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Issue 11-12, 2010
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Use of the parameterised finite element method to robustly and efficiently evolve the edge of a moving cell

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Abstract

In this paper we present a computational tool that enables the simulation of mathematical models of cell migration and chemotaxis on an evolving cell membrane. Recent models require the numerical solution of systems of reaction-diffusion equations on the evolving cell membrane and then the solution state is used to drive the evolution of the cell edge. Previous work involved moving the cell edge using a level set method (LSM). However, the LSM is computationally very expensive, which severely limits the practical usefulness of the algorithm. To address this issue, we have employed the parameterised finite element method (PFEM) as an alternative method for evolving a cell boundary. We show that the PFEM is far more efficient and robust than the LSM. We therefore suggest that the PFEM potentially has an essential role to play in computational modelling efforts towards the understanding of many of the complex issues related to chemotaxis.

Graphical abstract: Use of the parameterised finite element method to robustly and efficiently evolve the edge of a moving cell

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Article information


Submitted
28 May 2010
Accepted
23 Aug 2010
First published
20 Oct 2010

Integr. Biol., 2010,2, 687-695
Article type
Technical Innovation

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