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Description

The response of an isolated cardiac cell to a periodic stimulus is traditionally studied in terms of the duration of the action potential (APD) immediately following each stimulus. Experiments demonstrate that the rhythms generated by such stimulus protocols can vary widely, depending on frequency and amplitude of the stimulus. A theoretical approach based on the APD is capable of explaining some of the experimental observations but a complete understanding of the parameter dependence is beyond the scope of the APD approach. We discuss some fundamental problems with the APD approach and propose a new one dimensional map that relies on the presence of a one dimensional slow manifold in the dynamics. This slow manifold map extends the understanding offered by the APD approach to include an explanation of Wenckebach rhythms. In addition, the bifurcation structure of the map provides a unified description of the parameter dependence that agrees fairly well with experimental observation.