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Focal arrhythmias, which arise from delayed afterdepolarizations (DADs), areobserved in various pathophysiological heart conditions; these can lead tosudden cardiac death. A clear understanding of the electrophysiological factorsof cardiac myocytes, which lead to DADs, can suggest pharmacological targetsthat can eliminate DAD-induced arrhythmias. Therefore, we carry out multiscaleinvestigations of two mathematical models for human-ventricular myocytes,namely, the ten Tusscher-Panfilov and the HuVEC15 model, at the levels ofsingle myocytes, one- and two-dimensional (1D and 2D) tissue, and anatomicallyrealistic bi-ventricular domains. By using continuation analysis, we uncoversteady- to oscillatory-state transitions in the Ca\textsuperscript{2+}concentrations and show that they lead to DADs. We demonstrate that theSarco/endoplasmic reticulum Ca\textsuperscript{2+}-ATPase (SERCA) pump uptakerate and the Ca\textsuperscript{2+} leak through the ryanodine-receptor (RyR)channel impact this transition significantly. We show that the frequencies andamplitudes of the DADs are key features that can be used to classify them intothree types. By carrying out detailed parameter-sensitivity analyses, weidentify the electrophysiological parameters, in the myocyte models, that mostaffect these key features. We then obtain stability (or phase) diagrams fordifferent types of DADs. We demonstrate that theNa\textsuperscript{+}/Ca\textsuperscript{2+} exchanger plays a protective roleby suppressing DADs in the TP06 model. We present tissue simulations toillustrate how arrhythmogenic premature ventricular complexes (PVCs) emergefrom patches of DAD cells when we pace the tissue. We discuss the implicationsof our results for some DAD-induced ventricular arrhythmias, which we examinein detail in the companion Paper II.

Multiscale studies of delayed afterdepolarizations I: A comparison of two biophysically realistic mathematical models for human ventricular myocytes