6 Biomechanical Modelling of the Brain for Neurosurgical Simulation. . .
147
6.2.4 Models of Mechanical Properties of Brain Tissue
The first question to address is whether a single-phase continuum model for the
tissue should be used or if biphasic or even more complicated multiphase models
are required. Many researchers conclude that the brain is obviously a hydrated
tissue and therefore use biphasic models based on consolidation theory; see, e.g.
[65] and references cited therein. We are of the opinion that biphasic, consolidation
theory-based models are inconsistent with brain tissue behaviour observed in simple
experiments. For example, no leakage of CSF was observed in brain tissue samples
loaded by CSF pressure difference [66, 67]. Another argument against using
biphasic models is that during numerous unconfined compression experiments [68],
we never observed fluid leaking from the side of the samples. Such leakage is
predicted by biphasic theory. Therefore, in the remainder of this chapter, we will
discuss only single-phase modelling approaches.
Experimental results show that the mechanical response of brain tissue to
external loading is very complex. The stress-strain relationship is clearly non-linear
with no portion in the plots suitable for estimating a meaningful Young’s modulus.
It is also obvious that the stiffness of the brain in compression is much higher
than in extension [69]. The non-linear relationship between stress and strain rate
is also apparent. Detailed exposition of the current knowledge about the mechanical
properties of brain tissue is given in Chap. 4. Here we will only discuss issues
directly pertinent to modelling neurosurgery.
The great majority of brain models assume brain tissue is incompressible and
isotropic (see also Chaps. 4 and 5). The assumption of incompressibility is not
contentious. Whether it is reasonable to assume that brain tissue is isotropic (i.e.
mechanical properties the same in all directions) is less clear, especially in view
of the obviously directional character of white matter fibres. Brain tissues do not
normally bear mechanical loads and do not exhibit directional structure, provided
that a large-enough length scale is considered. Therefore, they may be assumed
to be initially isotropic; see, e.g. [69–77]. When modelling brain deformations
during surgery, we need to keep in mind that the accuracy of displacement
computations rarely needs to be better than about 1 mm – the claimed accuracy of
neurosurgery. Therefore, ‘average isotropic’ properties at the length scales relevant
to surgical procedures are most probably sufficient. These properties are relatively
well accounted for by an Ogden-type hyperviscoelastic model [78] described in
Chap. 4, Eqs. 4.4 and 4.5.
Average properties, such as those described above, are not sufficient for patientspecific computations of stresses and reaction forces because of the very large
variability inherent in biological materials. This variability is clearly demonstrated
in the biomechanics literature [69, 80–81]. Unfortunately, despite recent progress in
elastography using ultrasound [82, 83] and magnetic resonance (see Chap. 4) [84–
88], reliable methods of measuring patient-specific properties of the brain are not
yet available.
147
6.2.4 Models of Mechanical Properties of Brain Tissue
The first question to address is whether a single-phase continuum model for the
tissue should be used or if biphasic or even more complicated multiphase models
are required. Many researchers conclude that the brain is obviously a hydrated
tissue and therefore use biphasic models based on consolidation theory; see, e.g.
[65] and references cited therein. We are of the opinion that biphasic, consolidation
theory-based models are inconsistent with brain tissue behaviour observed in simple
experiments. For example, no leakage of CSF was observed in brain tissue samples
loaded by CSF pressure difference [66, 67]. Another argument against using
biphasic models is that during numerous unconfined compression experiments [68],
we never observed fluid leaking from the side of the samples. Such leakage is
predicted by biphasic theory. Therefore, in the remainder of this chapter, we will
discuss only single-phase modelling approaches.
Experimental results show that the mechanical response of brain tissue to
external loading is very complex. The stress-strain relationship is clearly non-linear
with no portion in the plots suitable for estimating a meaningful Young’s modulus.
It is also obvious that the stiffness of the brain in compression is much higher
than in extension [69]. The non-linear relationship between stress and strain rate
is also apparent. Detailed exposition of the current knowledge about the mechanical
properties of brain tissue is given in Chap. 4. Here we will only discuss issues
directly pertinent to modelling neurosurgery.
The great majority of brain models assume brain tissue is incompressible and
isotropic (see also Chaps. 4 and 5). The assumption of incompressibility is not
contentious. Whether it is reasonable to assume that brain tissue is isotropic (i.e.
mechanical properties the same in all directions) is less clear, especially in view
of the obviously directional character of white matter fibres. Brain tissues do not
normally bear mechanical loads and do not exhibit directional structure, provided
that a large-enough length scale is considered. Therefore, they may be assumed
to be initially isotropic; see, e.g. [69–77]. When modelling brain deformations
during surgery, we need to keep in mind that the accuracy of displacement
computations rarely needs to be better than about 1 mm – the claimed accuracy of
neurosurgery. Therefore, ‘average isotropic’ properties at the length scales relevant
to surgical procedures are most probably sufficient. These properties are relatively
well accounted for by an Ogden-type hyperviscoelastic model [78] described in
Chap. 4, Eqs. 4.4 and 4.5.
Average properties, such as those described above, are not sufficient for patientspecific computations of stresses and reaction forces because of the very large
variability inherent in biological materials. This variability is clearly demonstrated
in the biomechanics literature [69, 80–81]. Unfortunately, despite recent progress in
elastography using ultrasound [82, 83] and magnetic resonance (see Chap. 4) [84–
88], reliable methods of measuring patient-specific properties of the brain are not
yet available.