Action potential duration restitution portraits of mammalian ventricular myocytes: role of calcium current

Construction of the action potential duration (APD) restitution portrait allows visualization of multiple aspects of the dynamics of periodically paced myocytes at various basic cycle lengths (BCLs). For the first time, we obtained the restitution portrait of isolated rabbit and guinea pig cardiac ventricular myocytes and analyzed the time constant, tau, of APD accommodation and the slopes of different types of restitution curves, Sdyn and S12, measured at varying BCLs. Our results indicate that both tau and the individual slopes are species and pacing dependent. In contrast, the mutual relationship between slopes Sdyn and S12 does not depend on pacing history, being a generic feature of the species. In addition, the maximum slope S12, measured in the restitution portrait at the lowest BCL, predicts the onset of alternans. Further, we investigated the role of the L-type calcium current, ICa-L, in the restitution portrait. We found that ICa-L dramatically affects APD accommodation, as well as the individual slopes Sdyn and S12 measured in the restitution portrait. However, peak calcium current plays a role only at small values of BCL. In conclusion, the results demonstrate that the restitution portrait is a powerful technique to investigate restitution properties of periodically paced cardiac myocytes and the onset of alternans, in particular. Moreover, the data also show that ICa-L plays a crucial role in multiple aspects of cardiac dynamics measured through the restitution portrait.     

Effect of beta-adrenergic blockade on dynamic electrical restitution in vivo

The slope of the action potential duration (APD) restitution curve may be a significant determinant of the propensity to develop ventricular fibrillation, with steeper slopes associated with a more arrhythmogenic substrate. We hypothesized that one mechanism by which beta-blockers reduce sudden cardiac death is by flattening the APD restitution curve. Therefore, we investigated whether infusion of esmolol modulates the APD restitution curve in vivo. In 10 Yorkshire pigs, dynamic APD restitution curves were determined from measurements of APD at 90% repolarization with a monophasic action potential catheter positioned against the right ventricular septum during right ventricular apical pacing in the basal state and during infusion of esmolol. APD restitution curves were fitted to the three-parameter (a, b, c) exponential equation, APD = a.[1 - e((-b.DI))] + c, where DI is the diastolic interval. Esmolol decreased the maximal APD slope, 0.68 +/- 0.14 vs. 0.94 +/- 0.24 (baseline), P = 0.002, and flattened the APD restitution curve at shorter DIs, 75 and 100 ms (P < 0.05). To compare the slopes of the APD restitution curves at similar steady states, slopes were also computed at points of intersection between the restitution curve and the lines representing pacing at a fixed cycle length (CL) of 200, 225, 250, 275, and 300 ms using the relationship CL = APD + DI. Esmolol decreased APD restitution slopes at CLs 200-275 ms (P < 0.05). Esmolol flattens the cardiac APD restitution curve in vivo, particularly at shorter CLs and DIs. This may represent a novel mechanism by which beta-blockers prevent sudden cardiac death.     

Influence of channel subunit composition on L-type Ca2+ current kinetics and cardiac wave stability

Previous studies have demonstrated that the slope of the function relating the action potential duration (APD) and the diastolic interval, known as the APD restitution curve, plays an important role in the initiation and maintenance of ventricular fibrillation. Since the APD restitution slope critically depends on the kinetics of the L-type Ca(2+) current, we hypothesized that manipulation of the subunit composition of these channels may represent a powerful strategy to control cardiac arrhythmias. We studied the kinetic properties of the human L-type Ca(2+) channel (Ca(v)1.2) coexpressed with the alpha(2)delta-subunit alone (alpha(1C) + alpha(2)delta) or in combination with beta(2a), beta(2b), or beta(3) subunits (alpha(1C) + alpha(2)delta + beta), using Ca(2+) as the charge carrier. We then incorporated the kinetic properties observed experimentally into the L-type Ca(2+) current mathematical model of the cardiac action potential to demonstrate that the APD restitution slope can be selectively controlled by altering the subunit composition of the Ca(2+) channel. Assuming that beta(2b) most closely resembles the native cardiac L-type Ca(2+) current, the absence of beta, as well as the coexpression of beta(2a), was found to flatten restitution slope and stabilize spiral waves. These results imply that subunit modification of L-type Ca(2+) channels can potentially be used as an antifibrillatory strategy.     

Effects of [K(+)](o) on electrical restitution and activation dynamics during ventricular fibrillation

To test whether hyperkalemia suppresses ventricular fibrillation (VF) by reducing the slope of the action potential duration (APD) restitution relation, we determined the effects of the extracellular K(+) concentration ([K(+)](o)) ([KCl] = 2.7-12 mM) on the restitution of APD and maximum upstroke velocity (V(max)) the magnitude of APD alternans and spatiotemporal organization during VF in isolated canine ventricle. As [KCl] was increased incrementally from 2.7 to 12 mM, V(max) was reduced progressively. Increasing [KCl] from 2.7 to 10 mM decreased the slope of the APD restitution relation at long, but not short, diastolic intervals (DI), decreased the range of DI over which the slope was >/=1, and reduced the maximum amplitude of APD alternans. At [KCl] = 12 mM, the range of DI over which the APD restitution slope was >/=1 increased, and the maximum amplitude of APD alternans increased. For [KCl] = 4-8 mM, the persistence of APD alternans at short DI was associated with maintenance of VF. For [KCl] = 10-12 mM, the spontaneous frequency during VF was reduced, and activation occurred predominantly at longer DI. The lack of APD alternans at longer DI was associated with conversion of VF to a periodic rhythm. These results provide additional evidence for the importance of APD restitution kinetics in the development of VF.     

Long-Term Prognostic Value of Restitution Slope in Patients with Ischemic and Dilated Cardiomyopathies

Background

An action potential duration (APD) restitution curve with a steep slope ≥1 has been associated with increased susceptibility for malignant ventricular arrhythmias. We aimed to evaluate the “restitution hypothesis” and tested ventricular APD restitution slope as well as effective refractory period (ERP)/APD ratio for long-term prognostic value in patients with ischemic (ICM) or dilated cardiomyopathy (DCM).

Methodology/Principal Findings

Monophasic action potentials were recorded in patients with ICM (n = 32) and DCM (n = 42) undergoing routine programmed ventricular stimulation (PVS). Left ventricular ejection fraction was 32±7% and 28±9%, respectively. APD and ERP were measured at baseline stimulation (S₁) and upon introduction of one to three extrastimuli (S₂–S₄). ERP/APD ratios and the APD restitution curve were calculated and the maximum restitution slope was determined. After a mean follow-up of 6.1±3.0 years, the combined end-point of mortality and and/or implantable cardioverter-defibrillator shock was not predicted by restitution slope or ERP/APD ratios. Comparing S₂ vs. S₃ vs. S₄ extrastimuli for restitution slope (1.5±0.6 vs. 1.4±0.4 vs. 1.3±0.5; p = NS), additional extrastimuli did not lead to a steepening restitution slope. ERP/APD ratio decreased with additional extrastimuli (0.98±0.09 [S₁] vs. 0.97±0.10 [S₂] vs. 0.93±0.11 [S₃]; p = 0.03 S₁ vs. S₃). Positive PVS was strongly predictive of outcome (p = 0.006).

Conclusions/Significance

Neither ventricular APD restitution slope nor ERP/APD ratios predict outcome in patients with ICM or DCM.     

Suppression of alternans and conduction blocks despite steep APD restitution: electrotonic, memory, and conduction velocity restitution effects

We examine the utility of the action potential (AP) duration (APD) restitution curve slope in predicting the onset of electrical alternans when electrotonic and memory effects are considered. We develop and use two ionic cell models without memory that have the same restitution curve with slope >1 but different AP shapes and, therefore, different electrotonic effects. We also study a third cell model that incorporates short-term memory of previous cycle lengths, so that it has a family of S1-S2 restitution curves as well as a dynamic restitution curve with slope >1. Our results indicate that both electrotonic and memory effects can suppress alternans, even when the APD restitution curve is steep. In the absence of memory, electrotonic currents related to the shape of the AP, as well as conduction velocity restitution, can affect how alternans develops in tissue and, in some cases, can prevent its induction entirely, even when isolated cells exhibit alternans. When short-term memory is included, alternans may not occur in isolated cells, despite a steep APD restitution curve, and may or may not occur in tissue, depending on conduction velocity restitution. We show for the first time that electrotonic and memory effects can prevent conduction blocks and stabilize reentrant waves in two and three dimensions. Thus we find that the slope of the APD restitution curve alone does not always well predict the onset of alternans and that incorporating electrotonic and memory effects may provide a more useful alternans criterion.     

Short-term cardiac memory and mother rotor fibrillation

Short-term cardiac memory refers to the effects of pacing history on action potential duration (APD). Although the ionic mechanisms for short-term memory occurring over many heartbeats (also called APD accommodation) are poorly understood, they may have important effects on reentry and fibrillation. To explore this issue, we incorporated a generic memory current into the Phase I Luo and Rudy action potential model, which lacks short-term memory. The properties of this current were matched to simulate quantitatively human ventricular monophasic action potential accommodation. We show that, theoretically, short-term memory can resolve the paradox of how mother rotor fibrillation is initiated in heterogeneous tissue by physiological pacing. In simulated heterogeneous two-dimensional tissue and three-dimensional ventricles containing an inward rectifier K(+) current gradient, short-term memory could spontaneously convert multiple wavelet fibrillation to mother rotor fibrillation or to a mixture of both fibrillation types. This was due to progressive acceleration and stabilization of rotors as accumulation of memory shortened APD and flattened APD restitution slope nonuniformly throughout the tissue.     

Role of maximum rate of depolarization in predicting action potential duration during ventricular fibrillation

During ventricular fibrillation (VF) only 39% of the variation in action potential duration (APD) is accounted for by the previous diastolic interval [DI((n-1))], i.e., restitution, and the previous APD [APD((n-1))], i.e., memory. We tested the hypothesis that a characteristic of the AP upstroke, the maximum rate of depolarization (V(max)), also helps account for its APD. A floating microelectrode was used to make transmembrane recordings at 16,000 samples/s from the anterior left ventricular wall during four 20-s episodes of VF in each of six pigs. V(max), time from V(max) to 60% repolarization (APD(60)), and DI were calculated throughout all episodes. Stepwise linear regression was used to determine how well each APD(60) (APD(60n)) was predicted by V(max) of that AP, the four previous DIs (n-1, n - 2, n - 3, n - 4), and the three previous APD(60)s (n-1, n - 2, n - 3). V(max) entered in the regression equation significantly more often (86% of VF episodes) than either APD((n-1)) (47% of episodes) or DI((n-1)) (58% of episodes). When these three variables entered first or second, their coefficients were almost always positive, consistent with a longer APD associated with 1) a larger V(max), 2) a longer APD((n-1)), and 3) a longer DI((n-1)). R(2) of the regression for all entered variables was 0.51 +/- 0.01 (mean +/- SD). During the first 20 s of VF in swine, V(max) is a more important determinant of APD than the previous DI (restitution) or the previous APD (memory). All variables together account for only one-half of APD variation during VF.     

Action potential characterization in intact mouse heart: steady-state cycle length dependence and electrical restitution

Transgenic mice have been increasingly utilized to investigate the molecular mechanisms of cardiac arrhythmias, yet the rate dependence of the murine action potential duration and the electrical restitution curve (ERC) remain undefined. In the present study, 21 isolated, Langendorff-perfused, and atrioventricular node-ablated mouse hearts were studied. Left ventricular and left atrial action potentials were recorded using a validated miniaturized monophasic action potential probe. Murine action potentials (AP) were measured at 30, 50, 70, and 90% repolarization (APD(30)-APD(90)) during steady-state pacing and varied coupling intervals to determine ERCs. Murine APD showed rate adaptation as well as restitution properties. The ERC time course differed dramatically between early and late repolarization: APD(30) shortened with increasing S1-S2 intervals, whereas APD(90) was prolonged. When fitted with a monoexponential function, APD(30) reached plateau values significantly faster than APD(90) (tau = 29 +/- 2 vs. 78 +/- 6 ms, P < 0.01, n = 12). The slope of early APD(90) restitution was significantly <1 (0.16 +/- 0.02). Atrial myocardium had shorter final repolarization and significantly faster ERCs that were shifted leftward compared with ventricular myocardium. Recovery kinetics of intracellular Ca(2+) transients recorded from isolated ventricular myocytes at 37 degrees C (tau = 93 +/- 4 ms, n = 18) resembled the APD(90) ERC kinetics. We conclude that mouse myocardium shows AP cycle length dependence and electrical restitution properties that are surprisingly similar to those of larger mammals and humans.     

Spatial heterogeneity of the restitution portrait in rabbit epicardium

Spatial heterogeneity of repolarization can provide a substrate for reentry to occur in myocardium. This heterogeneity may result from spatial differences in action potential duration (APD) restitution. The restitution portrait (RP) measures many aspects of rate-dependent restitution: the dynamic restitution curve (RC), S1-S2 RC, and short-term memory response. We used the RP to characterize epicardial patterns of spatial heterogeneity of restitution that were repeatable across animals. New Zealand White rabbit ventricles were paced from the epicardial apex, midventricle, or base, and optical action potentials were recorded from the same three regions. A perturbed downsweep pacing protocol was applied that measured the RP over a range of cycle lengths from 1,000 to 140 ms. The time constant of short-term memory measured close to the stimulus was dependent on location. In the midventricle the mean time constant was 19.1 +/- 1.1 s, but it was 39% longer at the apex (P < 0.01) and 23% longer at the base (P = 0.03). The S1-S2 RC slope was dependent on pacing site (P = 0.015), with steeper slope when pacing from the apex than from the base. There were no significant repeatable spatial patterns in steady-state APD at all cycle lengths or in dynamic RC slope. These results indicate that transient patterns of epicardial heterogeneity of APD may occur after a change in pacing rate. Thus it may affect cardiac electrical stability at the onset of a tachycardia or during a series of ectopic beats. Differences in restitution with respect to pacing site suggest that vulnerability may be affected by the location of reentry or ectopic foci.     

Nonlinear dynamics of two-dimensional cardiac action potential duration mapping model with memory

The aim of this work is the analysis of the nonlinear dynamics of two-dimensional mapping model of cardiac action potential duration (2D-map APD) with memory derived from one dimensional map (1D-map). Action potential duration (APD) restitution, which relates APD to the preceding diastolic interval (DI), is a useful tool for predicting cardiac arrhythmias. For a constant rate of stimulation the short action potential during alternans is followed by a longer DI and inversely. It has been suggested that these differences in DI are responsible for the occurrence and maintenance of APD alternans. We focus our attention on the observed bifurcations produced by a change in the stimulation period and a fixed value of a particular parameter in the model. This parameter provides new information about the dynamics of the APD with memory, such as the occurrence of bistabilities not previously described in the literature, as well as the fact that synchronization rhythms occur in different ways and in a new fashion as the stimulation frequency increases. Moreover, we show that this model is flexible enough as to accurately reflect the chaotic dynamics properties of the APD: we have highlighted the fractal structure of the strange attractor of the 2D-map APD, and we have characterized chaos by tools such as the calculation of the Lyapunov exponents, the fractal dimension and the Kolmogorov entropy, with the next objective of refining the study of the nonlinear dynamics of the duration of the action potential and to apply methods of controlling chaos.

     

Sildenafil-nitric oxide donor combination promotes ventricular tachyarrhythmias in the swine right ventricle

We tested the hypothesis that sildenafil, singly or in combination with nitric oxide (NO) donors, promotes ventricular tachycardia (VT) and ventricular fibrillation (VF). Vulnerability to VT/VF was tested by rapid pacing in eight isolated normal swine right ventricles (RV). The endocardial activation was optically mapped, and the dynamic action potential duration (APD) restitution curves were constructed with metal microelectrodes. At baseline, no VT/VF could be induced. Sildenafil (0.2 microg/ml) or NO donor singly or in combination did not alter VT/VF vulnerability. However, when 2 microg/ml sildenafil was combined with NO donors, the incidence of VT and VF rose significantly (P < 0.01). VT with a single periodic wavefront was induced in five of eight RVs, and VF with multiple wavefronts was induced in all eight RVs. The sildenafil-NO donor pro-VT/VF combination significantly increased the maximum slope of the APD restitution curve and the amplitude of the APD alternans. The pro-VT/VF effects of sildenafil were reversible after drug-free Tyrode solution perfusion. We conclude that a sildenafil (2 microg/ml) and NO donor combination increases VT/VF vulnerability in the normal RV by a mechanism compatible with the restitution hypothesis.     

Cardiac mechano-electric feedback and electrical restitution in humans

Electrical restitution in the heart is the property whereby the action potential duration and conduction velocity of a beat of altered cycle length vary according to its immediacy to the preceding basic beat--the coupling interval, usually the diastolic interval. In general, action potential duration (APD) increases with increasing coupling interval, and the relation between action potential duration and the preceding diastolic interval describes the APD restitution curve. The latter has recently been the focus of considerable interest since the steepness of the initial part of the restitution curve plays an important role in electrical stability and arrhythmogenesis. Mechanical stretch has been shown to alter APD and hence refractoriness either through stretch activated channels or by influencing calcium cycling. Such an effect on refractoriness has been proposed as a mechanism of arrhythmogenesis particularly if spatially inhomogeneities manifest within the heart. Here, we review (1) the spatial and temporal characteristics of APD restitution in humans; (2) previously reported work showing that mechanical loading differentially effects APD of interpolated beats of altered cycle length, and hence alters the slope of the APD restitution curve; and (3) evidence that inhomogeneity of APD restitution slope may be an important factor in arrhythmogenesis.     

The Interrelations among Stochastic Pacing,Stability, and Memory in the Heart

Low pacing variabilty in the heart has been clinically reported as a risk factor for lethal cardiac arrhythmias and arrhythmic death. In a previous simulation study, we demonstrated that stochastic pacing sustains an antiarrhythmic effect by moderating the slope of the action potential duration (APD) restitution curve, by reducing the propensity of APD alternans, converting discordant to concordant alternans, and ultimately preventing wavebreaks. However, the dynamic mechanisms relating pacing stochasticity to tissue stability are not yet known. In this work, we develop a mathematical framework to describe the APD signal using an autoregressive stochastic model, and we establish the interrelations between stochastic pacing, cardiac memory, and cardiac stability, as manifested by the degree of APD alternans. Employing stability analysis tools, we show that increased stochasticity in the ventricular tissue activation sequence works to lower the maximal absolute eigenvalues of the stochastic model, thereby contributing to increased stability. We also show that the memory coefficients of the autoregressive model are modulated by pacing stochasticity in a nonlinear, biphasic way, so that for exceedingly high levels of pacing stochasticity, the antiarrhythmic effect is hampered by increasing APD variance. This work may contribute to establishment of an optimal antiarrhythmic pacing protocol in a future study.     

The Interrelations among Stochastic Pacing,Stability, and Memory in the Heart

Low pacing variabilty in the heart has been clinically reported as a risk factor for lethal cardiac arrhythmias and arrhythmic death. In a previous simulation study, we demonstrated that stochastic pacing sustains an antiarrhythmic effect by moderating the slope of the action potential duration (APD) restitution curve, by reducing the propensity of APD alternans, converting discordant to concordant alternans, and ultimately preventing wavebreaks. However, the dynamic mechanisms relating pacing stochasticity to tissue stability are not yet known. In this work, we develop a mathematical framework to describe the APD signal using an autoregressive stochastic model, and we establish the interrelations between stochastic pacing, cardiac memory, and cardiac stability, as manifested by the degree of APD alternans. Employing stability analysis tools, we show that increased stochasticity in the ventricular tissue activation sequence works to lower the maximal absolute eigenvalues of the stochastic model, thereby contributing to increased stability. We also show that the memory coefficients of the autoregressive model are modulated by pacing stochasticity in a nonlinear, biphasic way, so that for exceedingly high levels of pacing stochasticity, the antiarrhythmic effect is hampered by increasing APD variance. This work may contribute to establishment of an optimal antiarrhythmic pacing protocol in a future study.     

The Transfer Functions of Cardiac Tissue during Stochastic Pacing

The restitution properties of cardiac action potential duration (APD) and conduction velocity (CV) are important factors in arrhythmogenesis. They determine alternans, wavebreak, and the patterns of reentrant arrhythmias. We developed a novel approach to characterize restitution using transfer functions. Transfer functions relate an input and an output quantity in terms of gain and phase shift in the complex frequency domain. We derived an analytical expression for the transfer function of interbeat intervals (IBIs) during conduction from one site (input) to another site downstream (output). Transfer functions can be efficiently obtained using a stochastic pacing protocol. Using simulations of conduction and extracellular mapping of strands of neonatal rat ventricular myocytes, we show that transfer functions permit the quantification of APD and CV restitution slopes when it is difficult to measure APD directly. We find that the normally positive CV restitution slope attenuates IBI variations. In contrast, a negative CV restitution slope (induced by decreasing extracellular [K⁺]) amplifies IBI variations with a maximum at the frequency of alternans. Hence, it potentiates alternans and renders conduction unstable, even in the absence of APD restitution. Thus, stochastic pacing and transfer function analysis represent a powerful strategy to evaluate restitution and the stability of conduction.     

Stochastic Cardiac Pacing Increases Ventricular Electrical Stability—A Computational Study

The ventricular tissue is activated in a stochastic rather than in a deterministic rhythm due to the inherent heart rate variability (HRV). Low HRV is a known predictor for arrhythmia events and traditionally is attributed to autonomic nervous system tone damage. Yet, there is no model that directly assesses the antiarrhythmic effect of pacing stochasticity per se. One-dimensional (1D) and two-dimensional (2D) human ventricular tissues were modeled, and both deterministic and stochastic pacing protocols were applied. Action potential duration restitution (APDR) and conduction velocity restitution (CVR) curves were generated and analyzed, and the propensity and characteristics of action potential duration (APD) alternans were investigated. In the 1D model, pacing stochasticity was found to sustain a moderating effect on the APDR curve by reducing its slope, rendering the tissue less arrhythmogenic. Moreover, stochasticity was found to be a significant antagonist to the development of concordant APD alternans. These effects were generally amplified with increased variability in the pacing cycle intervals. In addition, in the 2D tissue configuration, stochastic pacing exerted a protective antiarrhythmic effect by reducing the spatial APD heterogeneity and converting discordant APD alternans to concordant ones. These results suggest that high cardiac pacing stochasticity is likely to reduce the risk of cardiac arrhythmias in patients.     

Electrical refractory period restitution and spiral wave reentry in simulated cardiac tissue

Theoretical and experimental studies have shown that restitution of the cardiac action potential (AP) duration (APD) plays a major role in predisposing ventricular tachycardia to degenerate to ventricular fibrillation, whereas its role in atrial fibrillation is unclear. We used the Courtemanche human atrial cell model and the Luo-Rudy guinea pig ventricular model to compare the roles of electrical restitution in destabilizing spiral wave reentry in simulated two-dimensional homogeneous atrial and ventricular tissue. Because atrial AP morphology is complex, we also validated the usefulness of effective refractory period (ERP) restitution. ERP restitution correlated best with APD restitution at transmembrane potentials greater than or equal to -62 mV, and its steepness was a reliable predictor of spiral wave phenotype (stable, meandering, hypermeandering, and breakup) in both atrial and ventricular tissue. Spiral breakup or single hypermeandering spirals occurred when the slope of ERP restitution exceeded 1 at short diastolic intervals. Thus ERP restitution, which is easier to measure clinically than APD restitution, is a reliable determinant of spiral wave stability in simulated atrial and ventricular tissue.     

Effects of amiodarone on wave front dynamics during ventricular fibrillation in isolated swine right ventricle

The effects of acute amiodarone infusion on dynamics of ventricular fibrillation (VF) are unclear. Six isolated swine right ventricles (RVs) were studied in vitro. Activation patterns during VF were mapped optically, whereas action potentials were recorded with a glass microelectrode. At baseline, VF was associated with frequent spontaneous wave breaks. Amiodarone (2.5 microg/ml) reduced spontaneous wave breaks and increased the cycle length (CL) of VF from 83.3 +/- 17.8 ms at baseline to 118.4 +/- 25.8 ms during infusion (P < 0.05). Amiodarone increased the reentrant wave front CL (114.4 +/- 15.5 vs. 78.2 +/- 19.0 ms, P < 0.05) and central core area (4.1 +/- 3.8 vs. 0.9 +/- 0.3 mm2, P < 0.05). Within 30 min of infusion, VF terminated (n = 1), converted to ventricular tachycardia (VT) (n = 1) or continued at a slower rate (n = 4). Amiodarone flattened the APD restitution curves. We conclude that amiodarone reduced spontaneous wave breaks. It might terminate VF or convert VF to VT. These effects were associated with the flattening of APD restitution slope and increased core size of reentrant wave fronts.