324
H. Courtecuisse et al.
After segmentation, most of the existing works rely on a 3D finite element mesh of
the domain. While hexahedral elements are preferred numerically, tetrahedrons are
often used for meshing simplicity.
13.2.1.2 Constitutive Law
Brain constitutive behaviour and brain modelling have been extensively described
in the previous chapters of this book. The behaviour of the brain tissues is widely
admitted as nonlinear, inhomogeneous, and patient specific. The range of modelling
strategies is, however, very large, with constitutive laws from linear to hyperelastic
or biphasic materials. For a use in the operating room, one of the major constraints
is computational efficiency. Therefore, a trade-off must be found between a fine
modelling and the practicability of the model. Any simulation requiring more than
a few minutes could obviously not be compatible with clinic.
13.2.1.3 Mechanical Properties
To our knowledge, virtually, all the existing models use generic mechanical
properties reported in the literature from experimental measurements. With some
exception, brain tissue stiffness is usually considered in the 1–10 kPa range (in
equivalent Young’s modulus, for the nonlinear materials), with Poisson’s ratio from
0.4 to 0.49 [10]. Tumour tissues are often modelled as stiffer, following clinical
recommendations but without clear supporting data.
Although these orders of magnitude of the mechanical parameters are adequate,
they cannot represent the variability among patients and their specificity and
inhomogeneity. Therefore, assessing patient-specific mechanical properties, for
example, with MR elastography [11], could be a valuable addition. While this may
not be crucial when using imposed displacements [12], patient-specific values could
improve the simulation accuracy when other types of loads are used (especially
forces).
13.2.1.4 Known Boundary Conditions
Some boundary conditions can be determined pre-operatively, typically at the
interface between the brain and dura mater. Depending on the procedure, inner
structures may also be considered as fixed during surgery, such as the brain stem
region, the tentorium cerebelli, the ventricles, or even the falx cerebri.
In most cases, the segmentation of these structures from MRI images is manual
or semiautomatic. However, some authors have proposed automatic methods to fix
the cerebellum [13] or simulate interactions with the cerebral falx and tentorium
cerebelli [14]. Once segmented, these structures are used to fix nodes or to set up
sliding contact boundary conditions.
H. Courtecuisse et al.
After segmentation, most of the existing works rely on a 3D finite element mesh of
the domain. While hexahedral elements are preferred numerically, tetrahedrons are
often used for meshing simplicity.
13.2.1.2 Constitutive Law
Brain constitutive behaviour and brain modelling have been extensively described
in the previous chapters of this book. The behaviour of the brain tissues is widely
admitted as nonlinear, inhomogeneous, and patient specific. The range of modelling
strategies is, however, very large, with constitutive laws from linear to hyperelastic
or biphasic materials. For a use in the operating room, one of the major constraints
is computational efficiency. Therefore, a trade-off must be found between a fine
modelling and the practicability of the model. Any simulation requiring more than
a few minutes could obviously not be compatible with clinic.
13.2.1.3 Mechanical Properties
To our knowledge, virtually, all the existing models use generic mechanical
properties reported in the literature from experimental measurements. With some
exception, brain tissue stiffness is usually considered in the 1–10 kPa range (in
equivalent Young’s modulus, for the nonlinear materials), with Poisson’s ratio from
0.4 to 0.49 [10]. Tumour tissues are often modelled as stiffer, following clinical
recommendations but without clear supporting data.
Although these orders of magnitude of the mechanical parameters are adequate,
they cannot represent the variability among patients and their specificity and
inhomogeneity. Therefore, assessing patient-specific mechanical properties, for
example, with MR elastography [11], could be a valuable addition. While this may
not be crucial when using imposed displacements [12], patient-specific values could
improve the simulation accuracy when other types of loads are used (especially
forces).
13.2.1.4 Known Boundary Conditions
Some boundary conditions can be determined pre-operatively, typically at the
interface between the brain and dura mater. Depending on the procedure, inner
structures may also be considered as fixed during surgery, such as the brain stem
region, the tentorium cerebelli, the ventricles, or even the falx cerebri.
In most cases, the segmentation of these structures from MRI images is manual
or semiautomatic. However, some authors have proposed automatic methods to fix
the cerebellum [13] or simulate interactions with the cerebral falx and tentorium
cerebelli [14]. Once segmented, these structures are used to fix nodes or to set up
sliding contact boundary conditions.