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Application of the control volume method to a mathematical model of cell migration

Mallet, Daniel G., Turner, Ian W., & Pettet, Graeme J. (2004) Application of the control volume method to a mathematical model of cell migration. The ANZIAM Journal, 45(E), C891-C904.

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Abstract

In recent years, mathematical models of cell migration have become increasingly complex. These models have evolved from simple diffusion models to computationally troublesome reaction-diffusionadvection models. As such, the use of "black box" numerical solvers has become less appropriate. We discuss the application of the control volume technique for resolving a complicated nonlinear cell migration model. The nonlinearity is treated using an inexact Newton solver and flux limiting ensures that the cell migration fronts are captured adequately. Specifically, we analyse the model due to Perumpanani et al. (1999), comparing the numerical results of the proposed computational model developed in this research to previous results published by other researchers. We show that the finite volume computational model captures the physics of the processes with good accuracy using coarse meshes.

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ID Code: 5277
Item Type: Journal Article
Additional Information: For more information, please refer to the journal’s website (see link) or contact the author. Author contact details: dg.mallet@qut.edu.au
Additional URLs:
Keywords: cell migration, control volume method, haptotaxis, mathematical model
ISSN: 1446-8735
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > APPLIED MATHEMATICS (010200) > Biological Mathematics (010202)
Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000)
Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > OTHER MATHEMATICAL SCIENCES (019900)
Divisions: Past > QUT Faculties & Divisions > Faculty of Science and Technology
Copyright Owner: Copyright 2004 Australian Mathematical Society
Deposited On: 20 Oct 2006
Last Modified: 29 Feb 2012 23:04

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