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arXiv · 1907.06590

A tractable mathematical model for tissue growth

Joe Eyles·John F. King·Vanessa Styles
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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.

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Joe Eyles, John F. King, Vanessa Styles. 2019-07-11. A tractable mathematical model for tissue growth. https://arxiv.org/abs/1907.06590

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