First-Principles Electrophysiological Models of Cardiac Ventricular Myocytes as a Basis of Multiscale Mechanics of the Heart

Cardiac electromechanics is a coupled multiphysics and multiscale problem. Of great interest to medicine and pharmacology is how the heart responds to changes in ion channel dynamics within the myocyte that are either caused by disease or by the administration of drugs. A successful model of cardiac mechanical response must therefore incorporate a first-principles description of electrophysiology of the cardiac myocyte including intracellular calcium dynamics, transmembrane ionic currents and action potential (AP) formation at the cellular level. This article reviews the evolution of electrophysiological models of cardiac ventricular myocytes in terms of coupled differential equations whose state variables include ion channel gating parameters, intracellular ionic concentrations and the membrane voltage. The myocytes are connected through gap junctions forming fibers, which in turn connect to form cardiac tissues. The electromechanical response of cardiac tissues is coupled through intracellular calcium dynamics and stretch induced/ modulated currents, and can be solved using suitable discretization schemes under appropriate initial and boundary conditions. We discuss in detail the single-cell dynamics of the ORd model of human ventricular myocytes and describe the propagation of AP in periodically paced 1D fibers and 2D tissues. The origin of tissue-level diseased conditions in altered subcellular dynamics are discussed.