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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