How Do Brain Fiber Tracts Influence Glioma Migration?

The invasion of tumor cells into healthy tissue is a highly complex process involving several scales, from the microscopic to the macroscopic level. Furthermore, most of the events taking place on the various scales are still not completely understood. In this work, we focus on glioma, a particularly invasive brain tumor, whose evolution, owing to the peculiarities of the nervous tissue structures, is characterized by highly anisotropic diffusion and heterogeneous patterns. A multiscale mathematical model for glioma cell migration, proliferation and therapy, is proposed. Starting from the microscopic description of the binding process between tumor cells and ECM, we derive a macroscopic model, using the parabolic limit and the Hilbert expansions in the mesoscopic moment system [1]. To asses the role of the nervous fibers in tumor migration, we perform an extensive study about the fiber density function [2], comparing different possible expressions, intending to understand their specific capability in describing the actual fiber distribution. Finally, some numerical simulations, based on real data of brain geometry and cell diffusivity, show how tumor migration is influenced by the different modeled processes.