Mathematical analysis of dynamics of cardiac memory and accommodation: theory and experiment

Decreasing the slope of the dynamic, but not conventional, restitution curves is antifibrillatory. Cardiac memory/accommodation underlies the difference. We measured diastolic interval (DI) and action potential duration (APD) in epicardial, endocardial, and Purkinje tissue from eight dogs. Consecutive 100-stimulus trains were given to study transitions between basic cycle lengths (BCL) ranging from 400 to 1,300 ms. (DI,APD) pairs aligned immediately on the line DI + APD = BCL (64/67) or oscillated (3/67). The shifting effect of up to 10 extrastimuli on restitution curves was also measured. These curves were fit with the equation APD = alpha + beta exp(-DI/tau), where alpha is asymptote, beta is drop, and tau is time constant. Linear regression of the parameters against the number of extrastimuli showed that premature and postmature stimuli decreased and increased alpha and beta and increased and decreased tau, respectively. Analysis of a mathematical model treating memory as an exponentially decreasing shift of restitution curves shows that oscillatory DI,APD is expected with large DeltaBCL, steep restitution slope, or increased cardiac accommodation. The model explains phase shifts and suggests a common mechanism for Purkinje and myocardial electrical alternans.     

Uncovering the dynamics of cardiac systems using stochastic pacing and frequency domain analyses

Alternans of cardiac action potential duration (APD) is a well-known arrhythmogenic mechanism which results from dynamical instabilities. The propensity to alternans is classically investigated by examining APD restitution and by deriving APD restitution slopes as predictive markers. However, experiments have shown that such markers are not always accurate for the prediction of alternans. Using a mathematical ventricular cell model known to exhibit unstable dynamics of both membrane potential and Ca²⁺ cycling, we demonstrate that an accurate marker can be obtained by pacing at cycle lengths (CLs) varying randomly around a basic CL (BCL) and by evaluating the transfer function between the time series of CLs and APDs using an autoregressive-moving-average (ARMA) model. The first pole of this transfer function corresponds to the eigenvalue (λ_alt) of the dominant eigenmode of the cardiac system, which predicts that alternans occurs when λ_alt≤−1. For different BCLs, control values of λ_alt were obtained using eigenmode analysis and compared to the first pole of the transfer function estimated using ARMA model fitting in simulations of random pacing protocols. In all versions of the cell model, this pole provided an accurate estimation of λ_alt. Furthermore, during slow ramp decreases of BCL or simulated drug application, this approach predicted the onset of alternans by extrapolating the time course of the estimated λ_alt. In conclusion, stochastic pacing and ARMA model identification represents a novel approach to predict alternans without making any assumptions about its ionic mechanisms. It should therefore be applicable experimentally for any type of myocardial cell.     

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.     

Formation of Spatially Discordant Alternans Due to Fluctuations and Diffusion of Calcium

Spatially discordant alternans (SDA) of action potential duration (APD) is a phenomenon where different regions of cardiac tissue exhibit an alternating sequence of APD that are out-of-phase. SDA is arrhythmogenic since it can induce spatial heterogeneity of refractoriness, which can cause wavebreak and reentry. However, the underlying mechanisms for the formation of SDA are not completely understood. In this paper, we present a novel mechanism for the formation of SDA in the case where the cellular instability leading to alternans is caused by intracellular calcium (Ca) cycling, and where Ca transient and APD alternans are electromechanically concordant. In particular, we show that SDA is formed when rapidly paced cardiac tissue develops alternans over many beats due to Ca accumulation in the sarcoplasmic reticulum (SR). The mechanism presented here relies on the observation that Ca cycling fluctuations dictate Ca alternans phase since the amplitude of Ca alternans is small during the early stages of pacing. Thus, different regions of a cardiac myocyte will typically develop Ca alternans which are opposite in phase at the early stages of pacing. These subcellular patterns then gradually coarsen due to interactions with membrane voltage to form steady state SDA of voltage and Ca on the tissue scale. This mechanism for SDA is distinct from well-known mechanisms that rely on conduction velocity restitution, and a Turing-like mechanism known to apply only in the case where APD and Ca alternans are electromechanically discordant. Furthermore, we argue that this mechanism is robust, and is likely to underlie a wide range of experimentally observed patterns of SDA.     

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.     

Spatially discordant alternans in cardiomyocyte monolayers

Repolarization alternans is a harbinger of sudden cardiac death, particularly when it becomes spatially discordant. Alternans, a beat-to-beat alternation in the action potential duration (APD) and intracellular Ca (Cai), can arise from either tissue heterogeneities or dynamic factors. Distinguishing between these mechanisms in normal cardiac tissue is difficult because of inherent complex three-dimensional tissue heterogeneities. To evaluate repolarization alternans in a simpler two-dimensional cardiac substrate, we optically recorded voltage and/or Cai in monolayers of cultured neonatal rat ventricular myocytes during rapid pacing, before and after exposure to BAY K 8644 to enhance dynamic factors promoting alternans. Under control conditions (n = 37), rapid pacing caused detectable APD alternans in 81% of monolayers, and Cai transient alternans in all monolayers, becoming spatially discordant in 62%. After BAY K 8644 (n = 28), conduction velocity restitution became more prominent, and APD and Cai alternans developed and became spatially discordant in all monolayers, with an increased number of nodal lines separating out-of-phase alternating regions. Nodal lines moved closer to the pacing site with faster pacing rates and changed orientation when the pacing site was moved, as predicted for the dynamically generated, but not heterogeneity-based, alternans. Spatial APD gradients during spatially discordant alternans were sufficiently steep to induce conduction block and reentry. These findings indicate that spatially discordant alternans severe enough to initiate reentry can be readily induced by pacing in two-dimensional cardiac tissue and behaves according to predictions for a predominantly dynamically generated mechanism.     

Toward prediction of the local onset of alternans in the heart

A beat-to-beat variation in the cardiac action potential duration is a phenomenon known as alternans. Alternans has been linked to ventricular fibrillation, and thus the ability to predict the onset of alternans could be clinically beneficial. Theoretically, it has been proposed that the slope of a restitution curve, which relates the duration of the action potential to the preceding diastolic interval, can predict the onset of alternans. Experimentally, however, this hypothesis has not been consistently proven, mainly because of the intrinsic complexity of the dynamics of cardiac tissue. It was recently shown that the restitution portrait, which combines several restitution curves simultaneously, is associated with the onset of alternans in isolated myocytes. Our main purpose in this study was to determine whether the restitution portrait is correlated with the onset of alternans in the heart, where the dynamics include a spatial complexity. We performed optical mapping experiments in isolated Langendorff-perfused rabbit hearts in which alternans was induced by periodic pacing at different frequencies, and identified the local onset of alternans, B^onset. We identified two regions of the heart: the area that exhibited alternans at B^onset (1:1_alt) and the area that did not (1:1). We constructed two-dimensional restitution portraits for the epicardial surface of the heart and measured the spatial distribution of three different slopes (the dynamic restitution slope, , and two local S1-S2 slopes, S₁₂ and ) separately for these two regions. We found that the S₁₂ and slopes differed significantly between the 1:1_alt and 1:1 regions just before the onset of alternans, and slopes were statistically similar. In addition, we found that the slopes of the dynamic restitution curve S_dyn were also statistically similar between these two regions. On the other hand, the quantitative values of all slopes were significantly different from the theoretically predicted value of one. These results demonstrate that the slopes measured in the restitution portrait correlate with the onset of alternans in the heart.     

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.     

Cellular and subcellular alternans in the canine left ventricle

Previous studies indicate that action potential duration (APD) alternans is initiated in the endocardial (END) and midmyocardial (MID) regions rather than the epicardium (EPI) in the canine left ventricle (LV). This study examines regional differences in the rate dependence of Ca(2+) transient characteristics under conditions that give rise to APD and associated T wave alternans. The role of the sarcoplasmic reticulum (SR) was further evaluated by studying Ca(2+) transient characteristics in myocytes isolated from neonates, where an organized SR is poorly developed. All studies were performed in cells and tissues isolated from the canine LV. Isolated canine ENDO, MID, and EPI LV myocytes were either field stimulated or voltage clamped, and Ca(2+) transients were measured by confocal microscopy. In LV wedge preparations, increasing the basic cycle length (BCL) from 800 to 250 ms caused alternans to appear mainly in the ENDO and MID region; alternans were not observed in EPI under these conditions. Ca(2+) transient alternans developed in response to rapid pacing, appearing in EPI cells at shorter BCL compared with MID and ENDO cells (BCL=428 +/- 17 vs. 517 +/- 29 and 514 +/- 21, respectively, P < 0.05). Further increases in pacing rate resulted in the appearance of subcellular alternans of Ca(2+) transient amplitude, which also appeared in EPI at shorter BCL than in ENDO and MID cells. Ca(2+) transient alternans was not observed in neonate myocytes. We conclude that 1) there are distinct regional differences in the vulnerability to rate-dependent Ca(2+) alternans in dog LV that may be related to regional differences in SR function and Ca(2+) cycling; 2) the development of subcellular Ca(2+) alternans suggests the presence of intracellular heterogeneities in Ca(2+) cycling; and 3) the failure of neonatal cells to develop Ca(2+) alternans provides further support that SR Ca(2+) cycling is a major component in the development of these phenomena.     

Dynamical effects of diffusive cell coupling on cardiac excitation and propagation: a simulation study

Cell coupling is considered to be important for cardiac action potential propagation and arrhythmogenesis. We carried out computer simulations to investigate the effects of stimulation strength and cell-to-cell coupling on action potential duration (APD) restitution, APD alternans, and stability of reentry in models of isolated cell, one-dimensional cable, and two-dimensional tissue. Phase I formulation of the Luo and Rudy action potential model was used. We found that stronger stimulation resulted in a shallower APD restitution curve and onset of APD alternans at a faster pacing rate. Reducing diffusive coupling between cells prolonged APD. Weaker diffusive currents along the direction of propagation steepened APD restitution and caused APD alternans to occur at a slower pacing rate in tissue. Diffusive current due to curvature changed APD but had little effect on APD restitution slope and onset of instability. Heterogeneous cell coupling caused APD inhomogeneities in space. Reduction in coupling strength either uniformly or randomly had little effect on the rotation period and stability of a reentry, but random cell decoupling slowed the rotation period and, thus, stabilized the reentry, preventing it from breaking up into multiple waves. Therefore, in addition to its effects on action potential conduction velocity, diffusive cell coupling also affects APD in a rate-dependent manner, causes electrophysiological heterogeneities, and thus modulates the dynamics of cardiac excitation. These effects are brought about by the modulation of ionic current activation and inactivation.     

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.     

Inferring the cellular origin of voltage and calcium alternans from the spatial scales of phase reversal during discordant alternans

Beat-to-beat alternation of the action potential duration (APD) in paced cardiac cells has been linked to the onset of lethal arrhythmias. Both experimental and theoretical studies have shown that alternans at the single cell level can be caused by unstable membrane voltage (V(m)) dynamics linked to steep APD-restitution, or unstable intracellular calcium (Ca) cycling linked to high sensitivity of Ca release from the sarcoplasmic reticulum on sarcoplasmic reticulum Ca load. Identifying which of these two mechanisms is the primary cause of cellular alternans, however, has remained difficult since Ca and V(m) are bidirectionally coupled. Here, we use numerical simulations of a physiologically detailed ionic model to show that the origin of alternans can be inferred by measuring the length scales over which APD and Ca(i) alternans reverse phase during spatially discordant alternans. The main conclusion is that these scales are comparable to a few millimeters and equal when alternans is driven by APD restitution, but differ markedly when alternans is driven predominantly by unstable Ca cycling. In the latter case, APD alternans still reverses phase on a millimeter tissue scale due to electrotonic coupling, while Ca alternans reverses phase on a submillimeter cellular scale. These results show that experimentally accessible measurements of Ca(i) and V(m) in cardiac tissue can be used to shed light on the cellular origin of alternans.     

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.     

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.     

Feedback-control induced pattern formation in cardiac myocytes: A mathematical modeling study

Cardiac alternans is a dangerous rhythm disturbance of the heart, in which rapid stimulation elicits a beat-to-beat alternation in the action potential duration (APD) and calcium (Ca) transient amplitude of individual myocytes. Recently, “subcellular alternans”, in which the Ca transients of adjacent regions within individual myocytes alternate out-of-phase, has been observed. A previous theoretical study suggested that subcellular alternans may result during static pacing from a Turing-type symmetry breaking instability, but this was only predicted in a subset of cardiac myocytes (with negative Ca to voltage (Ca→V_m) coupling) and has never been directly verified experimentally. A recent experimental study, however, showed that subcellular alternans is dynamically induced in the remaining subset of myocytes during pacing with a simple feedback control algorithm (“alternans control”). Here we show that alternans control pacing changes the effective coupling between the APD and the Ca transient (V_m→Ca coupling), such that subcellular alternans is predicted to occur by a Turing instability in cells with positive Ca→V_m coupling. In addition to strengthening the understanding of the proposed mechanism for subcellular alternans formation, this work (in concert with previous theoretical and experimental results) illuminates subcellular alternans as a striking example of a biological Turing instability in which the diffusing morphogens can be clearly identified.     

The Rate- and Species-Dependence of Short-Term Memory in Cardiac Myocytes

Short-term memory is an intrinsic property of paced cardiac myocytes that reflects the influence of pacing history, and not just the immediately preceding diastolic interval (DI), on the action potential duration (APD). Although it is recognized that short-term memory affects the dynamics of cardiac myocytes in general, and the onset of irregular cardiac rhythm in particular, its has never been adequately quantified or measured directly in experiments or numerical simulations, mainly due to the absence of appropriate techniques. As a result, very little is known about the rate- and species dependent behavior of short-term memory. In this study, we introduce a new approach that allows one to estimate how much short-term memory, M _S, is present in the cardiac myocyte at different pacing rates. The new quantification is based on the fact that pacing history affects not only the APD, but the entire dynamics of paced cardiac myocytes, in particular the restitution curve. Using the patch clamp technique and numerical simulations, we measured short-term memory restitution—the dependence of M _S on the cycle length—in isolated rabbit and guinea pig ventricular myocytes. In both species, M _S is rate- and species-dependent, displaying a biphasic behavior as a function of cycle length. Moreover, our results indicate that there is a significant difference in M _S measured between both species at small cycle lengths. Numerical simulations suggest that the kinetics of the rapidly activating delayed rectifier potassium current I _Kr is partially responsible for this difference.     

Steeper restitution slopes across right ventricular endocardium in patients with cardiomyopathy at high risk of ventricular arrhythmias

Steep action potential duration (APD) restitution slopes (>1) and spatial APD restitution heterogeneity provide the substrate for ventricular fibrillation in computational models and experimental studies. Their relationship to ventricular arrhythmia vulnerability in human cardiomyopathy has not been defined. Patients with cardiomyopathy [left ventricular (LV) ejection fraction <40%] and no history of ventricular arrhythmias underwent risk stratification with programmed electrical stimulation or T wave alternans (TWA). Low-risk patients (n = 10) had no inducible ventricular tachycardia (VT) or negative TWA, while high-risk patients (n = 8) had inducible VT or positive TWA. Activation recovery interval (ARI) restitution slopes were measured simultaneously from 10 right ventricular (RV) endocardial sites during an S1-S2 pacing protocol. ARI restitution slope heterogeneity was defined as the coefficient of variation of slopes. Mean ARI restitution slope was significantly steeper in the high-risk group compared with the low-risk group [1.16 (SD 0.31) vs. 0.59 (SD 0.19), P = 0.0002]. The proportion of endocardial recording sites with a slope >1 was significantly larger in the high-risk patients [47% (SD 35) vs. 13% (SD 21), P = 0.022]. Spatial heterogeneity of ARI restitution slopes was similar between the two groups [29% (SD 16) vs. 39% (SD 34), P = 0.48]. There was an inverse linear relationship between the ARI restitution slope and the minimum diastolic interval (P < 0.001). In cardiomyopathic patients at high risk of ventricular arrhythmias, ARI restitution slopes along the RV endocardium are steeper, but restitution slope heterogeneity is similar compared with those at low risk. Steeper ARI restitution slopes may increase the propensity for ventricular arrhythmias in patients with impaired left ventricular function.     

Alternans Resonance and Propagation Block during Supernormal Conduction in Cardiac Tissue with Decreased [K]o

Cardiac restitution is an important factor in arrhythmogenesis. Steep positive action potential duration and conduction velocity (CV) restitution slopes promote alternans and reentrant arrhythmias. We examined the consequences of supernormal conduction (characterized by a negative CV restitution slope) on patterns of conduction and alternans in strands of Luo-Rudy model cells and in cultured cardiac cell strands. Interbeat intervals (IBIs) were analyzed as a function of distance during S1S2 protocols and during pacing at alternating cycle lengths. Supernormal conduction was induced by decreasing [K⁺]_o. In control [K⁺]_o simulations, S1S2 intervals converged toward basic cycle length with a length constant determined by both CV and the CV restitution slope. During alternant pacing, the amplitude of IBI alternans converged with a shorter length constant, determined also by the action potential duration restitution slope. In contrast, during supernormal conduction, S1S2 intervals and the amplitude of alternans diverged. This amplification (resonance) led to phase-locked or more complex alternans patterns, and then to distal conduction block. The convergence/divergence of IBIs was verified in the cultured strands, in which naturally occurring tissue heterogeneities resulted in prominent discontinuities of the spatial IBI profiles. We conclude that supernormal conduction potentiates alternans and spatial analysis of IBIs represents a powerful method to locate tissue heterogeneities.