  Glioblastoma is a rapidly evolving high-grade astrocytoma that is
distinguished pathologically from lower grade gliomas by the presence of
necrosis and microvascular hiperplasia. Necrotic areas are typically surrounded
by hypercellular regions known as "pseudopalisades" originated by local tumor
vessel occlusions that induce collective cellular migration events. This leads
to the formation of waves of tumor cells actively migrating away from central
hypoxia. We present a mathematical model that incorporates the interplay among
two tumor cell phenotypes, a necrotic core and the oxygen distribution. Our
simulations reveal the formation of a traveling wave of tumor cells that
reproduces the observed histologic patterns of pseudopalisades. Additional
simulations of the model equations show that preventing the collapse of tumor
microvessels leads to slower glioma invasion, a fact that might be exploited
for therapeutic purposes.
