Abnormal calcium release and delayed afterdepolarizations: A comparison of two mathematical models for human ventricular myocytes

Focal arrhythmias, which arise from delayed afterdepolarizations (DADs), are observed in various pathophysiological heart conditions; these can lead to sudden cardiac death. A clear understanding of the interplay of electrophysiological factors of cardiac myocytes, which lead to DADs, can suggest pharmacological targets that can eliminate DAD-induced arrhythmias. Therefore, we carry out multiscale investigations of two mathematical models for human-ventricular myocytes, namely, the ten Tusscher-Panfilov TP06 model and the HuVEC15 model of Himeno, et al., at the levels of single myocytes, one- and two-dimensional (1D and 2D) tissue, and anatomically realistic bi-ventricular domains. We demonstrate that the Sarco/endoplasmic reticulum Ca2+-ATPase (SERCA) pump uptake rate and the Ca2+ leak through the ryanodine-receptor (RyR) channel impact this transition significantly. We show that the frequencies and amplitudes of the DADs are key features that can be used to classify them into three types, at the single-myocyte level. By carrying out detailed parameter-sensitivity analyses, we identify the electrophysiological parameters, in the myocyte models, that most affect these key features. We then obtain stability (or phase) diagrams that show the regions of parameter space in which different types of DADs occur. By comparing differences in model compartmentalizations, we show that these structural features can significantly influence both the occurrence and the types of DADs. We demonstrate in the TP06 model, the Na+/Ca2+ exchanger can also play a protective role in the elimination of DADs, and the presence of late calcium releases can enhance this effect. We present representative tissue simulations of the spatiotemporal evolution of waves of electrical activation, in these models, to illustrate how arrhythmogenic premature ventricular complexes (PVCs) emerge from patches of DAD cells, when we pace the tissue.