"Analysis of the Fenton-Karma model through approximation
by a one-dimensional map"
Alena Talkachova (Department Physics, Duke University,
Box 90305, Durham, NC 2779, USA), David Schaeffer, Colleen Mitchell (Department
Mathematics, Duke University, Box 90305, Durham, NC 2779, USA)
The Fenton-Karma (FK) model is a phenomenological simplification of complex
ionic models of cardiac
membrane. It reproduces quantitatively many of the characteristics
of heart cells, and its behavior is simple
enough to be understood analytically. In this paper, a map in a phase
space of one dimension is derived to
approximate the response of the FK model to periodic stimulation in
zero spatial dimension (patch model).
Results obtained from the iteration of the map and numerical simulations
of the FK model are in good
agreement. 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 and alternans). The
existence of various solution types and
their stability is determined analytically as a function of parameters.
Last Modified: 28-Mar-02