Acta Neurochir (2005) [Suppl] 95: 333–336
6 Springer-Verlag 2005
Printed in Austria
Brain tissue biomechanics in cortical contusion injury: a finite element analysis
A. Peña1,2, J. D. Pickard1,2,3, D. Stiller4, N. G. Harris1,2,3, and M. U. Schuhmann5
1 Academic Neurosurgery Unit, University of Cambridge, Cambridge, UK
2 Wolfson Brain Imaging Centre, University of Cambridge, Cambridge, UK
3 Cambridge Centre for Brain Repair, University of Cambridge, Cambridge, UK
4 In-vivo MRI Lab, Boehringer Ingelheim KG, Biberach, Germany
5 Department of Neurosurgery, University of Leipzig, Leipzig, Germany
Summary
The controlled cortical impact model has been used extensively to
study focal traumatic brain injury. Although the impact variables
can be well defined, little is known about the biomechanical trauma
as delivered to di¤erent brain regions. This knowledge however
could be valuable for interpretation of experiment (immunohistochemistry etc.), especially regarding the comparison of the regional
biomechanical severity level to the regional magnitude of the trauma
sequel under investigation. We used finite element (FE) analysis,
based on high resolution T2-weighted MRI images of rat brain,
to simulate displacement, mean stress, and shear stress of brain during impact. Young’s Modulus E, to describe tissue elasticity, was
assigned to each FE in three scenarios: in a constant fashion
(E ¼ 50 kPa), or according to the MRI intensity in a linear
(E ¼ ½10; 100 kPa) and inverse-linear fashion (E ¼ ½100; 10 kPa).
Simulated tissue displacement did not vary between the 3 scenarios,
however mean stress and shear stress were largely di¤erent. The linear scenario showed the most likely distribution of stresses. In summary, FE analysis seems to be a suitable tool for biomechanical simulation, however, to be closest to reality tissue elasticity needs to be
determined with a more specific approach, e.g. by means of MRI
elastography.
Keywords: Experimental traumatic brain injury; controlled cortical impact; magnetic resonance imaging; finite element analysis;
brain tissue biomechanics; Young’s modulus E; tissue elasticity.
Introduction
Since its original description in the late eighties [5, 6]
the controlled cortical impact injury model (CCI) has
been extensively used in di¤erent forms to investigate
focal traumatic brain injury. The rationale behind
these studies is that this type of injury might partially
replicate human brain contusions. A current Medline
search with the keywords ‘‘CCI’’ and ‘‘controlled cortical impact’’ will yield hundreds of publications. One
virtue of the model is, that it uses a known impact interface, a measurable impact velocity and a predefined
depth and duration of cortical compression and thus is
regarded as biomechanically well-defined. It has been
assumed that the quantifiable single mechanical input
would permit to conduct a standardized statistical
analysis (e.g. correlation) between the amount of deformation and the resultant pathology and functional
changes [6]. However, although the ‘‘external’’ biomechanical parameters can be well defined and described,
the ‘‘internal’’ biomechanics of the brain during impact according to the regionally di¤erent tissue elasticity, the amount of compression/pressure and the regional distribution of tissue pressures and strains
is unknown and has not been systematically investigated at large. Looking at the distribution of e.g. posttraumatic changes in CBF maps, MRI images or
(immuno-) histopathological stains, it remains often
unclear to which extent the observed findings are directly related to the local severity of the primary biomechanical trauma or rather to the many secondary
and tertiary reactions which widely unfold immediately following the biomechanical action. A deeper insight into this complex regional interaction between a
predominant ‘‘biomechanical’’ trauma and a predominant secondary/tertiary ‘‘neurochemical and molecular’’ trauma would be of significant value. For example, such a distinction could help identifying those
areas around contusions, which do not receive a lethal
biomechanical impact and therefore might be the target for salvage strategies summarized under the term
‘‘neuroprotection’’. Furthermore, it has become evident that ‘‘CCI’’ di¤ers between labs, and it is unknown how the di¤erent variables (brain size, impact
location, speed, depth, duration) actually influence
A. Peña et al.
334
comparability of results between labs. Therefore a biomechanical description of the applied trauma seems of
high interest to better interpret own results and to create a basis for a biomechanical standardization of the
brain trauma. Our study is a first attempt to achieve
those goals by using a finite element analysis of the
CCI, based on high resolution T2-weighted MRI images of rat brain, for a biomechanical simulation of
the resulting trauma inside the brain tissue.
Materials and methods
Several high resolution T2 weighted image series were obtained from a 260 g male Sprague Dawley rat in a Bruker Biospec
47/20 scanner at 4.7 T running Paravision8 software (Bruker
GmbH, Ettlingen, Germany). We used a CPMG sequence with a
TR 5000 ms, and di¤erent TE of 15, 30, 45, 60, 75, 90, 105,
120 ms, 8 echoes, FOV ¼ 2.56 2.56 cm, 2 averages, 1 mm slices.
We obtained at TE 45 ms the best contrast and delineation between
white and grey matter and between hippocampus, basal ganglia and
ventricles and chose a slice corresponding to 3.6 mm to Bregma.
(see Fig. 1a) as basis for the finite element analysis. Maps of stress
(force per unit area) were calculated following the indentation. The
Navier-Cauchy governing equations:
m‘ 2 ui þ ðl þ mÞ‘‘ui þ rbi ¼ 0
ð1Þ
where ‘ is the Laplacian operator, l and m are Lame’s elasticity constants, ui is the displacement vector, r is the density and bi is the body
force vector, were solved using the FE method. Stress was quantified
in terms of the magnitude of the mean stress (p) and the von Mises
shear stress (q). The equations (1) were solved using the FE software
FEMLAB 2.0 with the Structural Mechanics Module (COMSOL
Ltd, John Eccles House, The Oxford Science Park, Oxford OX4
4GP, UK). Second order triangular elements were used.
In order to ensure the convergence of the numerical solution, the
analysis was repeated at two levels of mesh refinement. Delaunay
tringulation was used to generate the meshes. Analyses were done using an Intel Pentium 4 computer with 512MB RAM and on HP-UX
Unix workstations. Because of the uncertainty regarding the tissue
elasticity, we considered three scenarios relating the magnitude of
Young’s modulus (E) and the MRI intensity (I). The first is the linear, in which E is directly proportional to I. The second is the inverse
linear, in which E is inversely proportional to I. Finally, the constant
scenario in which E is constant and thus independent of I.
For simulating the impact, we used standard previously-defined
parameters: impactor diameter 5 mm, impact speed 4 m/s, impact
depth 2.5 mm [8, 9].
Results
Fig. 1. Shows the high resolution T2 weighted MR image, which
formed the basis for construction of the finite element mesh and the
assignment of tissue properties (elasticity) to the single triangular
shaped finite elements. On the left side of the brain, an impact with
a round 5 mm indentor travelling at 4 m/s to an impact depth of
2.5 mm was simulated
Maps were calculated with deformed coordinates
– corresponding to the time of impact, when the
brain is indented – and un-deformed coordinates –
corresponding to the time thereafter, when the brain
has resumed its previous shape. At each scenario maps
were computed for displacement, mean stress (corresponding to compression or pressure) and shear stress
(corresponding to tissue distortion). Figure 2 shows
the resulting maps with un-deformed coordinates.
Tissue displacement (Fig. 2a) was similar in all three
scenarios of tissue elasticity with only little variation.
Mean stress distribution (Fig. 2b), however, varied
considerably. With constant elasticity (all brain regions were equally hard or soft), there was a rather
constant mean stress distribution inside the tissue with
highest compression in the ‘‘contusion core’’ at and
Brain tissue biomechanics in cortical contusion injury: a finite element analysis
335
Fig. 2. Shows the resulting computations in three rows: (A) tissue displacement, (B) mean stress (positive values correspond to tissue compression, negative values correspond to tissue stretch) and (C) shear stress (tissue distortion). All of these based on the undeformed coordinates. In the first column are results for constant brain elasticity (E ¼ 50 kPa), in the second for an inverse-linear relationship between MRI
intensity and elasticity (the brighter the pixels the softer the tissue) and in the third for a linear relationship between MRI intensity and elasticity
(the brighter the pixels the harder the tissue)
immediately below the impact site and higher compression along the axis of impact direction. In the cortex laterally to the impact site the map showed negative compression (tissue stretch – negative pressures).
In the inverse-linear scenario (the brighter pixels in
the MRI, the softer the tissue, e.g. the corpus callosum
was harder than cortex and hippocampus) the biomechanical impact appeared stronger, with a larger zone
of highest mean stress – compression – down to brain
above the skull base and also a pronounced tissue
compression on the contralateral side. In the linear
scenario (the brighter pixels in the MRI, the harder
the tissue, e.g. the corpus callosum was softer than cortex and hippocampus) the biomechanical burden appeared lower and more scattered than in the constant
scenario, with highest levels only at the borders of the
impact zone, smaller areas of negative compression –
stretch – laterally and some areas of stress discontinuity below the corpus callosum. At the ipsilateral base
of the brain there was an increase of compression like
a côntre-coup e¤ect. No changes in mean stress appeared on the contralateral side.
Regarding shear stress (Fig. 2c) there were similar
findings in all three scenarios of tissue elasticity. With
constant elasticity (all brain regions were equally hard
or soft) there appeared a broad area of maximum
shear stress – tissue distortion, which was larger than
the volume of maximum mean stress. Centrifugally
there was a rather constant decrease of shear stress distribution inside the tissue with higher distortion again
along the axis of impact direction. In the inverse-linear
scenario (the brighter pixels in the MRI, the softer the
tissue, e.g. the corpus callosum was harder than cortex
and hippocampus) the biomechanical distortion appeared again much stronger, with a very large zone of
highest shear stress almost down to the skull base and
also shear stress on the contralateral side. In the linear
scenario (the brighter pixels in the MRI, the harder the
tissue, e.g. the corpus callosum was softer than cortex
and hippocampus) the biomechanical impact again appeared lighter, with scattered areas of shear stress discontinuity. Higher distortion was seen mainly at the
borders of the impact zone, and below the corpus callosum. No e¤ects were seen on the contralateral side.
336
A. Peña et al.: Brain tissue biomechanics in cortical contusion injury: a finite element analysis
Discussion
We used a two-dimensional approach in the CCI
model of focal brain contusion to explore the ability
of finite element modelling for simulating primary biomechanical trauma – and how it relates to ‘‘mechanical’’ variables such as displacement, mean stress and
shear stress. High resolution MRI appears to be a adequate to be used to create the underlying finite element
mesh.
Obviously the knowledge of brain elasticity is crucial. In our constant model we used an E ¼ 50 kPa
for the whole brain according to the literature [4].
This is clearly unrealistic. Regional tissue properties
can be expected to influence regional elasticity. For example, the corpus callosum with a dense axonal and
oligodendrocytic structure should be di¤erent in elasticity than the cortex. Areas of packed neuronal density like basal ganglia should be di¤erent from the hippocampus with its distinct neuronal layers. The next
obvious step is to model brain tissue based on a functional relationship between MR intensity and Young’s
modulus. Our analysis was based on high resolution
T2 weighted MR imaging. It is unknown if such relationship exists, however, for modelling purposes we assumed a linear (the brighter the pixel the harder the tissue) and inverse-linear (the brighter the pixel the softer
the tissue) relationship between T2 signal intensity and
tissue elasticity, in order to capture the influence of regional variations of tissue elasticity on the distribution
of the internal stresses following impact.
As expected, our three scenarios had very small influence on the tissue displacement, after the indentation of the impactor. In contrast, we could observe
dramatic di¤erences for mean and shear stress, in other
words, between the amount of tissue compression or
stretch and tissue distortion between both models.
Most literature describes a predominantely unilateral
reaction of glial, microglial, and neuronal tissue following trauma [1–3, 7]. Therefore it can be assumed,
that the simulation with the linear relationship between tissue intensity in T2 images and brain elasticity,
which showed a unilaterally confined compression and
tissue distortion as well as influences of regional tissue
elasticity on stress patterns, is closer to reality than the
inverse-linear relationship.
Our three di¤erent models with constant and varying elasticity demonstrate that the key feature of a
modelling approach is a precise knowledge of regional
tissue elasticity. Only then a simulation will be reliable
enough to use it for standardisation of the CCI trauma
and to investigate the e¤ects of varying trauma severity with regard to impact depth and impact velocity on
a theoretical basis. And – most importantly – only then
this method will gain a potential usefulness with regard
to the di¤erentiation between a contribution of the primary trauma or of secondary neurochemical e¤ects if
it comes to the interpretation of e.g. regionally inhomogeneous patterns of neuronal, glial, microglial reactions or changes in CBF or glucose consumption.
MR elastography, which is a novel technique to obtain maps of tissue elasticity in vivo, might be a possible way to assign tissue properties on a pixel-by-pixel
basis, such that individual finite elements can reflect
the local elastic properties making the simulation
much more accurate.
In summary, we successfully used high resolution
MRI as a basis for finite element modelling of the biomechanical primary trauma in the CCI model. We
demonstrated that regional tissue elasticity has a large
influence on how the forces created by the initial tissue
displacement are transferred into the surrounding tissues, and these in turn a¤ect the regional distribution
patterns of mean stress and shear stress following
CCI. The linear scenario showed the distribution of
stresses that most resembles experimental data.
References
1. Baldwin SA, Sche¤ SW (1996) Intermediate filament change in
astrocytes following mild cortical contusion. Glia 16(3): 266–275
2. Chen S, Pickard JD et al (2003) Time-course of cellular pathology
after controlled cortical impact injury. Exp Neurol 182: 87–102
3. Dunn-Meynell AA, Levin BE (1997) Histological markers of neuronal, axonal and astrocytic changes after lateral rigid impact
traumatic brain injury. Brain Res 761(1): 25–41
4. Fung YC (1994) Biomechanics: mechanical properties of living
materials. Prentice-Hall, Englewood Cli¤s, NJ
5. Lighthall JW (1988) Controlled cortical impact: a new experimental brain injury model. J Neurotrauma 5(1): 1–15
6. Lighthall JW, Dixon CE et al (1989) Experimental models of
brain injury. J Neurotrauma 6(2): 83–97
7. Newcomb JK, Zhao X et al (1999) Temporal profile of apoptoticlike changes in neurons and astrocytes following controlled cortical impact injury in the rat. Exp Neurol 158(1): 76–88
8. Schuhmann MU, Mokhtarzadeh M et al (2003) Temporal profiles of cerebrospinal fluid leukotrienes, brain edema and inflammatory response following experimental brain injury. Neurol Res
25(5): 481–491
9. Schuhmann MU, Stiller D et al (2003) Metabolic changes in the
vicinity of brain contusions: a proton magnetic resonance spectroscopy and histology study. J Neurotrauma 20(8): 725–743
Correspondence: Martin U. Schuhmann, Klinik und Poliklinik
fuer Neurochirurgie, Universitaetsklinikum Leipzig, Liebigstrasse
20, 04103 Leipzig, Germany. e-mail: [email protected]