A flux-limited model for glioma patterning with hypoxia-induced angiogenesis

TL;DR

This paper introduces a flux-limited reaction-diffusion-taxis model for glioma pattern formation, incorporating hypoxia-induced angiogenesis and tissue anisotropy, to better understand tumor vascularization and histological patterning.

Contribution

It extends existing glioma models by including flux limitation and hypoxia-driven angiogenesis, providing a more comprehensive framework for tumor pattern analysis.

Findings

Numerical simulations demonstrate the impact of hypoxia on glioma patterning.

The model captures the formation of pseudopalisades under hypoxic conditions.

Flux limitation influences tumor invasion dynamics.

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 [34] 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.