Lattice-free models of cell invasion : discrete simulations and travelling waves

Plank, Michael & Simpson, Matthew (2013) Lattice-free models of cell invasion : discrete simulations and travelling waves. Bulletin of Mathematical Biology, 75(11), pp. 2150-2166.

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Abstract

Invasion waves of cells play an important role in development, disease and repair. Standard discrete models of such processes typically involve simulating cell motility, cell proliferation and cell-to-cell crowding effects in a lattice-based framework. The continuum-limit description is often given by a reaction–diffusion equation that is related to the Fisher–Kolmogorov equation. One of the limitations of a standard lattice-based approach is that real cells move and proliferate in continuous space and are not restricted to a predefined lattice structure. We present a lattice-free model of cell motility and proliferation, with cell-to-cell crowding effects, and we use the model to replicate invasion wave-type behaviour. The continuum-limit description of the discrete model is a reaction–diffusion equation with a proliferation term that is different from lattice-based models. Comparing lattice based and lattice-free simulations indicates that both models lead to invasion fronts that are similar at the leading edge, where the cell density is low. Conversely, the two models make different predictions in the high density region of the domain, well behind the leading edge. We analyse the continuum-limit description of the lattice based and lattice-free models to show that both give rise to invasion wave type solutions that move with the same speed but have very different shapes. We explore the significance of these differences by calibrating the parameters in the standard Fisher–Kolmogorov equation using data from the lattice-free model. We conclude that estimating parameters using this kind of standard procedure can produce misleading results.

Impact and interest:

8 citations in Scopus
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8 citations in Web of Science®

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ID Code: 61514
Item Type: Journal Article
Refereed: Yes
Keywords: cell migration, cell proliferation, crowding effects, travelling wave, lattice-free
DOI: 10.1007/s11538-013-9885-7
ISSN: 1522-9602
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > APPLIED MATHEMATICS (010200) > Biological Mathematics (010202)
Divisions: Current > Institutes > Institute of Health and Biomedical Innovation
Current > Schools > School of Mathematical Sciences
Current > QUT Faculties and Divisions > Science & Engineering Faculty
Copyright Owner: Copyright 2013 Society for Mathematical Biology
Deposited On: 23 Jul 2013 22:14
Last Modified: 24 Jun 2015 03:18

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