Restitution slope is determined by the steady state action potential duration: law and disorder

In this issue of Cardiovascular Research, Michael Shattock and coauthors publish data that support the statement that the maximum slope of the ventricular restitution curve is determined by the steady state action potential. Restitution, the relation between action potential duration (APD) and the preceding diastolic interval, is an important characteristic of myocardium because it allows shortening of the APD with increasing heart rates. The maximum slope of the restitution relation is important for arrhythmogenesis. A sudden change from a slow to a fast heart rate induces beat by beat variation in APD (alternation). It has been suggested that if the maximum slope of the restitution relation exceeds 1 this alternation does not die out but causes wave break and ventricular fibrillation. In hearts of patients undergoing cardiac surgery, restitution has been measured at multiple sites. The maximum slope regionally exceeded 1 in these patients at risk for arrhythmias. Also in models of classical reentry a steep restitution slope (although not necessarily with a slope >1) facilitates arrhythmia based on reentry. It is generally accepted that the dV/dtmax of the upstroke of the action potential is the equivalent of the maximum net inward current. Likewise, the dV/dtmin of the cardiac action potential is the equivalent of the maximum net outward current that causes repolarization. The concept that the maximum slope of the ventricular restitution curve is determined by the steady state action potential is directly derived from previous work by the authors in which they have demonstrated that the duration of the cardiac action potential depends on the repolarizing rate. The idea is summarized in the figure (compiled and modified from Winter et al. 7 and Shattock et al.). Winter et al. have previously demonstrated that a similar change between the slopes of the repolarization rates (depicted in the figure as angle a) results in a much larger difference in APD when the initial action potential is long than when the initial action potential is short (Figure 1A). This dependence is simply caused by the morphology of the action potential. Therefore, the relation between net repolarizing current (the slope of the repolarization rate of the action potential) and the APD is non-linear (Figure 1B). If the same increase in repolarizing current is applied to the starting points 1 and 3 (figure, arrows) a larger decrease in APD occurs when the action potential is long, than when it is short (Figure 1C). This is valid for any basic cycle length (S1 stimulation). Shattock et al. take this message a step further, by extrapolating their findings to the restitution curve. Following the same reasoning as in Winter et al., the authors now demonstrate that the maximum slope of the restitution curve, and indeed the restitution curve as a whole, is determined by the maximum APD of the restitution curve (the steady state APD). The figure (Figure 1D) schematically shows the last action potential of a train of S1 stimuli, followed by premature action potentials (after a S2 stimulus) with a short and long (steady state) diastolic interval. From the article of Shattock et al. in this issue of Cardiovascular Research it is now clear that the restitution curves belonging to a long steady state APD and that of a short steady state APD by necessity converge. This implies that if APD differences exist between the two restitution curves at long diastolic intervals (long cycle lengths), they tend to disappear at short diastolic intervals (short cycle lengths) and, therefore, that the slope of the restitution curve is steeper in the red (with the longer steady state APD) than in the green curve (with the shorter steady state APD). A scientific law is a statement that is based on multiple experimental observations that points to a causal relation between the components of the statement and that has general applicability in more or less equal conditions. Based on such a statement, predictions can be formulated and tested. The idea presented in the article by Shattock et al. shares characteristics with those of a biological law. The traditional response of a scientist to a statement that claims general applicability is to find the exception that proves the statement wrong. Our system of peer review is intended to challenge the ideas of authors to the extreme, in order to test and improve the scientific quality of a article. The peers thereby are incited to play the role of the ultimate skeptic, that of the ‘devil’s advocate’. It is only natural that the reviewers question the claim of general applicability and demand demonstration of the validity of the alleged law under all possible conditions. The article of Shattock et al. carries all signs inflicted by the skeptic’s peer review process. Despite these multiple and apparently disordered challenges of their idea, the authors have succeeded to write the story in a coherent manner. Their statement is tested under a plethora of conditions pertinent to normal heart function as well as to pathological heart function, involving pharmacological challenges with drugs that either prolong or shorten APD, but also with