ArticlePloS one2011
A discrete model to study reaction-diffusion-mechanics systems.
Article in PloS one, 2011. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 11 papers.
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Who cites it
11 citing papers in PubMed.
- Mechanochemical and machine-intelligent design of programmable materials: From molecular interactions to macroscale functionality.Materials today. Bio · 2026Review
- Discrete mechanical growth model for plant tissue.PloS one · 2019Article
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- Marker-Free Tracking for Motion Artifact Compensation and Deformation Measurements in Optical Mapping Videos of Contracting Hearts.Frontiers in physiology · 2018Article
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- Spiral-wave dynamics in ionically realistic mathematical models for human ventricular tissue: the effects of periodic deformation.Frontiers in physiology · 2014Article
- Article
- Spiral-wave dynamics in a mathematical model of human ventricular tissue with myocytes and fibroblasts.PloS one · 2013Article
- Generalized and improved (G'/G)-expansion method for (3+1)-dimensional modified KdV-Zakharov-Kuznetsev equation.PloS one · 2013Article
- Article
- Article
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3 authors.
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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.
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