Travelling wave analysis of a mathematical model of glioblastoma growth

Gerlee, Philip,1980Gothenburg University,Göteborgs universitet,Institutionen för matematiska vetenskaper, matematik,Department of Mathematical Sciences, Mathematics,University of Gothenburg,Chalmers tekniska högskola,Chalmers University of Technology,Chalmers, Math Sci, S-41296 Gothenburg, Sweden.;Univ Gothenburg, S-41296 Gothenburg, Sweden. (författare)

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.

Nelander, Sven,1974Uppsala universitet,Institutionen för immunologi, genetik och patologi(Swepub:uu)svene843 (författare)
Göteborgs universitetInstitutionen för matematiska vetenskaper, matematik (creator_code:org_t)

Om ämnet

MEDICIN OCH HÄLSOVETENSKAP: MEDICIN OCH HÄLS ...; och Klinisk medicin; och Cancer och onkol ...

Av lärosätet: Göteborgs universitet; Chalmers tekniska högskola; Uppsala universitet

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