A Flux-Limited Model for Glioma Patterning with Hypoxia-Induced Angiogenesis

Abstract

We propose a model for glioma patterns in a microlocal tumor environment under the influence of acidity, angiogenesis, and tissue anisotropy. The bottom-up model deduction eventually leads to a system of reaction–diffusion–taxis equations for glioma and endothelial cell population densities, of which the former infers flux limitation both in the self-diffusion and taxis terms. The model extends a recently introduced (Kumar, Li and Surulescu, 2020) description of glioma pseudopalisade formation with the aim of studying the effect of hypoxia-induced tumor vascularization on the establishment and maintenance of these histological patterns which are typical for high-grade brain cancer. Numerical simulations of the population level dynamics are performed to investigate several model scenarios containing this and further effects.

Keywords

• glioblastoma
• pseudopalisades
• hypoxia-induced angiogenesis
• flux-limited diffusion and taxis
• kinetic transport equations
• equilibrium-based moment closure