Analytical description of the slope of the APD-restitution curve to assess the interacting contribution of conduction and repolarization dynamics

The restitution of the action potential duration (APDR) is a mechanism whereby cardiac excitation and relaxation adapt to changes in heart rate. Several studies, mainly carried out in-vitro and in-silico, have demonstrated that a steep APDR curve is associated with increased vulnerability to fatal arrhythmias. However, the mechanisms that link the steepness of the APDR curve to arrhythmogenesis remain undetermined. Although APDR is known to interact with conduction dynamics, few studies have focused on these interactions. In this paper, an analytical expression of the slope of the APDR is derived. This expression explicitly describes the dependency of the slope of the APDR curve on the activation time and/or conduction velocity changes. The study of this expression shows that conduction dynamics are among the main determinants of the slope of the APDR curve. A small absolute increment in the steepness of the activation time restitution slope can cause the steepness of the APDR slope to dramatically increase. Theoretically, the APDR slope quickly diverges to infinity when the increase in activation time matches the decrease in the pacing interval. High density epicardial mapping performed in a patient undergoing open heart surgery, shows excellent agreement between measures of the slope of the APDR curve and its analytical prediction (linear correlation > 0.95). The in-vivo recordings suggest that activation time restitution is the main determinant of the slope of the APDR curve.