Electromechanical Coupling In Cardiac Dynamics: The Active Strain Approach

The coupling between cardiac mechanics and electric signaling is addressed in a nonstandard framework in which the electrical potential dictates the active strain (not stress) of the muscle. The physiological and mathematical motivations leading us to this choice are illustrated. The propagation of the electric signal is assumed to be governed by the FitzHugh-Nagumo equations, rewritten in material coordinates with a deforming substrate; the solution is compared with the rigid case, and differences in celerity and width of a pulse are discussed. The role of viscoelasticity is pointed out. We show that the stretching of coordinates is insufficient to originate electromechanical feedback; nevertheless, it can increase the energy of a perturbation enough to produce a traveling pulse: an energy estimate and numerical evidence are reported. To support these conclusions, numerical simulations in two dimensions show the interplay between electric propagation and mechanical strain.