Global coupling in excitable media provides a simplified description of mechanoelectrical feedback in cardiac tissue

Cardiac mechanoelectric feedback can play an important role in different heart pathologies. In this paper, we show that mechanoelectric models which describe both the electric propagation and the mechanic contraction of cardiac tissue naturally lead to close systems of equations with global coupling among the variables. This point is exemplified using the Nash-Panfilov model, which reduces to a FitzHugh-Nagumo-type equation with global coupling in the linear elastic regime. We explain the appearance of self-oscillatory regimes in terms of the system nullclines and describe the different dynamical attractors. Finally, we study their basin of attraction in terms of the system size and the strength of the stretch-induced currents.