A mathematical analysis of the action potential plateau duration of a human ventricular myocyte

The plateau phase of a human ventricular myocyte is analysed. The plateau duration is a function of the time required for a myocyte's transmembrane voltage to decrease by a certain voltage, DeltaV. The timing of the plateau is shown to be controlled by two slowly changing gate variables, the inactivation gate that controls the inward/depolarizing L-type calcium current and the inactivation gate that controls the outward/repolarizing slow rectifier potassium current. The amount of current controlled by these variables is a function of the net conductivity of the corresponding sodium and potassium channels. An equation is derived that relates action potential duration to these net conductivities and the time dependence of the slowly moving variables. This equation is used to estimate plateau duration for a given value of DeltaV. The initial conditions of the slowly moving inactivation variables are shown to affect plateau duration. These initial conditions depend on the amount of time that has elapsed between a previous repolarization and a current depolarization (diastolic interval). The analysis thus helps to quantify the characteristics of action potential duration restitution.