A Stochastic Model of Glioblastoma Invasion: The Impact of Phenotypic Switching

Abstract

In this chapter we present a stochastic model of glioblastoma (brain cancer) growth and invasion, which incorporates the notion of phenotypic switching between migratory and proliferative cell states. The model is characterised by the rates at which cells switch to proliferation ($q_p$) and migration ($q_m$), and simulation results show that for a fixed $q_p$, the tumour growth rate is maximised for intermediate $q_m$. We also complement the simulations by deriving a continuum description of the system, in the form of two coupled reaction-diffusion PDEs, and subsequent phase space analysis shows that the wave speed of the solutions closely matches that of the stochastic model. The model thus reveals a possible way of treating glioblastomas by altering the balance between proliferative and migratory behaviour.