Walker, BJ;
Celora, GL;
Goriely, A;
Moulton, DE;
Byrne, HM;
(2023)
Minimal Morphoelastic Models of Solid Tumour Spheroids: A Tutorial.
Bulletin of mathematical biology
, 85
(5)
, Article 38. 10.1007/s11538-023-01141-8.
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Abstract
Tumour spheroids have been the focus of a variety of mathematical models, ranging from Greenspan's classical study of the 1970 s through to contemporary agent-based models. Of the many factors that regulate spheroid growth, mechanical effects are perhaps some of the least studied, both theoretically and experimentally, though experimental enquiry has established their significance to tumour growth dynamics. In this tutorial, we formulate a hierarchy of mathematical models of increasing complexity to explore the role of mechanics in spheroid growth, all the while seeking to retain desirable simplicity and analytical tractability. Beginning with the theory of morphoelasticity, which combines solid mechanics and growth, we successively refine our assumptions to develop a somewhat minimal model of mechanically regulated spheroid growth that is free from many unphysical and undesirable behaviours. In doing so, we will see how iterating upon simple models can provide rigorous guarantees of emergent behaviour, which are often precluded by existing, more complex modelling approaches. Perhaps surprisingly, we also demonstrate that the final model considered in this tutorial agrees favourably with classical experimental results, highlighting the potential for simple models to provide mechanistic insight whilst also serving as mathematical examples.
| Type: | Article |
|---|---|
| Title: | Minimal Morphoelastic Models of Solid Tumour Spheroids: A Tutorial |
| Location: | United States |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1007/s11538-023-01141-8 |
| Publisher version: | https://doi.org/10.1007/s11538-023-01141-8 |
| Language: | English |
| Additional information: | Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. |
| Keywords: | Mathematical modelling, Morphoelasticity, Stress-dependent growth, Tumour dynamics, Humans, Spheroids, Cellular, Models, Biological, Mathematical Concepts, Neoplasms, Models, Theoretical |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10168370 |
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