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2014 | OriginalPaper | Chapter

Modelling Collective Cell Motion in Biology

Authors : P. K. Maini, R. E. Baker

Published in: Advances in Applied Mathematics

Publisher: 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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next chapter Modelling Oxygen Capillary Supply to Striated Muscle Tissues
Footnotes
1
We thank Louise Dyson for providing this figure.
 
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Metadata
Title
Modelling Collective Cell Motion in Biology
Authors
P. K. Maini
R. E. Baker
Copyright Year
2014
Book
Advances in Applied Mathematics

Print ISBN: 978-3-319-06922-7

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

Copyright Year: 2014

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

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