Nonlinear dynamics of rate-dependent activation in models of single cardiac cells

Recent studies in isolated cardiac tissue preparations have demonstrated the applicability of a one-dimensional difference equation model describing the global behavior of a driven nonpacemaker cell to the understanding of rate-dependent cardiac excitation. As a first approximation to providing an ionic basis to complex excitation patterns in cardiac cells, we have compared the predictions of the one-dimensional model with those of numerical simulations using a modified high-dimensional ionic model of the space-clamped myocyte. Stimulus-response ratios were recorded at various stimulus magnitudes, durations, and frequencies. Iteration of the difference equation model reproduced all important features of the ionic model results, including a wide spectrum of stimulus-response locking patterns, period doubling, and irregular (chaotic) dynamics. In addition, in the parameter plane, both models predict that the bifurcation structure of the cardiac cell must change as a function of stimulus duration, because stimulus duration modifies the type of supernormal excitability present at short diastolic interval. We conclude that, to a large extent, the bifurcation structure of the ionic model under repetitive stimulation can be understood by two functions: excitability and action potential duration. The characteristics of these functions depend on the stimulus duration.