Geometrical considerations in cardiac electrophysiology and arrhythmogenesis

The rate of repolarization (RRepol) and so the duration of the cardiac action potential are determined by the balance of inward and outward currents across the cardiac membrane (net ionic current). Plotting action potential duration (APD) as a function of the RRepol reveals an inverse non-linear relationship, arising from the geometric association between these two factors. From the RRepol-APD relationship, it can be observed that a longer action potential will exhibit a greater propensity to shorten, or prolong, for a given change in the RRepol (i.e. net ionic current), when compared with one that is initially shorter. This observation has recently been used to explain why so many interventions that prolong the action potential exert a greater effect at slow rates (reverse rate-dependence). In this article, we will discuss the broader implications of this simple principle and examine how common experimental observations on the electrical behaviour of the myocardium may be explained in terms of the RRepol-APD relationship. An argument is made, with supporting published evidence, that the non-linear relationship between the RRepol and APD is a fundamental, and largely overlooked, property of the myocardium. The RRepol-APD relationship appears to explain why interventions and disease with seemingly disparate mechanisms of action have similar electrophysiological consequences. Furthermore, the RRepol-APD relationship predicts that prolongation of the action potential, by slowing repolarization, will promote conditions of dynamic electrical instability, exacerbating several electrophysiological phenomena associated with arrhythmogenesis, namely, the rate dependence of dispersion of repolarization, APD restitution, and electrical alternans.