ArticleJournal of theoretical biology2019
A free boundary model of epithelial dynamics.
Article in Journal of theoretical biology, 2019. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 8 papers.
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Who cites it
8 citing papers in PubMed.
- Spatial Segregation Across Travelling Fronts in Individual-Based and Continuum Models for the Growth of Heterogeneous Cell Populations.Bulletin of mathematical biology · 2025Article
- Mechanical Cell Interactions on Curved Interfaces.Bulletin of mathematical biology · 2025Article
- A free boundary mechanobiological model of epithelial tissues.Proceedings. Mathematical, physical, and engineering sciences · 2020Article
- From a discrete model of chemotaxis with volume-filling to a generalized Patlak-Keller-Segel model.Proceedings. Mathematical, physical, and engineering sciences · 2020Article
- Spatial structure arising from chase-escape interactions with crowding.Scientific reports · 2019Article
- Polarization wave at the onset of collective cell migration.Physical review. E · 2019Article
- A one-dimensional individual-based mechanical model of cell movement in heterogeneous tissues and its coarse-grained approximation.Proceedings. Mathematical, physical, and engineering sciences · 2019Article
- Reversible signal transmission in an active mechanical metamaterial.Proceedings. Mathematical, physical, and engineering sciences · 2019Article
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Authors and funding
3 authors.
Funding
No grant is acknowledged in the PubMed record.
Abstract
In this work we analyse a one-dimensional, cell-based model of an epithelial sheet. In the model, cells interact with their nearest neighbouring cells and move deterministically. Cells also proliferate stochastically, with the rate of proliferation specified as a function of the cell length. This mechanical model of cell dynamics gives rise to a free boundary problem. We construct a corresponding continuum-limit description where the variables in the continuum limit description are expanded in powers of the small parameter 1/N, where N is the number of cells in the population. By carefully constructing the continuum limit description we obtain a free boundary partial differential equation description governing the density of the cells within the evolving domain, as well as a free boundary condition that governs the evolution of the domain. We show that care must be taken to arrive at a free boundary condition that conserves mass. By comparing averaged realisations of the cell-based model with the numerical solution of the free boundary partial differential equation, we show that the new mass-conserving boundary condition enables the coarse-grained partial differential equation model to provide very accurate predictions of the behaviour of the cell-based model, including both evolution of the cell density, and the position of the free boundary, across a range of interaction potentials and proliferation functions in the cell based model.
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