REU 2008 – A Macroscale Model for the Growth of Glioblastoma Multiforme Incorporating Tumor Cell Heterogeneity

Glioblastoma multiforme (GBM) is a highly lethal brain cancer–patients typically survive 12-18 months after diagnosis with treatment, and only six months without. Our continuum model describes the dynamics of GBM via a system of nine partial differential equations involving tumor cell, nutrient, toxin, and chemoattractor densities. We allow for genetic instability of the tumor cells by considering five different tumor cell clone types which may mutate upon proliferation. The mutations follow a linear progression pathway from clone A (the least aggressive type) to clone E (the most aggressive type). Since our model is macroscopic in nature, a key objective is to obtain results similar to those produced by previous agent-based models set on a microscale. Using numerical methods, we approximate the solution to our model in MATLAB and conduct in-silico experiments.