Spiral wave breakup manner in the excitable system with early afterdepolarizations

Abstract

Early afterdepolarization (EAD) is an important cause of lethal ventricular arrhythmias in heart failure because afterdepolarizations can promote the transition from ventricular tachycardia to fibrillation, which is related to the transition from spiral wave to spatiotemporal chaos. However, it remains unclear about how the EAD results in the breakup of spiral wave. In this paper, we explore the manner of spiral wave breakup induced by EADs under evenly distributed cells. The two-dimensional tissue is simulated with the Greenberg-Hasting cellular automaton model. The normal cells and aging cells are introduced into the model, in which the EAD only occurs in aging cells and can excite the resting cells. The numerical results show that the EAD can produce backward waves as well as forward waves. The EAD has no influence on the behavior of spiral wave in a few cases. The ratio of the number of unaffected spiral waves to the number of all tests is about 26.4%. The EAD can have various effects on spiral wave in other cases. The small influences on spiral wave are that the EAD leads to the meander, drift, and the deformation of spiral wave. The serious influences on spiral wave are that the EAD results in the disappearance and breakup of spiral wave. We find that spiral wave can disappear through the conduction block and transition from spiral wave to target wave. We observe the eight kinds of spiral wave breakups in connection with the excitation of EADs, such as symmetry breaking-induced breakup, nonsymmetry breaking-induced breakup, asymmetric excitation-induced breakup, conduction block-induced breakup, double wave-induced breakup, etc. Spiral wave generally breaks up into multiple spiral waves and spatiotemporal chaos. The ratio of the number of spiral wave breakup to the number of all tests is about 13.8%. However, the ratio of spiral wave breakup can reach about 32.4% under appropriately chosen parameters. The results are basically consistent with the survey results of arrhythmia-induced death rate. Furthermore, we also find that the excitation of EAD can prevent the spiral wave from disappearing and promote the breakup of spiral wave. The physical mechanisms underlying those phenomena are also briefly analyzed.