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A Discrete Model to Study Reaction-Diffusion-Mechanics Systems
This article introduces a discrete reaction-diffusion-mechanics (dRDM) model to study the effects of deformation on reaction-diffusion (RD) processes. The dRDM framework employs a FitzHugh-Nagumo type RD model coupled to a mass-lattice model, that undergoes finite deformations. The dRDM model descri...
Autores principales: | , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Public Library of Science
2011
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3133613/ https://www.ncbi.nlm.nih.gov/pubmed/21804911 http://dx.doi.org/10.1371/journal.pone.0021934 |
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author | Weise, Louis D. Nash, Martyn P. Panfilov, Alexander V. |
author_facet | Weise, Louis D. Nash, Martyn P. Panfilov, Alexander V. |
author_sort | Weise, Louis D. |
collection | PubMed |
description | This article introduces a discrete reaction-diffusion-mechanics (dRDM) model to study the effects of deformation on reaction-diffusion (RD) processes. The dRDM framework employs a FitzHugh-Nagumo type RD model coupled to a mass-lattice model, that undergoes finite deformations. The dRDM model describes a material whose elastic properties are described by a generalized Hooke's law for finite deformations (Seth material). Numerically, the dRDM approach combines a finite difference approach for the RD equations with a Verlet integration scheme for the equations of the mass-lattice system. Using this framework results were reproduced on self-organized pacemaking activity that have been previously found with a continuous RD mechanics model. Mechanisms that determine the period of pacemakers and its dependency on the medium size are identified. Finally it is shown how the drift direction of pacemakers in RDM systems is related to the spatial distribution of deformation and curvature effects. |
format | Online Article Text |
id | pubmed-3133613 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2011 |
publisher | Public Library of Science |
record_format | MEDLINE/PubMed |
spelling | pubmed-31336132011-07-29 A Discrete Model to Study Reaction-Diffusion-Mechanics Systems Weise, Louis D. Nash, Martyn P. Panfilov, Alexander V. PLoS One Research Article This article introduces a discrete reaction-diffusion-mechanics (dRDM) model to study the effects of deformation on reaction-diffusion (RD) processes. The dRDM framework employs a FitzHugh-Nagumo type RD model coupled to a mass-lattice model, that undergoes finite deformations. The dRDM model describes a material whose elastic properties are described by a generalized Hooke's law for finite deformations (Seth material). Numerically, the dRDM approach combines a finite difference approach for the RD equations with a Verlet integration scheme for the equations of the mass-lattice system. Using this framework results were reproduced on self-organized pacemaking activity that have been previously found with a continuous RD mechanics model. Mechanisms that determine the period of pacemakers and its dependency on the medium size are identified. Finally it is shown how the drift direction of pacemakers in RDM systems is related to the spatial distribution of deformation and curvature effects. Public Library of Science 2011-07-11 /pmc/articles/PMC3133613/ /pubmed/21804911 http://dx.doi.org/10.1371/journal.pone.0021934 Text en Weise et al. http://creativecommons.org/licenses/by/4.0/ This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are properly credited. |
spellingShingle | Research Article Weise, Louis D. Nash, Martyn P. Panfilov, Alexander V. A Discrete Model to Study Reaction-Diffusion-Mechanics Systems |
title | A Discrete Model to Study Reaction-Diffusion-Mechanics Systems |
title_full | A Discrete Model to Study Reaction-Diffusion-Mechanics Systems |
title_fullStr | A Discrete Model to Study Reaction-Diffusion-Mechanics Systems |
title_full_unstemmed | A Discrete Model to Study Reaction-Diffusion-Mechanics Systems |
title_short | A Discrete Model to Study Reaction-Diffusion-Mechanics Systems |
title_sort | discrete model to study reaction-diffusion-mechanics systems |
topic | Research Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3133613/ https://www.ncbi.nlm.nih.gov/pubmed/21804911 http://dx.doi.org/10.1371/journal.pone.0021934 |
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