Biomedical Engineering Reference
In-Depth Information
is the deformation gradient,
J
th
1+
e
th
3
is
the thermal volume ratio, and
e
th
is the thermal strain. The constants
µ
and
D
1
are related to the Young's modulus at zero strain
E
o
, and Poisson's ratio
υ
by
J
= det(
F
) is the volume ratio,
F
E
o
2(1 +
υ
)
D
1
=
6(1
−
2
υ
)
E
o
µ
=
and
(4)
The value
α
=
−
4
.
7 determined in [92] was adopted here. Since the brain bio-
mechanics literature includes varying accounts of brain tissue compressibility and
stiffness, in the experiments described below the effects of
µ
and
D
1
(equivalently
µ
and
υ
) on the proposed model were investigated.
4.3.4. Boundary conditions and interactions
The brain is surrounded by three meninges — the pia, the arachnoid, and the
dura mater — which are enclosed within the cranium that constrains the brain
deformation. The falx cerebri, which is the extension of the dura mater to in
between the two cerebral hemispheres, is more rigid than the brain tissue, and is
attached anteriorly and posteriorly to the skull. A large range of values for the
stiffness of the falx compared to that of brain tissue is present in the literature.
Here, as suggested by the experiments of Miga et al. [94], the brain is assumed
to be fixed at the points where the falx meets the skull, and the same material
properties assigned for the brain is used for the falx. Assuming negligible friction
between the brain meninges and the skull, all other points on the outer surface of
the brain are allowed to slide freely in the plane tangent to the surface of the brain,
with constrained motion in the normal direction. Initial experiments confirmed
that this choice of the boundary conditions for the brain makes the deformation
simulations more realistic and produce much lower errors compared to the use of
fixed boundary conditions over the whole brain surface [79,81,98].
The brain ventricles are assumed void since normal CSF circulation allows it to
leave the ventricles when pressure is imposed by the neighboring tissues. However,
for many large brain tumors, the opposite walls of the ventricles may come in
contact with each other, leading to propagation of the stresses and displacements
to the other side of the ventricle. In such cases, an appropriate model for the
contact between the ventricle walls is necessary.
The use of amodel of contact in the FE package ABAQUS requires satisfying a
number of conditions on the involved self-contacting surface, including that every
edge in that surfacemust be part of exactly two triangular surface patches in the used
FE mesh. Satisfaction of this condition was not possible in many cases since the
topology of the ventricular FE surface mesh depends on the input segmentation of
the ventricles, and on themeshing approach. To avoid this problem, for simulations
in which contact of ventricles is anticipated, the ventricles are assumed to be filled
with hyperfoammaterial [96]. This material responds by little resistance for values
of nominal strain up to 0.9, after which there is a rapid increase in the stress with
