Reaction–diffusion systems for the microscopic cellular model of the cardiac electric field

The paper deals with a mathematical model for the electric activity of the heart at microscopic level. The membrane model used to describe the ionic currents is a generalization of the phase-I Luo–Rudy, a model widely used in 2-D and 3-D simulations of the action potential propagation. From the mathematical viewpoint the model is made up of a parabolic reaction diffusion system coupled with an ODE system. We derive existence and some regularity results.