Mathematically Modeling the Mass-Effect of Invasive Brain Tumors

Abstract

When developing an accurate model of the development of glioblastomas multiforme, it is important to account not only for the invasion and diffusion of tumor cells into healthy tissue but also the resulting mass effect and brain tissue deformation. This motivates the model presented here, which implements the finite element method to solve a boundary value problem defined through classical continuum mechanics. Intended to improve existing models of tumor invasion, this model predicts the mass-effect of an invading tumor in heterogeneous brain tissue. Several parameters, taken from existing literature, dictate the behavior of differing types of brain matter. The model operates on a two-dimensional (2D) domain and outputs the displacement of brain tissue as a result of the pressure surrounding and within the tumor (peri-tumor pressure).