Biomedical Engineering Reference
In-Depth Information
computational nodes and integration points were distributed almost arbitrarily in
the brain as shown in Fig.
2f
, g. The size of the influence domain was predetermined
based on node densities so that each integration points would not be associated with
either too many or too few nodes. In the tested case, the number of nodes per
integration point was between 4 and 7. The corresponding finite element mesh was
built from the manual segmentation of tumor and ventricle with similar node
densities, as shown in Fig.
2b
. To avoid volumetric locking in the finite element
simulation, (almost incompressible materials are employed) we used the
nonlocking triangular element described in [
12
].
Despite continuing efforts [
13
], commonly accepted noninvasive methods for
determining patient-specific constitutive properties of the brain tissue have not been
developed yet. However, as explained in [
14
], the strength of the modeling
approach used in this study is that the calculated brain deformations depend very
weakly on the constitutive model of brain tissues. Therefore, following [
15
], we
used the simplest hyperelastic model, the neo-Hookean model. Based on the
experimental data [
16
] and prior modeling experience [
17
], the Young's modulus
was set to 3,000 Pa for the brain parenchyma tissue. For the tumor, we defined
Young's modulus two times larger than for the parenchyma. There is strong
experimental evidence [
18
] that the brain tissue is (almost) incompressible so we
assigned a Poisson's ratio of 0.49 for the parenchyma and tumor. Following [
14
],
the ventricles were assigned the properties of a very soft and compressible
hyperelastic material with Young's modulus of 10 Pa and Poisson's ratio of 0.1
to account for the possibility of leakage of the cerebrospinal fluid (CSF) from the
ventricles during surgery.
For the meshless method, the material properties were assigned to integration
points as explained in Sect.
2
. In the finite element model, material properties were
assigned based on corresponding element sets.
When defining boundary conditions for biomechanical models of the brain for
image registration one could prescribe forces/pressure due to gravity and interactions
between the brain and CSF [
18
,
19
]. However, such forces are very difficult tomeasure
and verify so that produce brain shift are not easily quantified and modeled. In the
present study, brain shift due to craniotomy was considered as a “displacement- zero
traction” problem (as suggested by [
20
,
21
]). Both models were loaded by enforced
motion of nodes (through imposing prescribed displacements on the brain surface
exposed during craniotomy area). The strength of our method is that it requires no
information about the physical or physiological processes leading to the brain shift.
The effects of all such processes are included in the prescribed nodal displacements,
and a difficult and so far unresolved question about the exact mechanisms causing
craniotomy-induced brain shift is bypassed. The nodal displacements for this motion
were determined using intra-operativeMRIs (as shown in Fig.
3c
) although they can be
also measured using methods that do not require intra-operative imaging (see e.g.,
[
22
]). The displacement in the present case is up to 6 mm. We employed fully
geometrically nonlinear total Lagrangian formulation [
23
] for solving the two compu-
tational models with explicit time integration via central difference method. The
formulation of appropriate boundary conditions for computation of brain deformation
