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We propose a model for glioma patterns in a microlocal tumor environmentunder the influence of acidity, angiogenesis, and tissue anisotropy. Thebottom-up model deduction eventually leads to a system ofreaction-diffusion-taxis equations for glioma and endothelial cell populationdensities, of which the former infers flux limitation both in theself-diffusion and taxis terms. The model extends a recently introduced [34]description of glioma pseudopalisade formation, with the aim of studying theeffect of hypoxia-induced tumor vascularization on the establishment andmaintenance of these histological patterns which are typical for high gradebrain cancer. Numerical simulations of the population level dynamics areperformed to investigate several model scenarios containing this and furthereffects.

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