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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.