Modelling the take-off voltage of the action potential during fast pacing

To date over 50 models for cardiac action potential have been developed, and while they vary widely in their complexity and the physiological characteristics that they reproduce, most fail to accurately replicate the takeoff potential during fast pacing and fibrillation. A specific aspect we focus is on the takeoff potential for an S2 stimulation following a steady S1 action potential. In microelectrodes and optical mapping experiment, the take-off voltage of an S2 action potential has been shown to be relatively high while most cardiac cell models do not reflect this feature, as the voltage needs to return close to the resting membrane potential before it can be reactivated. Since this difference can have great effects in electrical waves and their dynamics during tachycardia and fibrillation, we developed a framework that can be incorporated into the models to reproduce the experimentally observed higher take off potential. Recovery of inactivation in the Sodium current is the key to the activation from an S2 stimulus. Therefore, we focused on the sodium inactivation gates h and j. We hypothesized that the j gate is the source of the low take off potential because it recovers during AP final repolarization. Our procedure is to model the dynamics of both gates via a single one with an adjustable time constant tau. We model tau with an asymmetric equation. Using this equation form, we can manipulate the width, height, and asymptotic values of tau. The features that change the takeoff potential significantly are the midpoint and asymptotic value(s) of tau. By shifting the midpoint value of tau to a higher value, the takeoff potential increase, while rest of the sodium dynamics remains unaltered.