Analysis of the Fenton–Karma model through an approximation by a one-dimensional map

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Abstract
The Fenton–Karma model is a simplification of complex ionic models of cardiac membrane that reproduces quantitatively many of the characteristics of heart cells; its behavior is simple enough to be understood analytically. In this paper, a map is derived that approximates the response of the Fenton–Karma model to stimulation in zero spatial dimensions. This map contains some amount of memory, describing the action potential duration as a function of the previous diastolic interval and the previous action potential duration. Results obtained from iteration of the map and numerical simulations of the Fenton–Karma model are in good agreement. In particular, the iterated map admits different types of solutions corresponding to various dynamical behavior of the cardiac cell, such as 1:1 and 2:1 patterns.