Modelling brain deformations for computer-integrated neurosurgery

In this review paper we discuss Intelligent Systems for Medicine Laboratory's contributions to mathematical and numerical modelling of brain deformation behaviour for neurosurgical simulation and brain image registration. These processes can be reasonably described in purely mechanical terms, such as displacements, strains and stresses and therefore can be analysed using established methods of continuum mechanics. We advocate the use of fully non-linear theory of continuum mechanics. We discuss in some detail modelling geometry, boundary conditions, loading and material properties. We consider numerical problems such as the use of hexahedral and mixed hexahedral tetrahedral meshes as well as meshless spatial discretization schemes. We advocate the use of total Lagrangian formulation of both finite element and meshless methods together with explicit time-stepping procedures. We support our recommendations and conclusions with two examples: computation of the reaction force acting on a biopsy needle, and computation of the brain shift for image registration. Copyright (C) 2009 John Wiley & Sons, Ltd.