Abstract
Computer simulation of mathematical models of mammalian ventricular myocytes has become a very promising tool for understanding the underlying mechanisms of cardiac arrhythmias and may provide useful predictions of treatment in order to prevent fatal arrhythmias. In this paper, we employ the Luo–Rudy (LR) model of membrane action potential of the mammalian ventricular cell. Simulation is performed with the aid of a direct method for locating the equilibria and by an adaptive grid method for constructing bifurcation diagrams. Two-parameter bifurcation diagrams are constructed to show the parameter sets in which (a) spontaneous oscillations exist, (b) the equilibrium corresponding to the resting potential is stable, or (c) the equilibrium with the most depolarized potential is stable. Multiple attractors are detected near the boundary of these parameter sets. The generation of normal and abnormal pacemaking activities is elucidated via bifurcation analysis. Spontaneous oscillations appear and disappear via saddle-node homoclinic bifurcations, Hopf bifurcations, homoclinic bifurcations, or fold bifurcations of limit cycles. Limit cycles may become chaotic via period-adding cascades as the extracellular potassium concentration [K]o decreases. Pacemaking activities may also be generated when the time-independent potassium current is blocked.
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