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

Elena G. Tolkacheva1,4, Mónica M. Romeo2,4, Marie Guerraty2, and Daniel J. Gauthier1,3,4

  • 1Department of Physics, Duke University, Durham, North Carolina 27708, USA
  • 2Department of Mathematics, Duke University, Durham, North Carolina 27708, USA
  • 3Department of Biomedical Engineering, Duke University, Durham, North Carolina 27708, USA
  • 4Center for Nonlinear and Complex Systems, Duke University, Durham, North Carolina 27708, USA

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Phys. Rev. E 69, 031904 – Published 15 March, 2004

DOI: https://doi.org/10.1103/PhysRevE.69.031904

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 γ 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 γS12 stays approximately in the same range.

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Phys. Rev. E 69, 031904– Published 15 March, 2004
  • Received 17 July 2003

© 2004 American Physical Society

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