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2014 | OriginalPaper | Buchkapitel

Modelling Collective Cell Motion in Biology

verfasst von : P. K. Maini, R. E. Baker

Erschienen in: Advances in Applied Mathematics

Verlag: Springer International Publishing

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Abstract

This paper reviews three mathematical modelling approaches that have recently been used to understand three different modes of collective cell motion in biology. Firstly, a cell-based model is presented for the study of cell motion in epithelial sheets, then a hybrid discrete cell-based model is described for neural crest cell invasion and, finally, a traditional partial differential equation model is described for tumour cell invasion. It is shown that the behaviour of all of these models can, in limiting cases, be recapitulated by nonlinear diffusion equations where the particular nonlinearity of the diffusion coefficient captures, on the global scale, the inherent interactions on the local scale.

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We thank Louise Dyson for providing this figure.

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Titel: Modelling Collective Cell Motion in Biology
verfasst von: P. K. Maini
R. E. Baker
Verlag: Springer International Publishing
Buch: Advances in Applied Mathematics
Print ISBN: 978-3-319-06922-7

Electronic ISBN: 978-3-319-06923-4

Copyright-Jahr: 2014
DOI: https://doi.org/10.1007/978-3-319-06923-4_1

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