A tractable mathematical model for tissue growth
Tissues and Organs
2019-07-16 v1
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
@article{arxiv.1907.06590,
title = {A tractable mathematical model for tissue growth},
author = {Joe Eyles and John F. King and Vanessa Styles},
journal= {arXiv preprint arXiv:1907.06590},
year = {2019}
}