A tractable mathematical model for tissue growth
Joe Eyles
University of Sussex, Brighton, UKJohn R. King
University of Nottingham, UKVanessa Styles
University of Sussex, Brighton, UK
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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