Nonlinear ghost waves accelerate the progression of high-grade brain tumors

Abstract

We study a reduced continuous model describing the evolution of high grade gliomas in response to hypoxic events through the interplay of different cellular phenotypes. We show that hypoxic events, even when sporadic and/or limited in space, may have a crucial role on the acceleration of high grade gliomas growth. Our modeling approach is based on two cellular phenotypes. One of them is more migratory and a second one is more proliferative. Transitions between both phenotypes are driven by the local oxygen values, assumed in this simple model to be uniform. Surprisingly, even very localized in time hypoxia events leading to transient migratory populations have the potential to accelerate the tumor’s invasion speed up to speeds close to those of the migratory phenotype. The high invasion speed persists for times much longer than the lifetime of the hypoxic event. Moreover, the phenomenon is observed both when the migratory cells form a persistent wave of cells located on the invasion front and when they form a evanescent “ghost” wave disappearing after a short time by decay to the more proliferative phenotype.Our findings are obtained through numerical simulations of the model equations both in 1D and higher dimensional scenarios. We also provide a deeper mathematical analysis of some aspects of the problem such as the conditions for the existence of persistent waves of cells with a more migratory phenotype.