A mathematical model of the cardiac ventricular action potential is presented. In our previous work, the membrane Na+ current and K+ currents were formulated. The present article focuses on processes that regulate intracellular Ca2+ and depend on its concentration. The model presented here for the mammalian ventricular action potential is based mostly on the guinea pig ventricular cell. However, it provides the framework for modeling other types of ventricular cells with appropriate modifications made to account for species differences. The following processes are formulated: Ca2+ current through the L-type channel (ICa), the Na(+)-Ca2+ exchanger, Ca2+ release and uptake by the sarcoplasmic reticulum (SR), buffering of Ca2+ in the SR and in the myoplasm, a Ca2+ pump in the sarcolemma, the Na(+)-K+ pump, and a nonspecific Ca(2+)-activated membrane current. Activation of ICa is an order of magnitude faster than in previous models. Inactivation of ICa depends on both the membrane voltage and [Ca2+]i. SR is divided into two subcompartments, a network SR (NSR) and a junctional SR (JSR). Functionally, Ca2+ enters the NSR and translocates to the JSR following a monoexponential function. Release of Ca2+ occurs at JSR and can be triggered by two different mechanisms, Ca(2+)-induced Ca2+ release and spontaneous release. The model provides the basis for the study of arrhythmogenic activity of the single myocyte including afterdepolarizations and triggered activity. It can simulate cellular responses under different degrees of Ca2+ overload. Such simulations are presented in our accompanying article in this issue of Circulation Research.

A mathematical model of the membrane action potential of the mammalian ventricular cell is introduced. The model is based, whenever possible, on recent single-cell and single-channel data and incorporates the possibility of changing extracellular potassium concentration [K].. The fast sodium current, 'Nap is characterized by fast upstroke velocity (Vma.=400 V/sec) and slow recovery from inactivation. The time-independent potassium current, IKI, includes a negative-slope phase and displays significant crossover phenomenon as [K]

The action potential model presented in our accompanying article in this journal is used to investigate phenomena that involve dynamic changes of [Ca2+]i, as described below. Delayed afterdepolarizations (DADs) are induced by spontaneous Ca2+ release from the sarcoplasmic reticulum (SR), which, in turn, activates both the Na(+)-Ca2+ exchanger (INaCa) and a nonspecific Ca(2+)-activated current (Ins(Ca)). The relative contributions of INaCa and of Ins(Ca) to the generation of DADs are different under different degrees of Ca2+ overload. Early afterdepolarizations (EADs) can be categorized into two types: (1) plateau EADs, resulting from a secondary activation of the L-type Ca2+ current during the plateau of an action potential, and (2) phase-3 EADs, resulting from activation of INaCa and Ins(Ca) by increased [Ca2+]i due to spontaneous Ca2+ release from the SR during the late repolarization phase. Spontaneous rhythmic activity and triggered activity are caused by spontaneous Ca2+ release from the SR under conditions of Ca2+ overload. Postextrasystolic potentiation reflects the time delay associated with translocation of Ca2+ from network SR to junctional SR. The cell is paced at high frequencies to investigate the long-term effects on the intracellular ionic concentrations.

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