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Cardiovascular Research 2000 48(2):220-232; doi:10.1016/S0008-6363(00)00177-2
© 2000 by European Society of Cardiology
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Copyright © 2000, European Society of Cardiology

Dynamics of wavelets and their role in atrial fibrillation in the isolated sheep heart

Jay Chena, Ravi Mandapatib, Omer Berenfelda, Allan C Skanesc, Richard A Grayd and José Jalifea,*

aDepartment of Pharmacology, SUNY Upstate Medical University, Syracuse, NY, USA
bDepartment of Pediatrics (Cardiology), SUNY Upstate Medical University, Syracuse, NY, USA
cUniversity of London, London, Ontario Department of Medicine (Cardiology), London, Canada
dDepartment of Biomedical Engineering, University of Alabama at Birmingham, Birmingham, AL, USA

* Corresponding author. Tel.: +1-315-464-7949; fax: +1-315-464-8000 jalifej{at}upstate.edu

Received 6 December 1999; accepted 28 June 2000


   Abstract
Top
 Abstract
1 Introduction
 2 Methods
 3 Results
 4 Discussion
 5 Conclusion
 References
 
Background: The multiple wavelet hypothesis is the most commonly accepted mechanism underlying atrial fibrillation (AF). However, high frequency periodic activity has recently been suggested to underlie atrial fibrillation in the isolated sheep heart. We hypothesized that in this model, multiple wavelets during AF are generated by fibrillatory conduction away from periodic sources and by themselves may not be essential for AF maintenance. Methods and results: We have used a new method of phase mapping that enables identification of phase singularities (PSs), which flank individual wavelets during sustained AF. The approach enabled characterization of the initiation, termination, and lifespan of wavelets formed as a result of wavebreaks, which are created by the interaction of wave fronts with functional and anatomical obstacles in their path. AF was induced in six Langendorff-perfused sheep hearts in the presence of acetylcholine. High resolution video imaging was utilized in the presence of a voltage sensitive dye; two-dimensional phase maps were constructed from optical recordings. The major results were as follows: (1) the critical inter-PS/wavelet distance for the formation of rotors was 4 mm, (2) the spatial distribution of wavelets/PSs was non-random. (3) the lifespan of PSs/wavelets was short; 98% of PSs/wavelets existed for <1 rotation, and (4) the mean number of waves that entered our mapping field (15.7±1.6) exceeded the mean number of waves that exited it (9.7±1.5; P<0.001). Conclusions: Our results strongly suggest that multiple wavelets may result from breakup of high frequency organized waves in the isolated Langendorff-perfused sheep heart, and as such are not a robust mechanism for the maintenance of AF in our model.

KEYWORDS Acetylcholine; Arrhythmia (mechanisms); Mapping; Conduction (block); Supraventr. arrhythmias

This article is referred to in the Editorial by A.G. Kléber (pages 181–184) in this issue.


   1 Introduction
Top
 Abstract
 1 Introduction
2 Methods
 3 Results
 4 Discussion
 5 Conclusion
 References
 
For many years, atrial fibrillation (AF) has been generally accepted to be a reentrant arrhythmia. Yet, the exact electrophysiological mechanisms of its initiation and maintenance are still not fully understood. Two major hypotheses have been proposed to explain AF maintenance: (1) The multiple wavelet hypothesis, and (2) a single or small number of reentrant source(s) giving rise to fibrillatory conduction. Proponents of the more widely accepted multiple wavelet hypothesis, originally postulated by Moe et al. in the early 1960s [1–3], regard AF as being the result of spontaneous wavebreaks that constantly generate randomly wandering daughter wavelets, which collide, mutually annihilate, coalesce, or give rise to new wavelets in a self-sustaining turbulent process. Moe's computer model [3] predicted that a critical number of 23 to 40 wavelets was necessary for the maintenance of AF. Any factor that increased the total number of wavelets would serve to perpetuate the arrhythmia while, conversely, any factor that decreased the total number of wavelets would favor termination. In 1985, Allessie et al. [4] provided the first demonstration in vivo of multiple propagating electrical waves during cholinergic AF in the canine heart, and surmised that a minimum of four to six wavelets was necessary for the perpetuation of the AF. However, to our knowledge, definitive proof that the perpetuation of AF indeed depends on a critical number of wavelets has never been demonstrated.

Recent studies from our laboratory [5,6] in an isolated heart model of AF have demonstrated stable organized high frequency activity localized mainly to the left atrium supporting the idea that high frequency sources that are reentrant [5,6] or focal [7,8] in nature may be the underlying mechanism of AF. Breakup of such activity seemed to be responsible for the generation of multiple wavelets. This is in agreement with work from other investigators [7–12]. We therefore undertook to study and quantify in detail, the interaction of wavefronts with functional and anatomic obstacles, and to characterize the newly produced wavelets that result from that interaction. To this end, we used two-dimensional phase mapping [13,14], a newly developed analytical tool, that allows sensitive and accurate detection of wavebreaks and wavelets, in conjunction with high resolution video imaging, to quantify the dynamics of wavelets during acute sustained AF, induced in the presence of acetylcholine (ACh) in the isolated sheep heart. Using a different technique, recent novel work by Rogers et al. on ventricular fibrillation has also characterized and identified wavefronts in a similar fashion [15,16]. Our objectives were: (1) to study the dynamics of wave front–obstacle interactions, (2) to quantify the initiation, propagation, and termination of wavelets produced by wavebreaks during AF, (3) to elucidate the relative importance of these wavelets in the maintenance of AF in our model.

1.1 Terminology

  • Atrial fibrillation: as in previous publications from this laboratory [5,6,17,18], AF is indicated if the biatrial electrogram exhibits a rapid sustained irregular rhythm with variability in morphology and baseline on a beat-to-beat basis.
  • Wavebreak: a term assigned to the event of blockade of a wave segment while the rest continues to propagate [13,14,19]. In the edge of the propagating wave, and only there, the depolarizing front of the propagating wave meets its own repolarization tail, creating a phase singularity point.
  • Phase singularity (PS): occurs when a wavebreak is formed and is located at the instantaneous center of the rotational activity (for a more technical definition see below and Refs. [13,14,20,21]).
  • Chirality: the sense of rotation around a PS; ‘+’=clockwise rotation, ‘–’=counterclockwise rotation.
  • Wavelet: a segment of excitation wave front, regardless of size, bounded on each end by a PS or a boundary [22–25].
  • Rotor: a rotor is defined as a wave of excitation rotating around a PS for one or more cycles.
  • Critical inter-PS distance: the critical inter-PS distance is the smallest distance for which propagation between these two PSs succeeds. The inter-PS's distance was measured at the instant when the wavefronts of the two rotors with opposite chirality attempted to propagate between the PSs. At this phase of reentry, the wavelet is of minimal dimension in relation to the capacitance load sink immediately ahead and therefore the safety factor for propagation is lowest [20].


   2 Methods
Top
 Abstract
 1 Introduction
 2 Methods
3 Results
 4 Discussion
 5 Conclusion
 References
 
2.1 Experimental protocol
2.1.1 Langendorff-perfused sheep heart preparation
Healthy young sheep of either sex (18–25 kg) were anesthetized with 35 mg/kg of sodium pentobarbital. The heart was rapidly removed and connected to a Langendorff apparatus. This method has been described elsewhere in detail [5,6,17,18]. In short, the coronary arteries were continuously perfused via a cannula in the aortic root with warm (36–38°C) buffered Tyrode's solution at a flow-rate of 115–140 ml/min. To reduce the heart's motion to a minimum, methoxyverapamil (D600, 2 µM) was continuously perfused throughout the experiment [5,6,26]. A bolus injection of 5–10 ml of the potentiometric dye di-4-ANEPPS (10 mg/ml) dissolved in DMSO, injected into the perfusion cannula, enabled us to simultaneously image the fluorescence resulting from changes in transmembrane potentials from the epicardial surfaces of both atria in the absence of mechanical artifacts. After adding acetylcholine (ACh; 0.1–0.5 µM) to the perfusate, AF was induced by burst rapid atrial pacing from the epicardial surface of either the right atrium (RA) or left atrium (LA). AF was considered sustained if it lasted >2 min. In most experiments, once initiated, AF lasted more than 20 min.

2.1.2 High-resolution optical mapping
The video imaging approach used for these studies was a modification of that described elsewhere in detail [5,6,17]. We simultaneously recorded from 20 000 sites in the RA free wall and 10 000 sites in the LA appendage using two identical cameras. Briefly, quasimonochromatic light (530 nm) was shone directly onto the epicardial surface of the atria. The emitted fluorescence was transmitted through a 640 nm filter, projected onto two CCD video cameras (Cohu 6500; San Diego, CA, USA), and then acquired at a rate of 120 frames per second (sampling at 8.33 ms intervals). Both video cameras were triggered simultaneously by a delivered pulse. Spatial low-pass conic filtering was applied to improve the signal-to-noise ratio, which resulted in an effective spatial resolution of less than 0.5 mm (for details see Baxter et al. [27]). The areas of the mapped regions were as follows: 3x5 cm of the RA free wall, 3.5x3.5 cm of the LA appendage. This represents approximately 40% of the total surface area of the sheep atrium, including the septum.

2.2 Data analysis
2.2.1 Two-dimensional phase maps
We quantified the patterns of wave propagation during AF using phase mapping [13,14], a recently developed technique, which highlights the formation of wavebreaks and the resulting phase singularity points. In panel A of Fig. 1, the fluorescence (F) changes recorded by a single camera pixel (asterisk in panel C) during VF is presented as a function of time. In panel B, the fluorescence of this pixel at time ‘t’ F(t), was plotted against the fluorescence of the same pixel offset by a time interval {tau}. The value of {tau} was chosen as two frames (16.7 ms), which is the lowest average lag that significantly minimized the correlation of F(t) and F(t–{tau}). A cyclic return map of F(t) vs. F(t–{tau}) was constructed. This allowed a new parameter, the phase {theta}(t), to be defined as the angle of the coordinate [F(t), F(t–{tau})] around the mean fluorescence for that given pixel, with values between –{pi} and {pi}, represented as a continuous color scheme from red to purple. After the transformation, a new phase field, {theta}(x,y,t), was produced including all pixels, whereby the upstroke of the action potential, and hence the activation wave front, corresponded to the colors yellow/green, while the plateau of the action potential corresponded to the colors blue and purple. The refractory tail of the action potential corresponded to the colors red and yellow. A phase singularity (PS) was defined at the point where all phases converged. All phase singularity points were determined and analyzed by two investigators. Confirmation from both investigators was necessary for the analysis of a phase singularity point to continue. In panel C, we present a single snapshot (phase map) of a phase movie with a single wavelet that rotated clockwise around a PS (+). By analyzing return maps similar to those presented in panel B with different artificial levels of noise, we estimated the repeatability of localizing the PSs to be of about 1.0 mm [14,28]. We also studied the impact of noise on the formation of PSs. Based on examination of monomorphic tachycardia, we confirmed that up to a signal-to-noise ratio of 3 in our raw data, the PSs observed in our analysis are not an artifact of the noise [14].


Figure 1
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  		Fig. 1 Construction of two-dimensional phase maps. (A) Fluorescence of a single pixel during AF. (B) The fluorescence (F) is plotted as a return map {F(t-2) vs. F(t)}, where time, t, is the frame number and 2 is the number of lagging frames. The action potential phase, {theta}[t], is calculated around the mean fluorescence. The colors denoted for each value of {theta}[t] are shown, see Section 2.2.1 for details. (C) Two-dimensional phase map of a clockwise rotor during AF. The (+) sign indicates the PS location and corresponds to the rotor chirality. Yellow/green corresponds to the activated wave front; violet corresponds to the plateau of the action potential, and red corresponds to refractory or recovered tissue.

 
2.2.2 Spatial and temporal characteristics of wavelet behavior
To determine the drift and spatial distribution of PSs, their coordinates in space were followed over time. The critical inter-PS distance for the formation of rotors was obtained from analyzing 21 episodes of AF from six different hearts. For the analysis of drift, spatial distribution, lifespan of PSs, as well as counting the total number of wavebreaks (see below) that were especially time consuming, a subset of data (eight episodes from four hearts) was randomly selected. Finally, the number of electrical waves that entered and exited the field of view were measured by following activation wave fronts in 21 episodes from six hearts. In all cases, the last 50 frames (~400 ms) of each 400-frame episode (~3.3 s) were analyzed.

The measurement of wavelet lifespan consisted of identifying the wavelets flanking PSs and tracing their subsequent movement frame by frame until termination. Those PSs that drifted out of the field of view (<2%) were not included in this analysis since their lifespan could not be determined.

Two additional experiments were performed in the absence of methoxyverapamil (D600) to measure the lifespan of wavelets, as there have been studies suggesting that the L-type Ca++ channel current may become important for impulse propagation under conditions of current-to-load mismatch [29].

2.2.3 Statistical analyses
The data are presented as mean±standard error of the mean (SEM) for group comparisons and as mean±standard deviation of the mean (SDM) for individual group statistics. Comparisons were performed using standard analysis of variance (ANOVA). The randomness of the spatial distribution of wavebreaks was compared to a Poisson distribution using {chi}2-analysis. P<0.05 was considered to be statistically significant.

The investigation conforms with the Guide for the Care and Use of Laboratory Animals published by the US National Institutes of Health (NIH Publication No 85-23, revised 1996).


   3 Results
Top
 Abstract
 1 Introduction
 2 Methods
 3 Results
4 Discussion
 5 Conclusion
 References
 
3.1 Experimental confirmation of PS formation and termination
Wavebreaks, as indicated by the presence of PSs, occurred frequently during the analyzed episodes of AF. We counted a total of 69.4±39.6 (range 23–154) PSs formed per 400 ms of recording. We present in Fig. 2 the first in-depth experimental quantification of theoretical predictions for the initiation of a wavebreak, secondary to the interaction of a wave front with a functional obstacle during AF (i.e., vortex shedding) [20,23–25]. Here we demonstrate how a pair of phase singularity points is produced at the broken ends of the wavelets [13,14,18] on the epicardial surface of the LA, and leads to a relatively long-lasting episode of figure-eight reentry (~three rotations). In panel A, there are two depolarizing wave fronts present (depicted by the color green). The wave seen at the upper edge of the field of view propagates downward and extinguishes upon refractory tissue (red) in the center of the field of view. As shown in panel B (16 ms), the wave on the lower edge of our mapping field propagates upward and breaks upon a functional obstacle (red) resulting in two phase singularity points (‘+’ and ‘–’) of opposite chirality (sense of rotation). In panels C and D, 24 and 32 ms, respectively, the two counter-rotating wavelets begin to propagate around the two PSs. In Panel E (56 ms), the two free ends of the wavelets merge and begin to propagate between the phase singularities. At this time, the inter-PS distance is 6.8 mm. Panel F (80 ms) shows the wave front after successfully propagating through the isthmus and completing a full cycle of figure-of-eight reentry.


Figure 2
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  		Fig. 2 Complete reentry. (A) (0 ms), two wave fronts (green) moving in opposite directions (arrows) are shown. The first wave front (white arrow) propagates from the top edge and extinguishes on refractory tissue (red). The second wavefront (black arrow) propagates from the bottom edge. (B) (16 ms), the second wave front breaks upon refractory tissue resulting in formation of two PSs (+ and – indicate their corresponding chirality). (C and D) (24 and 32 ms, respectively), two wave fronts rotate around their PSs. (E) (56 ms), the wave fronts merge and begin to propagate between the two PSs (inter-PS distance=6.8 mm). (F) (80 ms), complete figure-of-eight reentry. The numbers at the bottom of each panel correspond to the time in milliseconds from frame A (arbitrarily chosen as time t = 0).

 
It is important to note that the distance between PSs varies during a cycle because of meander or drift; e.g., compare inter-PS distance in panels B and E of Fig. 2, where the distance between PSs is smaller at initiation of reentry (panel B) as compared to the time of inter-PS measurement (panel E). The inter-PS distance measurements were made for all AF episodes at the instant of time when the wavefronts of the two oppositely rotating wavelets attempted to propagate between the PSs. At this phase of reentry the wavelet is of minimal dimension in relation to the capacitance load immediately ahead and therefore the safety factor for propagation is lowest [20]. The wave, therefore, succeeds or fails to propagate between the phase singularity points, according to source–sink relationships.

Rotors had a propensity to drift and were rarely stationary from frame to frame. In many instances, after the initial formation, each separate PS drifted apart and one or both PS subsequently interacted with another PS of opposite chirality. In that case, there was mutual annihilation when the former came too close to the latter. If one of a pair was annihilated by a third PS, a single PS remained around which a wavelet could rotate for some time as a single rotor (see Fig. 1C). In Fig. 3, we present the X and Y coordinates of two long-lived PSs of opposite chirality (dark and shaded spheres) from the time of their formation until termination with another PS. Each rotor lasted approximately three rotations before annihilation. In this example, the rotors drifted anywhere between 0.1 mm and 5.3 mm in a single frame. In other examples, PSs drifted out of the field of view. For such cases, we were unable to follow their subsequent fate but it is likely that their behavior was similar to those PSs in the field of view.


Figure 3
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  		Fig. 3 Drift of two counter-rotating rotors. The X and Y coordinates of two counter-rotating PSs are plotted over time from initiation throughout three full rotations.

 
3.2 Critical inter-PS distance for complete reentry
In Fig. 4, we present phase maps from a different episode of AF where two counter-rotating wavelets, which formed after a wavebreak, were unable to complete a full rotation. In panel A, the activation wave front (green) is seen propagating into a heterogeneously recovered region, resulting in two wavebreaks, one on each side of the small obstacle of refractoriness in the center of the field (red). In panel B, the chirality of each of the two newly formed phase singularity points is indicated by ‘+’ and ‘–’. In panel C, the fronts of two counter-rotating wavelets appear midway through the rotation wrapping around the two phase singularity points. In panel D, the wavelets have fused and are attempting to propagate between the phase singularity points; the inter-PS distance is 3.3 mm. The two counter rotating wavelets mutually annihilate and incomplete reentry results (i.e. the wavelets initially rotate around their corresponding PSs but do not complete a full rotation) as shown in panel E.


Figure 4
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  		Fig. 4 Incomplete reentry. (A) (0 ms), A activated wave front (green) propagates from left to right. (B) (8 ms), the wave front (green) breaks upon refractory tissue (red) resulting in formation of two PSs (+ and – indicate their corresponding chirality). (C) (16 ms), the two wave fronts rotate around their PSs. (D) (24 ms), the wave fronts merge and attempt to propagate between the two PSs (inter-PS distance=3.3 mm). (E) (32 ms), failure to complete reentry. The numbers at the bottom of each panel correspond to the time in milliseconds from frame A = 0. See Section 3.2 for details.

 
In all cases, phase singularity points were observed to form and terminate in counter-rotating pairs. That is, a block of a wave segment always gave rise to two wavebreak points with opposite chirality PSs. Once formed, two phase singularity points may annihilate when a front intents to propagate between them and fails. However, unlike the example shown in Fig. 4, it was not always necessary for the two phase singularities that formed together to have mutually annihilated.

The data presented in Figs. 2 and 4Go clearly demonstrate that wavebreaks can result in either complete or incomplete reentry. To assess whether the distance between two PSs (inter-PS distance) determined the ability of two counter-rotating wavelets to complete a full rotation, the inter-PS distance, at the instant the front passed between them, was measured. All the figure-of-eight data were divided into two groups: Group A (n = 15) where a full rotation was completed and Group B (n = 25) where incomplete reentry occurred. As shown in Fig. 5, there is a distinct difference between the two groups. The average inter-PS distance for Group A was 8.2±2.4 mm as compared to 1.3±0.7 mm for Group B (P<0.001). Also, individual data points are shown for each group in Fig. 5. A clear separation is seen between groups A and B, and it appears that in these episodes, only above a critical inter-PS distance of about 4 mm, was complete reentry (figure-of-eight) observed.


Figure 5
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  		Fig. 5 Critical inter-PS distance for the formation of rotors. Individual data points for episodes of complete and incomplete reentry are shown. The mean±S.E. for complete (8.2±2.4 mm) and incomplete reentry (1.3±0.7 mm) are displayed (P<0.001) to the right of the individual data points. The critical inter-PS distance for the formation of rotors is approximately 4 mm.

 
3.3 Spatial distribution of wavebreaks during AF
To study the distribution of the wavebreak points on the epicardial surface of the RA and LA during AF, the X, Y coordinates of all PSs were recorded. Each atrium was then divided into bins of 2.8x1.4 mm and the number of PSs per bin per episode was counted. Panel A of Fig. 6 shows a representative example of one such plot where the PSs are seen to be distributed unevenly. As shown in panel B, the distribution (gray bars) was significantly different from the Poisson distribution (solid line) that is expected from a random distribution (P<0.001). In all eight analyzed cases (four LA–RA pairs) the spatial distribution of the PSs was significantly different from the Poisson distribution, indicating that wavebreaks were non-randomly distributed in space.


Figure 6
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  		Fig. 6 Spatial distribution of wavebreaks during a representative episode of AF. (A) The mapping region was divided into bins of 2.8x1.4 mm (gray tiles). Number of PSs per bin is plotted on the Z axis. (B) Histogram of actual number of PSs per bin (gray bars) and the expected value (solid line) as predicted by the Poisson distribution. The {chi}2-test between the actual number of PSs per bin and the Poisson distribution was significantly different (P<0.001), indicating that the PSs were non-randomly distributed.

 
3.4 Lifespan of wavelets during sustained AF
In the vast majority of cases, the lifespan of PSs, and their respective wavelets, were found to be exceedingly short. Fig. 7 illustrates the dynamics of short-lived phase singularity points. Here one can follow the formation and rapid termination of nine PSs, which are produced as a wave front interacts with an area of refractoriness and then fragments into small wavelets, each of which is unable to propagate in subsequent frames. In panel A, a wave front (green) is seen to propagate downward into relatively refractory tissue (red). In panel B (16 ms), the wave front fragments into three wavelets bounded by PSs labeled ‘a’ to ‘d’ (lengths of the wavelets are shown in the figure). Less than 8 ms later, the wavelet labeled ‘b–c’ rapidly shrinks and terminates, with subsequent disappearance of PSs ‘b’ and ‘c’ (see panel C). Note that PSs ‘b’ and ‘c’ were of opposite chirality (rotational direction). As such, the lifespan of wavelet ‘b–c’ and the corresponding PSs is approximately one frame. In panel C, the PS labeled ‘a’ has moved close to one of the edges of the tissue and may have drifted out of our field of view; hence its lifespan could not be accurately measured. Nevertheless, in all probability, this wavelet terminated as it is clearly seen to run into refractory tissue. Wavelet ‘d-boundary’ seen in Panel B fragments again into three wavelets flanked by PSs ‘d–e’, ‘f–g’ and ‘h-boundary’, as shown in panel C. In the following two frames (D and E), all wavelets contract and disappear, with lifespan of only one frame (‘d–e’) and two frames (‘f–g’ and ‘h–i’). Such short-lived PSs were seen frequently during AF as a result of breakup of spatiotemporally periodic waves [14] entering the mapping field from presumably some outside source.


Figure 7
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  		Fig. 7 Dynamics and lifespan of short-lived PSs. (A) (0 ms), An activated wave front (green) propagates into refractory tissue (red). (B) (16 ms), Three wavelets result: a — boundary, b–c, and d — boundary. Wavelet b–c undergoes decremental conduction and terminates (lifespan of PS b and c=8.3 ms). (C) (24 ms), Wavelet d — boundary fragments into wavelets d–e, f–g, and h — boundary. Wavelet a — boundary propagates downward and wavelet d–e extinguishes itself on refractory tissue (lifespan of PS d and e=8.3 ms). (D) (32 ms), Wavelet h — boundary fragments into wavelet h–i (lifespan of PS h, i=16.6 ms, 8.3 ms respectively) and the remainder of wavelet h — boundary decrements and blocks. Wavelet f–g extinguishes itself on refractory tissue (lifespan of PS f and g=16.6 ms). (E) (40 ms), All wavelets have blocked upon the refractory tissue. The size (length) of the wavelets is shown accordingly.

 
The mean lifespan of PSs was 19.5±18.3 ms with a range that varied from 8.33 ms (one frame) to 200 ms. As shown in Fig. 8, the lifespan distribution was skewed to the left, with 71% of PSs lasting only 16.67 ms or less. Approximately 98% of PSs existed less that the average rotation period of a rotor, which was ~85 ms in our experiments; only ten out of 554 PSs (~2%) were found to have a duration greater than or equal to one rotation during sustained AF. Furthermore, in the two additional experiments performed in the absence of methoxyverapamil (D600), similar lifespan of PSs were found (14.8±9.1 ms; 98% <one rotation), thus providing strong evidence that the short lifespan of wavelets was not attributable to the D600 used in our experiments.


Figure 8
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  		Fig. 8 Lifespan analysis of PSs for all experiments. See Section 3.4 for details.

 
3.5 Waves entering and leaving the field of view
We hypothesized that if wavebreaks and their resulting wavelets were not maintaining this arrhythmia, the number of waves entering our field of view should exceed the number of waves leaving our mapping field. For example, in Fig. 7, one wave was counted to enter our field of view, multiple wavelets were formed, annihilated, and no wave was counted as leaving the field. In general, the small short-lived wavelets as seen in Fig. 7, were not seen to enter or exit our field of view, but were instead the result of breakup from broad spatiotemporally periodic waves of activity entering the mapping field [5]. The high spatial resolution of our system, in conjunction with two-dimensional phase mapping, allowed us to accurately discern these wavelets for the first time. Panel A of Fig. 9 shows the summary of 21 episodes of AF. The mean number of waves entering the mapping region was 15.7±1.6, whereas the mean number of waves leaving was 9.7±1.5 (P<0.01). In panel B, the ratio of waves entering to leaving (E:L ratio) for each episode varied from 0.86 to 5.0 with a mean of 2.03±0.99 (hatched bar). During measurements of waves entering and leaving the mapping region, we recognized that an error of measurement could occur in determining a single wave from two or more different waves that are invisibly linked. To calculate the error associated with this measurement, we employed the basic theory of measurements [30], where for n independent waves, the uncertainty is of the level of the square root of n. We also calculated the SDM number of waves entering or leaving our mapping field per episode. In these measurements, the SDM was larger than the uncertainty due to individual measurement uncertainties (enter: 7.39 vs. 3.87; leave: 6.87 vs. 2.94). Consequently, when we applied the ANOVA test on the set of episodes, we could ignore the uncertainties of measurement in each episode. In 18 of 21 episodes (85.7%) the E:L ratios were greater than 1, two episodes (9.5%) had an E:L ratio less than 1, and one episode (4.8%) had an E:L ratio of 1. In this single example, few wavebreaks were seen and a single wave front entered and exited the mapping region relatively undisturbed. In the two cases where the E:L ratio was less than one, periodic breakthroughs were observed acting as a source of new wavelets.


Figure 9
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  		Fig. 9 Quantification of waves entering and leaving the mapping field for all experiments. (A) The mean number of waves entering and leaving the mapping region. *P<0.001. (B) Ratio of number of waves entering vs. leaving (E:L ratio) the mapping region in the 21 episodes. The mean E:L ratio is shown as a hatched bar.

 

   4 Discussion
Top
 Abstract
 1 Introduction
 2 Methods
 3 Results
 4 Discussion
5 Conclusion
 References
 
This study provides the first in depth experimental quantification of the initiation, propagation, and termination of wavelets produced by wavebreaks during AF. The extremely short lifespan of most wavelets, their non-random spatial distribution, and the number of waves entering the mapping region exceeding those exiting, suggest that multiple wavelet reentry, as originally postulated by Moe [1–3], (i.e., spontaneous wavebreaks perpetually giving rise to new independent daughter wavelets), is not the mechanism of AF maintenance in our model. Rather, the wavelets that are seen may result from breakup of high frequency organized waves [5,6,16] as they propagate through heterogeneous atrial tissue.

4.1 Wavebreaks during AF
Wavebreaks were found to occur frequently during sustained AF. The fragmentation of a wave into wavelets resulted in the formation of pairs of phase singularity points as predicted by theory [13,18,19,21]. Once formed, the broken wavelets were found to curl and undergo either complete (figure-of-eight; see Fig. 2) or incomplete (see Fig. 4) reentry, or undergo decremental conduction and block (see Fig. 7). Previous studies show that, under normal conditions, obstacles in the cardiac muscle should not cause waves to break or result in phase singularity points [20,25]. Under conditions of reduced excitability or high excitation frequency, heterogeneity allows the interaction of a wave front with an anatomical or functional obstacle and wavebreaks may occur. Winfree [31] hypothesized that if, following a wavebreak, the distance between two phase singularity points is not adequate, then neither of the two counter-rotating waves will have enough ‘elbow room’ and they will mutually annihilate. Our results demonstrate that if the PSs organizing any two counter-rotating wave fronts come within a critical distance less than 4 mm from each other they will mutually annihilate. This observation is in good agreement with those of Cabo et al. [20] who in ventricular tissue estimated a critical isthmus width of 2.5 to 3.5 mm for propagation failure depending on stimulation frequency and fiber orientation. It should be made clear however, that we did not attempt to normalize our distances for tissue parameters such as excitability or stimulation frequency (AF cycle length). This in part explains the scatter of distances in Fig. 5. Nonetheless, our data are in excellent agreement with theoretical predictions and previously published experimental results.

4.2 Spatial distribution of wavebreaks
We performed a careful assessment of the spatial distribution of sites of wavebreaks during four RA–LA paired recordings of AF. In no case was the distribution random (see Fig. 6); points of breakage were clustered in space over both the left atrial appendage and the right atrial free wall. These regions are known to possess complex three-dimensional endocardial structure in the form of pectinate musculature that provide an ideal substrate for the collision of fibrillatory, high frequency waves with both anatomic and functional obstacles. While no direct evidence is provided in this study to support the contention that the complex atrial architecture is responsible for the breaking of waves, we feel that this is likely.

4.3 Are wavebreaks and phase singularity points important in the mechanism of AF?
In Moe's original description of the multiple wavelet hypothesis, mother waves were found to give rise to new independent daughter wavelets by breaking on refractory tissue in a turbulent cascade [2,3]. Wavelets formed multiple unstable reentrant circuits which changed from activation to activation and the maintenance of the arrhythmia was critically dependent on the number of circulating wavelets. In 1985, Allessie et al. [4] was the first to demonstrate the presence of multiple propagating wavelets during AF. Since then, other groups have confirmed the presence of multiple wavelets during AF in both animal and human studies [4,9–12,32]. However, definitive proof that multiple wavelets are necessary for the maintenance of the arrhythmia is lacking.

In fact, Schuessler et al. [9] tested the validity of the multiple wavelet hypothesis, in an isolated right atrial preparation, by mapping wavelet propagation patterns of induced atrial arrhythmias in the presence of increasing concentrations of ACh. During episodes of non-sustained arrhythmias, multiple unstable reentrant circuits were seen. However, sustained fibrillation did not occur until the stabilization of a single high frequency reentrant circuit. This single source produced fibrillatory conduction in which the number of wavelets was proportional to the frequency of the reentrant source. In addition, other studies [8,10,33,34] report results that are seemingly inconsistent with the multiple wavelet hypothesis. Cox et al. [10] demonstrated the presence of a single reentrant circuit in select cases of human AF suggesting that "...some forms of atrial fibrillation may also be caused by a single reentrant circuit and more complex forms may result from multiple reentrant circuits." Kumagai et al. [11] showed that unstable reentrant circuits principally involving the septum appeared to be important for the maintenance of AF in their model.

In the current study, we used high resolution video imaging and a newly developed phase mapping technique [13,14] to accurately quantify the initiation, propagation, and termination of wavelets produced by breaking of waves during AF. Despite a large number of wavebreaks and wavelets being produced, the lifespan of newly formed ‘daughter’ wavelets was short; 98% had a lifespan of less than one rotation, and 71% had a lifespan less than 16.7 ms. If the lifespan of wavelets is very short, then these wavelets will have a decreased chance to give rise to new wavelets, which would make sustainment of ‘random’ fibrillation difficult. To further support this hypothesis, we looked at the number of waves entering and leaving the mapping region, as an estimate of the production of new wavelets occurring via wavebreaks (E:L ratio). According to the multiple wavelet hypothesis, there should be an equal or positive balance between the number of wavelets created and destroyed so that a critical number of wavelets still remains. In such a schema, the number of wavelets leaving our mapping field should be equal to or greater than the number of wavelets entering our mapping field. In the vast majority of cases, despite frequent wavebreaks, this process was self-limited and wavelets were constrained to the field of view (E:L ratio greater than one). In cases where robust wavelet production occurred, as indicated by an E:L ratio less than one, a focal source of wavelets (i.e. breakthrough or rotor) was found. Thus, AF in this experimental model cannot be explained by randomly propagating wavelets that give rise to new independent daughter wavelets in a self-perpetuating manner as the mechanism of AF in our model.

The above conclusions are further supported by two recent studies from our laboratory. Using the same model of AF, Skanes et al. [5] demonstrated spatiotemporal periodicity of wavefronts. That is, the same spatially oriented wave was found to propagate into the field of view in a temporally periodic pattern, highly suggestive of some stationary source(s) giving rise to this periodic activity. Mandapati et al. [6] used optical mapping in combination with multiple electrodes at sites inaccessible to optical mapping and localized these sources to the left posterior part of the atrium in the vicinity of the pulmonary veins. It is very likely that in these regions the E:L ratio would be <1, while regions distant from the left posterior part of the atrium (such as the LA and RA appendages) would have an E:L ratio ≥1, as these regions represent breakup of spatiotemporal periodic waves emanating from these sources (i.e. fibrillatory conduction — see Fig. 7). This hypothesis however, requires further investigation.

4.4 Limitations
There are certain limitations in our experiments: (1) Temporal resolution: the sampling rate of the optical mapping system was one frame every 8.33 ms. With an increase in temporal resolution it is very possible that a decreased lifespan of PSs would have been found. On the other hand, it may be argued that the lowest measurable limit of lifespan in our analysis is the two frames (16.7 ms) delay used for the phase maps generation. In a separate analysis (not shown) we have verified that PSs are detectable with a delay of one frame, indicating that indeed there is measurable phase activity at a resolution of a single frame. Even when we exclude the PSs that last for only one frame, the number of PSs that live less than one rotation is 93% of their total number. This confirms that even if we accept 16.7 ms as the lowest measurable lifespan of the PSs, the main conclusion is still that the lifespan of wavelets is exceedingly short. (2) Boundary effects: it is possible that we made a sampling error by only measuring the lifespan of PSs which remained within the field of view and therefore failed to measure the lifespan of long-lived drifting rotors. However, in our analysis, few PSs were seen to drift over long distances in short periods of time. Furthermore, there is no reason to believe that the behavior of PSs should dramatically change as they drift out of the field of view. As such, we feel that our analysis was reasonable with respect to lifespan of phase singularity points. (3) Mapping area: our mapping was limited to the epicardial surface of the right atrial free wall and left atrial appendage; an area that we have estimated to be ~40% of the total atrial surface, including the atrial septum. Recent studies have speculated that a stable long-lasting rotor could exist in the septum [11] or pulmonary vein region [6]. In light of recent success ablating some forms of AF within the PV region [8], it appears plausible that a single stable rotor driving AF can indeed exist at least in some instances. (4) Our experiments were performed in an acute model of atrial fibrillation in the Langendorff-perfused sheep heart. The relevance of this study to human AF remains to be determined.


   5 Conclusion
Top
 Abstract
 1 Introduction
 2 Methods
 3 Results
 4 Discussion
 5 Conclusion
References
 
The limitations outlined above, notwithstanding, results from this study suggest that multiple wavelets are not critical for the maintenance of the arrhythmia, but instead, are the product of high frequency waves ‘breaking’ as they propagate through heterogeneous atrial tissue. At least in our model, random reentry of multiple unstable wavelets is not necessary to maintain AF. A single or small number of relatively stable ongoing reentry circuits generating high frequency waves can provide the ‘engine’ to generate numerous wavebreaks and wavelets that characterize fibrillatory conduction and AF in the isolated sheep heart.

Time for primary review 29 days.


   Acknowledgements
 
This work was supported in part by Grants PO1-HL39707 and RO1-H260843 from the National Heart, Lung and Blood Institute NIH, a NASPE Fellowship awarded to Dr. Allan Skanes, and AHA N.Y. State Affiliate fellowships awarded to Jay Chen, and Drs. Omer Berenfeld and Ravi Mandapati. We would like to thank Jiang Jiang, Clara Wu, Fan Yang, and Tatiana Yuzyuk for their technical assistance. In addition, we would like to thank Dr.s Jacques Beaumont, Dhananjay Vaidya, and Arkady Pertsov for their invaluable discussion during the preparation of this manuscript.


   References
Top
 Abstract
 1 Introduction
 2 Methods
 3 Results
 4 Discussion
 5 Conclusion
 References
 

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S. R Kuo and N. A Trayanova
Action potential morphology heterogeneity in the atrium and its effect on atrial reentry: a two-dimensional and quasi-three-dimensional study
Phil Trans R Soc A, June 15, 2006; 364(1843): 1349 - 1366.
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