A free boundary model of epithelial dynamics

JOURNAL OF THEORETICAL BIOLOGY

卷:481

Article

Baker, Ruth E.¹  Parker, Andrew¹  Simpson, Matthew J.² 

[1] Univ Oxford, Math Inst, Oxford, England

[2] Queensland Univ Technol, Sch Math Sci, Brisbane, Qld, Australia

关键词: Cell-based model;    Individual-based model;    Mechanical model;    Cell migration;    Cell proliferation;    Free boundary problem;    Moving boundary problem;   

DOI  :  10.1016/j.jtbi.2018.12.025

来源: Elsevier

【 摘 要 】

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. (C) 2019 The Authors. Published by Elsevier Ltd.

【 授权许可】

Free