Stochastic pacing reveals the propensity to cardiac action potential alternans and uncovers its underlying dynamics

The electrical restitution of the non-propagated cardiac ventricular action potential

Sudden changes in pacing cycle length are frequently associated with repolarization abnormalities initiating cardiac arrhythmias, and physiologists have long been interested in measuring the likelihood of these events before their manifestation. A marker of repolarization stability has been found in the electrical restitution (ER), the response of the ventricular action potential duration to a pre- or post-mature stimulation, graphically represented by the so-called ER curve. According to the restitution hypothesis (ERH), the slope of this curve provides a quantitative discrimination between stable repolarization and proneness to arrhythmias. ER has been studied at the body surface, whole organ, and tissue level, and ERH has soon become a key reference point in theoretical, clinical, and pharmacological studies concerning arrhythmia development, and, despite criticisms, it is still widely adopted. The ionic mechanism of ER and cellular applications of ERH are covered in the present review. The main criticism on ERH concerns its dependence from the way ER is measured. Over the years, in fact, several different experimental protocols have been established to measure ER, which are also described in this article. In reviewing the state-of-the art on cardiac cellular ER, I have introduced a notation specifying protocols and graphical representations, with the aim of unifying a sometime confusing nomenclature, and providing a physiological tool, better defined in its scope and limitations, to meet the growing expectations of clinical and pharmacological research.

Advances in Cardiac Pacing: Arrhythmia Prediction, Prevention and Control Strategies

Cardiac arrhythmias constitute a tremendous burden on healthcare and are the leading cause of mortality worldwide. An alarming number of people have been reported to manifest sudden cardiac death as the first symptom of cardiac arrhythmias, accounting for about 20% of all deaths annually. Furthermore, patients prone to atrial tachyarrhythmias such as atrial flutter and fibrillation often have associated comorbidities including hypertension, ischemic heart disease, valvular cardiomyopathy and increased risk of stroke. Technological advances in electrical stimulation and sensing modalities have led to the proliferation of medical devices including pacemakers and implantable defibrillators, aiming to restore normal cardiac rhythm. However, given the complex spatiotemporal dynamics and non-linearity of the human heart, predicting the onset of arrhythmias and preventing the transition from steady state to unstable rhythms has been an extremely challenging task. Defibrillatory shocks still remain the primary clinical intervention for lethal ventricular arrhythmias, yet patients with implantable cardioverter defibrillators often suffer from inappropriate shocks due to false positives and reduced quality of life. Here, we aim to present a comprehensive review of the current advances in cardiac arrhythmia prediction, prevention and control strategies. We provide an overview of traditional clinical arrhythmia management methods and describe promising potential pacing techniques for predicting the onset of abnormal rhythms and effectively suppressing cardiac arrhythmias. We also offer a clinical perspective on bridging the gap between basic and clinical science that would aid in the assimilation of promising anti-arrhythmic pacing strategies.

Thermal modulation of epicardial Ca2+ dynamics uncovers molecular mechanisms of Ca2+ alternans

Ca²⁺ alternans (Ca-Alts) are alternating beat-to-beat changes in the amplitude of Ca²⁺ transients that frequently occur during tachycardia, ischemia, or hypothermia that can lead to sudden cardiac death. Ca-Alts appear to result from a variation in the amount of Ca²⁺ released from the sarcoplasmic reticulum (SR) between two consecutive heartbeats. This variable Ca²⁺ release has been attributed to the alternation of the action potential duration, delay in the recovery from inactivation of RYR Ca²⁺ release channel (RYR2), or an incomplete Ca²⁺ refilling of the SR. In all three cases, the RYR2 mobilizes less Ca²⁺ from the SR in an alternating manner, thereby generating an alternating profile of the Ca²⁺ transients. We used a new experimental approach, fluorescence local field optical mapping (FLOM), to record at the epicardial layer of an intact heart with subcellular resolution. In conjunction with a local cold finger, a series of images were recorded within an area where the local cooling induced a temperature gradient. Ca-Alts were larger in colder regions and occurred without changes in action potential duration. Analysis of the change in the enthalpy and Q₁₀ of several kinetic processes defining intracellular Ca²⁺ dynamics indicated that the effects of temperature change on the relaxation of intracellular Ca²⁺ transients involved both passive and active mechanisms. The steep temperature dependency of Ca-Alts during tachycardia suggests Ca-Alts are generated by insufficient SERCA-mediated Ca²⁺ uptake into the SR. We found that Ca-Alts are heavily dependent on intra-SR Ca²⁺ and can be promoted through partial pharmacologic inhibition of SERCA2a. Finally, the FLOM experimental approach has the potential to help us understand how arrhythmogenesis correlates with the spatial distribution of metabolically impaired myocytes along the myocardium.

Spatially Discordant Repolarization Alternans in the Absence of Conduction Velocity Restitution

Spatially discordant alternans (SDA) of action potential duration (APD) has been widely observed in cardiac tissue and is linked to cardiac arrhythmogenesis. Theoretical studies have shown that conduction velocity restitution (CVR) is required for the formation of SDA. However, this theory is not completely supported by experiments, indicating that other mechanisms may exist. In this study, we carried out computer simulations using mathematical models of action potentials to investigate the mechanisms of SDA in cardiac tissue. We show that when CVR is present and engaged, such as fast pacing from one side of the tissue, the spatial pattern of APD in the tissue undergoes either spatially concordant alternans or SDA, independent of initial conditions or tissue heterogeneities. When CVR is not engaged, such as simultaneous pacing of the whole tissue or under normal/slow heart rates, the spatial pattern of APD in the tissue can have multiple solutions, including spatially concordant alternans and different SDA patterns, depending on heterogeneous initial conditions or pre-existing repolarization heterogeneities. In homogeneous tissue, curved nodal lines are not stable, which either evolve into straight lines or disappear. However, in heterogeneous itssue, curved nodal lines can be stable, depending on their initial locations and shapes relative to the structure of the heterogeneity. Therefore, CVR-induced SDA and non-CVR-induced SDA exhibit different dynamical properties, which may be responsible for the different SDA properties observed in experimental studies and arrhythmogenesis in different clinical settings.

Short-Long Heart Rate Variation Increases Dispersion of Action Potential Duration in Long QT Type 2 Transgenic Rabbit Model

The initiation of polymorphic ventricular tachycardia in long QT syndrome type 2 (LQT2) has been associated with a characteristic ECG pattern of short-long RR intervals. We hypothesize that this characteristic pattern increases APD dispersion in LQT2, thereby promoting arrhythmia. We investigated APD dispersion and its dependence on two previous cycle lengths (CLs) in transgenic rabbit models of LQT2, LQT1, and their littermate controls (LMC) using random stimulation protocols. The results show that the short-long RR pattern was associated with a larger APD dispersion in LQT2 but not in LQT1 rabbits. The multivariate analyses of APD as a function of two previous CLs (APD_n = C + α₁CL_n−1 + α₂CL_n−2) showed that α₁ (APD restitution slope) is largest and heterogeneous in LQT2 but uniform in LQT1, enhancing APD dispersion under long CL_n−1 in LQT2. The α₂ (short-term memory) was negative in LQT2 while positive in LQT1, and the spatial pattern of α₁ was inversely correlated to α₂ in LQT2, which explains why a short-long combination causes a larger APD dispersion in LQT2 but not in LQT1 rabbits. In conclusion, short-long RR pattern increased APD dispersion only in LQT2 rabbits through heterogeneous APD restitution and the short-term memory, underscoring the genotype-specific triggering of arrhythmias in LQT syndrome.

Restitution and Stability of Human Ventricular Action Potential at High and Variable Pacing Rate

Despite the key role of beat-to-beat action potential (AP) variability in the onset of ventricular arrhythmias at high pacing rate, the knowledge of the involved dynamics and of effective prognostic parameters is largely incomplete. Electrical restitution (ER), the way AP duration (APD) senses changes in preceding cycle length (CL), has been used to monitor transition to arrhythmias. The use of standard ER (sER), though, is controversial, not always suitable for in vivo and only rarely for clinical applications. By means of simulations on a human ventricular AP model, I investigate the dynamics of APD at high pacing rate under sinusoidally, saw-tooth, and randomly variable pacing CLs. AP sequences were compared in terms of beat-to-beat restitution (btb-ER) and of the collections of sER curves generated from each beat. A definition of APD stability is also proposed, based on successive APD changes introduced in an AP sequence by a premature beat. The explored CL range includes values leading to APD alternans under constant pacing. Three different types of response to CL variability were found, corresponding to progressively higher rate of beat-to-beat CL changes. Low rates (∼1 ms/beat) generate a btb-ER dominated by steady-state rate dependence of APD (type 1), intermediate rates (∼5 ms/beat) lead to a btb-ER similar to a single sER (type 2), and high rates (∼20 ms/beat) to hysteretic btb-ER under periodic pacing and to a vertically spread btb-ER in the case of random pacing (type 3). Stability of AP repolarization always increases with the rate of CL changes. Thus, rather than looking at sER slope, which requires additional interventions during the recording of cardiac electrical activity, this study provides rationale for the use of btb-ER representations as predictors of repolarization stability under extreme pacing conditions, known to be critical for the arrhythmia development.

Isostable reduction of oscillators with piecewise smooth dynamics and complex Floquet multipliers

Phase-amplitude reduction is a widely applied technique in the study of limit cycle oscillators with the ability to represent a complicated and high-dimensional dynamical system in a more analytically tractable set of coordinates. Recent work has focused on the use of isostable coordinates, which characterize the transient decay of solutions toward a periodic orbit, and can ultimately be used to increase the accuracy of these reduced models. The breadth of systems to which this phase-amplitude reduction strategy can be applied, however, is still rather limited. In this work, the theory of phase-amplitude reduction using isostable coordinates is further developed to accommodate a broader set of dynamical systems. In the first part, limit cycles of piecewise smooth dynamical systems are considered and strategies are developed to compute the associated reduced equations. In the second part, the notion of isostable coordinates for complex-valued Floquet multipliers is introduced, resulting in one phaselike coordinate and one amplitudelike coordinate for each pair of complex conjugate Floquet multipliers. Examples are given with relevance to piecewise smooth representations of excitable cardiomyocytes and the relationship between the reduced coordinate system and the emergence of cardiac alternans is discussed. Also, phase-amplitude reduction is implemented for a chaotic, externally forced pendulum with complex Floquet multipliers and a resulting control strategy for the stabilization of its periodic solution is investigated.

Increased Vulnerability to Atrial Fibrillation Is Associated With Increased Susceptibility to Alternans in Old Sheep

Background Atrial fibrillation ( AF ) is common in the elderly, but rare in the young; however, the changes that occur with age that promote AF are not fully understood. Action potential ( AP ) alternans may be involved in the initiation of AF . Using a translationally relevant model, we investigated whether age-associated atrial vulnerability to AF was associated with susceptibility to AP alternans. Methods and Results AF was induced in conscious young and old sheep using 50 Hz burst pacing. Old sheep were more vulnerable to AF . Monophasic and cellular AP s were recorded from the right atrium in vivo and from myocytes isolated from the left and right atrial appendages. AP alternans occurred at lower stimulation frequencies in old sheep than young in vivo (old, 3.0±0.1 Hz; young, 3.3±0.1 Hz; P<0.05) and in isolated myocytes (old, 1.6±0.1 Hz; young, 2.0±0.1 Hz; P<0.05). Simultaneous recordings of [Ca2+]i and membrane potential in myocytes showed that alternans of AP s and [Ca2+]i often occurred together. However, at low stimulation rates [Ca2+]i alternans could occur without AP alternans, whereas at high stimulation rates AP alternans could still be observed despite disabling Ca2+ cycling using thapsigargin. Conclusions We have shown, for the first time in a large mammalian model, that aging is associated with increased duration of AF and susceptibility to AP alternans. We suggest that instabilities in Ca2+ handling initiate alternans at low stimulation rates, but that AP restitution alone can sustain alternans at higher rates.

Mechanisms linking T-wave alternans to spontaneous initiation of ventricular arrhythmias in rabbit models of long QT syndrome

KEY POINTS

T-wave alternans (TWA) and T-wave lability (TWL) are precursors of ventricular arrhythmias in long QT syndrome; however, the mechanistic link remains to be clarified. Computer simulations show that action potential duration (APD) prolongation and slowed heart rates promote APD alternans and chaos, manifesting as TWA and TWL, respectively. Regional APD alternans and chaos can exacerbate pre-existing or induce de novo APD dispersion, which combines with enhanced I_Ca,L to result in premature ventricular complexes (PVCs) originating from the APD gradient region. These PVCs can directly degenerate into re-entrant arrhythmias without the need for an additional tissue substrate or further exacerbate the APD dispersion to cause spontaneous initiation of ventricular arrhythmias. Experiments conducted in transgenic long QT rabbits show that PVC alternans occurs at slow heart rates, preceding spontaneous intuition of ventricular arrhythmias.

ABSTRACT

T-wave alternans (TWA) and irregular beat-to-beat T-wave variability or T-wave lability (TWL), the ECG manifestations of action potential duration (APD) alternans and variability, are precursors of ventricular arrhythmias in long QT syndromes. TWA and TWL in patients tend to occur at normal heart rates and are usually potentiated by bradycardia. Whether or how TWA and TWL at normal or slow heart rates are causally linked to arrhythmogenesis remains unknown. In the present study, we used computer simulations and experiments of a transgenic rabbit model of long QT syndrome to investigate the underlying mechanisms. Computer simulations showed that APD prolongation and slowed heart rates caused early afterdepolarization-mediated APD alternans and chaos, manifesting as TWA and TWL, respectively. Regional APD alternans and chaos exacerbated pre-existing APD dispersion and, in addition, APD chaos could also induce APD dispersion de novo via chaos desynchronization. Increased APD dispersion, combined with substantially enhanced I_Ca,L , resulted in a tissue-scale dynamical instability that gave rise to the spontaneous occurrence of unidirectionally propagating premature ventricular complexes (PVCs) originating from the APD gradient region. These PVCs could directly degenerate into re-entrant arrhythmias without the need for an additional tissue substrate or could block the following sinus beat to result in a longer RR interval, which further exacerbated the APD dispersion giving rise to the spontaneous occurrence of ventricular arrhythmias. Slow heart rate-induced PVC alternans was observed in experiments of transgenic LQT2 rabbits under isoproterenol, which was associated with increased APD dispersion and spontaneous occurrence of ventricular arrhythmias, in agreement with the theoretical predictions.

Stochastic Pacing Inhibits Spatially Discordant Cardiac Alternans

Depressed heart rate variability is a well-established risk factor for sudden cardiac death in survivors of acute myocardial infarction and for those with congestive heart failure. Although measurements of heart rate variability provide a valuable prognostic tool, it is unclear whether reduced heart rate variability itself is proarrhythmic or if it simply correlates with the severity of autonomic nervous system dysfunction. In this work, we investigate a possible mechanism by which heart rate variability could protect against cardiac arrhythmia. Specifically, in numerical simulations, we observe an inverse relationship between the variance of stochastic pacing and the occurrence of spatially discordant alternans, an arrhythmia that is widely believed to facilitate the development of cardiac fibrillation. By analyzing the effects of conduction velocity restitution, cellular dynamics, electrotonic coupling, and stochastic pacing on the nodal dynamics of spatially discordant alternans, we provide intuition for this observed behavior and propose control strategies to inhibit discordant alternans.

Cardiac dynamics: Alternans and arrhythmogenesis

Pre-existing heterogeneities present in cardiac tissue are essential for maintaining the normal electrical and mechanical functions of the heart. Exacerbation of such heterogeneities or the emergence of dynamic factors can produce repolarization alternans, which are beat-to-beat alternations in the action potential time course. Traditionally, this was explained by restitution, but additional factors, such as cardiac memory, calcium handling dynamics, refractory period restitution, and mechano-electric feedback, are increasingly recognized as the underlying causes. The aim of this article is to review the mechanisms that generate cardiac repolarization alternans and convert spatially concordant alternans to the more arrhythmogenic spatially discordant alternans. This is followed by a discussion on how alternans generate arrhythmias in a number of clinical scenarios, and concluded by an outline of future therapeutic targets for anti-arrhythmic therapy.