Oscillatory regime in excitatory media with global coupling: Application to cardiac dynamics

The goal of this paper is to describe the effects of simple electro-mechanical coupling in isotropic two-dimensional (2D) cardiac tissue. To this aim, we show that the Nash-Panfilov two variable model [PRL 95, 258104 (2005)] for electrical activation, which couples active stress directly to transmembrane potential, can be reduced in the linearly elastic regime to an excitatory system with global coupling. In the linear limit, numerical simulations of both models give the same dynamic evolution, including the appearance of an ectopic focus with origin at the center. Indeed, after an initial excitation, mechano-electrical coupling can generate sustained oscillations in the form of successive waves originated at the center. These oscillations have a large basin of attraction for different sample lengths and values of the stretching current, specially when the recovery time of the excitatory cells is short. We finally present and discuss the appearance of oscillatory waves whose origin is not the center of the 2D sample but a ring of tissue around it. These waves appear spontaneously under some conditions even when the first excitation is generated at the center.