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

E. G. Tolkacheva, D. G. Schaeffer, D. J. Gauthier, C. C. Mitchell

Research output: Contribution to journalArticle

27 Citations (Scopus)

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.

Original languageEnglish (US)
Pages (from-to)1034-1042
Number of pages9
JournalChaos
Volume12
Issue number4
DOIs
StatePublished - Dec 2002

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One-dimensional Maps
Action Potential
Approximation
approximation
Cardiac
Cell
cells
simplification
stimulation
Dynamical Behavior
Model
Simplification
iteration
Membrane
Cells
membranes
Membranes
intervals
Iteration
Data storage equipment

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Analysis of the Fenton-Karma model through an approximation by a one-dimensional map. / Tolkacheva, E. G.; Schaeffer, D. G.; Gauthier, D. J.; Mitchell, C. C.

In: Chaos, Vol. 12, No. 4, 12.2002, p. 1034-1042.

Research output: Contribution to journalArticle

Tolkacheva, E. G. ; Schaeffer, D. G. ; Gauthier, D. J. ; Mitchell, C. C. / Analysis of the Fenton-Karma model through an approximation by a one-dimensional map. In: Chaos. 2002 ; Vol. 12, No. 4. pp. 1034-1042.
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