An Anatomically Representative Atlas-Based Finite Element Model … · 2017. 8. 24. · An...

An Anatomically Representative Atlas-Based Finite Element Model of

the Human Brain for Studying Brian Injury Biomechanics:

Development, Validation and Comparison to Existing Models

By

Logan E. Miller

A Thesis Submitted to the Graduate Faculty of

VIRGINIA TECH – WAKE FOREST UNIVERSITY

SCHOOL OF BIOMEDICAL ENGINEERING & SCIENCES

In Partial Fulfillment of the Requirements

for the Degree of

MASTER OF SCIENCE

Biomedical Engineering

August 2015

Winston-Salem, North Carolina

Approved by:

Joel D. Stitzel, PhD, Advisor, Chair

Examining Committee:

F. Scott Gayzik, PhD

Ashley A. Weaver, PhD

ii

ACKNOWLEDGEMENTS

First, I would like to thank my advisor, Dr. Joel Stitzel for your guidance and support

throughout my graduate school experience. Thank you for your motivation, encouragement and

for creating an environment that fosters academic growth and exploration. I value your example

as a mentor, teacher, and researcher and I feel fortunate for the opportunity to learn from you.

I would also like to thank Jill Urban. Your feedback and advice have truly enriched my

experience at Wake over the past two years. I attribute much of my academic development to

your guidance and am extremely grateful. Also, I want to thank Dr. Ashley Weaver and Dr. Scott

Gayzik for serving on my committee.

I am thankful for all those who have inspired me throughout my academic career. I thank

Dr. Jake Socha, who introduced me to research as an undergraduate student. I am grateful for

your encouragement, advice and enthusiasm for science. Your example as a scientist and mentor

was instrumental in my decision to pursue a career in research. Thank you to Pat McGrath, my

high school calculus teacher, who shared my love for math and stimulated my love for learning

and pursuit of knowledge. Also, thank you to Adam Golman for being an excellent mentor when I

was a summer intern at Wake Forest. Your willingness to teach and your advice throughout that

summer were crucial to the satisfaction I felt after that internship and to my desire to return to the

lab as a graduate student.

I also would like to thank my peers in the Center for Injury Biomechanics for your

support and collaboration. I am grateful for the opportunity to work with and learn from everyone

in the CIB.

Finally, I’d like to thank my family for their endless support. Thank you to my parents for

inspiring a love of science and providing me with a wonderful education. And thank you to my

brother for being my first friend and remaining a wonderful one today.

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TABLE OF CONTENTS

Acknowledgements ........................................................................................................... ii

Table of Contents ............................................................................................................. iii

List of Tables .................................................................................................................... vi

List of Figures .................................................................................................................. vii

CHAPTER I: INTRODUCTION & BACKGROUND ................................................. 1

Background and Significance .......................................................................................... 1

Anatomy of the Human Head .......................................................................................... 3 Scalp ........................................................................................................................................... 3 Skull ........................................................................................................................................... 3 Meninges .................................................................................................................................... 4 Cerebrospinal fluid (CSF) ........................................................................................................ 5 Brain .......................................................................................................................................... 6 Cerebral Vasculature ............................................................................................................... 8

Mechanical Properties of Brain Tissue ........................................................................... 8 Creep Tests ................................................................................................................................ 9 Relaxation Tests ........................................................................................................................ 9 Shear Relaxation Tests ........................................................................................................... 10 Dynamic Mechanical Analysis ............................................................................................... 11

Mechanical Response to Impact .................................................................................... 12 Cadaver data ........................................................................................................................... 13 Animal data ............................................................................................................................. 14 Volunteer data ......................................................................................................................... 14

Biomechanics of Brain Injury ........................................................................................ 16 Positive Pressure ..................................................................................................................... 16 Negative Pressure.................................................................................................................... 16 Pressure Gradients ................................................................................................................. 17 Rotation ................................................................................................................................... 17

Head Injury Criteria....................................................................................................... 18 Gadd Severity Index (GSI) .................................................................................................... 18 Head Injury Criterion (HIC) ................................................................................................. 19 Head Impact Power (HIP) ..................................................................................................... 19 Brain Rotational Injury Criterion (BRIC) ........................................................................... 20

Finite Element Modeling of the Human Head ............................................................. 20 Model Geometry ..................................................................................................................... 20 Constitutive Models for Brain Material ............................................................................... 22

iv

Brain-Skull Interface .............................................................................................................. 23 Validation ................................................................................................................................ 24 Review of Finite Element Models of the Human Head ....................................................... 25

Chapter Summaries ........................................................................................................ 33 Chapter II: Development and Validation of an Atlas-Based Finite Element Brain Model

.................................................................................................................................................. 33 Chapter III: Comparison of Validation Data for Finite Element Models of the Human

Head ......................................................................................................................................... 33 Chapter IV: Summary of Research ...................................................................................... 33

References ........................................................................................................................ 34

CHAPTER II: DEVELOPMENT AND VALIDATION OF AN ATLAS-BASED

FINITE ELEMENT BRAIN MODEL .......................................................................... 41

Abstract ............................................................................................................................ 42

1 Introduction .................................................................................................................. 43

2 Methods ......................................................................................................................... 45 2.1 Brain Material Optimization ........................................................................................... 48 2.2 Experimental Tests ........................................................................................................... 49 2.3 Model Performance .......................................................................................................... 51 2.4 Falx Material Optimization ............................................................................................. 52 2.5 Data Analysis ..................................................................................................................... 52

3 Results ........................................................................................................................... 53 3.1 C755-T2 ............................................................................................................................. 55 3.2 C383-T1 ............................................................................................................................. 55 3.3 C291-T1 ............................................................................................................................. 56

4 Discussion...................................................................................................................... 58 4.1 Limitations ........................................................................................................................ 64 4.2 Future Work...................................................................................................................... 65

5 Conclusion .................................................................................................................... 66

6 Acknowledgements ...................................................................................................... 68

References ........................................................................................................................ 69

CHAPTER III: COMPARISON OF VALIDATION DATA FOR FINITE

ELEMENT MODELS OF THE HUMAN HEAD ....................................................... 72

Abstract ............................................................................................................................ 73

v

1 Introduction .................................................................................................................. 74

2 Methods ......................................................................................................................... 78 2.1 FEM Description and Comparison ................................................................................. 79 2.2 Validation against localized brain displacements .......................................................... 85 2.3 Model Performance .......................................................................................................... 88

3 Results ........................................................................................................................... 89

4 Discussion...................................................................................................................... 98 4.1 C755-T2 Occipital Impact ................................................................................................ 99 4.2 C383-T1 Frontal Impact ................................................................................................ 101 4.3 C291-T1 Parietal Impact ................................................................................................ 102 4.4 Overall Performance ...................................................................................................... 105

5 Conclusion .................................................................................................................. 106

6 Acknowledgements .................................................................................................... 108

References ...................................................................................................................... 109

Appendix. Model Development................................................................................ 10913

CHAPTER IV: SUMMARY OF RESEARCH .......................................................... 115

Scholastic Vita ............................................................................................................... 116

vi

LIST OF TABLES

Table 1. Material Properties of the ABM ......................................................................... 47

Table 2. Parameter Ranges for Latin Hypercube Sample ................................................. 48

Table 3. Summary of Experimental Test Conditions........................................................ 50

Table 4. Material Properties from each experimental configuration optimization ........... 54

Table 5. Comparison of FEMs .......................................................................................... 85

Table 6. CORA Scores for each model for all experimental configurations .................... 98

Table 7. Publication plan for research outlined in this thesis ......................................... 115

vii

LIST OF FIGURES

Figure 1. Percentage of annual TBI (combined emergency department visits,

hospitalizations, and deaths) by external cause [2]. ............................................................ 1

Figure 2. (A) External view of the human skull [9] and (B) the base of the cranial cavity

[10]. ..................................................................................................................................... 4

Figure 3. View inside the skull showing the protruding portions of the dura mater - falx

cerebri and tentorium cerebelli [9]. ..................................................................................... 5

Figure 4. The meningeal membranes in a coronal cross section ........................................ 5

Figure 5. T2-weighted MRI scan of a normal head. CSF is depicted as light gray, gray

matter is darker gray, and white matter is darkest. ............................................................. 6

Figure 6. (A) Internal structures of the human brain and (B) the four lobes of the

cerebrum. ............................................................................................................................ 7

Figure 7. Corpus callosum [9]. ........................................................................................... 7

Figure 8. Distribution of cerebral arteries on the base of the brain [9]. .............................. 8

Figure 9. In vitro relaxation moduli versus time from the literature [21]. ........................ 10

Figure 10. (A) Storage and (B) loss moduli of brain tissue from the literature of in vitro

dynamic frequency sweep tests in shear [21]. .................................................................. 11

Figure 11. Comparison of thresholds determined from various animal data [39, 40, 41]. 14

Figure 12. Combined probability of concussion contours relating concussion risk to linear

and rotational head acceleration [42]. ............................................................................... 15

Figure 13. Equivalent stress fields for models with varying geometries under the same

boundary conditions showing stress concentrations in the heterogeneous models [61]. .. 21

viii

Figure 14. (A) Direction of impact in experiment conducted by Nahum et al. [31] and

(B) locations of pressure measurements. .......................................................................... 24

Figure 15. (A) Skull model, (B) brain model, (C) section view of the KTH head and neck

model [65], and (D) cross section showing FE mesh and anatomical structures

represented in the KTH model [65]. ................................................................................. 26

Figure 16. Various versions of the WSUHIM. (A) The original model developed by Ruan

et al. [67], (B) the improved model with gray and white matter differentiation [70], and

(C) the current version of the model [69]. ........................................................................ 27

Figure 17. Overview of the head model developed by TUE [72]. .................................... 28

Figure 18. (A) Isometric view of the THUMS v4.01 head model with the brain exposed

and (B) midsagittal view of the FEM. .............................................................................. 29

Figure 19. (A) Isometric view of the GHBMC head model with the brain exposed and (B)

midsagittal view of the FEM [74]. .................................................................................... 30

Figure 20. Overview of the ULP head model [77]. .......................................................... 30

Figure 21. (A) Skull, (B), brain, (C), and sagittal cross section of the UCDBTM. .......... 31

Figure 22. (A) Isometric view of the SIMon FEM with exposed brain and (B) isometric

view of the FEM showing various anatomical features represented in the model. .......... 32

Figure 23. ABM showing the falx, tentorium, and ventricles .......................................... 47

Figure 24. Cross sections of ABM. (a) axial, (b) sagittal, (c) coronal, (d) axial isometric

........................................................................................................................................... 47

Figure 25. Approximate cross-sectional planes where NDT columns are located for each

experimental test (a), locations of NDTs in the XZ plane on the right side of the brain (b),

and locations of NDTs in the XZ plane on the left side of the brain (c) ........................... 49

ix

Figure 26. Relationships between CORA and brain material parameters from brain

parameter variations in three experimental configurations (using the original falx model

in all variations). The simulation with the highest CORA value for each individual impact

condition is highlighted..................................................................................................... 54

Figure 27. CORA relationships with falx pretension (a) and falx thickness (b) for the

C291-T1 impact ................................................................................................................ 55

Figure 28. Relationship between CORA and shear modulus, G0, for material

optimizations in occipital (a), frontal (b), and parietal (using optimized falx model) (c)

impact configurations. The simulation representing the optimal material model for each

condition optimized individually is shown (C755*, C383*, C291*), as well as optimized

concurrently (ALL*) ......................................................................................................... 56

Figure 29. Displacement results and individual CORA scores for the optimized material

properties for Hardy C755-T2 occipital impact for anterior (A) and posterior (P) NDT

columns ............................................................................................................................. 57


properties for Hardy C383-T1 frontal impact for anterior (A) and posterior (P) NDT

columns ............................................................................................................................. 57


properties for Hardy C291-T1 lateral impact for the anterior (A) and posterior (P) right

(R) and left (L) columns ................................................................................................... 58

Figure 32. (A) Sagittal and (B) coronal cross sections of the FEM developed by Hosey

and Liu [9] in 1981. .......................................................................................................... 75

Figure 33. Relaxation moduli versus time from the literature [15]. ................................. 76

x

Figure 34. (A) ABM showing the falx, tentorium, and ventricles, and (B) axial, (C)

sagittal, (E) coronal, (D) isometric cross sections. ........................................................... 79

Figure 35. (A) Isometric view of the SIMon FEM with exposed brain and (B) isometric

view of the FEM showing various anatomical features represented in the model. .......... 80


midsagittal view of the FEM [36]. .................................................................................... 81

Figure 37. (A) Isometric view of the THUMS v4.01 head model with the brain exposed

and (B) midsagittal view of the FEM. .............................................................................. 82

Figure 38. (A) Section view of the KTH head and neck model [28], and (B) cross section

showing FE mesh and anatomical structures represented in the model [12]. ................... 83

Figure 39. (A) Isometric view of the DHIM FEM and (B) isometric view of the FEM

showing various anatomical features represented in the model [48]. ............................... 84

Figure 40. Velocity load curves for the three experimental configurations. .................... 87

Figure 41. Approximate NDT locations in ABM, SIMon, GHBMC, and THUMS models

for C755-T2 occipital impact (A), C383-T1 frontal impact (B) and C291-T1 parietal

impact (C). ........................................................................................................................ 88

Figure 42. Linear velocity at head CG for ABM, SIMon, GHBMC, and THUMS

simulations. ....................................................................................................................... 90

Figure 43. Local displacement results for Hardy C755-T2 occipital impact for the anterior

NDT column. .................................................................................................................... 91

Figure 44. Local displacement results for Hardy C755-T2 occipital impact for the

posterior NDT column. ..................................................................................................... 92

xi

Figure 45. Local displacement results for Hardy C383-T1 frontal impact for the anterior

NDT column. .................................................................................................................... 93

Figure 46. Local displacement results for Hardy C383-T1 frontal impact for the posterior

NDT column. .................................................................................................................... 94

Figure 47. Local displacement results for Hardy C291-T1 parietal impact for the right


Figure 48. Local displacement results for Hardy C291-T1 parietal impact for the left



anterior NDT column. ....................................................................................................... 97

1

Chapter I: Introduction & Background

BACKGROUND AND SIGNIFICANCE

Traumatic brain injury (TBI) is the most severe and most common trauma-related

injury [1]. According to the Centers for Disease Control and Prevention (CDC), it is a

major public health concern in the United States, with approximately 1.7 million people

in the US suffering a TBI annually [2]. TBI has a mortality rate ranging from 6% to

23.1% and is also a leading cause of disability, which introduces significant societal and

economic costs [3]. The leading causes of TBI are falls, motor vehicle crashes (MVCs)

and struck by or against events (Figure 1) [2].

Figure 1. Percentage of annual TBI (combined emergency department visits,

hospitalizations, and deaths) by external cause [2].

2

Mild traumatic brain injury (mTBI), also called concussion, minor brain injury or

minor TBI, is an important subset of TBI that is of increasing research interest –

particularly sports-related concussion. A study conducted by the CDC estimates that

approximately 300,000 sports-related mTBIs occur each year, although the study

included only those injuries involving loss of consciousness [4]. This estimate of mTBI

incidence is likely severely underestimated due to underreporting and unrecognized

injuries. Other studies suggest that loss of consciousness may only occur for between 8%

and 19.2% of sports-related mTBIs [5];[6]. Combining this rate of occurrence with the

CDC estimate of mTBI incidence, it may be more accurate to assume that 1.6 to 3.8

million sports-related mTBIs occur each year, including those for which medical

attention is not sought.

Additionally, there have been growing concerns about the long-term effects of

exposure to repetitive, sub-concussive head impacts. Chronic traumatic encephalopathy

(CTE) is a neurodegenerative disease characterized by the deposition of tau proteins at

the depths of the sulci thought to be associated with repetitive head impacts, such as those

sustained in contact sports [7].

Despite the high incidence of TBI and mTBI and the growing concerns about

long-term consequences of such injuries, the underlying injury mechanisms are not well

understood. The fundamental biomechanics and injury thresholds associated with TBI

must be well-characterized and understood to allow us to prevent and treat these injuries.

While there are many theories about the underlying injury mechanisms of various brain

injuries, we still do not fully understand the biomechanical basis for many of these

injuries. Various methods have been used over the years to investigate and gain a deeper

3

understanding of brain injury mechanisms, including experimental testing of animal

models, post-mortem human subjects (PMHS), anthropomorphic test devices (ATDs), as

well as computational modeling of the brain [8].

ANATOMY OF THE HUMAN HEAD

The human head is made up of the scalp, skull, meningeal membranes,

cerebrospinal fluid (CSF), brain and cerebral vasculature. The shape and size of the

different tissues varies greatly between individuals, but they share many common

features.

Scalp

The scalp is defined as soft tissue layers of dermal skin and subcutaneous

connective tissues covering the top of the human head. It is 5 to 7 mm thick and consists

of the skin, subcutaneous connective tissue layer, galea aponeurotica, loose areolar

connective tissue layer and pericranium.

Skull

The skull rests at the superior end of the vertebral column and forms the cavity for

the brain. It is formed by two sets of bones; the 8 cranial bones and the 14 facial bones

(Figure 2A). The thickness of the skull varies between 4 and 7 mm and consists of three

4

Figure 2. (A) External view of the human skull [9] and (B) the base of the cranial cavity

[10].

layers: inner table, diploë, and outer table. The inner and outer tables are made up of

compact bone, while the diploë layer is spongy bone. The base of the cranial cavity is an

irregular surface of bone containing depressions and ridges as well as holes (foramen):

small holes for arteries, veins and nerves; and a large hole (foramen magnum), which is

the area where the brainstem transitions to the spinal cord. The skull base is made up of

the anterior cranial fossa, which houses the frontal lobes; the middle cranial fossa, which

houses the temporal lobes; and the posterior cranial fossa, which contains the cerebellum

(Figure 2B).

Meninges

Three membranes called the meninges surround the brain. The most superficial

membrane is the dura mater, which is a tough fibrous membrane that is adhered to the

inner surface of the skull. This membrane extends into the falx cerebri, which separates

the cerebral hemispheres and the tentorium cerebelli, which separates the cerebrum from

the cerebellum (Figure 3). Beneath the dura is the arachnoid, a thin and fibrous layer that

encloses the the CSF and blood vessels. The CSF is located in the subarachnoid space,

5

Figure 3. View inside the skull showing the protruding portions of the dura mater - falx

cerebri and tentorium cerebelli [9].

which is the area between the arachnoid and the third meningeal layer, the pia mater

(Figure 4). The pia mater is the innermost layer and is a thin, delicate membrane that is

closely adhered to the surface of the brain and follows the sulci (depressions in the

cerebral cortex) and gyri (ridges on the cerebral cortex).

Figure 4. The meningeal membranes in a coronal cross section

Cerebrospinal fluid (CSF)

CSF is a liquid that surrounds the brain between the pia and arachnoid meningeal

layers and maintains a uniform pressure within the cranium (Figure 5). It contains

6

sodium, chloride, glucose, proteins, lipids, and leukocytes, and allows the circulation of

nutrients and waste. Additionally, CSF serves as mechanical protection to the brain,

which would otherwise be exposed to hitting the bony walls of the cranium, while still

allowing relative motion between the brain and skull [11].

Figure 5. T2-weighted MRI scan of a normal head. CSF is depicted as light gray, gray

matter is darker gray, and white matter is darkest.

Brain

The average adult human head weights approximately 4.50–5.00 kg – one-third of

this mass is made up of the brain (1.60 kg in mean, 1.45 kg in women) [12]. The brain

consists of the cerebrum, cerebellum and brain stem (Figure 6A). The cerebrum is largest

part of the brain and consists of two hemispheres, which are each broken up into four

lobes: the frontal, temporal, parietal and occipital (Figure 6B). The outer layer of the

cerebrum is made up of gray matter (cerebral cortex), which consists of neuronal cell

bodies, synapses and glia. Immediately beneath the cerebral cortex, is white matter,

which consists of glial cells and myelinated axons. Due to the myelinated fiber, which

matter demonstrates directional dependence in its material properties. An important

7

Figure 6. (A) Internal structures of the human brain and (B) the four lobes of the cerebrum.

portion of the white matter is the corpus callosum, which connects the two hemispheres

of the cerebrum (Figure 7). The cerebellum is located inferior to the cerebrum in the

posterior cranial fossa. The cortex of the cerebellum is covered in gyri and sulci similar to

the cerebrum, but they are much smaller (Figure 6A). The brain stem, which originates at

the posterior part of the brain, is the lower extension of the brain and structurally joins the

brain to the spinal cord.

Figure 7. Corpus callosum [9].

8

Cerebral Vasculature

The cerebral vasculature consists of arteries that provide the brain with

oxygenated blood and veins that drain the circulated blood (Figure 8). Major arteries in

the cranial cavity include the vertebral, internal carotid, anterior cerebral, posterior

cerebral and inferior cerebellar arteries; major veins include the superior sagittal, inferior

sagittal, straight, cavernous, transverse, and sigmoid sinuses. The superior cerebral veins

communicate with the superior sagittal sinus through intermediate collection reservoirs

called the lateral venous lacunae. In the parasagittal region, these bridging veins are

thought to be associated with acute subdural hematoma (SDH) when compromised.

Figure 8. Distribution of cerebral arteries on the base of the brain [9].

MECHANICAL PROPERTIES OF BRAIN TISSUE

The material properties of brain tissue play a vital role in understanding the

mechanical response of the human head to impact. Researchers have been conducting in

9

vitro experimental testing of brain tissue since the 1960s. Even with over 50 years of

research and experimental data, material property values of the brain remain somewhat

controversial due to the large variation in reported values throughout the literature. In

some cases, the discrepancies can be attributed to methodological flaws, such as post

mortem testing time, tissue storage and hydration conditions, tissue preparation/excision

methods, and interfacial testing conditions [13]. Variation also results from the designed

testing conditions; specifically, many investigators have focused their efforts on

characterizing the tissue response under a specific type of loading, such as compression,

tension or shear, or a specific loading condition, such as ramp, hold or oscillation. Most

in vitro tests described in the literature were based on compression creep tests and

relaxation tests in compression and shear, or on dynamic frequency or strain sweep

experiments and are summarized in the following section.

Creep Tests

The first in vitro mechanical testing conducted on brain tissue considered

compression creep tests and used animal brain samples [14, 15]. Dodgson [14] performed

creep tests on mouse brain tissue and identified the quasi-linear relation between

logarithmic scaled time and compression strain. This quasi-linear behavior was later

confirmed by Koeneman [15] in 1966 who performed compression creep tests on

porcine, calf and rabbit brain samples.

Relaxation Tests

Compression stress relaxation tests were first conducted by Galford and

McElhaney [16] in 1970 on monkey and human brain samples. Their results showed a

quick relaxation for less than 100 s with an initial relaxation modulus of 6.65 kPa for

10

human and 10.3 kPa for monkey. This decrease in stress relaxation modulus has been

confirmed by more recent relaxation tests [36, 38, 39].

Shear Relaxation Tests

Shear relaxation tests were performed on porcine and bovine brain samples at

varying strain levels [40, 41]. The goal of these early studies was to estimate the limit of

linear viscoelastic response of brain tissue. A significant increase in shear relaxation

modulus was found below the 0.1% strain level, with a long time (t > 100 s) relaxation

modulus was determined to be less than 100 Pa. Since then, many additional shear

relaxation tests have been performed with a large range in results for the shear modulus

value. Figure 9 summarizes the relaxation moduli obtained through shear relaxation

testing, and superposes relaxation moduli determined from compressive relaxation testing

by assuming incompressibility. From Figure 9, it can be seen that relaxation was found to

be slower at higher strains – a behavior that was observed by all investigators.

Figure 9. In vitro relaxation moduli versus time from the literature [21].

11

Dynamic Mechanical Analysis

The first in vitro shear dynamic tests were performed by Fallenstein et al.

[22] at frequencies ranging from 9 to 10 Hz. Shortly after, in vitro studies of shear under

dynamic torsion were conducted by Shuck and Advani [23], who investigated frequencies

Figure 10. (A) Storage and (B) loss moduli of brain tissue from the literature of in vitro

dynamic frequency sweep tests in shear [21].

ranging from 5 to 350 Hz. The high frequency range is of particular importance when

characterizing brain tissue - it has been suggested that brain tissue should be

characterized over a range up to 1000 Hz [21]. To this end, a large range of frequencies

has been investigated by various researchers through oscillatory testing and the results are

presented as storage and loss moduli in Figure 10A and B, respectively. Although there is

a disparity in the results, the trend of shear moduli increasing with increasing frequency

12

exists for all sources. An interesting aspect of these results is the inflection point

occurring around 150 Hz that was observed by Shuck and Advani [23] and Thibault and

Margulies [24] and at more than 1000 Hz by Nicolle et al. [25]. This inflection point

characterizes an inversion of the elastic and viscous components of the response. In

general, the relationship between modulus and frequency demonstrates two major trends.

The first trend encompasses the majority of the studies reported and results in modulus

values ranging from 100 to 1000 Pa. Nicolle et al. [26] and Shuck and Advani [23],

however, measured values about 10 times higher.

MECHANICAL RESPONSE TO IMPACT

Various methods have been used over the years to investigate and characterize the

mechanical response of the human head to impact, including experimental testing of

animal models, cadavers, and human volunteers. Cadaver tests allow for well controlled

tests and have the same anatomical features as a living person, but are limited by the lack

of muscular and physiologic response. To account for the physiologic response, animal

models can be used; however, these models require scaling of shape and size to fit the

animal model to humans. Although human volunteers present an opportunity to capture

the physiologic response without the need to scale or extrapolate the data, there are

limitations to this method; that is, volunteer data are generally either obtained in

uncontrolled conditions (such as real-world athletic events) or at impact severities well

below injury level.

13

Cadaver data

Human response to impact was investigated using cadavers by Kallieries et al.

[27] by conducting frontal, lateral and occipital impacts using both a rigid and a padded

impactor. Subarachnoid hematomas were observed at the contrecoup site in 40% of the

experiments. In 1997, Hardy et al. [28] proposed a new technique for studying relative

motion of the brain with respect to the skull using neutral density accelerometers (NDA-

3’s) and neutral density targets (NDTs). Additional experiments using this method were

conducted by Hardy et al. studying a range of impact directions and severities [27, 28]. In

situ tests were conducted by Nahum et al. [31] and Trosseille et al. [32], but this time

looking at the pressure response. Nahum et al. [31] reported experimental data for a

frontal blow to the head for several seated cadavers. Various masses and velocities were

investigated, as well as different materials for padding. Trosseille et al. [32] later

conducted several impacts to the face of cadavers and measured pressure response

similarly to Nahum et al. [31].

Following these early cadaver tests, in situ strain and pressure experimental tests

were conducted [28, 29]. To determine local strain, these experiments used a high-speed

x-ray system to track the relative motion of radio-opaque neutral density targets (NDTs)

implanted in the brain and implanted cranial pressure transducers (CPTs) to measure the

intracranial pressure following head impacts at concussive severities. These experiments

observed an increase in brain pressure and strain as linear and rotational acceleration

increase.

14

Animal data

There were over 200 primate tests performed from 1966-1983, which primarily

looked at rotational acceleration [32, 33, 34]. For example, Gennarelli et al. [33]

produced traumatic coma in 45 monkeys by accelerating the head in one of three

directions without impact. The results of these experiments related the magnitude of head

motion to the duration of coma, degree of impairment, and amount of DAI. Various other

animal models have also been employed over the years, including pigs [36], ferrets [37],

and rats [38]. Experimental data derived from animal experiments can be used to

establish tolerance to various brain injury (Figure 11).

Figure 11. Comparison of thresholds determined from various animal data [39, 40, 41].

Volunteer data

Football and other contact sports present a unique opportunity to ethically study

real-world head impacts by providing a large sample of human volunteers.

0 2500 5000 7500 10000 12500 15000 17500 200000

10

20

30

40

50

60

Rotational Acceleration, rad/s2

Rota

tional V

elo

city,

rad/s

Concussion, Ommaya (1985)

DAI, Davidsson (2009)

DAI, Margulies (1992)

15

Instrumentation of football players with accelerometers has allowed the compilation of a

large biomechanical data set of linear and rotational acceleration. Biomechanical impact

data collected from NFL players, along with injury information (concussion incidence)

has been used to reconstruct impacts using anthropomorphic test dummies (ATDs) to

learn more about how head kinematics are correlated with risk of concussion.

Additionally, this data has been used to investigate head impact exposure as well to

assess concussion risk based on head kinematics. Rowson and Duma [42] proposed a

combined probability risk function for concussion that was developed from a large

dataset of real-world collegiate football impacts and accounted for both linear and

rotational accelerations. Figure 12 shows risk contours of the combined probability risk

function.

Figure 12. Combined probability of concussion contours relating concussion risk to linear

and rotational head acceleration [42].

16

BIOMECHANICS OF BRAIN INJURY

TBI is damage to the brain caused by high-energy mechanical loading, such as

impact, blast loading, or sudden acceleration or deceleration. TBI can be categorized

based on the affected area: diffuse (over widespread area) and focal (localized) injuries.

Diffuse injuries include cerebral concussion, diffuse axonal injury (DAI), and cerebral

edema. Concussion is the most common diffuse injury and results in temporary loss or

alteration in brain function. Focal injuries include hematomas and contusions. Numerous

theories exist about the underlying mechanisms of various brain injuries, including the

development of positive and negative pressures, pressure gradients, and rotational effects.

Positive Pressure

The theory of positive pressure is based on the theory that compressive stresses

develop in the brain at the site of impact due to the skull moving more quickly than the

brain, which causes damage to the brain. This accounts for coup injuries (injury

experienced at site of impact) when the head is impacted and contrecoup injuries (injury

experienced at contralateral site) during a fall.

Negative Pressure

Negative pressure develops in the contrecoup site upon impact as a result of

tension generated by the relative motion between the skull and the response-delayed

brain. Another possibility for the development of negative pressure at the contrecoup site

is due to a tensile wave formed by the reflection of the original compressive stress wave

from the impact site. In contrast, at the coup site, negative pressure develops as a result of

the deformed skull rapidly returning to its original geometry. Denny-Brown and Russell

17

[43] described this mechanism of injury, but state that contrecoup injury is not caused by

negative pressure alone.

Pressure Gradients

The formation of pressure gradients is proposed as another mechanism of brain

injury. It is thought that these gradients create shear stresses that result in local

deformation of brain tissue. Gurdjian and Lissner [44] and Thomas et al. [45] found that

impact-induced acceleration and pressure are responsible for the development of pressure

gradients. These pressure gradients cause injury as the brain attempts to ‘flow’ from areas

of high pressure to low pressure, and the brain experiences regional deformation in

response to the generated shear stresses. Additionally, these gradients can induce

damaging shear effects at the junctions between gray and white matter leading to DAI

[45].

Rotation

The hypothesis that brain injury is based on angular acceleration was introduced

by Holbourn [46] in 1943 states that injury is induced by shear strains generated by

angular acceleration. Major proponents of this theory are Gennarelli et al. [32, 42, 47,

48], whose experimental work focused on the rotational acceleration of subhuman

primates. Gennarelli et al. [47] related levels of concussion to angular acceleration and

showed good agreement with clinical findings. Generalli [48] stated that “virtually all

types of primary head injury can be produced by angular acceleration applied to the head

in the appropriate manner.” In contrast, Ommaya et al. [49] and Ommaya and Hirsch

[50], contend that rotation alone is not able to produce head injury. Additionally, Ono et

18

al. [51] found that the occurrence of concussion in monkeys did not correlate with

angular acceleration of the head.

HEAD INJURY CRITERIA

Mechanically relevant brain responses or parameters, such as accelerations,

intracranial pressure, stresses and strains, can be used as predictors of various brain

injuries. The current standards used by the sports and automotive industries are the Gadd

Severity Index (GSI) [52] and the Head Injury Criterion (HIC) [53], which were both

developed from the Wayne State Tolerance Curve (WSTC). There are opponents of these

indices for various reasons, such as the fact that rotational acceleration is not taken into

account [54], and that they were developed from WSTC data, which only considered

frontal impacts [55]. Taking into account the contribution of rotational acceleration of the

head, later studies proposed additional injury criteria such as Head Impact Power (HIP)

[56] and Brain Injury Criteria (BRIC) [57].

Gadd Severity Index (GSI)

The Gadd Severity Index (GSI), described by Gadd [52], is an extension of the

WSTC, whose basic finding was that high acceleration can be withstood for short

durations, while lower accelerations can be tolerated for longer intervals. The GSI is a

weighted integral of the form:

𝐺𝑆𝐼 = ∫[𝑎(𝑡)]2.5𝑑𝑡

(1)

19

where a is acceleration and t is time. A value of 1000 was suggested as an injury

threshold from analysis of data from Wayne State, the FAA and NASA. This index is not

valid for long durations.

Head Injury Criterion (HIC)

The Head Injury Criterion (HIC) was introduced by Versace [53] and was

eventually adopted by the National Highway Traffic Safety Administration (NHTSA) as

the head injury criterion for Federal Motor Vehicle Safety Standard (FMVSS) 208 [58]. It

has the form:

𝐻𝐼𝐶 = (𝑡2 − 𝑡1)[

1

𝑡2 − 𝑡1∫ 𝑎(𝑡)𝑑𝑡𝑡2

𝑡1

]𝑀𝑎𝑥2.5

(2)

where a is acceleration and t is time. This index is calculated by choosing the range of

integration (t1 – t2) such that the function is maximized. The duration of integration is

either 15 ms, recommended by the International Organization for Standardization (ISO),

or 36 ms, recommended by NHTSA. A tolerance limit of 1000 has been adopted by

NHTSA.

Head Impact Power (HIP)

The Head Impact Power (HIP) was proposed by Newman et al. [56]. It combines

translational and rotational head accelerations and has the form:

𝐻𝐼𝑃 = 4.50𝑎𝑥∫𝑎𝑥𝑑𝑡 + 4.50𝑎𝑦∫𝑎𝑦𝑑𝑡 + 4.50𝑎𝑧∫𝑎𝑧𝑑𝑡

+ 0.016𝛼𝑥∫𝛼𝑥𝑑𝑡 + 0.024𝛼𝑦∫𝛼𝑦𝑑𝑡 + 0.022𝛼𝑧∫𝛼𝑧𝑑𝑡

(3)

where a is acceleration, t is time and the coefficients were set to equal the mass and

appropriate mass moments of inertia for the human head.

20

Brain Rotational Injury Criterion (BRIC)

The Brain Injury Criterion (BRIC) was originally proposed by Takounts et al.

(2011) [59], but the formulation was revised in 2013 [57] to the current form:

𝐵𝑅𝐼𝐶 = √(

𝜔𝑥

𝜔𝑥𝑐)2 + (

𝜔𝑦

𝜔𝑦𝑐)2 + (

𝜔𝑧

𝜔𝑧𝑐)2

(4)

where ωx, ωy, and ωz are maximum angular velocities in the x-, y- and z-axes,

respectively, and ωxc, ωyc, and ωzc are the critical angular velocities in their respective

directions.

FINITE ELEMENT MODELING OF THE HUMAN HEAD

To overcome the limitations presented by other means of studying brain injury,

finite element modeling can be employed. FE modeling offers a cost-effective alternative

to many experimental methods and has the additional advantage of providing

exponentially more data through spatial and temporal distributions of stress and strains

and other biomechanical parameters of interest. The quality of a model’s predictions,

however, is dependent on the accuracy of the modeled geometry, the model’s ability to

describe complex material behavior, and the accuracy of the modeled interface

conditions.

Model Geometry

The FE model development process typically involves image segmentation of

medical images, such as computed tomography (CT) and magnetic resonance imaging

(MRI) to define three-dimensional (3D) surfaces of desired structures, which is then

followed by a surface-based mesh generation process. During this process, complex

21

anatomical features are frequently simplified and ‘smoothed’ to allow faster development

and simple contact interaction at model interfaces. One feature of particular importance

that is over-simplified in many brain FEMs is the gyral folds on the surface of the brain.

The brain surface is typically modeled with a smooth surface surrounded by a uniform

layer of cerebrospinal fluid (CSF), which ignores the intricate gyral folds throughout the

brain. This simplification and reduction in anatomic accuracy may significantly impact

the model’s local brain response and subsequent prediction of injury. Indeed, studies have

indicated that the intricate folding patterns on the surface of the brain greatly affect both

the distribution and magnitude of stress and strain throughout the brain [60]. Cloots et al.

[61] subjected four plane strain models of different geometries (a homogeneous model

and three heterogeneous models) to the same boundary conditions and examined the

equivalent stress and maximum principal strain to quantify the influence of morphologic

heterogeneities (Figure 13).

Figure 13. Equivalent stress fields for models with varying geometries under the same

boundary conditions showing stress concentrations in the heterogeneous models [61].

22

Constitutive Models for Brain Material

Some of the earliest brain FE models characterized brain tissue as linear elastic. A

linear viscoelastic constitutive model was adopted shortly after and better represents the

response of the brain by accounting for time-dependent properties. The shear relaxation

response of the linear viscoelastic model is described by the following expression:

𝐺(𝑡) = 𝐺∞ + (𝐺0 − 𝐺∞)𝑒−𝛽𝑡

(5)

where G∞ is the long term shear modulus, G0 is the short term shear modulus, and β is the

decay constant.

Another common model for brain tissue employed in FE modeling is a

hyperelastic formulation because it is capable of large elastic deformations. In a

hyperelastic material model, the stress is derived from a strain energy potential (W),

which can be written as a function of the principal invariants (I1, I2, I3) of the right

Cauchy-Green deformation tensor. Two hyperelastic constitutive models that are

frequently used are the Mooney-Rivlin model and the Ogden model. To model the brain

as an unconstrained material, a hydrostatic work term, WH(J), can be added to the strain

energy function, which is a function of the relative volume, J. The standard strain energy

function for an incompressible Mooney-Rivlin hyperelastic material is:

𝑊(𝐼1, 𝐼2) = 𝐶10(𝐼1 − 3) + 𝐶01(𝐼2 − 3) +𝑊𝐻(𝐽) (6)

where C10 and C01 are the Mooney-Rivlin material constants, I1 and I2 are principal

invariants, and J is relative volume [62]. Using an Ogden hyperelastic model, the strain

energy function takes the form:

23

𝑊(𝐼1, 𝐼2, 𝐼3) =∑𝜇𝑖𝛼𝑖(𝐼1

𝛼𝑖 + 𝐼2𝛼𝑖 + 𝐼3

𝛼𝑖 − 3) +1

2𝐾(𝐽 − 1)2

3

𝑖

(7)

where αi and μi are Ogden constants, I1, I2, and I3 are principal invariants, K is bulk

modulus and J is relative volume. For these hyperelastic models, the stress tensor is then

derived using:

𝑆𝑖𝑗 =

1

2(𝜕𝑊

𝜕𝐸𝑖𝑗+𝜕𝑊

𝜕𝐸𝑗𝑖)

(8)

in terms of the second Piola-Kirchhoff stress, Sij, and Green’s strain tensor Eij.

Additionally, hyperelastic constitutive models can be employed in combination

with viscoelasticity incorporating rate effects using a convolution integral of the form:

𝑆𝑖𝑗 = ∫𝐺𝑖𝑗𝑘𝑙(𝑡 − 𝜏)𝜕𝐸𝑖𝑗

𝜕𝜏𝑑𝜏

𝑡

0

(9)

where Sij is the second Piola-Kirchhoff stress, Eij is Green’s strain tensor, and Gijkl is the

stress relaxation function represented by a Prony series:

𝑔(𝑡) =∑𝐺𝑖𝑒−𝛽𝑖𝑡

𝑁

𝑖=1

(10)

where Gi are the shear moduli and βi are the decay constants.

Brain-Skull Interface

The boundary conditions at the brain-skull interface have been an important

aspect of FE modeling. Preservation of accurate relative motion between the brain and

skull is important in the simulation of head impact. In general, there are three accepted

methods of modeling the brain-skull interface. The first models the brain-skull interface

with a common set of nodes, which directly couples the brain to the skull. The second

24

method, which has been most common throughout FEMs models the CSF as a ‘soft’ solid

(solid with a low shear modulus). The third method employs various contact algorithms,

such as tied interface, sliding interface with separation, and sliding interface without

separation.

Validation

There are several sets of experimental data that are commonly used to validate FE

head models. These include the intracranial pressure (ICP) experiments conducted by

Nahum et al. [31] and Trosseille et al. [32], as well as the localized brain motion

experiments conducted by Hardy et al. [31, 32, 59]. Nahum et al. [31] impacted a seated

cadavers at the frontal bone (Figure 14A) using impactors with various padding material

and thicknesses. Pressure histories were measured during the impact using pressure

transducers at 5 locations within the brain (Figure 14B). Of this group of tests,

experiment 37 is frequently used for validation. Trosseille et al. [32] conducted six

experiments on seated cadavers and impacted with a 23.4 kg impactor at velocities

Figure 14. (A) Direction of impact in experiment conducted by Nahum et al. [31] and (B)

locations of pressure measurements.

25

varying from 5 to 7 m/s, resulting in longer impact durations than were observed by

Nahum et al. [31]. In the long-duration impacts of Trosseille et al. [32], pressure was

measured at five locations within the brain: frontal lobe, occipital lobe, parietal lobe,

lateral ventricle and third ventricle. Validation is frequently reported against experiment

MS 428-2 from the group of tests conducted by Trosseille et al. [32]. Hardy et al. [63]

conducted a total of sixty-two experiments using seventeen cadavers looking at relative

displacement between the brain and skull using high-speed biplanar x-ray to track the

location of implanted neutral density targets (NDTs) during impact. These tests varied in

setup configuration (impact surface, location and severity), as well the configuration of

NDT implantation (columns or clusters). Two of these experiments that are frequently

used in the validation of head FE models are C755-T2 and C383-T1, which are occipital

and frontal impacts, respectively.

Review of Finite Element Models of the Human Head

Many FE brain models with varying degrees of anatomical accuracy, element size

and material properties have been developed to study brain injury since the first 3D head

model described by Ward and Thompson [64] in 1975. A brief review of relevant 3D FE

head models is presented in the following section.

Kungliga Tekniska Högskolan (KTH)

The original Kungliga Tekniska Högskolan (KTH) model was a detailed and

parameterized FEM proposed by Kleiven and von Holst in 2002 [65]. It included the

scalp, skull, brain, meninges, CSF, bridging veins and a simplified neck. The current

version of the model consists of approximately 18,400 elements and 19,000 nodes

(Figure 15). The brain-skull interface is modeled with tied nodes between the skull and

26

dura and a sliding contact with no separation between the CSF and its contact with the

meningeal membranes and the brain. Brain tissue is modeled with a hyperelastic

Mooney-Rivlin model (6). The model was validated by Kleiven [66] in 2006 against two

pressure experiments: Experiment 37 conducted by Nahum et al. [31] and the long-

duration impact conducted by Trosseille et al. [32], as well as the following local brain

displacement experiments conducted by Hardy et al. [31, 32]: C755-T2, C383-T1, and

C291-T1.

Figure 15. (A) Skull,(B) brain, (C) section view of the KTH head and neck model [65], and

(D) cross section showing FE mesh and anatomical structures represented in the KTH

model [65].

Wayne State University Head Injury Model (WSUHIM)

The first version of the Wayne State University Head Injury Model (WSUHIM)

was described by Ruan et al. [67] in 1993 and consisted of a scalp, skull, dura, falx, brain,

27

and CSF. This model was later improved by Zhou et al. [68] in 1995 by adding ventricles

and differentiating between white and gray matter in the cerebrum. The model was again

revised in 2001 by Zhang et al. [69] to increase the mesh density and introduce a sliding

interface between the exterior surface of the arachnoid membrane and the interior surface

of the dura (Figure 16). The brain response is modeled with a linear viscoelastic model

with differentiation between gray matter, white matter, and the brainstem. This model

was validated by Zhang et al. [69] against the pressure data of Nahum et al. [31] and

Trosseille et al. [32], as well as the C755-T2 occipital impact from the brain displacement

experiments of Hardy et al. [29].

Figure 16. Various versions of the WSUHIM. (A) The original model developed by Ruan et

al. [67], (B) the improved model with gray and white matter differentiation [70], and (C) the

current version of the model [69].

Eindhoven University of Technology (TUE)

The FE model developed at Eindhoven University of Technology (TUE) was

developed by Claessens et al. [71] in 1997 based on CT and MRI scans from the Visible

Human Database and included the skull, brain and facial bone. Model geometry was

improved by Brands et al. [72] in 2002 along with the implementation of the CSF, dura,

28

falx and tentorium (Figure 17). The brain-skull interface was modeled with shared nodes

and brain response was modeled with a 4-term Mooney-Rivlin hyperelastic model. This

model was validated against Nahum’s pressure data [31].

Figure 17. Overview of the head model developed by TUE [72].

Total Human Model for Safety (THUMS)

The head model from the Total Human Model for Safety (THUMS) Version 4.01

(THUMS AM50 Ver4.01, Toyota TCRDL, Japan) was developed from the geometry of a

data set available in the Visible Human Project (NIH, USA) and was created according to

anatomical references. The THUMS head FEM consists of the skull and facial bones,

cerebrum (distinct white and gray matter), cerebellum, brainstem, CSF, meningeal

membranes, falx, tentorium, and the sagittal sinus (Figure 18). To represent contact with

the CSF, tiebreak interfaces were used to simulate frictionless sliding behavior. This

29

contact formulation was assumed between the dura and arachnoid layers, as well as

between the falx and surrounding soft tissue elements. A linear viscoelastic material

model was used to model the response of the gray and white matter. A previous version

of the THUMS head model was validated against pressure and brain displacement

experiments by Kimpara et al. [73], but the current version has not yet been validated.

Figure 18. (A) Isometric view of the THUMS v4.01 head model with the brain exposed and

(B) midsagittal view of the FEM.

Global Human Body Models Consortium (GHBMC)

The Global Human Body Models Consortium (GHBMC) head model was meshed

from a Computer Aided Design (CAD) dataset developed from MRI and CT scans of an

average adult male, and includes scalp, skull, facial bones, cerebrum, cerebellum, lateral

ventricles, corpus callosum, sinuses, thalamus, brainstem, meningeal layers, falx,

tentorium, and bridging veins (Figure 19). A tie-break contact was defined between the

30

dura and arachnoid layers to model the relative motion at the brain-skull interface and

Kelvin-Maxwell viscoelastic model was used to model the gray and white matter.


midsagittal view of the FEM [74].

Université Louis Pasteur of Strasbourg (ULP)

The Université Louis Pasteur of Strasbourg (ULP) model was developed by Kang

et al. [75] in 1997 and included the skull, falx, tentorium, CSF, scalp, cerebellum,

cerebrum, and brainstem. The model was later improved by Deck et al. [76] to include

the falx and tentorium and model subarachnoid space (Figure 20). Additionally a

Figure 20. Overview of the ULP head model [77].

31

Lagrangian formulation for CSF was implemented and an elastic-brittle constitutive law

for the brain-skull interface was employed. A linear viscoelastic constitutive model was

used to represent brain tissue. The ULP model has been validated against both sets of

pressure data [53, 54], as well as the C755-T2 impact conducted by Hardy et al. [29].

University College Dublin Brain Trauma Model (UCDBTM)

The University College Dublin Brain Trauma Model (UCDBTM) was developed

in 2003 by Horgan and Gilchrist [78] from skull geometries extracted from CT scans

from the Visible Human Database. The model includes a skull, scalp, dura, CSF, pia,

falx, tentorium, cerebrum, cerebellum and brainstem Figure 21. The brain-skull interface

Figure 21. (A) Skull, (B), brain, (C), and sagittal cross section of the UCDBTM.

is modeled with solid CSF elements with a very low shear modulus and brain tissue is

modeled with a hyperelastic constitutive model combined with a viscoelastic model in

shear. The model has been validated against the pressure data of Nahum et al. [31] and

Trosseille et al. [32], as well as the C383-T4 impact from the brain displacement

experiments of Hardy et al. [29].

32

Simulated Injury Monitor (SIMon)

The Simulated Injury Monitor (SIMon) model was developed by Takhounts and

Eppinger in 2003 and consists of a rigid skull, CSF, cerebrum, cerebellum, brain stem,

ventricles, bridging veins and a falx and tentorium (Figure 22). All part interfaces are

modeled with merged nodes. A Kelvin-Maxwell viscoelastic formulation is used to

model brain material. The model was validated by Takhounts et al. [79] in 2008 against

two pressure experiments: Experiment 37 conducted by Nahum et al. [31] and the long-



C291-T1.

Figure 22. (A) Isometric view of the SIMon FEM with exposed brain and (B) isometric view

of the FEM showing various anatomical features represented in the model.

33

CHAPTER SUMMARIES

Chapter II: Development and Validation of an Atlas-Based Finite Element Brain

Model

The development of the ABM FE model and the optimization of the brain material

properties using a Latin Hypercube Sample (LHS) of the five brain parameters is

described. Additionally, multiobjective optimization was performed against localized

brain motion data from three distinct cadaver impacts, using CORA as the optimization

parameter.

Chapter III: Comparison of Validation Data for Finite Element Models of the

Human Head

Validation of the ABM against the localized brain displacements of three cadaver impacts

is described. Model performance is quantified using CORA and compared to the

performance of other currently used FE models of the human head.

Chapter IV: Summary of Research

A brief overview of work presented in this thesis.

34

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41

Chapter II: Development and Validation of an Atlas-Based

Finite Element Brain Model

Logan E. Miller, Jillian E. Urban, Joel D. Stitzel

Virginia Tech – Wake Forest University Center for Injury Biomechanics,

Winston-Salem, NC

The following manuscript has been submitted to Biomechanics and Modeling in

Mechanobiology.

42

ABSTRACT

Traumatic brain injury (TBI) is a leading cause of disability and injury-related death. To

enhance our ability to prevent such injuries, we can study brain response using validated

finite element (FE) models. In the current study, a high-resolution, anatomically accurate

FE model was developed from the International Consortium for Brain Mapping (ICBM)

brain atlas. Due to the wide variation in published brain material parameters, a technique

called Latin Hypercube Sampling (LHS) was employed to optimize the brain material

properties against three experimental cadaver tests to achieve ideal biomechanics.

Additionally, pretension and thickness of the falx were varied in a lateral impact

configuration. The ABM was subjected to the boundary conditions from three high-rate

experimental cadaver tests with different parameter combinations for each test. Brain

displacements at the experimental neutral density target (NDT) locations in the model

were compared to the displacements observed experimentally and error was quantified

using CORA (CORrelation and Analysis), a method to evaluate the correlation of two

curves. An average CORA score was computed for each variation and maximized to

identify the optimal combination of parameters. The strongest relationships between

CORA and material parameters were observed for the shear parameters. Using brain

properties obtained through multi-objective optimization, the ABM was validated in three

impact configurations and shows good agreement with experimental data. The final

model developed in this study consists of optimized brain material properties and is

validated in three different, multidirectional cadaver impacts against local brain

displacement data.

43

1 INTRODUCTION

Each year, approximately 1.7 million people in the United States suffer from

traumatic brain injury (TBI) [1]. TBI is a major public health concern as it is a leading

cause of disability and injury-related death - accounting for nearly one third of all injury-

related deaths [2]. To prevent and treat these types of injuries, the fundamental injury

mechanisms need to be well-characterized and understood. While there are many theories

about the underlying injury mechanisms of various brain injuries, we still do not fully

understand the biomechanical basis for many of these injuries. Various methods have

been used over the years to investigate and gain a deeper understanding of brain injury

mechanisms, including experimental testing of animal models, post-mortem human

subjects (PMHS), anthropomorphic test devices (ATDs), as well as computational

modeling of the brain [3]. Finite element (FE) models are powerful tools for investigating

injury mechanisms because they can provide spatial and temporal distributions of stresses

and strains over the problem domain. The quality of a model’s predictions, however, is

dependent on the accuracy of the modeled geometry and the model’s ability to describe

complex mechanical behavior and material response.

Many FE brain models with varying degrees of anatomical accuracy, element size

and material properties have been developed to study brain injury over the last few

decades. Early models represented the brain-skull structure with a simple fluid-filled

spherical shell; subsequently, model complexity increased, and the most advanced

models now include major anatomical brain structures and different material properties

for each component in the brain. Among these are the Royal Institute of Technology

KTH (Kungliga Tekniska Högskolan) brain model, the Simulated Injury Monitor

44

(SIMon), Dartmouth Head Injury Model (DHIM), Wayne State University Brain Injury

Model (WSUBIM) as well as the head models of full-body FE models such as the Total

Human Model for Safety (THUMS) and Global Human Body Models Consortium

(GHBMC) [4, 3, 5, 6, 7, 8]. The geometry of various structures within these head models

were derived from medical images, such as computed tomography (CT) and magnetic

resonance imaging (MRI). The model development process typically involves image

segmentation to define three-dimensional (3D) surfaces of desired structures followed by

a surface-based mesh generation process. During this process, complex anatomical

features are frequently simplified and ‘smoothed’ to allow faster development and simple

contact definition at model interfaces. One feature of particular importance that is over-

simplified in many brain FEMs is the gyral folds on the surface of the brain. The brain

surface is typically modeled as a smooth surface surrounded by a uniform layer of

cerebrospinal fluid (CSF), which ignores the intricate gyral folds throughout the brain.

This simplification and reduction in anatomic accuracy may significantly impact the

model’s local brain response and subsequent prediction of injury. Indeed, studies have

indicated that the intricate folding patterns on the surface of the brain greatly affect both

the distribution and magnitude of stress and strain throughout the brain [9]. Another

limitation of previous models is the substantial amount of time required for the surface-

based mesh generation process, which hinders production of patient-specific models.

Patient-specific and population-specific models are desirable for studying head injury due

to significant variations in brain morphology between individuals [4, 10, 11, 12, 13].

45

Correct anatomical geometry is particularly important for modelling injuries like

concussion, whose occurrence and severity is dependent on deformation of specific areas

of the brain [14]. Another area of growing interest that is not well understood and could

benefit from FE modelling is chronic traumatic encephalopathy (CTE). The pathology of

this disease has been extensively studied and is characterized by the deposition of tau

proteins at the depths of the sulci [15]. Although the focal nature of CTE pathology has

been well characterized, there is relatively little known about the underlying injury

mechanisms. If finite element models are to be employed in studying CTE, the inclusion

of gyral folds in brain FE models is crucial to gaining a better understanding of the

disease, given the focal nature of CTE pathology.

The objective of this study is two-fold. The first objective was to create a high

resolution, anatomically accurate brain finite element model from the International

Consortium for Brain Mapping (ICBM) brain atlas using a voxel-based mesh generation

approach. The second objective was to optimize the brain and falx material properties

using cadaveric experimental data in three distinct impact configurations. This atlas-

based brain model (ABM) is proposed as a new tool for studying brain injury that can

accurately predict local stresses and strains in brain tissue by providing a high level of

anatomic accuracy, particularly at the brain-skull interface.

2 METHODS

The ABM was developed from the geometry of the ICBM adult brain atlas, a

probabilistic atlas derived from a large dataset of 7000 subjects (ages 18-90) that

represents the average adult brain [16]. The ICBM atlas contains 58 independently

46

labeled regions of the brain including cortical gyri, white matter, gray matter, and CSF.

An FE model was created from this image set by converting each 1mm isotropic voxel

into a single element of the same size using a custom code developed in MATLAB (The

MathWorks, Natick, MA). While the high level of detail provided by the atlas allows the

opportunity to represent many detailed brain structures, initial model development

included only four distinct parts from the atlas geometry: cerebrum (combined white and

gray matter), cerebellum, CSF, and ventricles. Because the model was developed from a

skull-stripped image set, there are places on the outer surface of the brain that are not

completely covered by CSF. Since this is not a realistic representation of the brain-skull

interface, a single, uniform layer of CSF was added around the entire model to ensure

that there was at least one CSF element between the brain and skull at all points. This

added layer of CSF was 74 mL, and increased the CSF volume from 192.3 mL to 266.3

mL, which is reasonable when compared to real world CSF volumes [17]. The falx

cerebri and tentorium cerebelli are important structures in the cranium which were not

represented in the ICBM atlas, so they were manually implemented into the model. The

falx was defined as a layer of shell elements along the midsagittal plane, and the

tentorium as a layer of shell elements on the superior surface of the cerebellum,

separating the cerebrum and cerebellum (Figure 23). Lastly, a layer of rigid shells

surrounding the external surface of the CSF was generated in LS-PrePost to completely

enclose the model. The current model, shown in Figure 24A-D, has approximately 2

million nodes and elements.

47

Figure 23. ABM showing the falx, tentorium,

and ventricles

Figure 24. Cross sections of ABM. (a) axial,

(b) sagittal, (c) coronal, (d) axial isometric

Initial material property values for all parts, excluding the brain material model, were

similar to the SIMon model (Table 1), with the exception of the CSF which was modeled

with the same material properties as the ventricles, as opposed to the Kelvin-Maxwell

fluid used in the SIMon model [3]. This implementation of the CSF was motivated by the

results of Chafi et al. (2009) which investigated brain response using an FEM that

modeled the CSF using three different formulations: elastic fluid, viscoelastic, and nearly

incompressible elastic material. Chafi et al. (2009) found that the most comparable results

to experimental data resulted from modelling the CSF as a fluid-like material. Contact at

all part interfaces was modeled with merged nodes.

Table 1. Material Properties of the ABM

Part LS-DYNA Material Model Material Properties

CSF/Ventricles Elastic fluid ρ=1000 kg/m

3, E=0 MPa, ν=0.5,

K=2100 MPa

Falx*/Tentorium Elastic ρ=1130 kg/m

3, E=31.5 MPa, ν=0.45,

K=2100 MPa

Skull Rigid ρ=35200 kg/m3, E=6900 MPa, ν=0.3

Brain Kelvin-Maxwell viscoelastic Optimized

48

2.1 Brain Material Optimization

The values of brain material parameters vary greatly throughout the literature,

which motivates the current optimization study (Table 2). Brain tissue is often modeled

using a linear viscoelastic material formulation [3, 7, 8, 18, 19, 20, 21]. The shear

relaxation behavior is described by:

𝐺(𝑡) = 𝐺∞ + (𝐺0 − 𝐺∞)𝑒−𝛽𝑡

(1)

where G∞ is the infinite shear modulus, G0 is the initial shear modulus, and β is the decay

constant. Therefore, this material model was selected for material optimization

(*MAT_061 in LS-DYNA). Brain density (ρ), bulk modulus (K), and the three shear

response parameters (G∞, G0, β) were varied using Latin Hypercube Sampling (LHS) to

generate 100 combinations of material parameters, or 100 distinct brain material models.

Because of the relationship between G∞ and G0 in defining shear relaxation, G∞ must be

less than G0 for every material model generated by the LHD. To accomplish this, instead

of varying G∞ and G0 independently, G0 and the ratio G∞/G0 were varied. In LHS each

Table 2. Parameter Ranges for Latin Hypercube Sample

Min/Max Reference

ρ

kg/m3

1000 Kimpara et al. (2006)

1140 Willinger et al. (1999)

K

GPa

0.002 Ji et al. (2014), (Ji et al. 2014)

2.19

Al-Bsharat et al. (1999), Willinger et al. (1999), Zhang et al. (2001),

Kimpara et al. (2006), Chafi et al. (2009), McAllister et al. (2012),

Kangarlou (2013), Mao et al. (2013), Post et al. (2014)

G0

kPa

0.772 Kleiven and Hardy (2002)

49 Pinnoji et al. (2010), Tinard et al. (2012)

G∞

kPa

0.185 Jirousek et al. (2005)

16.7 Pinnoji et al. (2010), Tinard et al. (2012)

G∞/G0 0.1 Ji et al. (2014)

0.5584 Takhounts et al. (2003)

β

s-1

0.06 Kimpara et al. (2006)

400 Kangarlou (2013)

49

parameter is varied over a predefined range (Table 2) independent of the values of other

variables and orthogonal sampling is employed over the multidimensional sample space

to ensure the generated samples are representative of the total variability. The parameter

ranges displayed in Table 2 were obtained from literature values and other published

finite element models. Because the literature-reported ranges for bulk modulus, shear

modulus and the decay constant span orders of magnitude, logarithmic sampling was

employed for these variables in order to appropriately sample the lower range of values.

To evaluate the effect of each parameter and determine optimal values for each, the

performance of the ABM with each material model is compared to experimental data.

2.2 Experimental Tests

Three experimental tests were investigated in this study: the C755-T2 (occipital

impact ), C383-T1 (frontal impact), and C291-T1 (parietal impact) [22, 23]. These three

Figure 25. Approximate cross-sectional planes where NDT columns are located for each

experimental test (a), locations of NDTs in the XZ plane on the right side of the brain (b),

and locations of NDTs in the XZ plane on the left side of the brain (c)

50

tests were chosen for optimization purposes because they cover a range of impact

velocities and directions. In the cadaveric tests, local displacements at various locations

within the brain were analyzed following impacts of varying severity and direction [23].

In each experiment, vertical columns of 5-6 radio-opaque neutral density targets (NDTs)

were implanted in the brain, and a high-speed biplanar X-ray system was used to track

their relative motion during the impact. Three-dimensional skull kinematics were

evaluated with an accelerometer array affixed to the cadaver skull to determine linear and

angular velocities at the head center of gravity (CG), which were then used as boundary

conditions to drive each ABM simulation [23]. To examine comparable displacements in

the ABM, nodes closest to the physical location of each NDT were identified with respect

to the Frankfurt plane (Figure 25) and their displacements were calculated throughout

each simulation. Summary characteristics for the three tests are shown in Table 3.

Table 3. Summary of Experimental Test Conditions

51

2.3 Model Performance

To evaluate the effect of varying each material parameter and identify the optimal

material properties, the accuracy of the ABM’s response for each combination of material

parameters was quantified. The metric used to quantify the difference between model

response and experimental data was CORA (CORrelation and Analysis) [24]. The CORA

method evaluates the correlation of two curves by calculating a rating using two methods:

the corridor method and the cross-correlation method. These two ratings range from 0 to

1 and are averaged to determine a total CORA score (1 indicates a perfect match). The

corridor method computes a rating based on where the comparison curve falls in relation

to corridors around the reference curve. The cross-correlation method is based on ratings

for the phase shift, size and progression of time-shifted curves.

The ABM was subjected to the boundary conditions from the three experimental

tests with each of the 100 brain material models implemented into the FEM, resulting in a

total of 300 simulations. Average CORA values computed from all NDTs were

calculated for all 300 simulations to identify the combination of properties that yielded

the best correlation to experimental data. It was hypothesized that this would result in

similar material parameters for each experimental condition. During our optimization

process, however, we observed ideal shear properties approximately five times larger for

the lateral condition than for the frontal and occipital cases (Table 4). Given the lateral

impact condition, one would anticipate the falx to play a major role in brain response.

Additionally, the high shear properties that resulted from the C291-T1 optimization

indicated that there was too much lateral motion; or in other words, that the falx was not

constraining lateral motion sufficiently.

52

2.4 Falx Material Optimization

The observation that brain shear stiffness were unusually high to satisfy the lateral

impact case motivated investigation and optimization of the falx model. An additional

LHS was conducted that varied pretension from 0-10% and falx shell thickness from 0.41

mm to 7 mm to optimize the falx model in the ABM. These ranges were adapted from

Golman et al. (2013). Pretension was implemented using an optional material card that

pre-strains the material by a desired factor. The resulting values for pretension and

thickness of the falx were then implemented into the ABM with each of the original 100

brain material models, and the C291-T1 variation was rerun. The frontal and occipital

cases were not rerun because the motion was in the sagittal plane for both cases, and not

greatly affected by the falx properties.

2.5 Data Analysis

A CORA score was computed for the ABM’s performance in all 300 simulations

– the three impact conditions with each combination of material parameters incorporated

into the model. The single CORA score for each simulation was calculated by first

averaging the X- and Z-CORA (or Y- and Z-CORA for the C291-T1 case) scores for

each NDT to get individual NDT CORA scores, and then averaging all NDT CORA

scores to determine an overall average CORA score for a given simulation. The

relationship between CORA scores and material parameters was evaluated by computing

the strength of the piecewise linear regression for each parameter. Material parameters

were optimized under each impact condition using CORA as the optimization parameter

and the combination of material properties that produced the best result was identified for

the three impact configurations. Additionally, we can concurrently optimize the material

53

properties against the three impact conditions simultaneously. We do this by averaging

the CORA scores for the C755-T2, C383-T1, and C291-T1 cases for the ABM with each

combination of material parameters. Finally, the model with the highest average CORA

between all three impact conditions (using the optimized falx model) was identified and

its material parameters were determined to be the optimal material properties.

3 RESULTS

The ABM has been developed from the ICBM brain atlas and currently contains 7

parts and about 2 million nodes and elements. The brain and CSF volumes are 1,639.4

mL and 277.1 mL, respectively, and the total model mass is 6.8 kg.

ABM response was compared with experimental data for all 100 variations for

each of the three test configurations and average CORA values for each simulation were

computed. Relationships between CORA scores and material parameters for each of the

test conditions are shown in Figure 26. The results for the lateral case shown in Figure 26

represent the ABM before the falx model was optimized. Also displayed in these plots

are piecewise linear regressions for CORA regressed against each material parameter.

The material properties for the variation with the highest CORA score from each

experimental configuration are shown in Table 4.

Figure 27 shows the relationships between CORA and the falx pretension and

thickness varied in the falx optimization using the lateral experimental configuration. The

results from this variation indicate that the optimal falx pretension is 6.52% and the

optimal thickness is 2.86 mm. Using these values in the falx model, the brain material

optimization in the C291-T1 parietal impact was rerun. The results of this updated

54

Figure 26. Relationships between CORA and brain material parameters from brain

parameter variations in three experimental configurations (using the original falx model in

all variations). The simulation with the highest CORA value for each individual impact

condition is highlighted.

optimization are included in Table 4 as well as the material properties that result from

concurrently optimizing the CORA values from the frontal, occipital, and updated lateral

conditions. We note, from Figure 26, that the shear parameter, G0, has the largest

influence on CORA. Considering the results from the frontal, occipital, and updated

lateral (with optimized falx model) optimizations, we examine the relationship between

G0 and CORA for each experimental configuration (Figure 28).

Table 4. Material Properties from each experimental configuration optimization

Optimization Condition ρ (kg/m3) K (GPa) G0 (kPa) G∞ (kPa) β (s

-1) CORA

C755* 1061 0.2539 4.121 2.160 33.48 0.453

C383* 1036 0.5326 4.634 1.321 64.75 0.424

C291* (original) 1021 0.1066 19.20 10.80 283.2 0.491

C291* (optimized falx) 1113 0.2706 17.26 5.099 247.4 0.473

ALL* 1123 0.1069 5.161 1.859 67.58 0.426

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Figure 27. CORA relationships with falx pretension (a) and falx thickness (b) for the C291-

T1 impact

3.1 C755-T2

The local displacements of each NDT for each experimental impact are presented

in Figure 29 - Figure 31 using the material model obtained through concurrent

optimization of all three experimental conditions. Relative displacement results for the

NDTs in the C755-T2 are shown in Figure 29. The average CORA score for all NDTs (in

x- and z-directions) is 0.445. The average CORA score in the x-direction is 0.383 and in

the z-direction is 0.508. The NDT with the highest CORA rating in the x-direction was

A2 and in the z-direction was P3 with ratings 0.653 and 0.713, respectively. When

considering combined x- and z-direction CORA scores, P2 had the highest score of 0.539

and A4 had the lowest with 0.275.

3.2 C383-T1

The results for the NDT relative displacements for the C383-T1 impact are shown

in Figure 30. The average CORA score for all NDTs for the frontal case is 0.421. The

average CORA score in the x-direction is 0.391 and in the z-direction is 0.452. The NDT

with the highest CORA rating in the x-direction and the z-direction was P6 with ratings

0.564 and 0.675, respectively. The NDT with the highest average x- and z-direction

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CORA rating was P6 with a score of 0.620 and the NDT with the lowest average CORA

score was P1 with a score of 0.261.

3.3 C291-T1

The results for the relative displacements of the NDTs in the C291-T1 case are

shown in Figure 31. The average CORA score for all NDTs for this case is 0.412. The

average CORA score in the y-direction is 0.416 and in the z-direction is 0.408. The NDT

Figure 28. Relationship between CORA and shear modulus, G0, for material optimizations

in occipital (a), frontal (b), and parietal (using optimized falx model) (c) impact

configurations. The simulation representing the optimal material model for each condition

optimized individually is shown (C755*, C383*, C291*), as well as optimized concurrently

(ALL*)

with the highest CORA rating in the y-direction and the z-direction was PL4 with ratings

0.519 and 0.689, respectively. The NDT with the highest average y- and z-direction

CORA rating was PL4 with a score of 0.604 and the NDT with the lowest average CORA

score was A4 with a score of 0.207. Refer to Figure 25 for anatomical reference of NDT

locations.

57


properties for Hardy C755-T2 occipital impact for anterior (A) and posterior (P) NDT

columns


properties for Hardy C383-T1 frontal impact for anterior (A) and posterior (P) NDT

columns

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properties for Hardy C291-T1 lateral impact for the anterior (A) and posterior (P) right (R)

and left (L) columns

4 DISCUSSION

A finite element model of the human brain was developed in the current study

using a voxel-based mesh generation approach. A novel method to determine the material

properties of the brain was employed using Latin Hypercube Sampling to vary material

parameter values and CORA to evaluate response and quantify error. During this process,

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brain and falx material properties were concurrently optimized against localized

displacement data from three cadaver experiments. The three experiments considered

(C755-T2, C383-T1, and C291-T1) were chosen because they are dynamic impacts,

varying in direction of impact as well as severity of impact which allows for evaluation

of the ABM in a wide range of loading conditions.

An important observation from the relationships displayed in Figure 26 is the

regression strengths between CORA and each material parameter. The parameter with the

strongest relationship to CORA is, by far, the shear modulus, G0 with piecewise

regression coefficients of 0.755, 0.686, and 0.887 for the occipital, frontal and lateral

impacts, respectively. The next largest coefficients result from regressing the shear ratio,

G∞/G0, and CORA, and the strongest of these achieves only 0.101, which signifies a

much weaker relationship than was observed for G0. This reinforces that G0 stands out as

the most important parameter in determining the response of the brain. The general trend

between G0 and CORA, is that increasing the shear stiffness improves the CORA rating

up until a critical value – after which continued increase in stiffness causes the response

to deviate from the experimental data and the CORA score to decrease. For the occipital

and frontal cases, this critical shear modulus value occurs around 4.5 kPa (log(4.5 kPa) =

1.50). The critical value for the lateral case, however, is almost 20 kPa (log(20 kPa) =

3.00). In other words, during this original material optimization process the frontal and

occipital cases optimized to similar material properties, while the optimal shear properties

for the lateral case were much stiffer. This can be deduced from the values in Table 4, as

well as by examining the plots in Figure 28 that relate CORA and the shear modulus, G0.

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The relationship between CORA and the shear parameters is comparable for the

C755-T2 and C383-T1 variations. The CORA score reaches a maximum at very similar

values of G0 for these two configurations, but the CORA score clearly peaks at a larger

G0 in the C291-T1 variation. Because the two cases with motion in the sagittal plane

(C755-T2 and C383-T1), which is parallel to the falx, gave similar results, while the

lateral case differed, we conducted an additional LHS varying falx pretension and

thickness. Examining the results of this variation (Figure 27), the general trend observed

in pretension, is an increase in model performance with increasing pretension up to about

4%, and then a plateau in CORA score to around 8%, followed by a slight decrease when

pretension is increased beyond 8%. We see a stronger relationship between CORA and

falx thickness than was observed between CORA and pretension. With increasing falx

thickness, there is an increase in the CORA score up to the peak thickness of 2.86 mm

followed by a relatively constant CORA score following this maximum. This plateau in

CORA scores between 2 and 3 mm supports falx thickness measurements reported in

literature, as opposed to the larger values investigated which were not derived from

physiological measurements. This plateau behavior indicates that optimized material

properties may be achieved without the need to use an unrealistically large falx thickness.

The upper value for the thickness range was derived from Takhounts et al. (2003), who

stated that this thickness value is larger than physiologically observed, but was used

anyway in an effort to avoid sharp contact along edges of the falx and to ease the

numerical contact interaction [3].

At first glance, there does not appear to be much improvement in the lateral

impact results after incorporating the optimized falx model (Table 4), considering the

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shear modulus only decreases from 19.20 kPa to 17.26 kPa, which is still much greater

than 4.121 kPa and 4.634 kPa, the values for the occipital and frontal cases, respectively.

Looking closer at the relationships between CORA and G0 (Figure 28), however, there is

an interesting characteristic of the relationship in the lateral variation (Figure 28C) – a

local maximum, which was not present when using the original falx model. While the

global maximum value of CORA for this variation occurs at 17.26 kPa, there is a local

maximum at 5.6 kPa, which is much more comparable to the optimal shear modulus

values obtained from the occipital and frontal variations. Furthermore, the result of

concurrently optimizing the three impact conditions produces a shear modulus value very

near this local maximum.

The results of the brain parameter variation study in the lateral case using the

optimized falx model (Table 4), along with the results from the occipital and frontal

variations suggest that the best model response is achieved by using the brain material

model determined by a concurrent optimization of the C755-T2, C383-T1, and C291-T1

impact conditions. Examining the experimental NDT motion following the C755-T2

occipital impact, the response is generally characterized by a figure-eight or looping

pattern. Each NDT displays a small (~1 mm) initial displacement followed by a larger

displacement and rotates either counterclockwise or clockwise, depending on the z

location of the NDT with respect to the CG. Counterclockwise rotation is observed in the

NDTs closer to the CG of the head, while the rotation is clockwise nearing the top of the

head. In general, ABM validation against C755-T2 local displacements shows good

agreement with experimental data for nearly all NDTs. ABM response in the x-direction,

in general, displays very good agreement in magnitude and shape for all NDTs, excluding

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A4, P4, and P5. We observe a magnitude discrepancy in A4 and P5, and in P4, there

appears to be a phase error. In the z-direction, there is very good shape and magnitude

agreement overall, however, there is a slight magnitude difference in A1 and a minor

shape difference in P1.

The ABM validation results from the frontal impact condition, C383-T1, show

good agreement with experimental data for many of the NDTs. As seen in Figure 30,

C383-T1 is a longer impact (118 ms) with a more complex response than the occipital

case (59 ms). In the C755-T2 case, the displacement responses, in general, are simple

curves with a single peak. For C383-T1, however, the responses have more complex

characteristics and usually contain multiple peaks. However, even with this added

complexity, the ABM predicts local brain displacements with comparable shape to the

experimental data. In the x direction, the ABM predicts response with very similar shape

to the experimental data for A1, A2, A5, A6, P1, P2, P5 and P6. While the overall shape

is similar, the ABM under-predicts displacement in the inferior NDTs, and over-predicts

displacement for more superior NDTs. For some NDTs, such as A4 and P3, the ABM

response generally agrees with the experimental data at some phases of the simulation,

while deviating at others. In the z direction, the ABM follows the overall trend of the

experimental data in most cases (A1-A5, P2-P6). When the predominant experimental

response is increasing displacement, the ABM also predicts increasing displacement

throughout the simulation, although in the case of the ABM we see more pronounced

local minimums and maximums when compared to the experimental curves, where the

response is steadier. Comparing the overall CORA score of the C755-T2 case (0.445) to

the C383-T1 case (0.421), we see that the ABM does not perform as well in the C383-T1

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frontal configuration. This is not unexpected since the NDT displacement responses are

more complex in the longer, frontal case, and therefore are more difficult to match.

Despite this challenge, however, the ABM still predicts overall displacement magnitude

with acceptable accuracy.

The experimental NDT displacements, as well as the local displacements

predicted by the ABM, for the C291-T1 parietal impact are shown in Figure 31. For this

experimental condition, there were three columns of five NDTs; one column in the

hemisphere of the brain which was impacted (right), and two columns in the hemisphere

opposite to the location of impact (left). For the right NDT column, displacement results

were reported for only 3 of the 5 NDTs (1, 4 and 5), and for the posterior column on the

left side, results were reported for 4 of the 5 NDTs (2 - 5). Examining the results of the

right NDT column, the ABM predicts response very well in overall shape as well as

magnitude in the y-direction. The predicted displacement in the z-direction does not

agree quite as well with experimental data over the whole simulation, but does display

reasonably good agreement at the beginning (~50 ms) of the response. Considering the

two NDT columns in the left cerebral hemisphere, the predicted y response generally

shows good agreement with experimental displacement, with the exception of A4 and

A5. The ABM considerably underestimated the magnitude of the y-displacement for both

of these NDTs. In the z-direction we see a similar trend – very good agreement for all

NDT’s except A4 and A5. Even though A4 and A5 show the worst agreement of all the

z-direction responses of the left NDTs, the ABM did estimate the z-displacements for

these two NDTs much better in the z-direction than the y-direction.

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The selection of material properties for the brain model and parameters is a vital

aspect of studying and understanding brain injury. There are several different material

models that are frequently used in current brain FEMs including linear elastic,

viscoelastic, and hyperelastic. Additionally, material parameter values differ significantly

throughout the literature due to the difficulty in characterizing the brain material

response. The range of values reported for shear properties in particular is quite large –

spanning two orders of magnitude (Table 2). Examining the values of shear moduli

reported throughout literature, we do see a large number of references to values between

5 and 15 kPa, despite the much larger overall range. The shear material properties

identified in this study are similar to those values consistently reported in literature.

4.1 Limitations

Limitations of this study include various simplifications and assumptions in the

model itself, as well as limitations of the experimental methods considered and their

application to FE models. Geometric simplifications of the ABM include the combined

gray and while matter in the cerebrum, as well as the omission of some other functionally

important brain structures, such as the corpus callosum. Also, while the cerebellum is

separate from the cerebrum, it does not have distinct material properties. Even with such

simplified geometry, however, the ABM was still able to achieve good overall response

and perform well in validation tests. Additional limitations are introduced by the

assumption that the brain is isotropic. We know from the examination of its complex

structure that brain matter is anisotropic - particularly white matter, which consists of

bundles of axons that are highly oriented [25]. The brain-skull interface is also simplified

in the ABM. It is modeled with shared nodes, which does not allow lateral motion at the

65

interface of the CSF and skull. While this is a simplification of the brain-skull interface,

we investigated other boundary conditions, such as surface to surface and sliding

contacts, and determined its formulation had little effect on the results of interest in the

current investigation. We concluded that the separation of the brain and skull with the

CSF material at all boundary locations was the most important and ensuring this resulted

in a good response. Another characteristic of the ABM that may introduce error is the

‘stair-stepped’ nature of the elements. Since the ABM was developed using a voxel-based

approach, all interfaces in the model possess cubic elements interacting with one another.

While this feature of the ABM is not ideal, we did not observe any unusual strains in the

edge elements at the boundary between the brain and CSF, probably owing to small

element size and the compliant boundary condition created by surrounding CSF.

Limitations of the application of the experimental conditions include errors introduced by

the difference in head geometry between the ABM and cadaveric specimens. The three

experimental configurations considered all used different cadavers with slightly different

head size and shape, which were all compared to the ABM, which represents the average

brain. However, the average brain dimensions for the three cadavers tested

experimentally did not differ greatly from the ABM. Additionally, there is error

associated with the location of the head CG since it was estimated with respect to the

Frankfurt plane using medical images.

4.2 Future Work

Future development of this model will involve a distinction between gray and

white matter, which will allow more differentiated and directional material models for

both. Additionally, there may be additional brain structures distinguished in the model,

66

such as the corpus callosum, brainstem, and meningeal layers. Additional improvements

to these material models may include the incorporation of directional anisotropy (white

matter), regional differences, if any, and age dependence. Also, adding a skull presents

great room for expanded capability. A more detailed skull model is of interest to be able

to model a wider variety of impacts, such as blunt impact which may involve skull

deformation. Improvement to the model may also include enhancement of the brain-skull

interface, which could involve smoothing of the elements resulting from the voxel-based

mesh generation method. Additionally, the voxel-based method presented in the current

study allows the production of patient or population-specific models in the future. The

detailed comparison of the model performance with other computational models from the

literature was beyond the scope and space limitations of the current study but will be

explored separately. Overall, the ABM CORA analysis demonstrated improvement over

the capabilities of existing, validated brain FE models, and is the first FE model to

determine brain material parameters through multi-objective optimization.

5 CONCLUSION

The model developed in the current study from the ICBM atlas is an anatomically

accurate brain model developed through voxel-based mesh generation. It is the first

dynamic biomechanical finite element brain model to include detailed three-dimensional

gyral folds for studying detailed brain deformation that has been validated in multiple

cadaver experiments against brain displacement data. It is also the first to utilize

multiobjective, multidirectional optimization with quantitative comparison between brain

deformations and experimental findings. A great deal of attention has been paid to the

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boundary conditions of the model and many mechanical parameters which influence its

biofidelity. The high image resolution of the atlas used in this approach allows detailed

modeling of the intricate gyral folds on the surface of the brain, which enables the study

of local tissue response, particularly at the depths of the sulci. Since there is substantial

variation in reported values of brain material properties throughout the literature, and

direct quantitative comparison to experimental results is lacking in the literature, the

parameters governing the viscoelastic response of the brain and the displacements of

multiple locations were examined in great detail in this study. Material optimization was

performed using a novel method which simultaneously optimized model response in

three distinct experimental configurations to establish appropriate values for brain

material parameters. The use of multiple experimental conditions in this optimization

process allows researchers to verify that the identified properties are actually approaching

the true properties of the brain, as opposed to creating a model that is highly optimized to

one impact configuration of a single severity and direction or developed based on

inconsistent material testing methods. Additionally, CORA is applied to the results of

each simulation and used to quantify the error between experimental and predicted

displacements. CORA is demonstrated to be a powerful metric for evaluating model

performance, as it is able to capture multiple aspects of curve similarities, such as phase

and progression.

The CORA ratings reveal that the ABM performs well in all dynamic

experimental configurations investigated- including frontal, lateral, and occipital. Even

with known simplifications, the ABM is able to predict local brain displacements with

considerable accuracy when compared to experimental cadaver data, which supports the

68

model’s use in the study and simulation of brain injury. Initial validation of the ABM

shows competitive results when compared with existing FE models, and the anatomic

accuracy permits enhanced representations of local stress and strain. Investigation of

stress and strain distributions throughout the brain from FE models may help characterize

injury mechanisms, and the enhanced detail and accuracy provided by the ABM may

allow greater insight into region-dependent injuries, such as concussion and CTE. Further

development of the ABM will lead to improved ability to model brain response and

predict injury, which aid in a deeper understanding of the biomechanics of head injury.

Ultimately, the investigation of injury mechanisms and thresholds through the use of

finite element models can be used to predict and prevent traumatic brain injuries.

6 ACKNOWLEDGEMENTS

Funding for this project is provided by the National Institutes of Health (R01 NS082453).

All simulations were run on the DEAC Cluster at Wake Forest University. The authors

would like to thank the ANSIR lab for providing the ICBM labelmaps and Elizabeth

Lillie for her work on the MATLAB code to produce the ABM from the labelmaps.

69

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72

Chapter III: Comparison of Validation Data for Finite Element

Models of the Human Head

Logan E. Miller, Jillian E. Urban, Joel D. Stitzel

Virginia Tech – Wake Forest University Center for Injury Biomechanics,

Winston-Salem, NC

73

ABSTRACT

Traumatic brain injury (TBI) is a leading cause of disability and injury-related death. To

prevent these injuries, we must develop a better understanding of the underlying injury

mechanisms. One way we can study brain injury is through finite element (FE) models.

In the current study, a high-resolution, anatomically accurate FE model, the ABM is

proposed as a new tool for studying brain injury with the ability to capture accurate local

stresses and strains throughout the sulci and gyri, which have been shown to be important

in injury prediction. Validation against local brain deformations for three experimental

cadaver tests (C755-T2, C383-T1, and C291-T1) is presented for the ABM and

quantitatively compared to other validated FEMs using a comparison metric called

CORA (CORrelation and Analysis). The model developed and presented in this study

will be used to better understand the fundamental mechanisms behind TBI and serve as a

tool to predict and prevent brain injury.

Keywords: Brain model, head injury, validation, optimization, finite element model,

CORA

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1 INTRODUCTION

Each year, approximately 1.7 million people in the United States suffer from

traumatic brain injury (TBI) [1]. TBI is a major public health concern as it is a leading

cause of disability and injury-related death - accounting for nearly one third of all injury-

related deaths [2]. To prevent and treat these types of injuries, the fundamental injury

mechanisms need to be well-characterized and understood. There are various theories

about what causes brain injury, such as the development of positive and negative pressure

in coup and contrecoup injuries, rotational effects, and relative motion between the brain

and skull [3, 4, 5, 6]. Although each of these mechanisms has been shown to induce

injury, there is still a great deal that we do not know about the fundamentals of brain

injury, as well as injury thresholds. Various methods have been used over the years to

investigate and gain a deeper understanding of brain injury mechanisms, including animal

tests, cadaver studies, anthropomorphic test devices (ATDs), and computational models

[7]. Finite element (FE) models are powerful tools because they can provide spatial and

temporal distributions of stresses and strains over the problem domain. The quality of a

model’s predictions, however, is dependent on the accuracy of the modeled geometry and

the model’s ability to describe complex mechanical behavior and material response.

The earliest efforts to study the human brain through FE modeling was conducted

in 1943 by Hardy and Marcal [8], who constructed a two-dimensional (2D) FE model

consisting of only the skull. As computation power improved, three-dimensional (3D)

models became more achievable. The earliest 3D models generally used very simplified

(spherical or ellipsoidal) geometry and generally considered detailed material properties

75

of only either the brain or skull. An example of an early 3D FEM developed by Hosey

and Liu [9] in 1981 is shown in (Figure 32). It was not until the 1990s that we began to

Figure 32. (A) Sagittal and (B) coronal cross sections of the FEM developed by Hosey and

Liu [9] in 1981.

see models developed based on the true geometry of the human head. The first of its kind

was described by Ruan et al. [10] in 1993. Since then, FEMs with varying degrees of

anatomical accuracy, element size and material properties, have been developed. The

process typically employed in current FEM development begins with image segmentation

of medical images, such as computed tomography (CT) and magnetic resonance imaging

(MRI), to define 3D surfaces of desired structures, followed by a surface-based mesh

generation process. During the mesh generation process, complex anatomical features are

frequently simplified and ‘smoothed’ to allow faster development and simple contact

definition at model interfaces. One feature of particular importance that is over-simplified

in many brain FEMs is the gyral folds on the surface of the brain. The brain surface is

76

typically modeled as a smooth surface surrounded by a uniform layer of cerebrospinal

fluid (CSF), which ignores the intricate gyral folds throughout the brain. This

simplification and reduction in geometrical accuracy could significantly impact the

model’s local brain response and prediction of injury. Indeed, studies have indicated that

the intricate folding patterns on the surface of the brain greatly affect both the distribution

and magnitude of stress and strain throughout the brain [11]. Another limitation of

previous models is the substantial amount of time required for the surface-based mesh

generation process, which hinders production of patient-specific models. Patient-specific

models are desirable to study head injury due to significant variations in brain

morphology between individuals [12, 13, 14].

Another challenge in FE modeling of the human head is the determination of

accurate material properties for various anatomic structures. Despite over 50 years of

biomechanical testing and data, there are large variations in reported mechanical

properties of brain tissue. Reported values for shear relaxation moduli, for example, span

Figure 33. Relaxation moduli versus time from the literature [15].

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orders of magnitude (Figure 33). Additionally, constitutive models for brain tissue vary in

the literature. These models include linear elastic models [5, 15, 16], linear and quasi-

linear viscoelastic models [17, 18, 19], hyperelastic [21], and fully nonlinear Green-

Rivlin models [21, 22].

Before numerical models are applied to injury prediction and simulation, they

must be validated against experimental data inputs to ensure that the model behaves the

way we expect. Brain FEMs are frequently validated against brain pressure and/or brain

motion data. The studies typically used to validate the pressure response are the cadaver

experiments conducted by Nahum et al. (1977) [24] and the long-duration impact

conducted by Troisseille et al. (1992) [25]. The localized brain motion data typically used

for validation purposes is the set of cadaver experiments conducted by Hardy et al. [13,

14]. Many currently used FEMs have only been validated intracranial pressure (ICP)

experiments, but it has been shown that the correct pressure response does not necessarily

mean the model is predicting the correct strain [27, 28]. Although the pressure data is

important to be able to replicate in a brain FEM, there is some controversy about whether

validating against only pressure data is sufficient, since some brain injuries (e.g., diffuse

axonal injury) are found to be dependent on strain [30]. This motivates validation using

the more robust displacement data set that captures the strain field that develops in the

brain, as opposed to a single value of pressure.

The objective of the current study is to present local brain motion validation

results for three experimental configurations for a high resolution, anatomically accurate

FEM, the ABM (atlas-based brain model), and compare results to other validated FEMs.

The three cadaver impact tests considered in the current study are: C755-T2, C383-T1,

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and C291-T1 [13, 19]. The additional FEM’s considered are the Simulated Injury

Monitor (SIMon), Global Human Body Models Consortium (GHBMC) head model,

Total Human Model for Safety (THUMS) head model, Kungliga Tekniska Högskolan

(KTH) model, and the Dartmouth Head Injury Model (DHIM). Results for three of these

models, SIMon, GHBMC, and THUMS, were obtained through simulation of the

experimental conditions, whereas results for the remaining models were obtained from

published literature.

2 METHODS

The ABM FE model [32] was developed from the geometry of the ICBM adult

brain atlas, which represents the average adult brain [33] (see Appendix for model

development summary). The ICBM atlas contains 58 independently labeled regions of

the brain including cortical gyri, white matter, gray matter, and CSF. An FE model was

created from this image set by converting each 1mm isotropic voxel into a single element

of the same size using a custom code developed in MATLAB (The MathWorks, Natick,

MA) (Appendix . The ABM consists of a rigid skull, cerebrum, cerebellum, CSF,

ventricles, falx and tentorium (Figure 23). The brain-skull interface was modeled with a

soft CSF layer between the brain surface and the skull to allow relative motion between

the two through CSF deformation (all part interfaces are modeled with shared nodes).

Brain tissue in the ABM is modeled using a linear viscoelastic material formulation

(*MAT_061 in LS-DYNA). The shear relaxation behavior is characterized by:

𝐺(𝑡) = 𝐺∞ + (𝐺0 − 𝐺∞) ∗ 𝑒−𝛽𝑡 (11)

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where G∞ is the infinite shear modulus, G0 is the initial shear modulus, and β is the decay

constant. The parameters for this material model were optimized in Miller et al. [32] and

are listed in Table 5.

Figure 34. (A) ABM showing the falx, tentorium, and ventricles, and (B) axial, (C) sagittal,

(E) coronal, (D) isometric cross sections.

2.1 FEM Description and Comparison

In the current study, the ABM response will be compared to five brain FEMs,

including two head models from full body FEMs. Brief descriptions and a comparison of

the models are provided in the following section and summarized in Table 5.

Simulated Injury Monitor (SIMon)

The SIMon model was developed by Takhounts and Eppinger in 2003 and

consists of relatively simple geometry with the goal of very short run time. The model

consists of a rigid skull, CSF, cerebrum, cerebellum, brain stem, ventricles, bridging

veins and a falx and tentorium (Figure 35). All part interfaces are modeled with merged

nodes and a Kelvin-Maxwell viscoelastic formulation is used to model brain material.

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Figure 35. (A) Isometric view of the SIMon FEM with exposed brain and (B) isometric view

of the FEM showing various anatomical features represented in the model.

The model was improved upon and validated by Takhouts et al. [35] in 2008 against two

pressure experiments: Experiment 37 conducted by Nahum et al. [24] and the long-



C291-T1.

Global Human Body Models Consortium (GHBMC)

The GHBMC head model was meshed from a Computer Aided Design (CAD)

dataset developed from MRI and CT scans of an average adult male. The set included

geometry representing skin surface, skull and facial bones, sinuses, cerebrum,

cerebellum, lateral ventricles, corpus callosum, thalamus, and brainstem (Figure 36).

Geometry for cerebral white matter was also used to develop white matter meshes.

Aspects of the anatomy not included in the CAD dataset but that were implemented into

the model include the falx and tentorium, bridging veins, and the meningeal layers (pia,

arachnoid, dura). A tie-break contact was defined between the dura and arachnoid layers

to model the relative motion at the brain-skull interface. A Kelvin-Maxwell viscoelastic

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midsagittal view of the FEM [36].

model was used to model the gray and white matter. The pressure response of the

GHBMC head model was validated against six cases from the study conducted by

Nahum et al. [24] and one case from Trosseille et al. [25]. Additionally, Mao et al. [36]

stated that eight impact cases from the series of cadaver impact tests conducted by Hardy

et al. [17, 18] were selected for validation, although only results for the C383-T3 case

were presented in [36].

Total Human Model for Safety (THUMS)

The head model from the Total Human Model for Safety (THUMS) Version 4.01

(THUMS AM50 Ver 4.01, Toyota TCRDL, Japan) was used in the current study. Model

development for previous versions of the head model are described in Kimpara et al. [37].

The basic anthropometry of the skull was partially obtained from a commercial data

package (Viewpoint Datalabs, USA) and then modified based on anatomical references

[38]. The basic geometry of the brain model was obtained from a male data set available

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in the Visible Human Project (NIH, USA) and was created according to anatomical

references. The THUMS head FEM consists of the skull and facial bones, cerebrum

(distinct white and gray matter), cerebellum, brainstem, CSF, meningeal membranes, falx

cerebri, tentorium cerebelli, and the sagittal sinus (Figure 37). To represent contact with

Figure 37. (A) Isometric view of the THUMS v4.01 head model with the brain exposed and

(B) midsagittal view of the FEM.

the CSF, tiebreak interfaces were used to simulate frictionless sliding behavior. This

contact formulation was assumed between the dura and arachnoid layers, as well as

between the falx and surrounding soft tissue elements. A linear viscoelastic material

model was used to model the response of the gray and white matter. A previous version

of the THUMS head model was validated against pressure and brain displacement

experiments by Kimpara et al. [37], but the current version has not yet been validated.

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Kungliga Tekniska Högskolan (KTH)

Kleiven and Hardy proposed an FEM of the human head in 2002 known as the

Kungliga Tekniska Högskolan (KTH) FEM [12]. This model includes the scalp, skull,

cerebrum, cerebellum, meninges, CSF, bridging veins, and a simplified neck (Figure 38).

Figure 38. (A) Section view of the KTH head and neck model [28], and (B) cross section

showing FE mesh and anatomical structures represented in the model [12].

The brain-skull interface is modeled with tied nodes between the skull and dura with a

sliding contact with no separation between the CSF and the meningeal membranes and

brain. Brain tissue is modeled with a hyperelastic Mooney-Rivlin constitutive model

combined with a linear viscoelastic model to account for rate effects. The Mooney-Rivlin

and shear constants used in this model (Table 5) are based on those derived by Mendis et

al. [39], but scaled corresponding to an effective (long-term) modulus of 520 Pa, while

the decay constants were not altered [40]. The model was validated by Kleiven [40] in

2006 against two pressure experiments: Experiment 37 conducted by Nahum et al. [24]

and the long-duration impact conducted by Trosseille et al. [25], as well as the following

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local brain displacement experiments conducted by Hardy et al. [17, 18]: C755-T2,

C383-T1, and C291-T1.

Dartmouth Head Injury Model (DHIM)

The Dartmouth Head Injury Model (DHIM) was created from a high-resolution

T1-weighted MRI of an athlete clinically diagnosed with concussion. The model features

a skull, facial bones, cerebrum (combined white and gray matter), cerebellum, brainstem,

corpus callosum, meningeal layers, CSF, ventricles, falx cerebri and tentorium cerebelli

(Figure 39). The brain-skull interface was modeled with a soft CSF layer between the

Figure 39. (A) Isometric view of the DHIM FEM and (B) isometric view of the FEM

showing various anatomical features represented in the model [48].

brain surface and the surrounding structures to allow brain interfacial sliding through

CSF deformation (nodes between all anatomical interfaces were shared) [41]. An Ogden

hyperelastic material model identical to the ‘average’ model reported by Kleiven [42] in

2007 was employed for brain tissue, in addition to a six-term Prony series characterizing

viscoelasticity. The model was validated by Ji et al. [43] against the following local brain

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C393-T4.

Table 5. Comparison of FEMs

#elements/

#nodes

Mass

(kg)

Material

Model Brain Shear Parameters

ABM 2,000,000/

2,000,000 1.74

† Viscoelastic G0 = 5.16 kPa, G∞ = 1.86 kPa, β = 67.58 s

-1

SIMon 46,000/

42,500 1.10

† Viscoelastic G0 = 1.66 kPa, G∞ = 0.928 kPa, β = 16.95 s

-1

GHBMC 230,000/

190,000 1.19

† Viscoelastic

G0 = 6 kPa, G∞ = 1.2 kPa, β = 12.5 s-1

(gray)

G0 = 7.5 kPa, G∞ = 1.5 kPa, β = 12.5 s-1

(white)

THUMS 62,000/

38,000 1.08

† Viscoelastic G0 = 6 kPa, G∞ = 1.2 kPa, β = 0.06 s

-1

KTH 18,000/

19,000 4.44* Hyperelastic

G1 = 1628 Pa, G2 = 930 Pa, β1 = 125 s-1

,

β2 = 6.67 s-1

DHIM 115,000/

101,000 4.56* Hyperelastic

g1 = 7.69e-1, τ1 = 1e-6 s

g2 = 1.86e-1, τ2 = 1e-5 s

g3 = 1.48e-2, τ3 = 1e-4 s

g4 = 1.90e-2, τ4 = 1e-3 s

g5 = 2.56e-3, τ5 = 1e-2 s

g6 = 7.04e-3, τ6 = 1e-1 s †brain mass

*total model mass

2.2 Validation against localized brain displacements

The validation experiments considered in the current study are the following

cadaveric tests: C755-T2, C383-T1, and C291-T1 [13, 19]. Summary characteristics for

the three tests are shown in Table 3. In these experiments, local displacements at various

locations within the brain were analyzed† using implanted radio-opaque neutral density

targets (NDTS) and a high-speed biplanar X-ray system to track their relative motion.

Three-dimensional skull kinematics were evaluated with an accelerometer array affixed

to the cadaver skull and used to determine linear and angular velocities at the head center

of gravity (CG), which were then used as boundary conditions to drive each FEM

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simulation [31]. The linear and rotational velocity curves for each experimental

configuration are shown in Figure 40. To compare local displacements between the ABM

Table 3. Summary of Experimental Test Conditions

Hardy C755-T2 Hardy C383-T1 Hardy C291-T1

Impact location occipital frontal parietal (R)

Impact type acceleration deceleration deceleration

Relative severity low medium high

Peak G 22 63 162

Delta V (m/s) 1.90 3.91 4.47

NDTs 2 columns of 5 2 columns of 6 3 columns of 5* *results for all NDTs in this test were not reported

and the experimental data, nodes closest to the physical location of each NDT were

identified for each test configuration and local displacements at these nodes were

computed throughout simulation. For each NDT, the element within which the initial

coordinate NDT location fell was located, and the 8 nodes used to define that cubic

element were tracked - the mean displacement of these 8 nodes was taken as the

displacement of the simulated NDT. Approximate NDT locations for the three impacts

are shown in Figure 41 in the plane of primary motion – for the occipital and frontal

impacts, the NDTs are displayed in the sagittal plane and for the lateral impact they are

displayed in the coronal plane. For the occipital and frontal cases, the locations of the

cross-sections are at the approximate y-location of the NDT columns – approximately 35

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mm in the negative y direction for both cases. For the lateral case, Table 3 shows that

there are three columns of NDTs: anterior and posterior columns on the left side of the

Figure 40. Velocity load curves for the three experimental configurations.

brain and a second posterior column on the right side. The coronal cross sections to

visualize the NDT locations for the C291-T1 impact are taken near the CG of the head, or

between the anterior and posterior columns. In Figure 41C, the two posterior columns are

displayed in white and the anterior column in gray.

The results for the SIMon, GHBMC, and THUMS models were obtained through

simulation, in a similar process as described above for the ABM. For each model, the

velocity curves were applied to the rigid skull with respect to the head center of gravity

(CG). For NDT tracking, the element that encompassed the coordinate NDT location was

identified, and the 8 nodes defining that element were tracked and the mean displacement

was calculated. The average element size for each of these three models is larger than in

the ABM, so the average distance from the true NDT coordinate to each of the 8 nodes

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was larger. Figure 41 shows the initial NDT locations for all three experimental

configurations for the ABM, SIMon, GHBMC and THUMS models.

Figure 41. Approximate NDT locations in ABM, SIMon, GHBMC, and THUMS models for

C755-T2 occipital impact (A), C383-T1 frontal impact (B) and C291-T1 parietal impact (C).

For the remaining models, validation results available in the literature were digitized for

comparison to results from the other FEMs. Results for all three tests for the KTH model

were reported in Kleiven (2006) [40]; not all NDTs were reported for the C291-T1 case,

however. For the DHIM model, Ji et al. (2014) [34] reported validation results for the

frontal and occipital cases only. Additionally, only the ‘corner’ NDTs were reported –

that is, the highest and lowest NDT in the anterior and posterior columns.

2.3 Model Performance

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To evaluate model performance for each impact condition, the error between

experimental and predicted displacements for each NDT was quantified using a metric

called CORA (CORrelation and Analysis) [44]. CORA evaluates the similarity of two

curves by calculating a rating using two methods: the corridor method and the cross-

correlation method. Both ratings range from 0 to 1 and are averaged to determine a total

CORA score (1 corresponds to a perfect match). The corridor method computes a rating

based on where the comparison curve falls in relation to corridors around the reference

curve. The cross-correlation method is based on ratings for the phase shift, size and

progression of time-shifted curves.

3 RESULTS

The boundary conditions for each experimental configuration were applied to the

four simulated models using an identical method, but since the geometry of the four

models differs, there were slight variations in the linear kinematics of the CG of the head.

The rotational velocity of the CG was identical for all models since the rotational

boundary conditions were prescribed about this point, but we see small differences in the

linear velocity of the CG between the four models (Figure 42).

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Figure 42. Linear velocity at head CG for ABM, SIMon, GHBMC, and THUMS

simulations.

The displacement results for the Hardy occipital impact (C755-T2) for the

anterior and posterior NDT columns are displayed in Figure 43 and Figure 44,

respectively. The displacement results for the frontal (C383-T1) impact for the anterior

and posterior NDT columns are displayed in Figure 45 and Figure 46, respectively.

Finally, the results from the parietal (C291-T1) impact for the right posterior column are

shown in Figure 47, and the left posterior and anterior columns are shown in Figure 48

and Figure 49, respectively. CORA scores for each displacement response for each model

are also displayed in Figure 43-Figure 49. Additionally, average CORA scores were

computed for each model under each of the three experimental configurations and are

displayed in Table 6.

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Figure 43. Local displacement results for Hardy C755-T2 occipital impact for the anterior

NDT column.

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Figure 44. Local displacement results for Hardy C755-T2 occipital impact for the posterior

NDT column.

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Figure 45. Local displacement results for Hardy C383-T1 frontal impact for the anterior

NDT column.

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Figure 46. Local displacement results for Hardy C383-T1 frontal impact for the posterior

NDT column.

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Figure 47. Local displacement results for Hardy C291-T1 parietal impact for the right

posterior NDT column.

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posterior NDT column.

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anterior NDT column.

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Table 6. CORA Scores for each model for all experimental configurations

C755-T2 C383-T1 C291-T1 Average

ABM 0.445 0.421 0.412 0.426

SIMon 0.342 0.411 0.393 0.382

GHBMC 0.433 0.386 0.241 0.353

THUMS 0.418 0.302 0.343 0.354

KTH 0.476 0.419 0.355 0.417

DHIM* 0.316 0.432 - 0.374 *only includes results for 4 ‘corner’ NDTs

4 DISCUSSION

To compare the performance of existing FEMs to experimental data and to each

other, the response under three distinct experimental configurations was examined. To

obtain results for each configuration, either the impact was simulated (for the ABM,

SIMon, GHBMC, THUMS) or results were digitized from existing literature (KTH,

DHIM). Validation data generated through simulation were verified with published data

when available. To verify the application of the boundary conditions for the simulated

models, kinematics of the head CG were tracked and compared to experimental data for

each model. The time history of angular velocity at the CG matched the applied angular

boundary conditions for each model since the boundary conditions were prescribed about

the coordinate system originating at the CG node; the linear velocity time history at the

CG, however, differed slightly between models (Figure 42) and from the applied

boundary curves since the size and geometry of the skull varied between the models. We

see similar trends for the three experimental impacts between the models. Overall, the

models track the experimental velocity curves well and verify that the boundary

conditions have been applied comparably between the four models.

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4.1 C755-T2 Occipital Impact

Experimental Response

Examining the experimental x-displacement of the NDTs following the C755-T2

occipital impact, we observe that each NDT displays a small (~1 mm) initial

displacement in the negative x-direction. The initial negative x-displacement is followed

by a larger displacement in the positive x-direction that peaks at approximately 26 ms

with maximum displacements of larger magnitude for the lowest NDTs (A1-A3, P1-P3).

The initial motion in the z-direction is positive for all NDTs. This motion is most

pronounced in the lowest three NDTs in the anterior column (A1-A3) – for the remaining

NDTs, displacement remains very close to zero for approximately the first 10 ms. Each of

the anterior NDTs experiences a local minimum around 17 ms, followed by the

maximum positive z-displacement around 30 ms. The z- responses then approach a peak

in negative displacement that varies in timing between different NDTs – the minimum

generally occurs later in the posterior NDTs. In general, the magnitude of NDT

displacement was greater in the x-direction than in the z-direction for this impact.

Comparison of FEM Response

The models examined in the current study display similar response when

compared to each other, as well as to the experimental data. We see, in most cases, the

models predict NDT motion in the direction that it was experimentally measured. There

is, however, significant variation between the different models in the predicted

displacement magnitudes for each NDT. Looking at the response of the anterior NDTs

(Figure 43) the ABM, KTH, and GHBMC models display very similar responses to one

another and the best performance overall when compared to the experimental data. The

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response deviates most drastically at the A1 location in the z-direction, where it appears

there may be a phase discrepancy, as well as over prediction by the models. The THUMS

model generally predicts motion of comparable magnitude and pulse width to

experimental displacements, but displays phase discrepancies at many of the NDT

locations (A3X and A4X). For numerous NDTs in the z-direction, the THUMS model

largely underestimates the displacement – specifically A1, A2 and A3. The SIMon model

agrees with experimental data very well in the x-direction for NDT A3, and relatively

well in the z-direction for NDTs A4 and A5, but the remaining responses do not perform

well. There is very little displacement predicted by the SIMon model at A1 and A2 in the

x direction, and at A1, A2, and A3 in the z direction, whereas the experimental data

display displacements between 2 and 3 mm. At NDTs A4 and A5 in the x-direction, a

significant phase error is observed. DHIM results were only reported for the ‘corner’

NDTs (A1, A5, P1, P5). The DHIM performs very well in the two anterior NDTs

reported except in the z direction for NDT A1, where there is a large under prediction in

displacement magnitude. In the posterior column, we again see similar responses for the

ABM, KTH, and GHBMC models for many of the NDTs, although we see diverging

behavior for P4 and P5 in the x-direction and P1 in the z-direction (Figure 44). The

remaining models display responses similar to their behavior in the anterior column. The

THUMS model generally performs better in the posterior column. The SIMon model

again predicts very small displacements at the most inferior NDTs (P1, P2, P3), and the

DHIM performs well at the corner NDTs.

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4.2 C383-T1 Frontal Impact

The frontal impact experiment was longer in duration (118 ms) than the occipital

impact (64 ms). This increase in response time resulted in more complex displacement

signals than were observed in the shorter, C755-T2 impact.


Similar to the C755-T2 experimental NDT response, there is an initial

displacement in the x-direction of approximately 1 mm, although for the frontal impact,

the initial displacements are in the positive x direction for most NDT locations, as

expected. Looking more closely at the experimental NDT response following the initial

displacement, we observe negative x- and z-motion in the inferior portion of the anterior

NDT column (A1-A3) until a peak occurs at approximately 25 ms; following this

minimum, the x- and z-displacements increase to reach maximum displacements around

90 ms ranging from 2 to 4 mm. The same pattern is observed, although slightly less

pronounced for NDTs A4, A5 and A6 in the z-direction. The x-response for these three

NDTs generally displays less total displacement, although all NDTs in the anterior

column do appear to reach a peak at approximately 90 ms. Looking at the posterior

column, for NDTs P1-P4, we again see behavior of the same shape as the response for

many of the anterior NDTs. The x-responses for the remaining NDTs (P5, P6), as well as

the z-responses for all posterior NDTs excluding P1, exhibit the behavior just described,

but of opposite polarity; there is initial negative displacement, a maximum around 25 ms,

followed by a minimum around 90 ms. The maximum displacement at these locations is

generally smaller than the x-displacement of inferior NDTs, but the trend still exists.

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Several models are able to capture the experimental displacement behavior for

many of the anterior NDTs. The ABM, KTH, and GHBMC models consistently

displayed this similar behavior to the experimental NDT motion. Both the ABM and

KTH models predict displacements that match the experimental shape very closely, but

there are magnitude discrepancies of varying size at different locations throughout the

brain. The GHBMC model displays good behavior for most anterior NDTs until about 90

ms, after which the predicted displacements deviate rather significantly from both the

experimental and other simulated data. SIMon predicts a displacement response with

comparable shape at a few anterior NDT locations (A2X, A3X, A3Z), but does not

reliably perform well when compared to experimental results. Examining the results in

the posterior column, all simulated responses appear to have captured the experimental

behavior well, with the exception of SIMon in the case of NDT P1. The overall shape is

accurately predicted by many models, as well as comparable values of displacement. The

largest discrepancies occur in the x-response of P4 and the z-responses of P1 and P3.

4.3 C291-T1 Parietal Impact

The final impact simulated in the current study is the C291-T1 parietal impact. It

is the most severe of the three considered, with a maximum head acceleration of 162 g’s.

This experiment was initialized with three columns of NDTs - an anterior and posterior

column in the left hemisphere of the brain (opposite to impact site), and a posterior

column in the right hemisphere (at impact site). Additionally, this is the only experiment

of the three considered where all data were not able to be collected. Two NDTs in the

right column and 1 NDT in the left posterior column were omitted from the published

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experimental data. This could be attributed to the severity of the impact, especially since

two of the omitted NDTs were located on the side of the head that was impacted, and

therefore sustained more severe boundary conditions. For this reason, the results for the

right NDT column are frequently omitted in model validation studies, so we are only able

to compare results from this column for the four models specifically simulated in the

current study.


Looking at the experimental response in the y-direction, or the direction of

impact, we see initial relative displacement in the negative y direction for NDTs PR4 and

PR5, which is expected as the brain lags behind the skull motion. The positive y-

displacement observed in the inferior-most NDT (PR1) likely occurs because this NDT is

closest to the skull, and therefore its motion does not lag behind skull movement like

locations deeper within the brain. The z-displacement for all the right NDTs oscillates

throughout the response and stays relatively close to zero, with a maximum z-

displacement of 2.2 mm. Considering the response of the other posterior NDT column

(left), we see an initial negative y-displacement, which is capturing the brain motion

lagging behind the skull. Similar to the right NDT column, the z-response displays less

overall motion than the y-direction. In the z-direction, there is a slight initial increasing

displacement, followed by a decreasing trend throughout the rest of the impact. For the

anterior column, the observed trend in y-response is an initial increase and peak around

15 ms, with subsequent decreasing y-displacement to a local minimum at approximately

20-30 ms. This overall trend is consistent in the y-response of the anterior NDTs, with the

exception of A5, whose response is initially in the negative y-direction. The remaining

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response of A5, however, agrees with the rest of the anterior NDTs. The z-response of the

anterior NDTs is similar, in that there is a peak in positive displacement occurring around

15 ms, although less prominent in the z-direction than in the y-direction. The initial z-

response for all anterior NDTs, however, is in the negative direction. Overall, the

displacement magnitudes are much smaller in the z-direction when compared to the y-

direction.


Looking at the response in the right posterior column, the ABM and THUMS

models generally track the experimental data, particularly in the y-direction, although the

ABM over predicts the initial displacement for the most inferior NDT (PR1). Both

models were able to capture the timing of local peaks throughout the response, as well as

overall magnitude for the NDT response in the y direction. In the z-direction, the ABM

and THUMS predictions deviate from the observed displacement, although both models

track relatively well at the beginning of the simulation, up to about 40 ms. The

displacement response predicted by the GHBMC model is much larger in magnitude than

was experimentally observed. This over prediction by GHBMC does not emerge until

about 30 ms into the simulation; the GHBMC estimation matches the actual response

fairly well up to that point. In the left posterior NDT column, all the models considered

capture the timing and magnitude of the initial y-response and peak and the behavior

immediately following the maximum, but we see some deviation approximately 30 ms

into the impact, specifically for NDTs PL2 and PL3. The GHBMC response deviates in

the y-response after 30 ms for all NDTs in this NDT column. A similar trend is observed

in the KTH and GHBMC z-response for this NDT column. The initial z maximum is

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estimated by all the models reasonably well, but after about 30 ms, the KTH and GHMC

responses diverge from the experimental data. The GHBMC response diverges rather

significantly in the z-response for all NDTs. In contrast, the ABM, SIMon and THUMS

models display acceptable agreement throughout the entire simulation. Considering the

response of the anterior NDT column, the KTH and GHBMC models, in general, are able

to capture the initial y-response, but the simulated displacements diverge from the

experimental data as the simulation progresses. In contrast, the ABM, SIMon and

THUMS models under predict the initial peak, but they better match the experimental

response later in the simulation. Although the KTH and GHBMC models were able to

predict the large displacements seen experimentally in the y-direction, these models also

predicted large displacements in the z-direction, which were not observed experimentally.

The models that did not match the large initial y-displacement well (ABM, SIMon,

THUMS) because of under predicted displacement, performed comparatively better in

the z-direction for this NDT column.

4.4 Overall Performance

Looking at model response in the C755-T2 impact, we see that all models perform

relatively well, with the KTH moel scoring the highest average CORA rating of 0.476.

Most of the models considered score the highest CORA rating under this impact

configuration. This is likely because it is the lowest severity impact with the simplest

experimental curves (i.e. few local maxima and minima). In the C383-T1 test, the DHIM

has the highest CORA score. It should be noted, however, that this CORA rating is based

on the response of only 4 of the 12 total NDTs, so it may not be representative of the

response of the DHIM in general. Considering the remaining models, whose performance

106

is based on the response of all 12 NDTs, the ABM performs best with a CORA score of

0.421. Considering the response in the C291-T1 parietal configuration, which was the

most severe impact simulated, the ABM scores the highest CORA rating (0.412).

Additionally, looking at each model’s average CORA score between the three impacts,

the ABM again scores the best CORA rating. This result indicates that of the models

considered, the ABM demonstrates the strongest ability to predict local brain

deformations under a range of impact severities and directions.

5 CONCLUSION

The model presented in the current study, the ABM, is a high-resolution,

anatomically accurate brain model developed through voxel-based mesh generation. It is

the first dynamic biomechanical finite element brain model to include detailed three-

dimensional gyral folds for studying localized brain deformations that has been validated

in multiple cadaver experiments against brain displacement data. The high image

resolution of the atlas used in this approach allows detailed modeling of the intricate

gyral folds on the surface of the brain, which enables the study of local tissue response,

particularly at the depths of the sulci. The ABM is also the first to utilize multiobjective,

multidirectional optimization of material properties, which was motivated by the

substantial variation in reported values of brain material properties throughout the

literature. The material parameters of the ABM were optimized using a novel method that

simultaneously optimized model response in three distinct experimental configurations

and used CORA as the optimization parameter. The use of multiple experimental

conditions in this optimization process allows researchers to verify that the identified

107

properties are actually approaching the true properties of the brain, as opposed to creating

a model that is highly optimized to one impact configuration of a single severity and

direction or developed based on inconsistent material testing methods. Additionally, a

great deal of attention has been paid to the boundary conditions of the model and many

mechanical parameters that influence its biofidelity.

In the current study, validation is presented against local brain displacements.

This is considered a more robust validation metric than frequently used pressure data

because it represents the strain field throughout the brain. Additionally, it has been shown

that a correct pressure response does not necessarily mean the model is predicting the

correct strain [27, 28].

The validation results for three experimental configurations are presented for the

ABM and compared to the following existing FEMs of the human head: SIMon,

GHBMC, THUMS, KTH and DHIM. CORA was applied to the results for each model

and used to quantify the error between experimental and predicted displacements. CORA

is demonstrated to be a powerful metric for evaluating model performance, as it is able to

capture multiple aspects of curve similarities, such as phase and progression. The CORA

ratings revealed that the ABM performs well in all dynamic experimental configurations

investigated, which supports the model’s use in the study and simulation of brain injury.

Additionally, when compared to existing FEMs, the ABM performs the best in the range

of impacts considered.

Investigation of stress and strain distributions throughout the brain from FE

models may help characterize injury mechanisms, and the enhanced detail and accuracy

provided by the ABM may allow greater insight into region-dependent injuries. Further

108

development of the ABM will lead to improved ability to model brain response and

predict injury, which aid in a deeper understanding of the biomechanics of head injury.

Ultimately, the investigation of injury mechanisms and thresholds through the use of

finite element models can be used to predict and prevent traumatic brain injuries.

6 ACKNOWLEDGEMENTS

Funding for this project is provided by the National Institutes of Health (R01 NS082453).

All simulations were run on the DEAC Cluster at Wake Forest University. The authors

would like to thank the ANSIR lab for providing the ICBM labelmaps, the THUMS and

GHBMC teams at Wake Forest University for providing the respective head models, and

Elizabeth Lillie for her work on the MATLAB code to produce the ABM from the

labelmaps.

109

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113

APPENDIX. MODEL DEVELOPMENT

115

Chapter IV: Summary of Research

The work presented in this thesis represents an important contribution to the study and

simulation of head injury. The ABM is proposed as a new method for simulating brain

response that possesses the novel qualities:

1) High-resolution representation of gyral folds on the surface of the brain.

2) Multi-objective parameter optimization of the brain material model against the

local brain displacements of three cadaver experiments.

3) The best performance of currently used FE models of the human head in a range

of experimental configurations of varying severity and direction, quantified using

CORA.

Investigation of stress and strain distributions throughout the brain from FE models may

help characterize injury mechanisms, and the enhanced detail and accuracy provided by

the ABM may allow greater insight into region-dependent injuries, such as concussion

and CTE. Ultimately, the investigation of injury mechanisms and thresholds through the

use of finite element models can be used to predict and prevent traumatic brain injuries.

Research presented in Chapter II and Chapter III is expected to be published in scientific

journals as listed in Table 7.

Table 7. Publication plan for research outlined in this thesis

Chapter Topic Journal

II

Development and Validation of an

Atlas-Based Finite Element Brain

Model

Biomechanics and Modeling in

Mechanobiology†

III

Comparison of Validation Data for

Finite Element Models of the Human

Head

Journal of Neurotrauma*

†Submitted

*Manuscript in preparation

116

Scholastic Vita

Logan E. Miller Graduate Student and Research Engineer Virginia Tech-Wake Forest University Center for Injury Biomechanics 575 N. Patterson Ave, Suite 120, Winston-Salem, NC 27101

Work: 336-716-0946 Cell: 540-908-1279

Email: [email protected]

EDUCATION Virginia Tech – Wake Forest University, Winston-Salem, NC Master of Science, Biomedical Engineering 2013 – Present Thesis: Development and Validation of an Atlas-Based Brain Finite Element Model Research Lab: Virginia Tech – Wake Forest University Center for Injury Biomechanics Advisor: Dr. Joel Stitzel Virginia Tech, Blacksburg, VA Bachelor of Science, Engineering Science and Mechanics 2009 – 2013 Minor: Mathematics

PROFESSIONAL EXPERIENCE Graduate Research Engineer 2013 – Present Virginia Tech- Wake Forest University Center for Injury Biomechanics Wake Forest School of Medicine Winston-Salem, NC - Toyota’s Collaborative Safety Research Center - Development of injury metrics using the Total Human Model for Safety

Undergraduate Research Intern Summer 2012 Virginia Tech-Wake Forest University Center for Injury Biomechanics Winston-Salem, NC Undergraduate Research Intern 2012-2013 Virginia Tech Comparative Biomechanics Lab Blacksburg, VA

LEADERSHIP

Session Tutor 2011 –2013

Academic tutor at Virginia Tech

Led tutoring sessions for individual classes

Social Chair, Engineering in Medicine and Biology Society 2013 – 2014 COMPUTING SKILLS - LS-DYNA

- LS-PrePost

- Matlab

- Microsoft Office

- Geomagic Studios

- Hyperworks

- R

- JMP

- Avizo

PROFESSIONAL AND STUDENT MEMBERSHIPS

Biomedical Engineering Society, VT-WFU Chapter 2013 - Present

Engineering in Medicine and Biology Society, VT-WFU Chapter 2013 - Present

117

PROFESSIONAL CERTIFICATION AND WORKSHOPS

LS-DYNA Fracture Training, Winston-Salem, NC March 2015

LS-DYNA Material Models Training, Winston-Salem, NC February 2014

LS-DYNA Contacts Training, Winston-Salem, NC January 2014

Hyperworks Training, Winston-Salem, NC October 2013

LS-PrePost and LS-DYNA Training, Troy, MI August 2013

BIBLIOGRAPHY

Papers in Refereed Publications

1. Golman AJ, Danelson KA, Miller LE, Stitzel JD. “Injury Prediction in a Side Impact Crash

Using Human Body Model Simulation.” Accident Analysis & Prevention, October 2013;

64:1-8.

2. Miller LE, Urban JE, Stitzel JD. “Development and Validation of an Atlas-Based Brain

Finite Element Model.” Biomechanics and Modeling in Mechanobiology, July 2015. (In

Review)

Papers in Refereed Conference Publications

1. Miller LE, Urban JE, Lillie EM, Stitzel JD. “Preliminary Development and Validation of an

Atlas-Based Finite Element Brain Model.” Biomed Sci Instrum. April 2015; 51:253-259.

2. Kelley, ME, Miller LE, Urban JE, Stitzel JD. “Mesh Smoothing Algorithm Applied to a

Finite Element Model of the Brain for Improved Brain-Skull Interface.” Biomed Sci

Instrum. April 2015; 51:253-259.

Other Conference Papers (Abstract Style or Non-Refereed)


Finite Element Model.” Summer Biomechanics, Bioengineering and Biotransport

Conference, Snowbird Resort, UT, June 2015.


Finite Element Model.” North American Brain Injury Society Annual Meeting, San

Antonio, TX, May 2015.


Finite Element Model.” VT-WFU SBES Graduate Research Symposium Oral

Presentation, Virginia Tech, Blacksburg, VA, May 2015.

4. Miller LE, Urban JE, Lillie EM, Stitzel JD. “Development of an Atlas-Based Finite Element

Head Model.” Biomedical Engineering Society Annual Fall Scientific Meeting, San

Antonio, TX, October 2014.

5. Miller LE, Urban JE, Lillie EM, Stitzel JD. “Development of a Voxel-Based Finite Element

Head Model.” VT-WFU SBES Graduate Research Symposium Poster Session, Wake

Forest, Winston-Salem, NC, May 2014.

Technical Reports

1. Gaewsky JG, Marcus IP, Jones DA, Kelley ME, Miller LE, Koya B, Weaver AA, Stitzel JD.

“Crash Simulation using the Total Human Model for Safety.” Year 4, Quarter 2, Report to

Toyota’s Collaborative Safety Research Center, Ann Arbor, MI, March, 2015.

118

2. Stitzel, JD, Danelson KA, Golman AJ, Gaewsky JG, Miller LE, Weaver CM. “Crash

Simulation using the Total Human Model for Safety.” Year 1 Annual Report to Toyota’s

Collaborative Safety Research Center, Ann Arbor, MI, September, 2012.

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