A tractable mathematical model for tissue growth

Eyles, Joe; King, John R.; Styles, Vanessa

Abstract

© European Mathematical Society 2019 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.

Citation

Eyles, J., King, J. R., & Styles, V. (2019). A tractable mathematical model for tissue growth. Interfaces and Free Boundaries, 21(4), 463-493. https://doi.org/10.4171/IFB/428

• Journal Article Type: Article
• Acceptance Date: Jul 30, 2019
• Online Publication Date: Dec 18, 2019
• Publication Date: Jan 1, 2019
• Deposit Date: Nov 5, 2020
• Publicly Available Date: Nov 5, 2020
• Journal: Interfaces and Free Boundaries
• Print ISSN: 1463-9963
• Electronic ISSN: 1463-9971
• Publisher: European Mathematical Society
• Peer Reviewed: Peer Reviewed
• Volume: 21
• Issue: 4
• Pages: 463-493
• DOI: https://doi.org/10.4171/IFB/428
• Public URL: https://nottingham-repository.worktribe.com/output/5018914
• Publisher URL: https://www.ems-ph.org/journals/show_abstract.php?issn=1463-9963&vol=21&iss=4&rank=3
• Additional Information: © 2020 EMS Publishing House. All rights reserved.