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Modelling Collective Cell Motion in Biology

  • P. K. MainiEmail author
  • R. E. Baker
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 87)

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.

Keywords

Cell-based model Vertex-based model Travelling waves Volume exclusion 

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Wolfson Centre for Mathematical BiologyUniversity of OxfordOxfordUK

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