A STUDY ON THE BIOMECHANICS
OF AXONAL INJURY
dedicated to Ingrid and Benjamin
A study on the biomechanics of
axonal injury
Robert W. G. Anderson
Road Accident Research Unit
and the
Department of Mechanical Engineering
The University of Adelaide
South Australia 5005
v
© Robert Anderson & the University of Adelaide 2000
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Abstract
The current focus of research efforts in the area of the biomechanics of traumatic
brain injury is the development of numerical (finite element) models of the human head. A validated numerical model of the human head may lead to better head injury criteria than those
used currently in crashworthiness studies. A critical step in constructing a validated finite element model of the head is determining the mechanical threshold, should it exist, for various
types of injury to brain tissue.
This thesis describes a biomechanical study of axonal injury in the anaesthetised
sheep. The study used the measurements of the mechanics of an impact to the living sheep, and
a finite element model of the sheep skull and brain, to investigate the mechanics of the resulting
axonal injury. Sheep were subjected to an impact to the left lateral region of the skull and were
allowed to survive for four hours after the impact. The experiments were designed specifically
with the numerical model in mind; sufficient data were collected to allow the mechanics of the
impact to be faithfully reproduced in the numerical model. The axonal injury was identified using immunohistological methods and the injury was mapped and quantified. Axonal injury was
produced consistently in all animals. Commonly injured regions included the sub-cortical and
deep white matter, the hippocampi and the margins of the lateral ventricles. The degree of injury
was closely related to the peak impact force and to kinematic measurements, particularly the
peak change in linear and angular velocity. There was significantly more injury in animals receiving fractures.
A three-dimensional finite element model of the sheep skull and brain was constructed to simulate the dynamics of the brain during the impact. The model was used to investigate different regimes of material properties and boundary conditions, in an effort to produce
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a realistic model of the skull and brain. Model validation was attempted by comparing pressure
measurements in the experiment with those calculated by the model. The distribution of axonal
injury was then compared with the output of the finite element model. The finite element model
was able to account for approximately thirty per cent of the variation in the distribution and extent of axonal injury, using von Mises stress as the predictive variable. Logistic regression techniques were used to construct sets of curves which related the extent of injury, to the predictions
of the finite element model, on a regional basis.
The amount of observable axonal injury in the brains of the sheep was clearly related to the severity of the impact, and was related to the predictions of a finite element model
of the impact. Future improvements to the fidelity of the finite element model may improve the
degree to which the model can explain the variation in injury throughout the brain of the animal
and variations between animals.
This thesis presents results, and a methodological framework, that may be used
to further our understanding of the limits of human endurance, in the tolerance of the brain to
head impact.
All experiments reported herein conformed with the Australian Code of Practice
for the Care and Use of Animals for Scientific Purposes.
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Foreword
To the best of my knowledge and belief, all the material presented in this thesis, except where
otherwise acknowledged, is my own original work and has not been published previously for
the award of any other degree or diploma in any university. If accepted for the award of the
degree of Doctor of Philosophy, I consent that this thesis be made available for loan and
photocopying.
ROBERT ANDERSON
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Contents
PAGE
1
2
3
Abstract
vii
Foreword
ix
Contents
xi
List of tables
xv
List of illustrations
xvii
Acknowledgments
xxi
Introduction
1
The tolerance of the brain to an impact to the head
2
Axonal injury and its study in biomechanics
4
The use of animals as models of human AI, for the study of
the biomechanics of AI
6
Aims of the study
6
Methodology
The sheep as a model of AI in the human •
Neuropathology • Head dynamics • Finite element
model • Axonal injury prediction • Ethics
7
Review of the literature
13
Axonal anatomy, physiology and the pathology of axonal injury
13
Biomechanics of axonal injury
Contact effects • Physiological considerations •
Summary
16
Methods used in the laboratory
35
Introduction
35
Sheep anatomy and physiology
The sheep SKull • The sheep brain
36
Animal preparation, monitoring and termination
Anaesthetic induction • Maintenance anaesthetic
and physiological monitoring • Animal
monitoring • Termination and Fixation
37
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Neuropathological investigation
Initial preparation of histology slides • Antigen
retrieval for immunohistochemistry • Application of
antibodies and stain
43
Biomechanical equipment and measurements
Data acquisition and signal processing • Captive
bolt stunner • Dynamic intracranial pressure
changes
46
Accelerometer array design
Background • Accelerometer array Mark 1 •
Accelerometer array Mark II
56
Array performance
Accelerometer misalignment • Effects of transverse
sensitivity and redundancy • Quality of attachment
and other considerations • Validation of
acceleration measurements using a reference
accelerometer • The reference coefficient •
Performance of the reference accelerometer •
Discussion
64
Transformation of measured accelerations to an anatomical
coordinate system
The definition of coordinate systems • Dual-plane
X-ray technique • Determining the location of an
object using dual plane X-ray images •
Determining the locations of the X-ray sources •
Technique using direct coordinate measurement •
Coordinate transformation between vector bases
4
Results of the sheep experiments
85
97
Introduction
Protocol changes
97
Biomechanical characterisation
Impact dynamics • Reference acceleration
measurements • Impact pressure dynamics
100
Baseline physiology and changes after impact
111
Macroscopic injury description
114
Axonal injury scores
Observation • Injury distribution • Quantification
of injury • Control animals
116
The relationship between injury and raised intracranial pressure
124
The relationship between injury and loading parameters
Impact force and injury • Skull kinematics and
brain injury
125
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Discussion
5
6
129
Application of the finite element method
133
Introduction
133
Mesh generation
Geometrical data collection • Surface extraction for
the finite element model • Definition of the
tentorium • Meshing the brain • Meshing the skull
134
Inertial properties of CT data
Inertial properties of the finite element model
142
Application of impact loads
148
Numerical aspects
Hourglass control • Damping
150
Pressure estimates
152
Material properties and interface definitions
Material properties of the brain • Properties used in
this study • Model A • Model B
153
Comparison between model results and histology data
Definition of results planes • Correlation between
model results and injury • Correlation analysis
using all simulation data
166
Discussion
174
A logistical regression model for injury prediction
SAIS probability in non-fracture experiments •
SAIS probability in all experiments
175
Discussion, conclusions and recommendations
Discussion
183
183
Kinematic measurements • The relationship
between the mechanics of the impact and the
resulting axonal injury. • The relationship between
the SAIS and the estimates of tissue loading as
estimated by the finite element model
7
Conclusions
189
Recommendations for future work
191
References
193
Appendix A Detailed results by experiment
Appendix B Publications arising from this thesis
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A1
A87
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List of tables
TABLE 3.1
TABLE 4.1.
TABLE 4.2.
TABLE 4.3.
TABLE 4.4.
TABLE 4.5.
TABLE 4.6.
TABLE 4.7.
TABLE 4.8.
TABLE 4.9.
TABLE 5.1
TABLE 5.2
TABLE 5.3
TABLE 5.4
TABLE 5.5
TABLE 5.6
TABLE 5.7
TABLE 5.8
TABLE 5.9
TABLE 5.10
Target values for baseline physiology
Experimental protocols
Summary of rigid body dynamic results
Gauge pressure measurements in the experiments
Baseline physiology
Blood gas physiology during the survival period
Macroscopic injury descriptions
Grading system for mapping axonal injury
BAIS and SAIS for the experiments
BAIS by fracture severity
Inertial properties of the CT data
Element numbers for the mesh of the sheep skull and brain
Published hyperelastic material properties of brain tissue
Published viscoelastic material properties of brain tissue
Material properties used to characterise brain tissue in
published finite element models
The characteristics of variants of the finite element model
Material properties assigned to the finite element model
Material properties used in Model B
Parameters for the ordinal logistical model of the regressions of
injury on von Mises stress and on principal logarithmic strain
Parameters for the ordinal logistical model of the regressions of SAIS
categories of all experimental results on von Mises stress and on
principal logarithmic strain
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101
107
113
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123
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List of illustrations
FIGURE 1.1.
FIGURE 2.1.
FIGURE 2.2.
FIGURE 2.3.
FIGURE 3.1.
FIGURE 3.2.
FIGURE 3.3.
FIGURE 3.4.
FIGURE 3.5.
FIGURE 3.6.
FIGURE 3.7.
FIGURE 3.8.
FIGURE 3.9.
FIGURE 3.10.
FIGURE 3.11.
FIGURE 3.12.
FIGURE 3.13.
FIGURE 3.14.
FIGURE 3.15.
FIGURE 3.16.
FIGURE 3.17.
FIGURE 3.18.
FIGURE 3.19.
FIGURE 3.20.
FIGURE 3.21.
FIGURE 3.22.
FIGURE 3.23.
FIGURE 3.24.
FIGURE 3.25.
FIGURE 3.26.
FIGURE 3.27.
FIGURE 3.28.
FIGURE 3.29.
FIGURE 3.30.
FIGURE 3.31.
Model for the threshold of axonal injury
Structure of a neuron
Anatomical features mentioned in the text
The falx cerebri
The bones of the sheep skull
Lateral view of the sheep brain
Ventral view of the sheep brain
Median section of the brain
Modified captive bolt gun
Impact location on the skull of the sheep
Striker designs, from top Mk.I, Mk. II and Mk. III
Velocity measurement technique using displacement sensors
Lumped parameter analogy of the striker
Rigid frame for mounting the captive bolt gun
Typical pressure transducer locations
Pressure transducer mounted in the modified Camino bolt
The tip of each transducer is mounted flush with the under
surface of the skull
Accelerometer scheme for measurement of linear and
angular acceleration of a body-fixed frame
An array of nine accelerometers (in a 3-2-2-2 arrangement),
allowing the calculation of angular accelerations independently
at each time point
3-2-2-2 accelerometer array for measuring head kinematics
The original array mounting plate system (left); later the
mounting technique was modified to increase the stiffness of the
attachment (right).
3-2-2-2 array mark 2 in position on the frontal bone
The frontal sinuses of the sheep
3-2-2-2 array layout
‘Back to side’ calibration setup for measuring transverse
sensitivities
‘True’ accelerations used to examine effect of transverse sensitivity
Effect of 5% transverse sensitivity on the measurement
of a typical head acceleration in the 6 and 9 accelerometer arrays
Typical array acceleration from the first array design
MADYMO model of the accelerometer array
Example of the velocity measured with the first array
Shaker test setup
Average transfer function and coherence between the predicted
and measured acceleration of the reference accelerometer
A sample of predicted and measured acceleration from the
transfer function test
Coordinate system definitions
Source-film plane system 1
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14
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FIGURE 3.32.
FIGURE 3.33.
FIGURE 3.34.
FIGURE 4.1.
FIGURE 4.2.
FIGURE 4.3.
FIGURE 4.4.
FIGURE 4.5.
FIGURE 4.6.
FIGURE 4.7.
FIGURE 4.8.
FIGURE 4.9.
FIGURE 4.10.
FIGURE 4.11.
FIGURE 4.12.
FIGURE 4.13.
FIGURE 4.14.
FIGURE 4.15.
FIGURE 4.16.
FIGURE 4.17.
FIGURE 4.18.
FIGURE 4.19.
FIGURE 4.20.
FIGURE 4.21.
FIGURE 4.22.
FIGURE 4.23.
FIGURE 4.24.
FIGURE 4.25.
FIGURE 5.1.
FIGURE 5.2.
FIGURE 5.3.
FIGURE 5.4.
FIGURE 5.5.
FIGURE 5.6.
FIGURE 5.7.
FIGURE 5.8.
Source-film plane system 2
Calibration system for determining the source of the X-rays
Image of calibration markers, subject to perspective distortion
Array acceleration in Experiment 1097
The trajectory of the centre of percussion in Experiment 0598
Impact force, linear acceleration and angular acceleration of
the head measured in Experiment 0298
Chart showing the predicted acceleration at the reference
location and that measured by the reference accelerometer in
Experiment 0997 (C = 0.484).
Reference accelerometer reading and that predicted by the array
in Experiment 1097 (C = 0.967)
Pressure and impact force readings in Experiment 0498
Pressure and impact force measurements in Experiment 0198
Pressure and impact force measurements in Experiment 0997
Pressure and impact force measurements in Experiment 0897
Pressure and impact force readings in Experiment 0598
Physiological changes in the first hour in Experiment 0897
Physiological changes during the survival period in
Experiment 0897
Macroscopic injury in Experiment 1896 displaying an impact
contusion, overlying subarachnoid haemorrhage and a cortical
defect from the use of an ICP monitor
A contre coup contusion was noted in Experiment 0298
Sections used for injury scoring
Typical levels of injury associated with an injury score of 2
Illustration of axonal injury at level 3
Composite figure showing commonly injured regions
The relationship between peak mean ICP and the Brain Axonal
Injury Score
The relationship between peak impact force and BAIS
The relationship between peak linear acceleration of the
anatomical origin and the BAIS
The relationship between peak angular acceleration and
the BAIS
Relationship between peak change in linear velocity and BAIS
Relationship between peak change in angular velocity and BAIS
The correlation between peak angular velocity and peak
impact force
Interior surface of skull produced by projection
A photograph of the tentorium and the mesh
Right hemisphere component divided for meshing
The brain mesh
The skull mesh
Each slice represented the tissue between it and the
following slice
The location of the centre of gravity of the head by analysis
of CT data
The von Mises stress in the skull at peak force in a simulation
of experiment 0598
xviii
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FIGURE 5.9.
FIGURE 5.10.
FIGURE 5.11.
FIGURE 5.12.
FIGURE 5.13.
FIGURE 5.14.
FIGURE 5.15.
FIGURE 5.16.
FIGURE 5.17.
FIGURE 5.18.
FIGURE 5.19.
FIGURE 5.20.
FIGURE 5.21.
FIGURE 5.22.
FIGURE 5.23.
Single point (solid) and fully integrated elements (wire frame)
used in the model of the cerebrum
151
Schematic diagram showing the location of pressure calculation
in the finite element model
153
Pressures predicted by Model A, and those recorded in
Experiment 0398, Experiment 0498 and Experiment 0598
161
Pressures predicted by Model B, and those recorded in Experiment 0398,
Experiment 0498 and Experiment 0598
164
Typical pressure response of Model B
165
A histology section and the equivalent MRI cross-section
168
Example of the histology plane transformed to finite element
coordinates
169
Relationship between peak von Mises stress in Model B and
the Sector Axonal Injury Score of each sector
171
Relationship between the peak principal logarithmic strain
in Model B and the Sector Axonal Injury Score of each sector
172
Relationship between peak von Mises stress in Model B and
the Sector Axonal Injury Score of each sector for experiments
and simulations
173
Relationship between peak maximum logarithmic strain in
Model B and the Sector Axonal Injury Score of each sector for
experiments and simulations
174
Logistic analysis comparing the predicted peak von Mises stress
in the model and the extent of 2+ injury in the brains of animals
that sustained no significant skull fracture
178
Logistic analysis comparing the predicted peak maximum
principal logarithmic strain in the model and the extent of
2+ injury in the brains of animals that sustained no significant
skull fracture.
178
Logistic analysis comparing the predicted peak von Mises stress
in the model and the extent of 2+ injury in the brains of animals
that sustained no significant skull fracture.
180
Logistic analysis comparing the predicted peak maximum
principal logarithmic strain in the model and the extent of
2+ injury in the brains of animals that sustained no significant
skull fracture.
181
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Acknowledgments
I would like to acknowledge the advice and help given by my colleagues. Without their sense of
collaboration and enthusiasm, this study would not have been possible. In particular I would
like to thank and acknowledge the contribution of Mr. Chris Brown of the Department of
Surgery (Neurosurgery), University of Adelaide1, who organised all aspects of the surgical
protocol, and ran the surgery on the experiment days. He was also instrumental in enhancing
the immunohistochemistry protocol, and was ever enthusiastic about the experimental design
of the study. He carried out the histology used in this study and supplied the
immunohistochemistry protocol included in Section 3.4. Others who worked at getting the
study off the ground, and generously gave their time and advice, include Prof. Peter Blumbergs
and Dr. Grace Scott, of the Institute of Medical and Veterinary Science (IMVS), who assisted
with the observation of injury, and whose department prepared the tissue for sectioning, Prof.
Nigel Jones and Prof. Peter Reilley of the Department of Surgery, University of Adelaide, Dr.
John Finney and Mr. Jim Manavis of the IMVS, and Dr. Corrina Van den Heuval, Dept. of
Pathology, University of Adelaide, who assisted in many of the experiments. I am grateful for
the excellent support of the animal services team at the IMVS, and I particularly thank Ms.
Glenda Summersides for her assistance.
For assistance with the construction of the equipment used in this study, I thank Mr. Ron Jager
and the team in the Mechanical Workshop in the Department of Mechanical Engineering. For
their instrumentation genius, I thank Mr. George Osborne and Mr. Silvio DeIeso from the
Instrumentation Section of the Department of Mechanical Engineering.
1. Affiliations are given as they were at the time. Some of these affiliations may have changed.
xxv
I would like to acknowledge the assistance of people from other institutions who freely gave of
their time and advice to either directly assist with the study or to critique and discuss my ideas.
Direct assistance was given by Dr. David Netherway of the Australian Craniofacial Unit, the
Department of Radiology at the Royal Adelaide Hospital, the Department of Radiology at the
Adelaide Women’s and Children’s Hospital, and Dr. Maurice Claessens of the Eindhoven
Technical University. For invaluable advice and encouragement, I thank Dr. Remy Willinger
from the University Louis Pasteur, Strasbourg, and Dr. Jac Wismans from of the Eindhoven
Technical University, both of whom spent a considerable amount of time advising me and
discussing the project in its early stages. Prof. Albert King of Wayne State University, Dr. David
Meaney and Dr. Susan Margulies of the University of Pennsylvania, willingly gave their time
and experience to encourage me at various stages. For advice on numerical modelling, thanks to
Mr. Douglas Bradshaw, of the University of Southampton, Dr. Ben Cazzolato and Dr. Carl
Howard of the Department of Mechanical Engineering, University of Adelaide.
Not least, I sincerely thank my supervisors Prof. Colin Hansen and Prof. Jack McLean; Prof.
Hansen for taking the project on, and Prof. McLean who was prepared to support me and the
project, both financially and morally, at every stage.
I acknowledge the support of the National Health and Medical Research Council, who
supported this project through a Research Unit Grant to the Road Accident Research Unit.
xxvi