Memory and Stability of the Cardiac Action Potential Repolarization in the Space of its Allowed States: A Single Cell Simulation Study

Abstract

The rate-dependent partition of the cardiac cycle into diastole and systole is measured at the cellular level as rate-dependence (RD) and electrical restitution (ER) of the action potential (AP) duration (APD), the first describing changes in APD after steady state changes in cycle length (CL), and the second APD changes after a sudden switch from constant to a variably delayed CL, as a function of the pre-switch CL (or DI). A dynamic ER curve (DER) can also be measured under beat-to-beat changes in pacing rate, and the increase in its slope is a recognized predictor of electrical alternance and ventricular fibrillation. An hysteretic behavior has been described previously in DER curve and associated with cardiac memory and repolarization stability. In the present study, by means of simulations with three numerical models of the human ventricular AP, I measure DER as APD vs DI and APD vs CL plots from high frequency paced AP series, and find that both show hysteresis with remarkably different phase shifts. Based on both representations, I define and measure a space of states (SPoS) for APs elicited, in turn, at constant, periodically changing, and randomly changing (1, 2, and 3 dimensional SPoS) pacing rates, and use them to study perturbations (a single missing beat) of the pacing protocol. I show how the maximum conductance and gating kinetics of three plateau ion currents (IKs, IKr, and ICaL), change shape and size of SPoS. I show how geometrical parameters of SPoS, for a given AP type and a given pacing law, can be used to numerically quantify memory and stability of its dynamics.