Rotors and the Dynamics of Cardiac Fibrillation

Introduction

The term “rotor” is becoming a household name in cardiac electrophysiology. It applies to the organizing source of functional reentrant activity, particularly in the context of tachycardia and fibrillation. Emerging evidence clearly supports a major role for rotors as the drivers of cardiac fibrillation in animal models and in humans. Remarkably, much of what we have learned about the dynamics of rotors and the spiral waves generated by them derives from the field of computational biology and from the study of wave propagation in excitable media. In the heart, the atria and ventricles share similar dynamics of electric wave propagation despite their vastly different geometry, global structure, and ionic mechanisms. More importantly, the behaviors of the electric rotors and spiral waves that form in their respective walls are also similar and may be analyzed using tools derived from the study of nonlinear systems. Thus, we make an attempt to reconcile such concepts with the more traditional ideas about mechanisms of cardiac fibrillation. First we set our current knowledge of reentry in a historical context, and then briefly define the basic notions and the terminology used throughout the article. Subsequently, we review our current understanding of how rotors are initiated and the technologies that are used to localize them in the atria or ventricles, as well as to quantify their properties, including their dynamics and frequency of activation. We then present evidence demonstrating the similarities in the dynamics of rotors and their consequences that exist in all mammals, including humans. Here, we give attention to universal scaling laws that may govern such similarities. Thereafter, we focus on triggers and substrate as the essential factors involved, respectively, in the mechanisms of initiation and maintenance of rotors, followed by the ionic bases of rotor dynamics and the manner in which antiarrhythmic drugs can modify rotor behavior. We close the article by briefly looking into new evidence supporting the idea that rotors may be critical in sustaining both atrial fibrillation (AF) and ventricular fibrillation (VF) in the human heart and the manner in which such evidence might lead to more mechanistic approaches to effectively terminate AF in the clinical electrophysiology laboratory.

Evolving Theories About Reentry Over the Past Century

The topic of the history of reentry has been reviewed in detail recently.¹ Only the main points are highlighted here. Studies of fibrillation and its mechanisms have been performed since the turn of the 20th century. The first known experiments were conducted by Mayer² in jellyfish rings and turtle ventricular muscle in 1906. In Mayer’s experiments,² isolated rings of muscle could sustain circulating activity for long periods of time. Soon thereafter, the studies of Mines and Garrey^3–5 in rings of canine ventricular muscle formed the basis for the concept of anatomic reentry as we know it today. Lewis^6–8 postulated that AF and atrial flutter could be attributed to a circulating reentrant wavefront that encroached on its own partially refractory tail. The main difference between fibrillation and flutter was the gap or the nature of the encroachment of the front into the tail: the gap was fully excitable and quite large in flutter, whereas it was smaller and partially excitable in AF, because of the intermingled front and tail. These ideas progressed forward in the 1940s with the theoretical studies of Wiener and Rosenblueth, ⁹ who postulated that reentry around an obstacle was necessary to sustain fibrillation. In the 1960s, Moe¹⁰ challenged the prevalent concepts about reentry by postulating that instead of a single reentrant circuit, multiple randomly propagating wavelets were responsible for sustaining AF. Remarkably, Moe’s hypothesis¹⁰ was partly based on results obtained via innovative computer modeling studies.¹¹ In the 1970s, Allessie et al^12–14 proposed the leading circle hypothesis based on experiments conducted in the rabbit atrial muscle, in which electrical waves rotated around a functional obstacle. Subsequently, in 1985, Allessie et al¹⁵ provided the first experimental proof for Moe’s multiple wavelet hypothesis¹⁰ of AF in the canine atria. Meanwhile, the concept of rotors generating spiral waves was being developed in parallel via theoretical studies conducted in the erstwhile Union of Soviet Socialist Republics by Krinsky¹⁶ and in the United States by Winfree.¹⁷ It was proposed that these reverberators or rotors also could exist in the heart and underlie functional reentry. The first experimental demonstration of a spiral wave in the heart was made in an isolated sheep ventricular muscle slice by Davidenko et al in 1990.¹⁸ This was mainly possible because of the use of voltage-sensitive dyes that allowed for high-resolution mapping of the cardiac electrical activity.¹⁹ The subsequent 2 decades have seen a vast amount of knowledge gained regarding rotors, spiral waves, and their underlying mechanisms, partly because of the development of sophisticated tools and algorithms for their analyses, which have led to our current concepts regarding rotors and their role in cardiac fibrillation.^1,20,21 There is still debate about the precise mechanisms of fibrillation (small number of driving sources or rotors vs multiple wavelets).^1,21–24 Nevertheless, the concept of rotors as underlying drivers of fibrillation has driven the field forward and is poised to prove immensely beneficial as both basic scientists and clinical investigators use these ideas in developing mechanism-based therapies and treatment modalities for AF and VF in the next decade.

What Is a Rotor?

The traditional view of a wave propagating in a fixed ring-like path with an excitable gap separating the wavefront from its tail of refractoriness (Figure 1A)²⁵ is an accurate representation of anatomical reentry. In this model, the wavelength is defined as the spatial extension of the propagating wave (all of the depolarized cells) and computed as the product of the refractory period and the conduction velocity. Functional reentry, however, was initially described via the leading circle hypothesis (Figure 1B).¹⁴ According to this model, reentry requires no anatomical obstacle and there is no fully excitable gap as the circulating excitation wavefront encroaches on its tail. The tissue inside the leading circle is deemed to receive a centripetal excitation wavefront, which renders it refractory. A rotor is a similar form of functional reentrant activity (Figure 1C) but with a critical difference: the curved wavefront and wavetail meet each other at a singularity (white asterisk, Figure 1C), and the tissue at the center is not refractory.²⁶ The terms “spiral wave” and “rotor” have been used interchangeably by some; however, in the context of cardiac arrhythmias, rotors are drivers or organizing sources of fibrillation, be it AF or VF, and a spiral wave is more accurately a 2-dimensional (2D) representation of the curved vortices generated by the spinning rotor in its immediate surroundings.¹ The 3-dimensional representation of a spiral wave is termed a “scroll wave,” and its center of rotation is a hollow filament formed by the revolving trajectory of the spiral tip (Figure 1D). The latter represents the core of the spiral viewed from one surface, as depicted with the broken circle in Figure 1E. The presence of both scroll waves and filaments has been demonstrated in the heart in both numerical²⁷ and experimental studies.²⁸

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A schematic representation of a rotor generating spiral waves is illustrated in Figure 1E to allow for a closer look at the curved activation wavefront, the curved wavetail, and the point at which wavefront and wavetail meet. The wavefront represents an area of depolarized cells as the cardiac impulse travels forward, and the wavetail comprises the group of cells that have undergone full excitation (action potential upstroke) and are returning to rest (action potential repolarization). As discussed in detail, in 1998, Gray et al²⁹ developed a technique based on phase plane analysis to investigate cardiac fibrillation in optical mapping experiments and to identify the rotor, which was demonstrated to be a singularity point or phase singularity (PS), represented in Figure 1E by an asterisk. This allowed for the tracking of the spiral and its tip dynamics, in space, over time. When a rotor is stationary, it pivots as a PS around a circular trajectory forming the core of the spiral wave (Figure 1E); however, when the rotor meanders, its trajectory can take various complex shapes, depending on the tissue excitability.³⁰ As noted, the 3-dimensional representation of a spiral wave is the scroll wave. If the rotor is completely stationary and spans from the epicardium to the endocardium, then the filament of the spiral would be a linear cylinder (I-shape).²⁸ The filament can also bend, adopting varying nonlinear shapes (L-shape, U-shape, O-shape, etc).²⁷ If, however, the scroll wave meanders, then the PS would not form a cylinder but would move along a trajectory of which the complexity will depend on the degree of meandering. In this case, the filament would be a line.

Three important points of difference become immediately apparent between the theory of rotors and the so-called leading circle reentry. First, the leading circle idea does not consider the curvature of the rotating wavefront³¹ as a factor controlling the velocity of the impulse and the dynamics of the reentrant activity. The theory of rotors envisions that the propagation velocity of a wavefront in the 2D or 3-dimensional myocardium very much depends on its curvature; waves for which the front is concave propagate faster than planar waves, but the velocity of planar waves is faster than convex waves. Rotating waves consist of wavefronts, and the curvature progressively increases toward the center (the core). At the very tip (the PS), the convex curvature reaches a critical value that makes it impossible for the activity to invade the core. This leads to the second difference: the leading circle assumes full refractoriness at the core, produced by the continuing invasion of centripetal waves forming a ring of excitation around a functionally unexcitable obstacle, not unlike the anatomic obstacle of circus movement reentry similar to that described by Mines.⁴ Whether functional or anatomic, the obstacle at the center of the leading circle would make it impossible for the reentry circuit to meander or drift. In contrast, rotors can meander because they pivot around unexcited but eminently excitable tissue.³² As such, the mechanism underlying the rotation does not depend on the refractoriness at the core but on the exceedingly steep wavefront curvature at the PS, which slows conduction to a critical level that renders the wavefront unable to invade the core.²⁰ Third, unlike the leading circle, there is no fixed wavelength in rotor-generated spiral waves. In fact, the expanse between the wavefront and the wavetail varies, increasing as a function of the distance (as one goes away) from the PS (Figure 1E). This is because electrotonic gradients established between cells at the core and cells in the near vicinity significantly shorten the action potentials of cells near the core.²⁵ This point is particularly important because concepts regarding wavelength prolongation are frequently used in the literature, such as for quantifying the effects of antiarrhythmic drugs.^33–35 The spiral wave properties remind us that the wavelength is variable and should be used with caution. More accurate quantification of drug effects on reentry would be obtained by studying how the drug changes the spinning frequency of the rotor (discussed later), as well as its degree of meandering and the number of wavebreaks that its spiraling waves undergo in the periphery, as it happens in fibrillatory conduction.³⁶

Another important concept in reentry is the so-called excitable gap.³⁷ Analyzing the rotor and spiral wave properties allows one to discern this variable in a clear and quantifiable fashion, as shown in Figure 1F. This figure shows a snapshot of a simulated rotor generated in a 2D sheet that incorporated numeric ionic models of human atrial cells.³⁸ Each cell in the sheet mimics the electrical action potential phenotype seen in persistent AF.^39,40 The top panel shows a snapshot of membrane voltage distribution in the sheet. One can appreciate how current from a depolarized group of cells (red/orange, representing the wavefront) invades the resting cells/tissue in front of it (in dark blue). The bottom panel shows a plot of the product of the variables “h.j”, which represents the fast (h) and slow inactivation variables (j) of the Na⁺ current, I_Na,⁴¹ which is the main ionic current driving the spiral wavefront. These variables represent the availability of I_Na, and their value varies between 0.0 and 1.0. In other words, when “h.j” is 0.0, no I_Na is available, and the tissue is unexcitable (the white area in the bottom panel of Figure 1F), whereas a value of 1.0 means that the tissue is fully available for excitation. All of the other values between 1.0 and 0.0 represent the excitable tissue or gap, where I_Na is available, and a stimulus in this area may elicit a response. Thus, the excitable gap underlying a spiral in a 2D sheet also takes a spiral shape (Figure 1F).

Initiation of Rotors and Spiral Waves via Vortex Shedding

A rotor may be initiated in multiple ways.³⁰ This can involve standard cross-field stimulation protocols in theoretical studies,^38,42 where a plane wave generated by a linear stimulus applied at 1 side of a cardiac tissue sheet is followed by a second stimulus applied perpendicularly while the tissue is only partially recovered. The second stimulus, when timed appropriately and when located spatially in the refractory tail of the first wavefront, can lead to wavebreak and initiate a rotor. Similarly, a rotor can be initiated by unidirectional conduction block in cardiac tissue, resulting from tissue heterogeneities in excitability, repolarization, or conduction velocity⁴³ or even dynamical properties such as action potential alternans.⁴⁴ The underlying basis for rotor and spiral wave initiation is also explained by the phenomenon known as “vortex shedding,”⁴⁶ which occurs when a wave encounters an obstacle with sharp edges. Vortex shedding is analogous to the formation of eddies and turbulence, when a water flow reaches a bifurcation or interacts with a narrow barrier, and is rooted in the concept of critical curvature.⁴⁵ In brief, as discussed, a planar wavefront propagates faster than a convex wavefront; in fact, the greater the wavefront curvature, the slower the conduction velocity, up to a critical level at which propagation cannot occur.

The mechanism of vortex shedding was explained by Cabo et al⁴⁶ on the basis of the concept of wavefront curvature (R). Figure 2A shows a schematic representation of R, at a time when the wavefront (white) reaches the edge of the obstacle (red). The white curve bounds the area adjacent to the obstacle, which needs to propagate to the left to circumnavigate the obstacle. The radius R of this area is comparable to the width of the wavefront, which determines whether that wavefront (ie, the source) will be able to excite the tissue ahead of it (ie, the sink). In a series of experiments and concomitant simulations, Cabo et al⁴⁶ demonstrated the principle of wavebreak generated by vortex shedding. In simulations, they used a 2D sheet of ventricular cells incorporating the 1991 kinetics of Luo and Rudy.⁴⁷ For experiments, they used a thin slice of sheep ventricular epicardium; the slice was perfused with a voltage-sensitive dye and optically mapped.⁴⁶ An artificial linear obstacle was etched into the ventricular muscle sheet in both simulations and experiments (depicted in a cartoon in Figure 2B, where the obstacle is represented by a red line). As illustrated by the top panel of Figure 2C (condition I), when the excitability of the tissue was normal and a wave was initiated by a point stimulus near the lower right margin of the obstacle (asterisk), the wavefront proceeded to circumnavigate the obstacle without breaking or detaching from it, eventually extinguishing after activating the entire sheet.⁴⁶ As shown by the lower panel of Figure 2C, when the excitability of the tissue was diminished somewhat (condition II), either by reducing the maximum conductance of I_Na by 75% in simulations or by superfusing the tissue with the sodium channel blocker tetrodotoxin (TTX) in experiments, the same stimulation protocol yielded completely different results: now the wavefront moved upward but detached from the obstacle, curled, and began to rotate around its broken tip, generating a vortex.⁴⁶ In the top panel of Figure 2C (condition I), R is larger than the minimum radius of excitation or critical curvature R_Cr. Under these conditions, the front progresses laterally without detachment, successfully circumnavigating the obstacle. When R < R_Cr, (condition II) then the wavefront curls, eventually detaching from the obstacle to generate a vortex around a PS. From the study of Cabo et al,⁴⁶ one can infer how pathophysiological conditions such as ischemia or an infarct in the ventricles or atrial remodeling because of persistent AF, in which both I_Na density and excitability are reduced and numerous obstacles in the form of patchy fibrotic tissue exist,^48–50 setting the stage for initiation of the rotors that maintain tachycardia or fibrillation.

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The inability of the excitation wavefront to depolarize tissue at the PS and its tendency to curve underlies rotor initiation and is important in rotor maintenance as well.⁴⁶ The latter is demonstrated in Figure 2D, in which the normalized conduction velocity of the spiral excitation wavefront is plotted vs the distance from its tip (red line in the z axis).¹ It can be seen that the wavefront curvature is highest at the tip, and this results in a lesser conduction velocity near the rotation center. Away from the tip, the curvature is reduced and the normalized conduction velocity increases.¹ At the tip, there is constant mismatch between the amount of current needed to depolarize tissue ahead of the wavefront (sink) and the amount of depolarizing current available at the wavefront (source) in play, which causes the rotor to pivot or to meander in complex trajectories. If enough excitable tissue is available, then sustained reentry will occur. Thus, wavefront curvature–related sink-to-source mismatch at the tip is responsible for both rotor initiation (vortex shedding) and maintenance.

Phase Mapping of Rotors and Singularities

A step forward in the analysis of rotor dynamics was the development of the phase mapping technique by Gray et al in 1998.²⁹Figure 3A shows a typical optical signal recorded from a point on the epicardial surface of a rabbit heart during VF. We call this time series F(t), where “t” is time. In Figure 3B, the same signal was plotted in 2D phase space as F(t+τ) vs F(t), where τ is an embedded delay. This approach revealed trajectories rotating around a circle in the center. Then a phase variable “θ” was computed at each site on the cardiac surface and was defined as θ(t) = arctan[F(t+τ) – F_mean, F(t) – F_mean], where F_mean = threshold value, defined as mean value of 4 seconds of VF activity and τ ≈ ¼ the value of the cycle length during fibrillation.

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Phase mapping allowed for the generation of color phase movies and the quantification of rotor dynamics, which led to the clear identification of PS points, as illustrated in Figure 3C. Each color represents a phase in the excitation recovery cycle, and a PS is defined as a site where all of the phases converge, because at the PS the phase is arbitrary; in contrast, the surrounding elements exhibit a continuous progression of phase that is equal to ±2π around the PS.²⁹ The original approach of plotting the dynamics on phase space has allowed investigators to systematically study the initiation, maintenance, and termination of rotors in normal and pathophysiological conditions.⁵¹ However, the approach requires a careful choice of the embedded delay τ. More recently, a Hilbert transform–based approach facilitated computing the instantaneous phase.^52,53 Regardless of the approach, it is clear that wavebreak and formation of a PS are essential conditions for a rotor to exist. Moreover, we have learned through experiments and simulations that rotors need not be stationary but may meander over complex trajectories,⁵⁴ giving rise to irregular electrograms (Figure 3D).⁵⁵ In many cases, fibrillation is terminated because of a PS colliding with a boundary,^42,51 thereby extinguishing the spiral waves.

Dominant Frequency Mapping

In the late 1990s and early 2000s, experimental mapping of both AF and VF in isolated hearts of various animal models using optical imaging demonstrated that rotors, whether single, in small numbers, or sometimes multiple, were consistently detected during cardiac reentry.^56,57 It was possible to visualize the rotors and phase mapping also allowed tracking of their spatiotemporal dynamics, revealing that rotors were either stable, as in monomorphic ventricular tachycardia (VT), or constantly meandered over complex trajectories, as in polymorphic VT.⁵¹ The meandering rotors also were postulated to underlie both torsade de pointes,⁵⁸ as well as VF.⁵⁹ A further important development in the analysis of rotors occurred when their time-dependent behavior was analyzed in the frequency domain.⁶⁰ Fast Fourier transform analysis of optical signals within a given time window across vast extensions of the epicardial surface of the fibrillating atria or ventricles yielded a spatial frequency map of the signals in the area of interest.^57,60,61 Selecting the maximum frequency in the Fourier spectrum of each recording location allowed for the construction of so-called dominant frequency (DF) maps, as shown in Figure 4.⁶¹ Examples of optical and electrical signals from the left atrium (LA) and the right atrium (RA) of sheep and their respective power spectra obtained during AF induced via burst pacing in the presence of acetylcholine are shown (Figure 4A–4D). The 3-second time-dependent signals are on the left, and their corresponding frequency spectra obtained after fast Fourier transform analysis are on the right. Although multiple peaks of frequency can be observed in the individual spectra, dominant peaks of frequency can be identified in all. In Figure 4E, DF peaks from multiple locations recorded with a charge-coupled device camera in a 5-second optical mapping movie are plotted as DF maps superimposed on a schematic representation of the sheep LA and RA.⁶¹ A consistent finding in power spectral analyses obtained in this manner was that, in a majority of the experiments, the frequency of atrial activation during AF was higher in the LA compared with the RA. This finding has been replicated for AF in other species, such as pigs,⁶² and also in the electrogram analysis of AF frequencies for paroxysmal AF in humans.^63–65

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Thus, representation of fibrillation in the frequency domain demonstrates that AF⁶¹ (and also VF⁶⁶), rather than being the result of randomly propagating wavelets, shows a consistent spatial organization of frequencies, which is chamber-dependent. This has led to the following postulates. First, a spatially distributed hierarchy of DFs of excitation indicates that, in most cases, AF is sustained by a small number of high-frequency drivers (rotors) in the LA that maintain the overall activity. Second, the DF of the rotor(s) is exceedingly high and, therefore, can only drive in a 1:1 fashion the tissue in its immediate surroundings. Beyond this 1:1 domain, the wavefronts undergo intermittent, spatially distributed wavebreaks, with the end result being fibrillatory conduction toward distal areas in both the LA and the RA.^1,61,67 Thus, DF analysis of experimental data provided evidence for organization in some forms of fibrillation,⁶⁸ and this experimental observation was also supported by computer simulations,⁶⁹ as well as by mapping of rotors in 2D monolayers of rat neonatal ventricular cells, as shown in Figure 4F through 4I.⁷⁰ In this representative experiment, the bottom half of the monolayer was infected with an adenoviral construct for the gene coding hERG, the molecular correlate of the rapid delayed rectifier K⁺ current, I_Kr, whereas the top half was uninfected. This resulted in an I_Kr density gradient with higher I_Kr current magnitude in the bottom half and sustained rotor formation (Figure 4F).⁷⁰ The spiral wavefronts generated by the rotor in the I_Kr-infected region blocked intermittently at the interface and could not drive the uninfected region in a 1:1 fashion. Instead, as shown by the DF map in Figure 4G, a frequency gradient was established, with a higher DF in the infected region compared with the uninfected region. These results are similar to the LA-RA gradients in cholinergic AF experiments in sheep (Figure 4E)^60,61 and paroxysmal AF in humans.^63–65 In addition, when a regularity index, defined as the ratio of DF:total spectral power, was calculated for each video camera pixel recording the potentiometric dye fluorescence changes in the 2D monolayer, the values were unequally distributed. A vertical line (X-X′) drawn in the 2D monolayer dish (Figure 4H) showed the regularity index to be lowest at the interface between the infected and the uninfected regions (Figure 4I).⁷⁰ These data suggest that the most complex fractionation of the signal is observed at the interface/boundary between the hERG-infected and noninfected regions, where there is a sharp change in refractoriness (because of changes in density of I_Kr). Altogether, DF mapping has allowed for the demonstration that fibrillation is deterministic and displays organization, with a hierarchy of frequencies indicating underlying chamber-specific ion channel gradients, and the location of complex fractionated signals, which are at the periphery of the rotors.

Universal Scaling of Fibrillation Frequency

Mechanisms of fibrillation are being investigated in many laboratories using hearts from a variety of species, ranging from the mouse to much larger mammals, including dogs, sheep, goats, and pigs, as well as explanted human hearts. Thus, important questions arise regarding whether rotors can be observed across different species and whether the rotor properties obey common laws. The questions are motivated in part by the long-held contention that fibrillation cannot sustain in cardiac tissue for which mass is lower than critical.⁷¹ This critical mass idea was first challenged by the studies of Vaidya et al, ⁷² who showed that with burst pacing, one could create conditions in small mouse hearts for functional reentry and sustained VF, and that rotors could be observed in an area as small as 100 mm². By the mid 2000s, rotors and spiral waves had been demonstrated in isolated hearts from mice, rats, guinea pigs, rabbits, sheep, pigs, and dogs. To understand their common link, Noujaim et al⁷³ endeavored to quantify the relationship between body mass (BM) and VF frequencies. They were partly motivated by previous studies in which it was shown that many biological phenomena, such as metabolic rate, life span, respiratory rate, and ECG parameters like the PR interval scale with BM.⁷⁴ The general relationship is Y = a × (BM)^b, where Y is the biological variable of interest, “a” is a constant, and “b” represents the scaling exponent.⁷³ Results obtained by Noujaim et al⁷³ are reproduced in Figure 5. Figure 5A shows DF maps obtained in optical experiments during VF in a mouse, a guinea pig, a rabbit, and a human heart with body weights of 30 g, 600 g, 3 kg, and 90 kg, respectively. In each map, the DF domain is indicated in red as follows: 38.0 Hz for the mouse; 26.0 Hz for the guinea pig; 15.0 Hz for the rabbit; and 6.8 Hz for the human heart. Notice that although the body weight changes 4 orders of magnitude from mouse to human, the DF changes only 1 order of magnitude. In Figure 5B, a meta-analysis of data collected from 40 studies in 11 different species, from mouse to horse, is plotted as VF frequency vs BM on a double-logarithmic graph.⁷³ Fitting the data points revealed that VF frequency is ≈18.9 × BM^–1/4; in other words, VF cycle length turned out to be ≈53.0 × BM^1/4. Thus, analysis of VF in the frequency domain allowed for an all-inclusive pattern to emerge across mammalian species. The underlying mechanisms have not been elucidated completely, but it seems clear that changes in the species-related action potential duration (APD), along with the heart size, play a significant role.⁷³

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Triggers, Cardiac Structure, and the Formation and Maintenance of Rotors

The onset and maintenance of cardiac fibrillation require an event (trigger) that initiates the arrhythmia and the presence of a predisposing substrate that perpetuates it. In AF, well-known clinical studies have demonstrated that the majority of ectopic discharges initiating the arrhythmia emerge from the pulmonary vein (PV) sleeves,⁷⁵ which are known to terminate in dead-end pathways. In some patients, the electric properties of the muscle bundles in the PV sleeves seem to make them highly prone to generate high-frequency automatic or triggered discharges, which propagate into the posterior LA wall, of which the highly heterogeneous and anisotropic fiber bundle arrangements and abrupt changes in thickness⁷⁶ provide an ideal substrate for sink-to-source mismatch, wavebreak, and reentry formation. In a recent study in which brief trains of electric stimuli were used to trigger PV discharges at a high frequency, most of the wavebreaks that initiated AF appeared at the septal side of the septopulmonary bundle near the right superior PV, where the myocardial thickness dramatically expands.⁷⁷ It was clear that the source current provided by certain PV impulses was insufficient to overcome the vast sink of the transition posterior LA septum, which resulted in wavebreak, reentry, and AF. A somewhat different but related mechanism can initiate reentry and fibrillation in the ventricles. For example, at the Purkinje–muscle junction,⁷⁸ anatomic expansions are prone to conduction delays and block specifically in areas of abrupt electric current source-to-sink mismatch.⁷⁹ As discussed for the study of Cabo et al,⁴⁶ whether in the atria or ventricles, source-to-sink unbalance can explain wave detachment from obstacles and vortex shedding leading to rotors and fibrillation.

Once initiated, rotors will spin at very high rates to generate electric turbulence (fibrillatory conduction). Recently, using a chronic RA tachypacing model of persistent AF in the sheep, along with continuous cardiac rhythm monitoring by dual implantable devices, we demonstrated that rotors are capable of maintaining cardiac fibrillation in the long-term, even after both structural and electric remodeling have taken place.⁸⁰ We demonstrated that in vivo DF values during AF progressively increased while preserving in the long-term a DF difference between the LA and the RA. After follow-up periods of 9 to 24 weeks, mapping of the atria and subsequent structural analyses ex vivo confirmed the presence of DF gradients from posterior LA to RA, together with patterns of activation, all of which were consistent with the contention that rotors in an enlarged LA are fully capable of maintaining AF dynamics in the long-term. Similar to AF, the papillary muscle ventricular structures have been postulated to play an important role in the generation and maintenance of both VF and VT.⁸¹

The importance of structure in initiating reentry and arrhythmias was further reiterated in recent experiments in monolayers of neonatal rat ventricular myocyte (NRVM) cultures. Auerbach et al⁸² showed that in patterned monolayers consisting of 2 wide regions connected by a thin isthmus, reflection and arrhythmogenesis were enhanced. Bian and Tung⁸³ showed that reentry is readily induced by rapid pacing in NRVM monolayers containing a central and asymmetrical island containing a predefined zigzag pattern.

Ionic Basis of Rotors

Many investigators using either pharmacological tools in experimental animal models or numeric simulations have contributed to our current understanding of the underlying ionic basis for the initiation and maintenance of rotors (only a few are cited here because of space limitations).^84–94 However, the availability of genetic mouse models⁹⁵ and the reproducibility of consistent rotors in 2D monolayers of neonatal rat cells,^96,97 coupled with the development of biophysically detailed ionic mathematical models of murine ventricular electrophysiology,^98,99 allowed for a more robust dissection of the contribution of individual ion channels to high-frequency rotors from the year 2000 onward. In this section, we mainly discuss studies performed in our laboratory over the past decade, although we acknowledge the important contributions of numerous other investigators to this particular field.^87–94

The earliest studies focused on the role of the inward rectifier K⁺ channel (I_K1). Computer modeling studies of 2D reentry¹⁰⁰ and experimental studies in guinea pig hearts⁶⁶ suggested an important role for I_K1 in the spatiotemporal organization of VF frequencies across different chambers of the heart. The importance of I_K1 received further support from studies that showed that VF frequencies were slowed and VF was subsequently terminated by BaCl₂ at concentrations of 1 to 50 µmol/L, which were relatively selective for I_K1 blockade.⁸⁴ The chamber-specific LA-RA spatiotemporal gradient of AF frequencies in the presence of acetylcholine was attributable to different densities of another inward rectifier K⁺ channel, the acetylcholine-activated K⁺ current, I_KACh.⁶⁷ The density of I_K1 also was found to be upregulated in atrial myocytes isolated from chronic AF patients.^101–103 When computer simulations were conducted to examine the consequences of I_K1 increase, the rotors were found to be faster, and the tip meander was reduced, being confined to a smaller area, thus stabilizing fibrillation.³⁸ Those simulations suggested that in addition to causing a shorter APD, I_K1 accelerated rotors by increasing the availability of I_Na; this was possible because of the hyperpolarization of the resting membrane potential by I_K1. Although this hyperpolarization was small (≈5 mV), the change in resting membrane potential occurred over the steep portion of the availability curve for I_Na and, thus, resulted in a dramatic acceleration of the rotor.

The first direct demonstration of the role of I_K1 was made possible when transgenic (TG) mice in which I_K1 was overexpressed became available.¹⁰⁴ Sustained rotors induced in isolated TG mouse hearts were very long-lasting (>1 hour) and extremely fast (≈50–60 Hz); by contrast, in wild-type hearts, rotors were much slower (≈20–25 Hz) and lasted less than ≈10 seconds.¹⁰⁵ In Figure 6A, we compare the activation map of a rotor observed experimentally in a TG mouse with I_K1 overexpression (right) vs a wild-type heart (left). It is clear that the rotor completes 1 rotation much earlier in the TG mouse (note the different time scales). These experimental results were confirmed in computer simulations, using a detailed ionic mathematical model of the mouse ventricular action potential, which incorporated all of the major K⁺ currents recorded experimentally.¹⁰⁵ The simulations further supported a key role for I_K1 and I_Na as important ionic mechanisms determining fast rotor activity.

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Although relevant, the studies in the mouse did not reveal the role of the 2 main repolarizing K⁺ currents in the human ventricle, that is, the fast and the slow delayed rectifier K⁺ currents, namely, I_Kr and I_Ks.¹⁰⁶ These currents do not contribute in a meaningful way to the short APD in the mouse ventricle.¹⁰⁶ Studies in higher mammalian hearts did show that E-4031, a relatively selective blocker of I_Kr, could slow VF frequencies.⁹⁴ In addition, in a rabbit model of 2D reentry created via cryoablation of the ventricular endocardium, it was shown that perfusion of nifekalant, a relatively selective blocker of I_Kr, terminated rotors mostly because of their collision with the atrioventricular groove.⁹³ Therefore, we investigated the role of these delayed rectifier K⁺ currents in monolayers of confluent electrically coupled NRVM using an approach modified from that described originally by Rohr et al.⁹⁶ At 5 to 6 days of age, the action potential of NRVMs present a plateau and APD of ≈200 ms, which would allow both I_Kr and I_Ks to activate. To further increase the density of either I_Ks or I_Kr, we used adenoviral transfer of genomic sequences of either KvLQT1-minK or hERG, respectively, in NRVM monolayers and studied their effects on rotor dynamics.^107,108 To our surprise, I_Ks overexpression did not increase rotor frequency at all; however, over time, the excessive I_Ks caused an increasing number of wavebreaks to occur. This is illustrated in Figure 6B by the representative phase maps in a control monolayer and a monolayer in which I_Ks was overexpressed.¹⁰⁷ Experiments in HEK cells and computer simulations suggested that the increased wavebreak incidence observed in monolayers was attributed to the phenomenon of postrepolarization refractoriness because of residual outward I_Ks current after the action potential.¹⁰⁷ This phenomenon was demonstrated previously in guinea pig ventricular myocytes in the late 1980s.^109,110

In Figure 6C, overexpression of I_Kr caused the rotor to accelerate significantly compared with control.¹⁰⁷ Concomitant simulations showed that the acceleration attributed to I_Kr increase was not comparable with that caused by I_K1 overexpression.¹⁰⁸ Interestingly, both simulations and experiments showed a novel mechanism underlying rotor acceleration, in addition to APD shortening: transient resting membrane potential hyperpolarization, which again would indirectly affect rotor frequency by modifying I_Na availability.¹⁰⁸ Sekar et al¹¹¹ conducted similar experiments with overexpression of I_K1 in rat neonatal monolayers, which supported the conclusions from our mouse studies.¹⁰⁵

In addition to K⁺ channels, the Ca²⁺ channels and the excitation-contraction (E-C) coupling machinery also influence the cardiac action potential and repolarization,¹¹² and both are also likely to influence the spiral wave dynamics, although the results remain controversial. In a study from our laboratory that examined the effect of verapamil on VF, the DF was reduced, core meander was increased, and VF was converted to VT.⁸⁵ However, these results must be interpreted with caution because at the concentrations of verapamil used in this study, verapamil blocks the L-type Ca²⁺ channel, I_CaL, and I_Kr.¹¹³ The role of intracellular Ca²⁺ in sustaining VF/spirals is also less clear and remains controversial. Studies from the Zaitsev laboratory^114,115 suggested that intracellular Ca²⁺ action potential dissociation during VF was a consequence, not a cause, of wavebreaks in VF and that no spontaneous voltage-independent intracellular Ca²⁺ waves could be seen. However, others have challenged these findings.¹¹⁶ In contrast, intracellular Ca²⁺ has been shown to be important in the initiation of spontaneous activity in Torsade de Pointes (TdP)¹¹⁷ and inherited arrhythmias, such as catecholaminergic polymorphic ventricular tachycardia, which can then give rise to the initiation of rotors and fibrillation.¹¹⁸ Finally, the Na⁺ current, I_Na, is key in determining excitability and the upstroke of the cardiac action potentials and is the main current driving the wavefront during normal propagation, as well as during rotor activity. We have assessed the role of I_Na in rotor dynamics either directly via TTX, which blocks I_Na,^86,119 or indirectly by elevating concentrations of extracellular K^+42,62 or simulating conditions of global ischemia,¹¹⁹ which limit the availability of I_Na because of a depolarized resting membrane potential. In every case, a reduced I_Na decreased the DF of the rotor and increased its meander. If I_Na was blocked sufficiently (by TTX or extracellular K⁺), then the rotor was terminated by collision with a boundary, abolishing AF or VF. However, in many instances, antiarrhythmic class I drugs that block I_Na, such as quinidine, do not always terminate fibrillation but either sustain it⁵⁸ or convert it to VT (unpublished observations). TG mice with ablation of SCN5A, the gene coding Na_V1.5, which is the molecular correlate of I_Na, display an increased susceptibility to arrhythmogenesis, including VT/VF.¹²⁰

Antiarrhythmic Drugs and Rotors

A direct consequence of the increase in the knowledge of the ionic mechanisms of rotors has been to understand how this information can be applied to design and select more efficacious antiarrhythmic drugs to treat cardiac fibrillation. As discussed, I_K1 and I_Na seem to have dominant effects on reentry properties (frequency and meander). Thus, we have begun to investigate drugs that can block these channels, particularly I_K1, and to examine their putative effects on reentrant activity. We compared the effects of chloroquine, an antimalarial drug, with that of quinidine, a class I antiarrhythmic, on VF and rotor dynamics.¹²¹Figure 7A shows DF maps during VF in a TG mouse heart overexpressing I_K1; the top panel shows the effect of quinidine, whereas the bottom panel depicts the effect of chloroquine, and the former reduced VF frequency but did not terminate the arrhythmia, whereas the latter restored sinus rhythm.¹²¹ The normalized DFs in the absence and presence of quinidine/chloroquine are shown in an aggregate of experiments and demonstrate that chloroquine terminated VF in all of the experiments (Figure 7B). Based on patch-clamp and molecular structure data, we hypothesize that the greater success for terminating VF in the case of chloroquine was, in part, attributed to its greater ability to block I_K1. Similar results were observed in a recent study conducted in a sheep model of stretch-induced AF.¹²²Figure 7C shows DF maps of the posterior LA during stretch-induced AF in an isolated heart before and after coronary perfusion of chloroquine; the drug reduced the rotor frequency.¹²² These data were compared with those of flecainide, another class I antiarrhythmic, as summarized in Figure 7D. Flecainide failed to terminate AF in any experiment but converted while converting AF to atrial tachycardia in 2 of 5 experiments at clinically relevant concentrations.¹²² In contrast, chloroquine terminated AF and restored sinus rhythm in 7 of 7 experiments.¹²² These initial experiments testify to the applicability of concepts learned through the theory of rotors as a mechanism of both AF and VF, that is, drugs that block I_K1 likely will have greater potency in abolishing cardiac fibrillation. These studies represent only a beginning and would be strengthened by the design of new drugs that can putatively block I_Na/I_K1 without being proarrhythmic and are tested in differentarrhythmia/pathophysiological models. An interesting corollary is the antiarrhythmic effect of regional cooling on the myocardium, which seems to reduce the frequency and then terminates VF by unpinning of rotors, which then drift toward the periphery, away from the cooled region, and extinguish by subsequent collision with a boundary.¹²³

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Spirals in the Human Heart

Most studies of rotors and their analysis until today have been confined to experimental animal models and numeric simulations. Computer modeling studies conducted in either simplified 2D sheets or complex and geometrically realistic 3-dimensional models of the human atria and ventricles have demonstrated that it is possible to induce sustained rotors that drive both AF^38,124 and VF.^125,126 However, experimental data from humans have been elusive and difficult to obtain. Recent in vivo or epicardial surface mapping studies in humans have demonstrated the presence of rotors during VF.^53,126 Nanthakumar et al^73,127 have demonstrated the presence of rotors or even scroll waves¹²⁸ during early VF with electric/optical mapping in Langendorff-perfused human hearts. An optically mapped rotor on the human ventricular epicardial surface is shown⁷³ (Figure 8A). Another case in point is the recent work of Narayan et al, ¹²⁹ who have used basket catheters to demonstrate sustained sources, a majority of them consisting of rotors, as key driving mechanisms underlying persistent AF. This study showed that patients with persistent AF had a higher number of sources and also had a shorter cycle length compared with patients in paroxysmal AF.¹²⁹ An example of a rotor in the LA generating fibrillatory conduction in the RA during AF is shown in Figure 8B.¹²⁹ Even more remarkably, the authors could target these spirals via catheter-based radiofrequency ablation and slow or terminate AF in a manner of minutes rather than hours, as is typically the case.¹³⁰ These initial reports are intriguing and exciting. They provide the first support for the role of rotors as key drivers of sustained AF in humans. If reproduced consistently by other laboratories, this mechanistically based approach could substantially improve the safety and the outcome of radiofrequency ablation and benefit many patients.

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Conclusions

Emerging evidence clearly supports a major role for rotors as the drivers of cardiac fibrillation in animal models and in humans. It is our prediction that in the next decade, more reliable and high-resolution methods and devices will be developed to identify rotors and spiral waves consistently during AF and VF in vivo. These studies will immensely benefit ablation and electric/defibrillator therapies in the short-term. However, we expect that as more mechanistic insights regarding the ionic/molecular basis of rotors continue to emerge, novel, more efficacious, and safer therapeutic approaches (either preventive or curative) will eventually come of age to provide relief from the debilitating and potentially lethal effects of rotors/fibrillation in less expensive ways to a much larger population worldwide.

Acknowledgments

The authors thank Kate Campbell and Sergey Mironov for assistance with some of the figures.

Footnotes