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A Discrete Model to Study Reaction-Diffusion-Mechanics Systems

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  • Louis D Weise
  • Martyn P Nash
  • Alexander V Panfilov

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.

Suggested Citation

  • Louis D Weise & Martyn P Nash & Alexander V Panfilov, 2011. "A Discrete Model to Study Reaction-Diffusion-Mechanics Systems," PLOS ONE, Public Library of Science, vol. 6(7), pages 1-13, July.
    • Handle: RePEc:plo:pone00:0021934
    DOI: 10.1371/journal.pone.0021934
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    References listed on IDEAS

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    1. Donald M. Bers, 2002. "Cardiac excitation–contraction coupling," Nature, Nature, vol. 415(6868), pages 198-205, January.
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    Cited by:

    1. Chao-Qing Dai & Yan Wang, 2014. "Three-Dimensional Structures of the Spatiotemporal Nonlinear Schrödinger Equation with Power-Law Nonlinearity in PT-Symmetric Potentials," PLOS ONE, Public Library of Science, vol. 9(7), pages 1-8, July.

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