Irregular Dynamics of Excitation in Biologic and Mathematical Models of Cardiac Cellsa

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Abstract
Excitation and impulse propagation in cardiac tissues are dependent on the heart rate and can occur in extremely complex patterns. In this chapter we present the results of Purkinje fiber experiments and of computer simulations using an ionic (Beeler & Reuter) model for the ventricular cell. We have studied the global rate-dependent behavior of cardiac cells through a systematic analysis of their response to single as well as repetitive depolarizing stimuli, and determined the role of nonlinearity in the mechanism(s) of their behaviors. To this end, we devised an analytical difference equation model of cardiac cell excitation which could be used to predict simple as well as chaotic behavior of both the Purkinje fiber and the Beeler & Reuter cell, depending on the stimulation rate. Both experimental and modeling results suggest that the presence of supernormal recovery in cell excitability establishes sufficient nonlinearity so that, during repetitive stimulation, the dynamics of cell response may be regular and predictable when the stimulus magnitude is either very small or very large, or they may be chaotic and very unpredictable when the stimulus magnitude is intermediate. The overall results suggest that the application of nonlinear systems theory to electrophysiology may have importance in the understanding of cardiac rhythm and conduction disturbances, and may have clinical implications as well.