Travelling wave analysis of a mathematical model of glioblastoma growth

• 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.

Subject headings

MEDICIN OCH HÄLSOVETENSKAP  -- Klinisk medicin -- Cancer och onkologi (hsv//swe)

MEDICAL AND HEALTH SCIENCES  -- Clinical Medicine -- Cancer and Oncology (hsv//eng)

NATURVETENSKAP  -- Matematik -- Beräkningsmatematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Computational Mathematics (hsv//eng)

Keyword

Cancer modelling

Cell-based model

Travelling waves

Glioblastoma

Glioblastoma

Publication and Content Type

ref (subject category)

art (subject category)