title: Analysis of the Fenton-Karma model through an approximation by a one-dimensional map.
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. (c) 2002 American Institute of Physics.
authors.affiliation: Department of Physics and Center for Nonlinear and Complex Systems, Duke University, Durham, North Carolina 27708.
authors.forename: E. G.
authors.initials: EG
authors.lastname: Tolkacheva
authors.forename: D. G.
authors.initials: DG
authors.lastname: Schaeffer
authors.forename: D. J.
authors.initials: DJ
authors.lastname: Gauthier
authors.forename: C. C.
authors.initials: CC
authors.lastname: Mitchell