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A discrete model to study reaction-diffusion-mechanics systems

Louis Weise, Martyn P Nash and Alexander Panfilov UGent (2011) PLOS ONE. 6(7).
abstract
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.
Please use this url to cite or link to this publication:
author
organization
year
type
journalArticle (original)
publication status
published
subject
keyword
MUSCLE, HEART, TISSUE, CHANNELS, CARDIAC EXCITATION, SPIRAL WAVES
journal title
PLOS ONE
PLoS One
volume
6
issue
7
article number
e21934
pages
13 pages
Web of Science type
Article
Web of Science id
000292680900018
JCR category
BIOLOGY
JCR impact factor
4.092 (2011)
JCR rank
12/84 (2011)
JCR quartile
1 (2011)
ISSN
1932-6203
DOI
10.1371/journal.pone.0021934
language
English
UGent publication?
yes
classification
A1
copyright statement
I have retained and own the full copyright for this publication
id
2008306
handle
http://hdl.handle.net/1854/LU-2008306
date created
2012-01-30 18:06:39
date last changed
2017-03-10 14:29:35
@article{2008306,
  abstract     = {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.},
  articleno    = {e21934},
  author       = {Weise, Louis and Nash, Martyn P and Panfilov, Alexander},
  issn         = {1932-6203},
  journal      = {PLOS ONE},
  keyword      = {MUSCLE,HEART,TISSUE,CHANNELS,CARDIAC EXCITATION,SPIRAL WAVES},
  language     = {eng},
  number       = {7},
  pages        = {13},
  title        = {A discrete model to study reaction-diffusion-mechanics systems},
  url          = {http://dx.doi.org/10.1371/journal.pone.0021934},
  volume       = {6},
  year         = {2011},
}

Chicago
Weise, Louis, Martyn P Nash, and Alexander Panfilov. 2011. “A Discrete Model to Study Reaction-diffusion-mechanics Systems.” Plos One 6 (7).
APA
Weise, L., Nash, M. P., & Panfilov, A. (2011). A discrete model to study reaction-diffusion-mechanics systems. PLOS ONE, 6(7).
Vancouver
1.
Weise L, Nash MP, Panfilov A. A discrete model to study reaction-diffusion-mechanics systems. PLOS ONE. 2011;6(7).
MLA
Weise, Louis, Martyn P Nash, and Alexander Panfilov. “A Discrete Model to Study Reaction-diffusion-mechanics Systems.” PLOS ONE 6.7 (2011): n. pag. Print.