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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
; | | Date: |
29 Feb 2004 | | Journal: | Phys Rev E, 69 (3 Pt 1), 031904 | | 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. | | Source: | PubMed, pmid15089319 | | Services: | Forum | Review | Favorites | |
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