Thursday, 10 March 2016

Travelling wave analysis of a mathematical model of glioblastoma growth

This paper has been on arxiv for a while (and the work dates back to 2011), but it was at last accepted for publication in Mathematical Biosciences after 1.5 years of review. The paper contains an analysis of a PDE-model of brain tumour growth that takes into account phenotypic switching between migratory and proliferative cell types. We derive an approximate analytic expression of the rate of spread of the tumour, and also show (and this is in my view the most intruiging result) that the inverse relationship between wave front steepness and its speed observed for the Fisher equation no longer holds when phenotypic switching is considered. By tuning the switching rates we can obtain steep fronts that move fast and vice versa.

Accepted version: