Murray, P J and Edwards, C. M. and Tindall, M. J. and Maini, P. K. (2012) Classifying general nonlinear force laws in cellbased models via the continuum limit. Physical Review E, 85 (2). 021921(11 pages). ISSN 1063651X

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Abstract
Although discrete cellbased 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:  29 May 2015 19:10 
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