Cardiac action potential alternans and early afterdepolarizations (EADs) are linked to cardiac arrhythmias. Periodic action potentials (period 1) in healthy conditions bifurcate to other states such as period 2 or chaos when alternans or EADs occur in pathological conditions. The mechanisms of alternans and EADs have been extensively studied under steady-state conditions, but lethal arrhythmias often occur during the transition between steady states. Why arrhythmias tend to develop during the transition is unclear. We used low-dimensional mathematical models to analyze dynamical mechanisms of transient alternans and EADs. We show that depending on the route from one state to another, action potential alternans and EADs may occur during the transition between two periodic steady states. The route taken depends on the time course of external perturbations or intrinsic signaling, such as β-adrenergic stimulation, which regulate cardiac calcium and potassium currents with differential kinetics.

T-wave alternans, a manifestation of repolarization alternans at the cellular level, is associated with lethal cardiac arrhythmias and sudden cardiac death. At the cellular level, several mechanisms can produce repolarization alternans, including: 1) electrical restitution resulting from collective ion channel recovery, which usually occurs at fast heart rates but can also occur at normal heart rates when action potential is prolonged resulting in a short diastolic interval; 2) the transient outward current, which tends to occur at normal or slow heart rates; 3) the dynamics of early afterdepolarizations, which tends to occur during bradycardia; and 4) intracellular calcium cycling alternans through its interaction with membrane voltage. In this review, we summarize the cellular mechanisms of alternans arising from these different mechanisms, and discuss their roles in arrhythmogenesis in the setting of cardiac disease.

Aims

Ventricular tachycardia (VT) and fibrillation (VF) are the most lethal cardiac arrhythmias. The degeneration of VT into VF is associated with the breakup of a spiral wave of the action potential in cardiac tissue. β-Adrenergic (βAR) signalling potentiates the L-type Ca current (ICaL) faster than the slow delayed rectifier potassium current (IKs), which transiently prolongs the action potential duration (APD) and promotes early after depolarizations. In this study, we aimed at investigating how βAR signalling affects the transition from VT to VF.

Methods and results

We used a physiologically detailed computer model of the rabbit ventricular myocyte in a two-dimensional tissue to determine how spiral waves respond to βAR activation following administration of isoproterenol. A simplified mathematical model was also used to investigate the underlying dynamics. We found that the spatiotemporal behaviour of spiral waves strongly depends on the kinetics of βAR activation. When βAR activation is rapid, a stable spiral wave turns into small fragments and its electrocardiogram reveals the transition from VT to VF. This is due to the transiently steepened APD restitution induced by the faster activation of ICaL vs. IKs upon sudden βAR activation. The spiral wave may also disappear if its transient wavelength is too large to be supported by the tissue size upon sudden strong βAR activation that prolongs APD transiently. When βAR activation is gradual, a stable spiral wave remains such, because of more limited increase in both APD and slope of APD restitution due to more contemporaneous ICaL and IKs activation.

Conclusion

Changes in APD restitution during βAR activation revealed a novel transient spiral wave dynamics; this spatiotemporal characteristic strongly depends on the protocol of isoproterenol application.

Ryanodine receptors (RyRs) mediate calcium (Ca)-induced Ca release and intracellular Ca homeostasis. In a cardiac myocyte, RyRs group into clusters of variable size from a few to several hundred RyRs, creating a spatially nonuniform intracellular distribution. It is unclear how heterogeneity of RyR cluster size alters spontaneous sarcoplasmic reticulum (SR) Ca releases (Ca sparks) and arrhythmogenic Ca waves. Here, we tested the impact of heterogeneous RyR cluster size on the initiation of Ca waves. Experimentally, we measured RyR cluster sizes at Ca spark sites in rat ventricular myocytes and further tested functional impacts using a physiologically detailed computational model with spatial and stochastic intracellular Ca dynamics. We found that the spark frequency and amplitude increase nonlinearly with the size of RyR clusters. Larger RyR clusters have lower SR Ca release threshold for local Ca spark initiation and exhibit steeper SR Ca release versus SR Ca load relationship. However, larger RyR clusters tend to lower SR Ca load because of the higher Ca leak rate. Conversely, smaller clusters have a higher threshold and a lower leak, which tends to increase SR Ca load. At the myocyte level, homogeneously large or small RyR clusters limit Ca waves (because of low load for large clusters but low excitability for small clusters). Mixtures of large and small RyR clusters potentiates Ca waves because the enhanced SR Ca load driven by smaller clusters enables Ca wave initiation and propagation from larger RyR clusters. Our study suggests that a spatially heterogeneous distribution of RyR cluster size under pathological conditions may potentiate Ca waves and thus afterdepolarizations and triggered arrhythmias.

Background

Most cardiac arrhythmias occur intermittently. As a cellular precursor of lethal cardiac arrhythmias, early afterdepolarizations (EADs) during action potentials(APs) have been extensively investigated, and mechanisms for the occurrence of EADs on a beat-to-beat basis have been proposed. However, no previous study explains slow fluctuations in EADs, which may underlie intermittency of EAD trains and consequent arrhythmias. We hypothesize that the feedback of intracellular calcium and sodium concentrations ([Na](i) and [Ca](i)) that influence membrane voltage (V) can explain EAD intermittency.

Methods and results

AP recordings in rabbit ventricular myocytes revealed intermittent EADs, with slow fluctuations between runs of APs with EADs present or absent. We then used dynamical systems analysis and detailed mathematical models of rabbit ventricular myocytes that replicate the observed behavior and investigated the underlying mechanism. We found that a dominance of inward Na-Ca exchanger current (I(NCX)) over Ca-dependent inactivation of L-type Ca current (I(CaL)) forms a positive feedback between [Ca](i) and V, thus resulting in 2 stable AP states, with and without EADs (ie, bistability). Slow changes in [Na](i) determine the transition between these 2 states, forming a bistable on-off switch of EADs. Tissue simulations showed that this bistable switch of cellular EADs provided both a trigger and a functional substrate for intermittent arrhythmias in homogeneous tissues.

Conclusions

Our study demonstrates that the interaction among V, [Ca](i), and [Na](i) causes slow on-off switching (or bistability) of AP duration in cardiac myocytes and EAD-mediated arrhythmias and suggests a novel possible mechanism for intermittency of cardiac arrhythmias.

Background

Transient outward K currents (Ito) have been reported both to suppress and to facilitate early afterdepolarizations (EADs) when repolarization reserve is reduced. Here, we used the dynamic clamp technique to analyze how Ito accounts for these paradoxical effects on EADs by influencing the dynamic evolution of repolarization reserve during the action potential.

Methods and results

Isolated patch-clamped rabbit ventricular myocytes were exposed to either oxidative stress (H2O2) or hypokalemia to induce bradycardia-dependent EADs at a long pacing cycle length of 6 s, when native rabbit Ito is substantial. EADs disappeared when the pacing cycle length was shortened to 1 s, when Ito becomes negligible because of incomplete recovery from inactivation. During 6-s pacing cycle length, EADs were blocked by the Ito blocker 4-aminopyridine, but reappeared when a virtual current with appropriate Ito-like properties was reintroduced using the dynamic clamp (n=141 trials). During 1-s pacing cycle length in the absence of 4-aminopyridine, adding a virtual Ito-like current (n=1113 trials) caused EADs to reappear over a wide range of Ito conductance (0.005-0.15 nS/pF), particularly when inactivation kinetics were slow (τinact≥20 ms) and the pedestal (noninactivating component) was small (<25% of peak Ito). Faster inactivation or larger pedestals tended to suppress EADs.

Conclusions

Repolarization reserve evolves dynamically during the cardiac action potential. Whereas sufficiently large Ito can suppress EADs, a wide range of intermediate Ito properties can promote EADs by influencing the temporal evolution of other currents affecting late repolarization reserve. These findings raise caution in targeting Ito as an antiarrhythmic strategy.

Background

Ryanodine receptors (RyR) mediate sarcoplasmic reticulum calcium (Ca²⁺) release and influence myocyte Ca²⁺ homeostasis and arrhythmias. In cardiac myocytes, RyRs are found in clusters of various sizes and shapes, and RyR cluster size may critically influence normal and arrhythmogenic Ca²⁺ spark and wave formation. However, the actual RyR cluster sizes at specific Ca²⁺ spark sites have never been measured in the physiological setting.

Methods and results

Here we measured RyR cluster size and Ca²⁺ sparks simultaneously to assess how RyR cluster size influences Ca²⁺ sparks and sarcoplasmic reticulum Ca²⁺ leak. For small RyR cluster sizes (<50), Ca²⁺ spark frequency is very low but then increases dramatically at larger cluster sizes. In contrast, Ca²⁺ spark amplitude is nearly maximal even at relatively small RyR cluster size (≈10) and changes little at larger cluster size. These properties agreed with computational simulations of RyR gating within clusters.

Conclusions

Our study explains how this combination of properties may limit arrhythmogenic Ca²⁺ sparks and wave propagation (at many junctions) while preserving the efficacy and spatial synchronization of Ca²⁺-induced Ca²⁺-release during normal excitation-contraction coupling. However, variations in RyR cluster size among individual junctions and RyR sensitivity could exacerbate heterogeneity of local sarcoplasmic reticulum Ca²⁺ release and arrhythmogenesis under pathological conditions.

In this technical note we show the promise of using graphic processing units (GPUs) to accelerate simulations of electrical wave propagation in cardiac tissue, one of the more demanding computational problems in cardiology. We have found that the computational speed of two-dimensional (2D) tissue simulations with a single commercially available GPU is about 30 times faster than with a single 2.0 GHz Advanced Micro Devices (AMD) Opteron processor. We have also simulated wave conduction in the three-dimensional (3D) anatomic heart with GPUs where we found the computational speed with a single GPU is 1.6 times slower than with a 32-central processing unit (CPU) Opteron cluster. However, a cluster with two or four GPUs is faster than the CPU-based cluster. These results demonstrate that a commodity personal computer is able to perform a whole heart simulation of electrical wave conduction within times that enable the investigators to interact more easily with their simulations.

Early afterdepolarizations (EADs) associated with prolongation of the cardiac action potential (AP) can create heterogeneity of repolarization and premature extrasystoles, triggering focal and reentrant arrhythmias. Because the L-type Ca(2+) current (ICa,L) plays a key role in both AP prolongation and EAD formation, L-type Ca(2+) channels (LTCCs) represent a promising therapeutic target to normalize AP duration (APD) and suppress EADs and their arrhythmogenic consequences. We used the dynamic-clamp technique to systematically explore how the biophysical properties of LTCCs could be modified to normalize APD and suppress EADs without impairing excitation-contraction coupling. Isolated rabbit ventricular myocytes were first exposed to H2O2 or moderate hypokalemia to induce EADs, after which their endogenous ICa,L was replaced by a virtual ICa,L with tunable parameters, in dynamic-clamp mode. We probed the sensitivity of EADs to changes in the (a) amplitude of the noninactivating pedestal current; (b) slope of voltage-dependent activation; (c) slope of voltage-dependent inactivation; (d) time constant of voltage-dependent activation; and (e) time constant of voltage-dependent inactivation. We found that reducing the amplitude of the noninactivating pedestal component of ICa,L effectively suppressed both H2O2- and hypokalemia-induced EADs and restored APD. These results, together with our previous work, demonstrate the potential of this hybrid experimental-computational approach to guide drug discovery or gene therapy strategies by identifying and targeting selective properties of LTCC.