Geometrical considerations in cardiac electrophysiology and arrhythmogenesis

Abstract

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.

Restitution slope is principally determined by steady-state action potential duration

“…Studies by Bányász et al and Bárándi et al demonstrate the importance of this relationship in steady-state adaptation of the ventricular action potential at long CLs (300–5000 ms), in a range of species 22 , 23 . In principle, the same mechanism may be an important determinant of the slope of the restitution curve, as we recently proposed 25 . However, some experimental evidence is contrary to this claim, as stimulation of the vagus nerve, and treatment with the anti-arrhythmic agents bretylium and ibutilide, have been reported to prolong APD but to flatten the relationship between APD and DI 1 , 26 , 27 .…”

“…In Figure 1A , data from hearts perfused with clofilium, veratridine, low [Ca] e and catecholamines are shown to fall along a single mono-tonic curve. This curve represents an intrinsic property of the cardiac membrane, a consequence of geometry, as previously described 22 , 25 Figure 1Modelling the influence of action potential duration on the electrical restitution curve.…”

“…The present study provides robust evidence that changes in APD ss/max , and not τ or b, are the principal determinant of restitution slope in the ventricle, and, moreover, we demonstrate a simple physical mechanism that accounts for this effect—i.e. that APD is an inverse and non-linear function of the rate of repolarization of the action potential (as shown in Figure 1 ) 21 , 22 , 25 . Consequently, the magnitude of change in APD for a given change in repolarization rate is intrinsically dependent upon the APD ss .…”

Arrhythmias and Heart Rate: Mechanisms and Significance of a Relationship

“…Longer repolarisation is intrinsically more labile to perturbations 11,12 and, as such, prone to become spatially inhomogeneous and temporally variable. 13 Moreover, repolarisation velocity is pivotal in preventing partial I CaL recovery and its immediate reactivation during the action potential plateau, which would result in major perturbation of the action potential profile (early-afterdepolarisations, EADs). 14 Prolonged repolarisation, either primary or acquired, is notoriously associated with proarrhythmia.…”

Electrophysiological Mechanisms of Bayés Syndrome: Insights from Clinical and Mouse Studies

“…It is increasingly recognized that passive and active properties are not independent of each other, since gap junctions and Na + channels co-localize in the connexome, and their close proximity to each other could enable ephaptic conduction (Rhett and Gourdie, 2012 ; Veeraraghavan et al, 2012 , 2014a , b , c , 2015 ; Rhett et al, 2013 ; George et al, 2015 ). Increased risk of arrhythmogenesis by either circus-type or spiral wave reentry can be explained by a reduction in excitation wavelength (λ) given by CV × ERP (Wiener and Rosenblueth, 1946 ; Smeets et al, 1986 ; Vaidya et al, 1999 ; Tse, 2015 ; Tse et al, 2016f , in press ). Selective atrial fibrosis could increase the heterogeneity of conduction by allowing micro-reentry to take place in smaller areas in atrial fibrosis (Spach and Josephson, 1994 ; Verheule et al, 2004 ).…”