A computational method for the coupled solution of reaction–diffusion equations on evolving domains and manifolds: application to a model of cell migration and chemotaxis

MacDonald, G., Mackenzie, J.A., Nolan, M. and Insall, R.H. (2016) A computational method for the coupled solution of reaction–diffusion equations on evolving domains and manifolds: application to a model of cell migration and chemotaxis. Journal of Computational Physics, 309, pp. 207-226. (doi:10.1016/j.jcp.2015.12.038) (PMID:27330221) (PMCID:PMC4896117)

[img]
Preview
Text
116683.pdf - Published Version
Available under License Creative Commons Attribution.

3MB

Abstract

In this paper, we devise a moving mesh finite element method for the approximate solution of coupled bulk–surface reaction–diffusion equations on an evolving two dimensional domain. Fundamental to the success of the method is the robust generation of bulk and surface meshes. For this purpose, we use a novel moving mesh partial differential equation (MMPDE) approach. The developed method is applied to model problems with known analytical solutions; these experiments indicate second-order spatial and temporal accuracy. Coupled bulk–surface problems occur frequently in many areas; in particular, in the modelling of eukaryotic cell migration and chemotaxis. We apply the method to a model of the two-way interaction of a migrating cell in a chemotactic field, where the bulk region corresponds to the extracellular region and the surface to the cell membrane.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Insall, Professor Robert
Authors: MacDonald, G., Mackenzie, J.A., Nolan, M., and Insall, R.H.
College/School:College of Medical Veterinary and Life Sciences > Institute of Cancer Sciences
Journal Name:Journal of Computational Physics
Publisher:Elsevier
ISSN:0021-9991
ISSN (Online):1090-2716
Copyright Holders:Copyright © 2016 The Authors
First Published:First published in Journal of Computational Physics 309:207-226
Publisher Policy:Reproduced under a Creative Commons License
Related URLs:

University Staff: Request a correction | Enlighten Editors: Update this record

Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
303051Molecular recognition, subunit interaction & structure function analysis of Recombinant human and plant PDCsJohn Gordon LindsayBiotechnology and Biological Sciences Research Council (BBSRC)17/B15672RI MOLECULAR CELL & SYSTEMS BIOLOGY