The Biomechanics of Impact Injury

Albert I. King

The Biomechanics of ImpactInjury

Biomechanical Response, Mechanismsof Injury, Human Tolerance and Simulation

Albert I. KingDepartment of Biomedical EngineeringWayne State UniversityDetroit, MI, USA

ISBN 978-3-319-49790-7 ISBN 978-3-319-49792-1 (eBook)DOI 10.1007/978-3-319-49792-1

Library of Congress Control Number: 2016957987

© Springer International Publishing AG 2018This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part ofthe material is concerned, specifically the rights of translation, reprinting, reuse of illustrations,recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmissionor information storage and retrieval, electronic adaptation, computer software, or by similar ordissimilar methodology now known or hereafter developed.The use of general descriptive names, registered names, trademarks, service marks, etc. in thispublication does not imply, even in the absence of a specific statement, that such names are exemptfrom the relevant protective laws and regulations and therefore free for general use.The publisher, the authors and the editors are safe to assume that the advice and information in thisbook are believed to be true and accurate at the date of publication. Neither the publisher nor theauthors or the editors give a warranty, express or implied, with respect to the material containedherein or for any errors or omissions that may have been made. The publisher remains neutral withregard to jurisdictional claims in published maps and institutional affiliations.

Printed on acid-free paper

This Springer imprint is published by Springer NatureThe registered company is Springer International Publishing AGThe registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

To the Holy Spirit for inspiring, guiding,and enabling me to write this bookTo Liz, my wife for 56 years, whose patience,love, and service have enabled me to pursuemy career and goals in injury biomechanicsDeo gratias

Preface

The aim of this book is to summarize the significant principles and research results

in injury biomechanics for graduate students and professionals in the field of

automotive safety. It is based on several decades of injury research and grew out

of a course in computer modeling of impact biomechanics that I developed and

taught for many years. Since modeling requires basic knowledge of the biome-

chanics of impact, a lot of material related to impact injury was included in the

course. As a result, this book provides the reader with not only the models available

to simulate impact on the human body but also the fundamental knowledge of

impact biomechanics. It covers injury to the entire body, from head to toe, and it

discusses the four main areas of the field, namely, mechanical response, injury

mechanisms, human tolerance, and simulation of impact to various body regions.

The book is organized by body region with topics of special interest added at the

end. Head injury is emphasized because there is currently no cure for this injury,

and it is hoped that the detailed information provided will lead to effective preven-

tion of this injury. Topics of interest to the automotive safety engineer include side

impact and car-pedestrian impact. The book concludes with a chapter on sports-

related impact (contact) injuries in football and baseball. A significant portion of the

material covered is based on the work done at Wayne State University by myself;

my colleagues Dr. King H. Yang, Dr. John M. Cavanaugh, and Dr. David Viano;

and my former and current graduate students, A. Al-Bsharat, P. Begeman, B. Deng,

A. El-Bohy, N. Hakim, W. Hardy, Y. Huang, A. Irwin, R. Jadischke, K. Krieger,

N. Mital, A. Padgaonkar, P. Prasad, J. Ruan, B. Smith, S. Tennyson, P. Vulcan,

K. Yang, and C. Zhou whose work is referenced in this book. The work of former

students of Dr. King Yang and that of Toyota visiting scholars are also acknowl-

edged. Dr. Yang’s former students are X. Jin, J. Hu, J. Lee, H. Mao, C. Shah,

K. Wang, and L. Zhang, and the Toyota visiting scholars are S. Hayashi,

M. Iwamoto, Y. Kitagawa, and A. Tamura. To all of them, I owe a debt of gratitude

as well as to many unnamed individuals who have provided assistance.

Since biomechanics is an interdisciplinary field, some basic understanding of

mechanics (dynamics) as well as human anatomy will be helpful. However, I have

vii

had biology majors with no background in physics, and mechanical and electrical

engineers with no training in anatomy take and pass my course. A fair amount of

statistics is used to assess the probability of an injury, and, for those who have no

background in statistics, some additional reading on statistics will be helpful. To

fully appreciate the mathematics behind the modeling of impact events, some

knowledge of differential equations is required.

The problems at the end of each chapter take the form of multiple choice

questions to test the student’s ability to grasp the concepts and to determine if the

student can sort out the correct answer from the many facts and figures presented in

the text.

Finally, I urge the reader to keep in mind this mantra: “You cannot prevent an

injury unless you know its cause.” Several examples are cited in the book, and some

of the unsolved problems are due precisely to a lack of understanding or knowledge

of their cause(s).

Detroit, MI, USA Albert I. King

viii Preface

Acknowledgements

The assistance of many individuals was essential to the completion of this book. In

addition to those people mentioned in the Preface, I would like to thank the

following individuals:

Dawn (Dan) Li, research assistant in the Biomedical Engineering Department, for

compiling the chapters and carefully checking all aspects of the book

Sherry Barclay, librarian of the Wayne State University Libraries, for finding the

many publications referenced in the book

I would also like to express my gratitude to those who donated their bodies for

impact biomechanics research. Without their generosity, crash dummies could not

be made humanlike and computer models could not be validated.

ix

Contents

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1 Injury and Injury Prevention . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 Some US and Global Statistics . . . . . . . . . . . . . . . . . . . . . . . . 2

1.3 Impact Biomechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.4 History of Impact Biomechanics . . . . . . . . . . . . . . . . . . . . . . . 5

1.5 The Role of the Federal Government and Automotive

Safety Standards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

1.6 Major Subdivisions of the Field of Impact Biomechanics . . . . . 9

1.6.1 Injury Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

1.6.2 Response to Impact . . . . . . . . . . . . . . . . . . . . . . . . . . 11

1.6.3 Human Tolerance to Impact . . . . . . . . . . . . . . . . . . . . 14

1.6.4 Technology Assessment . . . . . . . . . . . . . . . . . . . . . . . 21

Questions for Chapter 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

Answers to Problems by Chapter . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

2 Basics of the Biomechanics of Brain Injury . . . . . . . . . . . . . . . . . . 35

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

2.2 Anatomy of the Head and Brain . . . . . . . . . . . . . . . . . . . . . . . 36

2.2.1 Anatomy of the Brain . . . . . . . . . . . . . . . . . . . . . . . . . 38

2.2.2 Histology of Brain Cells . . . . . . . . . . . . . . . . . . . . . . . 42

2.3 Types of Head Injury . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

2.3.1 Brain Tissue Damage . . . . . . . . . . . . . . . . . . . . . . . . . 47

2.4 Theories of Brain Injury Mechanisms . . . . . . . . . . . . . . . . . . . 49

2.5 Mechanical Response of the Head and Brain . . . . . . . . . . . . . . 52

2.5.1 Visualization of Brain Response . . . . . . . . . . . . . . . . . 54

2.5.2 Mechanical Properties of the Pia-Arachnoid

Complex . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

xi

2.6 Tolerance of the Head and Brain to Blunt Impact . . . . . . . . . . . 64

2.6.1 Tolerance of the Skull to Fracture . . . . . . . . . . . . . . . . 65

2.6.2 Tolerance of the Brain to Blunt Impact . . . . . . . . . . . . 66

Questions for Chapter 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

Answers to Problems by Chapter . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

3 Head Injury Research: Experimental Studies . . . . . . . . . . . . . . . . . 77

3.1 Experimental Research on Head Injury Mechanisms . . . . . . . . . 78

3.1.1 The Linear Acceleration Mechanism . . . . . . . . . . . . . . 78

3.1.2 The Angular Acceleration Mechanism . . . . . . . . . . . . 80

3.2 Experimental Research on Head Impact Response . . . . . . . . . . 83

3.2.1 Visualization of Brain Motion during Impact . . . . . . . . 84

3.2.2 Experiments on Diffuse Axonal Injury . . . . . . . . . . . . 89

3.2.3 Experiments on Focal Brain Injuries . . . . . . . . . . . . . . 90

3.3 Experimental Research on Human Head Tolerance

to Impact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

3.4 A Hypothesis for the Cause of Acute Subdural Hematoma . . . . 94

3.4.1 The Dura Mater . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

3.4.2 The Arachnoids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

3.4.3 Anatomy of Cortical Vessels . . . . . . . . . . . . . . . . . . . 96

3.4.4 Acute Subdural Hematomas . . . . . . . . . . . . . . . . . . . . 97

3.4.5 Epidemiology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

3.4.6 Biomechanical Mechanisms for the Formation of ASDH 98

3.5 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

Questions for Chapter 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

Answers to Problems by Chapter . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

4 Head Injury Research: Computer Models of Head Impact . . . . . . . 111

4.1 Pre-finite Element Models of Head Impact . . . . . . . . . . . . . . . . 111

4.2 Finite Element Models of the Brain . . . . . . . . . . . . . . . . . . . . . 113

4.2.1 Brain Model by Ruan et al. (1994) . . . . . . . . . . . . . . . 113

4.2.2 Brain Model by Zhou et al. (1995) . . . . . . . . . . . . . . . 117

4.2.3 Brain Model by Al-Bsharat et al. (1999) . . . . . . . . . . . 118

4.2.4 Brain Model by Zhang et al. (2001): The Wayne

State University Brain Injury Model (WSUBIM) . . . . . 125

4.2.5 Other Finite Element Models of Brain Injury . . . . . . . . 129

4.3 Computer Models of Animal Brains . . . . . . . . . . . . . . . . . . . . . 130

4.3.1 Two-Dimensional Swine Model with an Inhomogeneous

Brain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

4.3.2 Models of Focal Brain Injuries . . . . . . . . . . . . . . . . . . 135

4.4 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145

Questions for Chapter 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146

xii Contents

Answers to Problems by Chapter . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149

5 Measurement of Angular Acceleration . . . . . . . . . . . . . . . . . . . . . . 153

5.1 The Unstable Six-Accelerometer Scheme . . . . . . . . . . . . . . . . . 153

5.2 The Stable Measurement of Angular Acceleration

Using the Wayne State Method . . . . . . . . . . . . . . . . . . . . . . . . 156

5.3 Other Methods of Measuring Angular Acceleration . . . . . . . . . 159

5.3.1 Other Measurement Schemes Using Linear

Accelerometers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159

5.3.2 Measurement Schemes Using Specially Designed

Angular Accelerometers . . . . . . . . . . . . . . . . . . . . . . . 160

5.4 Validation of the Wayne State Method . . . . . . . . . . . . . . . . . . . 161

5.4.1 Criteria for Validation . . . . . . . . . . . . . . . . . . . . . . . . 161

5.4.2 Validation of the Wayne State Method Using Sled

Impact Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163

5.4.3 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . 168

5.5 Miscellaneous Problems in the Measurement of Angular

Acceleration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169

5.5.1 Frequency Response of Linear Accelerometers . . . . . . 169

5.5.2 Cross Talk in Linear Accelerometers . . . . . . . . . . . . . 169

5.5.3 Methods of Calibrating Accelerometers . . . . . . . . . . . . 170

5.5.4 Low-Frequency Response of Accelerometer . . . . . . . . 171

5.5.5 Effect of Errors in the Data . . . . . . . . . . . . . . . . . . . . 172

5.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174

Questions for Chapter 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175

Answers to Problems by Chapter . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178

6 Real-World Brain Injuries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179

6.1 Tolerance of US Football Players to Mild Concussion . . . . . . . 179

6.1.1 Study Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . 180

6.1.2 Discussion of the Results of the NFL Study . . . . . . . . . 188

6.2 Simulation of Real-World Vehicular Crashes . . . . . . . . . . . . . . 189

6.3 Head Injuries Sustained in Indy Racecars . . . . . . . . . . . . . . . . . 193

6.3.1 Some Background Information About Racecar

Safety and Crash Severities . . . . . . . . . . . . . . . . . . . . 194

6.3.2 Use of the WSUHIM to Predict Brain Response

in Indy Car Crashes . . . . . . . . . . . . . . . . . . . . . . . . . . 196

6.4 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197

Questions for Chapter 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197

Answers to Problems by Chapter . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199

Contents xiii

7 Impact Biomechanics of Neck Injury . . . . . . . . . . . . . . . . . . . . . . . 201

7.1 A Brief Anatomical Review of the Spinal Column . . . . . . . . . . 201

7.2 Impact Injuries of the Cervical Spine . . . . . . . . . . . . . . . . . . . . 207

7.2.1 Activities that Can Cause Neck Injuries . . . . . . . . . . . 208

7.2.2 Mechanisms of Cervical Spine Injuries due to Impact . 208

7.3 Experimental Studies on Cervical Spine Injuries . . . . . . . . . . . . 213

7.4 Tolerance of the Cervical Spine . . . . . . . . . . . . . . . . . . . . . . . . 219

7.4.1 Tolerance of the Cervical Spine to Extension

and Flexion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219

7.4.2 Tolerance of the Cervical Spine to Compression . . . . . 221

7.4.3 Tolerance of the Cervical Spine to Tension . . . . . . . . . 222

7.4.4 Tolerance of the Cervical Spine in Shear . . . . . . . . . . . 223

7.5 Computer Models of the Cervical Spine . . . . . . . . . . . . . . . . . . 223

7.5.1 The Three-Dimensional Neck Model

by Yang et al. (1998) . . . . . . . . . . . . . . . . . . . . . . . . . 224

7.6 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232

Questions for Chapter 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234

Answers to Problems by Chapter . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239

8 The Biomechanics of Whiplash . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243

8.1 Anatomy of the Spinal Cord and Neurophysiology of Pain . . . . 243

8.1.1 Spinal Cord Anatomy . . . . . . . . . . . . . . . . . . . . . . . . . 244

8.1.2 Neurophysiology of Pain . . . . . . . . . . . . . . . . . . . . . . 244

8.2 Hypotheses for Whiplash Pain . . . . . . . . . . . . . . . . . . . . . . . . . 245

8.2.1 The Hyperextension Hypothesis for Whiplash Pain . . . 246

8.2.2 The Muscle Hypothesis for Whiplash Pain . . . . . . . . . 246

8.2.3 The Muscle Flexion Hypothesis for Whiplash Pain . . . 247

8.2.4 A Pinching Hypothesis . . . . . . . . . . . . . . . . . . . . . . . . 248

8.2.5 The Pressure Hypothesis . . . . . . . . . . . . . . . . . . . . . . 248

8.2.6 The Shear Hypothesis for Whiplash Pain . . . . . . . . . . . 249

8.3 Experimental Studies on Whiplash . . . . . . . . . . . . . . . . . . . . . 251

8.3.1 Whiplash Experiments Using Volunteers . . . . . . . . . . . 251

8.3.2 Whiplash Experiments Using Cadavers . . . . . . . . . . . . 253

8.3.3 Whiplash Experiments Using Cadavers

and High-Speed X-ray Cinematography . . . . . . . . . . . 254

8.4 Tolerance of the Neck to Whiplash . . . . . . . . . . . . . . . . . . . . . 271

8.5 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272

Questions for Chapter 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273

Answers to Problems by Chapter . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278

9 Impact Injuries of the Thoracolumbar Spine . . . . . . . . . . . . . . . . . 281

9.1 Brief Anatomical Review of the Thoracolumbar Spine . . . . . . . 281

9.2 Impact Injuries of the Thoracolumbar Spine . . . . . . . . . . . . . . . 283

xiv Contents

9.3 Experimental Studies on Lumbar Spine Injuries

due to +Gz Acceleration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 288

9.3.1 Early Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 290

9.3.2 Subsequent Test Results . . . . . . . . . . . . . . . . . . . . . . . 291

9.3.3 Commentary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303

9.4 Tolerance of the Thoracolumbar Spine . . . . . . . . . . . . . . . . . . . 304

9.5 The Issue of Acute Rupture of the Intervertebral Discs . . . . . . . 308

Questions for Chapter 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 310

Answers to Problems by Chapter . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315

10 Biomechanics of Facet Loading in the Lumbar Spine . . . . . . . . . . . 319

10.1 Direct Measurement of Lumbar Facet Loading . . . . . . . . . . . . . 319

10.2 The Sequence of Events Occurring During Seat Ejection . . . . . 328

10.3 Mechanism of Injury to the Thoracolumbar Spine

due to Ejection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 330

10.4 Early Models of the Spine Simulating Vertical Acceleration . . . 331

10.4.1 Lumped Parameter Spinal Models . . . . . . . . . . . . . . . . 331

10.4.2 Simple Continuum Models . . . . . . . . . . . . . . . . . . . . . 333

10.4.3 Discrete Parameter Models . . . . . . . . . . . . . . . . . . . . . 333

10.5 A Two-Dimensional Model of the Thoracolumbar Spine . . . . . . 333

10.6 Simulation of Combined Vertical and Horizontal

Acceleration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 338

10.6.1 Application of the 2-D Model to the Aircraft

Ditching Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339

10.7 Finite Element Modeling of the Thoracolumbar Spine . . . . . . . 343

10.8 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 349

Questions for Chapter 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 349

Answers to Problems by Chapter . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354

11 Impact Biomechanics of the Thorax . . . . . . . . . . . . . . . . . . . . . . . . 357

11.1 Brief Anatomical Review of the Thorax . . . . . . . . . . . . . . . . . . 357

11.2 Thoracic Injury Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . 362

11.2.1 Flail Chest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363

11.2.2 Lung Contusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364

11.2.3 Hemo- and Pneumothorax . . . . . . . . . . . . . . . . . . . . . 364

11.2.4 Injuries to the Heart and Great Vessels . . . . . . . . . . . . 364

11.3 Thoracic Injury Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . 367

11.4 Experiments on the Thorax: Frontal and Side Impact . . . . . . . . 367

11.4.1 Frontal Impact Experiments . . . . . . . . . . . . . . . . . . . . 367

11.4.2 Side Impact Experiments . . . . . . . . . . . . . . . . . . . . . . 373

11.5 Thoracic Response to Frontal and Side Impact . . . . . . . . . . . . . 381

11.6 Biomechanics of Aortic Rupture due to Thoracic Impact . . . . . 382

11.7 Tolerance of the Thorax to Impact Loading . . . . . . . . . . . . . . . 388

11.8 Modeling of Thoracic Response . . . . . . . . . . . . . . . . . . . . . . . 390

Contents xv

11.9 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 400

Questions for Chapter 11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 401

Answers to Problems by Chapter . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405

12 Impact Biomechanics of the Abdomen . . . . . . . . . . . . . . . . . . . . . . 409

12.1 Brief Anatomical Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . 409

12.1.1 Solid Abdominal Organs . . . . . . . . . . . . . . . . . . . . . . 410

12.1.2 Hollow Abdominal Organs . . . . . . . . . . . . . . . . . . . . . 413

12.2 Abdominal Injuries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413

12.3 Abdominal Injury Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . 414

12.4 Mechanical Response of the Abdomen . . . . . . . . . . . . . . . . . . . 414

12.4.1 Abdominal Response to Frontal Impact . . . . . . . . . . . . 414

12.4.2 Abdominal Response to Lateral Impact . . . . . . . . . . . . 420

12.5 Tolerance of the Abdomen to Impact . . . . . . . . . . . . . . . . . . . . 421

12.6 Mechanical Characterization of Abdominal Organs . . . . . . . . . 424

12.6.1 The QLV Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . 424

12.6.2 Stress–Strain Curves for Solid Abdominal

Organs (Tamura et al. 2002) . . . . . . . . . . . . . . . . . . . . 427

12.7 Computer Models of the Abdomen . . . . . . . . . . . . . . . . . . . . . 431

12.7.1 Model Geometry and Material Properties . . . . . . . . . . 431

12.7.2 Material Properties of the Model Elements . . . . . . . . . 434

12.7.3 Model Validation and Predictions . . . . . . . . . . . . . . . . 436

12.8 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 442

Questions for Chapter 12 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 442

Answers to Problems by Chapter . . . . . . . . . . . . . . . . . . . . . . . . . . . . 444

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445

13 Impact Biomechanics of the Pelvis . . . . . . . . . . . . . . . . . . . . . . . . . 447

13.1 Anatomy of the Skeletal Pelvis . . . . . . . . . . . . . . . . . . . . . . . . 447

13.2 Pelvic Injuries Due to Impact . . . . . . . . . . . . . . . . . . . . . . . . . 452

13.2.1 Femoral Neck Fractures in the Elderly . . . . . . . . . . . . 456

13.3 Mechanical Response of the Pelvis to Impact . . . . . . . . . . . . . . 457

13.3.1 Frontal Response of the Pelvis to Impact . . . . . . . . . . . 457

13.3.2 Lateral Response of the Pelvis to Impact . . . . . . . . . . . 461

13.4 Tolerance of the Pelvis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 463

13.5 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 464

Questions for Chapter 13 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 464

Answers to Problems by Chapter . . . . . . . . . . . . . . . . . . . . . . . . . . . . 466

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 466

14 Impact Biomechanics of the Lower Extremities . . . . . . . . . . . . . . . 469

14.1 Anatomy of the Thigh and Leg . . . . . . . . . . . . . . . . . . . . . . . . 469

14.2 Injury Mechanisms of the Thigh and Leg . . . . . . . . . . . . . . . . . 475

14.2.1 Long Bone Fractures Due to Tensile Strains . . . . . . . . 475

14.2.2 Injury Mechanisms Involving the Knee . . . . . . . . . . . . 477

14.2.3 Injury Mechanisms Involving the Ankle . . . . . . . . . . . 484

xvi Contents

14.3 Mechanical Response of the Thigh and Leg to Impact . . . . . . . 488

14.3.1 Response of the Femur (Knee) to Frontal Impact . . . . . 488

14.3.2 Tibial Response to Impact . . . . . . . . . . . . . . . . . . . . . 492

14.4 Tolerance of the Thigh and Leg to Impact . . . . . . . . . . . . . . . . 493

14.4.1 Tolerance of the Thigh (Femur) . . . . . . . . . . . . . . . . . 493

14.5 Tolerance of the Leg . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 494

14.6 The Tibia Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 495

14.7 An Impact Model of the Lower Extremity . . . . . . . . . . . . . . . . 496

14.8 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 500

Questions for Chapter 14 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 501

Answers to Problems by Chapter . . . . . . . . . . . . . . . . . . . . . . . . . . . . 505

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 505

15 Impact Biomechanics of the Foot . . . . . . . . . . . . . . . . . . . . . . . . . . 509

15.1 Anatomy of the Foot and Ankle . . . . . . . . . . . . . . . . . . . . . . . . 509

15.2 Injury Mechanisms and Tolerance of the Foot and Ankle . . . . . 514

15.3 The Lisfranc Fracture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 521

15.4 A Biomechanical Study of Foot Fracture . . . . . . . . . . . . . . . . . 523

15.5 Modeling of Foot Impact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 531

15.6 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 534

Questions for Chapter 15 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 534

Answers to Problems by Chapter . . . . . . . . . . . . . . . . . . . . . . . . . . . . 536

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 536

16 Side Impact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 539

16.1 The Kinematics of Side Impact . . . . . . . . . . . . . . . . . . . . . . . . 539

16.2 Side Impact Injuries and Injury Criteria . . . . . . . . . . . . . . . . . . 541

16.3 A Cadaveric Study of Side Impact—Sled Tests . . . . . . . . . . . . 545

16.4 A Cadaveric Study of Side Impact—Pendulum Impacts . . . . . . 548

16.5 Models of Side Impact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 551

16.5.1 Effect of Air Space . . . . . . . . . . . . . . . . . . . . . . . . . . 557

16.5.2 Effect of Padding . . . . . . . . . . . . . . . . . . . . . . . . . . . . 557

16.5.3 Reduction in Door Velocity . . . . . . . . . . . . . . . . . . . . 558

16.5.4 Loss of Shoulder Engagement . . . . . . . . . . . . . . . . . . 558

16.6 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 559

Questions for Chapter 16 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 561

Answers to Problems by Chapter . . . . . . . . . . . . . . . . . . . . . . . . . . . . 566

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 566

17 Car-Pedestrian Impact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 569

17.1 Epidemiology of Car-Pedestrian Impact . . . . . . . . . . . . . . . . . . 569

17.2 Car-Pedestrian Impact Experiments . . . . . . . . . . . . . . . . . . . . . 571

17.3 Modeling of Car-Pedestrian Impact . . . . . . . . . . . . . . . . . . . . . 580

17.4 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 590

Questions for Chapter 17 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 590

Answers to Problems by Chapter . . . . . . . . . . . . . . . . . . . . . . . . . . . . 594

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 594

Contents xvii

18 Biomechanics of Automotive Safety Restraints . . . . . . . . . . . . . . . . 597

18.1 Effectiveness of Restraints in Frontal Impact . . . . . . . . . . . . . . 597

18.2 Effectiveness of Restraints in Side Impact . . . . . . . . . . . . . . . . 602

18.3 Effectiveness of Restraints in Rear Impact . . . . . . . . . . . . . . . . 603

18.4 Types of Rollovers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 605

18.5 Rollover Crash Injury Statistics . . . . . . . . . . . . . . . . . . . . . . . . 610

18.6 Experimental Simulation of Rollover Crashes . . . . . . . . . . . . . 613

18.7 Modeling of Rollover Crashes . . . . . . . . . . . . . . . . . . . . . . . . . 614

18.8 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 617

Questions for Chapter 18 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 623

Answers to Problems by Chapter . . . . . . . . . . . . . . . . . . . . . . . . . . . . 626

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 627

19 Biomechanics of Sports Injuries . . . . . . . . . . . . . . . . . . . . . . . . . . . 629

19.1 Overview of Sports Injuries . . . . . . . . . . . . . . . . . . . . . . . . . . . 629

19.2 Mild Traumatic Brain Injury in American Football . . . . . . . . . . 629

19.2.1 What is Mild Traumatic Brain Injury? . . . . . . . . . . . . . 629

19.2.2 The American Football Helmet . . . . . . . . . . . . . . . . . . 631

19.3 Acute Subdural Hematoma (ASDH) . . . . . . . . . . . . . . . . . . . . 632

19.4 Sports-Related Catastrophic Neck Injuries . . . . . . . . . . . . . . . . 632

19.5 Fatal Arrhythmias in Baseball Impacts . . . . . . . . . . . . . . . . . . . 633

19.6 Ligament Injuries in Football . . . . . . . . . . . . . . . . . . . . . . . . . 637

19.7 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 643

Questions for Chapter 19 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 643

Answers to Problems by Chapter . . . . . . . . . . . . . . . . . . . . . . . . . . . . 645

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 646

20 Epilogue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 649

20.1 We Have Come a Long Way . . . . . . . . . . . . . . . . . . . . . . . . . . 649

20.2 What is Next for Impact Biomechanics? . . . . . . . . . . . . . . . . . 651

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 652

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 653

xviii Contents

List of Figures

Fig. 1.1 Fatality rate per 100 million vehicle miles traveled

from 1922 to 2012 in the USA .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Fig. 1.2 Dramatic drop in annual fatality rate between 2005

and 2008 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

Fig. 1.3 Professor H. R. Lissner (1908–1965) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

Fig. 1.4 Dr. E. S. Gurdjian (1900–1985) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

Fig. 1.5 The Wayne State Tolerance Curve for head injury . . . . . . . . . . . . . . 7

Fig. 1.6 The hip joint—Femoral neck fractures (hip fractures)

do not occur when the greater trochanter is impacted,

and they occur in the elderly when they fall to the side.

Thus, neck fracture due to osteoporosis is the cause

of the fall, and the statement that “Grandma fell

and broke her hip” is biomechanically incorrect . . . . . . . . . . . . . . . . . 11

Fig. 1.7 Example of impact biomechanical response—Chest

force-deflection response due to frontal

impact by a pendulum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

Fig. 1.8 Example of impact biomechanical response—Contact

force-time curves for frontal head impact . . . . . . . . . . . . . . . . . . . . . . . . 13

Fig. 1.9 Example of impact biomechanical response—Acceleration-

time curve for acceleration of the 4th rib due to lateral

impact to the chest. The dark curve represents the mean,

while the dotted curves form the corridor of data

from multiple cadavers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

Fig. 1.10 A typical logistic plot. This plot is an example

of using logistic regression to obtain the probability

of a chest injury of AIS4 or above as predicted

by using the independent parameter VCmax . . . . . . . . . . . . . . . . . . . . . . 16

Fig. 1.11 Logistic curve for the product of strain and strain rate

for mTBI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

xix

Fig. 1.12 Definition of true and false positives (TP and FP)

and true and false negatives (TN and FN) for an arbitrary

threshold. For the threshold selected, there are no false

negatives or positives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

Fig. 1.13 Receiver operator characteristic (ROC) curve for the product

of strain and strain rate based on data from Fig. 1.11.

The area under the curve is 0.943. It indicates that this

parameter is a good predictor of injury . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

Fig. 1.14 The first tolerance is for a sensitivity of 1.0

and is a conservative estimate of injury . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

Fig. 1.15 The second tolerance is for a specificity of 1.0

and is a liberal estimate of injury . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

Fig. 1.16 Optimal tolerance for which the sum of the sensitivity

and specificity ratios is a maximum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

Fig. 1.17 Hypothetical data for chest acceleration, demonstrating

the meaning of a 3-ms clip. In the figure, the cumulative

duration of the acceleration pulse above 60 g exceeds 3 ms

and the pulse in injurious to the chest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

Fig. 1.18 Stress-strain curve for mild steel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

Fig. 1.19 A lumped parameter model simulating the head and torso

subjected to vertical loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

Fig. 1.20 Finite element model of a lumbar vertebra . . . . . . . . . . . . . . . . . . . . . . . 25

Fig. 1.21 The ATB model developed by Calspan Corp.

The segment numbers are in green and the joint

numbers are in red . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

Fig. 2.1 Various causes of traumatic brain injury in 2010 . . . . . . . . . . . . . . . . 36

Fig. 2.2 Bones of the skull and face . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

Fig. 2.3 The cerebral meninges, the superior sagittal sinus and bridging

veins that bridge the CSF layer and transport the blood

from the brain into the superior sagittal . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

Fig. 2.4 Details of the three cerebral meninges, based on a study

by Haines (1991) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

Fig. 2.5 The brain. The cerebrum and the hindbrain are visible.

Approximate locations of the lobes of the cerebrum are

identified . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

Fig. 2.6 The approximate location of the center of gravity (cg) of the

head is in the midsagittal plane slightly anterior to the auditory

meatus and about 3 cm above the Frankfort plane which is at the

level of the inferior border of the orbit or eye socket. The

illustration of the skull was taken from Carola et al. (Eds.),

1992, Human Anatomy & Physiology. Republished with

permission of McGraw-Hill Education, from R. Carola, J.P.

Harley, C.R. Noback (eds.), Human Anatomy & Physiology,

2nd edn., 1992; permission conveyed through Copyright

Clearance Center, Inc. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

xx List of Figures

Fig. 2.7 Arteries of the human brain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

Fig. 2.8 Various types of neurons. Legend: cb stands for cell body

and ax stands for axon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

Fig. 2.9 A typical neuron and its components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

Fig. 2.10 (A–D) Microstructure of a microtubule . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

Fig. 2.11 The node of Ranvier of a myelinated axon . . . . . . . . . . . . . . . . . . . . . . . 44

Fig. 2.12 The four main types of neuroglia which are supporting

cells for the CNS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

Fig. 2.13 The role of astrocytes in the blood-brain barrier. Orthogonal

arrays of particles in the foot process of the astrocytes along

with the tight junctions in the endothelial cell layer may

play a role in the prevention of diffusion of molecules

from the capillaries into the brain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

Fig. 2.14 Diffuse axonal injury in the human corpus callosum.

Dark lines are swollen axons, and black circles are retraction

balls, made visible by means of β-APP staining . . . . . . . . . . . . . . . . . 48

Fig. 2.15 Pressure gradient produces shear stress . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

Fig. 2.16 In head impacts, linear and angular acceleration usually

increase monotonically . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

Fig. 2.17 Intracranial pressure data from a frontal impact

to a cadaver head . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

Fig. 2.18 Cadaver head impact data used to design the Hybrid III head.

The data were from cadaveric forehead impacts to a rigid

surface. The letter F adjacent to a data point indicates that there

was skull fracture. The abscissa, V2/2g, is an equivalent

free fall drop height . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

Fig. 2.19 Side view of a 50th percentile Hybrid III head . . . . . . . . . . . . . . . . . . . 54

Fig. 2.20 Photograph of the biplanar X-ray setup . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

Fig. 2.21 Schematic of a biplanar high-speed X-ray system. The 3-D

imaging area is in light blue (45� 30� 25 cm). The 3-D

accuracy is �0.1 mm. This system is located on the main

campus of Henry Ford Hospital, Detroit, MI . . . . . . . . . . . . . . . . . . . . . 56

Fig. 2.22 Neutral density targets made from tin spheres encased in a

plastic tube to reduce its density to approximately that

of the brain. The tin spheres are in the center of the

photograph. On the right are the plastic tubes and

on the left are end caps to keep the sphere in the tube . . . . . . . . . . 57

Fig. 2.23 Location of neutral density targets in a cadaveric brain

for a sagittal plane impact. AC stands for anterior column

and PC stands for posterior column . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

Fig. 2.24 Cadaveric head specimen suspended from a carriage

used to accelerate the head into a Lucite block . . . . . . . . . . . . . . . . . . 58

Fig. 2.25 The brain traces out a figure eight pattern during impact

relative to the center of gravity of the head. The motion

appears to decrease near the skull. The data were derived

from a frontal impact against a Lucite block with a resultant

List of Figures xxi

deceleration of 62 g and a peak angular acceleration

of 2529 rad/s2. AC stands for anterior column and PC

stands for posterior column . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

Fig. 2.26 Diagram of the pia-arachnoid complex, showing

a blood vessel in the subarachnoid space . . . . . . . . . . . . . . . . . . . . . . . . . 60

Fig. 2.27 This figure describes the specimen preparation procedure.

(A) The cortex of the brain with the PAC attached.

(B) PAC with the underlying brain removed and the pia

facing up. (C) A polyethylene block (marked P for pia)

was glued to the pia side of the PAC. (D) A second block

(marked A for arachnoid) was glued to the opposite side

of the PAC and the excess tissue was trimmed away . . . . . . . . . . . . 61

Fig. 2.28 Strain rate dependency of the PAC due to normal traction, as

demonstrated by its elastic modulus (A), ultimate stress (B),

and ultimate strain (C) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

Fig. 2.29 Loading fixture to test the PAC in shear . . . . . . . . . . . . . . . . . . . . . . . . . . 63

Fig. 2.30 Strain rate dependency of the PAC due to shear loading, as

demonstrated by its shear modulus (A), ultimate stress (B),

and ultimate strain (C) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

Fig. 2.31 Tolerance of the human skull to impact with a rigid

surface in terms of peak impact force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

Fig. 2.32 Tolerance of the human skull to impact with a rigid

surface in terms of peak head acceleration . . . . . . . . . . . . . . . . . . . . . . . 66

Fig. 2.33 Tolerance of the skull to fracture in terms of acceleration and

pulse duration. Clinically, a simple skull fracture is frequently

associated with a mild concussion. Thus, this curve can be

regarded as a tolerance curve for brain concussion. It is the

forerunner of the Wayne State Tolerance Curve shown in

the next figure. (Note: The units for acceleration along the

ordinate should be g’s instead of ft/s2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

Fig. 2.34 Comparison of HIC of about 1000 for a half-sine wave

with the WSTC .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

Fig. 2.35 Injury risk curve in terms of HIC based on the WSTC . . . . . . . . . . 69

Fig. 3.1 Summary of concussion data collected using the fluid

percussion device. The brain was concussed in the absence

of head acceleration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

Fig. 3.2 Photoelastic pattern in milling yellow in a plastic model of a

midsagittal section of the brain. The closeness of the contours

indicates a high shear stress in the brain stem region . . . . . . . . . . . . 81

Fig. 3.3 Tolerance curve for rhesus monkeys subjected to non-contact

head angular acceleration. At 40,000 rad/s2, over 99% of the

animals were concussed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

Fig. 3.4 Neutral density accelerometers (NDA) are triaxial

accelerometers which can measure brain kinematics of a

cadaveric brain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

xxii List of Figures

Fig. 3.5 Comparison of resultant acceleration of the skull with that of the

brain for two impacts, one at 100 g and the other at 40 g. The

NDA was used measure the brain acceleration which is much

lower than that of the skull and is shown as by a dotted and

dashed curve. The solid curves are the skull accelerations.

The inset shows the NDA in the brain which was not lacerated

by it because of its neutral density feature . . . . . . . . . . . . . . . . . . . . . . . . 85

Fig. 3.6 Comparison of displacement data measured using the NDA and

the high-speed biplanar X-ray method. The NDA acceleration

was integrated twice to yield displacement which matched the

X-ray displacement data perfectly. There are actually four

curves in this graph from two tests. Both were occipital impacts

at 2.7 m/s (Test C480-T1) and 4.2 m/s (Test C480-T2) . . . . . . . . . 85

Fig. 3.7 Calculated brain stretch or strain obtained by

differentiating the displacement data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

Fig. 3.8 Brain motion data for a posterior impact causing a peak

linear acceleration of 24 g and a peak angular acceleration

of 1995 rad/s2. The circled targets are selected for detailed

study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

Fig. 3.9 Linear and angular acceleration components of the cadaver head

in test C755-T3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

Fig. 3.10 The x- and z-displacements of the circled targets shown in

Fig. 3.9. It is seen that linear acceleration caused very little

displacement, while angular acceleration is responsible for most

of the displacement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

Fig. 3.11 Brain motion is due to the lag in brain rotation relative to the skull 88

Fig. 3.12 The Marmarou weight-drop device to produce DAI in the brain

of a rodent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

Fig. 3.13 The dynamic cortical deformation method of causing

a focal injury to the brain. A negative pressure pulse

is applied through the tube, and the brain is injured

by being sucked up the tube . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

Fig. 3.14 Validation of a FE model of CCI developed by Schreiber et al.

(1997) using data produced by the same authors . . . . . . . . . . . . . . . . . 91

Fig. 3.15 Test setup for a controlled cortical impact on a rat brain.

A coronal section of the brain is shown with the impactor

vertical and normal to the brain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

Fig. 3.16 Controlled cortical impact on a rat brain with the 2.5 mm

impactor tip normal to the brain but inclined at 22.5�

to the vertical. The velocity of the impactor was 4 m/s

and the penetration was 2 mm. Drawing based

on Chen et al. (2003) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

Fig. 3.17 Setup for a bilateral controlled cortical impact in

which the contralateral craniotomy allowed the brain

the bulge through it during impact. Drawing based

on Meaney et al. (1994) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

List of Figures xxiii

Fig. 3.18 A modified controlled cortical impact test using an impactor

with a rounded tip (A). The tip in (B) is enlarged to show its

exact shape . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

Fig. 3.19 (A) Bridging cortical artery connected to the dura.

(B) Adherence of cortical arterial knuckle to dura

and arachnoid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

Fig. 3.20 ASDH formation due to bridging vein rupture is not possible

in the subdural layer, based on principles of fluid mechanics . . 100

Fig. 4.1 Finite element model of the head by Ruan (1994) . . . . . . . . . . . . . . . 114

Fig. 4.2 Comparison of pendulum impact force . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

Fig. 4.3 Comparison of coup pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

Fig. 4.4 Comparison of contrecoup pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

Fig. 4.5 A parametric study using the model by Ruan et al. (1994).

The left half shows changes in response when pendulum

mass and velocity are decreased by 25 and 50%.

The effects of impact direction are shown on the right . . . . . . . . . . 116

Fig. 4.6 Inhomogeneous brain model by Zhou (1995). The gray

and white matter have different shear moduli based

on their microstructure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

Fig. 4.7 Comparison of predicted head-pendulum contact force

with data provided by Nahum et al. (1977) . . . . . . . . . . . . . . . . . . . . . . . 118

Fig. 4.8 Comparison of predicted coup and contrecoup pressures

with data provided by Nahum et al. (1977) . . . . . . . . . . . . . . . . . . . . . . . 119

Fig. 4.9 The brain model by Al-Bsharat et al. (1999)

is an improved version of that by Zhou et al. (1995).

It has a three-layered skull and a sliding interface

between the CSF layer and the dura . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

Fig. 4.10 Validation of the Al-Bsharat model—comparison of contact

force for a single run . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

Fig. 4.11 Validation of the Al-Bsharat model—comparison of contact

force for all five runs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

Fig. 4.12 Validation of the Al-Bsharat model—comparison of coup

pressure for all five runs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122

Fig. 4.13 Validation of the Al-Bsharat model—comparison

of contrecoup pressure for all five runs . . . . . . . . . . . . . . . . . . . . . . . . . . 122

Fig. 4.14 Validation of the Al-Bsharat model—comparison

of skull-brain relative displacement for Test No. C731-T3 . . . . 123

Fig. 4.15 Validation of the Al-Bsharat model—comparison

of skull-brain relative displacement for Test No. C731-T2 . . . . 124

Fig. 4.16 Validation of the Al-Bsharat model—comparison

of skull-brain relative displacement for Test No. C731-T4 . . . . 124

Fig. 4.17 The Wayne State University Brain Injury Model (WSUBIM)

developed by Zhang et al. (2001) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

xxiv List of Figures

Fig. 4.18 Definition of elasto-plastic characteristics of facial bone,

including fracture behavior. The failure strain is denoted

by ɛf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126

Fig. 4.19 Validation of the WSUBIM against intracranial and ventricular

pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

Fig. 4.20 Validation of the WSUBIM against brain motion data . . . . . . . . . . 128

Fig. 4.21 Validation of the WSUBIM against nasal impact data.

T stands for test data and S for simulation

or model prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

Fig. 4.22 Validation of the WSUBIM against maxillary impact

data taken from Allsop et al. (1988) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

Fig. 4.23 Hourglass energy to internal energy ratio computed

for a linear acceleration input of 200 g and an angular

acceleration input of 12,000 rad/s2, demonstrating stability

of the model under severe impact conditions . . . . . . . . . . . . . . . . . . . . . 130

Fig. 4.24 (A–C) The three 2-D models by Zhou et al. (1994)

which were the first models to feature an inhomogeneous

brain. When white matter was assumed to be 60% stiffer

than gray matter to achieve better correspondence

of strain with observed DAI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132

Fig. 4.25 Approximate locations of the three 2-D models

by Zhou et al. (1994) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

Fig. 4.26 Kinematic input for the 2-D model by Zhou et al. (1994) . . . . . . 134

Fig. 4.27 (A–C) Results of the three 2-D simulations by Zhou et al.

(1994). The shear strain magnitudes are shown along with

darkened areas of observed DAI in porcine experiments . . . . . . . . 136

Fig. 4.28 Finite element model of a rat brain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137

Fig. 4.29 Validation of the rat model by Mao et al. (2006) using

data from a DCD experiment performed by Shreiber et al.

(1997). The solid circles are the model predictions,

and the histograms represent the experimentally measured

means and standard deviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137

Fig. 4.30 The six different CCI experiments simulated

by Mao et al. (2006) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138

Fig. 4.31 Correlation of model predicted brain contusion volume

with that measured experimentally, using a first principal strain

of 30% as the contusion threshold. The residual variance

was 10 mm3. The 45-deg line represents a perfect correlation,

while the error bars represent� 1 standard deviation

from the experimentally determined mean contusion volume

for each test series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139

Fig. 4.32 Modeling the Igarashi et al. (2007) experiments

using the model by Mao et al. (2006) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139

Fig. 4.33 Computed maximum principal strains in the superficial

cortex (SC), deep cortex (DC), hippocampus (Hipp), lateral

List of Figures xxv

thalamus (Thala), and cerebellar vermin (CBV) for a moderate

injury . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140

Fig. 4.34 Correlation of computed maximum principal strain with

observed neuronal loss, for mild, moderate, and severe

injury, in the five regions of the brain monitored

by the model. The error bars are for �1 standard deviation

of the observed neuronal loss (see the caption for Fig. 4.33

above for an explanation of the symbols) . . . . . . . . . . . . . . . . . . . . . . . . . 140

Fig. 4.35 Two-dimensional parasagittal models of the brain,

(A) without blood vessels and (B) with blood vessels . . . . . . . . . . . 141

Fig. 4.36 Large arteries in a parasagittal section of the human

brain near the midsagittal plane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142

Fig. 4.37 A typical stress-stretch curve for cerebral arteries.

The modulus used in the model is 15 MPa. It is for stretch

beyond the physiological range but less than that at failure . . . . 142

Fig. 4.38 Comparison of experimental intracranial pressure

data from Nahum et al. (1977) with pressures predicted

by Models I and II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143

Fig. 4.39 Comparison of relative brain motion between data from Hardy

et al. (2001) and that predicted by Models I and II . . . . . . . . . . . . . . 144

Fig. 4.40 Parametric study of Model II in which Go was varied. For

Go¼ 5 kPa, the strains are lower, implying that blood vessels

enhance brain stiffness. For Go¼ 1 kPa and for a 40% lower

rotational input, the strains were comparable to those with

Go¼ 5 kPa, implying that the use of low values of Go may

require a brain model with a very fine vascular structure. The

brain regions are shown in the figure below the bar charts . . . . . 145

Fig. 5.1 Definition of coordinate systems for the moving rigid body.

The X-Y-Z system is the inertial reference frame while

the x-y-z system is the body-fixed frame . . . . . . . . . . . . . . . . . . . . . . . . . . 154

Fig. 5.2 The five accelerometers needed to compute angular

acceleration, using Eq. 5.3a, 5.3b, and 5.3c . . . . . . . . . . . . . . . . . . . . . . 155

Fig. 5.3 Arrangement of the nine accelerometers used in the Wayne

State method of measuring angular acceleration . . . . . . . . . . . . . . . . . 157

Fig. 5.4 A nine-accelerometer mount used for measuring angular

acceleration in cadavers and animals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158

Fig. 5.5 The nine accelerometers for measuring the angular

acceleration of a Hybrid III dummy head are built into the head

form, centered around the triaxial accelerometer at its cg . . . . . . 158

Fig. 5.6 Hypothetical data used to test the Bortz (1971) method . . . . . . . . . 162

Fig. 5.7 Angular velocity components for the X-, Y- and Z-sequenceof rotations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163

Fig. 5.8 Computed yaw, pitch, and roll for the hypothetical

data used . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163

xxvi List of Figures

Fig. 5.9 Schematic drawing of the experimental setup for a frontal

sled impact. It shows the cube for measuring the angular

data and the position of the three orthogonally placed

cameras . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164

Fig. 5.10 Calibration data of three of the accelerometers used

and of the standard accelerometer. A uni-axial shaker

at 20 Hz was used. The standard was calibrated against

a known NIST standard to calibrate all accelerometers

used in the experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165

Fig. 5.11 Raw (unfiltered) accelerometer data containing spikes

due to cable problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165

Fig. 5.12 Two channels of filtered accelerometer data

using an FFT filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165

Fig. 5.13 Angular velocity components of the dummy head computed

from the measured angular accelerations using the Wayne State

method. The dummy was restrained by a lap shoulder belt

and was subjected to a 15 g frontal impact . . . . . . . . . . . . . . . . . . . . . . . 166

Fig. 5.14 Angular displacements computed from the angular velocity data

shown in Fig. 5.13 are compared with measured 3-D film data.

The computed data at the end of the test also matched the

measured data and show a trend to return to their pre-impact

values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167

Fig. 5.15 Rotation vector computed using the Wayne State method

is compared with the optically measured rotation vector

for the 15 g sled run . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167

Fig. 5.16 Angular velocity components of the dummy head computed

from the measured angular accelerations using the Wayne State

method. The dummy was restrained by a lap belt and was

subjected to an 18 g frontal impact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167

Fig. 5.17 Rotation vector computed using the Wayne State method is

compared with the optically measured rotation vector for the

18 g sled run . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168

Fig. 5.18 Yaw, pitch, and roll computed from the measured head

accelerations. The 90� shift in yaw and roll is indicative

of the numerical problems that can be encountered

when the Euler angles are not used to define 3-D rotation . . . . . . 168

Fig. 5.19 Typical calibration curve provided by Meggitt (Endevco)

for their Model 7264C accelerometer. Its response is flat

to about 2 kHz and its resonant frequency is about 25 kHz . . . . . 170

Fig. 5.20 Errors magnify at low frequencies for three different brands

of accelerometers manufactured in the 1980s . . . . . . . . . . . . . . . . . . . . 171

Fig. 5.21 Error Analysis—Case 1: Velocity components for a

hypothetical case with a 10% error in the roll velocity

component but with no offset error (baseline shift) . . . . . . . . . . . . 172

List of Figures xxvii

Fig. 5.22 Computed angular displacements as a result of a 10% error

in ωx (roll axis) without offset (baseline shift) . . . . . . . . . . . . . . . . . . . 173

Fig. 5.23 Error Analysis—Case 2: Velocity components for a

hypothetical case with a 5% error in the roll velocity component

and with a 5% offset error (baseline shift) . . . . . . . . . . . . . . . . . . . . . . . 173

Fig. 5.24 Computed angular displacements as a result of a 5% error

in ωx (roll axis) with a 5% offset (baseline shift) . . . . . . . . . . . . . . . . 173

Fig. 5.25 Error Analysis—Case 3: Velocity components for a

hypothetical case with a 10% error in the roll velocity

component and with a 10% offset error (baseline shift) . . . . . . . . 174

Fig. 5.26 Computed angular displacements as a result of a 10% error

in ωx (roll axis) with a 10% offset (baseline shift) . . . . . . . . . . . . . . 174

Fig. 6.1 Drop test device used by Biokinetics, Inc. to reproduce

the on-field impacts recorded on game videos . . . . . . . . . . . . . . . . . . . 180

Fig. 6.2 Example of computed ICP in a concussed individual 9 ms

after impact. The peak positive pressure in the left frontal

area was 110 kPa, and the peak pressure in the right occipital

region was a negative 78 kPa . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182

Fig. 6.3 Comparing strain contours in an injury case

with a non-injury case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182

Fig. 6.4 Elements of the brain experiencing principal strain

in excess of 10 % for the injury case on the left and noninjury

case on the right . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183

Fig. 6.5 Cross plot of acceleration data from NFL data, obtained

from reconstructions of head impacts using dummies

by Biokinetics, Inc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184

Fig. 6.6 Logistic plot of the probability of an mTBI as a function

of the product of strain and strain rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185

Fig. 6.7 Logistic plot of the probability of an mTBI as a function

of strain rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185

Fig. 6.8 Logistic plot of the probability of an mTBI

as a function of HIC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186

Fig. 6.9 Logistic plot of the probability of an mTBI

as a function of linear acceleration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186

Fig. 6.10 Logistic plot of the probability of an mTBI

as a function of angular acceleration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186

Fig. 6.11 Estimation of tolerance levels from a logistic curve . . . . . . . . . . . . . 187

Fig. 6.12 The optimal tolerance is at 29 % for a product value

of 23 s�1. The first and second tolerances are also shown.

See Fig. 1.14 for an explanation of these tolerance values . . . . . . 187

Fig. 6.13 Damage to the two vehicles involved in an intersection

crash that occurred in Australia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190

xxviii List of Figures

Fig. 6.14 Computed damage to the struck vehicle (sedan) compared

to the actual damage shown on the left side of Fig. 6.13 . . . . . . . . 190

Fig. 6.15 Strain contours in the brain of the sedan driver as predicted

by the WSUHIM by Zhang et al. (2001). (A) Midsagittal

section and (B) coronal section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191

Fig. 6.16 Damage to exemplar vehicles used in a crash test to replicate

the intersection accident described by Franklyn et al. (2005).

The target vehicle is on the left and bullet vehicle

is on the right . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191

Fig. 6.17 Impact of a large sedan with a telephone pole, resulting

in massive intrusion of driver (right) side compartment

and an AIS 5 brain injury to the driver . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192

Fig. 6.18 A left-hand drive vehicle was used as an exemplar

vehicle to recreate the pole impact in a crash test . . . . . . . . . . . . . . . 192

Fig. 6.19 Posttest photographs of the pole tests show that it was a less

severe impact than the actual crash. The pole is seen in the

photograph on the right . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193

Fig. 6.20 Top and side cutaway views of a typical Indy-type

racecar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194

Fig. 6.21 Example of a vehicular deceleration pulse for a severe rear

impact causing a Delta V of 70 km/h (44 mph) . . . . . . . . . . . . . . . . . . 195

Fig. 7.1 (A–C) The spinal column viewed frontally, laterally,

and posteriorly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202

Fig. 7.2 Top, side, and rear views of a typical vertebra. In this case,

it is a lumbar vertebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203

Fig. 7.3 Annular layers of an intervertebral disc in which the collagen

fibers run at an oblique angle to the axis of the spine

with the angles in alternating layers almost orthogonal

to each other . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204

Fig. 7.4 Ligaments of the spine—there are three continuous ligaments

and several shorter ones that run between vertebrae . . . . . . . . . . . . . 204

Fig. 7.5 Sketch of the cross section of the spinal cord and a pair

of nerve roots. Unlike the brain, the white matter is in the

periphery of the cord enclosing the gray matter. Each nerve

root has a ventral (anterior) root that is mainly motor

and a dorsal (posterior) root that is mostly sensory . . . . . . . . . . . . . . 205

Fig. 7.6 The C1 and C2 vertebrae are linked through the odontoid

process which is held by a transverse ligament to C1 . . . . . . . . . . . 206

Fig. 7.7 Lateral view of the cervical spine which shows that

the slope of the facet (zygapophysial) joint tends

to decrease at the lower cervical levels . . . . . . . . . . . . . . . . . . . . . . . . . . . 207

Fig. 7.8 Jefferson fracture of C1 – Multipart fracture of the anterior

and posterior arch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209

List of Figures xxix

Fig. 7.9 A vertebral “burst” fracture in which the fractured segments

impact the spinal cord during the fracturing process . . . . . . . . . . . . 209

Fig. 7.10 Three forms of compression-flexion injuries: (A) Wedge

fracture. (B) Burst fracture. (C) Anterior dislocation

with locked facets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210

Fig. 7.11 Compression-flexion neck injury sustained by a motorcyclist.

The neck compression is generated by the inertia of the body

following the head and neck . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210

Fig. 7.12 Examples of tension extension injuries: (A) Chin impact

with an automotive dash. (B) Whiplash hyperextension

with neck tension. (C) Out-of-position occupant injured

by an airbag causing C1/C2 separation . . . . . . . . . . . . . . . . . . . . . . . . . . . 212

Fig. 7.13 Airbag induced C1/C2 separation in a cadaver . . . . . . . . . . . . . . . . . . . 212

Fig. 7.14 Hangman’s fracture at C2 which is separated at the pedicles

causing failure of the spinal cord and death . . . . . . . . . . . . . . . . . . . . . . 213

Fig. 7.15 Test setup for the pre-deployed airbag test. The airbag

and steering column are stationary, and the seated test

subject is on sled that is accelerated into the airbag . . . . . . . . . . . . . 215

Fig. 7.16 Neck drop test experiment conducted by Nightingale et al.

(1997) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216

Fig. 7.17 Surface orientations used for neck drop test experiments . . . . . . . 216

Fig. 7.18 Buckling of the cervical spine was observed during

the impact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217

Fig. 7.19 Effect of end conditions on the deformation of the cervical

spine. When unconstrained, the spine bends easily

and is not able to withstand axial loads. With rotational

constraints, it does not deform as much and can withstand

more axial load. When fully constrained, it is capable

of withstanding large axial loads with little bending

deformation. Injury severity increases with the degree

of constraint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218

Fig. 7.20 Neck loading corridor for extension (rearward bending),

based on Mertz et al. (1973) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219

Fig. 7.21 Neck loading corridor for flexion (forward bending),

based on Mertz et al. (1973) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220

Fig. 7.22 Neck loading corridor for lateral bending,

based on Patrick and Chou (1976) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220

Fig. 7.23 Tolerance of the cervical spine as a function

of duration of impact for the mid-size male . . . . . . . . . . . . . . . . . . . . . . 221

Fig. 7.24 Cervical spine tolerance values from Duke and the Medical

College of Wisconsin differ considerably . . . . . . . . . . . . . . . . . . . . . . . . . 222

Fig. 7.25 Tolerance of the cervical spine to tensile loading,

based on Mertz et al. (2003) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223

xxx List of Figures

Fig. 7.26 The 3-D neck model by Kleinberger (1993) . . . . . . . . . . . . . . . . . . . . . . 224

Fig. 7.27 The 3-D partial cervical spine model

by Yoganandan et al. (1996) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225

Fig. 7.28 Human neck geometry obtained from an MRI of a 50th

percentile male . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225

Fig. 7.29 Side view of the neck model by Yang et al. (1998) . . . . . . . . . . . . . 226

Fig. 7.30 Detailed view of the C1–C2 vertebrae in the model

by Yang et al. (1998) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227

Fig. 7.31 Detailed view of the C3 vertebra and the C2/C3 disc

in the model by Yang et al. (1998) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227

Fig. 7.32 Validation of the model by Yang et al. (1998) against crown

impact data from Nightingale et al. (1997) . . . . . . . . . . . . . . . . . . . . . . . 228

Fig. 7.33 Head kinematics as predicted by the model by

Yang et al. (1998) compared with sled data at time 60 ms . . . . . 229

Fig. 7.34 Head kinematics as predicted by the model by

Yang et al. (1998) compared with sled data at time 100 ms . . . . 229

Fig. 7.35 Head kinematics as predicted by the model by

Yang et al. (1998) compared with sled data at time 120 ms . . . . 229

Fig. 7.36 Head kinematics as predicted by the model by

Yang et al. (1998) compared with sled data at time 140 ms . . . . 230

Fig. 7.37 Horizontal and vertical head acceleration predicted

by the model by Yang et al. (1998) compared with

experimental data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231

Fig. 7.38 Predicted facet capsule stretch by the model by Yang et al.

(1998) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232

Fig. 7.39 Interaction of the head with a pre-deployed airbag,

predicted by the model by Yang et al. (1998) . . . . . . . . . . . . . . . . . . . . 233

Fig. 7.40 Demonstration of the mechanism of injury when the head

interacts with the pre-deployed airbag, as predicted by the

model by Yang et al. (1998) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234

Fig. 8.1 Anatomy of the spinal cord . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244

Fig. 8.2 The process for the perception of pain by the brain . . . . . . . . . . . . . 245

Fig. 8.3 High acceleration whiplash testing of rhesus monkeys in

forward-facing mode (+Gx acceleration) . . . . . . . . . . . . . . . . . . . . . . . . . . 246

Fig. 8.4 Muscles of the neck, highlighting the sternocleidomastoid

muscle which is stretched during head hyperextension . . . . . . . . . . 247

Fig. 8.5 (A–B) Spinal compression due to shoulder belt loading

on the chest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250

Fig. 8.6 Mini Hyge sled designed for us with the Henry Ford Hospital

high-speed X-ray unit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255

Fig. 8.7 Tools used to install radiopaque (tungsten) targets on individual

cervical vertebrae. (1) Tungsten markers. (2) Pin.

(3) Drill bit. (4) Pusher. (5) Guide tube. (6) Guide tube . . . . . . . . . 255

List of Figures xxxi

Fig. 8.8 Radiograph of a cadaver neck with a pair of tungsten targets

installed in each cervical vertebra. Note that C7 is shielded

by the shoulder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256

Fig. 8.9 Instrumented cadaver seated on a sled in front of a biplanar

high-speed X-ray unit. The strap holding the head upright

was released just prior to the initiation of sled acceleration . . . . 256

Fig. 8.10 A two-dimensional setup of a 0-deg seatback angle test

with head restraint. One X-ray unit and one image

intensifier was used . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257

Fig. 8.11 Transducer data for HFH19 (0� seatback run). (A) Sledacceleration and velocity. (B) Seat pan load. (C) Shear

and compressive force at occipital condyles. (D) Upper neck

moment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259

Fig. 8.12 Cervical vertebrae rotations in HFH19. (A) Absolute rotations

with respect to an inertial reference frame. (B) Relative rotation

of adjacent cervical vertebrae. The upper cervical vertebrae

are in flexion, while the lower vertebrae are in extension . . . . . . . 259

Fig. 8.13 Crash extension motion – Pattern of rotational angle

of each vertebra (From the horizontal plane) . . . . . . . . . . . . . . . . . . . . . 260

Fig. 8.14 Relative displacement of C1 with respect to C2

along the body-fixed x- and z-axes. C1P and C1A

are, respectively, the posterior and anterior targets

on the C1 vertebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260

Fig. 8.15 Relative displacement of C2 with respect to C3

along the body-fixed x- and z-axes. C2P and C2A

are, respectively, the posterior and anterior targets

on the C2 vertebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261

Fig. 8.16 Relative displacement of C3 with respect to C4 along

the body-fixed x- and z-axes. C3P and C3A are, respectively,

the posterior and anterior targets on the C3 vertebra . . . . . . . . . . . . 261

Fig. 8.17 Relative displacement of C4 with respect to C5

along the body-fixed x- and z-axes. C4P and C4A are,

respectively, the posterior and anterior targets on

the C4 vertebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262

Fig. 8.18 Relative displacement of C5 with respect to C6 along

the body-fixed x- and z-axes. C5P and C5A are, respectively,

the posterior and anterior targets on the C5 vertebra . . . . . . . . . . . . 262

Fig. 8.19 Coordinate systems for individual vertebrae based on neck

targets are used to estimate facet capsular strain as a function of

time. Bony landmarks on either side of the facet joint are

identified, and the change in distance between the landmarks

was used to estimate the strain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263

Fig. 8.20 (A) Trajectories of facet bony landmarks used to estimate

facet capsular strain shown in (B) for the C4/C5 capsule . . . . . . . 263

xxxii List of Figures

Fig. 8.21 Transducer data for HFH20 (20� seatback run). (A) Sled

acceleration and velocity. (B) Seat pan load. (C) Shearand compressive force at occipital condyles. (D) Upper

neck moment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264

Fig. 8.22 Comparison of relative rotations of cervical vertebrae

for the two seatback angles. The rotations for the 0-deg

seatback angle in Run HFH19 (A) are generally larger

than those for the 20-deg seatback angle in Run

HFH20 (B) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265

Fig. 8.23 Relative motion of C1 with respect to C2 from all available

tests (Deng et al. 2000) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266

Fig. 8.24 Relative motion of C2 with respect to C3 from all available

tests (Deng et al. 2000) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266

Fig. 8.25 Relative motion of C3 with respect to C4 from all available

tests (Deng et al. 2000) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267

Fig. 8.26 Relative motion of C4 with respect to C5 from all available

tests (Deng et al. 2000) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267

Fig. 8.27 Relative motion of C5 with respect to C6 from all available

tests (Deng et al. 2000) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268

Fig. 8.28 Neck injury criteria for a 50th percentile male . . . . . . . . . . . . . . . . . . . 271

Fig. 9.1 A typical thoracic vertebra. The articular facet surfaces

are almost vertical, and the ability of the facet to transmit

vertical load is unlikely . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282

Fig. 9.2 A typical lumbar vertebra. The articular facet is vertical

(normal to the laminae), diagonally oriented to resist

posteroanterior shear, and slightly curved when viewed

from above. The facets are located above the laminae

and act as a load path to transmit vertical loads down

the spine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283

Fig. 9.3 Wedge fracture of L1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284

Fig. 9.4 Examples of lumbar burst fractures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284

Fig. 9.5 Diagrammatic depiction of a burst fracture, showing the

fragments moving radially outward, impacting (and injuring)

the spinal cord . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285

Fig. 9.6 Fracture dislocation with locked facets . . . . . . . . . . . . . . . . . . . . . . . . . . . 286

Fig. 9.7 Types of Chance fracture according to Denis (1983). It can

involve one vertebra or two vertebrae with fractures through

the posterior aspect of the vertebra and rupture of the

interspinous ligament. The injury can result in splitting

of the intervertebral disc, the vertebral body, or both . . . . . . . . . . 287

Fig. 9.8 Thoracic hyperextension injury to T8–T9 . . . . . . . . . . . . . . . . . . . . . . . . 287

Fig. 9.9 One form of thoracic rotational injury due to compression

and twisting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 288

List of Figures xxxiii

Fig. 9.10 Schematic of the Wayne State University vertical

accelerator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289

Fig. 9.11 Vertical accelerator sled (simulated ejection seat) with an

embalmed cadaver ready for an ejection test. The cadaver

was restrained by a military lap-shoulder harness . . . . . . . . . . . . . . . 290

Fig. 9.12 The intervertebral disc load cell was used to measure

the load borne by the intervertebral disc and the line

of action of the load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292

Fig. 9.13 IVLC installed in the lumbar spine of a cadaver

by means of a double-bladed saw. The inferior portion

of a lumbar vertebra was removed to insert the load

cell above the disc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293

Fig. 9.14 (A) Measured intervertebral disc load and estimated

total load. (B) The difference between the two loads shown

in (A) is the facet load. It is negative or compressive at the

beginning of the impact and becomes tensile toward the end

of the impact due to spinal flexion. (C) Confirmation of facet

load from strain gages mounted on the posterior surface of the

lamina. The strain was compressive at the start of the impact

pulse but became tensile later on, in conformity with the

direction of the facet load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294

Fig. 9.15 (A) Vertical sled acceleration. (B) Estimated total spine load.

(C) Measured intervertebral disc load for the erect and

hyperextended modes. (D) Facet load for the erect and

hyperextended mode. In the erect mode, the facet load

goes from compression to tension, but in the hyperextended

mode, the facet load remains in compression.

(E) Confirmation of facet load based on laminar strain

at L3 and L4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294

Fig. 9.16 Reason why the intervertebral disc load can be larger

than the total load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295

Fig. 9.17 Schematic of the elements of the servo loop used

to duplicate a vertical accelerator experiment

in a material testing machine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296

Fig. 9.18 Lumbar segment in a material testing machine which duplicated

the vertical accelerator test this segment underwent while it was

in the body of the cadaver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296

Fig. 9.19 Duplication of a hyperextended run using a materials testing

machine to measure the total load. The facet load was in

compression throughout the run . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297

Fig. 9.20 Duplication of an erect run using a materials testing

machine to measure the total load. The facet load

did go into tension at the end of the run . . . . . . . . . . . . . . . . . . . . . . . . . . 297

Fig. 9.21 Vertical accelerator data from erect mode runs with

and without simulated abdominal pressure in a cadaver

(Unpublished data) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 298

xxxiv List of Figures

Fig. 9.22 Bank of homemade solid-state (impact-resistant) EMG

amplifiers used on board the vertical accelerator . . . . . . . . . . . . . . . . . 299

Fig. 9.23 Null check of the EMG system. The sled was fired

with the EMG system turned on but no animal on board

to ensure that the electrodes were not picking up spurious

signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300

Fig. 9.24 Junction box for EMG leads built into the jacket used

to protect the EMG needles from being pulled out

by the animal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301

Fig. 9.25 Anesthetized animal ready for testing after it wakes

up from the anesthesia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301

Fig. 9.26 Fully awake beagle in the vertical accelerator sled waiting

for the next test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302

Fig. 9.27 EMG data from the lumbar multifidus muscle. The sled

acceleration is superimposed on the EMG data so that

the delay time can be determined . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302

Fig. 9.28 EMG data from the spinalis cervicis muscle of a dog

subjected to a mild (5-g) vertical acceleration. The parabolically

shaped curve is called the rectified EMG and is said

to be proportional to the force generated in the muscle . . . . . . . . . 303

Fig. 9.29 Human tolerance to vertical acceleration as a function

of impact duration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304

Fig. 9.30 Typical burst fracture patterns created by Willen et al. (1984),

using a drop weight impact testing method. There was a sagittal

plane fracture and a couple of frontal plane fractures,

typical of four of the seven specimens tested . . . . . . . . . . . . . . . . . . . . . 306

Fig. 9.31 Herniated nucleus pulposus exerting pressure on the exiting

nerve root. Back pain comes from the herniation itself but

pressure on the nerve root causes leg pain as well . . . . . . . . . . . . . . . 308

Fig. 9.32 An artificially created disc rupture which occurred after the

intervertebral disc was loaded cyclically for over 7000 times.

The nucleus pulposus is viscous and does not flow

like a liquid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309

Fig. 9.33 The path taken by the nucleus pulposus for it to herniate

from an intervertebral disc. It is not radial, and each layer is

ruptured at a different location, indicating that process

is slow and quite unlike the bursting of a balloon . . . . . . . . . . . . . . . 310

Fig. 10.1 Schematic diagram of a facet pressure sensor . . . . . . . . . . . . . . . . . . . . 320

Fig. 10.2 X-ray of a facet pressure sensor installed in the tip of an inferior

facet just above the lamina . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321

Fig. 10.3 Schematic diagram of the test setup to measure facet

contact pressure (side view) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322

Fig. 10.4 Wires simulating muscle action are activated by turnbuckles

and attached to load cells anchored to the floor . . . . . . . . . . . . . . . . . . 323

List of Figures xxxv

Fig. 10.5 Photograph of a disc nucleus pressure transducer

made from a 13-gauge spinal needle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323

Fig. 10.6 Photograph of the test setup for sensing facet contact

pressure with the lamina . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324

Fig. 10.7 The test protocol was to simulate loading on the lumbar

spine due to body weight and to a weight carried in front

of the chest by hand. Simulation of extensor muscle action

was included . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324

Fig. 10.8 Facet pressure and disc pressure changes due to body

weight and an eccentric weight. See Table 10.2

for the testing sequence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325

Fig. 10.9 Simulated extensor muscle forces with the sum shown

as the curve at the top of the figure. See Table 10.2

for the testing sequence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325

Fig. 10.10 Average facet pressure for two loading cases, body weight

only and body weight plus a 45 N eccentric weight . . . . . . . . . . . . . 326

Fig. 10.11 Simulated muscle force for the two loading cases – body

weight only and body weight plus the 45 N eccentric weight.

The average increase was 182 N. (Re-do this plot using data

from El-Bohy’s dissertation, Table 4.2, p. 48) . . . . . . . . . . . . . . . . . . . 327

Fig. 10.12 Average nucleus disc pressure for the two loading

cases – body weight only and body weight plus the 45 N

eccentric weight . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327

Fig. 10.13 A zero-zero ejection in progress. The payload was a crash

dummy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 330

Fig. 10.14 The base-excitation model used to derive the Dynamic

Response Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 331

Fig. 10.15 Generic elements of Prasad’s 2-D spinal model

in which the facets were simulated by a spring

between A’ and B’ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334

Fig. 10.16 Comparison of model and experimental results

of a 6 g run in the erect mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335

Fig. 10.17 Comparison of model and experimental results

of an 8 g run in the erect mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 336

Fig. 10.18 Comparison of model and experimental results

of a 10 g run in the erect mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 336

Fig. 10.19 Comparison of model and experimental results

of an 6 g run in the hyperextended mode . . . . . . . . . . . . . . . . . . . . . . . . . 337

Fig. 10.20 Comparison of head horizontal displacement between

model results and experimental data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 338

Fig. 10.21 Comparison of head angular displacement between

model results and experimental data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339

Fig. 10.22 Comparison of head horizontal linear acceleration

between model results and experimental data . . . . . . . . . . . . . . . . . . . . 339

Fig. 10.23 Comparison of head angular acceleration between model

results and experimental data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 340

xxxvi List of Figures

Fig. 10.24 Assumed accelerations experienced by an aircraft ditching

in the ocean. The peak accelerations were either coincident

in time or one peak preceded the other in the three cases

that were modeled using the Tennyson model . . . . . . . . . . . . . . . . . . . 341

Fig. 10.25 Computed odontoid displacement for the helmet and

non-helmeted cases. The displacement was 5.2 mm for the

helmeted case for a 10 g pulse. It could exceed 10 mm for

higher inputs and cause a cord concussion which has the

same effect as a cerebral concussion on the pilot. The peaks

of the +Gz and the �Gx accelerations were coincident

for this case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342

Fig. 10.26 Computed spinal cord stretch for the helmeted and

non-helmeted case. The stretch was not increased by much due

to the helmet. The acceleration peaks were simultaneous . . . . . . . 342

Fig. 10.27 The computed chin-chest contact force for the helmeted and

non-helmeted cases. The force is not high enough to cause a

cerebral concussion. Again, the acceleration peaks were

simultaneous . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342

Fig. 10.28 Finite element model of a single vertebra. Due to limited

computational capabilities in the 1970s, only half a vertebra

could be modeled, but the facets were modeled so that they

could mate with an adjacent vertebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343

Fig. 10.29 Comparison of static model-predicted vertebral cortical

strains with those measured in a vertebra. The location

of the strain was the anterior aspect of the vertebral body

at the center of the body . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344

Fig. 10.30 Comparison of static model-predicted vertebral cortical

strains with those measured in a vertebra. The location

of the strain was the lateral aspect of the vertebral body

near the superior endplate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344

Fig. 10.31 Finite element model of a lumbar motion segment with

two vertebrae and a disc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345

Fig. 10.32 Validation of the King and Yang (1986) model of a lumbar

functional spinal unit, using intradiscal pressure . . . . . . . . . . . . . . . . . 346

Fig. 10.33 Finite element model of a lumbar motion segment

subjected to a variety of loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347

Fig. 10.34 Comparison of predicted disc bulge for a normal

and degenerated disc with the pivot at the center

of the disc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 348

Fig. 11.1 An anterior view of the rib cage. The lighter segments are the bony

parts of the ribs. The first 10 ribs are attached to the sternum

via the darker cartilaginous segments. Note also the downward

inclination of the rib cage which is reduced with age.

That is, the ribs become more horizontal with age. . . . . . . . . . . . . . . . . 358

Fig. 11.2 Compartments of the heart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359

List of Figures xxxvii

Fig. 11.3 Valves of the heart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 360

Fig. 11.4 Diagrammatic depiction of the systemic and pulmonary

circulatory systems. Oxygenated blood is in red and oxygen

depleted blood is in blue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361

Fig. 11.5 Electrical conduction system of the heart . . . . . . . . . . . . . . . . . . . . . . . . . 362

Fig. 11.6 The cardiac cycle—Correlation of mechanical and electrical

events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363

Fig. 11.7 Fatalities due to aortic rupture as a percentage of all

automotive fatalities from 1947 to 1997 . . . . . . . . . . . . . . . . . . . . . . . . . . 366

Fig. 11.8 Traumatic rupture of the aorta occurs frequently in the

peri-isthmic region, just distal to the aortic arch . . . . . . . . . . . . . . . . . 366

Fig. 11.9 First whole-body cadaveric tests were carried out by Patrick

et al. (1965) at Wayne State University. Embalmed cadavers

were used . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 368

Fig. 11.10 Thoracic force-deflection curves for a nominal

19.5-kg (43-lb) impactor at various velocities. Data from

12 tests are shown . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 369

Fig. 11.11 Thoracic force-deflection curves for a nominal 23.1-kg (51-lb)

impactor at various velocities. Data from 11 tests

are shown. The corridor envelopes seven tests for impactor

speeds between 6.7 and 7.4 m/s (15 and 16.6 mph) . . . . . . . . . . . . . 370

Fig. 11.12 Recommended thoracic response corridor for the

development of a biofidelic dummy. The original corridor

for the high speed response is shown as a shaded region . . . . . . . 371

Fig. 11.13 Comparison of initial thoracic stiffness data for frontal impact,

taken from cadavers and a volunteer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 372

Fig. 11.14 Comparison of thoracic plateau force data for frontal impact,

taken from cadavers and a volunteer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373

Fig. 11.15 Diagram of the test set-up for sternal impacts on rabbits using a

pneumatic impactor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374

Fig. 11.16 The type of lung injury is dependent on both impactor

displacement and velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374

Fig. 11.17 Thoracic response to lateral impact—whole-body drop tests

onto a rigid surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375

Fig. 11.18 Photograph of the Heidelberg side impact test set-up . . . . . . . . . . . . . 375

Fig. 11.19 The 12-accelerometer thoracic array mandated by the NHTSA

for cadaveric testing funded by the NHTSA .. . . . . . . . . . . . . . . . . . . . . 376

Fig. 11.20 Lateral pendulum impact test at an oblique angle, 30� anteriorto lateral . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379

Fig. 11.21 Force-deflection curves from lateral pendulum chest

impacts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 380

Fig. 11.22 Analysis of side impact data—Logistic plots for V*C, Cand Gsp at T8 with computed Chi square, p and r values . . . . . . . 381

Fig. 11.23 (A) Uncorrected corridor for chest response at 16 mph,

(based on Kroell et al. (1974)). (B) Corrected corridor for chest

xxxviii List of Figures

response at 16 mph with an average curve added, based on

Lobdell et al. (1973). The correction is substantial . . . . . . . . . . . . . . 382

Fig. 11.24 Thoracic response to lateral pendulum impact (30� from lateral)

at (A) 4.8, (B) 6.8 and (C) 9.7 m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383

Fig. 11.25 Comparison of frontal thoracic impact response (A) with lateral

thoracic impact response (B) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384

Fig. 11.26 Frontal impact to the chest of an inverted cadaver by a 32-kg

pendulum which shoveled the mediastinal contents towards the

head and the spine. An aortic rupture occurred . . . . . . . . . . . . . . . . . . 386

Fig. 11.27 Side impact to the chest with the arm moved out

of the way, causing an aortic rupture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 386

Fig. 11.28 Submarining test using a seatbelt that was retracted rapidly

by a belt pre-tensioner. The belt used was placed at an

angle to the torso to partially simulate submarining. An aortic

intimal tear resulted from this test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 387

Fig. 11.29 Oblique impact test at the level of the xiphoid process, 30� formlateral. An intimal tear was found after the test . . . . . . . . . . . . . . . . . . 387

Fig. 11.30 Empirical linear relationship between AIS and chest

deflection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 389

Fig. 11.31 Lumped parameter model for frontal chest impact. Human

impact response: measurement and simulation: proceedings by

King, William Frederic; et al. Reproduced with permission of

KLUWER ACADEMIC PUBLISHERS in the format Book via

Copyright Clearance Center . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 390

Fig. 11.32 Lobdell model predictions of Kroell et al. (1971) frontal chest

impacts at two different speeds and using two different

impactors. Human impact response: measurement and

simulation: proceedings by King, William Frederic; et al

Reproduced with permission of KLUWER ACADEMIC

PUBLISHERS in the format Book via Copyright Clearance

Center . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 391

Fig. 11.33 Frontal oblique view of the thoracic skeleton of the Wang

(1995) model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392

Fig. 11.34 Model of the mediastinum and diaphragm .. . . . . . . . . . . . . . . . . . . . . . . 393

Fig. 11.35 Stress-strain curve for heart muscle in compression used in the

model (Curve1) compared with quasi-static response obtained

by Yamada (1970). The modulus was increased tenfold . . . . . . . . 393

Fig. 11.36 Simulation of side impact tests performed

by Viano et al. (1989) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394

Fig. 11.37 Validation of the Wang (1995) model against force-deflection

data from a series of side impact tests performed

by Viano (1989) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394

Fig. 11.38 Validation of the Wang (1995) model against force-time

data from a series of side impact tests performed

by Viano (1989) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .395

List of Figures xxxix

Fig. 11.39 Computed deformation of the thorax at the level of the lower

sternum for a 4.4 m/s lateral impact, as predicted by the Wang

(1995) model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395

Fig. 11.40 Modified thoracic model by Shah et al. (2001). The model is on

the right. It is compared to thoracic anatomy shown on the left.

SVC stands for superior vena cava. The color of the arrows

matches that of the words below the figure (courtesy of Dr.

Chirag Shah) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 396

Fig. 11.41 Model of the thoracic aorta in the thoracic model by Shah et al.

(2001) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 397

Fig. 11.42 The Shah (2007) torso model simulating an oblique lateral

pendulum impact to the abdomen, reported by Viano et al.

(1989). (A) Initial set-up. (B) Kinematics at time of peak force 397

Fig. 11.43 Validation of the torso model by Shah (2007) in terms of an

abdominal force deflection curve against data generated by

Viano (1989) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 398

Fig. 11.44 Validation of the torso model by Shah (2007) in terms of an

abdominal force-time curve against data generated by Viano

(1989) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 398

Fig. 11.45 The Shah (2007) torso model simulating a frontal pendulum

impact to the thorax, reported by Kroell et al. (1974). (A) Initial

set-up. (B) Kinematics at time of peak force . . . . . . . . . . . . . . . . . . . . . 399

Fig. 11.46 Validation of the torso model by Shah (2007) against the

thoracic force-deflection curves developed by Kroell et al.

(1974) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 399

Fig. 12.1 Front view of the organs of the abdomen . . . . . . . . . . . . . . . . . . . . . . . . . 410

Fig. 12.2 Frontal view of organs of the torso to show the relative position

of the abdominal organs in relation to the rib cage and, in

particular, the position of the kidneys with respect to the other

abdominal organs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 411

Fig. 12.3 Quadrants or regions of the abdomen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 412

Fig. 12.4 Abdominal response to frontal impact by a 2.54-cm diameter

bar (Cavanaugh et al. 1986) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 417

Fig. 12.5 Abdominal response to frontal impact by the lower portion of a

steering wheel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 418

Fig. 12.6 Abdominal force-deflection curves from belt impact at the level

of L4, obtained from 13 of the 25 swine tests conducted by

Miller (1989) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 419

Fig. 12.7 Force-deflection curves for abdominal side impact at three

impact severities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 420

Fig. 12.8 Logist plots of V*C, compression and spinal acceleration at T12

with the computed values of χ2, p, and r (taken from Viano

(1989)) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 421

Fig. 12.9 Strain ramp of duration t0 with a slope¼ α. ε0¼ αt0and ε¼ αt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425

xl List of Figures

Fig. 12.10 Photograph of the test setup for performing relaxation tests on

solid abdominal specimens . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 427

Fig. 12.11 The reduced relaxation function G(t) for the liver . . . . . . . . . . . . . . . 429

Fig. 12.12 The reduced relaxation function G(t) for the kidney . . . . . . . . . . . . . 429

Fig. 12.13 The reduced relaxation function G(t) for the spleen . . . . . . . . . . . . . 429

Fig. 12.14 Stress–strain plots for the liver at different strain rates . . . . . . . . . . 430

Fig. 12.15 Stress–strain plots for the kidney at different strain rates . . . . . . . 430

Fig. 12.16 Stress–strain plots for the spleen at different strain rates. Note

the lack of strain rate sensitivity for the spleen . . . . . . . . . . . . . . . . . . 430

Fig. 12.17 Ultimate strain is independent of strain rate at the three rates

used in the experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 430

Fig. 12.18 Skeletal model for the abdominal model . . . . . . . . . . . . . . . . . . . . . . . . . . 432

Fig. 12.19 Frontal view of the liver. The top margin of falciform

ligament is attached to the undersurface of the diaphragm.

Together with the coronary ligament, they hold the liver

in the upper abdomen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433

Fig. 12.20 Frontal and rear views of the organs and soft tissues of the

abdominal mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433

Fig. 12.21 An oblique view of the complete Wayne State University

Human Abdominal Model (WSUHAM) . . . . . . . . . . . . . . . . . . . . . . . . . . 434

Fig. 12.22 Nonlinear viscoelastic material model used to simulate solid

abdominal organs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 435

Fig. 12.23 Kinematics of a pendulum side impact at 6.7 m/s, as predicted

by the WSUHAM, simulating impacts conducted by Viano

(1989) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 437

Fig. 12.24 Distortion of abdominal organs due to a 6.7-m/s pendulum side

impact as predicted by the WSUHAM. Maximum compression

occurred at about 30 ms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 438

Fig. 12.25 Stress contours in the liver at 22.5 ms into the impact by a 6.7-

m/s pendulum. The peak stress was 152 kPa (based on Lee and

Yang (2001)) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 439

Fig. 12.26 Comparison of model predicted force-time and force-deflection

curves with experimental data, for impacts at 6.7 m/s . . . . . . . . . . . 439

Fig. 12.27 Simulation of a cadaveric drop test conducted by Walfisch et al.

(1980). The abdomen was targeted to impact a simulated

armrest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 439

Fig. 12.28 Comparison of force-time data for abdominal impacts (A) the

1-m drop tests and (B) the 2-m drop tests. The experimental data

taken from Walfisch et al. (1980) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 440

Fig. 12.29 Simulation of frontal impact abdominal tests by a rigid bar at the

level of L3. The impact speeds were 6.2 and 10.4 m/s. The

experimental data were taken from Cavanaugh et al. (1986) . . . 441

Fig. 12.30 Comparison of model predicted force-time curves

with experimental corridor developed by Cavanaugh et al.

(1986). (A) is for low velocity impacts (6.1 m/s) and (B) is for

high velocity impacts (10.4 m/s) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 441

List of Figures xli

Fig. 12.31 Comparison of model predicted force-deflection curves with

experimental force-deflection curves obtained by Cavanaugh

et al. (1986). (A) is for low velocity impacts (6.1 m/s) and (B) is

for high velocity impacts (10.4 m/s) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 441

Fig. 13.1 Frontal view of the pelvis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 448

Fig. 13.2 Lateral view of the right hip bone or pelvis . . . . . . . . . . . . . . . . . . . . . . 448

Fig. 13.3 The acetabulum (hip socket) houses the head of the femur (thigh

bone) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 449

Fig. 13.4 Frontal views of the male (top) and female pelvis (bottom). Thefemale pelvis has evolved to facilitate childbirth . . . . . . . . . . . . . . . . 450

Fig. 13.5 A slightly oblique frontal view of the sacrum (taken from Gray’sAnatomy (1973)) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 450

Fig. 13.6 Transverse section of the pelvic and sacrum, showing the

sacroiliac joints which have a synovial segment anteriorly. A

large part of the joint is held together by strong interosseous

ligaments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 450

Fig. 13.7 Anterior ligaments between the ilium and the sacrum are shown

in this figure along with the sacrotuberous and the sacrospinous

ligaments on the floor of the pelvis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 451

Fig. 13.8 Posterior ligaments between the pelvis and the sacrum . . . . . . . . . 452

Fig. 13.9 Side view of the sacrum and coccyx . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 453

Fig. 13.10 Illustration of a rotationally unstable pelvic fracture caused by

internal rotation of the left hipbone. It is called a bucket handle

fracture because the fractured right pubic rami (on the left of the

figure) provides the image of a bucket handle on X-ray) . . . . . . . . 454

Fig. 13.11 Illustration of a vertically unstable pelvic fracture with

disruption of both the posterior and anterior arches . . . . . . . . . . . . . 454

Fig. 13.12 A U-shaped fracture of the sacrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 456

Fig. 13.13 Acetabular fracture patterns as described by Letournel (1980).

The simple patterns are (A) posterior wall, (B) posteriorcolumn, (C) anterior wall, (D) anterior column, and (E)

transverse fractures. The associated patterns are (F) fractures of

the posterior column with a posterior wall, (G) transverse

fracture of the posterior wall, (H) T-style acetabular fracture, (I)

fracture of the anterior column posterior hemitransverse, and (J)

fractures of both columns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 458

Fig. 13.14 Impact apparatus used impact the knee and fracture the

acetabulum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 458

Fig. 13.15 Orientation of the femur with respect to the pelvis viewed from

the top (A) and the side (B). The pelvis was fixed in a clamp . . 459

Fig. 13.16 Loading rates used in the acetabular fracture study by Rupp

et al. (2002) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 459

Fig. 13.17 (A) Pelvic force-deflection curves for lateral impact at 5.2 m/s

and (B) at 9.8 m/s (adapted from Viano (1989)) . . . . . . . . . . . . . . . . . 461

Fig. 13.18 Hypothetical pelvic force data showing that the cumulative

duration of the force in excess of 12 kN is greater than 3 ms. . . 462

xlii List of Figures

Fig. 13.19 Probability of hip fracture or dislocation as a function of peak

force at the hip. The probability of injury increases with

increased hip flexion and abduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 463

Fig. 14.1 Anterior (left) and posterior (right) views of the bones of the

right lower extremity. The femur articulates with the pelvis

proximally and the tibia distally. The tibia articulates with the

femur proximally and with the tarsal (ankle) bone distally . . . . . 470

Fig. 14.2 Anterior view of the right femur. The spherical femoral head fits

into the acetabulum of the pelvis while the condyles on the distal

end roll and slide on the two tibial plateaus . . . . . . . . . . . . . . . . . . . . . . 471

Fig. 14.3 Frontal view of the right tibia and fibula. In (A), the proximal

and distal articulations are shown. In (B), the location of the

head of the fibula is seen in detail. It does not articulate with the

femur. Also, in (B), the distal end of the fibula is the lateral

malleolus while the distal end of the tibia is the medial malleolus 472

Fig. 14.4 (A) Frontal view of the patella. (B) Rear view of the patella . . . 473

Fig. 14.5 Side view of the femoro-tibial joint showing the quadriceps and

patella tendons that hold the patella in place . . . . . . . . . . . . . . . . . . . . . 473

Fig. 14.6 Muscles of the thigh viewed in cross-section. The femur is

among the anterior extensor muscles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473

Fig. 14.7 Ligaments of the knee - The lateral and medial collateral

ligaments and the cruciate ligaments hold the knee in place. The

patella has been removed and the patellar tendon has been cut 474

Fig. 14.8 Expanded view of the cruciate ligaments of the knee - The ACL

is attached to the anterior aspect of the tibial plateau while the

PCL is attached to its posterior aspect . . . . . . . . . . . . . . . . . . . . . . . . . . . . 474

Fig. 14.9 Torsional load applied to a long bone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 476

Fig. 14.10 Free body diagram of an element of bone at the fracture site. The

shear resultants form a tensile force at 45 deg to the long axis of

the bone, causing a spiral fracture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 476

Fig. 14.11 Example of a greenstick fracture of the ulna and radius in a

3-year-old who fell with his hands outstretched. The bending

load caused the tensile side to be fractured while the

compression side buckled due to softness of the bone . . . . . . . . . . . 477

Fig. 14.12 Example of a comminuted Pilon fracture caused by a

compressive load applied to the distal end of the tibia by the

talus (ankle bone) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 478

Fig. 14.13 Cross-section of a 1978 VW Rabbit knee bolster designed to

protect the knee and to avoid PCL rupture . . . . . . . . . . . . . . . . . . . . . . . 479

Fig. 14.14 Stellate fracture of the patella due to direct impact against a

rigid surface. A stellate fracture is one with central point of

injury from which radiate numerous fissures . . . . . . . . . . . . . . . . . . . . . 479

Fig. 14.15 A condylar notch fracture is caused by the rearward motion of

the patella into the knee joint. It is likely to occur if the knee

load is not shared by the femoral condyles surrounding the

patella (Hayashi et al. 1996) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 480

List of Figures xliii

Fig. 14.16 Illustration of the effect of padding to distribute the knee load to

the condyles and thus prevent patella and condylar notch

fractures (Hayashi et al. 1996) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 480

Fig. 14.17 Illustration of large knee loads that develop if the dash is heavily

padded, pocketing the knee. The horizontal and vertical shear

forces in the pocket can fracture the femoral shaft . . . . . . . . . . . . . . 481

Fig. 14.18 Experimental set-up for knee impacts to validate the hypothesis

that padding affects the type of knee fracture and to determine

the optimal stiffness of the padding to prevent knee injury . . . . . 481

Fig. 14.19 Finite element model of knee impact simulating the Hayashi

experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 482

Fig. 14.20 Validation of the knee impact model by Hayashi et al. (1996)—

(A) Comparison of rigid impact response, (B) Comparison of

response for a rigid padding impact (450 psi), (C) Comparison

of response for a 100 psi pad impact, and (D) Comparison of

response for a 50 psi pad impact (Hayashi et al. 1996) . . . . . . . . . . 483

Fig. 14.21 Load sharing between the patella and the condyles as predicted

by the Hayashi model—The condyles share 16% of the load if a

100-psi pad was used . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 484

Fig. 14.22 Experimental set-up to produce a pilon fracture in a cadaver leg 485

Fig. 14.23 The tendon catcher was a modified rope holder with spikes

inside. However, the spikes were not enough to hold the tendon

and surgical suture was used to reinforce the assembly so that it

could resist a load of 2 kN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 485

Fig. 14.24 The measured tibial force is consistently 2 kN higher than the

impact force, whether the pilon fracture occurred or not . . . . . . . . 486

Fig. 14.25 The foot and ankle model developed by Beaugonin et al. (1997)

was used to simulate the impact experiments conducted by

Kitagawa et al. (1998) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 487

Fig. 14.26 Comparison of model predicted forces with experimental data

obtained by Kitagawa et al. (1998) for the simulation of pilon

fractures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 487

Fig. 14.27 Calculated first principal stress in the ankle joint. It is seen that

an area of tensile stress concentration is developed in the distal

tibia at the junction of plafond (the articular surface of the distal

end of the tibia) near the inside surface of the medial malleolus,

suggesting that a fracture could originate there and propagate

into the distal end of the femur to result in a pilon fracture . . . . . 488

Fig. 14.28 The first knee response curves recorded by Patrick et al. (1965).

The data were taken from a whole-body cadaveric sled test in

which both knee impact loads were measured . . . . . . . . . . . . . . . . . . . 489

Fig. 14.29 Femoral response curves for axial knee impacts. (A)Non-fracture response. (B) Fracture response . . . . . . . . . . . . . . . . . . . . 490

xliv List of Figures

Fig. 14.30 Estimate of the neutral axis for bending in femoral shaft in

relation to the axis of the femora neck, based on strain gage data.

Apparently, the lateral surface of the femur is in tension . . . . . . . 491

Fig. 14.31 (A) Knee impact response to Styrofoam DB impacts. (B) Knee

impact response to aluminum honeycomb impacts at 3.6 m/s

(11.8 ft/s) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 491

Fig. 14.32 Knee/femur impact set-up used by Melvin et al. (1975) who

were the first to test unembalmed cadaveric knees with a linear

impactor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493

Fig. 14.33 (A–B) The lower limb model moved into a driving position by

applying a spring load to the leg . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 497

Fig. 14.34 Validation of the foot and tibia model simulating a static load

applied to the foot. There were six tests on cadaveric specimens,

one of which was osteoporotic (Test No. 152). The model was

not as stiff as the averaged data but it compared well with data

from other tests performed by Hirsch and White (1965), Huang

et al. (1993) and Ker et al. (1987) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 499

Fig. 14.35 Drawing of the sled test set-up showing a restrained Hybrid III

dummy seated in front of VW knee bolster. The right leg is a

model of the human lower limb (LLMS) . . . . . . . . . . . . . . . . . . . . . . . . . 499

Fig. 14.36 Comparison of whole-body kinematics between sled test and

model (A) and (B). Details of skeletal contact with the knee

bolster are shown in (C) while in (D) details of patella contact

with bolster are shown. These details cannot be easily visualized

in a sled test but the model is capable of showing the interaction 500

Fig. 14.37 Comparison of knee impact force in the sled test using a VW

knee bolster. The peak deceleration was 35 g. (A) is a

comparison of the measured and predicted force in the femur in

the direction of impact. (B) Compares the three components of

force in the femur . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 501

Fig. 15.1 Top view of the right foot showing all the bones of the foot . . . 510

Fig. 15.2 Side (medial) view of the bones of the left foot, showing the

longitudinal arch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 511

Fig. 15.3 Definition of dorsiflexion, plantar flexion, inversion, and

eversion of the foot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 511

Fig. 15.4 (A) Medial muscles of the leg invert the foot. (B) Lateral

muscles of the leg evert the foot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 512

Fig. 15.5 Lateral ligaments and retinacula of the ankle . . . . . . . . . . . . . . . . . . . . 512

Fig. 15.6 Superficial medial ligaments of the ankle or the deltoid

ligament. The tibiospring ligament is denoted by (1), the

tibionavicular ligament by (9), the superficial tibiotalar ligament

by (10), the tibiocalcaneal ligament by (14). For details, see

Hintermann and Golano (2014) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 513

Fig. 15.7 Test setup for dorsiflexion testing of the foot and ankle . . . . . . . . 514

List of Figures xlv

Fig. 15.8 The injury status in dorsiflexion changes abruptly at 45 deg of

dorsiflexion, indicating that injury would likely occur at this

angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 515

Fig. 15.9 Instrumentation of the lower leg and foot used to study response

and tolerance of the ankle in dorsiflexion . . . . . . . . . . . . . . . . . . . . . . . . . 516

Fig. 15.10 Test device used to test the ankle in dorsiflexion. The foot was

impacted by a brake pedal at the ball of the foot . . . . . . . . . . . . . . . . 516

Fig. 15.11 Ankle inversion can result in sprain or rupture of the lateral

ligaments of the ankle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 517

Fig. 15.12 Drawing of the impact device used to apply inversion and

eversion loads to the foot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 517

Fig. 15.13 Test apparatus for inversion/eversion tests used by Funk et al.

(2002). The specimen can be subjected to an initial axial

compression as well as dorsiflexion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 520

Fig. 15.14 Test device used by Wei et al. (2010) to determine ankle

tolerance to external rotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 521

Fig. 15.15 The Lisfranc ligament spans the medial cuneiform and the

second metatarsal bone (courtesy of Dr. Brian Smith) . . . . . . . . . . 522

Fig. 15.16 Classification of Lisfranc fractures, proposed by Hardcastle

et al. (1982), based on injury patterns rather than mechanism of

injury . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 523

Fig. 15.17 (A–C) The three impact devices used by Smith (2003) to create

Lisfranc foot injuries. Five tendons were preloaded to simulate

braking, including the Achilles tendon . . . . . . . . . . . . . . . . . . . . . . . . . . . . 525

Fig. 15.18 A foot being tested in the plantar flexed configuration,

simulating braking by a short driver using the toes to press on

the brake pedal (courtesy of Dr. Brian Smith) . . . . . . . . . . . . . . . . . . . . 526

Fig. 15.19 Comparison of impactor load on the foot in the plantar flexed

(A) and plantar nominal (B) configurations. There is effective

load transmission through the metatarsals in the plantar flexed

configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 526

Fig. 15.20 Logistic plot of probability of injury vs. velocity of impact for

tests in the plantar flexed configuration with simulated muscle

loading (tendons pulled) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 527

Fig. 15.21 The definition of true and false positives and true and false

negatives applied to a Logistic plot for foot load. Experimental

data were used to demonstrate a special case of no overlap of

injury and non-injury data along the abscissa. This is not usually

the case for most data sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 528

Fig. 15.22 Logistic plot of probability of injury vs. foot load for tests in the

plantar flexed configuration with simulated muscle loading

(tendons pulled) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 530

Fig. 15.23 Receiver operating characteristics (ROC) curve for foot load

with tendons pulled. The area under the curve is 0.9667. Since

there are two changes in slope of the ROC, the changes

xlvi List of Figures

represent a threshold value for injury. The first threshold is at

3196 N with an injury probability of 18.5 % and the second is at

4499 N with a probability of 81.3% . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 531

Fig. 16.1 Side impact fatality rates in the USA from 1975 to 2004.

FMVSS 214 was phased into new cars from 1994 to 1997. The

rate remained unchanged in 2004 relative to the rates in

1994–1997 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 540

Fig. 16.2 Depiction of a broadside impact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 540

Fig. 16.3 Vehicle kinematics in a side impact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 541

Fig. 16.4 Frequency of vehicular impacts by angle of impact for single

and multiple vehicle accidents. Single vehicle side impacts are

usually with a fixed object, such as a tree or a utility pole . . . . . . 542

Fig. 16.5 Distribution of automotive fatalities by age. Young drivers tend

to impact fixed objects while older drivers are more involved in

intersection crashes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 543

Fig. 16.6 Motion of the scapular due to a side impact to the torso. (A)

Motion with no rib fracture. (B) Motion with rib fractures . . . . . 548

Fig. 16.7 Force-deflection curves from lateral pendulum abdominal

impacts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 549

Fig. 16.8 Force-deflection curves from lateral pendulum pelvic impacts . 550

Fig. 16.9 MADYMO model of a 50th percentile male simulating side

impact. It has 18 rigid body segments. 1 for the head, 3 for the

neck, 4 for the torso, 4 for upper extremities, and 6 for the lower

extremities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 552

Fig. 16.10 Mini-models used in the side impact model by Huang (1995) to

calculate the Viscous Criterion and TTI . . . . . . . . . . . . . . . . . . . . . . . . . . 552

Fig. 16.11 Validation of the side impact model by Huang et al. (1994a)

against sled test data from Cavanaugh et al. (1990). (A) Pelvic

offset test against a rigid wall. (B) Flat rigid wall (Fig. 16.11B

was taken from Huang (1995)) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 553

Fig. 16.12 Validation of the side impact model by Huang et al. (1994a)

against sled test data from Cavanaugh et al. (1990). (A) Impact

test against soft paper honeycomb padding. (B) Impact test

against Arsan foam padding (Fig. 16.12A was taken from

Huang (1995)) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 554

Fig. 16.13 Validation of the side impact model by Huang et al. (1994a)

against pendulum impact data from Viano et al. (1989). (A)

Thoracic force-deflection curves. (B) Abdominal force-

deflection curves (Fig. 16.13A was taken from Huang (1995)) . 555

Fig. 16.14 Side impact door velocity profiles used in a parametric study of

the Huang et al. (1994a) model. (A) The GM velocity profile.

(B) The Deng velocity profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 556

Fig. 16.15 Comparison of computed and measured chest deformation

profiles of one of the two sled-to-sled tests carried out by Huang

et al. (1994b) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 560

List of Figures xlvii

Fig. 16.16 US side impact fatalities from 1995 to 2003 stayed constant

despite the promulgation of FMVSS starting in 1994. The total

number of occupant fatalities during this period varied between

33,064 and 34,108 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 561

Fig. 17.1 Simulation of an actual pedestrian impact by an SUV with a

high hood (1 m) at 27.2 km/h (17 mph). The momentum

imparted to the lower part of the body caused the pedestrian to

cartwheel and strike the ground head first. The pedestrian

sustained a fatal head injury . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 571

Fig. 17.2 Schematic of the test setup for a car-pedestrian experiment

conducted by Krieger et al. (1976) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 572

Fig. 17.3 The pedestrian (cadaver) was tested in the sled area where it was

subjected to a side impact by the front end of passenger vehicle.

Out of five tests conducted, there was one frontal impact (based

on Krieger (1976)) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 572

Fig. 17.4 This figure shows the cadaver in position for impact. It was held

upright by a harness for a left-sided impact. The left knee was

prevented from buckling by taping a 1-cm diameter wooden

dowel rod across it. Just before impact, the harness was released

and at impact with the bumper, the dowel broke to allow the

knee to flex. Under the impacted leg, a load cell measured the

ground reaction force which was substantial (based on Krieger

(1976)) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 573

Fig. 17.5 The vehicle used for pedestrian impact was a 1973 full-size

Chevrolet. The cadaver was impacted by the left side of the

vehicle where the bumper was straight (no curvature, bends)

(based on Kreiger (1976)) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 574

Fig. 17.6 Instant of cadaveric head/hood impact of a left-sided 24-km/h

(15-mph) car-pedestrian impact (based on Krieger (1976)) . . . . . 575

Fig. 17.7 Sample data from car-pedestrian experiments by Krieger et al.

(1976). (A) Ground force reaction under impacted leg. (B)

Impacted lower leg lateral acceleration from two cadaveric tests

at about the same velocity. (C) Lateral head acceleration for the

same two tests. (D) Cadaver dummy head angular accelerations

are compared, using tests run at the same speed of 24.1 km/h

(15 mph) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 575

Fig. 17.8 The six front end profiles used in the car-pedestrian study by

Cavallero et al. (1983). The pedestrian is a 50th percentile

dummy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 579

Fig. 17.9 Inverted X-ray cassette with three load cells attached forming an

isosceles triangle. Lead markers were used to identify the

centroid of the triangle, as shown in Fig. 17.10 (based on

Krieger (1976)) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 581

Fig. 17.10 Locating the cg of the pelvis in the antero-posterior view. The

cg is at the intersection of the hash marks which is the centroid

of the isosceles triangle formed by the three load cells . . . . . . . . . . 582

xlviii List of Figures

Fig. 17.11 The circular object is the trifilar pendulum that is suspended

from the ceiling by three wires. The rectangular frame is used to

hold body segments in a fixed orientation so that inertial

properties can be measured by orthogonal rotations. Both the

pendulum and the rectangular frame are made of light weight

magnesium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 582

Fig. 17.12 Test setup for head drop tests on the hood to provide force-

deflection data for the ATB model. A dummy head is shown

facing the hood which is below it (based on Krieger (1976)) . . . 583

Fig. 17.13 Schematic of the test setup for lower leg drop tests on the

bumper to provide force-deflection data for the ATB model. The

impact force was measured by load cells below the bumper and

leg kinematics were recorded on high speed film . . . . . . . . . . . . . . . . 583

Fig. 17.14 Dynamic force-deflection curves for lower leg impact with the

bumper at different impact speeds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 584

Fig. 17.15 Validation of single-segment impacts (A) Comparison of the

x-axis (postero-anterior) head acceleration for a cadaveric head

dropped onto the hood of the test vehicle. (B) Comparison of the

predicted and measured pitch of the head in the same drop test 585

Fig. 17.16 Validation of single-segment impacts—Comparison of

predicted and measured roll angle of the lower leg during a leg

drop test onto the bumper of the test vehicle . . . . . . . . . . . . . . . . . . . . . 586

Fig. 17.17 Validation of the pedestrian model for single-segment

impacts—Comparison of the x-axis (postero-anterior) angular

acceleration of the right lower leg during a leg-bumper impact

(drop test) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 586

Fig. 17.18 Validation of the pedestrian model—Comparison of the head

z-axis (superior-to inferior) linear acceleration of a dummy

car-pedestrian impact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 587

Fig. 17.19 Validation of the pedestrian model—Comparison of the head

x-axis (postero-anterior) linear acceleration for a cadaveric

car-pedestrian impact at 24.1 km/h (15 mph) . . . . . . . . . . . . . . . . . . . . 587

Fig. 17.20 Validation of the pedestrian model—Comparison of the lower

torso z-axis (superior-to-inferior) linear acceleration for a

cadaveric car-pedestrian impact at 37.3 km/h (23.2 mph) . . . . . . 588

Fig. 17.21 Validation of the pedestrian model by Ishikawa et al. (1993).

The vehicular impact speed was 39 km/h (24.2 mph) and the

hood height was between 0.85 and 0.875 m (2.79 and 2.87 ft).

The simulation was terminated upon head contact with the

vehicle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 588

Fig. 17.22 The eight front end profiles used by Gupta and Yang (2013) to

simulate car-pedestrian impact. According to the Gupta-Yang

model, for SUV profiles, regardless of the shape, there

was secondary head to ground impact at an impact speed

of 40 km/h . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 589

List of Figures xlix

Fig. 18.1 History of the seatbelt from 1885 to 1983 . . . . . . . . . . . . . . . . . . . . . . . . 598

Fig. 18.2 Four-point belt systems proposed by Rouhana et al. (2003). The

standard three-point belt is shown in (A), the X4 cross-chest belt

is shown in (B) and the V4 belt is shown in (C) . . . . . . . . . . . . . . . . . 601

Fig. 18.3 A drawing of the ES-2re dummy. ES-2 stands for the second

version of the European side impact dummy and the letters re

indicate that the dummy was modified by the addition of a rib

extension in the rear to prevent the spine from catching on the

seat back during a side impact (courtesy of Mr. Michael

Jarouche, Humanetics Innovative Solutions, Inc.) . . . . . . . . . . . . . . . 604

Fig. 18.4 A photograph (A) and an engineering drawing (B) of a SID-IIs

dummy, showing its five ribs and asymmetric chest. The dummy

can only be impacted on one side (left) because the ribs havebeen lengthened to reduce lateral chest stiffness and are

anchored to a block on the right side (courtesy of Mr. Michael

Jarouche, Humanetics Innovative Solutions, Inc.) . . . . . . . . . . . . . . . 605

Fig. 18.5 Examples of rollover due to a trip-over. It occurs when the

lateral motion of the vehicle is resisted by an opposing force,

inducing a roll moment. The surface is deformed by the wheels 606

Fig. 18.6 Examples of rollover due to a flip-over. It occurs when the

vehicle mounts a guard rail or steep hillside and rolls back

towards the side of the guardrail or slope from which it came . 607

Fig. 18.7 Example of a rollover due to a turn-over which is caused by

centrifugal forces generated by a sharply turning or rotating

vehicle when resisted by normal surface friction, including

pavement, gravel, grass, or dirt. No furrowing, gouging,

deformation, curb or any physical obstruction of the surface

occurs at the point of the trip as opposed to a trip-over . . . . . . . . . 607

Fig. 18.8 Example of a rollover due to a climb-over. The vehicle climbs

up and over the fixed object which needs to be high enough to

lift the vehicle off the ground. It then rolls over to the opposite

side of the impacted object . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 608

Fig. 18.9 Example of a fall-over in which the vehicle is on a slope steep

enough to cause its cg to fall outside of the wheelbase . . . . . . . . . . 608

Fig. 18.10 Example of a bounce-over. The vehicle rebounds off of a fixed

object, such as a guardrail, and overturns, as a result . . . . . . . . . . . . 609

Fig. 18.11 (A–E) Various laboratory test methods to simulate vehicular

rollovers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 609

Fig. 18.12 Rollover test data using a Hybrid III dummy in a Chevrolet

Malibu show that the neck load peaked well before the roof

crushed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 614

Fig. 18.13 Modeling rollover with a belted Hybrid III dummy occupant

(taken from Hu (2007)) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 616

Fig. 18.14 (A–D) Tests used to validate the rollover model

by Hu (2007) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 616

l List of Figures

Fig. 18.15 Comparison of predicted and measured loads for the quasi-static

FMVSS 216 test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 617

Fig. 18.16 Simulation of an SAE J2114 dolly test—Comparison of model

predictions with test results. The simulated vehicular motion is

shown in (A) while the computed vehicular angular velocity,

lateral acceleration and vertical acceleration are compared with

test data in (B–D), respectively . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 618

Fig. 18.17 (A–D) Simulation of a curb trip. Comparison of model predicted

kinematics with experimental data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 619

Fig. 18.18 (A–D) Simulation of a corkscrew rollover with comparison of

model prediction with experimental data . . . . . . . . . . . . . . . . . . . . . . . . . 620

Fig. 18.19 Comparison of measured and predicted dummy head

accelerations in an SAE J2114 dolly rollover test for the near-

side occupant. (A) Lateral acceleration. (B) Vertical

acceleration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 621

Fig. 18.20 Comparison of head impact location and timing in an SAE

J2114 dolly rollover test for the near-side occupant . . . . . . . . . . . . . 621

Fig. 18.21 Comparison of measured and predicted dummy data in an SAE

J2114 dolly rollover test for the far-side occupant. (A) Vertical

head acceleration. (B) Axial neck force . . . . . . . . . . . . . . . . . . . . . . . . . . . 621

Fig. 18.22 Comparison of head impact location and timing in an SAE

J2114 dolly rollover test for the far-side occupant . . . . . . . . . . . . . . . 622

Fig. 18.23 Comparison of measured and predicted dummy head

accelerations in a curb-trip rollover test for the near-side

occupant. (A) Lateral acceleration. (B) Vertical acceleration . . . 622

Fig. 18.24 Comparison of head impact location and timing in a curb-trip

rollover test for the near-side occupant . . . . . . . . . . . . . . . . . . . . . . . . . . . 622

Fig. 18.25 Comparison of measured and predicted dummy data in a curb-

trip rollover test for the far-side occupant. (A) Vertical head

acceleration. (B) Axial neck force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 623

Fig. 18.26 Comparison of head impact location and timing in a curb trip

rollover test for the far-side occupant (taken from

Hu (2007)) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 623

Fig. 19.1 Acute ventricular fibrillation in a pig due to a non-penetrating

impact by a rubber bullet travelling at an estimated speed 50 m/s

and striking the sternum which was fractured . . . . . . . . . . . . . . . . . . . . 634

Fig. 19.2 Experimental set-up used by Kroell et al. (1986) to study

porcine thoracic response and injury, including cardiac injuries 636

Fig. 19.3 Posterior view of the left knee. The medial (or tibial) collateral

ligament is subjected to tensile loading when the knee is

impacted laterally on its lateral aspect . . . . . . . . . . . . . . . . . . . . . . . . . . . . 637

Fig. 19.4 (A) Proximal insertion locations of the ACL. (B) Distal

insertion locations of the ACL. PL is the posterior lateral bundle

and AM is the anterior medial bundle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 638

Fig. 19.5 A braced cadaveric knee ready for a lateral impact . . . . . . . . . . . . . . 640

List of Figures li

Fig. 19.6 Medial aspect of a braced knee, showing the MCL which was

stained dark green and targeted with two rows of white targets,

one along the anterior aspect and the other along the posterior

aspect of the MCL (based on Begeman et al. (1987)) . . . . . . . . . . . 641

Fig. 19.7 Dynamic and static response of the MCL in terms of force-

deflection. The static data were obtained from Kennedy et al.

(1976) (based on Begeman et al. (1987)) . . . . . . . . . . . . . . . . . . . . . . . . . 642

Fig. 19.8 Dynamic and static response of the MCL in terms of stress-

strain. The static data were obtained from Kennedy et al. (1976)

(based on Begeman et al. (1987)) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 642

Fig. 20.1 A typical Friedlander wave . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 650

lii List of Figures

List of Tables

Table 1.1 Road users killed in various modes of transport as a

percentage of regional road traffic deaths 2010 (Source: World

Health Organization) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Table 1.2 The Abbreviated Injury Scale (AIS) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

Table 1.3 Predictor variables for mTBI in the NFL (based on King et al.

2003) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

Table 1.4 Predictors of tolerance for mTBI (based on King et al.

(2003)) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

Table 2.1 Average impulse (in psi-s) for different degrees of concussion

in dogs for all 72 tests (Gurdjian et al. 1954) . . . . . . . . . . . . . . . . . . 50

Table 2.2 Summary of head kinematics measured during the Hardy

(2007) tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

Table 4.1 Material properties of head tissue used in the Ruan et al.

(1994) model of head impact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

Table 4.2 Comparison of computed and measured contact loads for three

occipital head impacts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

Table 4.3 Material properties of gray and white matter used in the

WSUBIM (Zhang et al. 2001) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126

Table 4.4 Validation against intracranial pressure data of Nahum et al.

(1977) in the WSUBIM by Zhang et al. (2001) . . . . . . . . . . . . . . . . 127

Table 4.5 Statistics for the 2-D porcine models (based on Zhou

(1995)) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

Table 4.6 Material properties of head tissue used in the 2-D porcine

model by Zhou et al. (1994) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

Table 6.1 NFL Data – 53 cases of head impact data reconstructed from

game films and drop testing (based on data supplied by the

NFL) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181

Table 6.2 List of predictor variables for logistic regression . . . . . . . . . . . . . . 184

liii

Table 6.3 Rank order of mTBI predictors based on logistic regression

(based on King et al. (2003)) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185

Table 6.4 Comparison of model-predicted values with field data . . . . . . . . 187

Table 6.5 Indy car crash data summary and head response (Courtesy

of Dr. L. Zhang) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195

Table 6.6 Summary of brain responses as predicted

by the WSUHIM .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196

Table 7.1 Neck response as a function of end condition restraints—peak

loads, peak deflections, and resulting injuries if the tolerance

of the neck is exceeded (based on

Nightingale et al. (1991)) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218

Table 8.1 List of cadavers used in the whiplash tests by Deng et al.

(2000) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258

Table 8.2 Peak relative rotations of cervical vertebrae for the 20-deg

seatback tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264

Table 8.3 Peak relative rotations of cervical vertebrae for the 0-deg

seatback tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265

Table 8.4 Peak relative displacements and axial deformations of facet

capsule landmarks of 20-degree seatback tests . . . . . . . . . . . . . . . . . 269

Table 8.5 Peak relative displacements and axial deformations of facet

capsule landmarks of 0-degree seatback tests . . . . . . . . . . . . . . . . . . 270

Table 9.1 Effect of spinal configuration on g-level for vertebral

fracture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292

Table 9.2 Student’s t-test of fracture data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292

Table 9.3 Average EMG onset delay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303

Table 9.4 Tolerance of the thoracolumbar spine to quasi-static

compression-flexion loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305

Table 9.5 Summary of motion segment test data . . . . . . . . . . . . . . . . . . . . . . . . . . 307

Table 10.1 Cadaveric data and test parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325

Table 10.2 Sequence of events in the facet pressure testa (based on

El-Bohy et al. (1989)) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 326

Table 10.3 Facet capsular strain due to applied extension and flexion

moments (The applied moments were 18 N.m in extension and

24 N.m in flexion) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 328

Table 10.4 Parametric study of the aircraft ditching scenario . . . . . . . . . . . . . . 341

Table 10.5 Predicted facet loads and nucleus pressures for the model

shown in Fig. 10.34 for the five loading cases with the pivot at

the center of the disc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347

Table 10.6 Predicted facet loads and nucleus pressures for the model

shown in Fig. 10.34 for the five loading cases with the pivot at

the center of the spinal canal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347

Table 11.1 Test conditions and results of WSU side impact tests . . . . . . . . . 377

Table 11.2 Chest injury criteria (date taken from Viano (1989)) (for

AIS� 4 and for a 25% probability of injury) . . . . . . . . . . . . . . . . . . 381

liv List of Tables

Table 11.3 Linear relationship between chest compression and AIS

(based on Fig. 11.30 above) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 389

Table 11.4 Model parameters used by Lobdell et al. (1973) . . . . . . . . . . . . . . . 391

Table 12.1 Summary of frontal abdominal tests performed using

cadaveric and porcine subjects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415

Table 12.2 Characteristics of the cadavers used in the frontal lower

abdominal impact tests conducted by Cavanaugh et al.

(1986) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 416

Table 12.3 Impact kinetics—lower abdominal impacts . . . . . . . . . . . . . . . . . . . . 417

Table 12.4 Abdominal injury criteria (for AIS� 4 and for a 25%

probability of injury) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 421

Table 12.5 Tolerance of the liver to frontal impact

by a rigid impactor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 422

Table 12.6 Tolerance of the liver to frontal impact by a shoulder belt

(based on 25 tests on porcine subjects) . . . . . . . . . . . . . . . . . . . . . . . . . 422

Table 12.7 Abdominal tolerance to side impact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 422

Table 12.8 Tolerance of the liver (Rouhana 1993) . . . . . . . . . . . . . . . . . . . . . . . . . . 423

Table 12.9 Tolerance of the kidney (Rouhana 1993) . . . . . . . . . . . . . . . . . . . . . . . 423

Table 12.10 Tolerance of the upper abdomen (Rouhana 1993) . . . . . . . . . . . . . 423

Table 12.11 Tolerance of the lower abdomen (Rouhana 1993) . . . . . . . . . . . . . 423

Table 12.12 Material constants for reduced relaxation functions . . . . . . . . . . . 429

Table 12.13 Material constants for elastic response fitted to the

QLV theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 429

Table 12.14 Weight distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434

Table 12.15 Material properties of tissues used in the abdominal model by

Lee and Yang (2001) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 435

Table 12.16 Material properties of abdominal solid organs . . . . . . . . . . . . . . . . . 436

Table 12.17 Comparison of experimental data from Viano (1989) and

predicted results by the WSUHAM for pendulum

side impact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 438

Table 12.18 Comparison of experimental data from Walfisch et al. (1980)

and predicted results by the WSUHAM for pendulum side

impact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 440

Table 13.1 Classification of pelvic disruption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 455

Table 13.2 Results of KTH testing resulting in many acetabular

fractures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 460

Table 14.1 Knee pendulum impact data from Hayashi et al. (1996) . . . . . . 482

Table 14.2 Of the 16 impact tests conducted there were five pilon

fractures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 486

Table 14.3 Tolerance of the Tibia for Anteroposterior and Lateromedial

loading for both sexes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 494

Table 14.4 Tolerance of the Tibia for Anteroposterior and Lateromedial

Loading for males only . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 494

List of Tables lv

Table 14.5 Tolerance of the Tibia for Anteroposterior and Lateromedial

loading for females only . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 495

Table 14.6 List of material properties used to model bone . . . . . . . . . . . . . . . . . 497

Table 14.7 List of simulations used to validate the lower limb model

by Beillas et al. (2001) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 498

Table 15.1 Summary of inversion and eversion ankle test data . . . . . . . . . . . . 518

Table 15.2 Ankle injuries due to inversion and eversion . . . . . . . . . . . . . . . . . . . 519

Table 15.3 Summary of significant ankle inversion and eversion injury

data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 520

Table 15.4 Sensitivity and specificity analysis of foot load data with

tendons pulled . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 529

Table 15.5 Sensitivity and specificity analysis of impact velocity data

with tendons pulled . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 532

Table 16.1 List of all 17 side impact sled tests performed by Cavanaugh

et al. at Wayne State University . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 546

Table 16.2 Model predictions of the effect of air space on the near-side

occupant (based on Huang (1995)) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 557

Table 16.3 Model predictions of the effect of padding on the near-side

occupant (based on Huang (1995)) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 557

Table 16.4 Model predictions of the effect of a reduction in door velocity

on the near-side occupant (based on Huang (1995)) . . . . . . . . . . . 558

Table 16.5 Model predictions of the effect of loss of shoulder engagement

on the near-side occupant (based on Huang (1995)) . . . . . . . . . . . 559

Table 18.1 Types of rollover initiation (based on NHTSA (2001)) . . . . . . . 606

Table 18.2 Distribution of rollover crashes by initiation type for MAIS 2

to 6 injuries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 610

Table 18.3 Injury distribution for belted occupants by body region . . . . . . . 611

Table 18.4 Injury distribution for unbelted occupants by body region

(taken from Hu (2007)) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 611

Table 18.5 Distribution of head injury by injury type or anatomic

structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 612

Table 18.6 Types of head injuries sustained by occupants

in a rollover . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 612

Table 18.7 Distribution of chest injuries among rollover occupants . . . . . . 612

Table 18.8 Distribution of neck injuries among rollover occupants . . . . . . . 613

Table 18.9 Relationship between head and neck injury among rollover

occupants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 613

Table 19.1 Scores for Glasgow Coma Scale (based on Teasdale and

Jennett (1974)) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 630

Table 19.2 MCL strains due to lateral impact

(values in percent strain) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 641

Table 19.3 MCL failure loads, strain rate and stiffness . . . . . . . . . . . . . . . . . . . . . 641

Table 19.4 Overall strain rate and loading rate for the MCL tests

conducted (based on Begeman et al. (1987)) . . . . . . . . . . . . . . . . . . . 642

lvi List of Tables