A Viscoelastic Model for Glioma Growth

Abstract

In this paper we propose a mathematical model to describe the evolution of glioma cells in the brain taking into account the viscoelastic properties of brain tissue. The mathematical model is established considering that the glioma cells are of two phenotypes: migratory and proliferative. The evolution of the migratory cells is described by a diffusion-reaction equation of non Fickian type deduced considering a mass conservation law with a non Fickian migratory mass flux. The evolution of the proliferation cells is described by a reaction equation. Numerical simulations that illustrate the behaviour of the mathematical model are included.