Abstract
Realistic computer simulation of neurosurgical procedures requires
incorporation of the mechanical properties of brain tissue in the
mathematical model. Possible applications of computer simulation
of neurosurgery include non-rigid registration, virtual reality training
and operation planning systems and robotic devices to perform minimally
invasive brain surgery. A number of constitutive models of brain
tissue, both single-phase and bi-phasic, have been proposed in recent
years. The major deficiency of most of them, however, is the fact
that they were identified using experimental data obtained in vitro
and there is no certainty whether they can be applied in the realistic
in vivo setting. In this paper we attempt to show that previously
proposed by us hyper-viscoelastic constitutive model of brain tissue
can be applied to simulating surgical procedures. An in vivo indentation
experiment is described. The force-displacement curve for the loading
speed typical for surgical procedures is concave upward containing
no linear portion from which a meaningful elastic modulus might be
determined. In order to properly analyse experimental data, a three-dimensional,
non-linear finite element model of the brain was developed. Magnetic
resonance imaging techniques were used to obtain geometric information
needed for the model. The shape of the force-displacement curve obtained
using the numerical solution was very similar to the experimental
one. The predicted forces were about 31% lower than those recorded
during the experiment. Having in mind that the coefficients in the
model had been identified based on experimental data obtained in
vitro, and large variability of mechanical properties of biological
tissues, such agreement can be considered as very good. By appropriately
increasing material parameters describing instantaneous stiffness
of the tissue one is able, without changing the structure of the
model, to reproduce experimental curve almost perfectly. Numerical
studies showed also that the linear, viscoelastic model of brain
tissue is not appropriate for the modelling brain tissue deformation
even for moderate strains.
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