  We propose a multiphase modeling approach to describe glioma pseudopalisade
patterning under the influence of acidosis. The phases considered at the model
onset are glioma, normal tissue, necrotic matter, and interstitial fluid in a
void-free volume with acidity represented by proton concentration. We start
from mass and momentum balance to characterize the respective volume fractions
and deduce reaction-cross diffusion equations for the space-time evolution of
glioma, normal tissue, and necrosis. These are supplemented with a
reaction-diffusion equation for the acidity dynamics and lead to formation of
patterns which are typical for high grade gliomas. Unlike previous works, our
deduction also works in higher dimensions and involves less restrictions. We
also investigate the existence of weak solutions to the obtained system of
equations and perform numerical simulations to illustrate the solution behavior
and the pattern occurrence.
