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An experimental model of blunt-impact induced traumatic brain injuries

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An experimental model of blunt-impact induced traumatic brain injuries

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Content An Experimental Model of Blunt-Impact Induced
Traumatic Brain Injuries
Dissertation by
Stylianos Koumlis
Submitted in partial fulllment of the requirements for the degree of
Doctor of Philosophy
in the Department of Aerospace and Mechanical Engineering
Faculty of the USC Graduate School
Doctoral Committee:
Veronica Eliasson, chair
Mitul Luhar
Megan McCain
University of Southern California
Los Angeles, California
Aug 2017
© Copyright by Stylianos Koumlis 2017
All Rights Reserved
I
Abstract
The brain is arguably the most complex organ in the human body. Its basic building
blocks are cells. Like any other organ in the human body, the brain can be injured.
Traumatic brain injury (TBI) is dened as an alteration in brain function or other
evidence of brain pathology due to an external force. The incidence of TBIs and the
corresponding societal impact and cost are enormous. TBIs can be classied as mild,
moderate, and severe based on clinical criteria, e.g. the Glascow Coma Scale. There is
no better prognostic measure other than these clinical criteria. But these classication
systems have limitations. This fact, along with the increased awareness in the long term
consequences of mild-TBIs, that often times are not reported or remain untreated, makes
the development of quantitative biological objective measures to diagnose TBIs crucial.
TBI is a bio-mechanical event, in which the cause is mechanical, e.g. impact force,
and the response is both mechanical, e.g. deformation of brain tissue, and biological, e.g.
in
ammation and cell death of biological tissue. Under the premise that excessive tissue
deformation, due to the mechanical stimulus, is the main cause of injury, we designed a
TBI model that is able to probe all relevant aspects of a TBI event.
Along this line of argument in this thesis a novel in-vitro model of TBI is presented.
Specically, low magnitude repeated blunt-impact loads, that would correspond to sub-
concussive injuries, are studied. The surrogate brain tissue used in the model is cell
cultures grown in a petri-dish, a monolayer of brain cells adhered at the glass-bottom
of the dish. The model of injury supplies an impact load to a simplied bio-mimetic
head model. The mechanical stimulus is controlled and quantied and the subsequent
mechanical and biological response of the surrogate brain tissue is monitored. A quan-
titative correlation between cause, impact force, and the response of the tissue in terms
of mechanical deformation experienced and biological response is drawn. A safe num-
ber of impacts that do not initiate an in
ammatory response of the biological tissue is
identied, and the biological response to a well determined input stimulus and mechan-
ical deformation history is explored in terms of a host of potential injury bio-markers.
New directions of application of the proposed TBI model are further explored in terms
of alternative surrogate tissues, such as hydrogels seeded with cells, that represent the
II
mechanics of the brain tissue deformation more appropriately.
III
Acknowledgments
I will try to conne this section of acknowledgments to the people that directly
made this work possible, in that if I tried to acknowledge all the people that indirectly
contributed, I would for sure forget to mention many. I would want to rst thank my
research advisor Professor Veronica Eliasson, for giving me the opportunity to work in
her lab, for her support and guidance through the years. During the period that I spent
in the Shockwave Dynamics laboratory at USC, I had the opportunity to collaborate
with a great number of people that helped me develop and evolve intellectually and
personally. Although my classical training is in engineering, the research presented in
this thesis is interdisciplinary. My very rst exposure to research in the eld of biology
was through our collaboration with Dr. Parijat Sengupta, who was very patient with me
as I was trying to catch-up with the eld. Her involvement early on, shaped the direction
and future path of this research work. I appreciate the time, eort, and her guidance
through the project. Next, I would like to thank Dr. Hank Cheng, with whom we had
a fruitful collaboration later on in this project, designing and conducting experiments
and analyzing the interesting and mind-boggling experimental results. Hank at the time
used to work in the lab of Professor Caleb Finch at USC, and with Dr. Todd Morgan.
I would like to thank both of them for their time and the resources that they put in the
project. Of course, I would like to thank my labmates Orlando, Stone, Hongjoo, Wan,
Gauri, and Chuanxi, for being an excellent group of people to work around every day,
learn, discuss, and most importantly for being great friends. Through the years at USC
I made a lot of good friends that were there to support me and I feel indebted to them.
I recognize how important it is to have people around you that are there for the good
and rough(er) times. They know who they are and I am certain that these friendships
will last for years to come. Last but not least, I am blessed with a loving and supportive
family that provides me everything in their capacity unconditionally and with the best
of intentions. I try to remind to myself that having a family like that is a privilege that
should not be taken for granted, and a special place exists in my heart for them.
IV
Dissertation
Stylianos Koumlis
July 18, 2017
Contents
1 Introduction 1
2 Theoretical Background 6
2.1 Morphology, Anatomy, and Histology of the Human Head . . . . . . . . . 7
2.2 Mechanical Properties of the Human Head . . . . . . . . . . . . . . . . . 10
2.2.1 Elastic Solids and Viscous Fluids: Qualitative Description . . . . 12
2.2.2 Viscoelastic Behavior: a Phenomenological Description . . . . . . 14
2.2.3 Mechanical Properties of the Human Head Tissues: Experimental
Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.3 Dynamic Loading of Materials . . . . . . . . . . . . . . . . . . . . . . . . 42
2.3.1 Governing Equation . . . . . . . . . . . . . . . . . . . . . . . . . 43
2.3.2 Interaction and Re
ection of Waves at an Interface . . . . . . . . 46
3 Current Understanding of the Bio-Mechanics of Traumatic Brain In-
juries 48
3.1 Models of Traumatic Brain Injury . . . . . . . . . . . . . . . . . . . . . . 49
3.1.1 Analytical and Numerical Models of TBI . . . . . . . . . . . . . . 50
3.1.2 Experimental Models of TBI . . . . . . . . . . . . . . . . . . . . . 53
3.1.3 Bio-Mechanical Models of TBI . . . . . . . . . . . . . . . . . . . . 56
3.2 Mechanisms of Traumatic Brain Injury . . . . . . . . . . . . . . . . . . . 57
4 A Novel In-Vitro Model of Traumatic Brain Injury 62
4.1 Rationalization of Model Design . . . . . . . . . . . . . . . . . . . . . . . 62
4.2 Injury Model Apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.2.1 Principle of Operation: Schematic . . . . . . . . . . . . . . . . . . 64
4.2.2 Principle of Operation: Detailed Design . . . . . . . . . . . . . . . 66
4.3 Surrogate Brain Tissue . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
4.4 Experimental Toolset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
4.4.1 Mechanical Stimulus Quantication . . . . . . . . . . . . . . . . . 69
4.4.2 Mechanical Response Quantication . . . . . . . . . . . . . . . . . 70
4.4.3 Biological Response Quantication . . . . . . . . . . . . . . . . . 71
5 Mechanical Characterization of TBI Model 73
5.1 Measurement of the Mechanical Stimulus . . . . . . . . . . . . . . . . . . 73
5.1.1 Impact Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
5.1.2 Impact Velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
5.1.3 Pressure Pulse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
5.2 Measurement of the Mechanical Response . . . . . . . . . . . . . . . . . 77
5.2.1 Quantication of Glass Substrate Deformation During Pressure
Pulse Loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
5.3 Conclusion on the Mechanical Characterization of the Model . . . . . . . 80
6 Biological Response of Surrogate Brain Tissue 82
6.1 Mice Cell Culture: Co-Culture of Neurons and Glial Cells . . . . . . . . . 82
6.1.1 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
6.1.2 Measurement of Biological Response . . . . . . . . . . . . . . . . 86
6.1.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
6.2 Rat Mixed Glial Cell Cultures . . . . . . . . . . . . . . . . . . . . . . . . 89
6.2.1 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
6.2.2 Measurement of Biological Response . . . . . . . . . . . . . . . . 93
6.2.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
7 Towards Models of TBI with Realistic Cytoarchitecture and Geometry 99
7.1 Quantication of Deformation in the Mid-Layer of a 3D Hydrogel During
Pressure Pulse Loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
7.2 Models of TBI with Realistic Geometries and Dimensions . . . . . . . . . 103
7.2.1 Spherical Acrylic Shell Filled with Water . . . . . . . . . . . . . . 104
7.2.2 Cylindrical Acrylic Shell Filled with Ballistic Gelatin . . . . . . . 106
8 Conclusions and Future Research 111
Bibliography 116
List of Figures
2.1 Stress-strain plot of linear elastic solid material . . . . . . . . . . . . . . 12
2.2 Response of dierent materials to a unit step load/strain . . . . . . . . . 16
2.3 Sinusoidal stimulus and corresponding time-lagged response of a linear
viscoelastic material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.4 Stress-strain plot for elastic, viscoelastic and viscous materials . . . . . . 20
2.5 Creep compliance curve for monkey scalp in tension and compression [24] 22
2.6 Stress-strain plot under tension for cranial bone specimens . . . . . . . . 24
2.7 Stress-strain response of brain tissue under quasi-static tensile loading
conditions [23] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.8 Stress-strain response under dynamic tensile loading conditions [33,34] . 30
2.9 Creep response curves of monkey and human brain specimens under com-
pression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.10 Stress-strain response at four dierent strain rates under constant strain
rate compression loading [41,42] . . . . . . . . . . . . . . . . . . . . . . . 36
2.11 Average stress-strain relationships in unconned compression test at dif-
ferent strain rates [38,39] . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.12 Compressive stress-strain curve at dynamic strain rates [43] . . . . . . . . 38
2.13 Compressive response of brain tissue . . . . . . . . . . . . . . . . . . . . 40
4.1 Hierarchy of layers that are being modeled in the skull-brain system by
HAMr . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
4.2 Schematic of the biomimetic 1D skull-brain model . . . . . . . . . . . . . 65
4.3 Model of HAMr and cross sectional view with internal details . . . . . . 67
4.4 Geometric details of protective plate, water bath, and petri dish . . . . . 68
4.5 Side view of DIC experimental setup schematic . . . . . . . . . . . . . . 72
5.1 Temporal proles of impact force . . . . . . . . . . . . . . . . . . . . . . 74
5.2 Day-to-day impulse variability . . . . . . . . . . . . . . . . . . . . . . . . 74
5.3 Impulse as a function of impact force . . . . . . . . . . . . . . . . . . . . 75
5.4 Temporal proles of pressure at two dierent depths inside the water bath. 77
5.5 Strain deformation of substrate caused by the applied pressure pulse. . . 79
6.1 An immunostained DIV-17 dissociated cortical network . . . . . . . . . . 84
6.2 Elevation in expression levels of IL-1 protein in networks after being
exposed to dierent numbers of repetitive impacts . . . . . . . . . . . . . 88
6.3 Expression levels of IL-1 . . . . . . . . . . . . . . . . . . . . . . . . . . 88
6.4 A higher magnication image of a network . . . . . . . . . . . . . . . . . 89
6.5 Phase-contrast optical microscopy of mixed glia cultures. . . . . . . . . . 94
6.6 GFAP and DAPI immuno
uorescence of mixed glial cultures. . . . . . . . 97
6.7 Gene expression of mixed glia cultures. . . . . . . . . . . . . . . . . . . . 98
7.1 Ballistic gelatin hydrogel block . . . . . . . . . . . . . . . . . . . . . . . . 101
7.2 Dynamic strain quantication on mid-section plane of ballistic gelatin block.102
7.3 Schematic of experimental setup of the physical pendulum . . . . . . . . 104
7.4 Impact response of a spherical \skull" model lled with water. . . . . . . 105
7.5 Cylindrical acrylic skull model . . . . . . . . . . . . . . . . . . . . . . . . 107
7.6 Strain history along the horizontal direction,
xx
(t), at dierent cross sec-
tions of the model captured at 13,000 fps . . . . . . . . . . . . . . . . . . 109
7.7 Strain history along the horizontal direction,
xx
(t), at dierent cross sec-
tions of the model captured at 13,000 fps. (a) Average strain versus time
along red line at 70% distance from the impact point, (b) Average strain
versus time along red line at 90% distance from the impact point . . . . 110
List of Tables
2.1 Tabulated values for thickness and porosity of dierent layers of the skull
using MicroCT [25] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.2 Comparison of elastic modulus and failure stress of outer table of skull bone 25
2.3 Comparison of elastic moduli under tensile loading between dierent studies 31
2.4 Comparison of initial elastic moduli under unconstrained compressive
loading between dierent studies at similar strain rates . . . . . . . . . . 37
5.1 Impact force measured for dierent experimental settings, using dierent
combinations of spring stiness and initial displacements. Errors rep-
resent standard deviation of 5 repeat experiments at each experimental
setting. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
Chapter 1
Introduction
\When Andre Waters, a hard hitting National Football League (NFL) safety from 1984
to 1995, made the front page of the New York Times on Thursday, January 18, 2007,
he became the third NFL player known to have died as a result of chronic traumatic
encephalopathy (CTE) attributed to the multiple concussions he experienced while playing
in the NFL. Preceding the 44-year-old Andre were Mike Webster, age 50, the Hall of
Fame Pittsburgh Steelers center who died homeless, and Terry Long, age 42, who, like
Waters, took his own life. All three of these athletes were known as iron men, hard
hitters who never came out of the game, continuing to play through countless injuries,
including concussions. All of these athletes, as well as Ted Johnson, whose front-page
story was widely circulated February 2, 2007 in the New York Times and Boston Globe,
shared symptoms of sharply deteriorated cognitive function, especially recent memory
loss and psychiatric symptoms such as paranoia, panic attacks, and major depression
after multiple concussions experienced in the NFL. The brains of all of these deceased
athletes were examined by Bennett Omalu, M.D., a forensic pathologist at the University
of Pittsburgh, and shared common features of CTE including neurobrillary tangles,
neutrophil threads, and cell dropout. He likened Waters' brain to that of an \octogenarian
Alzheimer's patient"
Cantu, 2007 [1]
1
Chapter 1. Introduction
Definition of Traumatic Brain Injuries
Traumatic Brain Injury (TBI) is dened as an alteration in brain function or
other evidence of brain pathology caused by an external force [2].
Incidence of TBIs
The estimated incidence of TBIs in the US is between 1.4 - 3.8 million injuries per
year [3], with 300,000 of them attributed to sports or other recreational activities [4{6].
Sports-related TBIs pose a substantial public health issue and have a huge societal
impact with possible long-term disability of the aected population. In sports like
American football, soccer, basketball, baseball, as well as boxing, skiing and cycling, the
most common injuries are due to dynamic loading of the head through blunt impacts.
Often times these injuries are repeated through an athlete's career.
Main Objective
On that account, this thesis is focused on brain injuries of the head being struck by
or against a blunt object and the eect of multiple low magnitude impacts. Penetrating
injuries, injuries due to blast, and injuries due to acceleration without external impact
will not be considered.
Traditionally, TBI is dened based on clinical criteria [7]. This means that the TBI
denition is usually based on direct observation of the patients, rather than theoretical
or laboratory studies. But these injury severity indicators come with limitations. For
example, classication of the same patient using dierent injury severity criteria is not
2
consistent. Moreover, for two patients classied with the same injury severity, their be-
havioral and functional outcome can be very dierent, regardless of the severity criterion
used [5]. So far, there is no biologically objective measure that quanties the severity
of brain pathology. Recent developments in diusion tensor Magnetic Resonance Imag-
ing [8] and other quantitative biological techniques may provide a host of new biomarkers
for the denition and diagnosis of TBIs.
In this work, a novel in-vitro model of TBI is proposed. The mechanical input
is controlled and quantied, while both the mechanical and biological response of the
surrogate brain tissue (in-vitro cell culture) is investigated. The novelty of the proposed
model lies in the biomimetic model of the skull-brain system and the adherence to a
realistic loading stimulus that produces an impact load through a blunt striker.
With the use of high-speed photography and digital image correlation techniques, the
time history of the dynamic deformation of the surrogate brain tissue can be probed.
Under the premise that excessive deformation of brain tissue is the main cause of injury
to the brain, the main goal is to correlate the mechanical response to the biological
response of the surrogate tissue in terms of dierent bio-markers. These markers may
potentially serve as the signature of the incidence and severity of the TBI event.
The TBI experimental model presented in this thesis, tries to shed light in the corre-
lation between the mechanical and biological response to the mechanical stimulus. The
thesis is organized as follows:
In Chapter 2, a brief introduction of the theoretical background is given, that aids
in the understanding of the mechanics of brain injuries. First, the main anatomical
features of the human head are presented, with an emphasis on the composite layered
macro-structure of the head. Starting with the skull which is a sti solid, and moving
3
Chapter 1. Introduction
inwards, one nds the cerebrospinal
uid, a viscous water like substance, which cushions
the brain - a very soft viscoelastic material. Then the mechanical properties of the
dierent components of the human head are presented. In the last section of Chapter 2,
we present the governing equations describing the dynamic behavior of materials under
impact loading, since brain injuries usually occur under dynamic loading conditions.
This leads to the next chapter of this thesis, Chapter 3, which presents the dierent
ways of modeling TBIs: computational, experimental, in-vivo, and in-vitro models of
TBI. Every dierent method oers its own advantages and disadvantages. For example,
computational models allow for the quantication of the deformation response of a real-
istic brain structure with complex anatomical features and material models. However,
they cannot provide insights into the biological response of the tissue; in contrast to
in-vivo and in-vitro models of TBI. Therefore, all the dierent modeling eorts should
be thought of as complimentary to each other. Subsequently, a discussion on the current
understanding of the causes of brain injuries along with the main pathological ndings
of TBI patients is presented.
Chapter 4 describes the in-vitro model of TBI proposed in this work, HAMr. A
rationalization of the model design is given, along with a detailed description of the
actual experimental model and the specic observables that we quantify during the
experiments. This should help the reader in understanding the results presented in the
chapters that follow.
Chapter 5, presents the mechanical characterization of HAMr. First, the mechanical
stimulus is quantied in terms of impact force and induced pressure pulse. Following the
mechanical stimulus characterization is the mechanical response of the model, in terms
of full-eld dynamic deformation elds.
4
Chapter 6, presents the results obtained for the biological response of the surrogate
brain tissues used with this model. Dierent biomarkers are explored and their relation
to the number of repeated impacts is discussed.
Chapter 7, presents one possible direction of moving forward with the experiments
presented up to this point. In particular it focuses on models of TBI with more realistic
surrogate brain tissues in terms of physical properties of the extracellular matrix and
the overall dimensions of the \head" model.
Finally, in Chapter 8, some concluding remarks about the research work presented
are given, along with possible future directions.
5
Chapter 2
Theoretical Background
The objective of this chapter is to introduce the gross anatomy of the skull-brain system,
its mechanical properties, and its response to dynamic loading conditions that prevail
during traumatic injury events.
In engineering practice, whenever faced with a problem in applied mechanics and
interested in a quantitative solution we need the problem to be \well-posed". Let us
elaborate on what is practically meant by that; rst, we need to have an accurate de-
scription of the geometry of the problem. Second, the mechanical properties of the
individual components of the system under consideration need to be obtained experi-
mentally and modeled mathematically using constitutive equations. These equations can
then be used for theoretical analysis and quantitative predictions. Third, the physical
laws that the system obeys need to be specied along with the employed assumptions.
In mechanics, these laws are framed by employing Newton's laws of motion. Combining
the fundamental laws of physics with the constitutive equations of the materials, we
obtain the governing equations of the system. Lastly, we solve the governing equations
(dierential or integral representation) analytically or numerically. We then compare
the theoretical results with corresponding experiments to validate or invalidate the un-
derlying assumptions and constitutive equations used. If the theory is validated, it can
be used as a predictive tool for dierent problems. If not, the constitutive equations
6
2.1. Morphology, Anatomy, and Histology of the Human Head
need to be redened and the process repeated until the theory matches the experiments.
Since we are interested in the analysis of the mechanical response of the skull-brain
system under injurious mechanical loads we need to know the following information:
(i) The geometry of the human head: morphology, anatomy, and histology. This in-
cludes the macroscopic shape, structure, size, and the microscopic internal struc-
ture of the tissue.
(ii) The mechanical properties of the individual components that appear in the human
head. Currently there exists no ab-initio way of calculating mechanical properties
of biological tissue, so we have to rely on experiments.
(iii) The governing equations of the system obtained through the use of axiomatic
relations that are formulated from the fundamental laws of physics in conjunction
with the constitutive equations dened from the step above.
Then, we need to solve analytically or numerically the governing equations along
with appropriate initial and boundary conditions.
2.1 Morphology, Anatomy, and Histology of the Human Head
In this section, a brief description of the basic anatomical features of the human head is
given. The human head consists of dierent successive layers starting from the supercial
outer layer that is called the scalp. Moving inwards, we nd the bony skull, the three
dierent layers of tissue that constitute the meninges and enclose the cerebrospinal

uid (CSF), which, in turn, surrounds and covers the brain [9].
7
Chapter 2. Theoretical Background
The Scalp thickness is between 3-7 mm, and consists of the hair bearing skin of
the scalp, a thin subcutaneous connective-tissue layer, a loose brous connective tissue
that attaches the skin to the deeper structures, and the pericranium which is a muscle
and fascial layer [9,10].
The Skull or cranium provides a protective cavity for the brain and consists of
three dierent layers. The outer table as well as the inner table that are made out of
compact bone, also known as cortical bone, and they sandwich the middle layer which is
a porous structure (cancellous or spongy bone) called diplo e that resembles an irregular
honeycomb. The skull has a spheroidal shape and its thickness varies from 9-13 mm.
It is composed of 8 cranial bones that connect at the sutures (immovable joints) [9,11],
and fourteen facial skeleton bones. The cranial bones are distinguished based on their
position as frontal, two bilateral temporal, left and right parietals, the occipital, the
sphenoid at the skull base, and the ethmoid. Bone is composed of collagen bers and
calcium salts. It encloses the entire brain, but it has an opening for the spinal cord at
the base of the skull, which is called the foramen magnum (which translates from Latin
as big opening). Facial bones of the skull also support sensory structures of the face
such as the eyes, nose, and ears [9].
The Meninges are composed of three dierent layers. The dura is the outermost
meninx, located below the skull. It is a tough, dense, inelastic and anisotropic membrane
consisting of an outer layer of connective tissue rich in blood and nerves, while the inner
layer is similarly composed, but exhibits far less vasculature. The next tissue inwards is
the arachnoid, which is separated from the dura by the subdural space. The arachnoid
is connected to the pia mater, which is attached to the surface of the brain and is the
innermost meninx. The subarachnoid space, which is the gap between the arachnoid
8
2.1. Morphology, Anatomy, and Histology of the Human Head
and pia matter, is occupied by the cerebrospinal fluid (CSF) that surrounds and
cushions the brain [9,12,13].
The Brain is arguably the most complex known living organ [14]. Like any other
organ, cells are the main building blocks of the brain. There are thousands of dierent
types of cells in the brain but they can mostly t within two main groups, namely the
neurons and the glial cells. There are about 86 billion neurons in an average human
brain. Glial cells outnumber neurons by ten times [15{17]. Here we are not going to
elaborate more on the cellular architecture of the brain but it is good to know of these
two general categories of cells as they come up often in the study of the brain.
At the tissue level, the brain consists of two types of tissue known as gray and white
matter due to the distinctive color that these areas possess when observing an unstained
brain. Gray matter consists mainly of cell bodies whereas white matter contains mainly
myelinated axons (the long tube-like part of the neuron along which electric signals get
conducted from the cell body to neighboring cells). At the organ level the brain has a
shape similar to cauli
ower with a convoluted outer surface that is called the cerebral
cortex [15].
A human brain weighs on average about 1.5 kg and its texture is between jelly and
paste. Its specic gravity is 1.16. It is composed of 78% water, 10-12% phospholipids
- fatty lipids which are the major component of cell membranes, 8% protein, and small
amounts of carbohydrates [15, 18]. The length, width, and height of the human brain
vary greatly between individuals. The average dimensions for an adult human brain are
167 mm long, 140 mm wide, and 93 mm high [15].
The main function of the brain remained illusive for many years. Mainly the parts
of the brain responsible for dierent functions of the brain were recognized and de-
9
Chapter 2. Theoretical Background
crypted through accidents or as R. Carter [15] puts it through \natural experiments".
A person would get a brain injury that would aect their normal function and usu-
ally post-mortem, doctors and physicians would relate the damaged area of the brain
to the particular diminished function of the person. Dr. Bennett Omalu [1], a foren-
sic pathologist, found pathological evidence on former football players, post-mortem
through autopsy, that was related to their abnormal behavior during the later years of
their lives. The corresponding disease is called chronic traumatic encephalopathy (CTE)
brain degeneration that is now widely accepted as occurring extensively to professional
football players that sustain repeated brain injuries during their active years of training
and competition. With the advent of new imaging techniques in the late 1900s, such as
functional Magnetic Resonance Imaging (fMRI), more information on the intricate de-
tails of a working brain became attainable. There have been huge strides in our current
understanding of the functions of the dierent parts of the brain, but it still remains a
eld of active research with many puzzles waiting to be solved.
2.2 Mechanical Properties of the Human Head
\Precise understanding of the eects of trauma, and thus an exact and rational prophy-
laxis and therapy of head injury cannot be satisfactorily achieved without a quantitative
description of the mechanical properties of the nervous tissues and their coverings, and
their behavior under stress"
Ommaya, 1968 [18]
Not many of us have exposure to the human brain tissue in terms of stiness, texture
and morphology since it is enclosed in the \rigid", optically opaque skull, and
oating
10
2.2. Mechanical Properties of the Human Head
in CSF. Thus, a qualitative description of its characteristics may prove useful to our
understanding. Ommaya, in his 1968 review paper [18] on the mechanical properties of
the nervous system tissues, described the brain tissue as a \soft, yielding structure, not
as sti as gel nor as plastic as paste". This description, albeit very qualitative, gives
us a good sense of what brain tissue feels like and puts the mechanical properties of
brain tissue in perspective, comparing it to materials of everyday experience such as gel
and paste. On the other hand, he described the cerebrospinal
uid as a water-white,
clear substance and gave a speculative mechanical role to its behavior as a material that
dampens brain movement inside the skull. The speculation of mechanical isolation was
partially conrmed by experimental evidence of the time. Although these qualitative de-
scriptions add to our understanding of the materials of interest, they are not adequate for
the quantitative comprehension, which we aim for, in scientic and engineering practice.
The mechanical behavior of a material deals with its response or deformation to a
given load. In order to characterize the mechanical response of a material, mechanical
properties are used that link the deformation to the given load. Currently, it is not in
general feasible to obtain the mechanical properties of materials from rst principles.
Therefore, since we cannot use concepts based on atomic and molecular models alone to
quantify the mechanical properties, we rely on mechanical characterization of materials
through careful experiments [19].
Before presenting the experimental data of mechanical properties of brain tissue,
the meninges, CSF, and the skull that have been obtained by a collective eort of the
scientic community over the span of more than 60 years, it is instructive to introduce
some general idealized classes of materials. Surprisingly, we will see that although the
number of dierent materials is enormous, many of them fall within these categories [20],
11
Chapter 2. Theoretical Background
Figure 2.1 Stress-strain plot of linear elastic solid material described by Hooke's law. Solid
line represents loading, dashed line unloading
which are the Hookean elastic solid and the Newtonian viscous
uid.
2.2.1 Elastic Solids and Viscous Fluids: Qualitative Description
For most structural materials, for example metals, at room temperature and for small
strains the stress-strain behavior obtained through an experiment (tensile, compressive,
or shear test) would look like Figure 2.1.
Just by looking at Figure 2.1, we can tell that a linear relationship between stress and
strain exists. The equation describing the above material behavior is given by:
=E" (2.1)
where is the stress in units of Pa, and " is the strain, a dimensionless measure of
deformation that can be dened as the fractional change of length of the specimen of
interest. This equation is called Hooke's law, in honor of the famous English scientist
Robert Hooke who rst introduced it. Here the law is presented in its simplest 1D form.
The constant of proportionality, E, is the Young's modulus or modulus of elasticity of
the material. The units of E are the same as the units for stress, since strain is a
12
2.2. Mechanical Properties of the Human Head
dimensionless quantity. A material that follows Hooke's law is called a Hookean solid or
a linear elastic material. The theory of elasticity for Hookean solids, is rather complex
in its more rigorous general treatment [21]. Notice that for a linear elastic material the
loading and unloading curves upon removal of the load causing the deformation, follow
the same path, as indicated in Figure 2.1 by the solid and dashed lines respectively.
Moreover, the deformation remains constant for a given load no matter how long we
apply the load for. Therefore, the deformation of a Hookean elastic solid is independent
of time.
There exists another situation in which the stress-strain relationship is not linear but
the strain, again, depends only on the applied stress and is independent of time. Not
only that, but also the loading and unloading curves follow the same trajectory. These
materials are also elastic but not linear. The main characteristic of an elastic material is
that it resists the deformation due to an applied load and after the removal of the load
the specimen returns to its original conguration, i.e. original size and shape. In other
words the deformations are non-permanent [21, 22]. It is worth emphasizing here that
an elastic material does not have to be linear; a common misconception.
One vivid example on the limitations of this idealization mentioned by Y.C. Fung in his
book on Biomechanics [20] is the limitation of Hooke's law to describe an ever-present
phenomenon in solid materials; fracture. As he puts it, any material can break under a
large enough load or deformation; but to break is to disobey Hooke's law!
A Viscous Fluid, unlike an elastic material, cannot resist shear loads. Under the
application of a shear stress, , the liquid
ows. A particular type of
uid exhibits the
following linear behavior with respect to the shear strain rate d
=dt:
13
Chapter 2. Theoretical Background
=
d
dt
(2.2)
where, the constant of proportionality, , is a property of the
uid called viscosity in
units of Ns=m
2
. This law is Newton's law for a viscous
uid, and the
uids whose
behavior is governed by the above relationship are called Newtonian
uids.
Surprisingly, many materials of everyday and engineering practice fall within these
two idealized simple categories of Newtonian
uids and Hookean solids. These descrip-
tions are just abstractions but nevertheless seem to capture the behavior of water, metals,
and many other materials within limited ranges of stresses and strains.
Unfortunately, or as was to be expected, the above simple idealized models cannot
describe adequately the behavior of most biological materials. Blood for example is a
non-Newtonian
uid (its viscosity is not independent of the shear stress and/or shear
strain rate). Another example is brain tissue whose behavior exhibits both elastic and
viscous material characteristics. This behavior is called viscoelastic and is very common
among biological materials and synthetic polymers. Metals also exhibit viscoelastic
behavior at high enough temperatures. Let us now see what we mean by viscoelastic
behavior.
2.2.2 Viscoelastic Behavior: a Phenomenological Description
The main characteristic of viscoelastic materials is that their mechanical behavior de-
pends on time. Viscoelasticity can be manifested in many dierent ways, all of which
are interrelated. Some examples are:
(i) Creep response: Under a constant load a viscoelastic material will continue to
14
2.2. Mechanical Properties of the Human Head
deform as time progresses.
(ii) Relaxation response: Under a constant deformation the stress required to maintain
the deformation reduces with time.
(iii) Hysteresis: Under a cyclic strain loading, i.e. sinusoidal in time, there will be a
time lag between the strain and stress response, leading to energy dissipation.
(iv) The eective stiness of the material depends on the strain/loading rate.
All of the above can be observed when conducting experiments on viscoelastic ma-
terials and are the basis for characterizing those materials. A familiar example of a
viscoelastic material is a silicon-based toy, Silly Putty™. It will continually deform un-
der its own weight, whereas it can bounce elastically when thrown to the ground (high
loading rate). In viscoelastic materials, since strain is both a function of load and time,
experiments are usually conducted by applying a step stress, that eectively isolates the
eect of time from the eect of the loading level by keeping the level of the stimulus con-
stant and observing the time variation of the eect. Another type of experiment would
apply a step strain and observe the stress response of the material to that stimulus.
Figure 2.2 demonstrates qualitatively the contrast between the responses of a viscoelas-
tic material to a unit step load, and that of the two idealized material models, namely
Hookean solids and Newtonian
uids, that were described previously. The exact re-
sponse of various viscoelastic material needs to be quantied by conducting experiments
but the overall trend for a linearly viscoelastic material is as shown in Figure 2.2.
The response of a viscoelastic material to a unit step stimulus is called transient
response. The transient response of the material to a constant stress,
0
, is called creep
15
Chapter 2. Theoretical Background
Figure 2.2 Response (eect in red) of dierent materials to a unit step load/strain (causal
stimulus in blue) (a) Cause, unit step load/strain, (b) strain/load response of an ideal linear
elastic material (eect), (c) strain/load response of an ideal (Newtonian) viscous material
(eect), (d) strain/load response of a viscoelastic material (eect)
16
2.2. Mechanical Properties of the Human Head
response. The level of stress and strain is monitored in time in a creep experiment and
a creep modulus, E
C
, is dened as:
E
C
(t) =

0
"(t)
: (2.3)
Sometimes experimentalists prefer to use the inverse of the creep modulus, denotedJ(t)
and called creep compliance. The strain increases with time while the load is maintained
constant. For a linearly viscoelastic material the creep modulus is independent of stress
level
0
at any given time.
In a stress relaxation measurement the specimen is rapidly subjected to and main-
tained at a constant level of strain, "
0
, and the stress required to maintain the defor-
mation is measured. The stress gradually decreases in time, and a stress relaxation
modulus, E
R
, is dened as:
E
R
(t) =
(t)
"
0
: (2.4)
In linear viscoelastic materials this modulus is independent of the strain level,"
0
, at any
given time.
Experimental data are obtained for dierent materials by conducting transient ex-
periments as described above. These data are collected and material models that aim to
recapitulate the response analytically are developed. The exact shape of strain versus
time for a creep experiment or stress versus time for a relaxation experiment depends
on the material being tested. The mathematical models, also known as constitutive
equations, describe the relaxation modulus and creep modulus analytically, using math-
ematical functions. Assuming that the material is linear, the obtained relationships for
17
Chapter 2. Theoretical Background
Figure 2.3 Sinusoidal stimulus and corresponding time-lagged response of a linear viscoelastic
material
the moduli, can be used to predict the response of a material to an arbitrary load by
using Maxwell's superposition principle.
Another typical type of experiment for the characterization of material properties
for viscoelastic materials is \dynamic", where a sinusoidal load or strain is applied to
the specimen. Assume that the strain is varying sinusoidally with time. Recording the
applied strain and the resulting stress and plotting them versus time, as shown in Figure
2.3, we observe that the eect, in this case the stress, lags behind the applied strain,
which is the cause. It can be demonstrated that the time lag, also known as hysteresis,
is related on the ability of the material to dissipate energy.
The angular frequency of the oscillatory strain is denoted ! (rad/s). The period of
one oscillation in seconds is, T = 2=!.
Suppose that the sinusoidally varying strain can be expressed as:
"(t) ="
0
sin(!t): (2.5)
18
2.2. Mechanical Properties of the Human Head
The stress response will also be a sinusoid for a linearly viscoelastic material but lagging
behind the cause (strain) by a phase angle
(t) =
0
sin(!t +): (2.6)
The dynamic stiness, E*, can be dened as:
E

=

"
: (2.7)
By using Euler's formula to express the stress and strain, it can be shown that the
dynamic stiness can be written in complex notation, where i is the imaginary unit, as:
E

=

=E
0
+iE
00
=

0

0
(cos() +isin()) (2.8)
where E
0
is the storage modulus and E
00
is the loss modulus. Notice that the primes
do not indicate derivatives. Instead they designate the real and complex parts of the
dynamic modulus E

.
As mentioned earlier, the phase lag,, is a measure of the viscoelastic damping of the
material, sometimes referred to as the loss angle. The dynamic modulus depends on the
frequency of the cyclic loading. To demonstrate that the phase lag has indeed units
of energy we can do the following. Plot stress versus strain by using the parametric
representation of the strain and stress with time t, where the horizontal axis is the
sinusoidal strain and the vertical axis is the sinusoidal stress lagging behind by the
phase angle. In Figure 2.4 it can easily be checked by using Equation 2.2 describing
viscous stress for a Newtonian viscous
uid, that the maximum stress occurs at the
maximum strain rate. The maximum strain-rate for a sinusoidal strain occurs at time
19
Chapter 2. Theoretical Background
-1.5 -1 -0.5 0 0.5 1 1.5
Strain,
-1.5
-1
-0.5
0
0.5
1
1.5
Stress,
Hookean Solid
Viscous Fluid
Viscoelastic, =30°
Figure 2.4 Stress-strain plot for elastic, viscoelastic and viscous materials
zero. So, the phase angle for a purely viscous
uid is 90°. For a linear solid, there is no
phase lag and the stress-strain plot follows a straight line, Equation 2.1.
For a viscoelastic solid, plotting stress-strain pairs, for the same time t, leads to an
elliptical curve. The area enclosed by the ellipse equals the dissipated energy per unit
volume per cycle, since the units of the integral on a stress-strain curve give the energy
per unit volume. The dissipated energy, and consequently the area enclosed by the
stress-strain curve, depends on the value of the angle . The elliptic shape of the curve
is a consequence of linear viscoelastic behavior where the induced stress is following the
sinusoidal strain excitation. The sinusoidal strain and stress represent parametric curves
of an elliptic Lissajous gure.
2.2.3 Mechanical Properties of the Human Head Tissues: Experimental Results
In this section the experimentally obtained mechanical properties of the human head tis-
sues, such as the scalp, skull, cerebrospinal
uid, meninges, and brain will be presented.
20
2.2. Mechanical Properties of the Human Head
The rst eorts to study the mechanical properties of the brain were to develop a
better understanding of the biomechanics of brain injury. Still to this day this is the
main drive for brain mechanics research, since the brain is not a load bearing structure
unlike the bones or muscles of the body. This drive is also linked with a research eort to
provide experimental data for the development of mathematical constitutive equations
that can be used for analytical and numerical solution of the mechanical behavior of
brain tissue [23].
Scalp
Galford and McElhaney [24] studied the viscoelastic properties of 20 scalp speci-
mens excised from Macaca mulatta (rhesus monkey). They quantied the response of
these specimens to creep under dierent stress levels, ranging from 69-414 MPa. The
creep compliance curve under tension and compression were approximately the same and
shown in Figure 2.5. The independence of the creep compliance curve to the stress level
indicates that scalp tissue can be adequately described by linear viscoelastic theories.
Moreover, they quantied the storage and loss modulus of the specimens through free
vibration tests. They obtained a storage modulus E
0
= 1.4 GPa and a loss modulus
E
00
= 510 MPa at a vibration frequency of 20 Hz. There are no recent studies on the
properties of scalp.
21
Chapter 2. Theoretical Background
0 20 40 60 80 100 120
0
1
2
3
4
5
6
7
Time (s)
Creep Compliance J(t) • 10
−4
(1/Pa)
Figure 2.5 Creep compliance curve for monkey scalp in tension and compression [24]
Skull
The human skull resembles an engineering sandwich structure [11]. The outer and
inner layers (tables) are sti and made out of compact bone, whereas the middle layer,
called diplo e, is porous and resembles a sponge. Over the years, separate research groups
have tested the properties of skull under dierent modes of loading. The tissues used
for the experiments presented below are specimens harvested from human cadavers.
Some of these were fresh, others fresh-frozen and thawed before the experiments, or
in some cases embalmed. The thickness of each layer, as well as the porosity of the
diplo e structure, varies considerably from one part of the cranium to another and also
from person to person. Thus, the observation of a huge dispersion on the experimental
data obtained should not be surprising, and as we shall soon see that is indeed the case.
Boruah et al. [25] obtained histograms of the thickness and porosity of the dierent
layers of 8 dierent skull specimens by using micro-CT scans. Their ndings are shown
22
2.2. Mechanical Properties of the Human Head
in tabular form in Table 2.1. From these measurements it can be concluded that the
inner cortical layer is signicantly thinner than the outer cortical layer. The diplo e show
a big variation from sample to sample as implied by higher standard deviation values.
Thickness (mm) Porosity
Outer Table 0:76 0:29 0:023 0:017
Inner Table 0:35 0:15 0:071 0:032
Diploe 5:08 2:01 0:399 0:194
Table 2.1 Tabulated values for thickness and porosity of dierent layers of the skull using
MicroCT [25]
23
Chapter 2. Theoretical Background
0 0.2 0.4 0.6 0.8 1 1.2 1.4
0
20
40
60
80
100
120
Strain (%)
Stress (MPa)

Wood (1971), 0.08/s
Wood (1971),2.4/s
Wood (1971), 95.0/s
Boruah (2017), 4.0/s
Figure 2.6 Stress-strain plot under tension for cranial bone specimens. The eect of strain rate
is shown. Each curve is the average of three tests at the same nominal strain rate [11,27]
Skull Properties in Tension
Wood [11] and McElhaney et al. [26] studied the response of human cranial bone
in tension. Wood tested 120 specimens taken from thirty subjects. The specimens
were excised during autopsy and taken from the compact layers of parietal, temporal,
and frontal bones, which means that the diplo e structure was removed. He conducted
experiments at a wide range of strain rates covering three orders of magnitude, starting
from 0.005 s
1
and going up to 150 s
1
. In Figure 2.6 the strain rate eect on the
stress-strain response under a tensile load is shown for a given sample.
It can be observed that the modulus of elasticity increases with increasing strain
rate. Although the rate variability of the elastic properties of bone is present under
tensile loading, the dierence in stiness is small compared to the stiness variations of
other soft viscoelastic materials. A prime example as we shall soon see is the human
brain, which shows a much greater extent of stiening as the strain rate of loading
increases. In a recent study by Boruah et al. [27], bone specimens were subjected to
24
2.2. Mechanical Properties of the Human Head
tensile loading at a nominal strain rate of 4 s
1
and the stress-strain response was
quantied using Digital Image Correlation [28] on both faces of the bones. Their data
show a less sti response compared to the study by Wood [11] for similar strain rates.
Boruah et al. [27] observed that engineering stress varied linearly with engineering strain
for most of the samples, almost up until the point of failure. This observation is similar
to the observation by Robbins et al. [29] that detected a brittle response of the bone
under quasi-static tension, and a linear response of the stress-strain curve for about two
thirds of the loading range. This linear response indicated that a Young's modulus is
a good measure for the characterization of the material behavior for the cranial bone
under tension. A comparison between the elastic moduli and failure stress for compact
skull bone derived by dierent researchers is shown in Table 2.2. Borouah et al. [27]
reported strain at the failure point of 0:59 0:15%.
Study Elastic Modulus Failure Stress Number of Deformation
(GPa) (MPa) Experiments Mode: Tensile
Robbins et al. [29] 14:5 65:50 50 static
Wood et al. [11] 16:0 123 dynamic
Boruah et al. [27] 12:0 3:2 64:95 21:08 97 quasistatic
Table 2.2 Comparison of elastic modulus and failure stress of outer table of skull bone
Skull Properties in Compression
Robbins and Wood [29] conducted cyclic loading from tension to compression at
quasi-static rates and observed that the modulus of elasticity in compression is similar
to the modulus in tension. The value for the modulus of elasticity was 14.5 GPa. They
also observed hysteresis to be large, which indicates a large amount of energy being
absorbed during cyclic loading. Nevertheless, they did not quantify the loss tangent,
25
Chapter 2. Theoretical Background
also known as phase angle,. They also conducted a few dynamic tests, which indicated
that the breaking stress and modulus of elasticity increase with increasing strain rate.
Moreover, they investigated the failure characteristics of the spongy diplo e layer of the
skull under compression in a direction perpendicular to the surface of the skull, and
obtained a structural modulus 1.3 GPa. A huge variation between the smallest and
largest values of the structural modulus, from 71 MPa to 3 GPa, can be explained
by the variation in the porosity and microstructure of the diplo e layer from sample to
sample and in dierent regions of the same sample as shown in the Table 2.1. In a more
recent study by Boruah et al. [25], 84 specimens from 10 male subjects were subjected
to compression perpendicular to the surface of the skull (through the thickness). The
compressive elastic modulus was quantied to be 450 135 MPa. The obtained elastic
modulus is an order of magnitude smaller compared to the results by Robbins et al. [29].
Meninges
As already mentioned in Section 2.1, the meninges consist of three layers: the dura
matter, arachnoid matter, and pia matter [12]. The knowledge of the mechanical prop-
erties of the meninges is crucial for the modeling of the mechanics of the human head
system, since they represent the interface between the skull and brain [13]. There do
not exist many studies quantifying the mechanical properties of the meninges. Galford
et al. [24] studied the viscoelastic response of dura matter for human specimens in creep,
relaxation, and free vibration tests. They found a storage modulus of E
0
= 31:5 MPa
and a loss modulus of E
00
= 3:54 MPa in the frequency range between 10-40 Hz. Om-
maya [18] used a penetrometer to measure the force it takes to puncture through the
dura matter in-vivo. The penetrometer used had a \spade" shaped tip. He observed
that the direction of the indenter relative to the direction of the collagen bers of the
26
2.2. Mechanical Properties of the Human Head
dura matter aected the measurements. When the indenter was placed perpendicular
to the direction of the bers the force required to puncture through the dura matter was
1023 N. This force is about 50% of the force required to penetrate skin around the eyes.
Cerebrospinal Fluid
CSF is a transparent liquid, which is slightly alkaline and composed of 99% water.
CSF contains a small amount of proteins, and some sugars, potassium, chloride, sodium,
along with blood cells [30]. Its specic gravity is 1.004-1.007 [9]. CSF viscosity has been
quantied over a range of shear rates (25-1460 s
1
) using a rotational viscometer [30].
These measurements clearly showed that CSF behaves as a Newtonian
uid, with a
viscosity at body temperature (37ºC) ranging between 0.7-1mPas. The volume of CSF
that can ll all the subarachnoid space and ventricles inside the skull is 100-150 ml [9,18].
The human brain is completely suspended inside CSF. Ommaya speculated that the
mechanical role of CSF is to protect against head trauma by dampening brain movement
through a \cushioning" eect of the
uid. An average negative pressure of about 7 MPa
is needed to cause cavitation [9]. This is an important measure since one possible cause
of brain damage is through the collapse of cavitation bubbles inside the brain, as we
shall see in a later section where we describe the mechanisms of brain injury.
Brain
The presented data are gathered from studies of the material properties of excised
brain tissue samples from various sources such as: human cadavers, non-human primates,
swine (porcine), calves (cows), sheep etc. This eort of the scientic community to
gather a quantitative description of brain tissue has spanned a period of over 50 years.
27
Chapter 2. Theoretical Background
A multitude of dierent deformation modes have been used to quantify the mechanical
properties of brain tissue, such as tension, compression, and shear loading. Material
testing has been conducted under creep, relaxation, constant strain-rate, and dynamic
(sinusoidal) loading. The material behavior of brain tissue varies signicantly between
studies. Most probably this variation is due to dierent methodological manipulation of
the tissue by dierent groups. Even though these studies are inconsistent quantitatively,
they all agree qualitatively that brain tissue is a very soft non-linear viscoelastic material,
with strain-rate sensitivity that makes its behavior stier at higher loading rates. In-vivo
studies of brain tissue will not be considered here but the interested reader is referred to
sources in the literature that describe eorts of Magnetic Resonance Elastography, in-
vivo indentation studies, as well as ultrasound tests. These eorts are valuable because
they allow one to probe the properties of interest at physiologically relevant conditions,
such as the correct body temperature, hydration conditions etc. Moreover, when using
in-vivo testing procedures there is no need for considerations of tissue preservation and
post-mortem time before testing. Nevertheless, these in-vivo methods are usually limited
in the range of the applied strain rates.
Brain Tissue Properties in Tension
Studies concerned with the characterization of brain tissue under tension are sparse.
The scarcity of those studies is mainly due to the diculty of conducting tensile studies
with brain tissue. One of the primary challenges is how to eectively grip the sample
while loading it in tension. There have been a few dierent approaches on eectively
gripping the specimen in a tensile loading experimental apparatus. The most commonly
used method is by using surgical glue. There are few studies available in the literature
that present brain tissue samples loaded in tension. The rst study appears in 2002 by
28
2.2. Mechanical Properties of the Human Head
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
0
200
400
600
800
1000
Strain
Stress (Pa)

Miller et al. (2002), 0.0064/s
Velardi (2005), 0.01/s
Miller et al. (2002), 0.64/s
Figure 2.7 Stress-strain response of brain tissue under quasi-static tensile loading conditions [23]
Miller & Chinzei [31] in which they conducted uniaxial tension experiments on swine
brain specimens at two dierent strain rates in the quasi-static loading regime, 0.64
and 0.0064 s
1
. They used cylindrical samples with a 30 mm diameter and 10 mm
height. Three years later, Velardi et al. [32] also conducted uniaxial tensile experiments
on swine specimens at a single quasi-static strain rate of 0.01 s
1
. The results from the
two studies are in agreement as illustrated in Figure 2.7.
However, the majority of brain injuries occur under dynamic loading conditions that
are associated with higher loading rates. Recently, two separate research groups con-
ducted high-rate extension experiments. Tamura et al. [33] subjected swine specimens
to uniaxial tension at strain rates ranging from 0.9 - 25 s
1
. Cylindrical specimens of
14 mm diameter and 14 mm height were excised from the cerebral cortex and the white
matter right beneath it (corona radiata) and subjected to tensile loading. The average
stress-strain responses for the three dierent strain rates are shown in Figure 2.8. As
29
Chapter 2. Theoretical Background
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
Strain
Stress (Pa)

Tamura et al. (2008), 0.9/s
Tamura et al. (2008), 4.5/s
Tamura et al. (2008), 25.0/s
Rashid et al. (2012), 30.0/s
Rashid et al. (2012), 60.0/s
Rashid et al. (2012), 90.0/s
Figure 2.8 Stress-strain response under dynamic tensile loading conditions [33,34]
can be seen the strain rate dependence remains throughout the loading rates spectrum.
A study by Rashid et al. [34] on swine brain tissue in tension at dynamic strain
rates tested the specimens at the highest-ever reported strain rates under tension, with
direct applicability to dynamic loading conditions that occur during TBIs. They tested
at three dierent strain rates, 30, 60, 90 s
1
. The stress strain response for the three
dierent loading conditions can be seen in Figure 2.8.
It is worth noting that there are two main qualitative characteristics in the response
of brain tissue under tensile loading that persist at every strain rate tested so far: the
stress-strain response is concave upwards and the material response becomes stier for
higher loading rates. The authors above reported the \initial" elastic (Young's) modulus
from 0-10% strain, as the average slope of the curve between these two values of strains.
A comparison of the quantitative values obtained is shown in Table 2.3. Between the
studies by Tamura et al. [33] and Miller et al. [31] there is a factor of 8 dierence,
30
2.2. Mechanical Properties of the Human Head
almost an order of magnitude, between the reported Young's modulus at similar strain
rates.
Reference Strain Rate (s
1
) Young's Modulus, E (Pa)
Miller et al. (2002) [31] 0.64 530
Tamura et al. (2008) [33] 0.90 4200 1600
25.00 18600 3600
Rashid et al. (2014) [34] 30.00 8120 2380
Table 2.3 Comparison of elastic moduli under tensile loading between dierent studies
The reason for that discrepancy was hypothesized to be the post-mortem time before
testing. Between the studies of Tamura et al. and Rashid et al. [33, 34] there is a 2.3
times dierence between the elastic modulus obtained at strain rates of 25 and 30 s
1
respectively. Tamura et al. [33] preserved the specimens in freezing conditions, which
may explain the stiening of the tissue. All of the above studies of brain specimens used
tissue excised from swine and tested under room temperature conditions. Among other
things, dierences exist in the protocols used by dierent groups for preservation and
post-mortem time before conducting the testing. These dierences might explain the
discrepancies between the results obtained from dierent labs.
Stress relaxation tests for tensile loading at dierent strain levels was conducted
by Rashid et al. [34] and Labus et al. [35]. In all the relaxation studies both groups
observed that the relaxation behavior is independent of the strain magnitude, or in
other words the initial \step" deformation. Moreover, the tensile force decreases rapidly
within a few milliseconds.
Franceschini et al. [36] conducted experiments with human tissues excised from au-
topsies. They subjected the specimens to cylic tension/compression at quasistatic strain
rates and recorded both the loading and unloading stress-strain response. They observed
31
Chapter 2. Theoretical Background
stress-strain behavior that exhibits strong nonlinearity, hysteresis, as well as dierent
stiness in tension and compression. In what follows experimental data for brain tissue
subjected to compression will be presented since the study by Franceshcini et al. [36]
suggests that the behavior of brain tissue is dierent in compression compared to tension.
Brain Tissue Properties in Compression
One of the rst studies conducted under compressive loading on brain tissue speci-
mens excised from humans or monkeys was by Galford et al. [24]. The human specimens
were obtained at autopsy and tested within 6 to 12 hours after death, while the Macaca
Mulatta monkey specimens were tested within 1 hour after sacrice of the animal. Creep
compliance and stress relaxation curves obtained from this study are shown in Figure
2.9. They observed a dierence in the creep response of brain tissue depending on the
initial step stress level, which indicates non-linear viscoelastic behavior of the tissue.
They did not nd the same behavior under stress relaxation tests, suggesting that the
use of linear viscoelastic theory might be a good rst order model for the description
of brain tissue behavior under compression. In the same study they conducted free vi-
bration tests of the brain samples and obtained the dynamic compressive modulus in
terms of a storage modulus E
0
= 66.7 kPa and a loss modulus E
00
= 26.2 kPa at a
frequency of 34 Hz. This is one of the last studies that can be found on brain properties
of non-human primates. Due to bio-ethical considerations, primates are no longer used
in experimental studies of mechanical property identication. Most of the recent studies
use porcine brains that have been found to possess similar architectural characteristics
to human brain and they also share some developmental similarities with their human
counterparts [37].
32
2.2. Mechanical Properties of the Human Head
Monkey 3.4kPa
Monkey 6.9kPa
Human 3.4kPa
Human 68.9kPa
Figure 2.9 Creep response curves of monkey (n=5 samples) and human (n=12 samples) brain
specimens under compression from 2 donors respectively [24]
Some recent studies on stress relaxation response under compressive loading can be
found in the literature. Tamura et al. [38] characterized 50 cylindrical specimens from
porcine tissue. The \step" strain had a rise time of 30 ms and the compressive strain
level was varied between 20-70%. The stress relaxation response appeared to change as
a function of strain in contrast to the ndings by Galford et al. [24]. The compressive
force decreased rapidly within the rst 25 ms, and within the rst second it decreased
by 75%. In a more recent study by Rashid et al. [39] on the relaxation response of
cylindrical porcine brain specimens, a \step" strain with an average rise time of 10 ms
and varying strain level from 10-50% was applied on 64 cylindrical specimens. They
also observed varying compressive forces for dierent initial strain amplitudes. The
relaxation of the compressive force was signicantly faster compared to the study by
Tamura et al. [38]. In particular, the compressive force decreased by approximately 70%
within 4 ms of the relaxation time, and continually decreased for the duration of the
33
Chapter 2. Theoretical Background
observations. The compressive force amplitude was consistent between the two studies;
the magnitude of the compressive forces was in the order of a few Newtons for the strain
levels experienced. In another study by Cheng et al. [40] the eect of strain rate of
loading on the relaxation response was obtained. They submitted calf brain specimens
to the same strain level of 5% at three dierent loading rates and observed that the
reaction force is a function of strain rate. Although the reaction force was found to be
a function of the initial loading ramp rate, the equilibrium reaction force is not aected
by the loading rate and reaches the same value for the three dierent cases.
So far, the transient response of brain tissue under compression has been presented.
Now we present unconned uniaxial compression studies with constant loading rates
conducted at a range of dierent strain rates. These studies can be conceptually, and
for our own convenience, divided into two groups. The rst group encompasses the
quasi-static loading regime, while the second group of experiments has been conducted at
dynamic loading rates. The quasi-static studies are useful for the modeling of brain tissue
related to robotic surgery applications, as mentioned earlier. In contrast, the dynamic
loading compression tests can nd applications in the study of transient dynamic events
such as numerical simulations of TBIs.
Miller et al. [41] conducted uniaxial compression tests, of porcine cylindrical brain
specimens under three dierent quasi-static strain rates that span ve orders of magni-
tude. They subjected the specimens to one load cycle at room temperature T 22 ºC.
The dura was removed from the specimens, which consisted of the arachnoid membrane,
white and gray matter. Most of the uniaxial compression studies described in this sec-
tion use experimental setups in which a cylindrical specimen is situated between two
platens. One of the platen is held rigidly xed while the other one is allowed to move
34
2.2. Mechanical Properties of the Human Head
under controlled fashion in order to compress the specimen at a pre-specied strain-rate.
As can be seen in the stress-strain response of the brain tissues, Figure 2.10, the shape of
the curve is concave upward for all compression rates, in contrast to the tensile response
of brain tissue described in the previous section which was concave downwards. This
shape of the curve indicates that as the strain increases the stiness of the tissue also
increases. Moreover, the tissue exhibits strain-rate sensitivity, with increasing stiness
as the strain rate applied rises. As mentioned before, the strain rates explored in this
study are relevant for clinical situations in terms of robotic surgery. The properties ob-
tained may be thought of as \homogenized" properties or the macroscopic response of a
composite white and gray matter tissue. Shen [42] also conducted unconned compres-
sion tests on porcine brain specimens at a strain rate of 0.01 s
1
that falls in between
the range of strain rates explored by (Miller & Chinzei, 1997a). The stress-strain re-
sponse obtained from that study is shown also in Figure 2.10. The compression test by
Shen [42] was conducted up to 5% compressive strain which is much lower compared to
the strains explored by Miller et al. [41] that reach levels up to 40% strain.
In the dynamic loading regime, Tamura et al. [38] conducted experiments on cylin-
drical porcine brain tissue specimens under uniaxial compression and under strain rates
that are relevant to TBI situations. Three dierent strain rates were explored, 1, 10 and
50s
1
. Their results, Figure 2.11, indicate concave upward stress-strain behavior similar
to the one found at dierent strain rates by Miller et al. [41]. Moreover the strain-rate
dependency of the material behavior seems to remain at dynamic strain rates, as can be
seen in Figure 2.11, where a stier response of the brain tissue is shown with increasing
strain rate. Tamura et al. [38] reported the initial average elastic modulus as the tangent
modulus from 0 to 20% strain at dierent strain rates and the obtained values are shown
35
Chapter 2. Theoretical Background
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35
Strain
0
500
1000
1500
2000
2500
3000
3500
Stress (Pa)
Miller et al. (1997a), 0.0000064/s
Miller et al. (1997a), 0.0064/s
Shen et al. (2006), 0.01/s
Miller et al. (1997a), 0.64/s
Figure 2.10 Stress-strain response at four dierent strain rates under constant strain rate
compression loading [41,42]
in tabular form in Table 2.4.
Rashid et al. [39] conducted unconned uniaxial compression tests at even higher
strain rates. In particular, they subjected cylindrical porcine brain samples to three
dierent strain rates of 30, 60, and 90 s
1
. Their results are shown in Figure 2.11, and
the initial modulus is compared against those found by Tamura et al. [38] in tabular
form, Table 2.4 . Their results show strain-rate sensitivity similar to Tamura et al. [38]
and are also quantitatively consistent. The compressive nominal stress at 30% strain
was 8:83 1:94 kPa, 12:80 3:10 kPa, and 16:00 1:41 kPa at strain rates of 30, 60,
and 90 s
1
respectively. These numbers exemplify the stiening of the brain tissue as
strain rate increases. Moreover, the concave upwards shape is consistent between all
the studies under uniaxial compressive strain found in the literature for all the dierent
strain rates tested so far.
Pervin and Chen [43] modied an existing experimental technique, known as the
36
2.2. Mechanical Properties of the Human Head
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
0
5000
10000
15000
20000
25000
30000
35000
Strain
Stress (Pa)

Tamura et al. (2007), 1.0/s
Tamura et al. (2007), 10.0/s
Rashid et al. (2012), 30.0/s
Tamura et al. (2007), 50.0/s
Rashid et al. (2012), 60.0/s
Rashid et al. (2012), 90.0/s
Figure 2.11 Average stress-strain relationships in unconned compression test at dierent strain
rates [38,39]
Reference Strain Rate (s
1
) Initial Young's Modulus, E
1
(kPa)
Tamura et al. (2007) [38] 1 5:7 1:6
10 11:9 3:3
50 23:8 10:5
Rashid et al. (2012) [39] 30 19:0 0:4
60 28:2 0:8
90 37:9 0:8
Table 2.4 Comparison of initial elastic moduli under unconstrained compressive loading be-
tween dierent studies at similar strain rates
Kolsky (Split-Hopkinson) pressure bar, in order to subject bovine cylindrical brain spec-
imens to loading rates on the order of 1000 s
1
. They also conducted experiments in
the quasi-static regime, 0.01 s
1
. The dynamic loading rates obtained with the Kol-
sky bar technique should be relevant for blast-induced TBIs and/or the initial transient
stress waves experienced by the human brain tissue during blunt impact loading of the
head. They observed that the strain-rate sensitivity does not disappear even at very
37
Chapter 2. Theoretical Background
for the first time, at maximum strain rate of 3000/s which is
significantly higher than previously reported, with the intension
of pursuing studies of constitutive models in future.
Examinationofstress–straincurvesforallexperimentalresults
revealed that the tissue stiffness increases with increasing strain
rate. At a certain strain, the dynamic stress can be two orders of
magnitude higher than the quasi-static counterpart, indicating
very strong strain-rate dependence for the compressive stress–
strain responses. In this study, the gray matter samples were
excised randomly from the frontal and parietal portions of the
brain hemisphere and the results showed nearly homogeneous
behavior of the gray. These results qualitatively agree with the
findings of Gefen and Margulies (2004) and Tamura et al. (2007).
The white matter of brain tissue was compressed in two
directions; one is along the transverse direction of the corona
radiata section (labeled as WM-D1 in figures) and perpendicular
to that direction (WM-D2). The compressive response of WM-D2
isslightlystifferthanthatofWM-D1,whichiswithindatascatter,
can be neglected (see Fig. 6b). As the stiffness variation is not
significant, the material may be regarded as nearly isotropic.
Nicolle et al. (2004) observed isotropic behavior of corona radiata
at strains up to 1% at the highest frequency of 6310Hz.
To evaluate intra-regional inhonogeneity, comparison was
made between the gray matterand white matter results obtained
from each strain rate. These results revealed that the corona
radiataisstifferthangraymatteratanystrainlevelovertheentire
ARTICLE IN PRESS
0 10 20 30 40 50 60 70 80
0 10 20 30 40 50 60 70 80
0 10 20 30 40 50 60 70 80
0
200
400
600
800
1000
1200
Engineering Stress (KPa)
Engineering Strain (%)
Brain - 1
0
200
400
600
800
1000
1200
Engineering Stress (KPa)
Engineering Strain (%)
Brain - 2
0
200
400
600
800
1000
1200
Engineering Stress (KPa)
Engineering Strain (%)
Brain - 3
Fig. 5. Repeatability of measurements at strain rate of 1000/s for (a) brain-1: 18
months old, (b) brain-2: 20 months old and (c) brain-3: 20 months old.
0
5
10
15
20
25
30
35
Engineering Stress (KPa)
Engineering Strain (%)
Gray matter: 0.01/s
Gray matter: 0.1/s
White matter-D1:0.01/s
White matter-D1:0.1/s
White matter-D2:0.01/s
White matter-D2:0.1/s
Miller & Chinze, 1997: 0.64/s
0 10 20 30 40 50 60 70 80
0 10 20 30 40 50 60 70
0
400
800
1200
1600
2000
2400
2800
Engineering Stress (KPa)
Engineering Strain (%)
Gray matter: 1000/s
Gray matter: 2000/s
Gray matter: 3000/s
White matter-D1: 1000/s
White matter-D1: 2000/s
White matter-D1: 3000/s
White matter-D2: 1000/s
White matter-D2: 2000/s
White matter-D2: 3000/s
Fig. 6. Average (N¼15) compressivestress–strain curveof grayand white matter
at (a) quasi-static and (b) dynamic strain rates.
F. Pervin, W.W. Chen / Journal of Biomechanics 42 (2009) 731–735 734
Figure 2.12 Compressive stress-strain curve at dynamic strain rates [43]
high loading rates between 1000-3000 s
1
, as seen in Figure 2.12. Moreover, the overall
shape of the stress-strain curve remains concave upwards up until the point of failure,
which is around 50% strain. In addition, by comparing dierent experimental results
at dierent strain rates one can observe that the compressive stress amplitude can be
up to two orders of magnitude higher at the same level of strain, which indicates a very
high sensitivity of the brain tissue response to strain rate.
Perhaps the most comprehensive study conducted so far on the compressive response
of brain tissue is that by Prevost et al. [44], Figure 2.13, on porcine samples. The loading
as well as the unloading stress-strain behavior was collected under uniaxial compression
conditions. Each specimen was subjected to 5 consecutive load-unload cycles up to 50%
strain. Each load-unload cycle consisted of 3 successive strain rates, more specically 1,
0.1, and 0.01s
1
. At the end of the 5 consecutive load-unload cycles the stress relaxation
38
2.2. Mechanical Properties of the Human Head
of the specimen was observed. The stress strain response of the porcine brain tissue
samples at the three dierent strain rates is shown in Figure 2.13a-c. Some of the ndings
of this study that are unique compared to the experimentally observed behavior of brain
tissue described thus far, are the following: brain tissue exhibits hysteresis, as observed
through the loading-unloading cycle. Moreover, it displays pre-conditioning eects, as
illustrated in Figure 2.13 by the dierence between the brain tissue response between
the 1st and 2nd loading cycle. This conditioning, which is manifested as softening of
the response to the subsequent loads after the rst cycle, has been observed to diminish
and the tissue returns to its original state after a period of 2 hours, indicating that
the softening may be due to the tissue losing some of its interstitial
uid. In addition,
the non-linear response is evident by the shape of the load-unload curve (not elliptic as
described in Section 2.2.2). Brain tissue behavior was probed in this study under three
orders of strain rate magnitudes in the large deformation regime (up to 50% strain) and
strain rate sensitivity was found similar to previous ndings, as stiening of the tissue
with increasing strain rate.
Brain Tissue Properties in Shear
The most well characterized mode of brain tissue deformation is under shear loading
[23]. The main thrust for studying the shear properties of brain tissue is due to an early
hypothesis by Holbourn in his seminal paper on the Mechanics of Head Injuries [45]
which postulates that brain injuries occur due to rotational acceleration of the head
that in turn leads to shear deformations of the brain tissue. This hypothesis is partly
validated, as we shall comment further later, and which describes the mechanisms of
brain injuries. As a prelude, it suces to say here that this hypothesis is still a matter
of controversy and it is debatable whether brain injury occurs only due to shear or due
39
Chapter 2. Theoretical Background
Figure 2.13 Compressive response of brain tissue (a) stress-strain response at 1 s
1
(b) stress-
strain response at 0.1s
1
(c) stress-strain response at 0.01s
1
(d) stress relaxation response [44]
to a combination of dierent modes of deformation [46]. But setting this discussion
aside, let us summarize here the ndings on the viscoelastic properties of brain tissue
under shear loading. The linear viscoelastic limit of brain tissue under shear is very low;
in particular, it lies somewhere between 0.1 and 1% strain. Moreover, it is found to be
strain rate sensitive under shear loading as was have seen with the two other modes of
deformation discussed earlier [23]. To this day, there is a huge variance in the specic
values for the shear properties reported in the literature, sometimes diering by an order
of magnitude [47].
Brain Tissue Properties using Non-Conventional Experiments
Recent studies using Atomic Force Microscopy (AFM) have probed the mechanical
properties of single cells, moving down from the tissue level to the cellular level. These
40
2.2. Mechanical Properties of the Human Head
studies show that cell bodies behave in a viscoelastic manner and exhibit similar charac-
teristics with the \macroscopic" tissue specimens, in terms of strain rate dependence of
the stiness, hysteresis, and non-linearities [48]. All of the mechanical behavior results
presented in this section are obtained by conducting measurements in-vitro. It is not
yet established whether the in-vivo properties will be similar to their in-vitro counter-
parts [49]. There are many eorts these days for obtaining mechanical properties of brain
tissue in its physiological conditions in-vivo. Magnetic Resonance Elastography (MRE)
is one of the promising techniques to study mechanical properties of soft biological tis-
sues under low deformation magnitudes in the quasi-static regime [50, 51]. Recently,
indentation of brain tissue has been conducted in-vivo, which presents a promising al-
ternative to MRE where the conditions of testing can be extended to larger amplitudes
and higher loading rates [44].
Summary of Findings of Brain Tissue Mechanical Properties
In summary, brain tissue is a very soft non-linear viscoelastic material that exhibits
signicant strain-rate dependence with increasing stiening at higher strain rate loadings
under all modes of deformation. This is a general characteristic of brain tissue that
has been consistently observed by all studies conducted thus far. While these studies
agree on the qualitative behavior of brain tissue, there still exist discrepancies in the
reported brain tissue properties values between dierent studies. These dierences may
be attributed to the dierent experimental protocols used by dierent research groups
and the lack of a consistent, uniform, and standardized ways of testing biological tissue.
We conclude this discussion by reminding you that the only way to obtain the mechanical
properties described above is through experiments.
41
Chapter 2. Theoretical Background
2.3 Dynamic Loading of Materials
\If it happens that a question which we wish to examine is too complicated to permit
all its elements to enter the analytical relation which we wish to set up, we separate the
more inconvenient elements, we substitute for them other elements less troublesome, but
also less real, and then we are surprised to arrive, notwithstanding our painful labor at
a result contradicted by nature; as if after having disguised it, cut it short, or mutilated
it, a purely mechanical combination would give it back to us"
Jean le Rond d'Alembert, 1752
The vast majority of TBIs occur under dynamic loading of the human head. In par-
ticular, we are interested in situations of blunt impact to the head by a foreign object
or of the head against an object. Application of a load is by denition a dynamic event.
By dynamic we mean that during load application the load changes in time, since it
goes from zero to a certain non-zero value within a nite amount of time. Disturbances
in every material travel with a nite velocity. The velocity at which mechanical dis-
turbances travel is a property of the material. A familiar analogy is an innitesimal
pressure disturbance in air, which propagates spherically outwards from the source, and
produces what we call sound, which travels at the speed of sound in air at the particu-
lar temperature. This propagating disturbance, also called a sound wave, is what gets
picked up by our eardrums and is perceived as sound by the auditory cortex, which is
the acoustic processing unit of the brain. Therefore, the transient time of propagation
of a disturbance inside a medium is nite and depends on the specic material and
geometry of the object under investigation. Similar to the pressure disturbance in air,
when a material gets impacted a local deformation occurs at the point of impact and
42
2.3. Dynamic Loading of Materials
this local disturbance is getting communicated to the rest of the body by stress wave
propagation. In the case where the rate of application of the load is large compared
to the transient characteristic time inside the material of interest, the dynamic eects
of wave propagation inside the material need to be considered and we cannot base our
analysis on the more familiar concepts of structural analysis under static equilibrium.
Here, the mathematical description of mechanical wave propagation in solid materials is
introduced.
2.3.1 Governing Equation
We shall start with the simplest possible scenario of wave propagation in a solid. Specif-
ically, the one-dimensional mechanical wave propagation in a linearly elastic solid mate-
rial. The physical law that describes the behavior and time evolution of the response of
the solid material is Newton's second law of motion. Assume that we have an innitely
long cylindrical bar made out of linear elastic material, such as aluminum or steel. Now,
if we cut an innitesimal cylindrical element of this material and draw the free body
diagram and apply Newton's second law we get:
F
x
=ma
x
: (2.9)
The sum of forces on the element of the bar between the cross sections of the innitesimal
element is:
F
x
=A( +
@
@x
dx)A =A
@
@x
dx (2.10)
Assuming that the material is linear elastic and obeys Hooke's law, Equation 2.1, the
43
Chapter 2. Theoretical Background
above can be written in terms of the displacement along the x-axis, u:
=E" =E
@u
@x
(2.11)
Combining Equations 2.10 and 2.11:
F =A
@
@x

E
@u
@x

dx =AE
@
2
u
@x
2
dx (2.12)
Now, substituting Equation 2.12 into Newton's second law, Equation 2.9, and expressing
the acceleration term as the second derivative in time of the displacement u, we get:
m
@
2
u
@t
2
=AE
@
2
u
@x
2
dx)Adx
@
2
u
@t
2
=AE
@
2
u
@x
2
dx)
@
2
u
@t
2
=c
2
@
2
u
@x
2
(2.13)
, where c =
q
E

. This is a linear 2
nd
order partial dierential equation for a wave
in one-dimension. There are dierent ways of obtaining the general solution of this
equation, namely the function u(x;t) which satises the above PDE and describes the
variation of the displacement componentu in space and time. The two principle methods
of solving this equation are the method of separation of variables and a transformation
method, which can be found in any standard textbook on partial dierential equations.
The general form of the solution is:
u(x;t) =f(x +ct) +g(xct): (2.14)
It can easily be shown by substitution that any functionf(x+ct) is a solution to the
above partial dierential equation which describes the motion of the element considered
above. Moreover, any function g(xct) is also a solution to this equation. And since
44
2.3. Dynamic Loading of Materials
this is a linear equation, the sum of the two solutions is also a solution, by virtue of
the superposition principle. There is an illuminating interpretation of this equation.
Take for example the rst term of the general solution which is described in terms of
the function f(x +ct). For a given time this function assumes a certain shape that
only depends on the spatial variable x. Now assume that time increased by an amount
t. The function would remain unchanged in shape but just translated in space by an
amount x equal toct. Thus, the functionf(x+ct) represents a pulse traveling to the
left with a velocityc. Similar arguments can be made for the functiong(xct), whereas
it can be seen that it describes a wave traveling to the right with velocityc. That is, the
general solution represents two waves traveling in opposite directions along the x-axis
with a velocity c which is a property of the material as can be seen in Equation 2.13.
The functions f and g are general functions and their exact form is specied by the
initial conditions imposed to the problem of interest [52,53].
The above partial dierential equation representation of the mechanical system of
interest can be solved, assuming the mechanical properties of the material are known, by
applying appropriate boundary and initial conditions. Remember that this is an over-
simplied case where 1D geometry is assumed in addition to linear elastic behavior of the
material. Whole books have been devoted to the subject of wave propagation in elastic
solids [52,54]. Nevertheless, on the bright side, it gives us a fundamental understanding
of the velocity of propagation of these disturbances and a \zero" order model that can
serve as the starting point for our understanding of mechanical deformation propagation
in solid materials. Some other geometries, not one-dimensional rods, are amenable to
analytical solutions and researchers have solved simplied models of TBI analytically.
Mathematical models are solved for a spherical skull shell that is lled internally with
45
Chapter 2. Theoretical Background
water (like a spherical water balloon), that will be described brie
y in the chapter that
follows. Before moving to the presentation of the eorts on analytical modeling of TBI,
we want to remind you that the above discussion considered a linear elastic material in
the derivation of the governing partial dierential equation describing the motion of the
1D element. As described in Section 2.2, biological tissue, and especially brain tissue,
exhibits viscoelastic material behavior. Similar dierential equations can be obtained
for wave propagation in viscoelastic media, but their solution becomes more dicult and
sometimes not possible with our existing mathematical toolset. For the viscoelastic case
of wave propagation, the wave will experience dispersion and attenuation eects [19].
2.3.2 Interaction and Re
ection of Waves at an Interface
The partial dierential equation describing the one dimensional longitudinal elastic wave
propagation is linear. Thus, if we have two solutions of the equation, their sum will
also be a solution. When studying elastic waves traveling along a solid medium we can
use the superposition principle.
Now assume that we have two compression waves traveling inside a cylinder far away
from its ends. One compression pulse is traveling to the right and the other compressive
pulse is traveling to the left. Moreover, assume that these pulses have the same amplitude
and duration. When the two pulses meet they create a region of compression where the
amplitude of the compressive pulse doubles. The particle velocities induced by the
pressure waves will cancel each other, because they have opposite sense. At the section,
m-n, where the two pulses rst met a state of zero velocity exists, which resembles the
boundary condition at a xed end where there is no motion allowed. After the pulses
pass each other, they continue traveling unchanged in magnitude, duration and type.
46
2.3. Dynamic Loading of Materials
Thus, when a compressive pulse impacts normally onto xed boundary it re
ects back
unchanged [53]. The stress close to the boundary will be twice as large as the amplitude
of the compression pulse.
In another conceptual exercise assume that we have two pulses inside a material
traveling in dierent directions. One of the pulses is compressive and the other is tensile.
At the region where the two pulses meet the stress will go to zero but the particle velocity
will be doubled. A state of zero stress is the same as the boundary condition at a free
end, where there are no traction forces. After the waves pass each other they continue
propagating unchanged. So when a compressive wave reaches a free end it will re
ect
back as a tensile wave in order for the zero stress boundary condition to be met. Of
course the opposite holds if a tensile wave reaches a free boundary, it will re
ect back
as a compression pulse.
We have examined the two extreme boundary conditions of a xed boundary and a
free end. When a wave encounters a medium with dierent sonic impedance it re
ects
and refracts at the interface. Sonic impedance is dened as the product of the medium's
density and elastic wave velocity [52].
47
Chapter 3
Current Understanding of the Bio-Mechanics of Trau-
matic Brain Injuries
\The assumption that there is a mechanics of head injuries implies that, when the head
receives a blow, the behavior of the skull and brain during and immediately after the
blow is determined by the physical properties of skull and brain and by Newton's laws of
motion"
Holbourn, 1943 [45]
Biomechanics is a compound word derived from mechanics and biology. Mechanics is
the area of science that is concerned with the behavior of physical bodies when subjected
to forces or displacements. Biomechanics in particular, focuses on the application of
mechanics to living matter, at the organ, tissue, or cellular level. This is a very broad
classication covering a wide area of topics of interest. In this research work our focus
is on the biomechanics of TBIs as occurring through impacts.
TBI is dened as an alteration in brain function or other evidence of brain
pathology caused by an external force. [2]
48
3.1. Models of Traumatic Brain Injury
• The external force may include any of the following events: the head being
struck by an object, the head striking an object, the brain undergoing acceleration
or deceleration without external trauma to the head (whiplash motion), forces
generated from events such as a blast or explosion, or other forces yet to be dened.
• Alteration in brain function is dened as one of the following clinical signs:
Loss or a decreased level of consciousness for any time duration, loss of memory
of events immediately before (retro-grade amnesia) or after injury (posttraumatic
amnesia), neurologic decits (loss of balance, change in vision, sensory loss, aphasia
etc.), or any alteration in mental state at the time of injury (confusion, disorien-
tation, slowed thinking etc.).
• Other evidence of brain pathology refers to: neuroradiologic evidence, or
laboratory conrmation of damage to the brain.
3.1 Models of Traumatic Brain Injury
One would imagine that once the mechanical properties of the human head have been
quantied (presented in Section 2.2.3) and the system of interest described analyti-
cally through the use of Newton's 2nd law (introduced in Section 2.3), the solution of
the mechanics of head injuries would be immediate. But the mechanical properties of
the human head and the corresponding analytical constitutive relations describing its
mechanical response are not understood yet, since as mentioned earlier, there still ex-
ists a large disparity in the quantitative experimental values obtained. Moreover, the
governing equations that are based on axiomatic laws, and in particular the partial dif-
ferential equations describing the motion of the human head system, can only be solved
49
Chapter 3. Current Understanding of the Bio-Mechanics of Traumatic Brain Injuries
analytically for a handful of problems with simplied geometries and material models.
Therefore, alternative ways of studying TBIs are needed and dierent approaches are
being used to study them. These will be presented here.
3.1.1 Analytical and Numerical Models of TBI
\Dynamic loading produces transient waves within the head that generate time-dependent
deformation at various locations; the approximate time for a transient to traverse the
skull is about 0.12 ms. Consequently, as indicated above, the only technique to determine
the state of strain of the various components of the head is the use of the equations of
motion, based on Newton's laws, applied to deformable solids, such as skull and brain,
and to liquids such as blood and the CSF. The result is a set of partial dierential equa-
tions in derivatives of the relevant displacements that are related to normal and shear
strains, subject to a prescribed external load history. A solution of such equations can be
executed analytically only for extremely simple geometries; for the realistic conguration
of a human head, this must be carried out by numerical methods, such as a nite-element
procedure provided the model has been validated. Data on failure strain of each element
can then be compared to the resulting values for a given mechanical input to ascertain
whether the tissue has ruptured. By means of the constitutive equations, this limiting
strain can be related to a corresponding failure stress. Of course, the physiological dys-
function may occur at a lower level than the mechanical failure limit, but the reverse
situation may occur when, for example, a skull fractures, but there is no brain damage"
Goldsmith, 2001 [9]
A few analytical models of TBI have been proposed over the years [55{61]. Most
of them deal with a spheroidal elastic skull lled with water. The spheroidal skull is
50
3.1. Models of Traumatic Brain Injury
modeled as an elastic thin shell through the use of the methods of linear elasticity, while
water is used to simulate the brain response as a non-viscous incompressible medium.
The choice of spherical geometry for the skull and water as the surrogate brain tissue is
due to practical limitations arising from the feasibility of the solution of the governing
equations of the system. The governing equations for a model like the one described, is a
set of coupled linear partial dierential equations, which together with the boundary con-
ditions and initial conditions constitute the boundary value problem. These equations
can be found in the literature and will not be presented here. The system of equa-
tions has been solved for dierent input loadings, such as impulsive loading uniformly
distributed over a small spherical cap on the skull, and other type of dynamic compres-
sion pulses such as sinusoidal functions in time. The solutions provide the response of
the \skull-brain" system in terms of transient strains of the spheroidal skull shell and
transient pressure eld histories in the water. Negative relative pressures indicate that
locations in the brain are subjected to tensile loading, which may cause tearing of the
brain tissue due to tension or even cavitation of the CSF with a subsequent collapse
of the cavitation bubbles. Locations close to point of impact, as well as removed on
the opposite side of the impact, have been identied where pressure magnitudes are the
highest. Such locations are considered to be prone to brain injury and parametric studies
have been conducted to correlate the most probable locations of injuries to pathological
ndings. Since at this point we have reached the current \state of the art" in terms of
solving the problem of interest with the use of pen and paper and we now understand
the limitations of our currently available mathematical toolset, we need to move towards
alternative methodologies for studying TBIs that will allow for more realistic geometries
and material models. For more realistic and consequently complicated geometries, as
51
Chapter 3. Current Understanding of the Bio-Mechanics of Traumatic Brain Injuries
well as implementation of higher delity material models (i.e. viscoelastic materials),
the options for analytical solutions are minimal. The analytical solution of the governing
equations is prodigiously dicult [54]. Eorts in the eld of stress wave propagation in
soft biological tissue are still areas of active research. In cases were analytical solutions
do not exist, we need to resort to other methods of solving the governing dierential
equations.
With the steady increase in computational power, numerical methods such as
nite dierence schemes and nite element methods, to name a few, can be used to
discretize the governing equations and make the solution of such equations feasible for
realistic geometries, materials, and loading conditions [62, 63]. Assuming that these
numerical studies use appropriate material models, boundary conditions, and detailed
geometries, they still suer from an inherent limitation: the inability to obtain the
ensuing biological response to the primary mechanical loading. Nevertheless, numerical
studies, and in particular Finite Element Methods (FEM), provide a powerful framework
for the solution of the mechanical response of brain tissue.
Thus we conclude that by using analytical and numerical models of TBI we can, at
best, only solve for the deformation of the human head and its contents! But injury has
a sequence of biological responses to the mechanical loading that cannot be taken into
account within that framework. The main assumption when we extrapolate the results
of the mechanical analysis to describe injury, is that excessive deformation of the brain
tissue is the cause of injury. Furthermore, we assume that the larger the deformation
magnitude, or strain level, the more severe the injury. By solving the transient loading
mechanical problem we try to identify the temporal and spatial locations in the brain
that exhibit maximum deformation for a given load. If the above premise is correct, the
52
3.1. Models of Traumatic Brain Injury
identication of maximum stresses and strains in the brain can provide valuable infor-
mation and insights about the cause and location of observed brain injuries. Although
biomechanics in its current framework cannot describe biological function, there is an
emerging eld called mechano-biology (in contrast to biomechanics) with primary focus
on the eect of mechanical stimuli on the biological response of cell function.
3.1.2 Experimental Models of TBI
Since TBIs happen under most circumstances accidentally, by default the traumatic
events are almost impossible or rather improbable to be captured and monitored as
they occur.
Quantitative information drawn from \natural experiments" -
accidents
An unfortunate occurrence of regular accidental TBIs happens under settings where
people voluntarily put themselves at a position of increased risk of sustaining brain
injuries; we specically refer to athletes, amateur or professional, that participate in
contact sports, e.g. boxing, martial arts, American football etc. Currently, available
video-capturing technology is wide spread and we have access to a substantial amount
of footage from accidental injuries occurring in sports. Some studies have been conducted
in which accident reconstruction through quantitative video analysis has provided kine-
matic parameters, such as linear and rotational accelerations of the head during injurious
events [64]. Moreover, a quite recent initiative of attaching accelerometers on protective
helmets worn by American football players [65, 66], as well as accelerometers embed-
ded in mouth-guards used by athletes to protect their teeth while competing [67,68], is
53
Chapter 3. Current Understanding of the Bio-Mechanics of Traumatic Brain Injuries
producing a signicant amount of real time head impact kinematic data. Analysis of
these data has lead to threshold kinematic, as opposed to kinetic, parameters of brain
injuries. Players at the high school, collegiate, and professional levels are monitored dur-
ing practices and games and whenever measured accelerations exceed a certain threshold
they are sidelined and evaluated through clinical personnel for establishing indications of
concussive brain injuries. These are great eorts that have yielded a wealth of data and
will keep on providing invaluable quantitative information on the kinematics of TBIs
obtained during accidents.
Brain deformation quantification - experimental efforts
Nevertheless, there still exists a debate on whether the relevant physical quantity
of interest should be explored in the form of kinematic parameters or in the form of
kinetic, also known as dynamic, parameters. A school of thought that prevails in terms
of physical reasoning is the following: kinetic parameters such as forces or stresses along
with the corresponding deformations or strains are the underlying causes of injuries
[9,63]. Kinetic parameters are certainly the natural variables for the description of injury
thresholds, since as described earlier the main premise of studying the mechanics of brain
injuries lies on the assumption that injury correlates with the extent of deformation. It is
evident that when the skull is accelerated, the brain deforms but the dynamic strain elds
experienced by the dierent tissues throughout the head are unknown [9]. Moreover, the
extent of deformation is not uniform across the brain structure, and global parameters
such as the linear or rotational accelerations of the head as a whole do not provide a
complete picture of the injury.
Of course measuring stresses and the resultant strains inside the optically opaque
human head, i.e. the dynamic response of the brain tissue, is very challenging if not
54
3.1. Models of Traumatic Brain Injury
impossible under most circumstances. However, there exist a few studies conducted on
human volunteers, that agreed to have their head subjected to sub-concussive linear and
angular accelerations while having the dynamic displacement of the brain tissue quan-
tied by the use of MRI [69{71]. In these low amplitude acceleration studies, relative
skull-brain displacements have been identied to occur in the order of millimeters, along
with \hot pockets" of strain with maximum amplitude of 5%. Moreover, information
about boundary conditions among the dierent structures of the head have been iden-
tied which help elucidate the brain-skull interface interactions, which in turn can be
used to inform the conditions imposed in the numerical studies of brain injuries. The
main limitation of these studies, primarily due to the available technology, lies in the low
temporal resolution of these measurements. The transient loading of the human head
at injurious conditions is too fast for the current capabilities of MRI. Another limita-
tion of the MRI techniques is that the loading is by design sub-concussive, at least for
human specimens due to ethical considerations, and therefore not relevant to injurious
conditions. Since we know that brain behaves in a highly non-linear viscoelastic manner,
the results of these sub-concussive experiments are of limited quantitative value for the
description of injury thresholds. They nevertheless give signicant information on the
inner dynamic response of brain tissue, as explained earlier. In addition to in-vivo MRI
studies there has been a dierent attempt to quantify the deformation of the brain tis-
sue with the use of bi-planar x-ray opaque markers attached to pork brain specimens or
human cadavers [72]. Each specimen is subjected to impact loading while the position of
these markers is tracked in space and time. The limitation of these studies is not in the
temporal resolution but rather in the spatial resolution due to the nite number and size
of the tracked markers. Another limitation of these studies is the disputed relevance of
55
Chapter 3. Current Understanding of the Bio-Mechanics of Traumatic Brain Injuries
post-mortem experiments on cadavers and the extrapolation of these results to a living
human brain subjected to similar loading.
3.1.3 Bio-Mechanical Models of TBI
It is evident that the last piece of the puzzle that remains out of reach within the
modeling methods described up to this point is the biological response of the brain
tissue to the external primary mechanical injury stimulus. In order to gain insight on
the biological response of brain tissue, we need to employ actual biological tissue by
using animals for experiments.
To this end, biologists in collaboration with engineers have developed a multitude
of dierent models to subject animal tissue to mechanical stimuli. There is a big moral
and ethical dilemma when conducting animal testing. Here, we are not going to delve
into the debate of whether such tests are ethically correct or not, but we would like
to mention that a huge degree of responsibility, translated into careful design and in-
terpretation of the experimental ndings, should be paramount in the eorts of the
scientic community which in turn should as a whole try to keep the number of these
unambiguously essential tests at the absolute bare minimum [73]. Currently there exist
two alternative ways of conducting experiments in which biological tissue is subjected
to mechanical loading. The distinction between the two dierent methods is based on
whether the biological tissue is tested under normal living conditions, known as in-vivo
testing [74], or whether the response of biological tissue is tested in cell cultures that
reside outside of their normal biological environment and grown in a dish, known as in-
vitro or test-tube experiments [75]. Mainly these models dier in the way they apply the
mechanical stimulus to the surrogate brain tissue. Transection models that model pen-
56
3.2. Mechanisms of Traumatic Brain Injury
etrating injuries [76{78], substrate deformation models [79{81] and shear-strain models
on cultures [82] and hydrogels [83], are few of the models in a dish that have been used
to study TBI. In these studies biological signatures of the tissue response to dierent
mechanical stimuli are explored. The tissue is usually obtained from mice or rats. The
probed biological markers oer a new dimension in our understanding of TBIs with an
ultimate goal of producing proper quantitative diagnostic measures, new approaches for
prevention, as well as novel therapeutic possibilities (e.g. development of medication).
3.2 Mechanisms of Traumatic Brain Injury
\Early characterizations of the causation of serious head injury, inappropriately labeled
\mechanisms", identied the culprits as acceleration-deceleration, compression, shear,
or alternatively, intracranial pressure changes, and waves of stress or cavitation. These
terms have precise physical meanings and occur in head impact (and most also in im-
pulsive loading). However, their application to head trauma is imprecise, because they
represent qualitative concepts whose magnitudes, even when measurable, do not dene
the basic cause of cranial trauma, that is, excessive tissue deformation or strain."
Goldsmith, 2001 [9]
In the eld of biology the term mechanism is used to describe parts of a process
that are causally related to produce an eect. The bio-mechanical community that is
engaged in TBI research has adopted the term mechanism to describe the causes of TBI
in terms of mechanical observables, such as accelerations, stresses, strains etc. These
observables can be global such as linear/rotational acceleration of the head that is a
57
Chapter 3. Current Understanding of the Bio-Mechanics of Traumatic Brain Injuries
kinematic variable, or local such as the kinetic variable quantifying deformation elds
of the brain.
Pathology of TBIs
First, we will present the dierent types of injuries that are observed clinically, and
then describe the dierent theories attempting to explain them. Injuries can be classied
clinically into two broad categories. The distinction is made between focal and diuse
brain injuries [47,84].
Focal injuries usually refer to hematomas and contusions. These injuries, as their
name suggests, are local and can be visualized by using standard imaging techniques
such as CT scans and MRI.
The other type of pathology that is observed clinically is not localized and is called
diuse injury. In other words, it is a widespread injury throughout the whole volume of
the brain. One manifestation of diuse injury is diuse axonal injury (DAI). DAI can
microscopically be observed as damage of neuronal axons within the volume of the brain.
Strich rst observed this widespread degeneration of white matter on the pathological
ndings of 20 human cadavers that had sustained closed-head injuries [85, 86]. This
was the rst experimentally observed evidence of the intuitive claim that Gama had
proposed in 1835, which stated that \bers as delicate as those of which the organ of
mind is composed are liable to break as a result of violence to the head". Observations
by Oppenheimer [87] further substantiated Strich's claims on DAIs in 59 cases of head
injuries where he also detected severing of nerve bers. Since then, many studies have
conrmed the widespread axonal damage in the brain due to traumatic loading [88] and
DAI has become one of the most important pathological features of TBI, since axons are
58
3.2. Mechanisms of Traumatic Brain Injury
responsible for the transfer of signals between neurons. Damage to the axons renders
the communication between neurons in the brain impossible. These structural changes
are linked to alteration in brain function and behavioral changes in the aected TBI
patients. Our aim in this section is to explore how these clinically observed injuries
occur mechanically.
Types of Loadings Causing TBIs
Brain injuries can occur due to dierent mechanical loading scenarios, as mentioned
in the denition of TBI, at the beginning of Chapter 3. One distinction would be static
versus dynamic loads. Since the vast majority of accidents happen dynamically, static
loads will not be considered in the description of injury mechanisms. For dynamic
loading we can dierentiate between contact loading and non-contact loading. Since in
this research work we are specically interested in brain injuries as they occur through
impact loading, the contact loading case is the predominant one and the one that we will
focus our discussion on. Contact loading to the head will produce deformation at the
point of impact. This local deformation will initiate a mechanical stress wave that will
propagate through the skull, CSF and brain. This is called a transient wave or pulse.
This kind of wave is absent in the non-contact loading scenario. Once the wave traverses
the brain and re
ects back from the other side of the skull, then inertial loading of the
head as a whole ensues. The time duration of the rst transient to travel through the
skull is approximately 120 s [9].
The exact mechanism of brain damage is not fully understood and it is still a subject
of controversy.
Focal injury has been hypothesized to occur due to tensile loading or the collapse of
cavitation bubbles formed due to tensile pulses in the CSF. Spatial pressure gradients in
59
Chapter 3. Current Understanding of the Bio-Mechanics of Traumatic Brain Injuries
the brain also give rise to shear strain within the brain. Another identied mechanism
is due to stress wave propagation through the brain that sets the brain and skull into
relative motion which can cause contact loading of the brain against the skull that could
explain contusion on the brain and tearing of veins. But, as mentioned by Goldsmith in
the quote starting Section 3.2, these phenomena described in this paragraph, although
present during a TBI, do not dene the basic cause of trauma, which is the excessive
deformation of brain tissue.
In terms of diuse injury mechanisms, there are two distinct schools of thought, both
of which unfortunately lie on the quantication of linear or rotational accelerations. The
rst regards linear acceleration as the main cause of brain injuries, while the second one
regards rotational accelerations as the main cause of diuse and focal injuries in the
brain. Here, we will brie
y discuss the arguments coming from both sides of the spectrum
and eventually conclude that none of these theses have been conclusively proven through
experiments; they are speculative and not indisputable facts. The reasons why this
issue has not yet been resolved lie mainly on the fact that deformations and strains,
as discussed earlier, are nearly impossible to quantify during an injurious event in-vivo.
Thus, the best alternative measure is the quantication of the mechanical input and
its correlation to the outcome of the event. Another limitation of both of these schools
of thought is that in reality no injurious event ever produces solely translational or
rotational accelerations but rather a combination of the two [89].
Moreover, in both of these two views, one of the most fundamental mechanical pro-
cesses that is taking part in the deformation of the brain tissue is neglected from the
start. We specically refer to the initial transient mechanical wave propagation through
the skull due to impact. Since no acceleration as a whole body can occur before the
60
3.2. Mechanisms of Traumatic Brain Injury
rst transient pulse traverses the skull, and we know that the time scale of this event is
in the order of a few hundred microseconds, the two eects, namely the transient pulse
and inertial linear or rotational motion, are by denition separated in time. With the
advent of experimental techniques that provide the needed temporal resolution to cap-
ture the initial transient wave, the two dierent modes can eectively be separated into
two distinct time-scales. The transient wave response can be observed experimentally
separately from the inertial response and the corresponding strain elds can then be
compared. In that way, the starting hypothesis of both prevailing current theses can at
least be conclusively proven, i.e. that the initial transient wave does not contribute to
the overall brain damage. A claim that seems unlikely for many researchers working in
the broader eld of dynamic behavior of materials. It is interesting to note that evidence
from the study by Ommaya et al. [90], who observed that a dierence exists between
the pathology produced through non-contact and contact loading at the same level of
acceleration. More specically they observed that half of the potential for brain injury
was due to head rotation, and their study pointed out that the other half should be
related to the contact phenomena of the impact.
61
Chapter 4
A Novel In-Vitro Model of Traumatic Brain Injury
This chapter is dedicated to the presentation of our proposed TBI model: the Highly
Automated Mechanical Impactor (HAMr) [91]. This is a new tool for exploring the
eects of repeated low-amplitude mechanical impacts onto in-vitro cell cultures. This
experimental design mimics the initial part of primary injury, by modeling the initial
stress wave propagation inside the skull and brain that occurs immediately after a blunt
impact to the head.
4.1 Rationalization of Model Design
In order to design a relevant model of impact induced TBIs the major characteristics
of the injurious event need to be identied and maintained in the model. We draw
inspiration from Holbourn's quote on his seminal paper on the Mechanics of Head Injuries
[45]
\The assumption that there is a mechanics of head injuries, implies that, when the
head receives a blow, the behavior of the skull and brain during and immediately after
the blow is determined by the physical properties of skull and brain and by Newton's laws
of motion"
In this, Holbourn identied two determining factors of the head's response to the
mechanical loading:
62
4.2. Injury Model Apparatus
1. The physical properties of the skull and brain
2. Newton's laws of motion
As was already described in Section 2.2, both the skull and the brain exhibit a strain
rate dependent response. Since the majority of TBI events occur under dynamic loading
conditions, e.g. impacts, in order to capture their mechanical response properly, the
loading needs to remain dynamic.
Moreover, the geometry in terms of gross anatomical features and architecture of the
dierent successive layers, described in Section 2.1, are idealized and maintained in the
1D model presented in detail in Section 4.2
4.2 Injury Model Apparatus
During an actual blunt-impact to the head, a local deformation occurs at the point
of impact on the skull. This local deformation will be propagated through the skull-
bone by a stress pulse, at a rate close to the speed of sound in the skull-bone. As was
mentioned in Section 2.1, moving from the human skull inwards, we nd the CSF that
surrounds the brain, as shown in Figure 4.1. At the interface between the skull and
CSF, part of the stress pulse will be re
ected back into the skull and part of it will
be transmitted through the CSF, due to acoustic-impedance mismatch between the two
media. The transmitted part of the stress wave, will propagate in the
uid CSF layer
as a pressure pulse and will interact with the brain tissue that is interfacing with the

uid. At this second interface a similar process of re
ection and transmission of the
pulse will occur due to impedance mismatch between the CSF and brain tissue. Once
the stress pulse traverses the brain and reaches the opposite side of the skull, it will
63
Chapter 4. A Novel In-Vitro Model of Traumatic Brain Injury
re
ect back as a tensile wave. This duration of the rst transient wave is approximately,
0.12 ms [9]. After the rst transient wave has propagated through the entire brain-skull
system, linear and/or rotational acceleration of the head structure as a whole ensues.
Skull
CSF
Brain
Skull
CSF
Brain
1D - model
Figure 4.1 Hierarchy of layers that are being modeled in the skull-brain system by HAMr
4.2.1 Principle of Operation: Schematic
In an equivalent manner, the proposed experimental apparatus, HAMr, delivers impacts
onto a solid protective plate that serves as the \skull" of our system, followed by a
nutrient bath that serves as the \cerebrospinal
uid", and nally followed by a monolayer
of cells cultured at the bottom of the petri dish that serve as the surrogate brain tissue,
Figure 4.2.
At the moment of impact between the piston and protective plate, Figure 4.2, local
deformation will initiate a compression wave to propagate inside the protective plate
64
4.2. Injury Model Apparatus
Cylindrical
piston
Protective Plate
Nutrient bath Cell culture
Protective Plate
Figure 4.2 Schematic of the 1D skull-brain model that mimics the succession of dierent layers,
moving from the skull to the brain. The protective plate mimics the skull, the nutrient bath
mimics the cerebrospinal
uid, and the cell culture is the brain surrogate tissue of our model
system
material. The amplitude of the compressive wave will depend upon the mass and velocity
of the impacting piston. The duration of the pulse is related with the time of contact
between the piston and protective plate, which depends on the mass and material of the
impactor. The compressive wave will travel through the protective plate until it reaches
the solid-liquid interface. The interface between the protective plate and the nutrient
bath is crucial, and the two surfaces need to be in contact. At this interface between
the protective plate and nutrient bath, part of the incident compression wave will re
ect
back into the protective plate and part of it will transmit through the nutrient bath, due
to acoustic impedance mismatch between the two media. The transmitted portion of
the wave propagates into the nutrient bath and will nally interact with the monolayer
of cell cultures that is attached at the bottom of the
uid lled petri dish. The action
of this compression pulse will act on the neuronal networks, which will cause them to
deform. In this model the compressive pulse is the mechanical stimulus imparted on our
65
Chapter 4. A Novel In-Vitro Model of Traumatic Brain Injury
brain surrogate material.
The protective plate can be designed to mimic skull bone material, with additional
layers of protective gear material on top of it. However, in all results reported here an
aluminum protective plate was used.
4.2.2 Principle of Operation: Detailed Design
A CAD rendering of the HAMr demonstrating its internal details is shown in Figure 4.3.
HAMr consists of an electrical DC motor that drives a cylindrical shaft. Attached on
the shaft is a sectored spur gear, which is a normal spur gear with a portion of its teeth
along the perimeter cut. When the motor is on, the shaft rotates and the gear rotates
with it. The gear engages with a rack of the same pitch, and this rack is mounted to a
piston that delivers the impact. As the gear engages with the rack it moves the piston
upwards. This gear remains engaged with the rack only for the portion that there are
teeth along its perimeter. The piston is enclosed in a stationary external cylindrical
unit, which also constrains the piston's movement along the vertical axis with internal
guided grooves. A helical spring is situated between the moving piston and the top of
the cylindrical unit. When the gear and rack are no longer engaged, the piston, which is
attached to the rack, is free to move downwards and accelerate due to the action of the
force of the helical spring. The piston impacts onto the protective plate that interfaces
with the liquid surface of the nutrient bath inside the petri dish. The dissociated cell
culture is prepared using cortical tissue from mice or rats and is attached at the bottom
(glass) substrate of this petri dish.
The magnitude of the stress pulse can be controlled both by selecting helical springs
with dierent stiness constants, and by changing the number of teeth on the sectored
66
4.2. Injury Model Apparatus
Figure 4.3 Model of HAMr and cross sectional view with internal details, (1) DC motor, (2)
shaft, (3) piston, (4) stationary cylindrical unit, (5) helical spring, (6) protective plate, (7)
petri dish with nutrient bath and neuronal network at the bottom [91]
spur gear which modies the displacement of the spring from its equilibrium position.
The duration of the stress pulse can be controlled by using dierent materials for the
impactor-piston system.
Due to this design, HAMr can deliver repeated impacts of constant force with a set
frequency. The frequency of impacts depends on the rotational velocity of the electric
DC motor that drives the whole mechanism. The current operating frequency range of
HAMr is 0.03-1 Hz. Another feature of this design is the replication of a dynamic impact
event. To the best of our knowledge this in-vitro experimental model is the only one
that accounts for repeated dynamic impact with high rate of load application and nite
stress pulse duration.
Details of the geometrical conguration of the protective plate, petri dish, and water
bath are given in Figure 4.4. The 15 mm-diameter impactor covers the area of the cell
culture that resides at the bottom of a standard 35 mm-diameter glass-bottomed petri
67
Chapter 4. A Novel In-Vitro Model of Traumatic Brain Injury
dish (MatTek Corporation, Ashland, MA). That allows the impactor to exert the forcing
to the whole area occupied by the cells in the petri dish.
50
15
35
7
5
5
δx
Figure 4.4 Geometric details of protective plate, water bath, and petri dish, x shows the
position that the pressure sensor was mounted relative to the protective plate - water interface.
All dimensions are in mm [91]
4.3 Surrogate Brain Tissue
In-vitro studies of TBI often contain two main components: the injury model and the
tissue surrogate. The injury model was described in detail in Section 4.2. There are a
few options for brain tissue surrogates which include: acute tissue preparations, organ-
otypic cultures, or dissociated primary cultures [75]. In the research presented herein,
dissociated in-vitro primary cultures was the surrogate brain tissue of choice. These are
monolayers of cells adhered at the glass-bottom substrate of a petri dish (MatTek Cor-
poration, Ashland, MA). Both post-natal rat and embryonic mice cultures were used.
Details on the protocols of preparation for the two dierent cultures used in this re-
search work are given in Chapter 6 before the presentation of the biological response of
the dierent surrogate tissues explored.
68
4.4. Experimental Toolset
4.4 Experimental Toolset
In a TBI event the stimulus is mechanical and the response is both mechanical and
biological. The proposed model of TBI allows us to probe the full spectrum of the me-
chanical and biological response of the surrogate brain tissue and correlate this response
to the mechanical input imposed on the system.
4.4.1 Mechanical Stimulus Quantication
The mechanical stimulus is quantied in terms of impact force history, induced pressure
pulse in the liquid medium, and impact velocity of the striker.
Impact Force
The impact force at the top of the protective plate was determined using a piezoelec-
tric quartz impact force sensor (PCB Piezotronics, Model 200B05) along with a signal
conditioner (PCB Piezotronics, Model 480C02). The force sensor was located at the
same position as the protective plate during the impact experiments on the neuronal
networks. The certied sensitivity of the sensor is S = 0:2124 mV/N and its range
is R = 22; 241 N. This sensor has an upper frequency of 75 kHz with a -3dB signal
attenuation, which gives a rise time from 10-90 % of a step function response of 6 s.
The output voltage signal was recorded with a digital oscilloscope (LeCroy Wavesurfer
24Xs-A, 200 MHz Oscilloscope 2.5 GS/s) and sampled every 4 ns. Impulse, I, is calcu-
lated by integrating the impact force in time; I =
R
t
2
t
1
F (t) dt, where F (t) is the impact
force and t is time.
Pressure Pulse
69
Chapter 4. A Novel In-Vitro Model of Traumatic Brain Injury
The pressure pulse transmitted through the water bath was measured using a piezo-
electric pressure sensor (PCB PIezotronics, Model 113B21). The pressure sensor was
mounted at two dierent depths separated by 5 mm inside the petri dish, see Figure 4.4.
The certied sensitivity of the sensor is S = 3:634 mV/Pa with a rise time capability
of less than 1 s. The output signal was recorded using the same oscilloscope used to
sample the impact force.
Impact Speed
The impact speed of the striker that impacts the \skull" model was quantied and
consequently the kinetitc-energy transferred to the system was estimated. For that
purpose we used a high-speed camera (Phantom V711) to track the piston-striker as it
was accelerated downwards by the helical spring. Images were captured at 25,000 fps.
4.4.2 Mechanical Response Quantication
The method for quantifying the mechanical response of the surrogate brain tissue was
a non-contact, optical, full-eld deformation measurement technique known as Digital
Image Correlation (DIC). Using 2D-DIC algorithms [92] it was feasible to capture the
short-lived deformation event using a high-speed camera at a framing rate of 25,000 fps
and spatial resolution of 9m/pixel, for a schematic of the setup see Figure 4.5. DIC is a
general technique used to quantify strains and deformations. The specimen of interest is
lmed and the succession of frames is post-processed to obtain the in-plane deformation
history of the specimen's surface. The specimen needs to have a gray-scale random
pattern variation, also known as speckle pattern, that can either be naturally occurring
or articially painted or adhered on the specimen surface. Here the glass bottom of
70
4.4. Experimental Toolset
the petri dish was spray painted with white matte paint, shown in Figure 5.5b. The
naturally occurring texture of the white paint imaged using a 2X microscope objective
gave a speckle pattern that could be successfully used with the correlation algorithms.
Moreover, in separate experiments, the glia cell-bodies were imaged under re
ected light
microscopy using the high-speed camera and a 10X microscope objective. The cell bodies
were used as the markers, the position of the markers in time were tracked, and their
relative displacement during deformation was quantied. From the high-speed footage
it is evident that the cells remain adhered onto the glass substrate for the duration of
the experiments, even after they are subjected to 64 repeated impacts. A laser point
source and a photodiode sensor were used to sense the impact and send a signal to the
camera to trigger the recording.
4.4.3 Biological Response Quantication
The methods used for the quantication of the biological response of the cell cultures
to impact experiments using HAMr are described brie
y in this section. More details
are given in each particular section, in Chapter 6, presenting the biological response
quantication of the dierent cultures used.
Expression levels of dierent in
ammation proteins were determined by immunos-
taining the cell cultures with suitable antibodies. A Carl Zeiss microscope with a

uorescent camera detector (Zeiss AxioCam MRm) was used to capture immuno
uores-
cence images and post-processing of the images yielded quantication of the expression
levels of the in
ammation proteins.
Moreover, polymerase chain reaction quantication was conducted in order to track
changes in mRNA gene expression of a number of dierent biomarkers.
71
Chapter 4. A Novel In-Vitro Model of Traumatic Brain Injury
High-Speed
Camera
Microscope
Objective
HAMr
Petri
Dish
Figure 4.5 Side view of DIC experimental setup schematic showing HAMr, the high-speed
camera, the microscope objective lens, the petri dish containing the glial network, and further
details of the experimental setup
72
Chapter 5
Mechanical Characterization of TBI Model
In order to elucidate the intricate mechanisms of TBI events a model should be able to
provide quantitative information regarding the cause, which is the mechanical stimulus,
and the eect, which is the mechanical and biological response. Moreover, a quantitative
correlation between the three aspects should be drawn that will aid in the fundamental
understanding of injuries to the brain tissue. This information can then be used to
better protect, diagnose, and treat people that are susceptible to TBI.
In Chapter 5 the quantication of the mechanical stimulus and mechanical response
of the injury model is presented.
5.1 Measurement of the Mechanical Stimulus
The mechanical stimulus was quantied in terms of the temporal proles of impact force,
pressure pulse and impact velocity.
5.1.1 Impact Force
Impact force was measured for dierent combinations of spring stiness and spring dis-
placements. The measurements were made at the interface between the piston and
protective plate using a piezoelectric sensor. In Figure 5.1, the temporal trace of the
impact force for a spring with stiness k
1
= 278 N/m and displacement x
2
= 22 mm
73
Chapter 5. Mechanical Characterization of TBI Model
Figure 5.1 Temporal proles of impact force for 5 separate experiments measured using a
piezoelectric quartz sensor at the interface between the impactor and protective plate for a
spring stiness k
1
= 278:62 N/m and displacement x
2
= 22 mm [91]
is shown for 5 dierent experiments. A maximum impact force of F = 420 30 N was
observed with a pulse duration of 182 12 s. The two separate peaks are due to high
frequency ringing associated with metal-to-metal impacts. The impulse for the same
setup was obtained through integration of the impact force with respect to time and was
shown to be I = 0:047 0:003 Ns. This is a measure of the momentum transferred to
the system due to impact.
Repeatability
1 2 3
0
0.01
0.02
0.03
0.04
0.05
0.06
Day
Impulse (Ns)
Figure 5.2 Day-to-day impulse variability
for the spring-displacement combination
k
1
= 278:62 N/m and x
2
= 22 mm [91]
The repeatability of the temporal prole of
the impact force imparted with same nominal
input conditions was quantied in terms of im-
pulse transferred, Figure 5.2. The experimen-
tal apparatus was disassembled and reassem-
bled for each set of experiments in order to
quantify potential dierences in impact condi-
74
5.1. Measurement of the Mechanical Stimulus
tions. The result shows a 7% day to day variability in terms of impulse transferred
during impact. These variations are mainly due to human factor while assembling the
experimental setup.
Range of Impact Loading
0 200 400 600 800
0
0.02
0.04
0.06
0.08
0.1
Impact Force (N)
Impulse (Ns)
Figure 5.3 Impulse as a function of impact force using three dierent settings as shown in
Table 5.1. Uncertainties are also given in Table 5.1 [91]
One of the design specications for HAMr was the ability to impart impact loading
with a force amplitude ranging 3 orders of magnitude, 10
0
10
3
N. HAMr's range was
quantied by using two dierent springs, with k
1
= 278 N/m and k
2
= 2973 N/m
stiness, and two dierent spring displacements, x
1
= 10 mm and x
2
= 22 mm, to
obtain a range of dierent impact conditions. An aluminum impactor was used for these
experiments. The results are summarized in Table 5.1 and Figure 5.3.
The scatter plot with pairs of impact force and impulse transferred during the impact
shows an almost linear relationship (Figure 5.3). The three data points correspond to
three dierent combinations of springs and displacements as shown in Table 5.1.
75
Chapter 5. Mechanical Characterization of TBI Model
Table 5.1 Impact force measured for dierent experimental settings, using dierent combina-
tions of spring stiness and initial displacements. Errors represent standard deviation of 5
repeat experiments at each experimental setting.
Setting Rate Displacement Max Pulse Rise Impulse
Constant Force Duration Time
k (N/m)
x
(mm) F (N) (s) (s) I (Ns)
01 278.62 10 265 14 150 7 22.4 1.7 0.026 0.001
02 278.62 22 420 30 182 12 22.4 1.4 0.047 0.003
03 2973.25 22 664 12 176 23 10.4 2.0 0.077 0.004
5.1.2 Impact Velocity
The impact velocity of the striker on the protective plate was quantied for both springs
stinesses. The initial displacement of the springs was x = 22 mm, which yielded an
impact speed of 3:60:3 m/s and 1:30:1 m/s, for the sti and soft spring, respectively.
The mass of the aluminum striker is 50 g, which yields a kinetic energy right before
impact of 300 mJ and 40 mJ respectively.
5.1.3 Pressure Pulse
The pressure history prole was measured at two dierent locations as shown in the
schematic of Figure 4.4. The temporal progression of the pressure pulse measured at
the top and bottom surface of the water bath are shown in Figure 5.4. The obtained
pressure trace had a maximum amplitude of 0.2 MPa, and the pulse duration shortens
as the pressure pulse propagates to the bottom of the petri dish. This is due to the
steepening of the tail of the compressive pressure pulse.
76
5.2. Measurement of the Mechanical Response
−10 0 10 20 30 40 50
−0.1
0
0.1
0.2
0.3
Time (μs)
Pressure (MPa)

δ x = 5mm
δ x = 0mm
Figure 5.4 Temporal proles of pressure at two dierent depths inside the water bath. Solid
blue and red lines represent averages of 8 separate runs shown with lighter blue and red
lines in the background of the gure. Spring stiness k
1
= 278:62 N/m and displacement
x
2
= 22 mm [91]
5.2 Measurement of the Mechanical Response
The mechanical response of the impact model is quantied in terms of deformation
elds induced by the impact loading and subsequent pressure pulse interaction with the
substrate. The method of choice for the quantication of the strain elds experienced
by the model is a full-eld non-contact optical quantication technique, known in the
experimental mechanics community as Digital Image Correlation (DIC). As seen in Sec-
tion 5.1 the loading durations are in the order of s, therefore high-speed imaging is
required. Moreover, since the cell cultures cover approximately a 10 mm 10 mm area,
optical microscopy and high-speed imaging need to be combined in order to perform
DIC that successfully captures the dynamic loading event of interest. A schematic of
the experimental setup is shown in Figure 4.5.
77
Chapter 5. Mechanical Characterization of TBI Model
5.2.1 Quantication of Glass Substrate Deformation During Pressure Pulse Loading
For quantication of the petri dish glass-bottom substrate deformation, Figure 5.5a,
water was used as the liquid interface between the protective plate of HAMr and the
substrate, Figure 4.2 and Figure 4.4. These experiments were conducted without the
presence of cultured cells at the bottom of the dish. Here we assume, that the presence
of cell bodies that are on the order of 10 million times less sti compared to glass
[48,93], would not aect the glass substrate deformation. Therefore, by quantifying the
deformation of the glass substrate, where the cells are normally adhered to, a lower
bound of the strain experienced by the cell network tissue under the pressure pulse
loading is obtained. The random pattern needed for correlation of the images was
eectively created and visualized using the naturally occurring texture of the white
matte paint under an optical microscope, as shown in Figure 5.5b . A schematic of
a bottom view of the petri dish along with its dimensions can be seen in Figure 5.5a.
Moreover, an image of a frame captured by the high-speed camera is shown using a
2X microscope objective in Figure 5.5b. The eld of view is a square area of 5 mm
5 mm, which gives an eective pixel size of 9 m/pixel. For correlation of the images
a subset size of 51 pixels and a step size of 25 pixels was used. At rst the noise

oor of the measurements was quantied (134 m/m strain) and the sensitivity of the
erroneous strain due to out-of-plane motion was 137m/m per mm of out of plane rigid
body displacement. Average strain versus time is plotted for two dierent springs with
stinesses k = 2973 N/m and k = 278 N/m.
The strain versus time plot shows that HAMr is capable of inducing strain levels
of dierent magnitudes. With the stier spring the maximum attained strain level is
about 905 m/m, whereas with the softer spring the maximum amplitude of the strain
78
5.2. Measurement of the Mechanical Response
Figure 5.5 Strain deformation of substrate caused by the applied pressure pulse.(a) Bottom
view schematic and dimensions of the 35 mm diameter petri dish. Glass substrate has a
diameter of 14 mm (b) Image of the eld of view of the glass substrate image after it has
been spray painted with white matte paint using the 2X objective lens and high-speed camera
(25,000 fps and 512 px 512 px). (c) Average Strain along the x-direction vs time for two
dierent spring settings using Digital Image Correlation (for n=5 separate runs)
pulse is around 330 m/m. The average strain rate from zero to maximum strain was
13.2s
1
and 3.3s
1
for the two dierent springs. The duration of the oscillation of the
glass substrate is 0.56 ms and is independent of the loading amplitude. The frequency
of the oscillation is dictated by the natural frequency of the thin glass substrate that is
attached at the bottom of the petri dish. After the rst compressive pulse the amplitude
of the strain oscillations dampens and dies out after a few oscillations. Since DIC is a
79
Chapter 5. Mechanical Characterization of TBI Model
full eld measurement technique, it was feasible to quantify the strain as a function of
space, and it was observed that the strain is mostly uniform across the whole eld of
view with a standard deviation of66m/m. It is worth noting that since the bottom
surface of the glass substrate is viewed as the pressure load is being applied, this surface
is subjected to a tensile loading rst with a subsequent compressive strain pulse. The
inner surface of the glass substrate will be subjected to a strain of same magnitude but
opposite sign, meaning a compressive pulse followed by a tensile pulse. This \inverted"
pulse would be the strain eld experienced by the cell culture network that is normally
adhered on the inner surface of the glass substrate. The strain along they y-direction
was almost identical with the strain along the x-direction. Whereas the measured shear
strain
xy
was negligible.
5.3 Conclusion on the Mechanical Characterization of the Model
In this Chapter, the mechanical characterization of the HAMr model of blunt-impact
induced TBIs was presented.
The input loading is produced through a blunt impact of a striker on a protective
plate that serves as the \skull" of the model. As described in Section 2.2, brain tissue
exhibits viscoelastic behavior that manifests as rate-dependent response. Since the trau-
matic events that we are trying to mimic are usually happening under dynamic loading
impact conditions, the choice of input loading for our model is a dynamic blunt-impact
load that produces rates of loading similar to the loadings occuring in an actual TBI
scenario. The dynamic mechanical stimulus was quantied for a range of dierent model
settings in terms of velocity and kinetic energy of impact. Moreover, the histories of the
impact force and subsequent pressure pulse was quantied. In the results presented in
80
5.3. Conclusion on the Mechanical Characterization of the Model
this chapter, the range of loading conditions was presented. All these observables give
a complete quantitative description of the loading stimulus.
In turn, the mechanical response to the input loading was quantied in terms of
the induced strain eld of the petri dish's glass-bottom substrate. The surrogate brain
tissue, monolayer of cells, is normally adhered to the substrate and under the premise
that it remains attached to the glass surface during loading, the measured strain elds
should give a proper lower bound for the strains experienced by the surrogate tissue
macroscopically. The strain rates attained for the dierent loading scenarios are in the
range between 3 - 15s
1
, which is in good agreement to what is believed to be the range
of strain rates related to mild-TBIs [83,94].
81
Chapter 6
Biological Response of Surrogate Brain Tissue
Two dierent surrogate brain tissue models were explored. One was a mice cell co-culture
of neurons and glial cells, while the second was a rat glial cell culture.
6.1 Mice Cell Culture: Co-Culture of Neurons and Glial Cells
In this section the protocols and methods for preparation of the cell cultures is described
rst. Then the results of the biological response of the network to impact loading are
presented.
6.1.1 Methods
The protocols and methods used for preparation of the neuronal networks and quanti-
cation of the biological response of the network due to impact experiments are described
in this section.
Preparation of Cortical Networks for Impact Experiments
Cortices isolated from embryonic day-18 C57BL/6 (CRL line) mice brain (BrainBits
LLC, Springeld, IL) were used to make 2-dimensional neuronal networks used in this
study. Under sterile conditions, cortical tissue was digested at 30

C for 25 minutes
in 2 mg/ml papain solution in Hibernate-E minus Ca
2+
(Brain Bits LLC, Springeld,
82
6.1. Mice Cell Culture: Co-Culture of Neurons and Glial Cells
IL), mechanically dissociated in Hibernate-E medium (Brain Bits LLS, Springeld, IL)
supplemented with 0.5 mM Glutamax (Life Technologies, Carlsbad, CA), and strained
with a 40 m cell strainer (BD Biosciences, San Jose, CA) to remove debris and tissue
fragments [95, 96]. Cells were spun down at 200 g for 3 minutes and the pellet was
re-suspended in warm Dulbecco's Modied Eagles Medium (DMEM) with high glucose
(Cat #D-6429, Sigma, St. Louis, MO) supplemented with 10% fetal bovine serum (FBS)
and 0.5 mM Glutamax. Approximately 10
5
cells in 40 l were plated on poly-D-lysine
coated 35 mm diameter glass-bottomed circular imaging dishes (MatTek Corporation,
Ashland, MA). Cells were incubated inside a 5% CO
2
incubator at 37

C. After 1.5 hours,
2 ml warm pre-equilibrated media was added to the cultures. After 4 hours half of the
growth medium was replaced with NbActiv4 (Brain Bits LLC, Springeld, IL) medium.
By day 3 in-vitro (DiV-03) cells formed an intricate network with numerous connections.
Cells were maintained in culture by feeding every third day by replacing half of the
culture medium with warm, fresh NbActiv4 medium pre-equilibrated in the incubator.
A cocktail of penicillin/streptomycin and gentamicin was used to keep cultures free from
microbial contamination an bacterial infection. All experiments reported here used DIV-
15 to DIV-20 cultures. Cell type analyses for these networks using immunostaining with
neuronal marker NeuN (ABN78 from Millipore, Billerica, MA), a suitable Alexa-633
conjugated secondary antibody (Life Technologies, Carlsbad, CA) and cell nuclei marker
Hoechst, Figure 6.1, show that 44 3% (n = 6 isolations) of cells are neurons in these
networks between DIV-11 and DIV-24 in culture. For the impact experiments, networks
were taken out of the incubator for pressure pulse exposure and then again returned to
the incubator for 4 hours. Impact-exposed networks were then xed, immunostained
for IL-1 protein and other cellular markers, and then imaged using a
uorescence
83
Chapter 6. Biological Response of Surrogate Brain Tissue
microscope.
Koumlis(et(al. (
HAMr:(A(mechanical(impactor(for(investigation(of(mild(TBI(induced(by(repeated(concussions (using(in(vitro(neuronal(networks !
9!
(
3.!Preparation!of!Cortical!Networks!for!Impact!Experiments(
Cortices( isolated(from( embryonic( day N 18( C57BL/6((CRL( line)(mice(brain((BrainBits( LLC,(
Springfield,(IL)(were(used(to(make(2 N dimensional(neuronal(networks(used(in(this(study.( Under(
sterile(conditions,(cortical(tissue(was(digested(at(30°C(for(25(minutes(in(2(mg/ml(papain(solution(
in(HibernateN E(minus(Ca
2+
((Brain(Bits(LLC ,(Springfield,(IL),( mechanically(dissociated( in(HibernateN
E( medium( ( Brain( Bits( LLC ,( Springfield,( IL)( supplemented( with( 0.5( mM( Glutamax( (Life(
Technologies,(Carlsbad,(CA ),(and(strained(with(a( 40(µm(cell(strainer( (BD(Biosciences,(San(Jose,(CA)(
to(remove(debris(and(tissue(fragments .(Cells(were(spun(down(at(200 (x(g(for(3(minutes(and(the(
pellet(was(re N suspended(in(warm( Dulbecco’s(Modified(Eagles(Medium((DMEM)(with(high(glucose(
(Cat(#(D N 6429,(Sigma,(St.(Louis,(MO)(supplemented(with(1 0%(fetal(bovine(serum((FBS )(and( 0.5mM(
Glutamax.(Approximately(1(x(10
5
(cells(in(40(μl(were(plated(on(poly N DN lysine(coated(35(mm(
diameter(glassN bottomed(circular(imaging(dishes((MatTek(Corporation,(Ashland,(MA) .(Cells(were(
incubated(inside(a(5%(CO 2(incubator(at(37°C.( After(1.5(hours, (2(ml(warm(pre N equilibrated(media(
was(added(to(the(cultures.( After(4(hours(half(of(the(growth(medium(was(replaced(with(NbActiv4(
(Brain(Bits(LLC ,(Springfield,(IL )(medium.(By(day(3( in#vitro((DIVN 03)(cells(formed(an(intricate(
network(with(numerous( connections.(Cells(were(maintained(in(culture(by(feeding(every(third(day(
by(replacing(half(of(the(culture(medium(with(warm,(fresh(NbActiv4(medium(pre N equilibrated(in(
the(incubator.(A(cocktail(of(penicillin/streptomycin(and(gentamicin(was(used(to(keep(cultu res(free(
from(microbial(contamination(and(bacterial(infection. (All(experiments(reported(here(used(DIV N 15(
to(DIVN 20(cultures.(Cell(type(analyses(for(these(networks(using( immunostaining(with(neuronal(
marker(NeuN([ABN78(from(Millipore,( Billerica,(MA),(a(suitable(AlexaN 633(conjugated(secondary(
antibody((Life(Technologies,(Carlsbad,(CA)( and(cell(nuclei(marker(Hoechst((Figure(S8)(show(that(
44(±(3%((n(=(6(isolations)(of(cells(are( neurons(in(these(networks(between( DIVN 11(and(DIV N 24(in(
culture.(For(impact(experiment s(networks(were(taken(out(of(the(incubator(for(pressure(pulse(
exposure(and(then(again(returned(to(the(incubator( for(4(hours.(ImpactN exposed(networks(were(
then(fixed,(immunostained(for(IL N 1β(protein(and(other( cellular(markers,(and(then( imaged(using(a(
fluorescence(microscope.(
!
Figure(S8:(A(DIVN 17(dissociated(cortical(network(immunostained(for(neuronal(nuclei(marker,(
NeuN(and(cell(nuclei(marker,(Hoechst .(! !
Figure 6.1 An immunostained DIV-17 dissociated cortical network, for neuronal nuclei marker,
NeuN and cell nuclei marker, Hoechst (scale bar 100 m)
Determination of IL-1 Expression Levels in Neurons
IL-1 expression levels in neurons were determined by immunostaining these net-
works with suitable antibodies. After impact experiment and incubation, networks were
washed twice with warm phosphate buered salin (PBS) solution, and then xed with
3.7% paraformaldehyde (PFA) solution in PBS for 20 minutes at room temperature.
Samples were washed thrice with PBS/50 mM glycine solution to neutralize PFA, and
then treated with 0.25% Triton-X for 10 minutes to make cell membranes permeable.
A blocking solution made of 3% bovine serum albumin (BSA), 5% goat serum and
50mM glycine in PBS was used to minimize nonspecic labeling with antibodies. Then
each network was treated with 2-3 drops of Image-IT FX (Life Technologies, Carlsbad,
CA) for 30 minutes at room temperature in humid environment. For immunostaining,
networks were rst incubated with primary antibody (IL-1, goat, AF-401-NA, (R&D
84
6.1. Mice Cell Culture: Co-Culture of Neurons and Glial Cells
Systems, Minneapolis, MN); Cy3 conjugated MAP-2, rabbit, AB2290C3 (Millipore, Bil-
lerica, MA); NeuN, rabbit, ABN78 (Millipore, Billerica, MA); Alexa-488 conjugated
NeuN, rabbit, ABN78A4 (Millipore, Billerica, MA)) for 2 hours, washed tree times with
PBS, and then treated with a suitable donkey anti-goat Alexa-633 or Alexa-488 labelled
secondary antibody (Life Technologies, Carlsbad, CA) for 2 hours. All reactions were
done at room temperature. Samples were washed twice and then labelled with NucBlue
reagent (Life Technologies, Carlsbad, CA). Immunostained samples were stored at 4

C
and were imaged within three days of preparation.
For
uorescence imaging experiments a
uorescence microscope (Axio Imager M2,
Zeiss) coupled to X-Cite Series 120Q (EXFO) illumination system and a digital camera
(Axio Cam MRm, Zeiss) was used. For all experiments the detector gain and the channel
exposure times used for recording images from immunostained samples were kept con-
stant. For every network, 6-10 elds (1000 m800 m for
uorescence microscope)
were imaged from dierent regions of the network. Higher
uorescence intensity was
interpreted as higher concentration of IL-1 protein.
Image processing and analyses were done using ImageJ software (National Institutes
of Health, MD). For every image, neuronal cell bodies were selected (50 cells per image,
4-6 images per network) using Region of Interest (ROI) Manager tool, and average

uorescence intensity for each ROI was measured. Finally, data from multiple networks
were combined, and the change in
uorescence intensity is presented as percent increase
using the average values of non-impactor exposed samples as controls. All experiments
were done using 4 independent cell isolations. Data from all preparations were combined
and presented as average standard deviation.
85
Chapter 6. Biological Response of Surrogate Brain Tissue
6.1.2 Measurement of Biological Response
HAMr was coupled to the dissociated neuronal networks. Networks were cultured ac-
cording to the protocol described in Section 6.1.1. For impact experiments, networks
were taken out of the incubator for pressure pulse exposure. It was not feasible to
instrument these experiments with force and pressure sensors so spring-displacement
combinations discussed in Chapter 5 were repeated, to subject the neuronal culture to
the quantied loading determined previously.
First, the eect of a single impact with the stier and softer spring was tested. One
impact delivered using the spring with stiness k
2
and displacement x
2
destroyed the
network creating a situation equivalent to an invasive wound. By using the spring with
stiness k
1
and the same displacement as before, no macroscopic physical damage was
observed on the network after one impact.
As our focus is cell damage caused by dynamic loading due to blunt impact and
not invasive wounds, the spring with stiness k
1
was used for the next set of experi-
ments. Networks were then subjected to 2, 4, 8, 16, 32, 64 and 128 repeated impacts
at a frequency of two impacts/min and examined for physical damage. Even after 32
repeated impacts, the network remained intact but 128 such impacts destroyed the net-
work macroscopically. A neuronal network exposed to 64 impacts showed local tears
(Figure 6.3a, white arrows pointing at the black regions) indicating some physical dam-
age of the network. The control networks observed under the microscope did not have
any black regions and the whole petri dish substrate was covered with cells.
Moreover, expression of the in
ammation protein IL-1 was quantied and compared
for networks exposed to dierent number of impacts ranging from 2 impacts up to 64 im-
pacts, shown in Figure 6.2. The networks where exposed to dierent number of repeated
86
6.1. Mice Cell Culture: Co-Culture of Neurons and Glial Cells
impacts, and returned to the incubator for 4 hours. Impact-exposed networks were then
xed, immunostained for IL-1 protein, microtubule associated protein 2 (MAP-2) and
nuclei marker Hoechst, and then imaged using a Zeiss AxioImager M2
uorescence mi-
croscope, shown in Figure 6.3a. MAP-2 marker is only used for visualization purposes
and its expression is not quantied. It is useful to show in what cells is the in
ammation
occuring, i.e. glial cells or neurons. Since MAP-2 is specic to neurons, its overlap with
other markers will indicate whehter those markers are expressed in neurons. Changes
in levels of expression of IL-1 were compared to no-impact controls, see Figures 6.2
& 6.3. The main premise in the quantication of the expression levels of IL-1 is that
regions of networks that have higher concentrations of IL-1 will emit more light, which
in turn will be detected and stored by the microscope camera sensor as a higher pixel
intensity value. In Figure 6.3 it is shown that even though 4 impacts did not cause any
measurable increase in expression levels of IL-1, an increase of50% in the expression
of IL-1 was observed with 64 repeated impacts compared to the control network that
was not exposed to any impacts. This data indicates the existence of a threshold num-
ber of low-magnitude impacts that does not initiate in
ammatory response. However,
further explorations are needed to obtain a quantitative correlation.
As can be seen in Figure 6.4, impact-induced expression of IL-1 shows in neurons,
since the IL-1 label colocalizes with the NeuN label that is specic to neuronal cell
bodies. IL-1 is a key mediator of central and peripheral in
ammatory response [97], and
it is often used as a marker to quantify the extent of in
ammation related to traumatic
brain injury [97{99].
87
Chapter 6. Biological Response of Surrogate Brain Tissue
0 4 8 16 32 64
0
0.5
1
1.5
2
Number of impacts N (#)
IL−1β expression level
Figure 6.2 Elevation in expression levels of IL-1 protein in networks after being exposed to
dierent numbers of repetitive impacts using the spring with stiness k
1
and displacement
x
2
[91]
(a)
(b)
Figure 6.3 Expression levels of IL-1 (a) Elevation in expression levels of IL-1 protein (green)
after 64 repetitive impacts using spring with stinessk
1
and displacement x
1
. Networks were
also labeled with microtubule associated protein 2 (MAP-2) and nuclei marker Hoechst. (b)
Even though 4 repeated impacts did not cause any in
ammatory response (p = 0.68, = 0.05),
64 impacts induced a robust increase (p = 0.000097, = 0.05) in IL-1 protein expression
levels in neurons [91]
88
6.2. Rat Mixed Glial Cell Cultures
Hoechst IL-1 NeuN Merge
Figure 6.4 A higher magnication image of a network labeled with a neuron specic neuronal
marker, NeuN (yellow) and IL-1 (red) shows impact induced expression of this proteins in
neurons [91]
6.1.3 Summary
In summary, mice cell cultures were subjected to repeated impact loading. The number
of repeated impacts was varied and the biological response of the networks was quantied
in terms of the expression levels of the in
ammation protein IL-1. A safe number of
impacts was identied which indicates a threshold for the initiation of in
ammation
due to repeated low amplitude impacts. Further, explorations are needed to obtain a
quantitative correlation.
6.2 Rat Mixed Glial Cell Cultures
The second surrogate brain tissue used was a mixed glial cell culture from rat. The pro-
tocols used for the culture and methods to quantify the biological response are presented
rst. Subsequently, the quantication of a host of dierent bio-markers due to impact
loading of the cell culture is presented.
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Chapter 6. Biological Response of Surrogate Brain Tissue
6.2.1 Methods
Animals and Ethics Statement
In-vitro mixed glia cultures were derived from postnatal day 3 (P3) Sprague Dawley rat
pups. The pregnant dams were received on pregnancy day 14 from Harlan Labs. Three
pregnant rats were received for three separate experimental replicates and were individ-
ually housed under standard conditions in the University of Southern California (USC)
vivarium. All procedures were approved by the USC Institutional Animal Care and
Use Committee (IACUC), and animals were maintained following National Institutes of
Health (NIH) guidelines by USC's department of animal resources (DAR).
Cell Culture
In-vitro primary mixed glia cultures comprised of 80% astrocytes and 20% microglia
were originated from the cerebral cortex of P3 rats of both sexes [100]. Brie
y, pups
were chilled prior to decapitation, and brains were removed and placed in chilled (4°C)
Hank's balanced salt solution (HBSS, Thermo Fisher). Subcortical regions and meninges
were removed and 6 cortices were pooled and dissociated via trituration 10 times prior
to adding 15 ml of pre-warmed (37°C) glial media. Glial media was Dulbecco's modied
Eagle's medium/Ham's F12 50/50 Mix (DMEM F12 50/50) supplemented with 10% fetal
bovine serum (FBS), 1% penicillin/streptomycin (pen/strep) and 1% L-glutamine. The
supernatant containing cells was then ltered with 70m cell strainers (Thermo Fisher)
prior to diluting in warm glial media (10 ml per
ask) and dividing into two 75 cm
2

asks
(Sigma-Aldrich) per cortex. Cultures were grown in a humidied incubator (37°C/5%
CO
2
). For secondary cultures, the primary glia were grown for 2.5 weeks to95%
90
6.2. Rat Mixed Glial Cell Cultures
con
uency. To dissociate the cultures, 5 ml of pre-warmed (37°C) trypsin was added
to each
ask for 7-10 minutes, then transferred to a 15 ml falcon tube containing 5 ml
of warm glial media, which neutralizes the trypsin. Each tube was then centrifuged for
10 minutes at 300 g to pellet the cells. The trypsin/media supernatant was removed
and all cell pellets were resuspended in a total of 24 ml of glial media. 2 ml of the
pooled cell suspension was then seeded into each coverslip petri-dish (MatTek Corp.
Glass Bottom Culture Dishes, 35 mm petri dish, 14 mm Microwell, No 1.0 coverglass).
Cells were allowed to settle for 48 hours prior to use for experiments. Experiments were
repeated 3 times.
HAMr Impacts
For impact experiments, cell culture petri dishes were secured in the HAMr apparatus.
Prior to impacts, an additional 2 ml of warm glial media was added to the petri dishes
to ensure that the culture media surface interfaces with the protective aluminum plate
of the HAMr apparatus. Because the cultures must be impacted outside the humidied
incubator, which may potentially stress the cells, a corresponding control culture is
removed from the incubator for an equivalent amount of time. These experiments are
conducted at ambient room temperature (25°C). Impacts are delivered once every 30
seconds, and the mechanical disruption of the cells is captured by a high-speed camera
attached to a 10x Nikon microscope objective lens. The glia networks are subjected to
64 repeated impacts at a frequency of two impacts per minute.
After 64 repeated impacts are delivered to each culture dish, HAMr is cleansed
with 70% ethanol to prevent contamination between subsequent cultures. The culture
media was replaced with 2 ml of glial media and cultures were transferred back into the
incubator for 4 hours.
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Chapter 6. Biological Response of Surrogate Brain Tissue
Immunofluorescence
Four hours after impacts, the media was removed and the cells were washed with phos-
phate buered saline (PBS, pH 7.4) prior to xation with 4% paraformaldehyde for
10 minutes. Cells were then PBS washed and permeabilized with 1% Nonidet P-40
(Sigma). To probe for astrocytic density, the cultures were blocked with 5% normal
goat serum (NGS) for 1 hour before overnight 4°C incubation with mouse anti-GFAP
antibody (1:400, Sigma) diluted in 2% NGS. The immuno
uorescence was visualized
using goat anti-mouse Alexa Fluor 488 secondary antibodies (1:400; Molecular Probes).
4', 6-diamidino-2-phenylindole (DAPI, Vector labs) was used as counterstain for nuclei.
Microscopy and Image Analysis
A Carl Zeiss microscope with a
uorescent camera detector (Zeiss AxioCam MRm) was
used to capture images. Nine images were taken from each coverslip at roughly the
same regions using a 3 3 grid system. Images were then analyzed using ImageJ [101]
software. Each GFAP image was converted to 8-bit prior to thresholding using the Otsu
algorithm for area coverage and integrated density. DAPI images were thresholded by
the Moments algorithm for intensity and nuclei size. Staining intensity was dened as
integrated density divided by total pixels per image.
Quantitative Polymerase Chain Reaction
RNA was extracted by TRIzol reagent (Sigma) for cell homogenization, and 1-bromo-
3-chloropropane (Sigma) for phase separation. cDNA was prepared from 500 ng of
RNA by Goscript reverse transcription system (Promega) and analyzed by qPCR with
92
6.2. Rat Mixed Glial Cell Cultures
appropriate primers for CT (cycle threshold) values. Genes examined by qPCR in-
clude TNF (forward: 5' CGTCAGCCGATTTGCTATCT 3'; reverse: 5' CGGACTC-
CGCAAAGTCTAAG 3'), IL-1 (forward: 5' TCGGGAGGAGACGACTCTAA 3'; re-
verse: 5' GTGCACCCGACTTTGTTCTT 3'), iNOS (forward: 5' CATTGGAAGT-
GAAGCGTTTCG 3'; reverse: 5' CAGCTGGGCTGTACAAACCTT 3'), GFAP (for-
ward: 5' GGTGGAGAGGGACAATCTCA 3'; reverse: 5' CCAGCTGCTCCTGGAGTTCT
3'), S100 (forward: 5' TTGCCCTCATTGATGTCTTCCA 3'; reverse: 5' TCTGC-
CTTGATTCTTACAGGTGAC 3'), CD68 (forward: 5' TTCTGCTGTGGAAATG-
CAAG 3'; reverse: 5' AGAGGGGCTGGTAGGTTGAT 3') and GAPDH (forward: 5'
AGACAGCCGCATCTTCTTGT 3'; reverse: 5' CTTGCCGTGGGTAGAGTCAT 3').
Data were normalized to GAPDH and quantied using the CT method.
Statistical Analysis
Graphpad Prism Version 5 was used to perform Student's unpaired t-tests, with signi-
cance at p< 0:05.
6.2.2 Measurement of Biological Response
Qualitative Assessment of Glial Networks Post-Impacts
Light microscopy (phase-contrast microscopy) of con
uent mixed glia control culture
show standard astrocyte and microglia (brighter cells that lie on astrocyte bedding)
morphology Figure 6.5a. Immediately after 64 impacts, mixed glia cultures show loss of
con
uency and altered morphology. Notably, dark round structures appear within the
cytoplasm of astrocytes. Four hours after impact, cells appear constricted, deformed,
and retracted with an apparent loss of culture density and con
uency Figure 6.5b.
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Chapter 6. Biological Response of Surrogate Brain Tissue
Figure 6.5 Phase-contrast optical microscopy of mixed glia cultures. (a) Representative images
of control mixed glia cultures without impact. (b) Representative images of mixed glia cultures
post-64 HAMr impacts. Left: immediately before returning to incubator after impact period.
Right: 4 hours after impact period. Scale bar = 100 m
Immunocytochemistry
Glial brillary acidic protein (GFAP), a cytoskeletal protein, is a marker of astro-
cyte reactivity to stress that is correlated with traumatic brain injury [102]. Immuno-
cytochemistry was used to assay GFAP intensity as well as astrocytic area coverage.
Although there was no dierence in GFAP integrated density in the cultures, there is
a 45% reduction of GFAP area coverage after impacts Figure 6.6, which corroborates
94
6.2. Rat Mixed Glial Cell Cultures
the light microscopy observations Figure 6.5b. Additionally, DAPI-staining in impacted
cultures show condensed nuclei with 100% increase in
uorescence intensity and 40%
reduction in size compared to controls Figure 6.6c.
Gene Expression Analysis of Cytokines and Glial Markers
To investigate the in
ammatory response, TNF, IL-1, and iNOS mRNA were mea-
sured 4 hours after HAMr impacts. The cytokines TNF and IL-1, but not iNOS were
signicantly increased after impacts compared to respective controls, see Figure 6.7a.
Because glia are frequently activated after injury [103], astrocyte (GFAP and S100)
and microglia (CD68) markers were also measured. However, no changes in mRNA for
glial markers were detected, see Figure 6.7b.
6.2.3 Summary
The stress waves generated by the impact of the metal protective plate simulate the
primary mechanical injury, which resulted in disruption of the glial cellular network
post-impact. Consequences of the repeated impacts were exacerbated with time with
appearance of dark vacuole-like structures, see Figure 6.5, and reduced cell nuclei size, see
Figure 6.6c, that may represent condensation of nuclear chromatin common in apoptotic
cells [104,105].
The drastic reduction of astrocytic density, see Figure 6.6b, could be due to cell
death initiated by excess excitotoxic glutamate release that occurs after brain injury
[106]. Although, astrocytic GFAP area was reduced after impacts, the gene expression
of GFAP, S100, and microglial CD68 mRNA were unchanged, see Figure 6.7b. While
not much is known regarding how these markers change in in-vitro cell culture models of
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Chapter 6. Biological Response of Surrogate Brain Tissue
TBI, in-vivo, GFAP and S100 correlate well with TBI [107,108]. This lack of response
may be a timing issue or even an in-vitro model issue, which lacks systemic inputs that
could in
uence in-vivo responses.
Neuroin
ammatory responses were detected as upregulation of cytokines TNF and
IL-1, see Figure 6.7a. TNF is a secreted or transmembrane cytokine that is implicated
in TBI pathology. Early studies showed variable roles of TNF during brain injury [109],
likely to be related to receptor activation. Deletion of the p55 TNF receptor 1 attenuates
neurobehavioral, histopathological, and apoptotic eects of controlled cortical impact
TBI in mice, while deletion of p75 TNF receptor 2 exacerbates those eects [110]. In
animal models of TBI, TNF rapidly increases within a few hours and is considered
an early mediator of CNS damage [111]. Additionally, TNF can induce apoptosis
via TNFR1 signaling [112]and activate astrocytes and microglia [113]. Like TNF,
IL-1 is also a secretable cytokine. However, the role of IL-1 in TBI is not as well
characterized, but it is known to be induced relatively quickly and is released by neurons
and astrocytes [114]. The elevation of these secretable cytokines may have paracrine
eects on nearby cells.
96
6.2. Rat Mixed Glial Cell Cultures
Figure 6.6 GFAP and DAPI immuno
uorescence of mixed glial cultures. (a) Representative
immunostaining for astrocytic GFAP in controls (CTL) and impacted cultures. GFAP in
green, DAPI in blue. (b) Quantication of relative GFAP intensity by integrated density and
area coverage. GFAP area was reduced from 12% in controls to 7% in impacted cultures. (c)
Quantication of DAPI intensity and nuclei size. In impacted cultures, DAPI intensity was
increased by 100% and nuclei size was decreased by 40% (*, p< 0:05; ***, p< 0:001). n = 3,
3 replicates. Scale bar = 100 m
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Chapter 6. Biological Response of Surrogate Brain Tissue
Figure 6.7 Gene expression of mixed glia cultures. (a) Pro-in
ammatory cytokine mRNA
induction of mixed glia cultures. TNF and IL-1 were both increased 200% and 220%
respectively 4 hours after impacts, while iNOS did not change (*, p < 0:05; **, p < 0:01).
(b) Astrocyte (GFAP, S100) and microglia (CD68) markers did not change with impacts.
n = 3, 3 replicates
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Chapter 7
Towards Models of TBI with Realistic Cytoarchitec-
ture and Geometry
The main drawback of the HAMr model of TBI, as presented up to this point, is the
sti glass substrate at the bottom of the petri dish that supports the two dimensional
cell cultures, for two reasons.
First, the morphology of the cells and the cytoarchitecture of the two-dimensional
culture are very dierent when compared to in-vivo tissues. There have been develop-
ments of in-vitro cell cultures, in which cells are seeded in hydrogels that resemble the
stiness of the extracellular environment of the native environment of these cells [115].
These hydrogels provide a scaold for the cells to grow in the third dimension and mimic
the in-vivo conditions of the cultures with higher delity, thus presenting a potentially
more realistic brain surrogate model that can be employed in in-vitro TBI models. An
example of using such a surrogate brain tissue in an in-vitro TBI model has been pre-
sented by LaPlaca et al. [83].
Second, the mechanical deformation of the cell culture is dictated by the sti glass
substrate at the bottom of the petri dish that these cells are adhered to. For example,
in the HAMr model the pressure pulse applied to the liquid bath in the petri dish has
a 20 s duration. This pressure pulse travels through the liquid substrate and loads
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Chapter 7. Towards Models of TBI with Realistic Cytoarchitecture and Geometry
the glass bottom of the dish. The mechanical response of the glass substrate due to
this pressure pulse loading can be thought of as an impulse response. It is dictated
by the material and geometric properties of the glass plate as well as the constraining
boundary conditions that keep the glass attached to the rest of the petri dish. Looking
at Figure 5.5, we observe that the frequency of oscillation of the substrate is independent
of the strain amplitude level, which indicates that the glass substrate is vibrating at the
natural frequency of the system which is a strong function of the material properties of
the very sti glass substrate as mentioned earlier.
In what follows we present two separate approaches to move beyond these 2D cell
cultures adhered at the glass-bottom of the imaging dishes. First, an extension of the
HAMr model that uses a hydrogel construct in a petri dish is presented. Then, a more
realistic physical head model lled with hydrogel as the brain simulant is proposed and
some preliminary results are shown.
7.1 Quantication of Deformation in the Mid-Layer of a 3D
Hydrogel During Pressure Pulse Loading
Ballistic gelatin, which is an alternative brain surrogate tissue widely used in the biome-
chanics community, was also explored using the HAMr model of TBI. Gelatin, Matrigel
©
,
has lately been used as a matrix to grow cell cultures in the third dimension [83, 115].
Therefore, the feasibility of quantifying the deformation experienced by a square gelatin
block, show in Figure 7.1 at a predetermined interior plane by using DIC is presented
here. In particular the deformation eld was quantied at the mid-section plane of the
ballistic gelatin block.
100
7.1. Quantication of Deformation in the Mid-Layer of a 3D Hydrogel During Pressure Pulse Loading
Figure 7.1 Ballistic gelatin hydrogel block (Left) Gelatin block positioned at the bottom of the

uid-lled petri dish, (Middle) overall dimensions and thickness of gelatin block and speckle
pattern at the mid-section of the gelatin, (Right) Field of view of the high-speed camera looking
at the gelatin block sample
The ballistic gelatin used was a Gelita
®
powder (250BL Type A Ordnance Gelatin).
A 10% by weight ballistic gelatin powder was mixed with water at room temperature
(25° C) and stirred gently in order to avoid entrapping air while wetting the powder
particles. The mixture was hydrated at room temperature for two hours before heating
to 60°C. After the gelatin particles were completely dissolved, a bottom layer of ballistic
gelatin solution (10% by weight) was poured into a mold with an approximate thickness
of 1 mm. It was then cooled in a refrigerator for about 8 hours. A random pattern was
then created on top of the surface by abrading pencil-graphite with a knife-edge, before
pouring a second layer of the same consistency of gelatin solution of approximately
1 mm thickness, a top view is shown in Figure 7.2a. The two-layered gelatin, with the
mid-section random pattern was then refrigerated overnight for about 20 hours before
experiments were conducted.
The deformation history at the mid-layer of a gelatin block, which was situated at the
glass-bottom substrate of the petri dish, was quantied using high-speed DIC. Graphite
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Chapter 7. Towards Models of TBI with Realistic Cytoarchitecture and Geometry
Figure 7.2 Dynamic strain quantication on mid-section plane of ballistic gelatin block. (a)
Parallelepiped gelatin with graphite particles in the mid-section of the gelatin block used as
the random pattern markers for Digital Image Correlation under high-speed imaging (Framing
rate 25,000 fps, 512 px 512 px, gelatin thickness 2.84 mm, eld of view 5 mm 5 mm),
(b) Black line is showing the mean strain versus time at the mid-surface of a gelatin block
structure along the x-direction. Gray dashed lines are the strain proles of 3 separate runs
particles in the mid layer of this 2.8 mm thick gelatin block were used as markers and
tracked using a DIC algorithm. In Figure 7.2, the in-plane strain vs time is plotted. It
can be observed that the frequency of oscillation of this gelatin surface is much lower
compared to the glass substrate, due to the dierence in mechanical properties and
boundary conditions of the two dierent materials. Moreover, the results shown below
are obtained using the soft spring, k = 278 N/m, and the strain level for the same
pressure pulse loading is almost four times larger compared to the strain amplitude of
the glass substrate. This was expected since glass is a lot stier than gelatin. The
maximum strain measured is 916 m/m, and the average strain rate going from zero
strain to the rst peak of the strain pulse is =t = 4s
1
. The strain eld was uniform
across the eld of view (5 mm 5 mm) with a standard deviation for the strain equal
to 81 m/m. The period of oscillation is 1 ms, and as time progresses the oscillations
102
7.2. Models of TBI with Realistic Geometries and Dimensions
are dampened and eventually die out.
It is arguably accepted in the TBI community that in-vitro models utilizing 3D cell
cultures compared to the traditional 2D cell monolayers used, might represent the in-
vivo environment that they are trying to mimic more accurately [115]. Therefore, in
the proposed model of TBI, HAMr, the strain eld experienced at the mid-layer plane
of a 2 mm thick gelatin structure was quantied, see Section 7.1. Cells can be seeded
in such hydrogels in order to grow networks in the third dimension. In the experiments
presented here, the hydrogels were not seeded with cells but the feasibility of obtaining
the dynamic deformation history of an interior plane of such hydrogels is shown. The
dynamic response in terms of the strain history of this mid-layer of the gelatin was
quantied. The average strain rate obtained was 4 s
1
, which lies in the same range
that is believed to occur during mild-TBIs [94].
7.2 Models of TBI with Realistic Geometries and Dimensions
The timescales of the transient stress waves produced by an impact to the skull depend
on the material properties, the dimensions and geometry of the skull-brain system.
Therefore, in order to accurately mimic the transient response characteristics of the
dynamic loading we should use a model with realistic geometry and dimensions. Here
we developed a simplied skull model which is a spherical/cylindrical acrylic shell and
quantied the response of this skull model by using two dierent types of surrogate brain
tissues. The average dimension of the human brain is around 150 mm and the thickness
of the skull varies between 3 - 7 mm. Therefore, the acrylic shell used to model the
skull had a diameter of 150 mm and 6 mm thickness. The experimental setup utilized a
simple physical pendulum to produce the impact, as shown in Figure 7.3.
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Chapter 7. Towards Models of TBI with Realistic Cytoarchitecture and Geometry
Electromagn
Striker
Pendulum
Rig
Rail
Hybrid III
50th neck
dummy
Physical
Head
Model
Sensor
Ports
Figure 7.3 chematic of experimental setup of the physical pendulum producing the impact
load onto the physical head model. An electromagnet arrangement on two linear stages is
used in order to control the initial de
ection of the pendulum. The striker used can be varied
to produce dierent impact magnitudes. The head model has ports for attaching sensors at
dierent locations of the \skull".
7.2.1 Spherical Acrylic Shell Filled with Water
First, the transient pressure pulse inside the skull model was explored by using water as
the surrogate brain tissue. The impact force history and pressure response was quantied
at dierent locations around the perimeter of the skull. In particular the dynamic
pressure characteristics of two qualitatively dierent impact force histories was explored.
In particular the pressure response due to a load with long impact duration compared
to the duration of the rst transient stress pulse was explored and compared against the
response due to a load with an impact duration in the same order of magnitude as the
duration of the transient pulse, around 100 s, shown in Figure 7.4.
The total mass of the
uid lled \skull" is 1910 g. An 8.4 g spherical steel striker
released from an initial de
ection angle
4
= 46

, produces an impact of 300 N force
104
7.2. Models of TBI with Realistic Geometries and Dimensions
Figure 7.4 Impact response of a spherical \skull" model lled with water. (Top row) Impact
force histories for two dierent strikers and initial de
ection angles. Impact velocities were
measured using a high-speed camera, and force histories using a piezoelectric force sensor
(Piezotronics, PCB200B05). Impact duration varies for the two dierent strikers. (Bottom
row) Pressure histories (Piezotronics, PCB113B21) at dierent locations around the perimeter
of the skull
amplitude and 100 s duration. The impact velocity was measured with a high-speed
camera to be 2.25 m/s. The impact force duration achieved with this striker is on the
same order of magnitude as the duration of the rst transient stress pulse to reach the
opposite end of the skull. The impact force duration using a 270 g striker is 2 ms, almost
20 times longer than the rst transient pulse. The force amplitude achieved with this
striker when released from an initial de
ection angle
2
= 23

, is the same as the impact
produced by the lighter striker.
Here we are interested in studying the pressure histories of the contents of the skull
for the two dierent loading situations. The response of this system was studied for
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Chapter 7. Towards Models of TBI with Realistic Cytoarchitecture and Geometry
loading durations ranging from approximately one to ten times the interval required
for the rst disturbance to reach the opposite pole of the shell. Pressure histories were
probed at three separate locations around the perimeter of the skull, at 45

, 135

, and
180

from the impact point. The pressure histories are qualitatively dierent. The most
striking dierence is the large transients associated with the pressure histories produced
by the short impact duration. At 45

we observe a positive pressure pulse followed by a
negative (tensile) pressure pulse of similar magnitude. This transient characteristic from
positive to negative pressures is not observed for longer impact durations. It is worth
noting that on the opposite side of the impact, at 180

the pressure history reverses
sign, meaning that we observe a negative (tensile) pressure. These ndings corroborate
with the physical head model proposed by Kenner et al. [58] in which they observed
that \a negative pressure of nearly the same magnitude as that of the compressive peak
is transmitted immediately following the initial disturbance". They attributed this to a
snapback of the shell and they also observed that it is prominent for the short impact
duration case. The ndings here are also in good agreement with the computational
studies by Young et al. [116] where they also observed large negative pressures developing
for the short impact durations studies they conducted. These negative pressures may
correlate with the experimental ndings of cavitation bubble collapse that may cause
damage of brain tissue at sites close to and opposite to the site of impact.
7.2.2 Cylindrical Acrylic Shell Filled with Ballistic Gelatin
In order to quantify the induced strain elds of the surrogate brain tissue enclosed by
the \skull" cavity, a thin cylindrical model of the skull was utilized, with a 150 mm
diameter and 6 mm thickness. This model was lled with ballistic gelatin, which served
106
7.2. Models of TBI with Realistic Geometries and Dimensions
as the surrogate brain tissue. Full-eld deformation elds due to impact loading on
this brain-skull physical model were quantied on the interior mid-plane surface of the
gelatin. A random speckle pattern was created at the mid-surface plane of the ballistic
gelatin construct, as can be seen in Figure 7.5.
Figure 7.5 Cylindrical acrylic skull model (Left) Schematic of cylindrical skull, (Right) Cylin-
drical skull lled with gelatin, mid-layer marked with a random speckle pattern to be used for
DIC purposes
The model was impacted from the left side. The striker used was a 40 mm diameter
steel spherical steel ball, and was released from an initial de
ection angle
2
. The
impact event was captured using a high-speed camera (Phantom V711) at a framing
rate of 13,000 fps and digital image correlation algorithms were employed to quantify
the full-eld dynamic deformation elds produced by the impact on the gelatin surrogate
brain tissue.
We observe that close to the point of impact the normal horizontal component of
the strain starts as a compressive pulse and immediately transitions to a tensile pulse,
oscillating back and forth between tension and compression, see Figure 7.6(a). As we
move away from the point of impact, Figure 7.6(b), the strain amplitude decreases but
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Chapter 7. Towards Models of TBI with Realistic Cytoarchitecture and Geometry
the pulse remains quantitatively similar up until the mid-section of the \head" model.
As can be seen in Figure 7.6(c), the strain around the mid-section of the model goes to
zero.
Moving further away from the point of impact, Figure 7.7(a), the strain response
reverses sign and the rst pulse is tensile followed by compression. The amplitude of the
strain increases as we move further downstream from the point of impact and reaches a
maximum tensile value at the opposite end of the \skull", see Figure 7.7(b).
Regions of maximum deformation are found to be located immediately close to the
point of impact and exactly opposite to the side of impact. Under the assumption
that regions of the brain that experience maximum deformation would be the most
susceptible regions to injury, we can use the information gained from the full-eld strain
measurement to identify \hot pockets" of strain in which injury might be more likely to
occur. Moreover, we can extend these models by seeding the hydrogel with cells in these
regions of maximum strain and observe the biological response of these 3D-cultures due
to the dynamic strain elds produced by the impact loading.
These preliminary results show that the physical model of TBI presented in this
section agrees with pathological ndings of coup and contre-coup injuries [117], close
to the site of impact and exactly opposite to the site of impact. Moreover, with the
introduction of cells seeded in hydrogel scaolds in regions of maximum strain one can
convert these physical models to hybrid in-vitro models which can be used to study
the biological response of the cells to mechanical deformation loadings that mimic the
transient stress wave reverberations with high delity.
108
7.2. Models of TBI with Realistic Geometries and Dimensions
(a)
(b)
(c)
Figure 7.6 Strain history along the horizontal direction,
xx
(t), at dierent cross sections of
the model captured at 13,000 fps, (a) at 10%, (b) at 30% and, (c) at 50% distance from the
impact point 109
Chapter 7. Towards Models of TBI with Realistic Cytoarchitecture and Geometry
(a)
(b)
Figure 7.7 Strain history along the horizontal direction,
xx
(t), at dierent cross sections of the
model captured at 13,000 fps. (a) Average strain versus time along red line at 70% distance
from the impact point, (b) Average strain versus time along red line at 90% distance from the
impact point
110
Chapter 8
Conclusions and Future Research
In conclusion, HAMr, a novel in-vitro model for low-amplitude repeated blunt-impact
induced TBIs was presented. In this model the rate dependence of the brain tissue
response was accounted for, by using cell cultures grown in a dish as the surrogate
tissue and by applying the input loading through a dynamic impact. Moreover, this
model allowed the quantication of the mechanical stimulus as well as the mechanical
and biological response of the surrogate tissue, providing access to the full spectrum of
the injury. In particular, it enabled a connection between the cause, i.e. mechanical
stimulus, and the eect, i.e. deformation history and biological response. To the best of
our knowledge, this is the rst in-vitro model that allows the quantication of all three
relevant aspects of TBIs under realistic loading conditions.
The in-vitro model presented here, would be comparable to the in-vivo repetitive
closed-head modied controlled cortical impact injury [118{120], which encapsulates
the neurobehavioral spectrum and histopathologic markers of chronic traumatic en-
cephalopathy (CTE). Although the quantication of behavioral outcomes and post-
mortem biomarkers is feasible in in-vivo models of TBI, the quantication of brain
tissue deformation is most of the time not realizable, since the optically opaque skull
encloses and blocks optical access to the brain. However, there have been a few attempts
that quantied the strain elds in the rat brain using MRI [121] or high-speed biplanar
111
Chapter 8. Conclusions and Future Research
X-ray measurements of a small number of radio-opaque markers embedded in physical
models of TBI using cadaver brains [72]. The caveat is that the temporal resolution
(approximately 3.9 ms) for the MRI study is not adequately fast to capture the tran-
sient deformations due to impact events [121], which may cause an underestimation of
the occurring strain level. On the other hand the temporal resolution of the biplanar
X-ray measurements is suciently high but the spatial resolution is limited to the nite
number of markers used [72].
Alternatively, in-vitro models oer the advantage of making the quantication of
the mechanical response of the brain surrogate tissues attainable. For the design and
implementation of an experimental model of TBI some fundamental facts of brain injury
occurrences need to be taken into account. It is well known that the vast majority of the
injuries occur under dynamic loading events, i.e. impacts, with a negligible percentage
of those injuries occurring due to a semi-static loading [9]. Moreover, the mechanical
properties of brain tissue and individual cells have been studied extensively and it has
been shown that they exhibit nonlinear viscoelastic mechanical behavior [23], which
manifests as time dependent mechanical behavior. In other words, brain tissue would
deform dierently if a load with the same amplitude were to be applied at a slow rate
compared to a higher rate. High rate loading occurs under impact loading conditions.
Stretch injury models [79{81], and shear strain models [82, 83, 122], that either char-
acterize the deformation of the substrate or/and the tissue, at strain rates thought to
occur during TBIs, are invaluable tools, but these models lack the delity of modeling
closed-head impact induced TBIs since they are applying the strain by directly deform-
ing the substrate or the surrogate brain tissue, thus characterized as strain controlled
models. The levels of strains and strain rates that some of these models can achieve
112
can be widely varied, and they are informed by predictions of macroscopic loads from
numerical simulations or physical models for the deformation amplitudes expected for
dierent types of injury scenarios. Although this strain level variation is very useful, still
the condence in strain levels and strain rates obtained from numerical simulations and
physical models is not high, since the experimentally obtained mechanical properties of
brain tissue used to construct constitutive relations show huge disparities between dier-
ent studies, as described in Section 2.2. Compression models, weight-drop and impactor
methods, directly deform the tissue through contact forces but both applied force and
tissue deformation are hard to quantify [75].
In the in-vitro model described herein, experimental challenges arose due to the
short timescales, in the order of milliseconds, associated with impact as well as due to
the short length-scale and spatial constraints caused by the microscopic nature of the
cell cultures. But it was concluded that there was no viable alternative that would
circumvent the described challenges due the fundamental constraints imposed by our
understanding of the injurious event. Moreover, the premise that the biological response
due to a traumatic event is correlated to the mechanical deformation and disruption of
the tissue, renders the debate of applying the load quasi-statically obsolete, since the
deformation obtained under slow rate loading will not be indicative of the high loading
rate events that prevail in TBI occurrences. The HAMr model is a valuable addition
to the arsenal of in-vitro TBI modeling tools, since it provides a high-delity model for
repeated blunt-impact induced TBIs, with controlled mechanical input and capabilities
of quantifying both the mechanical and biological response of the brain surrogate tissue
used.
HAMr manages to capture the loading and mechanical characteristics of impact
113
Chapter 8. Conclusions and Future Research
induced brain injury according to the 1D hierarchical model shown in Figure 4.1 and
4.2. The stress pulse produced by the impact eventually deforms the cells and the glass
substrate that supports them. In the case where this mechanical deformation exceeds
the ultimate stretch/shear limits of the cells, it causes mechanical failure of the cell
tissue, i.e. fracture and tearing of the cells, which corresponds to an invasive wound or a
severe TBI event. Evidence suggests that the deformation of the cells needs not exceed
the ultimate stretch/shear limit of the cells before a biological reaction to this agitation
initiates [123]. From a qualitative point of view and after observing that the cells remain
adhered to the glass substrate during the loading event, it is fair to condently assume
that the cells follow the substrate as it deforms. By DIC and high-speed photography,
the strain rates attained in this study ware determined to be between 3-15 s
1
, which
is in the range of strain rates expected to occur in mild-TBIs [83,94].
A host of dierent bio-markers that have previously been shown to relate to TBIs
were explored. Evidence of initiation of cell death was observed, and a threshold number
of \safe" impacts before initiation of in
ammation was detected. The biological response
quantication gives another dimension for exploration of the TBI event, with potential
applications in better diagnostic tools and therapeutic targets.
A natural extension of this research should include realistic geometries. Since the
main premise of studying the bio-mechanics of brain injury, is that primary injury is due
to excessive deformation of the tissue, replicating the geometric and boundary conditions
of a realistic human head is imperative for the faithfulness to the mechanics of the
problem. In the past decade new protocols that allow for cell-cultures that can grow
in the third dimension, in contrast to the traditional 2D monolayer cultures used so
far, give the
exibility of embedding tissues in dierent geometries that resemble the
114
cytoarchitecture and general morphological characteristics of a realistic human head.
In that way the dynamic characteristics of the transient waves inside the skull can
be properly modeled. The wave reverberations depend on the geometry and material
properties of the system, and can only be captured accurately by using models with
realistic dimensions and surrogate tissues that mimic the properties of the tissue of
interest, such as cells embedded in hydrogel matrices or organotypic cell cultures.
At this point a reasonable question may arise: Did the current model conclusively
identify thresholds of injury and quantitative diagnostic bio-markers? Unfortunately, the
answer to this question is no. But it is our hope that the TBI community will embrace
this model for the reasons described up to this point. Moreover, it is our belief that
further utilization of this new model of TBI will enhance our understanding on the causes
of brain injuries and will aid towards a direction of quantifying injury thresholds and
identifying diagnostic bio-markers. Future applications may include improved protective
gear designs and the development of therapeutic options for TBIs. We do not claim that
HAMr is the silver bullet to the complex problem of TBIs and we recognize that every
model has advantages and disadvantages. But the aforementioned accomplishments
can only happen by acting synergistically with other modeling eorts to elucidate the
intricate details of TBIs.
115
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Abstract (if available)

Abstract The brain is arguably the most complex organ in the human body. Its basic building blocks are cells. Like any other organ in the human body, the brain can be injured. Traumatic brain injury (TBI) is defined as an alteration in brain function or other evidence of brain pathology due to an external force. The incidence of TBIs and the corresponding societal impact and cost are enormous. TBIs can be classified as mild, moderate, and severe based on clinical criteria, e.g. the Glascow Coma Scale. There is no better prognostic measure other than these clinical criteria. But these classification systems have limitations. This fact, along with the increased awareness in the long term consequences of mild-TBIs, that often times are not reported or remain untreated, makes the development of quantitative biological objective measures to diagnose TBIs crucial. ❧ TBI is a bio-mechanical event, in which the cause is mechanical, e.g. impact force, and the response is both mechanical, e.g. deformation of brain tissue, and biological, e.g. inflammation and cell death of biological tissue. Under the premise that excessive tissue deformation, due to the mechanical stimulus, is the main cause of injury, we designed a TBI model that is able to probe all relevant aspects of a TBI event. ❧ Along this line of argument in this thesis a novel in-vitro model of TBI is presented. Specifically, low magnitude repeated blunt-impact loads, that would correspond to sub-concussive injuries, are studied. The surrogate brain tissue used in the model is cell cultures grown in a petri-dish, a monolayer of brain cells adhered at the glass-bottom of the dish. The model of injury supplies an impact load to a simplified bio-mimetic head model. The mechanical stimulus is controlled and quantified and the subsequent mechanical and biological response of the surrogate brain tissue is monitored. A quantitative correlation between the cause, e.g. impact force, and the response of the tissue in terms of mechanical deformation experienced and biological response is drawn. A safe number of impacts that do not initiate an inflammatory response of the biological tissue is identified, and the biological response to a well determined input stimulus and mechanical deformation history is explored in terms of a host of potential injury bio-markers. New directions of application of the proposed TBI model are further explored in terms of alternative surrogate tissues, such as hydrogels seeded with cells, that represent the mechanics of the brain tissue deformation more appropriately.

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Asset Metadata

Creator Koumlis, Stylianos (author)

Core Title An experimental model of blunt-impact induced traumatic brain injuries

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Mechanical Engineering

Publication Date 07/24/2017

Defense Date 06/09/2017

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag brain,cell,cell culture,concussions,HAMr,impact,in vitro,injury,mild,Model,OAI-PMH Harvest,repeated,TBI,traumatic brain injuries,traumatic brain injury

Format application/pdf (imt)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Eliasson, Veronica (committee chair)

Creator Email koumlee@gmail.com,koumlis@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c40-412466

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