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Iterative Method to Detect Atrial Activations and Measure Cycle Length From Electrograms During Atrial Fibrillation Jason Ng∗ , Vinod Sehgal, Justin K. Ng, David Gordon, and Jeffrey J. Goldberger
Abstract—Atrial fibrillation (AF) electrograms are characterized by varying morphologies, amplitudes, and cycle lengths (CLs), presenting a challenge for automated detection of individual activations and the activation rate. In this study, we evaluate an algorithm to detect activations and measure CLs from AF electrograms. This algorithm iteratively adjusts the detection threshold level until the mean CL converges with the median CL to detect all individual activations. A total of 291 AF electrogram recordings from 13 patients (11 male, 58 ± 10 years old) undergoing AF ablation were obtained. Using manual markings by two independent reviewers as the standard, we compared the cycle length iteration algorithm with a fixed threshold algorithm and dominant frequency (DF) for the estimation of CL. At segment lengths of 10 s, when comparing the algorithm detected to the manually detected activation, the undersensing, oversensing, and total discrepancy rates were 2.4%, 4.6%, and 7.0%, respectively, and with absolute differences in mean and median CLs were 7.9 ± 9.6 ms and 5.6 ± 6.8 ms, respectively. These results outperformed DF and fixed thresholdbased measurements. This robust method can be used for CL measurements in either real-time and offline settings and may be useful in the mapping of AF. Index Terms—Biomedical signal processing, cardiology, electrocardiography, fibrillation.
I. INTRODUCTION ONTACT atrial electrograms recorded during atrial fibrillation (AF) are characterized by rapid deflections with changing amplitudes, cycle lengths (CLs), and morphologies. Unlike other atrial tachyarrhythmias with regular activation patterns, AF has complex activation patterns that make elucidation of AF mechanisms difficult. Mapping of atrial CL or atrial activation rates has been proposed as an alternative to mapping activation sequences [1]–[5]. It has been hypothesized that sites with the fastest activation rates represent the locations of the drivers of AF (focal or reentrant) and could be possible ablation targets.
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Evidence of this has been shown in both clinical [2], [5], [6] and experimental studies [7], [8]. One of the main limitations of this activation rate mapping approach is the technical difficulties involved in obtaining reliable measurements. The complexity of AF electrograms can make detection of deflections and the calculation of the CLs and activation rates difficult in both the time and frequency domains [9], [10]. Deflection-to-deflection intervals can be measured manually by calipers but because of the variability of AF CLs, an average of several intervals are needed to characterize the AF CL. However, this is an arduous task for the operator making the measurements. An alternative method is a manual setting of an amplitude or slope threshold value that can be used to detect deflections. The limitation for manual thresholds is the subjectivity required to distinguish noise from atrial activation. Additionally, automatic algorithms which detect deflections based on fixed threshold levels are prone to oversensing or undersensing [11]. Dominant frequency (DF) analysis uses the frequency that contains the most power to be the estimate of activation rate. DF analysis works well in the estimation of activation rates if the AF electrograms have a certain amount of regularity, but the correlation is reduced with highly irregular waveforms and complex morphologies [9], [10]. Thus, more robust algorithms validated with rigorous testing are needed. In this study, we evaluated a new algorithm which uses cycle length iteration (CLI) to detect atrial complexes. The algorithm operates on observations from previous work [9] that AF CLs have distributions where mean and median CLs are approximately equal. Using manually marked electrograms as the standard, we evaluated the accuracy of the CLI algorithm to detect activations and compute AF CLs, and compared it with fixed threshold algorithms and DF analysis. II. METHODS A. Electrogram Dataset
Manuscript received August 1, 2013; revised October 7, 2013 and October 30, 2013; accepted October 31, 2013. Date of publication November 7, 2013; date of current version January 16, 2014. Asterisk indicates corresponding author. ∗ J. Ng is with the Feinberg School of Medicine and Northwestern University, Chicago, IL 60611 USA (e-mail: [email protected]). V. Sehgal is with the University of Illinois College of Medicine, Chicago, IL 60612 USA (e-mail: [email protected]). J. K. Ng, D. Gordon, and J. J. Goldberger are with the Feinberg School of Medicine and Northwestern University, Chicago, IL 60611 USA (e-mail: [email protected]; [email protected]; j-goldberger@ northwestern.edu). Digital Object Identifier 10.1109/TBME.2013.2290003
Electrogram recordings from 13 patients (11 male/2 female, 58 ± 10 years old) undergoing AF ablation were obtained prior to radiofrequency ablation at Northwestern Memorial Hospital. Four patients had paroxysmal AF and nine had persistent AF. Mapping and recording were performed using a Navi-Star catheter (Biosense Webster, Inc., Diamond Bar, CA). Bipolar electrograms were sequentially obtained from at least ten sites in the right atrium and at least ten sites in the left atrium and stored on the Prucka CardioLab EP System (GE Healthcare, Waukesha, WI). The electrograms were sampled at a rate of
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977 Hz and filtered with a 30-Hz high-pass filter. The protocol was approved by the Office for the Protection of Research Subjects’ Institutional Review Board of Northwestern University. B. Manual Marking of Electrograms All electrogram analyses were performed offline using tools developed in MATLAB (Mathworks, Natick, MA). Activation complexes for each electogram recording were manually marked by two independent operators. The operators were instructed to mark each activation at the point of the highest absolute amplitude. For electrograms with discrete but fractionated activation complexes with clear isoelectric periods before and after the complex, the highest amplitude deflection was chosen. No markings were made within 50 ms of a previous mark. Simultaneous surface ECG recordings were available to distinguish ventricular far-field activity from atrial activations when performing manual markings. Signals were excluded if the amplitudes of the ventricular far-field complexes were greater than that of the atrial complexes. The manual reviewers were otherwise instructed not to mark ventricular complexes using the surface ECG as a reference. In addition to the two independent sets of markings, we also evaluated the CLI algorithm using the intersection of the two sets of manual marking. The intersection set was intended to provide a set of activations that both reviewers were most confident in. The intersection was defined as the marks that are common to both sets of manual markings within 50 ms. If the marked points agreed, then the time point of the first set was used.
Fig. 1.
Flowchart describing the steps of the CLI algorithm.
C. CLI Algorithm The electrograms are first preprocessed with similar steps used by Botteron and Smith [12]: 1) 40-Hz high-pass filtering (second-order Butterworth); 2) rectification; and 3) 30-Hz lowpass filtering (second-order Butterworth). The iterative process for detecting the activations is summarized in the flowchart of Fig. 1. The peak with the highest magnitude is the first detected activation time. Next, all peaks occurring within 50-ms blanking period before and after the detected beat are excluded. The next largest peak is then detected and added to the set. Then, the blanking period is applied again. The process of detecting the next peak and applying the blanking period is repeated until the mean calculated CL is less than 275 ms and one of the following two conditions are met: 1) the mean CL is less than median CL plus 5 ms or 2) the magnitude of the current peak is 20% less than the magnitude of the previously detected peak. The mean and median CL convergence criterion is based on previous observations that AF CLs have distributions where mean and median CLs are approximately equal [9]. Atrial rates measured during human AF activity have been shown to be in the 4–9 Hz range, which is equivalent to CLs between 250 and 111 ms [13]. Therefore, we have selected a CL of 275 ms as upper bound for the activation detection in case the mean/median crossings occur prematurely. Fig. 2 shows an example of the mean/median CL convergence when the 18th activation is added to the set.
Fig. 2. Graphical illustration of the CLI method: (a) raw unfiltered electrograms, (b) electrograms after rectification and low-pass filtering with peaks numbered in order of the highest to lowest amplitude, (c) graph showing mean and median CLs calculation after adding peaks one by one. Mean and median CLs converge after 18 peaks.
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In order to detect potentially missed activations within longer intervals, a final postprocessing step involves finding activation intervals greater than 1.5 times the median CL. The largest peak, if present, within the interval and not within 50 ms of another peak is included in the set of activations. This process is repeated until there are no more intervals greater than 1.5 times the median CL with peaks between them.
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TABLE I NUMBER OF SEGMENTS AND ACTIVATIONS ANALYZED FOR EACH SEGMENT LENGTH STUDIED
D. Evaluation of the CLI Algorithm The CLI algorithm was evaluated on contiguous AF segments of each of the following segment lengths: 2, 4, 6, 8, 10, 12, 14, and 16 s. Detected activation by the CLI algorithm that is within 75 ms of a manually marked activation was considered matched activations. As the manual marks were made on unfiltered signals and the tested algorithms were performed on filtered electrograms, a 75 ms window was chosen to encompass the width of a fractionated electrogram. Detected activations not within 75 ms of a manually marked activation that had not already been classified as a matched activation were considered oversensed activations. Manually marked activations that were not within 75 ms of a detected activation were considered undersensed activations. Oversensed or undersensed activations that were either the first or last activation in the segment were not counted in the oversensing and undersensing rates. Oversensing and undersensing rates were calculated as percentages of the total number of marked activations. Agreement in CL was measured by calculating the absolute difference between the mean/median CL of each segment between the manual and CLI algorithm. E. Comparison With Other CL Estimation Methods Agreement of the CLI algorithm with the manually marked activations was compared against the following: 1) activations detected using an optimum fixed detection threshold; and 2) CL calculated from DF. Fixed threshold detection was performed using the filtered and rectified signal to detect the activations. With this approach, all peaks (taking into account the 50-ms blanking period) above a giving threshold value were considered activations. A range of threshold values were tested to determine the optimal threshold value. Thresholds based on raw amplitude (in μVs) were tested in a 1–50 μV range with 1 μV increments. The amplitudes of bipolar electrograms are in the microvolt range as they are significantly attenuated following low-pass filtering. Thresholds based on the percentage of the maximum amplitude were tested in a 0.5–25% range with 0.5% increments. Thresholds based on the percentage of one standard deviation were tested in a 2–100% range with 2% increments. For each type and segment duration, the thresholds producing the minimum combined oversensing and undersensing rates were considered the optimum thresholds. DFs in this study were calculated as previously described [5]. First, the electrogram segments were bandpass filtered with cutoff frequencies of 40 and 250 Hz using a second-ordered Butterworth filter. The filtered signals were then rectified and lowpass filtered at 20 Hz also using a second-ordered Butterworth
filter. The power spectrum was then calculated using the Fast Fourier Transform. The DF was defined as the frequency with the highest power in the 3–20 Hz band. The AF CL from DF (DF CL) was calculated as 1000/DF. As DF estimates activation rate without the detection of activations, only the absolute difference between DF CL and manual CL was evaluated for each segment duration. F. Statistics Absolute differences in CL measurements and manually marked CLs of the multiple methods were compared using the Wilcoxon signed rank test. P values less than 0.05 were considered statistically significant. III. RESULTS A. Electrogram Characteristics In total, 291 electrogram recordings were obtained. Twentyseven electrograms where the atrial activations could not be easily distinguished from the noise were excluded. The remaining set of electrograms were obtained from a total of 123 right atrial sites and 141 left atrial sites with an average duration of 27.5 ± 9.0 s. The average mean and median CLs determined by manual marking were 159.9 ± 24.9 ms and 161.0 ± 24.9 ms, respectively. The average difference between the mean and median CLs was 0.5 ± 5.7 ms and 82% of the recordings had absolute mean and median CL differences less than 5 ms which suggests that our assumptions of mean and median CL convergence used for the algorithm are valid for the large majority of the recordings. The average percent agreement between the two sets of manual markings was 92%. The number of contiguous segments analyzed for each segment duration is summarized in Table I. B. CLI Performance The oversensing, undersensing, and total discrepancy rates of the CLI algorithm compared to the two sets of manual markings and the intersection of the manual markings for the different segment durations are shown in Fig. 3(a)–(c). The undersensing rates were highest when shorter segment durations were used. The oversensensing rate was more stable across the different segment durations. Undersensing rates were higher for CLI when compared to the A markings than to the B markings.
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Fig. 3. Evaluation of the CLI algorithm against the manual markings from markers A and B and the intersection of the markings of A and B (A ∩ B) for different segment lengths: panel (a) undersensing rate, (b) oversensing rates, (c) total discrepancy rates, (d) mean CL difference, and (e) median CL difference.
Oversensing rates were higher when compared to the B markings than to the A markings. Undersensing rates were lower and oversensing rates were higher when CLI was compared to the intersection of A and B than when compared to either markings A or B. At 10 s durations, when the total discrepancy rate seems to stabilize, the undersensing, oversensing, and total discrepancy rates when CLI was compared to the A and B intersection markings were 2.4%, 4.6%, and 7.0%, respectively. Absolute differences in mean CL between the CLI algorithm and the manual markings are shown in Fig. 3(d). The absolute differences in median CL between the CLI and manual markings are shown in Fig. 3(e). Tracking with the undersensing rates, the absolute differences in CL are the highest with shorter segment durations. At 10 s durations, the absolute differences in mean and median CLs compared to the A and B intersection markings were 7.9 ± 9.6 ms and 5.6 ± 6.8 ms, respectively. For the 10 s segments, 25% of the recordings had CL standard deviations less than 25 ms, 39% had standard deviations between 25 and 40 ms, and 36% had standard deviations greater than 40 ms. The recordings with standard deviations less than 25 ms had oversensing, undersensing, and total discrepancy rates of 0.3%, 1.2%, and 1.5%, respectively. Recordings with standard deviations between than 25 and 40 ms had oversensing, undersensing, and total discrepancy rates of 2.8%, 2.2%, and 5.1%, respectively. Recordings with standard deviations greater than 40 ms had oversensing, undersensing, and total discrepancy rates of 9.5%, 3.3%, and 12.8%, respectively. 2-s segments required an average of 4 ± 2 ms computation time running on MATLAB with a computer equipped with a 2-GHz Intel Core2Duo processor. 16-s segments required an average of 26 ± 5 ms computation time.
Fig. 4. Comparisons of (a) undersensing rates, (b) oversensing rates, and (c) total discrepancy rates with manual marking for the CLI algorithm and the fixed threshold algorithms based on: absolute amplitude (fixed-abs), percentage of maximum amplitude (fixed-per), and percentage of standard deviation (fixed-sd).
C. CLI Versus Other CL Estimation Methods The results comparing the undersensing, oversensing, and total discrepancy rates of the CLI algorithm with other activation detection methods are shown in Fig. 4. For this analysis, we present only the data using the intersection markings as the standard. Fixed threshold detections were evaluated using the optimal thresholds that minimized the total discrepancy rates. The optimum absolute threshold values ranged from 8 to 9 μV depending on segment duration. The optimum threshold as a percentage of the maximum peak amplitude ranged from 5.5% to 9.5%. The optimum threshold as a percentage of one standard deviation ranged from 12% to 14%. Detection with the optimum raw threshold values had the highest discrepancy rates for all segment durations. The CLI algorithm had much lower oversensing rates than any of the fixed threshold methods and lower undersensing rates for segment lengths of 6 s or greater. Overall CLI had the lowest total discrepancy rates for all the segment lengths. The absolute difference in mean and median CLs of the automatic algorithms (including DF derived CL) with the manually marked intersection activations is shown in Fig. 5. CLI had significantly lower absolute differences in both mean and median CLs than the other algorithms for all segment lengths. For the 10 s segment length, the CLI absolute difference in mean CL (7.5 ± 9.6 ms) was significantly less than that of DF
NG et al.: ITERATIVE METHOD TO DETECT ATRIAL ACTIVATIONS AND MEASURE CYCLE LENGTH
Fig. 5. Comparisons of (a) mean CL difference and (b) median CL difference with manual marking for the CLI algorithm, DF derived CL, and the fixed threshold algorithms based on: absolute amplitude (fixed-abs), percentage of maximum amplitude (fixed-per), and percentage of standard deviation (fixed-sd).
(13.3 ± 15.7 ms, p < 0.0001), fixed absolute threshold (28.2 ± 49.2 ms, p < 0.0001), fixed percentage threshold (13.9 ± 19.2 ms, p < 0.0001), and fixed standard deviation threshold (11.5 ± 15.1 ms, p < 0.0001). The CLI absolute difference in median CL (5.4 ± 7.2 ms) was also significantly less than that of DF (12.2 ± 14.8 ms, p < 0.0001), fixed absolute threshold (16.0 ± 33.5 ms, p < 0.0001), fixed percentage threshold (8.4 ± 13.9 ms, p < 0.0001), and fixed standard deviation threshold (7.1 ± 10.1 ms, p < 0.0091). IV. DISCUSSION The proposed CLI algorithm was shown to accurately detect atrial activations from bipolar electrograms recorded during AF and provide CL estimations that more closely matched manually marked activations than fixed threshold or DF-based methods. The criteria for mean and median CL convergence of this algorithm provide detection criteria amidst the potentially very complex activation and morphology patterns of AF electrograms. Although this study evaluated the algorithm on electrograms in an offline setting, this automated algorithm is efficient enough to be used for real-time applications. A variety of methods have been previously proposed to detect activations from electrograms in the setting of AF. Holm et al. [14] used a process which incorporates a cubic spline interpolation of the activation wave and chooses the point that divides the interpolated wave to two equal parts as the activation time. However, these methods require manual threshold selection. Faes et al. [15] introduced an adaptive activation detection method which sets a threshold based on the amplitude of the last ten detected peaks with exponentially decreasing weights and a blanking period of 55 ms. This method was compared with manual activation markings with differences ranging from 2.6 to 20 ms depending on the complexity of the AF.
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Sensitivity and specificity of the measures were not reported. Lee et al. [16] evaluated a similar adaptive threshold algorithm from 20 000 electrograms recorded during a canine model of AF. They showed that CLs obtained by the algorithm had a correlation of 0.96 when compared with those obtained by manual marking. Although we have not directly compared the CLI with these other methods, we postulate that the CLI algorithm would have performance advantages for electrograms with highly variable electrogram amplitudes and longer durations, while the other adaptive threshold methods may have advantages with more variable CLs and shorter durations. We have attempted to use manually marked electrograms as the basis for the evaluation of the CLI detection algorithm and comparison with DF and the fixed threshold algorithms. The manual marking of AF electrograms is also not a straightforward process, as it requires sometimes subjective determinations of what is considered an activation. Electrograms during AF can have changing amplitudes and morphologies and can have very fractionated morphologies that make activation markings very difficult. Thus, we used the intersection set of markings from two independent reviewers that in theory would include the only activations with the highest confidence. The CLI algorithm had the lowest percentage of combined undersensed and oversensed activations when the intersection set of manual markings was used as the reference. Although the sensitivity and specificity of detecting atrial activations are important characteristics of the detection algorithm, the more critical evaluation criteria are the ability to robustly estimate CL. When manually marking AF electrograms, a human is able to see the recording in its entirety. The human eye can process signals to identify where activations are expected to occur based on the basic CL and thereby assign an activation to a low amplitude electrogram that may not be marked or detected by more rigid criteria. The iteration process of the CLI algorithm to detect activation until the mean and median CLs converge more closely mimics the human detection process, whereas fixed threshold methods do not use the contextual information when detecting deflections. Thus, the CLI algorithm provides a very robust measurement of AF CL. There are some limitations to the CLI technique. First, there is a requirement for clinical stability during the recording segment in order for the algorithm to take advantage of mean and median CL convergence. Therefore, errors may occur if attempting to use the technique during phases of rapid change in AF CL that may occur with drug or autonomic interventions. Second, the CLI algorithm works significantly better with longer segment lengths, although the CL measurements at the short lengths were still better than those obtain with DF or fixed thresholds. Segment lengths of 10 s or more appear to provide optimal activation detection and CL estimation. We show, however, that for a subset of recording with highly irregular CLs, discrepancy rates compared to manual marking were considerably higher than those with less variable CLs. It is expected that far-field ventricular complexes would remain an issue with the CLI algorithm, as they do with CLs estimated with DF and fixed threshold techniques. However, there are a variety of techniques that may be able to alleviate the effect of ventricular complexes.
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[17] Finally, it is not known whether the results of the CLI algorithm will provide more meaningful insights about AF mechanisms. This will need to be explored in future studies. V. CONCLUSION Mapping AF CLs for the understanding of AF pathophysiology requires a certain amount of precision of the measurements to detect the subtle differences that exist with regions, interventions, and between subjects. Obtaining precise measurements is complicated by the complex nature of AF electrograms. The CLI offers some improvement in this regard over other commonly used techniques and can be used in either offline or real-time settings. REFERENCES [1] M. Ha¨ıssaguerre, P. Sanders, M. Hocini, L. F. Hsu, D. C. Shah, C. Scav´ee, Y. Takahashi, M. Rotter, J. L. Pasqui´e, S. Garrigue, J. Cl´ementy, and P. Ja¨ıs, “Changes in atrial fibrillation cycle length and inducibility during catheter ablation and their relation to outcome,” Circulation, vol. 109, pp. 3007–3013, 2004. [2] P. Sanders, O. Berenfeld, M. Hocini, P. Ja¨ıs, R. Vaidyanathan, L. F. Hsu, S. Garrigue, Y. Takahashi, M. Rotter, F. Sacher, C. Scav´ee, R. PloutzSnyder, J. Jalife, and M. Ha¨ıssaguerre, “Spectral analysis identifies sites of high-frequency activity maintaining atrial fibrillation in humans,” Circulation, vol. 112, pp. 789–797, 2005. [3] J. Sahadevan, K. Ryu, L. Peltz, C. M. Khrestian, R. W. Stewart, A. H. Markowitz, and A. L. Waldo, “Epicardial mapping of chronic atrial fibrillation in patients: Preliminary observations,” Circulation, vol. 110, pp. 3293–3299, 2004. [4] S. R. Dibs, J. Ng, R. Arora, R. S. Passman, A. H. Kadish, and J. J. Goldberger, “Spatiotemporal characterization of atrial activation in persistent human atrial fibrillation: Multisite electrogram analysis and surface electrocardiographic correlations—A pilot study,” Heart Rhythm, vol. 5, pp. 686–693, 2008. [5] S. Lazar, S. Dixit, F. E. Marchlinski, D. J. Callans, and E. P. Gerstenfeld, “Presence of left-to-right atrial frequency gradient in paroxysmal but not persistent atrial fibrillation in humans,” Circulation, vol. 110, pp. 3181– 3186, 2004. [6] A. Michelucci, P. Bartolini, G. Calcagnini, F. Censi, A. Colella, S. Morelli, L. Padeletti, P. Pieragnoli, and V. Barbaro, “Mapping the organization of atrial fibrillation with basket catheters. Part II: Regional patterns in chronic patients,” Pacing Clin. Electrophysiol., vol. 24, pp. 1089–1096, 2001.
[7] D. Filgueiras-Rama, N. F. Price, R. P. Martins, M. Yamazaki, U. M. Avula, K. Kaur, J. Kalifa, S. R. Ennis, E. Hwang, V. Devabhaktuni, J. Jalife, and O. Berenfeld, “Long-term frequency gradients during persistent atrial fibrillation in sheep are associated with stable sources in the left atrium,” Circulation Arrhythm Electrophysiol., pp. 5:1160–1167, 2012. [8] R. Mandapati, A. Skanes, J. Chen, O. Berenfeld, and J. J. , “Stable microreentrant sources as a mechanism of atrial fibrillation in the isolated sheep heart,” Circulation, vol. 101, pp. 194–199, 2000. [9] J. Ng, A. H. Kadish, and J. J. Goldberger, “Effect of electrogram characteristics on the relationship of dominant frequency to atrial activation rate in atrial fibrillation,” Heart Rhythm, vol. 3, pp. 1295–1305, 2006. [10] J. Ng, A. H. Kadish, and J. J. Goldberger, “Technical considerations for dominant frequency analysis,” J. Cardiovascular Electrophysiol., vol. 18, pp. 757–764, 2007. [11] O. Berenfeld, S. Ennis, E. Hwang, B. Hooven, K. Grzeda, S. Mironov, M. Yamazaki, J. Kalifa, and J. Jalife, “Time- and frequency-domain analyses of atrial fibrillation activation rate: The optical mapping reference,” Heart Rhythm, vol. 8, pp. 1758–1765, 2011. [12] G. W. Botteron and J. M. Smith, “A technique for measurement of the extent of spatial organization of atrial activation during atrial fibrillation in the intact human heart,” IEEE Trans. Biomed. Eng., vol. 42, no. 6, pp. 579–586, Jun. 1995. [13] J. Slocum, A. Sahakian, and S. Swiryn, “Computer discrimination of atrial fibrillation and regular atrial rhythms from intra-atrial electrograms,” Pacing Clin. Electrophysiol., vol. 11, pp. 610–621, 1988. [14] M. Holm, R. Johansson, S. B. Olsson, J. Brandt, and C. L¨uhrs, “A new method for analysis of atrial activation during chronic atrial fibrillation in man,” IEEE Trans. Biomed. Eng., vol. 43, no. 2, pp. 198–210, Feb. 1996. [15] L. Faes, G. Nollo, R. Antolini, F. Gaita, and F. Ravelli, “A method for quantifying atrial fibrillation organization based on wave-morphology similarity,” IEEE Trans. Biomed. Eng., vol. 49, no. 12, pp. 1504–1513, Dec. 2002. [16] S. Lee, K. Ryu, A. L. Waldo, C. M. Khrestian, D. M. Durand, and J. Sahadevan, “An algorithm to measure beat-to-beat cycle lengths for assessment of atrial electrogram rate and regularity during atrial fibrillation,” J. Cardiovascular Electrophysiol., vol. 24, pp. 199–206, 2013. [17] J. J. Rieta and F. Hornero, “Comparative study of methods for ventricular activity cancellation in atrial electrograms of atrial fibrillation,” Physiol. Meas., vol. 28, pp. 925–936, 2007.
Authors’ photographs and biographies not available at the time of publication.
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Iterative Method to Detect Atrial Activations and Measure Cycle Length From Electrograms During Atrial Fibrillation Jason Ng∗ , Vinod Sehgal, Justin K. Ng, David Gordon, and Jeffrey J. Goldberger
Abstract—Atrial fibrillation (AF) electrograms are characterized by varying morphologies, amplitudes, and cycle lengths (CLs), presenting a challenge for automated detection of individual activations and the activation rate. In this study, we evaluate an algorithm to detect activations and measure CLs from AF electrograms. This algorithm iteratively adjusts the detection threshold level until the mean CL converges with the median CL to detect all individual activations. A total of 291 AF electrogram recordings from 13 patients (11 male, 58 ± 10 years old) undergoing AF ablation were obtained. Using manual markings by two independent reviewers as the standard, we compared the cycle length iteration algorithm with a fixed threshold algorithm and dominant frequency (DF) for the estimation of CL. At segment lengths of 10 s, when comparing the algorithm detected to the manually detected activation, the undersensing, oversensing, and total discrepancy rates were 2.4%, 4.6%, and 7.0%, respectively, and with absolute differences in mean and median CLs were 7.9 ± 9.6 ms and 5.6 ± 6.8 ms, respectively. These results outperformed DF and fixed thresholdbased measurements. This robust method can be used for CL measurements in either real-time and offline settings and may be useful in the mapping of AF. Index Terms—Biomedical signal processing, cardiology, electrocardiography, fibrillation.
I. INTRODUCTION ONTACT atrial electrograms recorded during atrial fibrillation (AF) are characterized by rapid deflections with changing amplitudes, cycle lengths (CLs), and morphologies. Unlike other atrial tachyarrhythmias with regular activation patterns, AF has complex activation patterns that make elucidation of AF mechanisms difficult. Mapping of atrial CL or atrial activation rates has been proposed as an alternative to mapping activation sequences [1]–[5]. It has been hypothesized that sites with the fastest activation rates represent the locations of the drivers of AF (focal or reentrant) and could be possible ablation targets.
C
Evidence of this has been shown in both clinical [2], [5], [6] and experimental studies [7], [8]. One of the main limitations of this activation rate mapping approach is the technical difficulties involved in obtaining reliable measurements. The complexity of AF electrograms can make detection of deflections and the calculation of the CLs and activation rates difficult in both the time and frequency domains [9], [10]. Deflection-to-deflection intervals can be measured manually by calipers but because of the variability of AF CLs, an average of several intervals are needed to characterize the AF CL. However, this is an arduous task for the operator making the measurements. An alternative method is a manual setting of an amplitude or slope threshold value that can be used to detect deflections. The limitation for manual thresholds is the subjectivity required to distinguish noise from atrial activation. Additionally, automatic algorithms which detect deflections based on fixed threshold levels are prone to oversensing or undersensing [11]. Dominant frequency (DF) analysis uses the frequency that contains the most power to be the estimate of activation rate. DF analysis works well in the estimation of activation rates if the AF electrograms have a certain amount of regularity, but the correlation is reduced with highly irregular waveforms and complex morphologies [9], [10]. Thus, more robust algorithms validated with rigorous testing are needed. In this study, we evaluated a new algorithm which uses cycle length iteration (CLI) to detect atrial complexes. The algorithm operates on observations from previous work [9] that AF CLs have distributions where mean and median CLs are approximately equal. Using manually marked electrograms as the standard, we evaluated the accuracy of the CLI algorithm to detect activations and compute AF CLs, and compared it with fixed threshold algorithms and DF analysis. II. METHODS A. Electrogram Dataset
Manuscript received August 1, 2013; revised October 7, 2013 and October 30, 2013; accepted October 31, 2013. Date of publication November 7, 2013; date of current version January 16, 2014. Asterisk indicates corresponding author. ∗ J. Ng is with the Feinberg School of Medicine and Northwestern University, Chicago, IL 60611 USA (e-mail: [email protected]). V. Sehgal is with the University of Illinois College of Medicine, Chicago, IL 60612 USA (e-mail: [email protected]). J. K. Ng, D. Gordon, and J. J. Goldberger are with the Feinberg School of Medicine and Northwestern University, Chicago, IL 60611 USA (e-mail: [email protected]; [email protected]; j-goldberger@ northwestern.edu). Digital Object Identifier 10.1109/TBME.2013.2290003
Electrogram recordings from 13 patients (11 male/2 female, 58 ± 10 years old) undergoing AF ablation were obtained prior to radiofrequency ablation at Northwestern Memorial Hospital. Four patients had paroxysmal AF and nine had persistent AF. Mapping and recording were performed using a Navi-Star catheter (Biosense Webster, Inc., Diamond Bar, CA). Bipolar electrograms were sequentially obtained from at least ten sites in the right atrium and at least ten sites in the left atrium and stored on the Prucka CardioLab EP System (GE Healthcare, Waukesha, WI). The electrograms were sampled at a rate of
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977 Hz and filtered with a 30-Hz high-pass filter. The protocol was approved by the Office for the Protection of Research Subjects’ Institutional Review Board of Northwestern University. B. Manual Marking of Electrograms All electrogram analyses were performed offline using tools developed in MATLAB (Mathworks, Natick, MA). Activation complexes for each electogram recording were manually marked by two independent operators. The operators were instructed to mark each activation at the point of the highest absolute amplitude. For electrograms with discrete but fractionated activation complexes with clear isoelectric periods before and after the complex, the highest amplitude deflection was chosen. No markings were made within 50 ms of a previous mark. Simultaneous surface ECG recordings were available to distinguish ventricular far-field activity from atrial activations when performing manual markings. Signals were excluded if the amplitudes of the ventricular far-field complexes were greater than that of the atrial complexes. The manual reviewers were otherwise instructed not to mark ventricular complexes using the surface ECG as a reference. In addition to the two independent sets of markings, we also evaluated the CLI algorithm using the intersection of the two sets of manual marking. The intersection set was intended to provide a set of activations that both reviewers were most confident in. The intersection was defined as the marks that are common to both sets of manual markings within 50 ms. If the marked points agreed, then the time point of the first set was used.
Fig. 1.
Flowchart describing the steps of the CLI algorithm.
C. CLI Algorithm The electrograms are first preprocessed with similar steps used by Botteron and Smith [12]: 1) 40-Hz high-pass filtering (second-order Butterworth); 2) rectification; and 3) 30-Hz lowpass filtering (second-order Butterworth). The iterative process for detecting the activations is summarized in the flowchart of Fig. 1. The peak with the highest magnitude is the first detected activation time. Next, all peaks occurring within 50-ms blanking period before and after the detected beat are excluded. The next largest peak is then detected and added to the set. Then, the blanking period is applied again. The process of detecting the next peak and applying the blanking period is repeated until the mean calculated CL is less than 275 ms and one of the following two conditions are met: 1) the mean CL is less than median CL plus 5 ms or 2) the magnitude of the current peak is 20% less than the magnitude of the previously detected peak. The mean and median CL convergence criterion is based on previous observations that AF CLs have distributions where mean and median CLs are approximately equal [9]. Atrial rates measured during human AF activity have been shown to be in the 4–9 Hz range, which is equivalent to CLs between 250 and 111 ms [13]. Therefore, we have selected a CL of 275 ms as upper bound for the activation detection in case the mean/median crossings occur prematurely. Fig. 2 shows an example of the mean/median CL convergence when the 18th activation is added to the set.
Fig. 2. Graphical illustration of the CLI method: (a) raw unfiltered electrograms, (b) electrograms after rectification and low-pass filtering with peaks numbered in order of the highest to lowest amplitude, (c) graph showing mean and median CLs calculation after adding peaks one by one. Mean and median CLs converge after 18 peaks.
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In order to detect potentially missed activations within longer intervals, a final postprocessing step involves finding activation intervals greater than 1.5 times the median CL. The largest peak, if present, within the interval and not within 50 ms of another peak is included in the set of activations. This process is repeated until there are no more intervals greater than 1.5 times the median CL with peaks between them.
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TABLE I NUMBER OF SEGMENTS AND ACTIVATIONS ANALYZED FOR EACH SEGMENT LENGTH STUDIED
D. Evaluation of the CLI Algorithm The CLI algorithm was evaluated on contiguous AF segments of each of the following segment lengths: 2, 4, 6, 8, 10, 12, 14, and 16 s. Detected activation by the CLI algorithm that is within 75 ms of a manually marked activation was considered matched activations. As the manual marks were made on unfiltered signals and the tested algorithms were performed on filtered electrograms, a 75 ms window was chosen to encompass the width of a fractionated electrogram. Detected activations not within 75 ms of a manually marked activation that had not already been classified as a matched activation were considered oversensed activations. Manually marked activations that were not within 75 ms of a detected activation were considered undersensed activations. Oversensed or undersensed activations that were either the first or last activation in the segment were not counted in the oversensing and undersensing rates. Oversensing and undersensing rates were calculated as percentages of the total number of marked activations. Agreement in CL was measured by calculating the absolute difference between the mean/median CL of each segment between the manual and CLI algorithm. E. Comparison With Other CL Estimation Methods Agreement of the CLI algorithm with the manually marked activations was compared against the following: 1) activations detected using an optimum fixed detection threshold; and 2) CL calculated from DF. Fixed threshold detection was performed using the filtered and rectified signal to detect the activations. With this approach, all peaks (taking into account the 50-ms blanking period) above a giving threshold value were considered activations. A range of threshold values were tested to determine the optimal threshold value. Thresholds based on raw amplitude (in μVs) were tested in a 1–50 μV range with 1 μV increments. The amplitudes of bipolar electrograms are in the microvolt range as they are significantly attenuated following low-pass filtering. Thresholds based on the percentage of the maximum amplitude were tested in a 0.5–25% range with 0.5% increments. Thresholds based on the percentage of one standard deviation were tested in a 2–100% range with 2% increments. For each type and segment duration, the thresholds producing the minimum combined oversensing and undersensing rates were considered the optimum thresholds. DFs in this study were calculated as previously described [5]. First, the electrogram segments were bandpass filtered with cutoff frequencies of 40 and 250 Hz using a second-ordered Butterworth filter. The filtered signals were then rectified and lowpass filtered at 20 Hz also using a second-ordered Butterworth
filter. The power spectrum was then calculated using the Fast Fourier Transform. The DF was defined as the frequency with the highest power in the 3–20 Hz band. The AF CL from DF (DF CL) was calculated as 1000/DF. As DF estimates activation rate without the detection of activations, only the absolute difference between DF CL and manual CL was evaluated for each segment duration. F. Statistics Absolute differences in CL measurements and manually marked CLs of the multiple methods were compared using the Wilcoxon signed rank test. P values less than 0.05 were considered statistically significant. III. RESULTS A. Electrogram Characteristics In total, 291 electrogram recordings were obtained. Twentyseven electrograms where the atrial activations could not be easily distinguished from the noise were excluded. The remaining set of electrograms were obtained from a total of 123 right atrial sites and 141 left atrial sites with an average duration of 27.5 ± 9.0 s. The average mean and median CLs determined by manual marking were 159.9 ± 24.9 ms and 161.0 ± 24.9 ms, respectively. The average difference between the mean and median CLs was 0.5 ± 5.7 ms and 82% of the recordings had absolute mean and median CL differences less than 5 ms which suggests that our assumptions of mean and median CL convergence used for the algorithm are valid for the large majority of the recordings. The average percent agreement between the two sets of manual markings was 92%. The number of contiguous segments analyzed for each segment duration is summarized in Table I. B. CLI Performance The oversensing, undersensing, and total discrepancy rates of the CLI algorithm compared to the two sets of manual markings and the intersection of the manual markings for the different segment durations are shown in Fig. 3(a)–(c). The undersensing rates were highest when shorter segment durations were used. The oversensensing rate was more stable across the different segment durations. Undersensing rates were higher for CLI when compared to the A markings than to the B markings.
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Fig. 3. Evaluation of the CLI algorithm against the manual markings from markers A and B and the intersection of the markings of A and B (A ∩ B) for different segment lengths: panel (a) undersensing rate, (b) oversensing rates, (c) total discrepancy rates, (d) mean CL difference, and (e) median CL difference.
Oversensing rates were higher when compared to the B markings than to the A markings. Undersensing rates were lower and oversensing rates were higher when CLI was compared to the intersection of A and B than when compared to either markings A or B. At 10 s durations, when the total discrepancy rate seems to stabilize, the undersensing, oversensing, and total discrepancy rates when CLI was compared to the A and B intersection markings were 2.4%, 4.6%, and 7.0%, respectively. Absolute differences in mean CL between the CLI algorithm and the manual markings are shown in Fig. 3(d). The absolute differences in median CL between the CLI and manual markings are shown in Fig. 3(e). Tracking with the undersensing rates, the absolute differences in CL are the highest with shorter segment durations. At 10 s durations, the absolute differences in mean and median CLs compared to the A and B intersection markings were 7.9 ± 9.6 ms and 5.6 ± 6.8 ms, respectively. For the 10 s segments, 25% of the recordings had CL standard deviations less than 25 ms, 39% had standard deviations between 25 and 40 ms, and 36% had standard deviations greater than 40 ms. The recordings with standard deviations less than 25 ms had oversensing, undersensing, and total discrepancy rates of 0.3%, 1.2%, and 1.5%, respectively. Recordings with standard deviations between than 25 and 40 ms had oversensing, undersensing, and total discrepancy rates of 2.8%, 2.2%, and 5.1%, respectively. Recordings with standard deviations greater than 40 ms had oversensing, undersensing, and total discrepancy rates of 9.5%, 3.3%, and 12.8%, respectively. 2-s segments required an average of 4 ± 2 ms computation time running on MATLAB with a computer equipped with a 2-GHz Intel Core2Duo processor. 16-s segments required an average of 26 ± 5 ms computation time.
Fig. 4. Comparisons of (a) undersensing rates, (b) oversensing rates, and (c) total discrepancy rates with manual marking for the CLI algorithm and the fixed threshold algorithms based on: absolute amplitude (fixed-abs), percentage of maximum amplitude (fixed-per), and percentage of standard deviation (fixed-sd).
C. CLI Versus Other CL Estimation Methods The results comparing the undersensing, oversensing, and total discrepancy rates of the CLI algorithm with other activation detection methods are shown in Fig. 4. For this analysis, we present only the data using the intersection markings as the standard. Fixed threshold detections were evaluated using the optimal thresholds that minimized the total discrepancy rates. The optimum absolute threshold values ranged from 8 to 9 μV depending on segment duration. The optimum threshold as a percentage of the maximum peak amplitude ranged from 5.5% to 9.5%. The optimum threshold as a percentage of one standard deviation ranged from 12% to 14%. Detection with the optimum raw threshold values had the highest discrepancy rates for all segment durations. The CLI algorithm had much lower oversensing rates than any of the fixed threshold methods and lower undersensing rates for segment lengths of 6 s or greater. Overall CLI had the lowest total discrepancy rates for all the segment lengths. The absolute difference in mean and median CLs of the automatic algorithms (including DF derived CL) with the manually marked intersection activations is shown in Fig. 5. CLI had significantly lower absolute differences in both mean and median CLs than the other algorithms for all segment lengths. For the 10 s segment length, the CLI absolute difference in mean CL (7.5 ± 9.6 ms) was significantly less than that of DF
NG et al.: ITERATIVE METHOD TO DETECT ATRIAL ACTIVATIONS AND MEASURE CYCLE LENGTH
Fig. 5. Comparisons of (a) mean CL difference and (b) median CL difference with manual marking for the CLI algorithm, DF derived CL, and the fixed threshold algorithms based on: absolute amplitude (fixed-abs), percentage of maximum amplitude (fixed-per), and percentage of standard deviation (fixed-sd).
(13.3 ± 15.7 ms, p < 0.0001), fixed absolute threshold (28.2 ± 49.2 ms, p < 0.0001), fixed percentage threshold (13.9 ± 19.2 ms, p < 0.0001), and fixed standard deviation threshold (11.5 ± 15.1 ms, p < 0.0001). The CLI absolute difference in median CL (5.4 ± 7.2 ms) was also significantly less than that of DF (12.2 ± 14.8 ms, p < 0.0001), fixed absolute threshold (16.0 ± 33.5 ms, p < 0.0001), fixed percentage threshold (8.4 ± 13.9 ms, p < 0.0001), and fixed standard deviation threshold (7.1 ± 10.1 ms, p < 0.0091). IV. DISCUSSION The proposed CLI algorithm was shown to accurately detect atrial activations from bipolar electrograms recorded during AF and provide CL estimations that more closely matched manually marked activations than fixed threshold or DF-based methods. The criteria for mean and median CL convergence of this algorithm provide detection criteria amidst the potentially very complex activation and morphology patterns of AF electrograms. Although this study evaluated the algorithm on electrograms in an offline setting, this automated algorithm is efficient enough to be used for real-time applications. A variety of methods have been previously proposed to detect activations from electrograms in the setting of AF. Holm et al. [14] used a process which incorporates a cubic spline interpolation of the activation wave and chooses the point that divides the interpolated wave to two equal parts as the activation time. However, these methods require manual threshold selection. Faes et al. [15] introduced an adaptive activation detection method which sets a threshold based on the amplitude of the last ten detected peaks with exponentially decreasing weights and a blanking period of 55 ms. This method was compared with manual activation markings with differences ranging from 2.6 to 20 ms depending on the complexity of the AF.
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Sensitivity and specificity of the measures were not reported. Lee et al. [16] evaluated a similar adaptive threshold algorithm from 20 000 electrograms recorded during a canine model of AF. They showed that CLs obtained by the algorithm had a correlation of 0.96 when compared with those obtained by manual marking. Although we have not directly compared the CLI with these other methods, we postulate that the CLI algorithm would have performance advantages for electrograms with highly variable electrogram amplitudes and longer durations, while the other adaptive threshold methods may have advantages with more variable CLs and shorter durations. We have attempted to use manually marked electrograms as the basis for the evaluation of the CLI detection algorithm and comparison with DF and the fixed threshold algorithms. The manual marking of AF electrograms is also not a straightforward process, as it requires sometimes subjective determinations of what is considered an activation. Electrograms during AF can have changing amplitudes and morphologies and can have very fractionated morphologies that make activation markings very difficult. Thus, we used the intersection set of markings from two independent reviewers that in theory would include the only activations with the highest confidence. The CLI algorithm had the lowest percentage of combined undersensed and oversensed activations when the intersection set of manual markings was used as the reference. Although the sensitivity and specificity of detecting atrial activations are important characteristics of the detection algorithm, the more critical evaluation criteria are the ability to robustly estimate CL. When manually marking AF electrograms, a human is able to see the recording in its entirety. The human eye can process signals to identify where activations are expected to occur based on the basic CL and thereby assign an activation to a low amplitude electrogram that may not be marked or detected by more rigid criteria. The iteration process of the CLI algorithm to detect activation until the mean and median CLs converge more closely mimics the human detection process, whereas fixed threshold methods do not use the contextual information when detecting deflections. Thus, the CLI algorithm provides a very robust measurement of AF CL. There are some limitations to the CLI technique. First, there is a requirement for clinical stability during the recording segment in order for the algorithm to take advantage of mean and median CL convergence. Therefore, errors may occur if attempting to use the technique during phases of rapid change in AF CL that may occur with drug or autonomic interventions. Second, the CLI algorithm works significantly better with longer segment lengths, although the CL measurements at the short lengths were still better than those obtain with DF or fixed thresholds. Segment lengths of 10 s or more appear to provide optimal activation detection and CL estimation. We show, however, that for a subset of recording with highly irregular CLs, discrepancy rates compared to manual marking were considerably higher than those with less variable CLs. It is expected that far-field ventricular complexes would remain an issue with the CLI algorithm, as they do with CLs estimated with DF and fixed threshold techniques. However, there are a variety of techniques that may be able to alleviate the effect of ventricular complexes.
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[17] Finally, it is not known whether the results of the CLI algorithm will provide more meaningful insights about AF mechanisms. This will need to be explored in future studies. V. CONCLUSION Mapping AF CLs for the understanding of AF pathophysiology requires a certain amount of precision of the measurements to detect the subtle differences that exist with regions, interventions, and between subjects. Obtaining precise measurements is complicated by the complex nature of AF electrograms. The CLI offers some improvement in this regard over other commonly used techniques and can be used in either offline or real-time settings. REFERENCES [1] M. Ha¨ıssaguerre, P. Sanders, M. Hocini, L. F. Hsu, D. C. Shah, C. Scav´ee, Y. Takahashi, M. Rotter, J. L. Pasqui´e, S. Garrigue, J. Cl´ementy, and P. Ja¨ıs, “Changes in atrial fibrillation cycle length and inducibility during catheter ablation and their relation to outcome,” Circulation, vol. 109, pp. 3007–3013, 2004. [2] P. Sanders, O. Berenfeld, M. Hocini, P. Ja¨ıs, R. Vaidyanathan, L. F. Hsu, S. Garrigue, Y. Takahashi, M. Rotter, F. Sacher, C. Scav´ee, R. PloutzSnyder, J. Jalife, and M. Ha¨ıssaguerre, “Spectral analysis identifies sites of high-frequency activity maintaining atrial fibrillation in humans,” Circulation, vol. 112, pp. 789–797, 2005. [3] J. Sahadevan, K. Ryu, L. Peltz, C. M. Khrestian, R. W. Stewart, A. H. Markowitz, and A. L. Waldo, “Epicardial mapping of chronic atrial fibrillation in patients: Preliminary observations,” Circulation, vol. 110, pp. 3293–3299, 2004. [4] S. R. Dibs, J. Ng, R. Arora, R. S. Passman, A. H. Kadish, and J. J. Goldberger, “Spatiotemporal characterization of atrial activation in persistent human atrial fibrillation: Multisite electrogram analysis and surface electrocardiographic correlations—A pilot study,” Heart Rhythm, vol. 5, pp. 686–693, 2008. [5] S. Lazar, S. Dixit, F. E. Marchlinski, D. J. Callans, and E. P. Gerstenfeld, “Presence of left-to-right atrial frequency gradient in paroxysmal but not persistent atrial fibrillation in humans,” Circulation, vol. 110, pp. 3181– 3186, 2004. [6] A. Michelucci, P. Bartolini, G. Calcagnini, F. Censi, A. Colella, S. Morelli, L. Padeletti, P. Pieragnoli, and V. Barbaro, “Mapping the organization of atrial fibrillation with basket catheters. Part II: Regional patterns in chronic patients,” Pacing Clin. Electrophysiol., vol. 24, pp. 1089–1096, 2001.
[7] D. Filgueiras-Rama, N. F. Price, R. P. Martins, M. Yamazaki, U. M. Avula, K. Kaur, J. Kalifa, S. R. Ennis, E. Hwang, V. Devabhaktuni, J. Jalife, and O. Berenfeld, “Long-term frequency gradients during persistent atrial fibrillation in sheep are associated with stable sources in the left atrium,” Circulation Arrhythm Electrophysiol., pp. 5:1160–1167, 2012. [8] R. Mandapati, A. Skanes, J. Chen, O. Berenfeld, and J. J. , “Stable microreentrant sources as a mechanism of atrial fibrillation in the isolated sheep heart,” Circulation, vol. 101, pp. 194–199, 2000. [9] J. Ng, A. H. Kadish, and J. J. Goldberger, “Effect of electrogram characteristics on the relationship of dominant frequency to atrial activation rate in atrial fibrillation,” Heart Rhythm, vol. 3, pp. 1295–1305, 2006. [10] J. Ng, A. H. Kadish, and J. J. Goldberger, “Technical considerations for dominant frequency analysis,” J. Cardiovascular Electrophysiol., vol. 18, pp. 757–764, 2007. [11] O. Berenfeld, S. Ennis, E. Hwang, B. Hooven, K. Grzeda, S. Mironov, M. Yamazaki, J. Kalifa, and J. Jalife, “Time- and frequency-domain analyses of atrial fibrillation activation rate: The optical mapping reference,” Heart Rhythm, vol. 8, pp. 1758–1765, 2011. [12] G. W. Botteron and J. M. Smith, “A technique for measurement of the extent of spatial organization of atrial activation during atrial fibrillation in the intact human heart,” IEEE Trans. Biomed. Eng., vol. 42, no. 6, pp. 579–586, Jun. 1995. [13] J. Slocum, A. Sahakian, and S. Swiryn, “Computer discrimination of atrial fibrillation and regular atrial rhythms from intra-atrial electrograms,” Pacing Clin. Electrophysiol., vol. 11, pp. 610–621, 1988. [14] M. Holm, R. Johansson, S. B. Olsson, J. Brandt, and C. L¨uhrs, “A new method for analysis of atrial activation during chronic atrial fibrillation in man,” IEEE Trans. Biomed. Eng., vol. 43, no. 2, pp. 198–210, Feb. 1996. [15] L. Faes, G. Nollo, R. Antolini, F. Gaita, and F. Ravelli, “A method for quantifying atrial fibrillation organization based on wave-morphology similarity,” IEEE Trans. Biomed. Eng., vol. 49, no. 12, pp. 1504–1513, Dec. 2002. [16] S. Lee, K. Ryu, A. L. Waldo, C. M. Khrestian, D. M. Durand, and J. Sahadevan, “An algorithm to measure beat-to-beat cycle lengths for assessment of atrial electrogram rate and regularity during atrial fibrillation,” J. Cardiovascular Electrophysiol., vol. 24, pp. 199–206, 2013. [17] J. J. Rieta and F. Hornero, “Comparative study of methods for ventricular activity cancellation in atrial electrograms of atrial fibrillation,” Physiol. Meas., vol. 28, pp. 925–936, 2007.
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