Spiral wave initiation in the Reaction-Diffusion-Mechanics models
We introduce 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 we study and find new mechanisms of spiral wave initiation in the contracting excitable medium in homogeneous and heterogeneous cases. In particular, we show that deformation alters the "classical," and forms a new vulnerable zone at longer coupling intervals. This mechanically caused vulnerable zone results in a new mechanism of spiral wave initiation, where unidirectional conduction block and rotation directions of the consequently initiated spiral waves are opposite compared to the mechanism of spiral wave initiation due to the "classical vulnerable zone." We also study and classify mechanisms of spiral wave initiation in excitable tissue with heterogeneity in passive and in active mechanical properties.