JournalsifbVol. 21 , No. 4pp. 463–493

A tractable mathematical model for tissue growth

  • Joe Eyles

    University of Sussex, Brighton, UK
  • John R. King

    University of Nottingham, UK
  • Vanessa Styles

    University of Sussex, Brighton, UK
A tractable mathematical model for tissue growth cover
Download PDF

A subscription is required to access this article.

Abstract

Using formal asymptotic methods we derive a free boundary problem representing one of the simplest mathematical descriptions of the growth and death of a tumour or other biological tissue. The mathematical model takes the form of a closed interface evolving via forced mean curvature flow (together with a ‘kinetic under-cooling’ regularisation) where the forcing depends on the solution of a PDE that holds in the domain enclosed by the interface. We perform linear stability analysis and derive a diffuse-interface approximation of the model. Finite-element discretisations of two closely related models are presented, together with computational results comparing the approximate solutions.

Cite this article

Joe Eyles, John R. King, Vanessa Styles, A tractable mathematical model for tissue growth. Interfaces Free Bound. 21 (2019), no. 4 pp. 463–493

DOI 10.4171/IFB/428