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

G. MacDonald, J.A. MacKenzie, M. Nolan, R.H. Insall

Research output: Contribution to journalArticle

16 Citations (Scopus)

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.
LanguageEnglish
Pages207–226
Number of pages28
JournalJournal of Computational Physics
Volume309
Early online date21 Dec 2015
DOIs
Publication statusPublished - 16 Mar 2016

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reaction-diffusion equations
Computational methods
mesh
cells
Surface reactions
Cell membranes
partial differential equations
surface reactions
Partial differential equations
finite element method
Finite element method
Experiments
interactions

Keywords

  • reaction-diffusion
  • bulk-surface equations
  • cell migration
  • chemotaxis
  • evolving finite elements
  • moving mesh methods
  • ALE methods

Cite this

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title = "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",
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.",
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author = "G. MacDonald and J.A. MacKenzie and M. Nolan and R.H. Insall",
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AU - MacKenzie, J.A.

AU - Nolan, M.

AU - Insall, R.H.

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N2 - 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.

AB - 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.

KW - reaction-diffusion

KW - bulk-surface equations

KW - cell migration

KW - chemotaxis

KW - evolving finite elements

KW - moving mesh methods

KW - ALE methods

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