In this talk we will present results derived by analysing a previously proposed cell‐based
model of glioblastoma growth, which is based on the assumption that the cancer cells switch
phenotypes between a proliferative and motile state [1]. The dynamics of this model can be
described by a system of partial differential equations, which exhibits traveling wave
solutions whose wave speed depends crucially on the rates of phenotypic switching. We
show that under certain conditions on the model parameters, a closed form expression of
the wave speed can be obtained, and using singular perturbation methods we also derive an
approximate expression of the cell density profile. These new analytical results agree with
simulations of the cell‐based model, and importantly show that the inverse relationship
between the wave front steepness and speed observed for the Fisher equation no longer
holds when phenotypic switching is considered.
[1] Gerlee P, Nelander S (2012) The Impact of Phenotypic Switching on Glioblastoma Growth
and Invasion. PLoS Comput Biol 8(6): e1002556