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Travelling wave analysis of a mathematical model of glioblastoma growth
Chalmers, Math Sci, S-41296 Gothenburg, Sweden.;Univ Gothenburg, S-41296 Gothenburg, Sweden..
Uppsala University, Disciplinary Domain of Medicine and Pharmacy, Faculty of Medicine, Department of Immunology, Genetics and Pathology.
2016 (English)In: Mathematical Biosciences, ISSN 0025-5564, E-ISSN 1879-3134, Vol. 276, 75-81 p.Article in journal (Refereed) Published
Abstract [en]

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, 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.

Place, publisher, year, edition, pages
2016. Vol. 276, 75-81 p.
Keyword [en]
Cancer modelling, Cell-based model, Travelling waves, Glioblastoma
National Category
Medical and Health Sciences
Identifiers
URN: urn:nbn:se:uu:diva-302238DOI: 10.1016/j.mbs.2016.03.004ISI: 000376708500008PubMedID: 27021919OAI: oai:DiVA.org:uu-302238DiVA: diva2:957101
Funder
Swedish Cancer SocietySwedish Research Council, 2014-6095Swedish Foundation for Strategic Research , AM13-0046
Available from: 2016-09-01 Created: 2016-08-31 Last updated: 2016-09-01Bibliographically approved

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Nelander, Sven
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