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A discrete model to study reaction-diffusion-mechanics systems

(2011) PLOS ONE. 6(7).
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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.
Keywords
MUSCLE, HEART, TISSUE, CHANNELS, CARDIAC EXCITATION, SPIRAL WAVES

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Please use this url to cite or link to this publication:

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.
@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},
}

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