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Travelling wave analysis of a mathematical model of glioblastoma growth

Journal article
Authors Philip Gerlee
Sven Nelander
Published in Mathematical Biosciences
Volume 276
Pages 75-81
ISSN 0025-5564
Publication year 2016
Published at Department of Mathematical Sciences, Mathematics
Pages 75-81
Language en
Links dx.doi.org/10.1016/j.mbs.2016.03.00...
Keywords Cancer modelling, Cell-based model, Travelling waves, Glioblastoma
Subject categories Applied mathematics, Cancer and Oncology

Abstract

In this paper we analyse a previously proposed cell-based model of glioblastoma (brain tumour) growth, which is based on the assumption that the cancer cells switch phenotypes between a proliferative and motile state (Gerlee and Nelander, PLoS Comp. Bio., 8(6) 2012). The dynamics of this model can be described by a system of partial differential equations, which exhibits travelling 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 wave front shape. These new analytical results agree with simulations of the cell-based model, and importantly show that the inverse relationship between wave front steepness and speed observed for the Fisher equation no longer holds when phenotypic switching is considered.

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