Differentiation of atrial rhythms from the electrocardiogram with coherence spectra

Journal of Electrocardiology Vol. 35 No. 1 2002

Differentiation of Atrial Rhythms From the Electrocardiogram With Coherence Spectra

Lara S. Sarraf, MS,* James A. Roth, MD,† and Kristina M. Ropella, PhD*

Abstract: Automated electrocardiogram (ECG) interpretation systems fail to reliably discriminate atrial fibrillation from sinus rhythm and other more regular atrial arrhythmias. Previously, magnitude-squared coherence (MSC), a frequency domain measure of the linear phase relation between 2 signals, has been shown to be a reliable discriminator of fibrillatory and nonfibrillatory cardiac rhythms when applied to intracardiac electrograms. This study determines whether MSC, when applied to the surface electrocardiogram, would discriminate between atrial fibrillation and nonfibrillatory atrial rhythms. MSC was analyzed by using 2 surface leads of a 10-second ECG. For 68 ECG recordings (23 sinus rhythm, 22 atrial flutter, and 23 atrial fibrillation), MSC was computed between leads II and V1 and the mean MSC in several frequency bands was examined. The performance of MSC was compared to previously published measures of ventricular irregularity and percent power in discriminating atrial fibrillation from nonfibrillatory rhythms. As hypothesized, atrial fibrillation exhibited low coherence in the 2 to 9 Hz band while nonfibrillatory atrial rhythms exhibited relatively moderate to high levels of coherence in the same frequency band. Mean MSC in the 2 to 9 Hz band was significantly lower for atrial fibrillation (range, 0.04 to 0.48; mean ⫾ SD: 0.15 ⫾ 0.11) than for sinus rhythm (range, 0.18 to 0.81; 0.47 ⫾ 0.17) (P ⬍ .0005) and atrial flutter (range, 0.06 to 0.80; 0.44 ⫾ 0.21) (P ⬍ .0005). Mean MSC in the 2 to 9 Hz band showed less overlap between atrial fibrillation and atrial flutter than R-R variability and percent power. However, R-R variability showed less overlap between atrial fibrillation and sinus rhythm than mean MSC and percent power. Thus, MSC and RRV both discriminate atrial fibrillation from more organized atrial rhythms. Conversely, percent power was highly variable for both atrial fibrillation and organized atrial rhythms. Results suggest that MSC applied to surface ECG may be used to quantify rhythm organization. Key words: Spectral analysis, arrhythmias, atrial fibrillation, detection schemes.

From the *Department of Biomedical Engineering, Marquette University, Milwaukee, WI; and †Division of Cardiology, Department of Medicine, Medical College of Wisconsin, Milwaukee, WI. This work was supported in part by a Biomedical Research Grant from The Whitaker Foundation and a Anthony J. and Rose Eannelli Bagozzi Medical Research Fellowship, both to K. M. R. Reprint requests: Kristina M. Ropella, PhD, Department of Biomedical Engineering, Marquette University, P.O. Box 1881, Milwaukee, WI 53201-1881; e-mail: [email protected]. Copyright © 2002 by Churchill Livingstone® 0022-0736/02/3501-0008$35.00/0 doi:10.1054/jelc.2002.29944

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Computerized electrocardiographic systems have difficulty discriminating atrial fibrillation from more organized cardiac rhythms. Atrial fibrillation, present in over 1% of the population, is one of the largest classes of arrhythmia seen in the 12-lead electrocardiogram (ECG) (1). Proper detection of atrial fibrillation from the surface ECG is essential to the proper functioning of computerized arrhythmia monitors and ECG interpretation systems. Poor detection results in false alarms and often a ceasing of other interpretation schemes. Current methods for detecting atrial fibrillation from the surface ECG include measures of ventricular (R-R) irregularity (2), autocorrelation, and power spectrum analysis of a remainder ECG (ECG recording with the dominant QRS complexes removed) (3–5), and contextual analysis (6). In the case of ventricular irregularity, shortcomings include the assumption that atrial fibrillation is accompanied by an irregular ventricular response. Whereas this assumption holds true for the majority of atrial fibrillation, a small fraction of atrial fibrillation is accompanied by regular R-R intervals. Examples include atrial fibrillation with atrioventricular block and regular escape rhythms, pacemaker rhythms, and ventricular tachycardia (4). Furthermore, rhythms other than atrial fibrillation, such as atrial flutter with variable AV block, are associated with irregular ventricular responses. Algorithms that quantify properties of atrial activity rather than ventricular activity have been proposed to improve discrimination of atrial arrhythmias such as atrial fibrillation (3– 6). In addition to serving as detection schemes, such quantitative properties may be useful for studying mechanisms of atrial arrhythmias from surface ECG (7–9). Quantitative properties of atrial activity include autocorrelation and power spectrum analysis of the ECG and the association or disassociation of detected atrial events with detected ventricular events using contextual analysis. Autocorrelation analysis (3,5), power spectrum analysis (4), and contextual analysis (6), which requires detection of distinct atrial waves that may be absent or ambiguous during atrial fibrillation, all show marked variation across patients and are critically dependent on signal morphology and amplitude. Furthermore, these detection schemes only quantify information from a single lead. Magnitude-squared coherence is a multilead measure that quantifies the constancy of phase relationship or time delay between 2 signals as a function of frequency. Previously, Ropella et al. (10,11) have shown that magnitude-squared coherence (MSC) between 2 intracardiac electrograms discriminates fibril-

latory rhythms from nonfibrillatory rhythms. Furthermore, the discriminative power of MSC is relatively insensitive to signal amplitude and morphology. In the present study, we are interested in using MSC between 2 surface ECG recordings to discriminate atrial fibrillation from regular atrial rhythms. We hypothesized that the existence of multiple wavelets during atrial fibrillation (12) would lower MSC between 2 electrically orthogonal leads with respect to MSC during nonfibrillatory rhythms. For each rhythm, MSC was performed between the remainder ECGs of leads II and V1 and mean MSC was compared to currently available classification schemes, R-R variability and percent power, in its ability to differentiate atrial fibrillation from sinus rhythm and atrial flutter.

Materials and Methods Patient Data The database for this study consisted of 68 standard 12-lead ECGs acquired from 63 patients at the Froedert Memorial Lutheran Hospital (Milwaukee, WI) who exhibited one or more of the following rhythms: atrial fibrillation (n ⫽ 23), atrial flutter (n ⫽ 22), and sinus rhythm (n ⫽ 23). Multiple ECGs from a single patient were used only when the ECGs were of different rhythm type. The ECG rhythms were interpreted by 2 independent cardiologists with standard surface ECG criteria. Specifically, atrial flutter was defined by the presence of “sawtooth” flutter waves or more discrete atrial waves that occurred at rates of 200 to 350 bpm. Atrial fibrillation was defined as an absence of discrete P waves and atrial activity that was highly irregular in timing and morphology and consisted of low-amplitude baseline oscillations. Of the 68 ECGs, the 2 cardiologists differed in rhythm diagnosis in 4 recordings. A third cardiologist reading was used to resolve the conflicting diagnoses. The patients’ ages (22 women and 41 men) ranged from 25 to 86 years (mean ⫽ 62 years). Recordings/Preprocessing Ten-second resting ECGs recorded in the electrophysiology laboratory or the cardiac care unit were retrieved from a MUSE electrocardiographic database system (Marquette Electronics, Inc., Milwaukee, WI). Ten-second ECGs for each rhythm recorded were antialias bandpass filtered

Differentiation of Atrial Rhythms •

from 0.05 Hz to 109 Hz before being sampled at 250 Hz to a 12-bit accuracy with a 4.88 ␮V/bit resolution. Only leads II and V1 were retained for analysis. A 4th order bidirectional high pass filter (13) with 0.6 Hz corner frequency was used to correct the baseline of all the ECGs prior to any arrhythmia analysis. Generation of Remainder ECGs To examine atrial activity in the ECG, ventricular activity was eliminated by using a template scheme. For each of leads II and V1, a remainder ECG was created by automatically detecting and averaging together all QRS-T complexes in a single 10-sec ECG recording and subtracting a mean QRS-T template from each QRS-T complex in the original ECG. QRS complexes were detected using a modified Pan and Tompkins (14) algorithm, and the QRS-T template length (window) was equal to a percentage of the mean R-R interval. For each 10-sec ECG recording, the locations of maximum R-wave amplitude were marked as fiducial points, and a mean QRS-T template was computed by averaging together all detected QRS-T complexes aligned with respect to their fiducial points. For each 10-sec ECG record, the mean QRS-T template was subtracted from each QRS-T complex in the original ECG to generate the remainder ECG. Template length and alignment were carefully chosen to avoid inadvertent removal of atrial activity associated with the QRST complex. Premature ventricular complexes (PVCs), if present in an ECG recording, did not contribute in the creation of the QRST template and were zeroed in the remainder ECG. MSC Computation The coherence function is a frequency-domain measure of the constancy in phase delay between two signals. The MSC function is defined as (15,16) MSC共f兲 ⫽

S xy 共f兲 2 S xx 共f兲S yy 共f兲

where x(t) and y(t) are the two simultaneous remainder ECGs of leads II and V1, and Sxy(f) is the cross-power spectrum between x(t) and y(t) at frequency f. In practice, x(t) and y(t) are segmented into several time intervals, and the auto- and crosspower spectra are averaged over those multiple time intervals of x(t) and y(t). Sxx(f) and Syy(f) are

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the respective auto-power spectra of x(t) and y(t) averaged over the same time intervals. In the absence of noise and system nonlinearities, if x(t) is simply a time-delayed and amplified version of y(t), MSC will be unity at all frequencies present in both x(t) and y(t). In other words, coherence measures the constancy of temporal relation between 2 leads. In this sense, high coherence indicates that activation in one lead may be well predicted by the activation in another lead. Linear operations on either or both x(t) and y(t) will not change the MSC. MSC is reduced by system nonlinearities and noise not common to both signals. For each ECG recording, the remainder ECGs of leads II and VI were analyzed for MSC. The 10-second (2,500 points) records were divided into 17 equal length segments with 50% overlap of adjacent segments. MSC was determined using 256-point fast Fourier transforms and a Hanning window (17). MSC in the 1 to 59 Hz region was retained for analysis. For each recording, mean MSC was determined by averaging MSC over all frequencies in the 2 to 9 Hz band. In addition to examining those frequency bands previously reported in the literature (4,10, 18), the average MSC spectrum of all recordings for a specific rhythm was determined and those frequency bands that showed marked differences between atrial fibrillation, sinus rhythm, and atrial flutter were noted. R-R variability In this study, the R-R interval was defined as the interval between 2 successive fiducial points in an ECG record where fiducial points were determined by our modified Pan and Tompkins (14) algorithm. Premature ventricular complexes were excluded from analysis. R-R variability (RRV) was calculated as the standard deviation of the R-R intervals normalized by the mean R-R interval expressed as a percentage. This nomalization to the mean RR interval was performed to adjust for increased regularity that tends to occur with increased heart rates during AF. RRV was determined from lead II for each 10-second ECG recording. Percent Power The power spectrum was calculated on remainder ECGs by using the method of Slocum et al. (5). The power spectra were estimated using a 2,048point fast Fourier transform (FFT) over the first 8.2 seconds (first 2,048 data points) of the ECG. This

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technique measures the percent power in a narrow 2 Hz wide band around the peak power in the 5 to 9 Hz region normalized to an estimate of the total power in the 2 to 57 Hz band. Thus, percent power is a measure of the total power in the frequency spectrum that is concentrated about the peak power. The power spectrum and percent power were determined from each of leads II and V1 for each 10-second ECG recording. Statistics A Student’s t-test was used to compare the performance of mean MSC to R-R variability and percent power in its ability to differentiate atrial fibrillation from sinus rhythm and atrial flutter.

Results MSC on Remainder ECGs Magnitude-squared coherence was evaluated between leads II and VI for each of the 68 pairs of remainder ECGs of sinus rhythm (n ⫽ 23), atrial flutter (n ⫽ 22) and atrial fibrillation (n ⫽ 23). At low frequencies (2 to 9 Hz band) MSC was typically moderate to high (⬎0.3) for sinus rhythm and atrial flutter. In contrast, atrial fibrillation exhibited low levels (⬍0.25) of MSC throughout the 2 to 9 Hz range. For all three rhythm classes, MSC at frequencies above 10 Hz varied from low to high in no consistent manner. Discrete peaks of MSC at harmonic intervals were present in some of the nonfibrillatory rhythms. Harmonics were not evident in the MSC of atrial fibrillation. Figure 1 illustrates the MSC spectra for individual examples of each of sinus rhythm, atrial flutter and atrial fibrillation, respectively. Figure 2 illustrates the average MSC spectra for sinus rhythm (n ⫽ 23), atrial flutter (n ⫽ 22) and atrial fibrillation (n ⫽ 23). Note that the low frequency bands (2–9 Hz) show higher MSC for sinus rhythm and atrial flutter than for atrial fibrillation. In the 2 to 9 Hz band (Fig. 3), atrial fibrillation exhibited a lower mean MSC (0.04 to 0.48; mean ⫾ SD: 0.15 ⫾ 0.11) compared to sinus rhythm (0.18 to 0.81; 0.47 ⫾ 0.17) (P ⬍ .0005) and atrial flutter (0.06 to 0.80; 0.44 ⫾ 0.21) (P ⬍ .0005). If a mean MSC threshold of 0.225 is chosen such that all rhythms with mean MSC in the 2 to 9 Hz band lower than threshold were considered atrial fibrillation, then 23 of the 23 sinus rhythms and 16 of 22

Fig. 1. MSC is plotted for examples of sinus rhythm, atrial flutter, and atrial fibrillation.

atrial flutters will be correctly classified as nonfibrillatory, and 20 of 23 atrial fibrillations will be correctly classified as atrial fibrillation. The sensitivity and specificity of this MSC threshold for atrial fibrillation is 87% (20 of 23) and 87% (39 of 45), respectively.

Differentiation of Atrial Rhythms •

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Fig. 3. Mean MSC for the 2 to 9 Hz band is shown for the 23 sinus rhythm (SR), 22 atrial flutter (AFLT), and 23 atrial fibrillation (AFIB) rhythms.

R-R Variability The results of RRV grouped by specific rhythm type are presented in Figure 4. RRV for atrial fibrillation was greater (1.1 to 32.6%; 18.5 ⫾ 8.0%) than for sinus rhythm (0.5 to 13.2%; 2.7 ⫾ 3.2%) (P ⬍ .005) and atrial flutter (0.1 to 24.3%; 8.0 ⫾ 8.4%) (P ⬍ .005). If an 8% RRV threshold is chosen such that all rhythms with RRV exceeding threshold are considered atrial fibrillation, then 21 of the 23 sinus rhythms and 14 of 22 atrial flutters will be considered nonfibrillatory, and 22 of 23 atrial fibrillations will be correctly classified as atrial fibrillation. The sensitivity and specificity this RRV threshold for atrial fibrillation are 95.6% (22 of 23) and 77.8% (35 of 45), respectively. Percent Power The power spectra of surface ECGs during atrial fibrillation and nonfibrillatory atrial rhythms were

Fig. 2. Mean MSC is plotted for all sinus rhythm (n ⫽ 23), atrial flutter (n ⫽ 22) and atrial fibrillation (n ⫽ 23) evaluated. One standard deviation is shown along with the mean MSC. Note that at low frequencies (2 to 9 Hz band) MSC was typically moderate to high for sinus rhythm and atrial flutter. In contrast, atrial fibrillation exhibited low levels of MSC throughout the 2 to 9 Hz range. Fig. 4. R-R Variability for lead II is shown for the 23 sinus rhythm (SR), 22 atrial flutter (AFLT), and 23 atrial fibrillation (AFIB) rhythms.

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Discussion

Fig. 5. Percent power in the 5 to 9 Hz band for each of leads II and V1 is shown for the 23 sinus rhythm (SR), 22 atrial flutter (AFLT), and 23 atrial fibrillation (23) rhythms.

commensurate with those spectra reported previously by Slocum et al. (4). Atrial fibrillation exhibited a large peak of power in the 5 to 9 Hz band with very little power outside of this region, and conversely, nonfibrillatory rhythms showed a broader spectrum. Figure 5 summarizes the results of percent power for leads II and V1 grouped by rhythm type. The percent power for lead V1 showed less overlap than lead II between atrial fibrillation and the nonfibrillatory atrial rhythms. Percent power, obtained from lead V1, exhibited higher values for atrial fibrillation (9.4 to 93.4%; 37.8 ⫾ 25.1%) than for sinus rhythm (4.0 to 67.8%; 13.1 ⫾ 12.8%) (P ⬍ .0005) and atrial flutter (4.2 to 48.2%; 14.5 ⫾ 11.1%) (P ⬍ .01). Based on percent power for lead V1, if an 18% power threshold is chosen such that all rhythms with percent power exceeding threshold are considered atrial fibrillation, then 5 of 23 atrial fibrillations will be incorrectly classified as nonfibrillatory rhythms, and 7 of 45 nonfibrillatory atrial rhythms (2 of 23 sinus rhythms and 5 of 22 atrial flutters) will be incorrectly classified as atrial fibrillation. The sensitivity and specificity of this percent power threshold for atrial fibrillation are 78.3% and 84.4%, respectively.

The quintessential feature that differentiates atrial fibrillation from nonfibrillatory atrial rhythms is the break down in phase between neighboring sites in the cardiac tissue (19). In this study, we examine the feasibility of using magnitude-squared coherence to quantify this break down in phase in the surface ECG. MSC is a bivariate measure by which 2 signals can be compared quantitatively in the frequency domain. MSC quantifies the constancy of the phase relationship (time delay) between 2 signals as a function of frequency and is relatively independent of signal amplitude and morphology. Nonfibrillatory rhythms (such as sinus rhythm and atrial flutter) are expected to exhibit high coherence between 2 simultaneous lead recordings because multiple sites of the heart are activated in an orderly coordinated fashion. Conversely, we hypothesized that the loss of synchrony in the electrical activity between two or more sites in the atrium during atrial fibrillation (12) would result in a lower level of coherence between 2 electrically orthogonal leads. For intracardiac electrograms, the presence of multiple wavelets (12) resulted in low MSC (⬍0.02) between multiple sites during atrial fibrillation. However, because of the volume conductor effects of the body torso, detection of atrial fibrillation from the surface ECG with MSC is not so obvious. The volume conductor effects will increase the correlation between the electrical potentials sensed by the various surface leads despite the presence of multiple wavelets (12) during atrial fibrillation. Discrimination of atrial fibrillation by MSC depends on a lack of correlation between two surface leads. We hypothesized that the use of electrically orthogonal leads would increase the likelihood of the 2 leads measuring different electrical activity during atrial fibrillation (due to multiple circulating wavelets). Magnitude-squared Coherence To our knowledge, this study is the first to address the use of MSC for discrimination of atrial arrhythmias recorded from the surface ECG. Atrial fibrillation typically exhibited low levels of coherence in the 2 to 9 Hz band. Conversely, sinus rhythm and atrial flutter exhibited moderate to high levels of coherence in the same frequency band. These differences in coherence spectra between atrial fibrillation and nonfibrillatory rhythms were quantified by mean MSC in the 2 to 9 Hz

Differentiation of Atrial Rhythms •

band. With respect to other frequency bands examined, the 2 to 9 Hz band showed the least overlap between the mean MSC of atrial fibrillation versus nonfibrillatory atrial rhythms with the mean MSC of atrial fibrillation significantly lower than that of sinus rhythm and atrial flutter. For mean MSC, four episodes of atrial fibrillation were misclassified as nonfibrillatory rhythms. Two of these episodes were coarse atrial fibrillation, one of which required a third cardiologist to confirm the diagnosis. Coarse atrial fibrillation, also known as flutter-fibrillation, is characterized by a relatively organized atrial activation (20). Because of the presence of some degree of organization in the atrial activity during coarse atrial fibrillation, a higher level of coherence was not surprising. In fact, the distinction between atrial fibrillation and atrial flutter is often unclear with respect to underlying mechanism, and such a binary classification may not be possible, thereby hampering the performance of arrhythmia classification schemes. Two other examples of atrial fibrillation, which exhibited high MSC, contained artifact introduced by the baseline correction process. The bidirectional filter used for baseline correction introduced T-P segment shifts away from baseline in some of the ECG recordings. These artifacts may have resulted in increased correlation between the two leads thereby increasing MSC. The bidirectional filter was selected to avoid phase shifts in the ECG during baseline correction; however, other filters for baseline correction may be more appropriate for generation of a remainder ECG. Another factor that may have contributed to increased MSC during atrial fibrillation is the volume conductor effects of the torso which, for all ECG recordings, tend to increase the correlation between activity seen in leads II and V1. All but 6 episodes of atrial flutter exhibited higher mean MSC values compared to atrial fibrillation. The remainder ECGs of these six atrial flutter episodes exhibited low amplitude flutter waves and/or marked fragments of QRS complexes that differed in amplitude and location between remainder leads II and V1. The results obtained from MSC applied to the remainder ECGs (leads II and V1) were similar to that reported by Ropella et al. (10) for intracardiac data. However, MSC applied to intracardiac data showed complete separation of fibrillatory and nonfibrillatory rhythms (10). We hypothesize that more localized measurements of atrial activity using specialized surface leads (eg, Lewis leads [21]) would improve the discrimination capabilities of MSC.

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R-R variability R-R variability showed considerable amount of overlap between atrial fibrillation and atrial flutter. RRV detects atrial fibrillation based on the presence of irregular ventricular responses (22). The low RRV observed for one episode of atrial fibrillation occurred when the atrial fibrillation was accompanied by regular R-R intervals because of the presence of a junctional tachycardia. It was also noted that all 8 episodes of atrial flutter, which exceeded the RRV threshold for atrial fibrillation, had variable AV block. Furthermore, 1 sinus rhythm with supraventricular complexes and one sinus rhythm with premature atrial complexes exhibited values of RRV greater than the 8% RRV threshold. Each of these episodes that exceeded the RRV threshold for atrial fibrillation had a common feature: an irregularity in the ventricular response. These episodes of nonfibrillatory rhythms would be misclassified by RRV as atrial fibrillation. Nine of the 12 rhythms misclassified by RRV (7 of 8 atrial flutters, 1 of 2 sinus rhythms and 1 atrial fibrillation) were correctly classified by the MSC algorithm. In turn, 4 of 5 atrial flutter episodes, 1 of 2 sinus rhythm episodes, and all 3 atrial fibrillation episodes that were misclassified by mean MSC were correctly classified by RRV. A comparison of the RRV algorithm to that of mean MSC in the 2 to 9 Hz band showed that while the RRV algorithm improved sensitivity to atrial fibrillation, mean MSC resulted in improved specificity for atrial fibrillation. A combination of mean MSC and ventricular irregularity (RRV) may improve both sensitivity and specificity for detection of atrial fibrillation. Percent Power Percent power was able to discriminate sinus rhythm from atrial fibrillation. However, percent power showed considerable overlap between atrial flutter and atrial fibrillation. Episodes of atrial fibrillation with low percent power occasionally exhibited baseline wander or artifact due to mean beat subtraction that contributes to a broader power spectra and thus, a lower percent power in the 5 to 9 Hz band. If the atrial flutter had a rapid atrial rate with variable AV block, most of the flutter waves remained in the remainder ECG thereby contributing to a higher percent power in the 5 to 9 Hz band. Of the 5 atrial flutter episodes misclassified by percent power as atrial fibrillation, one atrial flutter was differentiated from atrial fibrillation by RRV alone, 2 were differentiated by both mean MSC and

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RRV, and 2 (atrial flutter with variable AV block) were separated from atrial fibrillation by mean MSC alone. All episodes of atrial fibrillation and sinus rhythm that were misclassified by percent power were correctly classified by both mean MSC and RRV. Mean MSC, RRV and percent power differentiated atrial fibrillation from sinus rhythm and atrial flutter to varying degrees. In terms of sensitivity and specificity, a combination of algorithms (mean MSC and RRV) will likely provide better discrimination of atrial fibrillation than any one algorithm. Magnitude-squared coherence is relatively independent of signal amplitude and morphology, does not require explicit detection of atrial activity and bases its classification of atrial fibrillation on characteristics unique to atrial fibrillation. These characteristics make MSC a desirable and perhaps more reliable differentiation scheme to be used for ECG interpretation systems. Both MSC and RRV can be analyzed in real time and on-line, for ambulatory and telemetric monitoring of patients. Furthermore, these parameters may also be easily estimated from Holter recordings where detection of atrial fibrillation, using explicit event detection, is severely hindered by signal quality. However, a test set of atrial rhythms needs to be analyzed by using the thresholds established with the training set to assess the full potential of such an arrhythmia classification scheme. It may be that more localized surface measurements of atrial activity will improve the performance of MSC from the surface ECG. A pair of Lewis leads (21), comprised of 2 electrodes are placed in the second and fourth intercostal spaces on the right side of the sternum, may amplify atrial activity not identified in the standard 12-lead system, potentially improving the ability of MSC to differentiate atrial fibrillation from nonfibrillatory rhythms. Coherence maps that use body surface mapping recordings might also be useful in the noninvasive study of the mechanisms of atrial fibrillation. The evaluation of arrhythmia discrimination schemes assumes that ECG recordings may be categorized into distinct, nonoverlapping rhythm classes. For atrial arrhythmias, such as atrial flutter and atrial fibrillation, such a distinct classification may not be possible. Indeed, the physiologic mechanisms underlying these atrial arrhythmias suggest a continuum of rhythm disorders from flutter to fibrillation, rendering a binary classification inappropriate. Thus, in those instances where our arrhythmia classification schemes failed, the distinction between atrial flutter and atrial fibrillation may

not have been feasible from a mechanistic view. Although we could have chosen only those examples of flutter and fibrillation that were clearly differentiable by standard clinical descriptions, we felt that such data selection would unfairly bias the results. We chose to use a data sample that was as closely representative of clinical occurrence as possible.

Acknowledgment The authors express their thanks to Drs E. Sadek and S. Swiryn, for assistance classifying the ECG rhythms, and to Marquette Medical Systems. (Milwaukee, WI) for their technical assistance in data retrieval.

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