Condition for alternans and its control in a two-dimensional mapping model of paced cardiac dynamics.
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.
Tolkacheva
Elena G
EG
Department of Physics, Duke University, Durham, North Carolina 27708, USA.
Romeo
Mónica M
MM
Guerraty
Marie
M
Gauthier
Daniel J
DJ
D000200:Action Potentials; D000222:Adaptation, Physiological; D000818:Animals; D001145:Arrhythmias, Cardiac / Q000503:physiopathology* / Q000628:therapy*; D001683:Biological Clocks; D002304:Cardiac Pacing, Artificial; D005246:Feedback; D006329:Heart Conduction System / Q000503:physiopathology*; D006801:Humans; D008955:Models, Cardiovascular; D008959:Models, Neurological; D032342:Muscle Cells; D017711:Nonlinear Dynamics