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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...

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Detalles Bibliográficos
Autores principales: Weise, Louis D., Nash, Martyn P., Panfilov, Alexander V.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Public Library of Science 2011
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.
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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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