Background Atrial activation during atrial fibrillation (AF) is frequently described as random or chaotic. We propose that activation during AF is constrained by the principles of reentrant excitation; that these constraints impart a measurable spatial organization to activation during AF; and that the distance over which activation sequences remain well correlated can be readily measured and related both to the propensity of AF to sustain itself as well as to atrial tissue wavelength.
Methods and Results We describe a novel signal-processing technique that quantifies the correlation in activation sequences recorded from five equally spaced sites in the right atrium in patients undergoing electrophysiology studies. In 20 patients in AF (12 with paroxysmal AF, 5 with chronic AF, and 3 with no clinical history of AF), the average correlation was 0.54±0.12 at 11 mm and 0.32±0.11 at 44 mm, compared with 0.95±.023 and 0.91±.023 in sinus rhythm. In AF, the correlation versus distance relation was monotonically decreasing, well fit by a decaying exponential function. The space constant of this exponential function, termed the activation space constant, provides a single objective metric of the spatial organization of activation during AF. The mean activation space constant for the group was 2.6±1.15 cm. Chronic AF had the lowest mean activation space constant (1.84±0.36 cm) and AF in patients with no prior history of AF had the highest (3.06±0.40 cm) (P<.05), with paroxysmal AF characterized by intermediate values (2.80±1.4 cm).
Conclusions Using a novel method to measure the spatial organization of atrial activation during AF, we have demonstrated that AF in the intact human heart is organized over a length scale consistent with reentrant excitation. Preliminary results suggest a relationship between measured spatial organization and the clinical course of the arrhythmia. Further work is needed to determine whether measurement of spatial organization may be useful in prospective patient-specific selection of therapeutic options.
Atrial fibrillation is a common disorder, occurring in up to 10% of individuals >70 years old.1 It is associated with devastating complications, chief among them embolic stroke, which has an overall incidence of 4% to 6% per year.2 The electrophysiological determinants responsible for increased susceptibility to AF are incompletely understood and poorly characterized. As a result, therapy remains largely empirical and plagued by relatively low efficacy. Additionally, the risks of proarrhythmia associated with empirical antiarrhythmic therapy further complicate the management of patients with AF.
Theoretical formulations and high-density mapping studies have suggested that the electrophysiological mechanism responsible for the maintenance of AF is the presence of multiple, simultaneous reentrant depolarization wave fronts or ‘wavelets’ that circulate throughout the atrial tissue.3 4 5 The trajectory, size, and shape of each of these wavelets evolves in time, determined by the complex interaction of activation wave fronts with spatially and temporally varying tissue excitability and refractoriness.
It has been hypothesized that susceptibility to sustained AF can be quantitatively characterized by the magnitude of the tissue wavelength, defined as the product of refractory period and tissue conduction velocity.6 7 In an experimental animal model with multisite, epicardial mapping, Rensma et al7 demonstrated that neither refractoriness nor conduction velocity alone served as an accurate predictor of susceptibility to sustained reentrant arrhythmias. Tissue wavelength, however, appeared to accurately track susceptibility to such arrhythmias. One interpretation of these findings is that the tissue wavelength determines the minimum size of a reentrant wavelet, and as tissue wavelength increases without associated increase in atrial size, it becomes increasingly difficult to support enough simultaneous wavelets to sustain AF.
If migratory reentrant activation as described in the multiple-wavelet hypothesis is an appropriate description of the mechanism underlying AF in humans, then sequences of atrial activation during AF would be constrained by the principles of reentrant excitation, subject to local tissue wavelength. Such constraints may be viewed as imposing a characteristic spatial organization on atrial activation during AF. Atrial sites within the domain of a single wavelet would have related activation sequences. As tissue wavelength determines the minimum size of a reentrant wavelet, tissue wavelength would also be expected to determine the minimum distance over which sequences of activations remain similar during AF.
We have developed a novel signal-processing method to determine the extent of correlation between sequences of activations recorded from multiple equispaced sites along the endocardial surface of the right atrium in patients during AF. By quantifying the correlation of activation as a function of distance, we determined the activation space constant, ie, the distance over which activation sequences remain well correlated during AF. Using this technique, we set out to determine (1) whether activation sequences during AF are spatially organized; (2) whether the extent of spatial organization is readily and reproducibly measurable in the intact human heart; (3) whether the extent of organization varied across different patient populations; and (4) whether the extent of spatial organization is in concert with that predicted by the multiple-wavelet hypothesis.
The protocol was approved by the Washington University Human Studies Committee, and informed consent was obtained from each participant. Patients who were referred for invasive EPS between February 1993 and April 1994 were considered for enrollment into this study. Patients were excluded from the study if they had prior cardiac surgery or if they were on antiarrhythmic drug therapy at the time of their EPS. The study group consisted of 20 patients (19 men, one woman; average age, 48 years; age range, 26 to 73 years) who met the above criteria and who experienced sustained AF, defined as lasting for >5 minutes, during their EPS. Twelve of the 20 patients had a clinical history of PAF, defined as documented episodes of both sinus rhythm and AF within 48 hours before EPS. Of these 12 patients, 8 had no other known heart disease, 1 each had CAD and long-standing hypertension, and 2 had WPW syndrome. Five patients had chronic AF (defined for this study as >2 weeks in duration); of these 5 patients, 2 had significant CAD, 1 had dilated cardiomyopathy, 1 had WPW syndrome and a nonischemic cardiomyopathy, and 1 had no known structural heart disease. Of the 3 patients with no history of AF, 1 each had CAD, atrioventricular nodal reentrant tachycardia, and WPW syndrome. In the 9 patients in sinus rhythm at the beginning of the EPS, AF was initiated either spontaneously during catheter manipulation or with routine atrial extrastimuli in the course of the clinical EPS.
A standard 6F decapolar catheter with ten 2-mm electrodes with 2-mm interelectrode spacing and 11-mm interpolar spacing (Bard Electrophysiology), was introduced via the left femoral vein and retroflexed into the right atrium. The catheter was positioned along the anterolateral wall in a manner that optimized contact at all electrode sites (Fig 1⇓). Additional catheters were placed as clinically indicated, typically including an additional decapolar catheter in the coronary sinus, a quadripolar catheter in the right ventricular apex, and a tripolar catheter for the recording of His bundle potentials. Bipolar electrogram recordings from each of the five closely spaced bipoles in the right atrium were direct coupled, amplified, and band-pass filtered at 0.5 to 400 Hz with a Bloom amplifier/stimulator system (Bloom and Associates). Signal quality was continuously monitored with a 16-channel video display. All signals were digitized with 12-bit resolution at 1000 Hz with a 16-channel analog-to-digital board (National Instruments) by use of a Macintosh IIci computer (Apple Computer) interfaced with customized record/display programs (LabView, National Instruments).
For each of the 20 patients in the current study, recordings of 60 to 120 seconds of continuous atrial electrograms during AF were made. Additionally, 60-second recordings of normal sinus rhythm and atrial flutter were made in 8 patients each.
Correlation analysis for each segment of recorded electrogram data was performed off-line on a Sun Sparc 10 Model 30 workstation (Sun Microsystems Inc) by use of the LabView software package in the following manner: Two of the continuous atrial electrograms from the five bipolar electrodes of the right atrial decapolar catheter, in a parallel fashion, were parsed into nonoverlapping segments of approximately 1.5 to 2 seconds in length, with adjustment of the duration optimized for the data file such that 10 to 12 activations typically occurred in that segment. Each data segment was first band-pass filtered at 40 to 250 Hz with digital, zero-phase, third-order Butterworth filters. The absolute value of the output of the band-pass filter was then low-pass filtered with a 20-Hz cutoff. This process extracts a smoothed signal proportional to the high-frequency (40 to 250 Hz) energy present in the original electrograms.8 9 Each segment was then normalized to contain unit energy, thus constructing a waveform of unit energy with peaks corresponding to the occurrence of local activations for that particular data segment (see Fig 2⇓). The cross-correlation function between these two sequences of activations was then calculated in the standard fashion for a range of lag values encompassing slightly more than one typical cycle length during AF (usually 175 ms). The peak in the resultant cross-correlation function was taken as a measure of the correlation between the sequence of activations for these two electrode locations for that interval in time. This operation was repeated for each sequential data segment for a total of 50 to 60 seconds of continuous data. The correlation versus time relation and the average correlation over the entire data record were determined. This procedure was repeated for each of the 10 possible combinations of the five bipolar electrograms in each data collection.
Because the five bipolar recording electrodes created from the decapolar catheter were spaced on 11-mm centers, for each data collection, four estimates of the correlation of sequences of activation at 11 mm were available, 3 were available at a center-to-center spacing of 22 mm, 2 for a spacing of 33 mm, and 1 for the maximal spacing of 44 mm (see Fig 2⇑). The available measures of correlation at each of the four interelectrode separations were averaged, resulting in a single mean correlation coefficient at each of the four interbipole distances.
Determination of the Activation Space Constant
The relation between correlation and distance was found to be well approximated by a decaying exponential function. To obtain a single measure to characterize this relationship we used the formula:
where CC(d) is the cross-correlation value as a function of interelectrode distance, d is the distance (in centimeters), and δ is the space constant (in centimeters). The statistical best-fit activation space constant for each data set was determined by minimizing the weighted mean-squared error between the exponential function and the data with each value of cross-correlation weighted by the number of observations available at that interbipole distance. Thus, the measure of correlation at 11-mm interelectrode distance was the average of four measures, with error at that point weighted by four, whereas that at 44 mm was a single measure, with the error at that point receiving unity weighting.
The activation space constant (δ) served as a single, objective, and quantitative measure of the extent of spatial organization of activation during AF.
Data are expressed as mean±SD. Student’s paired t test was used to evaluate differences in correlation. A value of P<.05 was considered statistically significant.
Correlation Between Sequences of Activation During Normal Sinus Rhythm and Atrial Flutter
The average correlation calculated at the closest interelectrode spacing of 11 mm during sinus rhythm (n=8) and atrial flutter (n=8) was 0.95±.02 and 0.94±.02, respectively. There was minimal decrease in the extent of correlation at the greatest interelectrode distances of 44 mm (0.94±.03 and 0.89±.03 for sinus rhythm and atrial flutter, respectively).
Correlation Between Sequences of Activation During AF
At the closest interelectrode spacing (11 mm), the correlation coefficient between activation sequences ranged from 0.77 to 0.36 (n=20). The correlation coefficient diminished with increasing interelectrode spacing, with an average correlation coefficient of 0.54±0.12 measured at 11 mm, decreasing to 0.32±0.11 at 44 mm (P<.0001) (see Table⇓). A typical graph of the correlation coefficient versus distance for one subject is provided in Fig 3⇓. Note that the correlation coefficient decreases monotonically with increasing interelectrode spacing.
Correlation as a Function of Distance During AF: The Activation Space Constant
The relation between correlation and distance was found to be well fit by a decaying exponential. This formulation allowed the relation to be represented by a single measure, the activation space constant (see “Methods”). Fitting the calculated correlation of activation sequences during AF to the exponential form, activation space constants were calculated for each set of patient recordings. For the data provided in Fig 3⇑, the activation space constant was 1.90 cm. The mean activation space constant for the group was 2.6±1.15 cm, with a range of 1.48 to 5.99 cm (see Table⇑). Unlike AF, in sinus rhythm and atrial flutter, the correlation versus distance relation is essentially constant over the length scale of these measurements.
Stability of the Activation Space Constant Measure Over Time
To assess the reproducibility of the measurement of the activation space constant over time, multiple repeat measurements were made over continuous data segments in 10 randomly selected patients. The mean activation space constant was determined for contiguous 30-second data segments over the entire 60- to 120-second data files. The activation space constant for each segment was then compared with that for the subsequent 30-second data segment. Fig 4⇓ shows the activation space constant at one data segment plotted against the space constant of the next data segment. The unity line is drawn for reference. By regression analysis, there is a 93% correlation between repeated measures (P<.0001). In 5 of the 10 patients with continuous data runs of 90 or 120 seconds, the length of the averaged data segment was increased to 45 seconds (n=3) or 60 seconds (n=2). With these longer data segments, there was a 97% correlation between contiguous measures (P<.008).
Relation of Activation Space Constant to Clinical Manifestation of AF
The mean activation space constant for this group of patients (n=20) was 2.6±1.15 cm. Fig 5⇓ depicts the relation between activation space constant and clinical AF history. The mean activation space constant for the 5 patients with chronic AF was lower than the overall population mean (1.84±0.36 cm), whereas the group of patients with no history of AF had the highest mean activation space constant (3.06±0.40 cm). The difference between these two groups is statistically significant (P<.05). The 12 patients with a history of PAF had a wide range of activation space constants and an intermediate mean of 2.80±1.4 cm.
Atrial Activation During AF Is Organized
The multiple-wavelet hypothesis of AF proposes that atrial activation during AF is the result of multiple, migratory, reentrant wavelets of activation. If this model reflects the pathophysiology of human AF, then principles of reentrant excitation must provide some constraints to the process of atrial activation. Physiological limitations further constrain the possible values for refractory periods and conduction velocity of human atrial tissue during AF. Atrial activation during AF, therefore, is not a random process but rather is inherently organized by these principles, with the spatial extent of this organization strongly influenced by tissue properties of refractoriness and conduction velocity.
Previous work describing the relative organization of human AF has been limited. Comparison of isochronal maps made during intraoperative studies of AF in humans suggested that the process of atrial activation is not random.4 5 In the intact human heart, attempts to ascribe a relative degree of organization to AF have focused on qualitative descriptions of atrial electrogram morphology recorded from two atrial sites, description of beat-to-beat similarities in the direction of depolarization fronts from a single location, and quantitative analysis of the similarity between electrogram signals at two separate sites by use of the coherence spectrum.10 11 12 These strategies have drawn attention to the varying characteristics of wave-front propagation during AF and have further demonstrated that such propagation is nonrandom.
In an attempt to provide a measure of the spatial organization of activation during AF that is directly related to the underlying pathophysiological mechanisms responsible for AF, we described the relative organization in terms of the similarity in the sequences of activation measured at five sites in a region of the right atrium in 20 patients undergoing EPS. We found that during AF, the correlation in sequences of activation is a monotonically decreasing function of the distance between the recording sites and that the relation between correlation and distance is well fit by a decaying exponential function. This finding is consistent with the multiple-wavelet hypothesis. Sequences of activation recorded from closely spaced electrodes would be expected to be similar if the interelectrode spacing were much smaller than the size of a reentrant wavelet, because both recording sites would most frequently be activated by the same wavelet. As the distance between recording sites grows, the sequences of activation would be expected to become less similar as it becomes less likely that the two sites are excited by the same wavelet. In contrast, during sinus rhythm and atrial flutter, two rhythms in which there is a single wave front of depolarization responsible for all atrial tissue activation, there was no significant decrease in the extent of correlation in activation with increasing distance, indicative of the same activation wave front depolarizing all tissues.
Although our observations are consistent with the multiple-wavelet hypothesis, they are not at odds with the intimately related concept of wandering rotors serving as the arrhythmia mechanism. Any arrhythmia mechanism based on reentrant activation would be expected to demonstrate organization of activation over a distance equal to or greater than a minimal distance determined by local conduction velocity and refractory period.
As the observed relation between correlation of activation sequences and distance was well fit by a decaying exponential, it was possible to describe the extent of spatial organization of activation sequences during AF by a single metric: the activation space constant, that is, the distance over which activation remains well correlated (to within a value of 1/e). In our patient population, the activation space constant ranged from 1.48 to 5.99 cm.
Temporal Variability in Organization
The activation space constant is derived from the average correlation of the sequences of activation over ≈60 seconds. It has been noted previously that highly similar activation sequences may exist for brief periods of time, ie, transient linking for 1 to 2 seconds.12 In the present study, a longer observation interval was chosen to average over such transients. We have shown a high degree of reproducibility in the measured activation space constant under stable physiological conditions. The activation space constant determined for two contiguous, 30-second data segments showed a 93% correlation, and increasing the observation period to 45 to 60 seconds improved the agreement to 97%. This high correlation demonstrates the reproducibility of the technique and also suggests that little benefit is gained from determining this measure with >60 seconds of continuous data under physiologically stationary conditions.
Organization of AF in Relation to Its Clinical Course
We speculated that the different clinical manifestations of AF would be strongly related to the relative spatial organization of the process. Chronic AF, characterized by a vanishingly small likelihood of spontaneous termination, represents one end of this spectrum, and rapidly self-terminating AF, such as that induced in patients with no prior history of AF, represents the other extreme. In this group of patients referred for EPS, the mean activation space constant for patients with a history of chronic AF was 1.84±0.36 cm, compared with a mean activation space constant of 3.06±0.40 cm in patients with no clinical history of the arrhythmia. For patients with a history of PAF, values of activation space constant fell between these two extremes, with a mean of 2.80±1.4 cm.
These observations agree well with the multiple-wavelet hypothesis and previous work on the importance of tissue wavelength in establishing the inducibility for sustained fibrillation. The propensity for induced AF to spontaneously terminate has been hypothesized to relate to the total number of simultaneous wavelets, the number of which is determined by tissue wavelength and overall tissue size, with larger wavelength (fewer wavelets) favoring termination. Under the hypothesis that activation space constant reflects wavelet size, we would expect self-terminating AF to be characterized by long activation space constants and sustained, nonterminating AF to be characterized by short activation space constants. This was the case in the present study group, as patients with chronic AF had the shortest activation space constants, patients with spontaneous PAF had intermediate values, and patients with no clinical history of AF who had self-terminating AF artificially induced had the longest activation space constants.
Comparison of Activation Space Constant to Tissue Wavelength
The observed range of values for activation space constant are substantially smaller than the estimated minimal critical wavelength (λ) necessary to support AF in humans, λ=12 cm.13 However, a direct comparison between wavelength and activation space constant during AF would not be appropriate. The activation space constant is a measure derived from activation sequences recorded from a linear array of electrodes in the right atrium. High-density mapping studies confirm that wavelets of activation do not follow reproducible paths on a beat-to-beat basis but rather have circuitous and ever-changing trajectories.4 5 As such, the activation space constant reflects an average cross section of the domain of a reentrant wavelet rather than the circumference of a reentrant loop or the wake of a propagating wavelet. Under the constraint that the domain of a single wavelet is modeled as a circle (ie, leading-circle reentry), the minimum circumference of the domain is determined by tissue wavelength and the average cross section of the domain is approximated by its radius. With this idealized model, the activation space constant may then be viewed as roughly proportional to tissue wavelength, with λ=2π×δ.9 This model would provide an estimate of tissue wavelength in the present study group of 13±3.6 cm, in good agreement with the 12-cm projected minimal wavelength necessary to support AF in humans.13
In an attempt to minimize radiation exposure, procedure time, and overall patient risk, the electrogram data obtained for the present study were limited to recordings from the right atrium and the coronary sinus. In all cases, recordings from the right atrium were made from the anterolateral region because both catheter stability and electrode-tissue contact were excellent in this region. Although no attempt was made to specifically align the recording catheter to the crista terminalis, the proximity of the crista terminalis to this recording location may have influenced our measure of spatial organization. Additional recordings at multiple sites within the right and/or left atrium would be required to fully assess the extent of spatial variability in this measure of organization.
Recordings made from within the coronary sinus contained both atrial and ventricular activity, and contamination of these signals with highly correlated ventricular activity precluded meaningful correlation analysis.
Finally, the relationship between activation space constant and tissue wavelength could not be based on independent measurement of tissue wavelength owing to the limitations of reliably measuring tissue wavelength in the minimally invasive setting of the electrophysiology laboratory.
We have demonstrated that atrial activation during AF is not random but is organized over a characteristic length scale described by a single measure, the activation space constant. This measure varies between patients and is related to the clinical course of the arrhythmia. In this cohort, the activation space constant is shorter in chronic AF, longer in newly induced AF (induced in patients with no prior history of AF), and of an intermediate value in patients with a history of PAF. We have provided a rationale for interpreting this distance in relation to atrial tissue wavelength as described by Allessie and colleagues13 and have found good agreement between our resultant estimate of tissue wavelength and the minimal wavelength thought to be required to support AF in humans. Further research is needed to establish whether measurement of the relative organization of AF on a patient-by-patient basis will be useful in delineating important differences in electrophysiological substrate and in guiding the selection of therapeutic approaches.
Selected Abbreviations and Acronyms
|CAD||=||coronary artery disease|
This work was supported by a beginning scientist research grant from Washington University School of Medicine, a grant (No. RO1-HL-50295-01) from the National Heart, Lung, and Blood Institute, and a research grant from InControl, Inc (Redmond, Wash).
- Received June 1, 1995.
- Revision received September 19, 1995.
- Accepted September 24, 1995.
- Copyright © 1996 by American Heart Association
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