  Computational biomechanics of the brain for neurosurgery is an emerging area
of research recently gaining in importance and practical applications. This
review paper presents the contributions of the Intelligent Systems for Medicine
Laboratory and it's collaborators to this field, discussing the modeling
approaches adopted and the methods developed for obtaining the numerical
solutions. We adopt a physics-based modeling approach, and describe the brain
deformation in mechanical terms (such as displacements, strains and stresses),
which can be computed using a biomechanical model, by solving a continuum
mechanics problem. We present our modeling approaches related to geometry
creation, boundary conditions, loading and material properties. From the point
of view of solution methods, we advocate the use of fully nonlinear modeling
approaches, capable of capturing very large deformations and nonlinear material
behavior. We discuss finite element and meshless domain discretization, the use
of the Total Lagrangian formulation of continuum mechanics, and explicit time
integration for solving both time-accurate and steady state problems. We
present the methods developed for handling contacts and for warping 3D medical
images using the results of our simulations. We present two examples to
showcase these methods: brain shift estimation for image registration and brain
deformation computation for neuronavigation in epilepsy treatment.
