Intracellular Dynamics of Human Cardiac Ventricular Myocyte: ORd Model

Abstract

Human heart is elegantly articulated to mechanically contract in response to electrical excitation. Cardiac electrical activity may be described as a multiscale process from sub-cellular to cellular to tissue level. Ion movement at the cellular level through ion channels results in an action potential that propagates as an electrical wave in tissue. A first-principles-based mathematical description of the cellular-level dynamics of cardiac electrophysiological behavior provides a better understanding of the functioning of the heart. The mathematical models describing cellular dynamics often involve a coupled system of ordinary differential equations (ODEs) with variables including transmembrane voltage, ion concentrations and ion channel gating variables, whose evolution describes activation/inactivation of ion channels. In this study we discuss a mathematical model of the human ventricular myocyte (O’Hara–Rudy model), defined as a system of 41 ODEs, with variables involving membrane voltage, 29 gating variables describing activation of Na[Formula: see text], K[Formula: see text], Ca[Formula: see text] channels, 11 variables describing ion concentrations and Ca[Formula: see text] related flux. Runge–Kutta method with variable order and variable time step was adopted to solve the system numerically. We discuss the action potential (AP) profile of a healthy human ventricular myocyte and corresponding dominant ionic currents. We present a phase plot that describes the change in voltage and its rate as the system evolves over time. The phase plot seems to provide more details of the underlying events than the AP curve.