Using novel simplified models of excitation for analytic description of initiation propagation and blockage of excitation waves

We consider applications of a recently suggested new asymptotic approach to detailed ionic models of cardiac excitation. First, we describe a three-variable approximation for the excitation fronts in a detailed ionic model of human atrial kinetics. It predicts not only the speed of the fronts but also a condition for failure of propagation, i.e. gives an operational definition of absolute refractoriness. This prediction is confirmed by direct simulations of the full model. Next, we consider problem of initiation of excitation waves, using a piecewise linear caricature of the I_Nalpha-driven excitation front. We identify the unstable propagating front solution ("critical front") as the threshold event between successful initation and decay, which plays a role similar to the "critical nucleus" in the theory of initiation of waves in the FitzHugh-Nagumo system.