178 73 23.0 15.3 LS/RS 2.5 0.002 2.87 0.14 39.9 1.00 9009 9 86 M 178 73 23.0 21.3 MNB/RS 0.5 0.004 8.95 0.03 47.3 0.09 9010 9 86 M 178 73 23.0 24.3 MNB/RS 1.5 0.011 7.59 0.05 26.8 0.09 9012 9 86 M 178 73 23.0 30.3 MNB 0.5 0.002 6.51 0.09 60.1 0.41 9013 9 86 M 178 73 23.0 33.3 MNB 1.5 0.005 3.4 0.03 27.5 0.12 9014 9 86 M 178 73 23.0 33.3 MNB 2.5 0.001 0.82 0.06 27.3 1.00 9015 9 86 M 178 73 23.0 38.3 All Free 0.5 0.018 81.9 0.44 67.5 0.18 9016 9 86 M 178 73 23.0 40.3 All Free 1.5 0.029 3.91 0.14 11.6 0.20 9017 9 86 M 178 73 23.0 40.3 All Free 2.5 0.003 2.84 0.09 30.8 0.49

187

Appendix E: Impulse Response Functions & Model Fits

-1 IRF: H = (1/Δt)*Cxx Cxy

-βt Parametric Model: G = x(t) / F(t)UNIT IMPULSE = A e sin (2πft + φ)

Test 1003 – PMHS 1, MNB/LS/RS Fixed, 0.5 m/s

Test 1004 – PMHS 1, MNB/LS/RS Fixed, 1.5 m/s

Test 1005 – PMHS 1, MNB/LS/RS Fixed, 2.5 m/s

188 Test 1006 – PMHS 1, LS/RS Fixed, 0.5 m/s

Test 1007 – PMHS 1, LS/RS Fixed, 1.5 m/s

Test 1008 – PMHS 1, LS/RS Fixed, 2.5 m/s

Test 1009 – PMHS 1, MNB/RS Fixed, 0.5 m/s

189 Test 1010 – PMHS 1, MNB/RS Fixed, 1.5 m/s

Test 1011 – PMHS 1, MNB/RS Fixed, 2.5 m/s

------NO IRFs WITH VAF > 60%------

Test 1012 – PMHS 1, MNB Fixed, 0.5 m/s

Test 1013 – PMHS 1, MNB Fixed, 1.5 m/s

Test 1014 – PMHS 1, MNB Fixed, 2.5 m/s

190 Test 2003 – PMHS 2, MNB/LS/RS Fixed, 0.5 m/s

Test 2004 – PMHS 2, MNB/LS/RS Fixed, 1.5 m/s

Test 2005 – PMHS 2, MNB/LS/RS Fixed, 2.5 m/s

Test 2006 – PMHS 2, LS/RS Fixed, 0.5 m/s

191 Test 2007 – PMHS 2, LS/RS Fixed, 1.5 m/s

Test 2008 – PMHS 2, MNB/RS Fixed, 0.5 m/s

Test 2009– PMHS 2, MNB/RS Fixed, 1.5 m/s

Test 2010 – PMHS 2, MNB Fixed, 0.5 m/s

192 Test 2011– PMHS 2, MNB Fixed, 1.5 m/s

------NO IRFs WITH VAF > 60%------

Test 3003 – PMHS 3, MNB/LS/RS Fixed, 0.5 m/s

Test 3004 – PMHS 3, MNB/LS/RS Fixed, 1.5 m/s

Test 3005 – PMHS 3, MNB/LS/RS Fixed, 2.5 m/s

Test 3006 – PMHS 3, LS/RS Fixed, 0.5 m/s

193 Test 3007 – PMHS 3, LS/RS Fixed, 1.5 m/s

Test 3008 – PMHS 3, LS/RS Fixed, 2.5 m/s

Test 3009 – PMHS 3, MNB/RS Fixed, 0.5 m/s

Test 3010 – PMHS 3, MNB/RS Fixed, 1.5 m/s

194 Test 3011 – PMHS 3, MNB/RS Fixed, 2.5 m/s

Test 3012 – PMHS 3, MNB Fixed, 0.5 m/s

Test 3013 – PMHS 3, MNB Fixed, 1.5 m/s

Test 3014 – PMHS 3, MNB Fixed, 2.5 m/s

195 Test 3015 – PMHS 3, All Free, 0.5 m/s

Test 3016 – PMHS 3, All Free, 1.5 m/s

Test 3017 – PMHS 3, All Free, 2.5 m/s

Test 4003 – PMHS 4, MNB/LS/RS Fixed, 0.5 m/s

196 Test 4004 – PMHS 4, MNB/LS/RS Fixed, 1.5 m/s

Test 4005 – PMHS 4, MNB/LS/RS Fixed, 2.5 m/s

Test 4006 – PMHS 4, LS/RS Fixed, 0.5 m/s

Test 4007 – PMHS 4, LS/RS Fixed, 1.5 m/s

197 Test 4008 – PMHS 4, LS/RS Fixed, 2.5 m/s

Test 4009 – PMHS 4, MNB/RS Fixed, 0.5 m/s

Test 4010 – PMHS 4, MNB/RS Fixed, 1.5 m/s

Test 4011 – PMHS 4, MNB/RS Fixed, 2.5 m/s

198 Test 4012 – PMHS 4, MNB Fixed, 0.5 m/s

Test 4013 – PMHS 4, MNB Fixed, 1.5 m/s

Test 4014 – PMHS 4, MNB Fixed, 2.5 m/s

Test 4015 – PMHS 4, All Free, 0.5 m/s

199 Test 4016 – PMHS 4, All Free, 1.5 m/s

Test 4017 – PMHS 4, All Free, 2.5 m/s

Test 5003 – PMHS 5, MNB/LS/RS Fixed, 0.5 m/s

Test 5004 – PMHS 5, MNB/LS/RS Fixed, 1.5 m/s

200 Test 5005 – PMHS 5, MNB/LS/RS Fixed, 2.5 m/s

Test 5006 – PMHS 5, LS/RS Fixed, 0.5 m/s

Test 5007 – PMHS 5, LS/RS Fixed, 1.5 m/s

Test 5008 – PMHS 5, LS/RS Fixed, 2.5 m/s

201 Test 5009 – PMHS 5, MNB/RS Fixed, 0.5 m/s

Test 5010 – PMHS 5, MNB/RS Fixed, 1.5 m/s

Test 5011 – PMHS 5, MNB/RS Fixed, 2.5 m/s

Test 5012 – PMHS 5, MNB Fixed, 0.5 m/s

202 Test 5013 – PMHS 5, MNB Fixed, 1.5 m/s

Test 5014 – PMHS 5, MNB Fixed, 2.5 m/s

Test 5015 – PMHS 5, All Free, 0.5 m/s

Test 5016 – PMHS 5, All Free, 1.5 m/s

203 Test 5017 – PMHS 5, All Free, 2.5 m/s

Test 6003 – PMHS 6, MNB/LS/RS Fixed, 0.5 m/s

Test 6004 – PMHS 6, MNB/LS/RS Fixed, 1.5 m/s

Test 6005 – PMHS 6, MNB/LS/RS Fixed, 2.5 m/s

204 Test 6006 – PMHS 6, LS/RS Fixed, 0.5 m/s

Test 6007 – PMHS 6, LS/RS Fixed, 1.5 m/s

Test 6008 – PMHS 6, LS/RS Fixed, 2.5 m/s

Test 6009 – PMHS 6, MNB/RS Fixed, 0.5 m/s

205 Test 6010 – PMHS 6, MNB/RS Fixed, 1.5 m/s

Test 6011 – PMHS 6, MNB/RS Fixed, 2.5 m/s

Test 6012 – PMHS 6, MNB Fixed, 0.5 m/s

Test 6013 – PMHS 6, MNB Fixed, 1.5 m/s

206 Test 6014 – PMHS 6, MNB Fixed, 2.5 m/s

Test 6015 – PMHS 6, All Free, 0.5 m/s

Test 6016 – PMHS 6, All Free, 1.5 m/s

Test 6017 – PMHS 6, All Free, 2.5 m/s

207 Test 7003 – PMHS 7, MNB/LS/RS Fixed, 0.5 m/s

Test 7004 – PMHS 7, MNB/LS/RS Fixed, 1.5 m/s

Test 7005 – PMHS 7, MNB/LS/RS Fixed, 2.5 m/s

Test 7006 – PMHS 7, LS/RS Fixed, 0.5 m/s

208 Test 7007 – PMHS 7, LS/RS Fixed, 1.5 m/s

------NO IRFs WITH VAF > 60%------

Test 7008 – PMHS 7, LS/RS Fixed, 2.5 m/s

Test 7009 – PMHS 7, MNB/RS Fixed, 0.5 m/s

Test 7010 – PMHS 7, MNB/RS Fixed, 1.5 m/s

Test 7011 – PMHS 7, MNB/RS Fixed, 2.5 m/s

------NO IRFs WITH VAF > 60%------

209 Test 7012 – PMHS 7, MNB Fixed, 0.5 m/s

Test 7013 – PMHS 7, MNB Fixed, 1.5 m/s

Test 7014 – PMHS 7, MNB Fixed, 2.5 m/s

Test 7015 – PMHS 7, All Free, 0.5 m/s

210 Test 7016 – PMHS 7, All Free, 1.5 m/s

Test 7017 – PMHS 7, All Free, 2.5 m/s

Test 8003 – PMHS 8, MNB/LS/RS Fixed, 0.5 m/s

Test 8004 – PMHS 8, MNB/LS/RS Fixed, 1.5 m/s

211

Test 8005 – PMHS 8, MNB/LS/RS Fixed, 2.5 m/s

Test 8006 – PMHS 8, LS/RS Fixed, 0.5 m/s

Test 8007 – PMHS 8, LS/RS Fixed, 1.5 m/s

Test 8008 – PMHS 8, LS/RS Fixed, 2.5 m/s

212 Test 8009 – PMHS 8, MNB/RS Fixed, 0.5 m/s

Test 8010 – PMHS 8, MNB/RS Fixed, 1.5 m/s

Test 8011 – PMHS 8, MNB/RS Fixed, 2.5 m/s

Test 8012 – PMHS 8, MNB Fixed, 0.5 m/s

213 Test 8013 – PMHS 8, MNB Fixed, 1.5 m/s

Test 8014 – PMHS 8, MNB Fixed, 2.5 m/s

------NO IRFs WITH VAF > 60%------

Test 8015 – PMHS 8, All Free, 0.5 m/s

Test 8016 – PMHS 8, All Free, 1.5 m/s

Test 8017 – PMHS 8, All Free, 2.5 m/s

214 Test 9003 – PMHS 9, MNB/LS/RS Fixed, 0.5 m/s

Test 9004 – PMHS 9, MNB/LS/RS Fixed, 1.5 m/s

Test 9005 – PMHS 9, MNB/LS/RS Fixed, 2.5 m/s

Test 9006 – PMHS 9, LS/RS Fixed, 0.5 m/s

215 Test 9007 – PMHS 9, LS/RS Fixed, 1.5 m/s

Test 9008 – PMHS 9, LS/RS Fixed, 2.5 m/s

Test 9009 – PMHS 9, MNB/RS Fixed, 0.5 m/s

Test 9010 – PMHS 9, MNB/RS Fixed, 1.5 m/s

216 Test 9011 – PMHS 9, MNB/RS Fixed, 2.5 m/s

------NO IRFs WITH VAF > 60%------

Test 9012 – PMHS 9, MNB Fixed, 0.5 m/s

Test 9013 – PMHS 9, MNB Fixed, 1.5 m/s

Test 9014 – PMHS 9, MNB Fixed, 2.5 m/s

Test 9015 – PMHS 9, All Free, 0.5 m/s

217 Test 9016 – PMHS 9, All Free, 1.5 m/s

Test 9017 – PMHS 9, All Free, 2.5 m/s

218

Appendix F: PMHS Anthropometry

219

Table F.1. PMHS anthropometry summary

Parameter 1 2 3 4 5 6 7 8 9 AVG SD Mass (kg) 60.9 86.4 58.2 72.3 84 59.1 54 58 72.3 67.2 11.3 Stature (cm) 168 170 157 159 178 165 155 168 172 165.8 7.1 Shoulder Breadth (cm) 33.1 35.7 25.8 38 33.5 33.5 28.7 36.5 32.9 33.1 3.8 Chest Breadth (cm) 28.6 30.6 26.6 32.8 30.3 26.4 24.7 30.1 30.8 29.0 2.6 Waist Breadth (cm) 29.4 31.5 32.5 29.2 32.5 27.8 28.8 30.4 30.5 30.3 1.6 Hip Breadth (cm) 31.9 37.4 33.4 33 37 33.6 32.3 33.7 32 33.8 2.0

220 Head Height (cm) 20.6 21.3 21 21 21.1 20 21.4 20.8 20.4 20.8 0.4

Head Length (cm) 18.8 19.4 19 18.8 18 17.7 17.3 19.7 19.4 18.7 0.8 Head Breadth (cm) 13.3 13.9 13.8 14.3 13.2 13.1 13.1 13.6 13.7 13.6 0.4 Head Circumference (cm) 54.1 55.9 55 56.6 54.6 52.8 55 56.8 59.5 55.6 1.9 Neck Circumference (cm) 31.2 34.8 30 41.7 34 31.8 32.3 35.5 36 34.1 3.5 Chest Circumference (cm) 78.5 92.4 77 95 94.3 79.4 74.3 90.3 96.5 86.4 8.9 Waist Circumference (cm) 81.1 87.3 89 86.5 89 79.4 84 86 91.2 85.9 3.8 Chest Depth (cm) 17.8 20.8 16.4 16 20.1 17.8 16.8 19.4 19.8 18.3 1.8 Waist Depth (cm) 18.5 19 17.8 22.7 19 15 17.1 17 16.7 18.1 2.1

220

Appendix G: UTS Model Solution for X Axis Displacement

The second order differential equation for each 9.5 mm segment of displacement is solved using the method of undetermined coefficients for both steady state

(homogeneous) and transient (particular) portions of the response. The homogeneous part of the solution to the differential equation is obtained by solving the roots of the equation by way of the quadratic formula:

x + 2ζ ω x + ω x = (G.1) UTS UTS UTS

2 2 -2ζ ωUTS (2ζ ωUTS) - 4 1 (ωUTS ) UTS UTS 2 2 r1,2 = = -ζ ω (ζ ω ) - (ω ) (G.2) 2(1) UTS UTS UTS UTS UTS

Based on ISM results, the UTS system is underdamped. Therefore, the quantity under the radical will be negative and thus the roots are complex:

2 2 r1,2 = -ζ ω (ω ) - (ζ ω ) i (G.3) UTS UTS UTS UTS UTS

221 The real part of the root is applied to the exponential term, while the imaginary part is applied to the cosine and sine portion of the assumed solution form:

-ζUTSωUTS t x t =e (c1cosωdt + c2sinωdt) (G.4)

where ω (ω 2) - (ζ ω ) 2 (G.5) d UTS UTS UTS

This is the homogeneous, or transient, part of the solution. Next, the particular, or steady state, solution is solved by first assuming that the UTS displacement is caused by a sinusoidal driving force (the sled):

2 FSLED x UTS + 2ζ ωUTS x + ωUTS xUTS = sin(ωSLEDt)=x SLEDsin(ωSLEDt) (G.6) UTS UTS MUTS

Where x SLED is a constant, the peak sled acceleration magnitude. We assume a solution of the form

=Acos(ωSLEDt) Bsin(ωSLEDt) (G.7)

Differentiating,

x (t)=ωSLED(-Asin(ωSLEDt)+Bcos(ωSLEDt)) (G.8)

222

(t)= ωSLED (-Acos(ωSLEDt)-Bsin(ωSLEDt)) (G.9)

Substituting into the differential equation,

ω (-Acos(ω t)-Bsin(ω t))+ 2ζ ω ω (-Asin(ω t)+Bcos(ω t)) SLED SLED SLED UTS UTS SLED SLED SLED

2 + ωUTS (Acos(ωSLEDt) Bsin(ωSLEDt) = x SLEDsin(ωSLEDt) (G.10)

Collecting the cosine and sine terms,

-ω 2 + 2ζ ω ω ω 2A (G.11) SLED UTS UTS SLED UTS

-ω 2 - 2ζ ω ω ω 2B x (G.12) SLED UTS UTS SLED UTS SLED

Solving for A using the cosine terms,

ω 2-ω 2 = 2ζ ω ω (G.13) SLED UTS UTS UTS SLED

2ζ ω ω UTS UTS SLED A = 2 2 (G.14) (ωSLED -ωUTS )

Substituting this expression into the sine term equation,

2ζ ω ω 2 UTS UTS SLED 2 -ωSLED - 2ζ ωUTS ωSLED 2 2 ωUTS B x SLED (G.15) UTS (ωSLED - ωUTS )

223 (2ζ ω ω )2 2 2 UTS UTS SLED -(ω - ωUTS ) - 2 2 = x SLED (G.16) SLED (ωSLED - ωUTS )

x B = SLED (G.17) Zm

(2ζ ω ω )2 2 2 UTS UTS SLED where Zm= -(ω - ωUTS ) - 2 2 (G.18) SLED (ωSLED - ωUTS )

The “A” coefficient then becomes

2ζ ω ω UTS UTS SLED x SLED A = 2 2 (G.19) (ωSLED -ωUTS ) Zm

Assigning new variables D and E:

D = 2ζ ω ω (G.20) UTS UTS SLED

2 2 E = (ωSLED -ωUTS ) (G.21)

We have also

D2 Zm = - E - (G.22) E

The steady state solution is therefore

x SLED x SLED = cos(ωSLEDt) sin(ωSLEDt) (G.23) Zm Zm

Combining the homogeneous and particular parts, the full solution for the UTS displacement is then:

224 x x -ζUTSωUTS t SLED SLED x t = e (c1cosωdt + c2sinωdt) cos(ωSLEDt) sin(ωSLEDt) (G.24) Zm Zm

The coefficients c1 and c2 are determined by considering the initial conditions:

x 0 =0 x 0 =v0 (G.25)

We consider the displacement first to determine c1:

(0) x SLED x SLED x 0 = e (c1(1) +(0) (1) (0) (G.26) Zm Zm

x SLED c1= - (G.27) Zm

The displacement can be differentiated to obtain the expression for UTS velocity:

(0) x SLED x SLED x t = v0 = e ((0) -ζ ωUTSc1(1)+c2ωd(1) –(0)) + ) ωSLED(1) (G.28) UTS Zm Zm

x SLED v0 -ζ ωUTSc1+c2ωd ωSLED (G.29) UTS Zm

x SLED v0 + ζ ωUTSc1 - ωSLED UTS Zm c2= (G.30) ωd

x SLEDD x SLED v0 + ζ ωUTS - - ωSLED UTS ZmE Zm c2= (G.31) ωd

225

Substituting c1 and c2 back into the full equation,

x D x v + ζ ω - SLED – SLED ω x D 0 UTS UTS Z E Z SLED -ζUTSωUTS t SLED m m x t = e - cosωdt + sinωdt + ZmE ωd

x SLED x SLED cos(ωSLEDt) + sin(ωSLEDt) (G.32) Zm Zm

Equation 3.56 is the model-predicted UTS (at T3) displacement in the sled tests. This equation relates the ISM dynamic properties (ζUTS, ωUTS), sled pulse input characteristics

(x SLED, ωSLED , and T3 vertebra kinematics. The T3 velocity and acceleration expressions can be obtained by differentiating the displacement equation (G32).

226

Appendix H: 3D Kinematic Processing of Sled Data

Figure H.1 shows the relationship between global (sled XYZ) and body-fixed

(skeletal x', y', z') coordinate systems.

x' s' y' P

p r r Z X Y

Figure H.1. Rigid body transformation vectors for the head

Position. The expression for global displacement is

rP = r + A s'P (H.1)

where:

227 rP = [xp, yp, zp]T are the global coordinates of the point P (the position/orientation of the

3aω block relative to the sled reference/origin as obtained by FARO arm).

r = [x, y, z]T are the global coordinates of the origin in the body-fixed coordinate system

(the position/orientation of the skeletal reference point to which the 3aω block is

affixed relative to the sled reference as obtained by FARO arm).

s'P = [x' p, y' p, z' p]T are the local body-fixed coordinates of the point P on the rigid body

(position of the 3aω block relative to the origin in the body-fixed coordinate

system).

A is a transformation matrix between the body-fixed and global coordinate systems using time-dependent Euler angles:

cos cos sin sin sin -cos sin sin sin cos sin cos A = cos sin cos cos -sin -sin cos cos sin sin sin sin cos sin cos cos cos

(H.2)

Next, normalized vectors were calculated from FARO points taken from a given

3aω block to get the matrix values for the initial transformation matrix. The initial transformation matrix A is obtained by taking the vectors of the 3aω using 3D FARO position data:

228

X x Y = A y Z z

X x -1 A = Y y (H.3) Z z

Where „1‟ is (x1, y1, z1), „2‟ is (x2, y2, z2), and „3‟ is (x3, y3, z3). „X‟, „Y‟, and „Z‟ are unit vectors in the global (sled) coordinate system. The vector „2-1‟ is the vector from point 1 to point 2, and vector „2-3‟ is the vector from point 2 to point 3. The direction and order of these vectors varied depending on the body location and orientation of the block with respect to SAE J211. The cross product of the two known normal vectors is taken to locate the third orthogonal vector. This approach minimizes human error due to FARO measurement. By equating the matrix values from eq. (H.3) with the expressions in eq.

(H.2), we can determine the initial Euler angles:

-1 -sin θ = A23  θinitial = sin (-A23)

-1 sin cos / cos cos = A13 / A33  tan = A13 / A33  initial = tan (A13 / A33)

-1 sin cos / cos cos = A21 / A22  tan σ = A21 / A22  σinitial = tan (A21 / A22)

There are two possible values for each Euler angle (angle and π ± angle).

Because there are three Euler angles, there are 8 possible combinations of initial Euler angles. If the polarities and block orientation are correctly defined, the initial Euler

229 angles are correct and the FARO-derived transformation matrix values will match those in equation (H.3).

Velocity. An expression for velocity can be obtained by differentiating equation

(H.1) and manipulating to include angular velocity per Kang et al. (2011):

ṙP = ṙ + A ῶ' s'P (H.4)

The relationship between the angular velocity in the body-fixed coordinate system and the angular velocity of the Euler angles in the global coordinate system is:

0 sin - cos cos - sin ῶ' = sin - 0 cos sin - cos cos cos sin cos sin cos 0

(H.5)

0 –

ῶ' = 0 (H.6) 0

The time-dependent angular velocities ( , , and ) of the 2-1-3 Euler angles can be obtained:

cos θ sin cos 0 = cos θ cos -sin 0 (H.7) -sin θ 0 1

230

The Euler angles at each subsequent time step can be obtained in the sled test by numerically integrating the angular velocities of the Euler angles using equations (H.8 –

H.10):

= + 0.5 + t (H.8)

θ = θ + 0.5 + t (H.9)

= +0.5 + t (H.10)

Acceleration. When equation (H.4) is differentiated, an expression for acceleration in the global coordinate system is obtained:

P = + (Aῶ +Aῶ'ῶ')s'P (H.11)

To calculate the acceleration of the local point P in global space, the transformation matrix, with Euler angles updated at each time step using the initial Euler angles and changes in angle measured with the angular rate sensors, is multiplied by the local acceleration measured by accelerometers on the 3aω block. The sled X acceleration was subtracted from the global X acceleration of the skeletal body point to determine the body point motion with respect to the sled for comparison with video analysis. In addition, because gravity represents a significant portion of acceleration in this testing, a technique presented by Wu et al. (2008) was applied.

231 Using equations (H.1), (H.4), and (H.11), the global displacement, velocity, and acceleration for a given skeletal location can be obtained using data from FARO and the

3aω block instrumentation.

232

Appendix I: PMHS 7, 8 , and 9 Sled Test Time Histories

233

Figure I.1. Data from PMHS 7 sled test (set 1)

234

Figure I.2. Data from PMHS 7 sled test (set 2)

235

Figure I.3. Data from PMHS 8 sled test (set 1)

236

Figure I.4. Data from PMHS 8 sled test (set 2)

237

Figure I.5. Data from PMHS 9 sled test

238

Appendix J: Distribution of ISM Dynamic Properties

Figures J.1 – J.6 show the full distribution of natural frequencies and damping ratios for the set of 9 PMHS.

Figure J.1. UTS-PG natural frequency (X axis, all speeds & constraints)

Figure J.2. UTS-PG damping ratio (X axis, all speeds & constraints)

239

Figure J.3. UTS-PG natural frequency (Z axis, all speeds & constraints)

Figure J.4. UTS-PG damping ratio (Z axis, all speeds & constraints)

240

Figure J.5. UTS-PG natural frequency (rotation about Y, all speeds & constraints)

Figure J.6. UTS-PG damping ratio (rotation about Y, all speeds & constraints)

241

Appendix K: Student T-tests on Anthropometry Data (Child vs. Adult)

242

Table K.1. Student t-tests comparing means for child (n=39) and adult (n=9) geometry

Clavicle Length Clavicle Angle Sternal Angle Rib 1 Angle Rib 6 Angle SN-T1Depth t-Test: Two-Sample Assuming Unequalt-Test: Variances Two-Sample Assuming Unequalt-Test: Two-Sample Variances Assuming Unequalt-Test: Variances Two-Sample Assuming Unequalt-Test: Variances Two-Sample Assuming Unequalt-Test: Variances Two-Sample Assuming Unequal Variances

Child Adult Child Adult Child Adult Child Adult Child Adult Child Adult Mean 11.1 14.8 Mean 44.4 30.0 Mean 60.7 73.0 Mean 28.0 40.0 Mean 30.0 40.4 Mean 3.67 2.88 Variance 3.1 2.6 Variance 56.3 25.1 Variance 65.3 61.3 Variance 70.0 110.0 Variance 69.5 107.0 Variance 0.67 0.57 Observations39 9 Observations39 9 Observations39 9 Observations 39 9 Observations 39 9 Observations 39 9 Hypothesized Mean0 Difference Hypothesized0 Mean Difference Hypothesized Mean0 Difference Hypothesized Mean0 Difference Hypothesized Mean0 Difference Hypothesized Mean0 Difference df 13 df 17 df 12 df 10 df 11 df 13 t Stat -6.048 t Stat 7.034 t Stat -4.23 t Stat -3.21 t Stat -2.8009 t Stat 2.797238 P(T<=t) one-tail2E-05 P(T<=t) one-tail1E-06 P(T<=t) one-tail0.0006 P(T<=t) one-tail0.0047 P(T<=t) one-tail0.0086 P(T<=t) one-tail0.007555 t Critical one-tail1.7709 t Critical one-tail1.74 t Critical one-tail1.7823 t Critical one-tail1.8125 t Critical one-tail1.7959 t Critical one-tail1.770933 P(T<=t) two-tail4E-05 P(T<=t) two-tail2E-06 P(T<=t) two-tail0.0012 P(T<=t) two-tail0.0093 P(T<=t) two-tail0.0172 P(T<=t) two-tail0.015109 t Critical two-tail2.1604 t Critical two-tail2.11 t Critical two-tail2.1788 t Critical two-tail2.2281 t Critical two-tail2.201 t Critical two-tail2.160369

T1BodyAng T6BodyAng T1T6BA T1T6HtP T1T6HtA T1BodyD t-Test: Two-Sample Assuming Unequalt-Test: Variances Two-Sample Assuming Unequalt-Test: Two-Sample Variances Assuming Unequalt-Test: Variances Two-Sample Assuming Unequalt-Test: Variances Two-Sample Assuming Unequalt-Test: Variances Two-Sample Assuming Unequal Variances

243 Child Adult Child Adult Child Adult Child Adult Child Adult Child Adult Mean 8.7 13.1 Mean -15.8 -15.4 Mean 24.6 28.5 Mean 9.8 12.5 Mean 9.1 11.6 Mean 5.2 6.4

Variance 19.9 30.1 Variance 46.6 29.4 Variance 51.7 61.7 Variance 3.2 0.5 Variance 2.8 0.9 Variance 0.6 0.4 Observations39 9 Observations39 9 Observations39 9 Observations 39 9 Observations 39 9 Observations 39 9 Hypothesized Mean0 Difference Hypothesized0 Mean Difference Hypothesized Mean0 Difference Hypothesized Mean0 Difference Hypothesized Mean0 Difference Hypothesized Mean0 Difference df 11 df 15 df 11 df 34 df 21 df 13 t Stat -2.209 t Stat -0.183 t Stat -1.381 t Stat -7.617 t Stat -6.155 t Stat -4.71032 P(T<=t) one-tail0.0247 P(T<=t) one-tail0.429 P(T<=t) one-tail0.0974 P(T<=t) one-tail4E-09 P(T<=t) one-tail2E-06 P(T<=t) one-tail0.000204 t Critical one-tail1.7959 t Critical one-tail1.753 t Critical one-tail1.7959 t Critical one-tail1.6909 t Critical one-tail1.7207 t Critical one-tail1.770933 P(T<=t) two-tail0.0493 P(T<=t) two-tail0.858 P(T<=t) two-tail0.1947 P(T<=t) two-tail7E-09 P(T<=t) two-tail4E-06 P(T<=t) two-tail0.000408 t Critical two-tail2.201 t Critical two-tail2.131 t Critical two-tail2.201 t Critical two-tail2.0322 t Critical two-tail2.0796 t Critical two-tail2.160369

T6BodyD T6BodyW SkeletalFraction T1T6AntDep SN-T1Height T1BodyW t-Test: Two-Sample Assuming Unequalt-Test: Variances Two-Sample Assuming Unequalt-Test: Two-Sample Variances Assuming Unequalt-Test: Variances Two-Sample Assuming Unequalt-Test: Variances Two-Sample Assuming Unequalt-Test: Variances Two-Sample Assuming Unequal Variances

Child Adult Child Adult Child Adult Child Adult Child Adult Child Adult Mean 5.2 6.0 Mean 5.2 6.8 Mean 0.82 0.92 Mean 1.8 4.4 Mean 2.4 3.2 Mean 6.1 7.9 Variance 0.6 0.2 Variance 0.7 0.4 Variance 0.002 0.000 Variance 0.4 1.5 Variance 1.2 1.3 Variance 0.9 0.1 Observations39 9 Observations39 9 Observations39 9 Observations 39 9 Observations 39 9 Observations 39 9 Hypothesized Mean0 Difference Hypothesized0 Mean Difference Hypothesized Mean0 Difference Hypothesized Mean0 Difference Hypothesized Mean0 Difference Hypothesized Mean0 Difference df 22 df 15 df 42 df 9 df 12 df 36 t Stat -4.092 t Stat -6.406 t Stat -10.54 t Stat -6.177 t Stat -1.9089 t Stat -9.34184 P(T<=t) one-tail0.0002 P(T<=t) one-tail6E-06 P(T<=t) one-tail1E-13 P(T<=t) one-tail8E-05 P(T<=t) one-tail0.0402 P(T<=t) one-tail1.85E-11 t Critical one-tail1.7171 t Critical one-tail1.753 t Critical one-tail1.682 t Critical one-tail1.8331 t Critical one-tail1.7823 t Critical one-tail1.688298 P(T<=t) two-tail0.0005 P(T<=t) two-tail1E-05 P(T<=t) two-tail2E-13 P(T<=t) two-tail0.0002 P(T<=t) two-tail0.0805 P(T<=t) two-tail3.71E-11 t Critical two-tail2.0739 t Critical two-tail2.131 t Critical two-tail2.0181 t Critical two-tail2.2622 t Critical two-tail2.1788 t Critical two-tail2.028094

243

Appendix L: NASS-CDS Data

244

Table L.1. NASS-CDS case data summary

245

Table L.1. NASS-CDS case data summary (continued)

246

Appendix M: Statistical Analysis of Experimental Head Displacements

To compare with real-world head displacement estimates in this study, five lap/shoulder belted PMHS tests (child and adult) from the literature (Ash et al, 2009;

Shaw et al, 2009) were used to anchor the high end of the normalized head displacement by deltaV data distribution (Table M.1). Forward head excursions from the Shaw subjects were obtained from UVA test reports located in the NHTSA biomechanics database. While the relative belt position for the same restraint geometry varies for different sized subjects, it is assumed that for a given subject size and given restraint geometry, the relative belt position is consistent.

Table M.1. Child & adult PMHS head displacements & occupant characteristics

Test Source Age Height Weight DeltaV Forward Head ID (Years) (mm) (kg) (km/hr) Displacement (mm) N/A Ash (ESV 2009) 13 1470 50 41 360 1294 Shaw (Stapp 2009) 76 1780 70 40 440 1378 Shaw (Stapp 2009) 72 1840 81 40 293 1379 Shaw (Stapp 2009) 40 1790 88 40 374 1380 Shaw (Stapp 2009) 37 1800 78 40 409

Arbogast, et al (2009) reported kinematic data from low speed tests with volunteers age 6 through 30. They found a statistically significant inverse relationship between normalized head excursion and age at low speeds (6.9 – 8.3 km/hr). They

247 commented on the probable difference in spinal flexibility that could be causing this inverse relationship with age. Table M.2 shows the relevant experimental parameters from these tests. This data was used as the middle anchor of the data distribution for normalized head displacement versus deltaV.

Table M.2. Child & adult volunteer head displacements (from Arbogast et al 2009)

Age Height Weight DeltaV Forward Head (Years) (mm) (kg) (km/hr) Displacement (mm) 6 1220 24 8.3 345 7 1230 24 8.3 304 7 1330 28 8.3 361 8 1300 29 8.3 348 8 1400 35 8.3 305 9 1240 25 8.3 314 10 1360 29 8.3 308 10 1380 40 8.3 375 10 1440 33 8.3 283 11 1340 31 8.3 300 11 1510 36 8.3 319 12 1430 40 8.3 313 12 1540 48 8.3 363 12 1550 40 8.3 310 12 1650 50 8.3 325 13 1500 47 8.3 324 13 1540 49 8.3 296 13 1570 44 8.3 224 13 1640 65 8.3 246 14 1730 61 8.3 255 18 1850 74 6.9 269 19 1790 84 6.9 236 20 1780 97 6.9 251 22 1660 65 6.9 340 22 1720 65 6.9 273 22 1760 87 6.9 270 22 1800 107 6.9 230 24 1650 68 6.9 262 24 1690 74 6.9 244 30 1800 81 6.9 260

248 Plots were created for head displacement normalized by occupant height, weight, and body mass index using the volunteer and PMHS data (Figures M.1 – M.3). A logarithmic trend line was hypothesized with a (0,0) point added to anchor the distributions. Occupant height appeared to be the most effective normalization parameter for head displacement, with the highest R-squared values.

Volunteer & PMHS Only

0.30 y = 0.0359Ln(x) + 0.1588 R2 = 0.8112 0.25

0.20

0.15 y = 0.0261Ln(x) + 0.1046 R2 = 0.7954

0.10 Age > 13 Age 6-13

0.05 Log. (Age 6-13) Displacement / Displacement Ht Log. (Age > 13)

0.00 Available Space (NASS) or Head or Head Available (NASS) Space 0 10 20 30 40 50 DV Total (km/hr)

Figure M.1. Head displacement normalized by occupant height, by age group

249 Volunteer & PMHS Only

16 Age > 13 14 Age 6-13 Log. (Age > 13) y = 1.2145Ln(x) + 6.2385 12 Log. (Age 6-13) R2 = 0.2842 10

Displacement / Displacement Wt 2 y = 0.6024Ln(x) + 2.409 R2 = 0.618

0 Available Space (NASS) or Head or Head Available (NASS) Space 0 10 20 30 40 50 DV Total (km/hr)

Figure M.2. Head displacement normalized by occupant weight, by age group

Volunteer & PMHS Only

25 y = 2.4355Ln(x) + 12.148 R2 = 0.5658 20

10 y = 1.9541Ln(x) + 7.2909 R2 = 0.6815 Age > 13 5 Age 6-13 Log. (Age > 13)

Displacement / Displacement BMI Log. (Age 6-13) 0

Available Space (NASS) or Head or Head Available (NASS) Space 0 10 20 30 40 50 DV Total (km/hr)

Figure M.3. Head displacement normalized by occupant body mass index (in kg / m2), by

age group

250 After transforming the head displacement normalized by subject stature with a log function to linearize the response and removing the artificial (0, 0.0001) low-end anchor data point, a two-way ANOVA was conducted between the two age groups to statistically compare their linear fits. It was determined that the log of the occupant height- normalized head displacement was affected significantly by delta V (p=0.033) and age group (p < 0.0001). The age group – delta V interaction term was insignificant

(p=0.1686). The positive slope for delta V (0.0071) indicates that normalized head displacement increases with delta V for both age groups, as expected. The negative slope for age group (-0.325) indicates that the younger age group experienced a higher head displacement for a given delta V. A second two-way ANOVA was conducted by treating age as a continuous variable rather than a binary categorical variable. The log of the normalized head displacement was affected significantly by both delta V and age (p <

0.0001 for each). The age – delta V interaction term was significant this time

(p=0.0065). The positive slope for delta V (0.0106) again indicates that normalized head displacement increases with delta V. The negative slope for age (-0.0258) indicates that the normalized head displacement decreases with increasing age. Table M.3 summarizes the statistical model parameters (estimates and their p-values) for binary or continuous age models of head displacement normalized by occupant height, weight, and body mass index.

251 Table M.3. Statistical comparison to determine best normalization factor

Age*D Norm. Treat Age Age Age DV P- Age*DV Intercept DV Est V P- Factor As Est P-Value Value Est Value Height Binary -1.598 -0.325 <0.0001 0.0071 0.033 0.0084 0.1686 Height Continuous -1.383 -0.0258 <0.0001 0.0106 <0.0001 0.00083 0.0065 Weight Binary 2.052 -0.803 <0.0001 0.0052 0.428 0.0237 0.0583 Weight Continuous 2.627 -0.0649 <0.0001 0.0102 0.121 0.0022 <0.000 BMI Binary 2.761 -0.405 <0.0001 0.0057 0.178 0.0206 0.01261 BMI Continuous 3.091 -0.0354 <0.0001 0.008 0.0706 0.0013 <0.000 1

It was concluded that, because of the highest R-squared values and significance of deltaV as a predictive variable, occupant height was the best normalization parameter. It was also concluded that continuous age was more appropriate than binary age because age, which is statistically significant in either case, provides more information to the model. Thus, the occupant height-continuous age statistical model was used for development of the large child head response criteria:

Predicted Log (Head Displacement / Height) = -1.38 - 0.0258*(Age) +

0.01056*(DeltaV) + 0.00083*((Age-19.2)*(DeltaV-12.4571))

The interaction term of age*deltaV was evaluated by cross-plotting the log(response) vs. deltaV for the two age groups. The significant interaction between age and deltaV seems to be due to the intersection of the two lines at high speeds (Figure

M.4). This indicates that the difference between head displacement of younger versus older occupants becomes less significant at higher speeds. However, this conclusion

252 should be used with caution, as this convergence may be an artifact of less data points at high speeds than at lower speeds.

Interaction between Age Group and DeltaV

0.0 0 10 20 30 40 50 60

-0.5

Kids Age 6-13 -1.0 y = 0.0034x - 1.5474 Age > 13 R2 = 0.0184 Linear (Age > 13) -1.5 Linear (Kids Age 6-13)

y = 0.0118x - 1.9855

Log(Head Disp / Ht) Log(Head Occ -2.0 R2 = 0.6508

-2.5 DeltaV (km/hr)

Figure M.4. Adults & children head displacements converge at higher deltaV

253

Appendix N: Radiology Plots

(*Age is independent variable in each)

254

255

256