Content uploaded by Svein Kleiven
Author content
All content in this area was uploaded by Svein Kleiven on Sep 02, 2014
Content may be subject to copyright.
Content uploaded by Svein Kleiven
Author content
All content in this area was uploaded by Svein Kleiven on Aug 28, 2014
Content may be subject to copyright.
02S-76
Stapp Car Crash Journal, Vol. 46 (November 2002), pp. 123-144
Copyright © 2002 The Stapp Association
Correlation of an FE Model of the Human Head with Local Brain Motion –
Consequences for Injury Prediction
Svein Kleiven
Department of Aeronautics, Royal Institute of Technology, Stockholm, Sweden.
Warren N. Hardy
Bioengineering Center, Wayne State University, Detroit, MI, U.S.A.
__________________________________
ABSTRACT – A parameterized, or scalable, finite element (FE) model of the human head was developed and validated against
the available cadaver experiment data for three impact directions (frontal, occipital and lateral). The brain material properties
were modeled using a hyperelastic and viscoelastic constitutive law. The interface between the skull and the brain was modeled
in three different ways ranging from purely tied (no-slip) to sliding (free-slip). Two sliding contact definitions were compared
with the tied condition. Also, three different stiffness parameters, encompassing the range of published brain tissue properties,
were tested. The model using the tied contact definition correlated well with the experimental results for the coup and contrecoup
pressures in a frontal impact while the sliding interface models did not. Relative motion between the skull and the brain in low-
severity impacts appears to be relatively insensitive to the contact definitions. It is shown that a range of shear stiffness properties
for the brain can be used to model the pressure experiments, while relative motion is a more complex measure that is highly
sensitive to the brain tissue properties. Smaller relative motion between the brain and skull results from lateral impact than from a
frontal or occipital blow for both the experiments and FE simulations. The material properties of brain tissue are important to the
characteristics of relative brain-skull motion. The results suggest that significantly lower values of the shear properties of the
human brain than currently used in most three-dimensional (3D) FE models today are needed to predict the localized brain
response of an impact to the human head.
KEYWORDS – Finite element (FE) analysis; human head; brain displacement; intracranial pressure; brain material properties;
brain-skull interface.
__________________________________
INTRODUCTION
A significant number of road accidents influence the
central nervous system in a devastating way.
Mechanical input to the nervous tissue initiates a
cascade of biochemical processes, and often results in
severe injuries with poor prognosis. There has been
increased interest for the use of FE modeling for the
human head during the last decade (Bandak and
Eppinger, 1994; Zhou et al., 1995; Willinger et al.,
1995; Ruan et al., 1997; Claessens et al., 1997;
Zhang et al., 2001). However, the FE models of the
human head today are often average models (such as
50th percentile male), and have fixed mesh density.
The geometry of these models varies in detail. Of
particular importance to a given model of the human
head are the brain-skull interface characteristics, the
constitutive properties used for various structures,
and level of validation that has been achieved.
Because motion between the brain and skull during
head impact has been considered potentially
important to head injury for more than fifty years
(Pudenz and Shelden, 1946; Gurdjian et al., 1968), a
primary concern in FE modeling of the human head
has been the interface between the brain and skull.
Modeling the cerebral spinal fluid (CSF) using linear
elastic solid elements with low shear modulus (Ruan
et al. 1997; Willinger et al.; 1995; Turquier et al.,
1996; Zhou et al., 1995; Zhang et al., 2001) is likely
to allow only small relative motion between the brain
and skull (Al-Bsharat et al., 1999). Another approach
to modeling the brain-skull interface applies contact
algorithms between the brain and the dura mater.
This contact has been defined in different ways
ranging from completely fixed to frictionless sliding
(Bandak and Eppinger, 1994; Cheng et al., 1990;
Dimasi et al., 1991). Few models include the cranial
123
Kleiven and Hardy / Stapp Car Crash Journal 46 (November 2002)
124
aspect of the spinal column together with the
important foramen magnum interface.
Kuijpers et al. (1995) used a 2D FE model of a
parasagittal cross section of the human head to
simulate impacts to the frontal bone of human
cadavers (Nahum et al., 1977). Good agreement was
found between the simulations and experiments for
the coup pressure when using sliding contact
conditions, while the model with the coupled (no-
slip) interface showed poor agreement. Claessens et
al. (1997) developed a 3D FE model of the human
head, also using sliding and coupled conditions for
the brain-skull interface, and also compared the
model results to the experiments of Nahum et al.
(1977). In contrast with the work of Kuijpers et al.
(1995), the no-slip model showed good agreement
with the experiments for the coup pressures, while
the sliding interface model did not. However, neither
study was able to accurately simulate the
experimental contrecoup pressures.
Miller et al. (1998) used a 2D coronal cross section to
simulate rotational tests performed in an
experimental model of severe diffuse axonal injury
(DAI) in the miniature pig. In one version of the
model the CSF was represented by linear elastic solid
elements with low shear modulus. In a second
version a sliding contact algorithm was specified
between the dura mater and the brain with a
coefficient of friction of 0.2. By comparing principal
strain, von Mises stress, and pressure, it was shown
that the sliding interface approach was better able to
predict the location and distribution of axonal injury
and cortical contusions. This study also found the
effect of the coefficient of friction (varied between
0.001 and 0.4) in the sliding interface to be small.
Another important issue in modeling of the human
head is the selection of material properties for various
intracranial structures. The aforementioned three-
dimensional (3D) models use linearly elastic or
viscoelastic constitutive properties and conventional
(displacement-based) finite element formulations that
can create severe numerical instabilities when dealing
with nearly incompressible materials. The choice of
shear properties for the brain tissue is difficult since
the span of published values varies several orders of
magnitude. Donnelly (1998) reviewed and reported
the average values of the shear relaxation modulus
for brain tissue. According to this study, the average
value of the instantaneous shear relaxation modulus
for brain tissue is the order of 1 kPa. Most 3D FE
modeling studies have included properties that are
around 10-1000 times larger than the average
published values. Bandak et al. (1995) used 68 MPa
for the linearly elastic brain in a study of a procedure
for generating a 3D FE model of the human head
from CT images. However, no simulations were
performed using this model. The only study using a
instantaneous shear modulus near 1 kPa is a 2D study
reported by Al-Bsharat et al. (1999). However, the
only result reported was that a high level of distortion
was produced in the model.
Perhaps of greatest importance to FE modeling of the
human head is the level to which a given model has
been validated. Most models have been validated
against the pressure data of Nahum et al. (1977).
However, Bradshaw and Morfey (2001) concluded
that it is not acceptable to validate FE models for
pressure and then use them for injury prediction. This
is apparent since tissue level models (Bain and
Meaney, 2000) have shown that diffuse axonal injury
(DAI) is a function of strain not pressure. The more
relevant parameter for validation of a FE model of
the human head should therefore be strain. Such
strain data do not exist, but relative displacement data
between the brain and skull are available, and provide
a means of model validation of localized brain
motion that is more complete than pressure alone.
Al-Bsharat et al. (1999) published the first data
showing the relative motion between the brain and
the skull in the human cadaver. These data were in
the form of resultant magnitudes, and were not
resolved into components with respect to an
anatomical coordinate system. Therefore, the
resulting FE model was validated against magnitudes
of relative motion between the brain and skull for a
few tests.
The first relative motion recorded during human
cadaver head impacts in anatomical coordinate
components was provided by Hardy et al. (2001).
The generalized 3D kinematics of the head was
compared to the relative brain-skull motion for
translational and rotational input to the frontal and
occipital regions within the sagittal plane. A high-
speed bi-plane x-ray system was used to image
columns of neutral density targets (NDTs) implanted
within the cadaver brain. More recently, King et al.
(2002) compared relative brain-skull displacements
for rotation in the coronal plane to those in the
sagittal plane. The results of the cadaver tests show
that the local brain motions follow loop or figure
eight patterns within the plane of rotation, with peak
displacements on the order of ± 5 mm.
Comprehensive correlation between FE model output
and relative motion between the human cadaver brain
and skull in anatomical X, Y, and Z components has
Kleiven and Hardy / Stapp Car Crash Journal 46 (November 2002)
125
not been demonstrated previously. Therefore, a goal
of this study was to examine the effects of the brain-
skull interface modeled by various FE contact
definitions and brain-tissue constitutive parameters
on the relative brain-skull displacement time
histories. Another goal of this study was to compare
model results with cadaver experiments conducted
for three impact directions: Frontal and occipital
(sagittal rotation), and lateral (coronal rotation).
METHODS
A parameterized Finite Element (FE) model of the
adult human head was created including the scalp,
skull, brain, meninges, cerebrospinal fluid (CSF), and
eleven pairs of parasagittal bridging veins (Fig.1). A
simplified neck, including the extension of the brain
stem to the spinal cord, dura mater, pia mater,
vertebrae, and muscles, was modeled also. In order to
better simulate the distribution of stress and strain,
separate representations of gray and white matter
were included, and distinct ventricles were
implemented.
Fig. 1 – Finite element mesh of the human head.
The parameterized nature of the model allows it to be
scaled to the dimensions of a particular segment of
the population, or to the dimensions of a specific test
specimen. The spatial coordinates of points on the
boundaries of different tissues are scaled. The inner
and outer surfaces of the skull are scaled
independently. The width, length, height, and
thickness of the skull can be adjusted, as well as the
overall size of the head and neck. Also, the mesh
density was parameterized and a convergence
analysis was performed to assure sufficient mesh
resolution. The model was comprised of 19350
nodes, 11454 eight-node brick elements, 6940 four-
node shell and membrane elements, and 22 two-node
truss elements. A typical simulation of 100 ms
required 16 hours running on a PC with a single
AMD processor operating at 1.8 GHz. This
comparatively reasonable computation time allowed
results to be obtained relatively rapidly, which is
desirable for parametric studies as well as for use of
the model as a development tool.
Material Properties
To cope with large elastic deformations, a Mooney-
Rivlin hyperelastic constitutive law was used for the
CNS tissues. Hyperelasticity or Green elasticity is
path-independent and fully reversible, and the stress
is derived from a strain energy potential. It can be
shown (Malvern, 1969) that the stored strain energy
for a hyperelastic material which is isotropic with
respect to the initial, unstressed configuration can be
written as a function of the principal invariants (I
1
, I
2
,
I
3
) of the right Cauchy-Green deformation tensor, i.e.,
W=W(I
1
,I
2
,I
3
). Mooney and Rivlin showed that the
simple form:
)()(),( 33
20111021
−
+−
=
ICICIIW
(1)
closely matches results from large deformation
experiments on incompressible rubber.
To model the brain tissue as an unconstrained
material a hydrostatic work term, W
H
(J), is included
in the strain energy functional which is a function of
the relative volume, J (Ogden, 1984):
)()()(),,( JWJCJCJJJW
H
+−+
−
=
33
20111021
(2)
31
11
/−
= JIJ
32
22
/−
= JIJ
The stress tensor corresponding to the strain energy
density is derived using:
)(
jiij
ij
E
W
E
W
S
∂
∂
+
∂
∂
=
2
1
(3)
in terms of the second Piola-Kirchhoff stress, S
ij
, and
Green’s strain tensor, E
ij
. In addition, rate effects are
taken into account through linear viscoelasticity by a
convolution integral of the form:
∫
∂
∂
−=
t
ij
ijklij
d
E
tGS
0
τ
τ
τ
ν
)(
(4)
This stress is added to the stress tensor determined
from the strain energy functional. The stress
relaxation function, G
ijkl
, is represented by two terms
in a prony series, given by:
Kleiven and Hardy / Stapp Car Crash Journal 46 (November 2002)
126
(1995). Based on the previous work by Mendis et al.
(1995) and Donnelly and Medige (1997), the stiffness
parameters C
10
, C
01
, G
1
, and G
2
were scaled, while
the decay constants were not altered (Table. 1).
∑
=
−
=
N
i
t
i
i
eGtg
1
β
)(
(5)
This is effectively a Maxwell fluid that consists of
dampers and springs in series. Where G
i
represents
the shear moduli, and
β
i
are the decay constants.
Mendis et al. (1995) derived the rate dependent
Mooney-Rivlin constants C
10
and C
01
and time decay
constants
β
i
, using experiments published by Estes
and McElhaney (1970) on white matter from the
corona radiata region.
Table 1 – Mooney-Rivlin, and linear viscoelastic
constants used in this study.
C
10
C
01
G
1
G
2
Stiff 620.5 689.4 8149 4657 125 6.7
Average 62 69 814 465 125 6.7
Compliant 31 35 407 233 125 6.7
β
1
β
2
Using the relationship G=2(C
10
+C
01
) for the prony
terms gives the following constants: G
1
=8149 Pa,
β
1
=125 1/s, G
2
=4657 Pa, and
β
2
=6.67 1/s. The law
has been introduced for both white matter (Estes and
McElhaney, 1970) and the gray matter (Prange et al.,
2000). The Mooney-Rivlin constants for the brain
stem were assumed to be 80 % higher than those for
the gray matter in the cortex (Arbogast and
Margulies, 1997). Although significantly less stiff
than those used in previous 3D FE models of the
human head, these parameters give stiffness for the
brain tissue that is higher than the average published
values (Donnelly, 1998). A curve fit of the data
presented by Donnelly and Medige (1997) revealed
almost identical decay factors and ratios between
prony terms and long-term moduli, similar to the
constitutive parameters proposed by Mendis et al.
Two additional, more compliant models were
implemented. One model used properties slightly less
than the most compliant data available on brain tissue
(those of Prange et al. (2000) hereafter referred to as
“compliant”). In an intermediate model (hereafter
referred to as “average”), the properties were adjusted
to levels near the average values reviewed by
Donnelly (1998). These values fell between the
compliant and stiff data reported by Mendis et al.
(1995). The average relaxation function chosen in
this study agrees very well with the stress relaxation
results of Arbogast et al. (1997), and with the
transformed results of the complex modulus by
Arbogast and Margulies (1997) presented by
Donnelly, (1998). The shear relaxation moduli can be
seen in Fig. 2.
Figure 2 – Shear relaxation moduli used in this study (the initial value of the stiff modulus is cut-off by the scale of
the figure).
Kleiven and Hardy / Stapp Car Crash Journal 46 (November 2002)
127
A selectively reduced (S/R) integration scheme,
which uses reduced integration for the volumetric
(pressure) terms, and full integration for the
deviatoric (shear) terms was used for the brain tissue.
The S/R scheme was used to avoid hourglass
instabilities associated with reduced integration, and
locking phenomenon that is associated with full
integration of lower order elements. A summary of
the properties used in this study is given in Table 2
Table 2 – Tissue properties used in this study.
Tissue Young's modulus
[MPa]
Density
[kg/dm
3
]
Poisson's ratio
Outer table/Face 15,000 2.00 0.22
Inner table 15,000 2.00 0.22
Diploe 1000 1.30 0.24
Neck bone 1000 1.30 0.24
Neck muscles 0.1 1.13 0.45
Brain Hyperelastic/Viscoelastic 1.04 0.4999994-0.49999997
Cerebrospinal Fluid K=2.1 GPa 1.00 0.5
Sinuses K=2.1 GPa 1.00 0.5
Dura mater 31.5 1.13 0.45
Falx/Tentorium 31.5 1.13 0.45
Scalp 16.7 1.13 0.42
Bridging veins EA=1.9 N
K=Bulk modulus, and EA=load/unit strain.
The Poisson’s ratio was varied (Table 2) to keep the
bulk modulus of constant value of 2.1 GPa
(Stalnaker, 1969, McElhaney et al., 1976), for all the
chosen shear moduli.
This FE model is described in more detail by Kleiven
and von Holst, (2001 and 2002a) and comprises
nonlinear viscoelastic and incompressible material
modeling, experimental validation and parametric
studies. This model has been experimentally
validated against pressure data, as well as relative
motion magnitude data in previous studies.
Interface Conditions
Based on the anatomy and physiology of the brain-
skull interface, the interface between the dura and the
skull was modeled with a tied-node contact definition
in LS-Dyna. Because of the presence of CSF between
the meningeal membranes and the brain, sliding
contact definitions were used for these interfaces.
Different sliding contact definitions were compared
with a tied contact definition. Three different
strategies were tested: A tied interface including the
CSF as fluid, a sliding interface that allowed
separation, and a sliding interface that did not allow
any separation. The sliding interface without
separation consisted of an additional layer of pia
mater, which was modeled within and close to the
outer surface of the cortex and tied to the dura. This
contact definition allowed sliding in the tangential
direction and transfer of tension and compression in
the radial direction. This was done in part because a
fluid structure interface is likely to experience a
vacuum when a pressure wave reflects at the
contrecoup site, or when inertia forces create tension
in brain regions opposite impact.
Average CSF thickness of roughly 2 mm was used,
which corresponds to approximately 120 ml of
subdural and subarachnoidal CSF. For all the sliding
interfaces a coefficient of friction of 0.2 was used, as
proposed by Miller et al. (1998).
Intracranial Pressure
Results from simulations with the FE model were
compared with the intracranial pressure-time
recordings from experiment No. 37 conducted by
Nahum et al. (1977), where impacts to the forehead
by a padded impactor were performed. The
kinematics of this experiment was applied to the
skull. The intracranial pressure-time characteristics in
the frontal and occipital regions from this experiment
were compared to the ability of the different contact
definitions to transfer tensile and compressive loads
in the direction normal to the surfaces, as well as the
differences in pressure characteristics due to a change
in shear stiffness of the brain tissue.
Relative motion between the brain and skull
New experimental data has been presented by Hardy
et al. (2001) and King et al. (2002), which describes
the relative displacement between the brain and skull
of the human cadaver. The cadaver experiments
Kleiven and Hardy / Stapp Car Crash Journal 46 (November 2002)
128
focused on measuring the relative brain-skull motion
using a high-speed biplane x-ray system and neutral
density targets. The NDTs are polystyrene cylinders
that are 3.9 mm long and 2.3 mm in diameter.
Centered within the polystyrene tubing are 1.9-mm
tin granules. The density of these targets is roughly
that of brain tissue. Typically, the NDTs were
implanted in two vertical columns located in the
occipitoparietal region, and in the temporoparietal
region, with spacing between the centers of the NDTs
of approximately 10 mm. The cadaver head was
inverted and suspended in a fixture that allowed
rotation and translation. Each specimen was mounted
to the moving fixture at the level of T2. Frontal (Fig.
3, left), occipital, and lateral (Fig. 3, right) impacts
toward an angled acrylic surface were conducted.
The impact speed ranged from 2.5 to 3.5 m/s. The
rigid body motion of the skull was eliminated from
the NDT (brain) motion data, leaving the brain-skull
relative displacements. The NDT’s numbered “a6”
and “p6” were located in the brain toward the apex of
the skull, while the “a1” and “p1” were located just
above the base of the skull.
2.5-3.5 m/s
Figure 3 – Specimen and test configurations from the cadaver tests showing the NDT implant schemes for a frontal
impact involving sagittal rotation (left) and a lateral impact involving coronal rotation. (right). The markers used in
the parametric studies of interface modeling and shear properties for the brain tissue are highlighted for the frontal
impact condition.
Four experiments from the literature were simulated
using the model. To increase accuracy, the actual
geometry of the specimen (overall length, width and
height) was reproduced. The kinematics and HIC
values for the impacts are summarized in Table 3.
Table 3 – Summary of Head Kinematics.
Test C383-T1 C383-T2 C383-T4 C291-T1
Impact type Frontal Frontal Occipital Lateral
Linear Accel. X 5/-46 6/-35 90/-104 11/-8
c.g. (g) Y 6/-2 11/-3 20/-18 37/-2
Z 20/-41 15/-25 19/-34 11/-22
A
ngular Accel
.
X 0.4/-0.4 0.5/-1.0 2.1/-3.3 3.2/-7.7
c.g. (krad/s/s) Y 2.6/-1.9 1.9/-2.2 7.5/-6.4 1.6/-1.5
Z 0.9/-0.5 1.9/-0.9 10.3/-9.4 0.5/-1.9
HIC
15
47 34 164 38
The first three tests were conducted using one
cadaver, and involved rotation in the sagittal plane.
Two of these impacts were to the frontal region, and
one to the occipital region. The fourth experiment
was a lateral impact involving a separate cadaver and
coronal rotation. The linear and angular accelerations
for a typical frontal impact can be seen in Fig. 4. The
initial positions of the neutral density targets used in
the experiments were used to locate the targets within
the FE model. The targets were modeled as rigid
beams. For each simulation, the full kinematics (all
six degrees of freedom) of the experiments was
applied to the skull. One of the frontal impacts
(C383-T1) was used to evaluate the influence of
shear properties of the brain tissue and the ability of
the different contact definitions to describe the
relative motion between the skull and the brain. Since
the displacement characteristics in the experiments
and simulations were similar for most locations, the
X
Z
X
Y
2.5-3.5 m/s
a1 p1
a3 p3
a6 p6
Kleiven and Hardy / Stapp Car Crash Journal 46 (November 2002)
129
peak magnitudes as well as the temporal differences
in peak values were used as an assessment of the
correlation. For a few locations (e.g. the second peak
in X-displacement of NDT a3, Fig.6), there were
differences in the response characteristics between
the simulation and experiment. In such cases the
model response values at the time of the experimental
peaks were used for comparison, and the temporal
differences for these peaks were not included in the
analysis.
Figure 4 – Linear and angular accelerations of a typical frontal impact.
RESULTS
Intracranial Pressure
The predicted intracranial pressure responses from
the FE model varied based on the interfacial
condition, with some of the interfacial conditions
producing responses that agreed well with previously
published intracranial pressure recordings during
impact. As seen from Fig. 5, the calculated curves for
the frontal and occipital pressures gave magnitudes
and characteristics similar to the experimental results
for the tied interface, while the sliding interface (with
separation) produced coup pressure magnitudes 90%
higher than in the experiments. Also, the sliding
interface with separation gave a positive pressure in
the occipital area due to the lack of tensile resistance
which made the inertia forces of the spinal cord and
brain stem apply pressure on the cerebellum and
occipital pole. The sliding interface without
separation provided a way to allow sliding while
giving tensile resistance in countercoup areas. This
produced negative occipital pressure magnitudes that
were 20% lower than the experiments, and that
occurred about 0.5-1.0 ms later in time. The frontal
pressure magnitudes for the sliding-only interface
were 45% higher and occurred approximately 1.0 ms
earlier than in the experiments.
Figure 5 - Simulation of the pressure results from the cadaver experiments by Nahum et al. (1977) as a function of
interface properties using a FE model of the human head (left), and as a function of shear properties of the brain
tissue (right).
Kleiven and Hardy / Stapp Car Crash Journal 46 (November 2002)
130
A summary of the peak frontal and occipital
pressures in the experiments and simulations is seen
in Fig. 6. The magnitudes of the pressures show a
low sensitivity for a variation of the stiffness
properties of the brain tissue (Fig. 6A). The different
contact formulations used for the brain-skull interface
result in large variation in the magnitudes of the
pressures (Fig. 6B).
Relative motion between the brain and skull
The results for the relative displacement of six
locations in the occipitoparietal and temporoparietal
regions for a 3 m/s frontal impact are shown in Fig. 7,
and are used to assess the ability of different material
properties of brain tissue to reproduce the
experimental relative brain-skull motion. Each plot
represents a given NDT location. The curves in the
top half of the figure show relative displacement in
the X direction, and the bottom curves show relative
Z-direction displacement for the same locations. The
motion of the markers is typically characterized by a
maxima or minima occurring between 20-40 ms
before rebounding through the initial position (zero)
between 70-90 ms, and then reaching a minima or
maxima between 90-105 ms.
It was found that the magnitude of the relative motion
in the brain increases with decreasing stiffness of the
brain tissue. When comparing the model having the
stiffest shear properties for the brain with the
experiments, the maxima and minima were
underestimated by an average 69 percent for relative
displacement in the X direction, and 67 percent in the
Z direction. These values reflect the average
discrepancy between the model and experimental
results for all six target locations examined, and
represent an average difference in the prediction of
the displacement magnitudes of 68 percent for both
the X and Z directions. The opposite was found when
using the compliant properties, where the average
overestimation of the maxima and minima was 104
percent for relative displacement in the X direction,
and 147 percent in the Z direction. When using the
average published values of shear properties for the
brain tissue, an average difference of 59 percent (72
percent in the X direction and 46 percent in the Z
direction) between the model and experimental
displacement peaks was found.
An increased delay in the relative motion was seen
when using the more compliant properties for the
brain, which increased with decreasing stiffness. This
was examined by comparing the temporal difference
between the experimentally seen peaks in
displacement and the results from the simulations
using the various stiffness properties. It was found
that the displacement peaks in the X direction were
occurring (average for the six targets) 16.4 ms earlier
in the simulation using the stiffest properties, while
they were observed 13.6 ms earlier in the Z direction.
When using the average properties, this lead effect
was reduced to 7.3 ms for the peaks of the X
displacements, and 5.9 ms for the Z displacements.
For the model using the most compliant properties
the opposite of was true, and a lag of (average for the
six targets) 9.7 ms and 9.5 ms compared to the
experiments was found for the timing of the peak X
displacements and Z displacements, respectively.
-100
-50
0
50
100
150
200
250
300
Peak frontal pressure (kPa) Peak occipital pressure (kPa)
Experiment Average Compliant Stiff
-100
-50
0
50
100
150
200
250
300
Peak frontal pressure (kPa) Peak occipital pressure (kPa)
Experiment Tied Sliding Sliding only
(A) (B)
Figure 6 - A summary of the pressure magnitudes observed in the experiments and simulations. (A): Pressure
magnitudes for a variation of the stiffness properties of the brain tissue. (B): Pressure magnitudes for the different
approaches used for the brain-skull interface.
Kleiven and Hardy / Stapp Car Crash Journal 46 (November 2002)
131
C383-T1, Frontal Impact using different Stiffness Parameters
Figure 7 - Simulation of relative motion in the sagittal plane. Results for the model with tied contact interfaces
between the brain (pia mater) and the CSF, and varying stiffness parameters of the brain. For marker locations and
coordinate system directions, see Fig. 3, left.
The results for six locations in the occipitoparietal,
and temporoparietal regions for a 3 m/s frontal
impact are shown in Fig. 8, and are used to assess the
ability of the different approaches used to model the
brain-skull interface to reproduce the experimental
relative brain-skull motion.
The comparison between various contact definitions
shows a small sensitivity to the interface for relative
motion, and insignificant differences were found both
for the timing of the displacement peaks as well as
for the magnitudes of the peaks in the X direction
(Fig. 8). However, differences related to the various
contact definitions are more pronounced for relative
motion data in the Z direction (Fig. 8). When
comparing the magnitudes of the displacements in the
Z direction, it was found that the tied interface
resulted in peak magnitudes that were an average of
46-percent higher than in the experiments for the six
chosen targets. The corresponding value for the
sliding interface was 66 percent, and the value for the
sliding without separation interface was 65 percent.
Kleiven and Hardy / Stapp Car Crash Journal 46 (November 2002)
132
C383-T1, Frontal Impact using different Contact Definitions
Figure 8 - Simulation of relative motion in the sagittal plane for a frontal impact (C383-T1). Results for the model
with various contact interfaces between the skull and the brain. For marker locations and coordinate system
directions, see Fig. 3, left.
A summary of the average values of the peak
displacement magnitudes observed in the
experiments and simulations is seen in Fig. 9. The
difference shown is between the average magnitudes
for all six NDT locations. The average magnitudes of
the local brain motion show a high sensitivity for a
variation of the stiffness properties of the brain tissue
(Fig. 9A). The different contact formulations used for
the brain-skull interface result in less variation in the
average magnitudes of peak displacements (Fig. 9B).
For the second frontal impact (C383-T2) simulation
using the average properties for the brain tissue and a
tied interface, correlation between the experiment and
the model similar to that for the first impact (C383-
T1) was found (Fig. 10). The results of both the
frontal impacts are in agreement, where an
underestimation of the magnitudes of the X
displacements and an over prediction of the Z
displacement are found for most of the markers. This
can be seen when looking at the magnitudes of the
motion in the X direction for the posterior-superior
markers (p3 and p6), which are smaller (20-100
percent) in the model than in the experiments, while
the magnitudes for the motion in the Z-direction for
the same markers are larger (30-100 percent) in the
model than in the experiments.
Kleiven and Hardy / Stapp Car Crash Journal 46 (November 2002)
133
0
1
2
3
4
Average peak X-displacement
(mm)
Average peak Z-displacement
(mm)
Experiment Average Compliant Stiff
5
0
1
2
3
4
5
Average peak X-displacement
(mm)
Average peak Z-displacement
(mm)
Experiment Tied Sliding Sliding only
(A) (B)
Figure 9 - The average values of the peak displacement magnitudes observed in the experiments and simulations.
(A): For variation of the stiffness properties of brain tissue. (B): For the different brain-skull interfaces used.
C383-T2, Frontal Impact
Figure 10 - Simulation of relative motion in the sagittal plane for a frontal impact (C383-T2). For marker locations
and coordinate system directions, see Fig. 3, left.
Kleiven and Hardy / Stapp Car Crash Journal 46 (November 2002)
134
Typical target motions in the sagittal plane for the
C383-T2 (Frontal) impact can be seen in Fig. 11. The
markers are plotted together with the falx and the
tentorium to clarify target orientation and direction of
motion, and the initial positions of the markers are
superimposed in black. The motion of the superior
markers (the lower markers in this figure) is shown to
be opposite the direction of the inferior markers for
both the experiments and simulations. This is
especially apparent at 20 and 90 ms, where the
magnitudes of the displacements are near their peak
values.
For the occipital impact (C383-T4) simulation using
the average properties for the brain tissue and the tied
interface, a better correlation between the model and
the experimental results is seen for the superior
markers when compared to the frontal impacts (Fig.
12). There is 45-percent difference (average for both
X and Z directions) in displacement magnitudes
X
Z
a3 p3
a1 p2
a6 p6
T=0ms T=20ms
T=50ms T=90ms
Figure 11 – Target motion in the sagittal plane for six markers in a frontal impact (C383-T2). The initial positions of
the markers are shown in black, while the brain targets are shown in gray.
Kleiven and Hardy / Stapp Car Crash Journal 46 (November 2002)
135
between the experiment and simulation for the two
superior markers (a6 and p6) in the occipital impact,
whereas the first frontal impact (C383-T1) exhibits
83-percent difference between the experiment and
simulation for the same two target locations. On the
other hand, the simulated Z-direction motion of the
a1 and a3 markers deviates from the experiments
more than 4 mm after 60 ms. Also, for the X-
direction motion of the p1 and p3 markers, a 6-7 mm
smaller magnitude of the second peak is found for the
simulation, while the general shapes of the responses
are similar for the simulation and experiment. The
prediction of larger X-direction displacement for the
anterior-superior target (a6), and the prediction of
smaller motion for the inferior targets (a1 and p1)
compared to the experiments are effects common to
all the frontal and occipital impacts. When simulating
the lateral impact, the characteristics similar to those
seen in the experiment were found for Y and Z
displacements (Fig. 13). The motion of the brain
targets relative to the skull shows a characteristic
peak around 10-15 ms, which subsequently decays.
When comparing the experimental magnitudes to the
simulation at this initial peak, it was found that for all
the superior markers (aL5, pL5, and pR5), the
differences were within 1.7 mm. While the model
and experiment showed a discrepancy of 3.3 mm for
the initial peak in Z displacement of the left anterior-
inferior marker (aL2), the differences were within 0.9
mm for the Z displacement of the remaining targets.
C383-T4, Occipital Impact
Figure 12 - Simulation of relative motion in the sagittal plane for an occipital impact (C383-T4). For marker
locations and coordinate system directions, see Fig. 3, left.
Kleiven and Hardy / Stapp Car Crash Journal 46 (November 2002)
136
A summary of the average values of the peak
displacement magnitudes observed in the
experiments and simulations for different impact
directions (separated by test) is seen in Fig. 14. The
prediction of larger Z-direction displacement and
smaller X-direction displacement by the model has
been described using the average error between peak
displacement results obtained from the model and
experiments. This phenomenon is further illustrated
by the average values of the peak displacement
magnitudes. This is evident for the first frontal
impact and the occipital impact. For the second
frontal impact there is essentially no average
difference between the simulation and experiment in
the Z direction. In the lateral-impact case the average
values of both the peak Y- and Z-displacement
magnitudes are larger in the model than in the
experiments. The maximal principal strain (Green St.
Venant) in the central parts of the brain showed
variation for the different interface conditions and
material properties used in this study (Fig. 15). The
stiffness properties used for the brain tissue
especially affected the strains in the brain. A result
similar to that of the comparison with the relative
motion experiments is seen. The stiff properties
produced 60-80 percent lower peak values of
maximal principal strains, which occurred 15-20 ms
earlier than when using the average properties. The
more compliant properties produced peaks roughly
100-percent higher, which occurred 5-10 ms later
(Fig 15, left). Some smaller differences can also be
seen when comparing the various contact interfaces,
where the sliding interfaces produced stresses located
centrally in the brain having peaks 20-30-percent
higher in magnitude than the simulations produced
using the tied interface (Fig 15, right).
C291-T1, Lateral Impact
Figure 13 - Simulation of relative motion in the coronal plane for a lateral impact (C291-T1). For marker locations
and coordinate system directions, see Fig. 3, right.
Kleiven and Hardy / Stapp Car Crash Journal 46 (November 2002)
137
0
1
2
3
4
5
Average peak X-
displacement (mm)
Average peak Z-
displacement (mm)
Frontal exp. #1 Frontal sim. #1
0
1
2
3
4
5
Average peak X-
displacement (mm)
Average peak Z-
displacement (mm)
Frontal exp. #2 Frontal sim. #2
0
1
2
3
4
5
Average peak X-
displacement (mm)
Average peak Z-
displacement (mm)
Occipital exp. Occipital sim.
0
1
2
3
4
5
Average peak Y-
displacement (mm)
Average peak Z-
displacement (mm)
Lateral exp. Lateral sim.
Figure 14 - A summary of the average values of the peak displacement magnitudes observed in the experiments and
simulations for the various impact directions.
Comparison of Maximal Principal Strain in the Central parts of the Brain
Figure 15 – Resulting maximal principal strain at the same element adjacent to the corpus callosum region of the
brain for the various stiffness properties used for the brain tissue (left), and for the different contact interfaces
between the brain and the skull (right).
Kleiven and Hardy / Stapp Car Crash Journal 46 (November 2002)
138
DISCUSSION
The local motion of brain tissue described by Hardy
et al. (2001) and King et al. (2002) has been
simulated for three impact directions (Frontal,
occipital and lateral), using a selection of material
properties and interface conditions. The results of this
effort show that simulation of local brain motion is
highly sensitive to the shear properties of the brain
tissue. The local brain motion in response to low
severity impact seems to be relatively insensitive to
the type of brain-skull interface used for simulation
as well. The pressure response, on the other hand,
seems to be more dependent upon the type of brain-
skull interface than on the constitutive parameters
chosen for the brain tissue.
Interface Conditions
Fluid elements should be used to simulate the CSF as
proposed by Zhou et al. (1995), Bandak and
Eppinger (1994), Miller et al. (1998), and Al-Bsharat
et al. (1999,) in order to adequately represent the
effect of the ventricles, subarachnoid space, and
brain-skull interface. However, adequate
representation of fluid-structure interaction still
remains a major limitation of most commercially
available FE packages. Due to this problem, two
different approaches that do not implement fluid
elements for the CSF have been developed to model
the brain-skull interface.
The first approach models the subarachnoid CSF
using linear elastic solid elements with low shear
modulus. This approximation has been used by
several researchers (Ruan et al.,1997; Willinger et
al., 1995; Turquier et al., 1996; Zhou et al., 1995).
An alternate way of modeling the brain-skull
interface includes contact algorithms between the
brain and the dura mater. The contact has been
defined in different ways ranging from completely
fixed to frictionless sliding. Several parametric
studies have been performed, where the effects of
different interface conditions between the brain and
skull have been studied (Cheng et al., 1990; Kuijpers
et al., 1995; Claessens et al., 1997, and Miller et al.,
1998). These studies concluded that the impact
response of the human head is sensitive to the
modeling of this interface condition. This is in
keeping with the results from the present study,
where the pressure response is sensitive to the
interface conditions.
Localized brain motion during a low severity impact
seems relatively insensitive to interface conditions.
The sliding (with separation) contact algorithm used
by Kuijpers et al. (1995) and Claessens et al. (1997),
was found to be insufficient for the brain-membrane
interfaces in the contrecoup region, and a gap was
created in this region due to limited load transfer to
compression only. In our study, a sliding-only contact
algorithm, which transfers load in tension was also
implemented. Because of this, large relative motion
between the brain and skull was allowed and load
was supported in tension at the contrecoup region.
This resulted in comparable magnitude and shape of
the pressure-time responses between the simulations
and experiments even in the contrecoup region.
The sliding interface with separation resulted in
positive pressure in the occipital area due to the lack
of tensile resistance, which made the inertia forces of
the spinal cord and brain stem apply pressure on the
cerebellum and occipital pole. The looser connection
between the brain and skull that is provided by
sliding interfaces also makes it possible for the brain
to slide forward due to the inertia forces, creating
higher pressures frontally when simulating the
pressure experiments. Further, this looser connection
could explain the temporal differences of the
maximal frontal and occipital pressures for the
sliding interfaces when comparing the model to the
experiments. For the tied interface the opposite is true
since the connection does not allow any motion
between components in the contact surface giving a
more direct impulse transferred to the brain.
The hydrodynamics of a sealed, pressurized cranial
cavity dictate that positive pressure cannot develop at
the interface between the brain and skull at the
contrecoup site. This effect is not reproduced in the
model for the sliding interface simulations. In
addition, since the model pressures were measured at
locations at the surface of the brain as specified by
Nahum et al. (1977), which are closer to the interface
than the locations of some of the NDTs, it is
reasonable that the pressure results should have a
greater dependence on interface conditions than some
of the NDT displacements.
The simulations showed larger differences in results
between the interface conditions for the posterior
markers during a frontal impact. An explanation
might be that the frontal parts of the brain are
naturally constrained by the skull base and anterior
middle fossa during frontal impact so that the brain-
skull interface would have less influence for the
anterior markers. The posterior target located closest
to the tentorium and the countercoup area for a
frontal impact (p1), had the greatest sensitivity to the
interface conditions. This is likely due to the
influence of both the looser connection for the sliding
Kleiven and Hardy / Stapp Car Crash Journal 46 (November 2002)
139
interfaces, as well as the influence of the brain-
tentorium interface. Relative motion between the
brain and skull is a more complex response that
requires unambiguous material characteristics.
However, the relative motion response was found to
be relatively insensitive to the interface conditions,
since very small differences in magnitude and
characteristics of the localized brain motion were
seen (Fig. 6) for the different interfaces. This could
be related to the relative motion primarily resulting
from local distortions of brain tissue with little
sliding occurring at the brain-skull interface.
The experimental data do not indicate whether there
is, or there is not, sliding between the brain and skull.
The model, however, showed a small relative motion
(less than 1 mm) at the skull brain interface for the
relatively low severity impacts used for the relative
motion experiments. It has been shown (Kleiven and
von Holst, 2001, 2002b), that when applying higher
magnitudes of rotational accelerations, the motion
close to the skull increases to several mm in
magnitude. A larger difference should therefore be
expected between the various contact definitions
ability to describe localized brain motion for
rotational inputs of higher magnitude.
Brain Shear Stiffness Dependency
A range of brain material properties can be used to
effectively model the intracranial pressure responses
obtained from cadaver experiments. It is possible to
predict the pressure data of Nahum et al. (1977)
using material properties for the brain 2000 times
stiffer than the average published values (in keeping
with levels used by many other modeling efforts).
From the results (Fig. 5, right) it can be seen that the
pressure responses for the models using stiff and
compliant stiffness parameters for the brain tissue are
virtually indistinguishable, although the parameters
were varied more than one order of magnitude. This
is in contrast to the aforementioned sensitivity of the
pressure response to the type of contact interface,
where the tied interface showed better correlation
with the pressure experiments as compared to the
sliding interfaces.
Relative motion between the brain and skull is very
sensitive to the choice of stiffness for the brain tissue.
When using the parameters reported by Mendis et al.
(1995), significantly smaller relative motion than that
found in the experiments was observed. Since this
constitutive law is more compliant than what is used
in most other 3D FE head models, it is tenuous to
suggest that significantly less stiff parameters should
be used in future FE modeling efforts. Two prony
terms with a fast decay and a slow decay in the
viscoelastic terms of the model were used, and are
probably necessary to simulate these relative motion
experiments. This is apparent since a large-magnitude
impulse (a couple of ms in duration) is followed by a
long duration motion (150ms). It can only be
conjectured as to what extent additional terms might
improve the correlation.
A selectively reduced (S/R) integration scheme was
used to avoid hourglass instabilities associated with
reduced integration. This was necessary to stabilize
the elements representing the brain when using the
compliant brain tissue properties since the large-
magnitude initial rotational impulse followed by long
duration motion resulted in unacceptably high
artificial (hourglass) energies when utilizing reduced
integration. To the authors’ knowledge, brain
properties roughly half the stiffness of the average
published values (around those of Prange et al.,
2000) have never been successfully implemented in a
simulation before. However, by using such compliant
properties a significant increase in relative motion as
well as the strain in the brain appeared. The
characteristics of the response changed as well,
producing a “delay” in the local brain tissue motion.
Brain Motion Considerations
There is symmetry in the motion of the superior and
inferior markers for both the model and the
experiments for both sagittal, and coronal rotation.
This might be explained by the nearly incompressible
properties of brain tissue and skull geometry, and the
associated response to rotation with little response to
linear input. The model shows larger relative motion
in the X-direction for superior markers, while the
opposite is true for the inferior markers. For the
central markers (between 1 and 6), the similar
magnitudes are observed, while the characteristics are
slightly different for markers located in the anterior
column. All markers tend to go back to the initial
position for both simulations and experiments. The
relative influences of the characteristics of the
superior regions of the model on the motions in the
inferior regions are not known. However,
discrepancies between the simulations and the
experiments in one region will likely result in
discrepancies in the other.
Both the model and the experiments show similar
magnitudes of relative motion between the skull and
the brain for the occipital and frontal impact
scenarios. The lateral impact resulted in smaller
relative motion than the frontal impact of similar
severity. This is true for the cadaver experiments and
Kleiven and Hardy / Stapp Car Crash Journal 46 (November 2002)
140
the simulations. This is mainly thought to be due to
the supporting structure of the falx cerebri.
Gennarelli et al. (1982, 1987) produced traumatic
coma in monkeys by accelerating the head without
impact in various non-centroidal rotation scenarios. It
was found that the majority of the animals that were
subjected to coronal rotation suffered more prolonged
coma. Also, all the laterally impacted animals had a
degree of DAI in the corpus callosum and superior
cerebellar peduncle similar to that found in severe
human head injury. The present study supports the
findings of Gennarelli et al. (1982, 1987): Smaller
relative motion between the brain and skull suggests
the influence of the falx, which may impinge upon
adjacent structures such as the corpus callosum,
potentially causing injury. This is also supported by
the findings of higher shear stresses in the corpus
callosum for coronal rotation compared to sagittal
rotation when imposing a sinusoidal acceleration
pulse corresponding to the same head impact power
(HIP), which has been reported previously by
Kleiven and von Holst (2002b).
The maximal principal strain (Green St. Venant) in
the central parts of the brain varies depending upon
the material properties used in this study (Fig. 15).
The stiffness properties for the brain tissue especially
affect the strains in the brain. The stiff properties
produced 60-80-percent lower peak values of
maximal principal strain, which occurred 15-20 ms
earlier in time than when using the average
properties. The compliant properties produced
approximately 100-percent higher peaks, which
occurred 5-10 ms later in time. It can also be noted
that when using the stiff properties the peaks in
maximal principal strains occurred close to the peaks
in the acceleration pulses (Fig. 4). When using the
average and compliant properties, the strain peaks
occurred 20-30 ms, and 30-40 ms after the
acceleration peaks, respectively. These differences
are crucial for a FE model of the human head
designed to predict Traumatic Brain Injury (TBI),
and reinforces the need for comparison with the
relative motion experiments. The importance of
intracranial motion differences due to shear
properties of the brain becomes apparent when
looking at published tissue thresholds for DAI. Bain
and Meaney (2000) estimated a tissue threshold for
axonal damage to a Lagrangian principal strain of
about 0.2 in experiments on optic nerves of guinea
pigs. Using this value, the potential for DAI is
predicted for the relative motion experiments using
the compliant and average properties, while the stiff
properties predict values far below 0.2. When using
the average properties, principal strain just above this
level is found for the central parts of the brain.
The simulations of this study were compared to
previously reported experimental local brain motion
data. The tests showed that the local brain motions
followed loop or figure eight patterns within the
plane of rotation. The peak relative displacements
between the brain and skull were on the order of ± 5
mm. The general path of the loop or figure eight
patterns were described as having a major
displacement axis (MDA) within the plane of
rotation, similar to the description for an ellipse. The
perpendicular bisectors from each MDA were said to
intersect at an average instant center (AIC) of
rotation, which is a common point about which the
movements of the brain at each target location for a
given column of targets seem to be organized. The
MDA orientations also rotated from inferior to
superior. Motion for sagittal and coronal plane
rotation was remarkably similar, as was the angular
speed of each test. The brain motions exhibited
interesting anterior-posterior and right-left symmetry.
In general, the motion of the brain seemed to lag that
of the skull for rotational input to the skull, while the
brain moved little (less than 1 mm) for linear input to
the skull. These phenomena are in keeping with the
near incompressible nature of the intracranial
contents. The model developed for this study
exhibited many of the same trends of the
experiments, as shown in the component-wise
comparisons between the simulations and
experiments (Fig. 6 through Fig. 11).
Limitations
The intracranial pressure measurements of Nahum et
al. (1977) have been simulated by Kleiven and von
Holst (2002). In that study the impact was simulated
by modeling impactor padding, using elastic models
for the skull and the scalp, and imposing the given
impactor velocity. In this study, the kinematics of the
head was imposed to avoid errors in the transferred
impulse. However, to impose the kinematics of an
impulse, the skull must be assumed rigid. In this case,
the experimental impacts were padded so deflection
of the skull should not have a great influence.
Nevertheless, the initial pressure response is smaller
and smoother in the experiments, which possibly
could be explained by the presence of the padding
and small local skull deflection. There are obvious
differences between the experimental pressure data
and the simulations, especially in the occipital region.
However, since the differences between the right and
left pressures (Occipital #1, and Occipital #2)
reported in Nahum et al. (1977) are greater than the
differences between experiments and simulations
(Fig. 16), the differences between the experiments
and simulations are considered insignificant.
Kleiven and Hardy / Stapp Car Crash Journal 46 (November 2002)
141
Figure 16 – Comparison of Occipital pressures reported in Nahum et al. (1977), and simulation using a tied interface
between the brain and skull.
In the model, the effect of baseline pressurization was
not included. Baseline pressure results from
atmospheric pressure and repressurization. When
gage pressure is observed under such conditions, the
contrecoup pressure will decrease from zero as
compression of the brain decreases during impact.
This occurs irrespective of the interface type. Some
discrepancies between the simulation and
experimental pressure results could result from the
absence of baseline pressure in the model. However,
it should be noted that the baseline pressure used in
the relative motion experiments was small, being
roughly 10 kPa.
In the cadaver experiments, the greatest specimen-
preparation concerns were related to evacuation of
gasses from the intracranial space to maintain
coupling between the brain and the skull. If small air
bubbles were trapped beneath the tentorium, the
larger motion in the caudal cerebrum seen in the
experiments as compared to the simulations may be
explained in part. However, the high-speed x-ray
images provided no indication of air within the
intracranial contents. Parametric analyses conducted
by introducing small levels of air (amounts that
should be visible on x-ray) within the model showed
minor differences in output as compared to the air-
free simulations. These two factors combine to
suggest that intracranial air had small influence on
the experimental results, and therefore is a minimal
factor in the discrepancies between the simulations
and experiments.
Other limitations of this numerical study are the
assumptions of isotropy, homogeneous properties,
and lack of details in the boundaries between the
ventricles and brain tissue. Also, the kinematics is
applied to the skull, and the simplified neck is forced
to follow this motion without accounting for the
relative motion of the vertebrae in the neck. This
should, however, have a limited effect on the
localized motion of brain tissue since the targets are
located on a distance from the spinal cord.
Bradshaw and Morfey (2001) showed that the
intracranial pressure response in the experiments by
Nahum et al. (1977) is a hydrostatic problem,
controlled only by the density of the cerebrum. The
impulse used in the intracranial pressure experiments
by Nahum et al. (1977) is long (6-10 ms) compared
to the transit time of dilatational waves within the
brain (approximately 0.1 ms), so static equilibrium
prevails (only inertia forces are acting) and wave
effects are of no consequence (Graff, 1975).
Therefore, intracranial pressure should be
independent of the bulk modulus and shear modulus.
This is supported by this study and the results of
Thomas et al. (1967). In the presence of local skull
deformation, the bulk modulus would play a larger
role. However, the local skull deformation was
insignificant in the relative motion experiments, and
was not simulated in the model. High accuracy is
required for relative displacement validation since
strain is always a function of the spatial derivatives of
the displacements. Since Bain and Meaney (2000)
suggest that axonal injury is related to distortional
Kleiven and Hardy / Stapp Car Crash Journal 46 (November 2002)
142
strain, validation against local displacement of brain
tissue is particularly relevant for an FE model of the
human head that is developed for traumatic brain
injury prediction.
CONCLUSION
A parameterized finite element (FE) model of the
human head has been developed. The parameterized
nature of the model allows the user to adjust the
geometry of the model to fit that of a particular
specimen, reducing some of the concerns associated
with scaling or the use of generic models.
It is possible to simulate both the magnitude and
characteristics (shape) of complex three-dimensional
localized brain tissue motion. This motion can be
simulated for impacts of the head in multiple
directions (frontal, occiptal, lateral) and for motion in
different planes (sagittal, coronal). Regarding relative
brain-skull motion, and intracranial pressure, this
study shows:
1. The pressure response seems to be more
dependent upon the type of brain-skull interface
than on the constitutive parameters chosen for
the brain tissue, and the tied interface provided
the best correlation with the experiments.
2. Smaller relative motion between the brain and
skull results from a lateral impact than from a
frontal or occipital blow for both the experiments
and the FE model.
3. There is symmetry in the motion of the superior
and inferior markers for both the simulations and
the experiments during both sagittal, and coronal
rotation.
4. Simulation of local brain motion is highly
sensitive to the shear properties of the brain
tissue, and average published values provided the
best correlation with the experiments.
5. The local brain motion in response to low-
severity impact is relatively insensitive to the
type of brain-skull interface used for the
simulation.
6. The results suggest that significantly lower
values of shear properties than are currently used
in most 3D FE models of the human brain should
be used to predict local brain response during
impact to the human cadaver head.
7. Further investigation into the effects of brain
tissue shear properties for prediction of localized
brain motion is needed.
ACKNOWLEDGMENTS
This work was supported by the Swedish Transport
& Communications Research Board, Grant No. 1999-
0847. This work was supported in part by the Centers
for Disease Control and Prevention, National Center
for Injury Prevention and Control Grant No.
R49/CCR503534-12, and also in part by a Ford
Biomedical Engineering Graduate Fellowship
provided by Ford Motor Company. The authors wish
to thank Matthew Mason of the Wayne State
University Bioengineering Center, and Bill Anderst
of the Bone and Joint Specialty Center, Henry Ford
Hospital for their valuable assistance with the relative
motion data. Appreciation is extended to Professors
Albert I. King and King H. Yang of the Wayne State
University Bioengineering Center for receiving Svein
Kleiven at the Bioengineering Center and inviting
him to collaborate on the experimental parts of this
project. The authors wish to thank Professor Hans
von Holst of the Royal Institute of Technology,
Stockholm, for his helpful suggestions and valuable
assistance.
REFERENCES
Al-Bsharat, A.S., Hardy, W.N., Yang, K.H., Khalil,
T.B., King, A.I., and Tashman, S. (1999). Brain-
skull relative displacement magnitude due to blunt
head impact: New experimental data and model.
Proc. 43
rd
Stapp Car Crash Conference, pp. 321-
332. Society of Automotive Engineers,
Warrendale, PA.
Arbogast, K.B., Prange, M.T., Meaney, D.F., and
Margulies, S.S. (1997). Properties of Cerebral Gray
and White Matter Undergoing Large Deformation.
Prevention Through Biomechanics, Symposium
Proceedings, Wayne State University, pp. 33-39.
Arbogast, K.B., and Margulies, S.S. (1997). Regional
differences in mechanical properties of the porcine
central nervous system, Proc. 41
st
Stapp Car Crash
Conference, SAE Paper No. 973336, Society of
Automotive Engineers, Warrendale, PA.
Bandak, F.A., and Eppinger, R.H. (1994). A three-
dimensional FE analysis of the human brain under
combined rotational and translational accelerations,
Proc. 38
th
Stapp Car Crash Conference, pp. 145-
163, Society of Automotive Engineers,
Warrendale, PA.
Kleiven and Hardy / Stapp Car Crash Journal 46 (November 2002)
143
Bain, A.C., and Meaney, D.F. (2000). Tissue-Level
Thresholds for Axonal Damage in an Experimental
Model of Central Nervous System White Matter
Injury. Journal of Biomechanical Engineering 16,
pp. 615-622.
Bradshaw, D.R.S., and Morfey, C.L. (2001). Pressure
and shear response in brain injury models.
Proceedings of the 17
th
Int. Technical Conferance
on the Enhanced Safety of Vehicles, Amsterdam,
The Netherlands.
Cheng, L.Y., Rifai, S., Khatuna, T., and Piziali, R.L.
(1990). Finite element analysis of diffuse axonal
injury. In Vehicle Crashworthiness and Occupant
Protection in Frontal Collisions, SAE Paper No.
900547, Society of Automotive Engineers.
Claessens, M., Sauren, F., and Wismans, J. (1997).
Modeling of the Human Head Under Impact
Conditions: A Parametric Study. Proc. 41
st
Stapp
Car Crash Conference, SAE Paper No. 973338, pp.
315-328. Society of Automotive Engineers,
Warrendale, PA.
DiMasi, F., Eppinger, R.H., Gabler, H.C., and
Marcus, J. (1991). Simulated head impacts with
upper interior structures using rigid and anatomic
brain models. In Auto and Traffic Safety, ed. R.
Strombotne. National Highway Traffic Safety
Publication, Vol. 1., No. 1.
Donnelly, B.R., and Medige, J. (1997). Shear
properties of human brain tissue. Journal of
Biomechanical Engineering, 119, pp. 423-432.
Donnelly, B.R. (1998). Brain tissue material
properties: A comparison of results. Biomechanical
research: Experimental and computational, Proc.
Of the 26th int. Workshop., pp. 47-57.
Estes M.S., and McElhaney, J.H. (1970). Response of
Brain Tissue to Compressive Loading. ASME
paper no. 70-BHF-13.
Gennarelli, T.A., Thibault, L.E., Adams, J.H.,
Graham, D.I., Thompson, C.J., and Marcincin, R.P.
(1982). Diffuse Axonal Injury and Traumatic
Coma in the Primate. Ann. Neurol. 12: 564-574.
Gennarelli, T.A., Thibault, L.E., Tomei, G., Wiser,
R., Graham, D.I., and Adams, J. (1987).
Directional dependence of axonal brain injury due
to centroidal and non-centroidal acceleration, SAE
Paper No. 872197, pp. 49-53, Proc. 31
st
Stapp Car
Crash Conference, Society of Automotive
Engineers, Warrendale, PA.
Graff, K.F. (1975). Wave motion in elastic solids.
Dover Publ. Inc., New York.
Gurdjian, E.S., Hodgson, V.R., Thomas, L.M., and
Patrick, L.M. (1968). Significance of relative
movements of scalp, skull, and intracranial
contents during impact injury of the head. Journal
of Neurosurgery 29(1): 70-72.
Hardy, W.N., Foster, C., Mason, M., Yang, K., King,
A., and Tashman, S. (2001). Investigation of Head
Injury Mechanisms Using Neutral Density
Technology and High-Speed Biplanar X-ray. 45
th
Stapp Car Crash Journal, pp. 337-368. The Stapp
Association, Ann Arbor, MI.
King, A.I., Hardy, W.N. Mason, M.J., and Tashman,
S. (2002). Comparison of Relative Motion
Between the Brain and Skull of the Human
Cadaver for Rotation in the Coronal and Sagittal
Planes, 4
th
World Congress of Biomechanics.
August 2002, Calgary, Alberta, Canada.
Kleiven, S., and von Holst, H. (2001). Consequences
of Brain Size following Impact in Prediction of
Subdural Hematoma evaluated with Numerical
Techniques. Proc. IRCOBI Conference, pp. 161-
172, Isle of Man (UK). International Research
Council on the Biomechanics of Impact, Bron,
France.
Kleiven, S., and von Holst, H. (2002a).
Consequences of Head Size following Trauma to
the Human Head, Journal of Biomechanics 35 (2):
153-160.
Kleiven, S., and von Holst, H. (2002b). Influence of
Direction and Duration of Impact to the Human
Head, 4
th
World Congress of Biomechanics.
August 2002, Calgary, Alberta, Canada.
Kuijpers, A.H.W.M., Claessens, M.H.A., and Sauren,
A.A.H.J. (1995). The influence of different
boundary conditions on the response of the the
head to impact: A two-dimensional finite element
study. Journal of Neurotrauma 12 (4): 715-724.
Livermore Software Technology Corporation (2001).
“LS-Dyna Keyword User’s Manual, Version 960”
and “LS-Dyna Theory Manual”, Livermore, CA,
U.S.A.
Malvern, L.E. (1969). Introduction to the mechanics
of a continuous medium.
Prentice-Hall, Englewood
Cliffs, N.J.
Kleiven and Hardy / Stapp Car Crash Journal 46 (November 2002)
144
McElhaney, J.H., Roberts, V.L., and Hilyard, J.F.
(1976). Properties of human tissues and
components: nervous tissues, in Handbook of
human tolerance, Automobile Research Institute
Inc., Tokyo, Japan, p. 143.
Mendis, K.K., Stalnaker, R.L., and Advani, S.H.
(1995). A constitutive relationship for large
deformation finite element modeling of brain
tissue, Journal of Biomechanical Engineering 117
(4): 279-285.
Miller, R.T., Margulies, S.S., Leoni, M., Nonaka, M.,
Chen, X., Smith, D.H., and Meaney, D.F. (1998).
Finite Element Modeling Approaches for
Predicting Injury in an Experimental Model of
Severe Diffuse Axonal Injury. Proc. 42
nd
Stapp Car
Crash Conference, SAE Paper No. 983154, pp.
155-166, Society of Automotive Engineers,
Warrendale, PA.
Nahum, A.M., Smith, R., and Ward, C. (1977).
Intracranial pressure dynamics during head impact.
Proc. 21
st
Stapp Car Crash Conf, SAE Paper No.
770922, pp. 337-366. Society of Automotive
Engineers, Warrendale, PA.
Ogden, R.W. (1984). Non-Linear Elastic
Deformations. Dover Publications, Inc., Mineola,
New York.
Prange, M.T., Meaney, D.F., and Margulies, S.S.
(2000). Defining Brain Mechanical Properties:
Effects of Region, Direction, and Species. Proc.
44
th
Stapp Car Crash Journal, Paper No. 2000-01-
SC15. The Stapp Association, Ann Arbor, MI.
Pudenz, R.H., and Shelden, C.H. (1946) The Lucite
calvarium - a method for direct observation of the
brain. II. Cranial trauma and brain movement.
Journal of Neurosurgery 3:487-505.
Ruan, J.S., Khalil, T.B., and King, A.I. (1997).
Impact Head Injury Analysis Using an Explicit
Finite Element Human Head Model, Journal of
Traffic Medicine 25: 33-40.
Stalnaker, R.L. (1969). Mechanical properties of the
head, Ph.D. dissertation, West Virginia University.
Thomas, L.M., Roberts, V.L., and Gurdijan, E.S.
(1967). Impact-induced pressure gradients along
three orthogonal axes in the human skull. Journal
of Neurosurgery 26: 316-349.
Turquier, F., Kang, H.S., Trosseille, X., Willinger,
R., Lavaste, F., Tarriere, C., and Dômont, A.
(1996). Validation Study of a 3D Finite Element
Head Model Against Experimental Data. Proc. 40
st
Stapp Car Crash Conference, pp. 283-294. SAE
Paper No. 962431, Society of Automotive
Engineers, Warrendale, PA.
Willinger, R., Taled, L., and Pradore, P. (1995). Head
biomechanics: from the finite element model to the
physical model. Proc. IRCOBI Conference, pp.
245-260, Brunnen, Switzerland. International
Research Council on the Biomechanics of Impact,
Bron, France.
Zhang, L., Yang, K.H., and King, A.I. (2001).
Comparison of Brain Responses Between Frontal
and Lateral Impacts by Finite Element Modeling.
Journal of Neurotrauma 18 (1): 21-30.
Zhou, C., Khalil, T.B., and King, A.I. (1995). A new
model comparing impact responses of the
homogeneous and inhomogeneous human brain.
Proc. 39
th
Stapp Car Crash Conference, pp. 121-
137. Society of Automotive Engineers,
Warrendale, PA.
