6 Biomechanical Modelling of the Brain for Neurosurgical Simulation. . .
151
6.3.2 Displacement Loading
The models were loaded by prescribing displacements on the exposed part (due
to craniotomy) of the brain surface. As this requires only replacing the brain-skull
contact boundary condition with prescribed displacements, no mesh modification
is required at this stage. At first the pre-operative and intra-operative coordinate
systems were aligned by rigid registration. Then the displacements at the mesh
nodes located in the craniotomy region were estimated with the interpolation
algorithm we described in [101].
As explained above (Sect. 2.3 and 2.4), for problems where loading is prescribed
as forced motion of boundaries, the unknown deformation field within the domain
depends very weakly on the mechanical properties of the continuum. This feature is
of great advantage in biomechanical modelling where there are always uncertainties
in patient-specific properties of tissues [102].
6.3.3 Boundary Conditions
The stiffness of the skull is several orders of magnitude higher than that of the brain
tissue. Therefore, in order to define the boundary conditions for the unexposed nodes
of the brain mesh, a contact interface [103] was defined between the rigid skull
model and the deformable brain. The interaction was formulated as a finite sliding,
frictionless contact between the brain and the skull. The effects of assumptions
regarding the brain boundary conditions on the results of prediction of deformations
within the brain have been analysed and discussed in [96, 104] and more recently in
[51].
6.3.4 Mechanical Properties of the Intracranial Constituents
For Dirichlet-type problems, the predicted deformation field within the brain is
only weakly affected by the constitutive model of the brain tissue [98]. Therefore,
for simplicity a hyper-elastic neo-Hookean model was used [105]. The Young’s
modulus of 3000 Pa was selected for parenchyma [106]. The Young’s modulus for
tumour was assigned a value two times larger than that for the parenchyma, keeping
it consistent with the experimental data of Sinkus et al. [107]. As the brain tissue
is almost incompressible, a Poisson’s ratio of 0.49 was chosen for the parenchyma
and tumour [96]. The ventricles were assigned properties of a very soft compressible
elastic solid with a Young’s modulus of 10 Pa and Poisson’s ratio of 0.1 [96].
151
6.3.2 Displacement Loading
The models were loaded by prescribing displacements on the exposed part (due
to craniotomy) of the brain surface. As this requires only replacing the brain-skull
contact boundary condition with prescribed displacements, no mesh modification
is required at this stage. At first the pre-operative and intra-operative coordinate
systems were aligned by rigid registration. Then the displacements at the mesh
nodes located in the craniotomy region were estimated with the interpolation
algorithm we described in [101].
As explained above (Sect. 2.3 and 2.4), for problems where loading is prescribed
as forced motion of boundaries, the unknown deformation field within the domain
depends very weakly on the mechanical properties of the continuum. This feature is
of great advantage in biomechanical modelling where there are always uncertainties
in patient-specific properties of tissues [102].
6.3.3 Boundary Conditions
The stiffness of the skull is several orders of magnitude higher than that of the brain
tissue. Therefore, in order to define the boundary conditions for the unexposed nodes
of the brain mesh, a contact interface [103] was defined between the rigid skull
model and the deformable brain. The interaction was formulated as a finite sliding,
frictionless contact between the brain and the skull. The effects of assumptions
regarding the brain boundary conditions on the results of prediction of deformations
within the brain have been analysed and discussed in [96, 104] and more recently in
[51].
6.3.4 Mechanical Properties of the Intracranial Constituents
For Dirichlet-type problems, the predicted deformation field within the brain is
only weakly affected by the constitutive model of the brain tissue [98]. Therefore,
for simplicity a hyper-elastic neo-Hookean model was used [105]. The Young’s
modulus of 3000 Pa was selected for parenchyma [106]. The Young’s modulus for
tumour was assigned a value two times larger than that for the parenchyma, keeping
it consistent with the experimental data of Sinkus et al. [107]. As the brain tissue
is almost incompressible, a Poisson’s ratio of 0.49 was chosen for the parenchyma
and tumour [96]. The ventricles were assigned properties of a very soft compressible
elastic solid with a Young’s modulus of 10 Pa and Poisson’s ratio of 0.1 [96].