Abstract
Early afterdepolarizations (EADs) are triggers of lethal ventricular arrhythmias such as Torsade de Pointes in patients with long QT syndromes and heart failure. The mechanism that underlies EAD generation is thought to be the reactivation of the L-type calcium channel. However, why the L-type calcium channel is reactivated is not yet fully understood. Our objective was to understand the generative mechanism of EADs from the viewpoint of the nonlinear dynamical system. Herein, we have proposed a numerical calculation method for analyzing the dynamical stability of action potentials observed in an electrophysiological mathematical model of the periodically stimulated ventricular myocyte. Such a system can be defined as a nonautonomous system driven by a discontinuous periodic force. Based on dynamical system theory, the study of the qualitative properties of the periodic solution observed in the nonautonomous system can be reduced to that of a diffeomorphism, called a Poincare map. Even though the system had a discontinuous nature, we showed that the Poincare map could be constructed as successive submaps. Thereby, we can directly assess the stability of the action potential.
