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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.

Original publication

DOI

10.1103/PhysRevE.85.021921

Type

Journal article

Journal

Phys Rev E Stat Nonlin Soft Matter Phys

Publication Date

02/2012

Volume

85

Keywords

Animals, Cell Movement, Computer Simulation, Humans, Mechanotransduction, Cellular, Models, Biological, Nonlinear Dynamics, Stress, Mechanical