The Mathematical Institute, University of Oxford, Eprints Archive

Classifying general nonlinear force laws in cell-based models via the continuum limit

Murray, P J and Edwards, C. M. and Tindall, M. J. and Maini, P. K. (2012) Classifying general nonlinear force laws in cell-based models via the continuum limit. Physical Review E, 85 (2). 021921-(11 pages). ISSN 1063-651X

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Abstract

Although discrete cell-based frameworks are now commonly used to simulate a whole range of biological phenomena, it is typically not obvious how the numerous different types of model are related to one another, nor which one is most appropriate in a given context. Here we demonstrate how individual cell movement on the discrete scale modeled using nonlinear force laws can be described by nonlinear diffusion coefficients on the continuum scale. A general relationship between nonlinear force laws and their respective diffusion coefficients is derived in one spatial dimension and, subsequently, a range of particular examples is considered. For each case excellent agreement is observed between numerical solutions of the discrete and corresponding continuum models. Three case studies are considered in which we demonstrate how the derived nonlinear diffusion coefficients can be used to (a) relate different discrete models of cell behavior; (b) derive discrete, intercell force laws from previously posed diffusion coefficients, and (c) describe aggregative behavior in discrete simulations.

Item Type:Article
Subjects:A - C > Biology and other natural sciences
Research Groups:Centre for Mathematical Biology
ID Code:1477
Deposited By:Philip Maini
Deposited On:25 Feb 2012 08:45
Last Modified:25 Feb 2012 08:45

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