Traveling Waves of a Go-or-Grow Model of Glioma Growth

Abstract

Glioblastoma multiforme is a deadly brain cancer in which tumor cells excessively proliferate and migrate. The first mathematical models of the spread of gliomas featured reaction-diffusion equations, and later an idea emerged through experimental study called the “Go or Grow” hypothesis in which glioma cells have a dichotomous behavior: a cell either primarily proliferates or primarily migrates. We analytically investigate an extreme form of the “Go or Grow” hypothesis where tumor cell motility and cell proliferation are considered as separate processes. Different solution types are examined via approximate solution of traveling wave equations, and we determine conditions for various wave front forms.