Mechanisms of Ventricular Arrhythmias: From Molecular Fluctuations to Electrical Turbulence

Abstract

Ventricular arrhythmias have complex causes and mechanisms. Despite extensive investigation involving many clinical, experimental, and computational studies, effective biological therapeutics are still very limited. In this article, we review our current understanding of the mechanisms of ventricular arrhythmias by summarizing the state of knowledge spanning from the molecular scale to electrical wave behavior at the tissue and organ scales and how the complex nonlinear interactions integrate into the dynamics of arrhythmias in the heart. We discuss the challenges that we face in synthesizing these dynamics to develop safe and effective novel therapeutic approaches.

1. INTRODUCTION

Cardiac arrhythmias have been recognized as a key complication of heart diseases for centuries (1, 2). Generally defined, cardiac arrhythmias refer to conditions in which the electrical activity of the heart becomes too slow, too fast, and/or too irregular. Slow heart rhythms can be readily treated with electronic pacemakers, but rapid heart rhythms that culminate in atrial fibrillation or ventricular fibrillation (VF), in which the electrical activity in the atria or ventricles becomes turbulent, remain leading causes of morbidity and mortality, including sudden cardiac death, particularly in industrialized countries (3). From the first demonstration of electrical activity of the heart in 1856 (1) to today’s modern technologies unraveling the genetic basis of many cardiac arrhythmias (4, 5), this problem has been a major focus of medicine for more than a century. However, successful pharmacological treatment is still problematic. Current antiarrhythmic drugs have limited effectiveness, and many can have unintended proarrhythmic effects (6, 7). The most effective treatment for VF is an implantable cardioverter defibrillator (ICD), which can promptly and effectively terminate life-threatening arrhythmias. However, 80% of patients who will die suddenly each year in the United States do not meet current clinical criteria for prophylactic implantation of an ICD (8); moreover, even among those who do meet such criteria, only one in five ICDs will deliver a life-saving shock because of the difficulty in identifying those at highest risk (9). Additionally, ICD treatment is expensive and has significant morbidity.

The limited effectiveness of biologically based antiarrhythmic therapies, as opposed to bioengineering-based strategies, is related to the ubiquitous problem in biomedicine that the relevant biological targets for drug or gene therapy exist at the molecular scale, whereas the arrhythmias exist at the organ scale. Predicting how the behavior of a molecule will affect the properties of the organ is very complex because at each more integrated level, from molecule to molecular signaling complex to organelle to cell to tissue to organ to organism, qualitatively new properties emerge from the complex nonlinear interactions between properties at that level of integration and properties at the next-higher level of integration. In other words, the heart, as is any other organ in the body, is regulated at multiple spatial and temporal scales, and each scale has its own dynamics that then give rise to the dynamics at the next scale.

In this review article, we summarize our current understanding of ventricular arrhythmias, focusing on the multiscale and complex dynamic nature of the problem. After a brief summary of the multiscale dynamics in the heart, we then deconstruct the excitation dynamics in the reverse order: tissue-scale electrical wave dynamics, cellular-scale action potential dynamics, and subcellular- and molecular-scale dynamics. The goal is to illustrate, in a stepwise fashion, how the higher-scale dynamics emerge from lower-scale dynamics. We discuss the challenges and the potential for nonlinear dynamics, combined with new systems approaches, to lead to the development of robust and effective therapeutics. The article involves some important concepts of nonlinear dynamics relevant to arrhythmias (10), such as dynamic instabilities, bifurcation, chaos, synchronization, criticality, and basins of attraction. To help the readers who are not familiar with these concepts, they are explained in more detail in the Supplemental Text (follow the Supplemental Material link from the Annual Reviews home page at http://www.annualreviews.org).

2. MULTISCALE DYNAMICS IN THE HEART

The dynamics of excitation and contraction at different scales in the heart have distinct features. At the molecular scale, dynamics is governed mainly by thermodynamic fluctuations. For instance, ion channels open and close randomly (Figure 1a), and thousands of ion channels and ion transporters are distributed in the cell membrane to generate ionic currents for the action potential (Figure 1b). The channels and transporters are typically organized into molecular signaling complexes regulating their activity. In addition to the surface plasma membrane, these molecular signaling complexes often form clusters in intracellular organelles, such as the sarcoplasmic reticulum (SR) and mitochondria. These ion channel clusters open and close collectively to result in organelle-scale dynamics, such as calcium (Ca²⁺) sparks and mitochondrial flickers (11). For example, a Ca²⁺ spark (Figure 1c) is a Ca²⁺ release event of a Ca²⁺ release unit due to the collective opening of the ryanodine receptors (RyRs) triggered by the opening of the associated L-type Ca²⁺ channel cluster or by high intracellular Ca²⁺. Under normal conditions, the L-type Ca²⁺ channel–triggered Ca²⁺ sparks integrate to give rise to the whole-cell Ca²⁺ transient (Figure 1b). Under diseased conditions and/or high intracellular Ca²⁺ load, the Ca²⁺ sparks organize to form different types of intracellular Ca²⁺ waves (Figure 1d) to generate whole-cell Ca²⁺ oscillations [the analogy for mitochondria is mitochondrial depolarization waves and oscillations (12)].

Figure 1.

Subcellular and cellular dynamics of ventricular myocytes. (a) A single ion channel opening and closing stochastically. (b) Normal action potentials and Ca²⁺ transient for endocardial myocytes (left) and epicardial myocytes (right). A spike-and-dome morphology occurs in epicardial myocytes. (c) A Ca²⁺ release unit (CRU) that is composed of a ryanodine receptor (RyR) cluster in the sarcoplasmic reticulum (SR) membrane and an L-type Ca²⁺ channel (LCC) cluster in the apposing T-tubule (TT) membrane (left) and a Ca²⁺ spark (right). The spark image was downloaded from https://sites.google.com/site/sparkmasterhome/faq. (d ) A planar Ca²⁺ wave (left; arrows indicate the direction of propagation, and the numbers indicate time in milliseconds) from a Purkinje cell (from Reference 150 with permission) and a spiral Ca²⁺ wave (right) (from Reference 151 with permission). (e) Early afterdepolarizations (EADs), delayed afterdepolarizations (DADs), and triggered activity (TA). (f) Action potential alternans. ( g) Spontaneous oscillations (automaticity).

At the cellular scale, the subcellular dynamics couple with surface membrane ionic currents to result in various excitation and contraction dynamics. Under normal conditions, a ventricular myocyte is excitable: A normal action potential and a corresponding Ca²⁺ transient triggering contraction are generated in response to a stimulus (Figure 1b). The action potential morphology and duration are heterogeneous throughout the heart, with epicardial but not endocardial myocytes tending to exhibit a spike-and-dome morphology (right panel in Figure 1b). Under certain diseased conditions when outward currents are reduced and/or inward currents are increased, voltage depolarizations (oscillations) can occur during the repolarization phase of the action potential, termed early afterdepolarizations (EADs) (Figure 1e). During the diastolic phase, a spontaneous Ca²⁺ wave elevates intracellular Ca²⁺, which increases the Na⁺-Ca²⁺ exchange current (I_NCX) to cause a voltage depolarization termed a delayed afterdepolarization (DAD) (Figure 1e). If the Ca²⁺ transient is large enough to depolarize the voltage to the threshold for Na⁺ channel activation, a full action potential occurs, which is termed triggered activity. An EAD, if its takeoff potential is low and amplitude is large, can also cause triggered activity. During rapid pacing, the action potential duration (APD) of a normal ventricular myocyte may exhibit a long-short-long-short pattern termed APD alternans (Figure 1f). Under diseased conditions, APD alternans can often occur at much slower heart rates. A ventricular cell can also become oscillatory (Figure 1g) due to aberrant ionic current or Ca²⁺ cycling properties, termed automaticity.

At the tissue and organ scales, the cellular dynamics combine with tissue heterogeneities and cell coupling properties to generate the electrical wave dynamics underlying normal sinus rhythm, as well as different types of arrhythmias. During normal sinus rhythm, the impulses originating from the sinoatrial node follow an anatomically defined conduction pathway culminating in synchronous excitation of the ventricles. These excitation waves are termed rectilinear (or planar) waves (Figure 2a). Under diseased conditions, different types of electrical waves can occur in the ventricles, resulting in different types of ventricular arrhythmias. The first type of wave is termed a target wave (or focal excitation), in which spontaneous excitation originates from a local region of the ventricles due to heterogeneities in cellular properties and propagates outward to excite other regions of the heart (Figure 2b). The second type of wave is an excitation wave propagating around an obstacle, termed anatomical reentry (Figure 2c). The third type of wave does not require heterogeneities or an obstacle and can even occur in completely homogeneous tissue; this type is termed a spiral wave (Figure 2d ) or sometimes a rotor or functional reentry. Because the heart is a three-dimensional object, the spiral wave in two-dimensional tissue is technically a scroll wave in the real heart (Figure 2e,f ), but here we use spiral wave to refer to both.

Figure 2.

Tissue-scale excitation dynamics. (a) A rectilinear (planar) wave. (b) A focal excitation (target wave). (c) Reentry around an obstacle. (d ) A spiral wave. (e) A scroll wave. (f) A scroll wave in the ventricles (from Reference 152 with permission). Voltage levels are indicated by the color bar, and arrows indicate the directions of propagation in panels a–e. In panel f, only voltage higher than a certain value is colored in red for three-dimensional visualization.

The dynamics at a higher scale depend on the dynamics at lower scales, but the information flow is bidirectional so that the dynamics at a lower scale are also modulated by the dynamics at the higher scales. For example, EADs in an action potential are caused by aberrant ion currents and Ca²⁺ cycling properties, but the occurrence of EADs can bring more Ca²⁺ into the cell to potentiate Ca²⁺ waves due to L-type Ca²⁺ channel opening during the EADs. Furthermore, besides the typical Ca²⁺ cycling, action potential, and electrical wave dynamics shown in Figures 1 and 2, more complex dynamics can emerge due to heterogeneities and dynamic instabilities. These dynamics at different scales play critical roles in initiating arrhythmias, as well as giving rise to different types of arrhythmias. Therefore, to understand the mechanisms of arrhythmias and to develop molecularly based therapeutics, one needs to understand how molecular behaviors relate to electrical wave dynamics; i.e., one needs to relate the dynamics at each lower scale (in both time and space) to the dynamics at the next higher scale, sequentially from molecule to organism. For example, to understand how a mutation in RyRs is linked to arrhythmias, one needs to understand, in sequence, the following: how the mutation modifies the opening and closing properties of RyRs; how RyRs in a cluster interact with each other to affect Ca²⁺ spark behavior both normally and when various signaling pathways are activated; how Ca²⁺ sparks organize into Ca²⁺ waves and oscillations; how Ca²⁺ waves and oscillations affect the cellular action potential dynamics, such as alternans, EADs, and DADs; and finally how these cellular action potential dynamics synchronize at the tissue and organ levels to generate the electrical wave dynamics leading to different types of arrhythmias. In the sections below, we summarize our current understanding of the multiscale dynamics in the heart to illuminate first how the dynamics at a higher scale emerge from the dynamics of a lower scale and then how the dynamics at the higher scale feed back to modulate the properties at the lower scale.

3. ARRHYTHMOGENIC ELECTRICAL WAVE DYNAMICS AT THE TISSUE AND ORGAN SCALES

Different electrical wave dynamics at the tissue and organ scales give rise to different types of arrhythmias. These wave dynamics are caused by either preexisting tissue heterogeneities or dynamic instabilities or their interactions, which are summarized in the sections below.

3.1. Focal Excitations Due to Triggered Activity and Automaticity

A focal excitation (Figure 2b) is a spontaneous firing of a group of cells in cardiac tissue. Spontaneous firing can be due to either triggered activity or automaticity. Under normal conditions, thousands of cells need to fire synchronously to overcome the strong sink effect of the adjacent unexcited cells, but under conditions of weak gap junction coupling, such as in fibrotic or ischemic tissue, the number of the spontaneously firing cells required to form a focal excitation is substantially reduced (13).

Traditionally, focal excitations have been thought to require heterogeneous tissue, i.e., one region of the tissue exhibiting spontaneous firing that propagates into surrounding quiescent regions. Intuitively, if all cells are identical and therefore spontaneously fire simultaneously in a homogeneous tissue, the whole tissue fires together, and no localized focus can form. However, focal excitations can also occur in homogeneous tissue via self-organizing pattern formation (Supplemental Figure 1a). Our recent study (14) showed that when the action potential develops EADs, the dynamics at the cellular level can be chaotic such that at the tissue level, regional chaos synchronization results in the formation of islands of long APD with EADs next to regions with normal APD without EADs, forming a complex spatiotemporal pattern. The EADs propagate out of the islands, forming a pattern of multiple, shifting focal excitations. The foci formed via this mechanism are not stable but vary dynamically in space and time due to the spatiotemporal chaotic dynamics. In contrast, focal excitations purely due to a tissue heterogeneity remain fixed in space. This dynamic feature agrees with the experimental observations of focal arrhythmias in drug-induced long-QT (LQT) syndrome, in which multiple foci arising dynamically from different locations occur in space and time (15, 16). Tissue heterogeneities and random ion channel fluctuations potentiate these dynamics (17, 18). The dynamic mechanisms of multiple foci nicely account for two features of polymorphic ventricular tachycardia (VT): (a) the observation that polymorphic VT can be sustained for long periods in tissue, even though single cells usually exhibit only one or several EAD-triggered action potentials (17), and (b) the frequent spontaneous termination of polymorphic VT, in particular torsade de pointes (19).

A clear example of heterogeneity interacting with dynamics is bidirectional VT in catecholaminergic polymorphic VT (CPVT), in which two focal excitations can perpetuate each other to form a stable reciprocal firing pattern (20). A simulation study by Baher et al. (21) demonstrated this mechanism. Specifically, as the heart rate increases, a focal excitation due to a DAD occurs at a certain location (e.g., the left bundle branch), which propagates reciprocally to the contralateral (right) bundle branch and causes a focal excitation there via the same mechanism. The excitation from the right then propagates to the left and causes another focal excitation in the left branch, and so on in a reciprocating ping-pong fashion.

3.2. Reentry

Two general categories of reentry occur in cardiac tissue: reentry around an obstacle (anatomical reentry; Figure 2c), such as reentry using a specialized pathway (e.g., a bypass tract or around a scar), and spiral wave reentry (also known as scroll wave, rotor, or functional reentry; Figure 2d ). Anatomical reentry was first demonstrated experimentally in an annulus of cardiac tissue by Mines (22) approximately a century ago. In many cases, anatomical reentry is stable, resulting in monomorphic VT. However, depending on the path length of the reentry circuit relative to the wavelength of the impulse, reentry may become unstable, leading to more complex morphologies of arrhythmias, such as polymorphic VT and VF.

Spiral waves are a generic feature of wave dynamics in excitable media that can occur in both homogeneous tissue and heterogeneous tissue. Spiral waves were first demonstrated in chemical reactions (23) and later in cardiac tissue (24). Spiral waves can be stable, resulting in a periodic behavior manifesting as monomorphic VT, but can also be unstable. In the latter case, the spiral wave meanders and drifts and can spontaneously break up into multiple spiral waves—a turbulent state of electrical waves. A meandering or drifting spiral wave can give rise to polymorphic VT or torsade de pointes, whereas frank breakup along the arm of a spiral wave results in fibrillation due to the generation of new spiral waves and/or fibrillatory conduction block.

Computer modeling as well as experimental studies have shown that the slope of the APD restitution curve is a key parameter that determines the stability of the spiral wave reentry in cardiac tissue such that a spiral wave becomes more unstable as the slope of APD restitution curve becomes steeper (25, 26). APD restitution is defined as the relationship between the APD and its preceding diastolic interval (see Supplemental Figure 2 for more detailed definition), which is a measure of the state of ion channel recovery from their openings in the previous action potential. When the APD restitution curve is steep enough, there is spiral wave breakup (Supplemental Figure 1b,d,e), in which a turbulent electrical state maintained by irregular spiral waves (or wavelets) appears and disappears in a chaotic manner. Spiral breakup as a mechanism of fibrillation agrees with Moe et al.’s (27) original multiple wavelets hypothesis, in which fibrillation is characterized by multiple wandering wavelets in the heart. However, tissue heterogeneities can also promote spiral wave meandering and wave breaks. For example, in a tissue with large refractory gradient, fibrillatory conduction block can occur. In this scenario, a fast spiral wave generates higher-frequency excitations that are unable to propagate 1:1 into surrounding regions with longer refractory periods, resulting in wave breaks generating turbulent wave patterns (Supplemental Figure 1c). This mechanism is termed mother-rotor fibrillation (2). Because cardiac tissue is heterogeneous, the dominant mechanism depends on the specific disease conditions, and in some conditions, both mechanisms may work in synergy to generate the electrical turbulence of VF.

3.3. Biexcitability

Biexcitability is a novel wave conduction behavior demonstrated in recent studies (28–30). In both atrial and ventricular tissue, normal wave conduction is driven mainly by the Na⁺ current (I_Na), which mediates the initial rapid upstroke of the action potential. Under certain conditions—such as LQT syndrome, in which prolonged APD and EADs occur due to reduced repolarization reserve—cells can develop two stable resting membrane potentials: one typically at approximately −80 mV and one at approximately −50 mV (31). Under these conditions, bistable wave propagation can occur; i.e., a slow conduction mediated by L-type Ca²⁺ current (I_Ca,L) from the more depolarized resting potential (at which I_Na is mostly inactivated) and a fast conduction mediated by both I_Na and I_Ca,L from the fully repolarized resting potential occur in the same tissue. This behavior is therefore referred to as biexcitability. Chang et al. (28) demonstrated this behavior by showing, in computer simulations, that in a homogeneous tissue two distinct types of spiral waves can be induced, depending on the method of initiation. In the first type of fast spiral wave (Supplemental Figure 3a), voltage recovers close to the resting potential (−80 mV), and both I_Na and I_Ca,L are activated. In the second type of slow spiral wave (Supplemental Figure 3b), however, voltage recovers only to approximately −50 mV. Because I_Na is inactivated above −60 mV, only I_Ca,L is activated, which results in a slower propagation. Under some conditions, both types of conduction occur interchangeably in the same tissue (Supplemental Figure 3c). This behavior was experimentally observed in cultured myocyte monolayers (28, 29) and can be seen in recordings during arrhythmias in LQT syndrome (16, 32). Biexcitability may provide a mechanism for torsade de pointes and may explain why torsade de pointes often spontaneously terminates but sometimes degenerates into VF (28, 29).

3.4. Arrhythmia Initiation: Trigger and Substrate Interactions

Although understanding reentrant and focal electrical wave behaviors during arrhythmias is important, even more important is understanding how these waves and foci are initiated because from the therapeutic viewpoint, the ideal strategy is to prevent the initiation of arrhythmias. Generally speaking, initiation of reentry requires two factors: a critically timed trigger such as a premature ventricular complex (PVC) and a tissue substrate exhibiting dispersion of refractoriness. On the basis of past studies, we can summarize the most relevant settings as follows.

3.4.1. Induction of arrhythmias around an anatomical obstacle

Reentry around an obstacle can form by different mechanisms (Figure 3a). When the tissue around the obstacle is homogeneous and the pathways are wide, a PVC can successfully conduct through both pathways (case i in Figure 3a) and does not induce reentry. When the tissue around the obstacle is electrically heterogeneous, however, unidirectional conduction block of a properly timed PVC can occur due to dispersion of refractoriness, allowing the antegrade impulse to conduct retrogradely into the blocked pathway, initiating reentry (case ii in Figure 3a) (22). Another scenario is source-sink mismatch (33, 34), in which one of the pathways has a very narrow exit (case iii in Figure 3a) and the impulse fails to propagate out of the narrow pathway due to the strong sink effect from the cells outside the exit (i.e., a small number of cells at the exit of the narrow pathway provides the electrical source for a large number of cells outside, and thus the source is weaker than the sink). However, the impulse from the other pathway can enter into the narrow pathway because the source from the outside cells is strong enough (i.e., a large number of cells outside provides the electrical source for a small number of cells in the narrow pathway, and thus the source is stronger than the sink). Because of this source-sink mismatch, reentry can form. This mechanism of reentry initiation can underlie concealed Wolff-Parkinson-White syndrome, a common cause of paroxysmal supraventricular tachycardia, as well as reentry in scarred and fibrotic tissue, such as in the border zone of an infarct.

Figure 3.

Mechanisms of reentry initiation. (a) Reentry around an anatomic obstacle. (i ) Homogeneous refractoriness: A premature ventricular complex (PVC) successfully propagates through both sides of the obstacle without forming reentry. (ii ) Heterogeneous refractoriness: The refractory period in one region is longer than elsewhere (e.g., the gray zone in the right pathway) such that a properly timed PVC is blocked in the right pathway, propagates successfully through the contralateral pathway (e.g., the left), and then reenters the right pathway from the retrograde direction, initiating reentry around the obstacle (red arrows). (iii ) Narrow pathway: The right pathway has a very narrow exit (indicated by the circle) such that a PVC cannot conduct out of the pathway, but the impulse from outside can enter the pathway, resulting in reentry (red arrows). (b) Reentry in heterogeneous tissue in which the central region has a longer refractory period than the rest of the tissue. (c) Reentry induction by a trigger and substrate from the same source. Cells in the central region exhibit early afterdepolarizations.

3.4.2. Induction of arrhythmias by a trigger in heterogeneous tissue without anatomic obstacles

In tissue with no obstacles or specialized pathways, unidirectional conduction block can still occur due to dispersion of refractoriness (35). A typical scenario is shown in Figure 3b: The central region of the tissue has a longer refractory period so that a PVC originating from a peripheral location may fail to propagate through the central region and propagate around it, reentering from the other side to form so-called figure-of-eight reentry. For reentry to form by this mechanism, the central region needs to be large enough and the PVC timed in a proper window termed the vulnerable window.

3.4.3. Induction of arrhythmias by a trigger and substrate arising from the same process

In the above two mechanisms, the trigger and the substrate emanate from two separate etiologies. In a third mechanism of reentry initiation, both the trigger and the substrate arise from the same cause. For example (Figure 3c), if the cells in the central region of a tissue exhibit EADs, but asymmetrical heterogeneities in the tissue alter electrical loading conditions (source-sink mismatch), EADs can propagate outward from one side of the heterogeneous region, but not from the other, leading to initiation of reentry. This scenario has been demonstrated in real cardiac tissue with drug-induced LQT syndrome (32, 36). This same scenario is also responsible for phase 2 reentry (Supplemental Figure 4), in which the action potential in the central region exhibits a spike-and-dome morphology (Figure 1b) whereas the action potential in the surrounding area exhibits early repolarization (short APD) without a dome. Phase 2 reentry initiates reentrant arrhythmias in both acute ischemia and Brugada syndrome (37–39).

3.4.4. Induction of arrhythmias via dynamic instabilities

In the three mechanisms of reentry initiation described above, the heterogeneities can either be preexisting or arise from dynamic instabilities. For example, spatially discordant APD alternans (Figure 4a) creates tissue heterogeneity via dynamic instabilities (40, 41), even when all the cells in the tissue have identical properties. Moreover, dynamic instabilities can simultaneously generate triggers and create a heterogeneous substrate that is vulnerable to initiation of reentry by those same triggers. As Sato et al. (14) showed in tissue exhibiting EADs, chaos synchronization results in the formation of tissue islands exhibiting action potentials with EADs next to tissue regions exhibiting action potentials without EADs (Figure 4b). If the EADs in these islands have sufficient amplitude to generate triggered activity, the impulses propagate readily into the regions without EADs and may then be blocked when they encounter another island with a long APD, thereby inducing reentry or a mixture of multiple foci and reentry. In the presence of preexisting tissue heterogeneities, dynamic instabilities are generally potentiated, increasing the probability that triggers will induce reentry.

Figure 4.

Dynamically induced dispersion of refractoriness. (a) Spatially discordant action potential duration (APD) alternans in which APD is short in one region but long in another region. In the following beat, the spatial APD pattern is reversed. (b) Spatiotemporal chaotic dynamics in the presence of early afterdepolarizations (EADs). The APD distribution in tissue exhibits an irregular spatial pattern and varies from beat to beat. EADs occur in long-APD regions (red ), but not in short-APD regions (blue).

4. ARRHYTHMIA DYNAMICS AT THE CELLULAR SCALE

The tissue-scale wave dynamics are collective behaviors of the myocytes that form the tissue. A single myocyte can exhibit a variety of action potential dynamics, including APD and Ca²⁺ alternans, EADs, DADs, automaticity, and random and chaotic dynamics. Understanding the cellular dynamics is key for understanding the mechanisms of arrhythmias because they are not only important for understanding the tissue-scale mechanisms but also important for mechanistically linking the molecular and subcellular dynamics to the tissue- and organ-scale dynamics.

4.1. Alternans

Pulsus alternans and T-wave alternans are commonly observed clinically and are recognized as precursors of cardiac arrhythmias (42, 43). Because the T-wave is a measure of repolarization in the ventricles, T-wave alternans corresponds to APD alternans at the cellular scale, at which the action potential exhibits a long-short-long-short pattern (Figure 1f).

APD alternans can be caused either by instabilities originating from voltage (voltage-driven alternans) or by instabilities originating from Ca²⁺ cycling (Ca²⁺-driven alternans) (44). However, because voltage and Ca²⁺ are bidirectionally coupled, alternans is always influenced by both factors, although one may predominate over the other, depending on the specific setting.

Voltage-driven alternans can be classified into three categories, all of which are related to APD restitution properties. The first and the most widely studied case is rapid, pacing-induced APD alternans (Figure 1f ), which is caused by a steep slope of the APD restitution curve at short diastolic intervals. Theoretically, when the slope of the APD restitution curve at the equilibrium state for a given pacing rate exceeds one, the equilibrium state becomes unstable, and the system transitions to a new state. The instability, combined with nonlinear properties of APD restitution, can eventually lead to a stable long-short-long-short alternating pattern (i.e., APD alternans) or to much more complex periodic and frankly chaotic patterns (45, 46). Even though APD restitution is a collective property that arises from the recovery of all ionic currents and their interactions with voltage, the kinetics of recovery of I_Ca,L is a particularly key factor regulating the steepness of APD restitution curve at fast heart rates (diastolic interval < 100 ms), because its recovery time constant is typically in this range of the diastolic interval (47). However, all other currents also contribute to the steepness of APD restitution either directly as a result of their own recovery from inactivation kinetics or indirectly by affecting other currents influencing the APD.

A second mechanism of voltage-driven alternans is transient outward K⁺ current (I_to)-driven APD alternans, which occurs at slow or normal heart rates. This type of alternans was first observed in ischemic tissue by Lukas & Antzelevitch (48) and later in a computer model by Hopenfeld (49), who showed that alternans is induced by the sensitive dependence of the spike-and-dome action potential morphology on I_to. This mechanism of alternans can be responsible for the T-wave alternans seen in patients with Brugada syndrome (50). The mechanism of this type of alternans is also related to the steepness of APD restitution. However, due to short-term memory effects, the slope of APD restitution curve alone is not an accurate predictor (44). In addition to I_to, the slow component of the delayed rectifier K⁺ current (I_Ks) also plays an important role due to its slow recovery kinetics.

The third mechanism of voltage-driven alternans is APD alternans at normal or slow heart rates caused by the interaction of window and pedestal I_Ca,L with I_Ks, which can cause the T-wave alternans seen in patients with LQT syndrome (50). Under normal conditions, APD does not change dramatically at slow heart rates, because most of the ion channels are fully recovered. However, under the conditions of reduced repolarization reserve causing EADs, such as in LQT syndrome, APD varies sensitively with heart rate (51), causing alternans and more complex patterns at slow heart rates (52). The two major ionic currents critical to this slow-rate instability are the window and pedestal components of I_Ca,L and I_Ks. Late I_Na [a persistent small conductance due to incomplete inactivation of the Na⁺ channel (53–55)] can substitute for or enhance the role of window and pedestal I_Ca,L.

For Ca²⁺-driven alternans, two mechanisms have been characterized (56, 57). In the first mechanism, alternans is caused by a steep fractional SR Ca²⁺ release relationship, first proposed by Eisner et al. (58). Later theoretical analyses (45, 59) showed that, besides a steep fractional SR release relationship, reduced SERCA pump activity is also required. A condition required by this mechanism is that SR Ca²⁺ load alternates concomitantly with cytosolic Ca²⁺, which was observed in experiments from Eisner’s group (60, 61) and others (62). However, later experimental studies also showed that this condition is not met under all circumstances and that cytosolic Ca²⁺ alternans can occur without SR Ca²⁺ load alternans (63, 64). That is, before each beat, the SR loads to the same level, but the amount of Ca²⁺ released exhibits an alternating pattern. These observations supported a different mechanism, in which refractoriness of the Ca²⁺ release channels (RyRs) is the major factor promoting alternans. Under such conditions, SR Ca²⁺ load alternans is not required. Refractoriness alone, however, is not sufficient to induce alternans, unless coupling of the Ca²⁺ release units is also present to allow a Ca²⁺ spark from one Ca²⁺ release unit to recruit a neighboring Ca²⁺ release unit to fire (65–67).

Alternans not only is a precursor but also can be a direct cause of arrhythmias. First, when APD alternans occurs, conduction block can occur at much slower pacing rates due to the long APD on alternate beats (45). Second, in cardiac tissue, APD alternans can be out of phase in different regions, forming spatially discordant APD alternans (Figure 4a), resulting in a large dispersion of refractoriness that creates a substrate vulnerable to initiation of reentry (68). Theoretical studies (40, 41) supported by experimental observations (69, 70) show that the formation of spatially discordant alternans requires conduction velocity restitution (Supplemental Figure 2c), i.e., a dependence of conduction velocity on its preceding diastolic interval. Because conduction velocity restitution is determined mainly by the recovery of Na⁺ channels at very short diastolic intervals, spatially discordant alternans is a cause of arrhythmias only at very fast heart rates in the normal heart (>300 beats per min, as in pacing-induced VF). However, in the presence of Na⁺ channel–blocking drugs that slow recovery from inactivation (71), during acute ischemia, or in electrically remodeled diseased hearts, spatially discordant alternans may develop at much slower heart rates (72).

4.2. Early Afterdepolarizations

EADs are voltage oscillations during the plateau and repolarization phases of the action potential (Figure 1e) and occur in cardiac diseases such as acquired and congenital LQT syndrome (73, 74) and heart failure (75, 76). In general, EADs occur when outward currents are reduced and/or inward currents are increased (77–80), a condition termed reduced repolarization reserve (81). However, whereas reduced repolarization reserve is sufficient to prolong APD, it is not sufficient to produce EADs. Other conditions are required to generate the voltage oscillations pathognomonic of EADs, which arise from different causes. These conditions are summarized in a recent review article (82) providing a holistic analysis of underlying mechanisms based on nonlinear dynamics. Even though each of the ionic currents in a cardiac myocyte can affect EADs, the most critical to the dynamics of oscillations include window I_Ca,L, late I_Na, and I_Ks. In addition, EADs can also be promoted by intracellular Ca²⁺ oscillations (83, 84) or by prolonged Ca²⁺ transients inducing EADs during the rapid repolarization phase of the action potential (phase 3 EADs) via I_NCX (85, 86).

A very interesting property of EADs is their sensitive all-or-nothing behavior in response to heart rate changes (Supplemental Figure 5a), which result in a steep, nonlinear APD restitution property (Supplemental Figure 5b). This nonlinear property can give rise to dynamic chaos (Supplemental Figure 5c) (14, 18), which is responsible for the irregularly appearing EAD behavior widely observed in experiments (Supplemental Figure 5d). The consequence of the chaotic dynamics at the tissue scale is the induction of dispersion of refractoriness. The dispersion of refractoriness arises from the competition between the chaotic dynamics at the cellular level, which tends to create APD dispersion between cells, and the gap junction coupling at the tissue level, which forces APD to be regionally quasi-uniform. As a result, the chaotic EAD behavior becomes synchronized regionally but desynchronized globally, forming islands of long action potentials with EADs separated by regions without EADs (Figure 4b). The presence of preexisting tissue heterogeneity further amplifies this effect. In regions where EADs are too small to propagate, they create dispersion of refractoriness resulting in a tissue substrate vulnerable to reentry; in regions where EADs reach the threshold to propagate (e.g., Figure 3c), they generate triggers to initiate reentry. Depending on the cellular and tissue properties, this behavior can result in purely reentrant arrhythmias, multiple shifting foci, and a mixture of multiple shifting foci and reentry (14, 17).

4.3. Delayed Afterdepolarizations

DADs are spontaneous depolarizations during diastole that often occur following a train of rapid pacing (Figure 1e) (87). DADs are caused by spontaneous Ca²⁺ release from the SR that propagates as a Ca²⁺ wave through the myocyte (Supplemental Figure 6a) (88, 89). During a Ca²⁺ wave, cytoplasmic free Ca²⁺ concentration is elevated, which increases inward I_NCX and other Ca²⁺-sensitive inward currents, causing a depolarization. If the voltage elevation does not reach the threshold for I_Na activation, there is only a small voltage deflection. Once the threshold for I_Na activation is exceeded, an action potential is elicited (Figure 1e). The magnitude of a DAD depends on the magnitude of the Ca²⁺ transient and the conductance of I_NCX and I_K1 (90, 91). DADs are easier to induce in heart failure (91, 92) and CPVT (20, 93–96) than in normal hearts. In both heart failure and CPVT, RyRs become leaky, promoting spontaneous Ca²⁺ waves when the SR becomes Ca²⁺ loaded, e.g., by fast heart rates and adrenergic stimulation. In heart failure, I_NCX is upregulated and I_K1 is downregulated, giving rise to favorable conditions for the formation of superthreshold DADs. The formation of Ca²⁺ waves is a self-organizing critical phenomenon (97, 98), exhibiting large fluctuations and thus resulting in the irregular occurrence of DADs (Supplemental Figure 6b). When a DAD triggers an action potential, it can result in a PVC, but when a DAD does not trigger an action potential, it may still create dispersion of excitability, promoting regional conduction block (99). Subthreshold DADs manifest as a U-wave on the electrocardiogram (100, 101). A key issue that still remains to be elucidated is how irregular DADs become synchronized regionally in tissue to induce arrhythmias (102, 103).

4.4. Spike-and-Dome Action Potentials and Early Repolarization

In the ventricles, the higher I_to density in epicardial myocytes produces a characteristic spike-and- dome action potential morphology (Figure 1b) (104). Even though I_to is an outward current, it can prolong APD via secondary effects on other ion channels (105). If I_to is too large, however, the action potential abruptly shortens and loses the spike-and-dome morphology (Supplemental Figure 4a,b). Due to this steep, nonmonotonic response, alternans and irregular (chaotic) action potential dynamics can occur, as shown in experiments (48) and simulation studies (44, 49, 106, 107). When I_to is heterogeneously distributed, the region with the spike-and-dome action potential can propagate during phase 2 into the region with early repolarization and very short APD, inducing phase 2 reentry (Supplemental Figure 4c). In computer simulation studies of tissue exhibiting action potential heterogeneity due to I_to gradients, phase 2 reentry can be induced over a wide range of parameter space when irregular (chaotic) action potential dynamics are present (106, 107), whereas the parameter space is very narrow otherwise (108). Phase 2 reentry has been demonstrated experimentally (37, 109) and is thought to be a major mechanism of arrhythmias during acute ischemia and in Brugada syndrome (110), although other factors, such as regional fibrosis promoting slow conduction, have also been proposed (111).

4.5. Automaticity

Under normal conditions, ventricular myocytes are excitable cells that remain at rest in the absence of a physiological pacemaker or electrical stimulus. However, ventricular myocytes can become oscillatory under abnormal conditions, termed automaticity (Figure 1g), which can generate PVCs or repetitive focal excitations in tissue. Multiple factors can cause automaticity. For example, Na⁺ channel inactivation defects, such as aconitine-induced automaticity (112), or I_K1 reduction (113), cause spontaneous beating. Coupling of myocytes to myofibroblasts via heterocellular gap junctions can also depolarize the myocyte’s resting membrane potential sufficiently to induce automaticity (114), which may be relevant to the increased ventricular ectopy seen in diseased hearts with fibrosis. Periodic Ca²⁺ oscillations, similar to the mechanisms causing DAD-mediated triggered activity, can also result in automaticity. The bidirectional coupling of voltage and Ca²⁺ (i.e., voltage affects Ca²⁺ at the same time that Ca²⁺ affects voltage) potentiates this mechanism such that spontaneous Ca²⁺ release elicits an action potential, and consequently, the action potential brings in more Ca²⁺ through Ca²⁺ channels to enhance spontaneous Ca²⁺ release. This coupling process forms a positive feedback loop in a manner similar to that of the Ca²⁺ oscillation that drives the sinoatrial node (115). A third mechanism is similar to that of EADs, in which oscillations mediated by I_Ca,L during the plateau become sustained due to failure of full repolarization (30).

4.6. Dynamics Arising from Heterocellular Coupling

The cellular dynamics summarized above do not always arise from myocytes but can emerge from heterocellular coupling of myocytes to nonmyocytes. For example, coupling of a myocyte to a fibroblast/myofibroblast through heterocellular gap junctions can result in automaticity (114), EADs (116), spike-and-dome action potential morphology, and alternans (117). Normal excitable ventricular cells coupled to nonexcitable ischemic ventricular cells may result in sustained oscillations (118). Two cells with different APDs under conditions of reduced repolarization reserve can also result in EADs (36).

5. SUBCELLULAR DYNAMICS AND THE MOLECULAR AND IONIC BASIS OF ARRHYTHMIAS

The cellular dynamics and the corresponding dynamic parameters (e.g., APD, APD restitution, conduction velocity, and conduction velocity restitution) are properties that emerge from the nonlinear interactions between multiple molecular and ionic factors (Figure 5). For example, APD restitution is not controlled by a single current but is a collective behavior of the recovery of all ionic currents and their interactions with voltage. However, some currents have greater influence than others. Moreover, molecular interactions at the subcellular scale, such as Ca²⁺ alternans and Ca²⁺ waves that influence the cellular dynamics through their aggregate effects on ionic currents, create subcellular dynamics. Although complex, the situation is not hopelessly so. Each molecular factor plays a specific role in promoting dynamics that can ultimately be dissected by a combined approach integrating nonlinear dynamics, modeling, and experiment. Here we briefly summarize the roles of some of the key molecular factors promoting the subcellular and cellular dynamics.

Figure 5.

Schematic diagram of ionic currents, transporters, signaling pathways, and their interactions in a ventricular myocyte. A dashed line with arrow indicates that signaling enhances activity, and a dashed line with bar indicates suppression of activity. See text for details.

5.1. Ion Channels and Transporters

There are many types of ion channels and transporters in the membranes of a ventricular myocyte (Figure 5). Alterations of the ion channel and transporter properties may result in cellular action potential dynamics that lead to arrhythmias at the tissue and organ scales. Here we review their specific roles in generating the cellular action potential dynamics.

5.1.1. Na⁺ channels

I_Na is the main current responsible for the rapid upstroke of the action potential in ventricular myocytes. By determining the speed of the upstroke (dV/dt_max), I_Na is a major determinant of excitability and conduction velocity. For this reason, I_Na (specifically its recovery from inactivation) largely determines conduction velocity restitution, which is exacerbated in chronic ischemia by slowed recovery from inactivation (119). I_Na affects APD indirectly and directly. The amplitude of I_Na determines the maximum voltage of the action potential, which affects voltage-dependent activation of other currents influencing action potential repolarization. I_Na therefore contributes to APD restitution at very short diastolic intervals when its recovery from inactivation is still incomplete, which in turn affects the stability of reentry. I_Na properties also become altered under diseased conditions, failing to inactivate fully during the action potential and thus resulting in late I_Na. Late I_Na can result from genetic mutations in Na⁺ channels, causing LQT3 syndrome, or can be induced by signaling pathways such as Ca²⁺/calmodulin-dependent protein kinase II (CaMKII) (Figure 5) (53), which is activated in heart failure. Late I_Na directly prolongs APD and can cause EADs by reducing repolarization reserve. Moreover, late I_Na brings extra Na⁺ into the cell, which increases intracellular Na⁺ and thus intracellular Ca²⁺ via Na⁺-Ca²⁺ exchangers. Elevation of Ca²⁺ can promote Ca²⁺ alternans and waves and further activate the CaMKII signaling pathway, generating more late I_Na in a positive feedback loop, with arrhythmogenic consequences (53–55).

5.1.2. L-type Ca²⁺ channels

L-type Ca²⁺ channels play two major roles under normal conditions: triggering Ca²⁺ release from the SR essential for contraction and maintaining the plateau phase of the action potential. Due to the latter, I_Ca,L is a major determinant of APD and thus APD restitution. More importantly, because the time constant of recovery of I_Ca,L is less than 100 ms, I_Ca,L has a major effect on the steepness of APD restitution at short to intermediate diastolic intervals. Thus, I_Ca,L plays an important role in the development of APD alternans at fast heart rates, as well as in spiral wave stability. Blocking I_Ca,L suppresses APD alternans and prevents spiral wave breakup (26). The late component of I_Ca,L (termed the window and pedestal I_Ca,L), although relatively small compared with peak I_Ca,L, plays a key role in promoting EADs (78, 120), as well as APD alternans at slow heart rates (52). In addition, increasing I_Ca,L increases Ca²⁺ entry and thus promotes intracellular Ca²⁺ loading, which can promote Ca²⁺ alternans and waves, as well as activating the CaMKII signaling pathway. I_Ca,L is regulated by Ca²⁺ in two ways (Figure 5): Ca²⁺ binds with calmodulin to form a Ca²⁺/calmodulin complex, which causes Ca²⁺-dependent inactivation to decrease I_Ca,L, forming a negative feedback loop, and activation of the CaMKII pathway increases I_Ca,L, forming a positive feedback loop.

5.1.3. K⁺ channels

There are a wide variety of K⁺ currents in ventricular myocytes (121) (Figure 5), including the fast and slow I_to (I_to,f and I_to,s), the fast and slow components of the delayed rectifier K⁺ current (I_Kr and I_Ks), I_K1, the plateau K⁺ current (I_Kp), ATP-sensitive K⁺ current [I_K(ATP)], stretch-activated K⁺ current (I_SAC,K), and small-conductance Ca²⁺-activated K⁺ current (I_SK) (122–124). The common role of K⁺ currents is to facilitate repolarization of the action potential such that reducing these currents generally lengthens APD. In general, reducing K⁺ currents has a larger effect on lengthening APD at slow heart rates than at fast heart rates, resulting in a steeper APD restitution curve, which promotes alternans and spiral wave instability. The reduction in repolarization reserve also promotes EAD-mediated arrhythmias. Due to their different kinetics and Ca²⁺ dependencies, however, different K⁺ currents play different roles in promoting these arrhythmogenic dynamics. For example, by enhancing early repolarization reserve, I_to lowers the early plateau voltage into the window range of I_Ca,L and slows the activation of I_Ks, paradoxically reducing late repolarization reserve and promoting EADs (125). In contrast, I_Ks activates and deactivates very slowly, thereby preferentially lengthening APD at slow heart rates, which plays a major role in EAD formation. Under conditions of reduced repolarization reserve, slow deactivation of I_Ks plays a major role in steepening APD restitution at slow heart rates, which promotes APD alternans at slow heart rates (52). I_K1 is a time-independent current responsible for phase 3 (rapid repolarization) of the action potential as well as for maintaining a stable diastolic resting potential. Therefore, I_K1, like I_Na, is a major determinant of both excitability and conduction velocity. For this reason, reduction of I_K1 is an important contributor to DADs (91), as well as to automaticity (113).

When K⁺ currents are enhanced, in contrast, increased repolarization reserve can also promote arrhythmogenic dynamics by different mechanisms. I_to produces the spike-and-dome morphology required for phase 2 reentry when repolarization reserve is increased due to either enhanced K⁺ conductance or decreased inward conductance, as in Brugada syndrome and short-QT syndrome characterized by gain-of-function mutations in K⁺ channels or loss-of-function mutations in Na⁺ or Ca²⁺ channels (126). Activation of I_K(ATP) serves a similar role in acute ischemia by summing with I_to to induce early repolarization promoting phase 2 reentry (37). In addition, mitochondrial depolarization causing I_K(ATP) activation during acute ischemia/reperfusion has been proposed to generate regional metabolic sinks that enhance electrical dispersion and create a tissue substrate vulnerable to reentry (127). Recent studies (123, 124) show that I_SK, normally expressed in atrial tissue, becomes upregulated in ventricular tissue during heart failure and may promote ventricular arrhythmias by shortening APD relative to the Ca²⁺ transient, promoting EADs in the late part of phase 3 (85, 86, 123, 128).

5.1.4. Ion transporters

Maintaining proper ion gradients across the cell membrane is required for cardiac myocytes to remain excitable and oscillatory. To maintain intracellular ion concentrations, Na⁺-Ca²⁺ exchange transports one Ca²⁺ ion for three Na⁺ ions, and Na⁺-K⁺ ATPase transports three Na⁺ ions for two K⁺ ions. Because both transporters are electrogenic, they affect both action potential and Ca²⁺ cycling dynamics. I_NCX prolongs APD and can promote EADs and is also a key player in DADs (91, 129) and automaticity (113). Blocking the Na⁺-K⁺ pump current (I_NaK) causes intracellular Na⁺ elevation, which promotes intracellular Ca²⁺ loading via the Na⁺-Ca²⁺ exchanger, Ca²⁺ waves, and thus DADs (130).

5.1.5. Miscellaneous ion channels and transporters

Other ion channels and transporters in ventricular myocytes may also play important roles in cellular dynamics. For example, Ca²⁺-activated nonselective cation channels [I_ns(Ca)] (14), Ca²⁺-activated Cl⁻ channels [I_Cl(Ca)] (131), and stretch-activated nonselective cation channels [I_SAC,ns] (132) are inward currents, which may contribute to EAD and DAD formation, as well as influencing repolarization and affecting APD restitution properties. Ion channels and transporters located in intracellular organelles, such as RyRs and SERCA in the SR and a variety of ion channels in mitochondria, also play critical roles in regulating subcellular Ca²⁺ cycling and cardiac energetics. These channels and transporters indirectly affect subcellular and cellular arrhythmia dynamics by modulating the properties of sarcolemmal ion channels and transporters, as discussed in more detail in the next section.

5.2. Ionic Homeostasis and Subcellular Ca²⁺ Cycling Dynamics

Intracellular Ca²⁺ cycling plays multiple critical roles in cardiac arrhythmias (88, 133). First, Ca²⁺ levels during systole and diastole directly affect Ca²⁺-dependent ionic currents, such as I_Ca,L, I_NCX, I_Ks, and I_SK, which then modulate cellular action potential dynamics. Second, Ca²⁺ regulates Ca²⁺-dependent signaling pathways, such as CaMKII, that in turn modulate ionic currents and Ca²⁺ cycling (Figure 5). Third, Ca²⁺ cycling can generate its own arrhythmogenic dynamics, including Ca²⁺ alternans and Ca²⁺ waves. As shown by recent studies, these dynamics are self-organizing phenomena of spatiotemporal systems. A ventricular myocyte contains more than 20,000 Ca²⁺ release units, which are coupled by Ca²⁺ diffusion via Ca²⁺-induced Ca²⁺ release. Each Ca²⁺ release unit contains a RyR cluster in which the RyRs fire collectively, producing an all-or-nothing, localized Ca²⁺ release event termed a Ca²⁺ spark (134, 135). Ca²⁺ sparks are random events but also have their own complex dynamics (135–137). Ca²⁺ alternans is a self-organized phenomenon arising from the interaction of Ca²⁺ sparks (i.e., the coupling of Ca²⁺ release units), as analyzed in our recent theoretical studies (56, 65, 66). In addition, different patterns of spatiotemporal subcellular Ca²⁺ alternans dynamics, including spatially discordant alternans (138) and transition from microscopic alternans to macroscopic alternans (139), have been demonstrated. The transition from Ca²⁺ sparks to Ca²⁺ waves reflects a signaling hierarchy: individual sparks, spark clusters, abortive waves, and persistent waves (140, 141), which can be described by the theory of criticality (97, 98). Three general properties of a diffusively coupled Ca²⁺ release unit network can account for the essential dynamics: random activation, refractoriness, and recruitment [the 3R theory (56)]. Self-organized criticality can be used to explain why Ca²⁺ waves occur much later than RyR recovery and SR refilling time, a time delay termed the idle period (142). In the formation of both Ca²⁺ alternans and Ca²⁺ waves, the coupling of Ca²⁺ release units plays a key role.

Dysregulation of intracellular Na⁺ can also promote arrhythmogenic dynamics (143). Elevation of intracellular Na⁺ enhances the Na⁺-K⁺ pump (increasing outward I_NaK) but slows intracellular Ca²⁺ removal by Na⁺-Ca²⁺ exchange (decreasing inward I_NCX). These effects tend to shorten the action potential and elevate intracellular Ca²⁺, which can promote arrhythmogenic Ca²⁺ cycling dynamics. The presence of late I_Na can cause Na⁺ overload, which then causes Ca²⁺ overload, facilitating CaMKII activation. CaMKII activation in turn amplifies late I_Na in a positive feedback loop, potentiating arrhythmia dynamics (53–55).

K⁺ (particularly extracellular K⁺) also affects arrhythmia dynamics. Normal extracellular [K⁺] concentration is 3.5 to 5 mM, and both lower and higher extracellular [K⁺] can cause arrhythmias. Specifically, elevation of extracellular [K⁺] depolarizes resting membrane potential and increases I_K1 and I_Kr, which shortens the action potential. Elevation of the resting potential first increases and then slows conduction velocity, eventually resulting in conduction failure. In contrast, lowering extracellular [K⁺] decreases I_K1 and I_Kr, which lengthens APD and destabilizes the resting potential. Lengthening APD can promote EADs, as well as increased Ca²⁺ loading. Lowering extracellular [K⁺] also inhibits the Na⁺-K⁺ pump, further promoting Na⁺ and Ca²⁺ overload. Ca²⁺ overload can then activate the CaMKII signaling pathway, which further potentiates Na⁺ and Ca²⁺ loading by increasing late I_Na and I_Ca,L. These effects act synergistically to promote arrhythmogenic cellular action potential dynamics, such as alternans, EADs, and DADs.

5.3. Genetic Factors

Genetic mutations in ion channels, transporters, and their regulatory and trafficking partners that predispose to cardiac arrhythmias have provided powerful insights illuminating the molecular basis of cardiac arrhythmias (4, 5). Although too broad a field to review in detail here, channelopathies that are caused by gene mutations, such as LQT syndrome, CPVT, short-QT syndrome, and Brugada syndrome, have been highly informative. So far, 13 genes for LQT, 4 genes for CVPT, and 7 genes for Brugada syndrome, with hundreds of mutations, have been identified (126, 144). A mutation may cause gain or loss of function that affects action potential or Ca²⁺ cycling dynamics through the dynamic mechanisms outlined above. For example, LQT mutations lengthen APD and predispose the myocytes to EADs, whereas CPVT mutations increase the RyR open probability and predispose the myocytes to DADs. A single gene mutation may have multiple consequences for cellular dynamics and disease phenotypes. For example, Na⁺ channel mutation 1795insD can cause both LQT syndrome and Brugada syndrome (145). Although genetic channelopathies are relatively rare, they share important commonalities with ventricular arrhythmias associated with common diseases. For example, arrhythmias in the setting of heart failure recapitulate features of LQT syndromes (e.g., reduced repolarization reserve promoting EAD-mediated arrhythmias such as polymorphic VT), and arrhythmias during acute ischemia recapitulate features of Brugada syndrome (phase 2 reentry). Both types of arrhythmias recapitulate features of CPVT (abnormal Ca²⁺ cycling promoting alternans, Ca²⁺ waves, and DAD-mediated arrhythmias).

5.4. Signaling Pathways

By modifying ion channel and transporter properties at the molecular level, a variety of signaling pathways critically influence arrhythmia dynamics (133, 146, 147–149), both acutely through post-translational modification of their protein targets (e.g., phosphorylation) and chronically by altering transcription, trafficking, and protein turnover (electrical remodeling, including gap junction remodeling). In addition to their effects on sarcolemmal ion channels/transporters, these signaling pathways also regulate Ca²⁺ cycling elements both acutely and chronically (excitation-contraction coupling remodeling), as well as gap junction coupling (gap junction remodeling). These pathways alter cellular metabolism (metabolic remodeling) and influence (a) nonmyocytes such as fibroblasts (structural remodeling), (b) vascular components (vascular remodeling), and (c) neural components (neural remodeling). Although too broad a field to review here, the most widely studied signaling pathways include the adrenergic/cholinergic, angiotensin/aldosterone, and CaMKII/calcineurin axes. They promote arrhythmias through their effects on Ca²⁺ cycling and ionic currents, as well as through modifying tissue coupling properties. Figure 5 plots part of the signaling pathways of protein kinases A and C and CaMKII and their effects on the SERCA pump, RyRs, and many ionic currents. By destabilizing subcellular-, cellular-, and tissue-scale dynamics and exacerbating tissue heterogeneity, these signaling pathways play a key role in increasing the susceptibility of the heart to arrhythmias.

6. CONCLUDING REMARKS

As this article reviews, cardiac dynamics are regulated by multiple factors operating over different temporal and spatial scales in a complex interactive network. We can briefly summarize the important general concepts as follows. First, molecular-scale events, such as genetic mutations, signaling, and metabolism, regulate ion channel and Ca²⁺ cycling properties. Second, the ionic currents determine the action potential and intracellular ion concentrations, but they are also regulated by voltage and ion concentrations as well as by signaling pathways. Third, Ca²⁺ cycling can independently give rise to arrhythmogenic subcellular and cellular dynamics. Fourth, because Ca²⁺ and voltage are bidirectionally coupled, the feedback loops between them give rise to a rich variety of cellular action potential dynamics. Fifth, the cellular action potential dynamics combined with tissue-scale factors promote tissue-scale dynamics, creating tissue substrates that generate focal excitations and are susceptible to initiation of reentry due to electrical dispersion. Sixth, the systems dynamics at the organism scale activate reflexes that feed back to the molecular level through activation of a variety of signaling pathways. Finally, even though these multiscale interactions are very complex, the two key hubs are voltage and Ca²⁺. Understanding the action potential and Ca²⁺ cycling dynamics is critical for relating molecular-scale events to the development of ventricular arrhythmias.

Table 1 summarizes our current understanding of the subcellular, cellular, and tissue-scale action potential and Ca²⁺ cycling dynamics, their corresponding mechanisms, their electrocardiographic characteristics, and their link to clinical diseases. We hope that this can be a useful platform that will facilitate the quest to move beyond engineering approaches (devices and ablation) to treat ventricular arrhythmias and to move toward the development of novel biological approaches. In this quest, we note that, even in the normal heart, lethal arrhythmias can be induced by rapid pacing or electrical shocks. In other words, from a dynamics perspective, both sinus rhythm and arrhythmias are solutions of the normal heart as well as the diseased heart. The occurrence of arrhythmias is a probabilistic transition from sinus rhythm to turbulent ventricular behavior. In the view of nonlinear dynamics, the objective of an effective therapy is to elevate the threshold governing the transition from sinus rhythm to arrhythmias without markedly altering normal sinus rhythm, i.e., to enlarge the basin of attraction of normal sinus rhythm while suppressing the basin of attraction of arrhythmias.

Table 1.

From subcellular/cellular/tissue dynamics to arrhythmias

Cellular (subcellular) dynamics	Tissue dynamics	Dynamic mechanisms/parameters	ECG characteristics	Related disease conditions
APD and Ca2+ alternans, chaos	APD and Ca2+ alternans, DOR, reentry	Steep APDR and CVR, steep FSRCR, 3R theory	TWA	LQTS, BS, HF, ischemia
EAD (Ca2+ oscillations)	Foci, DOR, biexcitability	RRR, Hopf bifurcation, steep APDR, chaos synchronization	PVC, TWA, NSVT, TdP	LQTS, HF
DAD (Ca2+ wave)	Foci	Criticality, synchronization	PVC, U-wave	CPVT, HF
Spike-and-dome	Phase 2 reentry	ERR, APDR, chaos	TWA, J-wave	BS, ERS, SQTS, acute ischemia
Automaticity (Ca2+ oscillations)	Foci	Hopf bifurcation, synchronization	PVC, NSVT	Idioventricular rhythms

Abbreviations: 3R theory, theory of Ca²⁺ alternans involving random activation, refractoriness, and recruitment of Ca²⁺ release units; APD, action potential duration; APDR, APD restitution; BS, Brugada syndrome; CPVT, catecholaminergic polymorphic ventricular tachycardia; CVR, conduction velocity restitution; DAD, delayed afterdepolarization; DOR, dispersion of refractoriness; EAD, early afterdepolarization; ECG, electrocardiogram; ERR, enhanced repolarization reserve; ERS, early repolarization syndrome; FSRCR, fractional sarcoplasmic reticulum Ca²⁺ release; HF, heart failure; LQTS, long-QT syndrome; NSVT, nonsustained ventricular tachycardia; PVC, premature ventricular complex; RRR, reduced repolarization reserve; SQTS, short-QT syndrome; TdP, torsade de pointes; TWA, T-wave alternans.

To achieve this goal, however, there are considerable challenges to overcome. First, a given molecular target, such as an ion channel, often has effects on multiple aspects of arrhythmia dynamics such that a drug effective at treating one mechanism may worsen another, potentially substituting one lethal arrhythmia for another. For example, class I antiarrhythmic drugs, which block Na⁺ channels, can successfully suppress PVCs. The CAST trial (6) was designed to test the hypothesis that suppressing PVCs with class I antiarrhythmic drugs would reduce mortality by reducing arrhythmia triggers. However, such drugs also lower excitability, especially in ischemic hearts, enhancing the vulnerability of the tissue substrate to reentry, which led to a higher death rate in the treated group in the CAST trial (6). Class III antiarrhythmic drugs, which block K⁺ channels, lengthen APD to prevent reentry. The SWORD trial (7) was designed to test the hypothesis that lengthening APD with class III antiarrhythmic drugs would reduce mortality by preventing reentry. However, these drugs also reduce repolarization reserve and promote EADs, which may have caused increased mortality in the treated group in the SWORD trial (7). Therefore, the ideal therapeutic intervention should suppress all dynamic mechanisms of arrhythmias described above or, at the very least, suppress one without exacerbating the others. Second, the occurrence of arrhythmias, especially VF, is unpredictable. These events are rare events, even when potential triggering events such as PVCs are common. One of the greatest challenges is to predict which patients are at the highest risk and need to be treated, whether by biologics or device therapy. In our view, future efforts not only should focus on specific arrhythmia mechanisms but also should require a systems view of ventricular arrhythmias to accurately predict arrhythmia risk, to identify the right therapeutic targets, and to develop effective and robust therapeutics.