Discrete and continuous approaches to modeling cell movement in the presence of a foreign stimulus
Authored by Alicia Prieto-Langarica, Hristo V Kojouharov, Benito M Chen-Charpentier
Date Published: 2012
DOI: 10.1016/j.camwa.2011.11.058
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Abstract
Cell movement is a complex process. Cells can move in response to a
foreign stimulus in search of nutrients, to escape predation, and for
other reasons. Mathematical modeling of cell movement is needed to aid
in achieving a deeper understanding of vital processes such as
embryogenesis, angiogenesis, tumor metastasis, and immune reactions to
foreign bodies. In this work we consider cell movement that can be
separated into two parts: one part is in direct response to a stimulus
and the other is due to uncertainties and other reasons for the
movement. In order to deal with the deterministic and random aspects of
cell movement, an individual based model is created to simulate cells
moving in the presence of heterogeneously distributed stimulus
molecules. The model is then upscaled, starting with an analysis of the
transition probabilities of individuals at each site, to obtain a
continuous partial differential equation model. Finally, the two models
are numerically compared to each other for a variety of different
parameter values. (C) 2011 Elsevier Ltd. All rights reserved.
Tags
Reinforced random-walks