Condition for alternans and its control in a two-dimensional mapping model of paced cardiac dynamics

Elena G. Tolkacheva, Mónica M. Romeo, Marie Guerraty, Daniel J. Gauthier

Research output: Contribution to journalArticle

47 Citations (Scopus)

Abstract

We investigate a two-dimensional mapping model of a paced, isolated cardiac cell that relates the duration of the action potential to the two preceding diastolic intervals as well as the preceding action potential duration. The model displays rate-dependent restitution and hence memory. We derive a criterion for the stability of the 1:1 response pattern displayed by the model. This criterion can be written in terms of experimentally measured quantities-the slopes of restitution curves obtained via different pacing protocols. In addition, we analyze the two-dimensional mapping model in the presence of closed-loop feedback control. The control is initiated by making small adjustments to the pacing interval in order to suppress alternans and stabilize the 1:1 pattern. We find that the domain of control does not depend on the functional form of the map, and, in the general case, is characterized by a combination of the slopes. We show that the gain gamma necessary to establish control may vary significantly depending on the value of the slope of the so-called standard restitution curve (herein denoted as S12), but that the product gammaS12 stays approximately in the same range.

Original languageEnglish (US)
Article number031904
Pages (from-to)31904
Number of pages1
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume69
Issue number3
DOIs
StatePublished - Mar 2004

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Cardiac
Slope
Action Potential
slopes
intervals
Curve
Interval
Closed-loop Control
curves
guy wires
feedback control
Model
Feedback Control
Adjustment
adjusting
Vary
Necessary
Dependent
Cell
products

Cite this

Condition for alternans and its control in a two-dimensional mapping model of paced cardiac dynamics. / Tolkacheva, Elena G.; Romeo, Mónica M.; Guerraty, Marie; Gauthier, Daniel J.

In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, Vol. 69, No. 3, 031904, 03.2004, p. 31904.

Research output: Contribution to journalArticle

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