Modeling invasion of brain tissue by glioblastoma cells: ECM alignment and motility

A key stage in the development of highly malignant brain tumors (Glioblastoma Multiforme) is invasion of normal brain tissue by motile cells moving through a crowded, complex environment. Evidence from \emph{in vitro} experiments suggests the cell motion is accompanied by considerable deformation and alignment of the extra-cellular matrix (ECM) of the brain. In the case of breast cancer, alignment effects of this sort have been seen \emph{in vivo}. We have modeled features of this system including stress confinement in the non-linear elasticity of the ECM and contact guidance of the cell motion.