- Email: [email protected]
Non-invasive organization variation assessment in the onset and termination of paroxysmal atrial fibrillation
c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 9 3 ( 2 0 0 9 ) 148–154
journal homepage: www.intl.elsevierhealth.com/journals/cmpb
Non-invasive organization variation assessment in the onset and termination of paroxysmal atrial fibrillation Raúl Alcaraz a,∗ , José Joaquín Rieta b a b
Innovation in Bioengineering Research Group, University of Castilla-La Mancha, Spain Biomedical Synergy, Valencia University of Technology, Spain
a r t i c l e
i n f o
a b s t r a c t
Article history:
Atrial Fibrillation (AF) is the most common supraventricular tachyarrhythmia. Recently, it
Received 12 February 2008
has been suggested that AF is partially organized on its onset and termination, thus being
Received in revised form
more suitable for antiarrhythmia and to avoid unnecessary therapy. Although several inva-
28 May 2008
sive and non-invasive AF organization estimators have been proposed, the organization
Accepted 1 September 2008
time course in the first and last minutes of AF has not been quantified yet. The aim of this work is to study non-invasively the organization variation within the first and last minutes
Keywords:
of paroxysmal AF. The organization was evaluated making use of sample entropy, which
Organization time course
can robustly estimate electrical atrial activity organization from surface ECG recordings.
Electrocardiogram analysis
This work proves an organization decrease in the first minutes of AF onset and an increase
Paroxysmal atrial fibrillation
within the last minute before spontaneous AF termination. These results are in agreement
Sample entropy
with the conclusions reported by other authors who made use of invasive recordings. © 2008 Elsevier Ireland Ltd. All rights reserved.
1.
Introduction
Atrial Fibrillation (AF) is a common arrhythmia being a significant public health problem worldwide. It affects up to 1% of the general population and nearly 1 out of 10 people over 80 years [1], thus, AF prevalence increases with advancing age [2]. Data from the Framingham Heart Study show that AF is associated with a 1.5- to 1.9-fold higher risk of death, which may be due to thromboembolic stroke [3]. Moreover, this arrhythmia considerably reduces the patient’s quality of life [4]. During the first minutes following the onset of AF, profound changes occur in the atrial tissue, provoking a progressive alteration of its electrophysiological properties [5]. Concretely, several instants after the onset, a progressive variation in atrial refractory period, conduction velocity and ion concentrations is started. Changes in these electrophysiological parameters cause variations in the number of simultaneous
reentries wandering the atrial tissue [4] and, as a consequence, in the organization degree of the atrial activity (AA) [6]. Thus, a recent study from invasive recordings has reported a progressive AA organization deterioration within the first 3 min [7]. In addition, several invasive studies have also demonstrated a decrease in the number of reentries prior to AF termination, thus producing a more organized AA [8–10]. Although several indices have been proposed to quantify non-invasively the AA organization degree, their performances are far from being optimal [11,12]. Moreover, no indices have been applied yet to evaluate the time course of AA organization during paroxysmal (spontaneously terminated) AF episodes from surface ECG recordings, which can be easily and cheaply obtained and could avoid the risks associated to invasive procedures. From a clinical point of view, this temporal evaluation of AA organization is interesting because useful information about AF mechanisms could be obtained
∗ Corresponding author at: E. U. Politecnica de Cuenca, Campus Universitario, 16071 Cuenca, Spain. Tel.: +34 969 179 100x4847/4768; fax: +34 969 179 119. E-mail address: [email protected] (R. Alcaraz). 0169-2607/$ – see front matter © 2008 Elsevier Ireland Ltd. All rights reserved. doi:10.1016/j.cmpb.2008.09.001
c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 9 3 ( 2 0 0 9 ) 148–154
and, consequently, AF treatment could be improved. Thereby, the aim of this work is to evaluate the AA organization variation both within the first minutes after AF onset and the last minutes prior to its spontaneous termination, from the surface ECG. Sample entropy (SampEn), that is a non-linear index for quantifying time series regularity [13], is used to estimate this organization because it has been recently demonstrated that this index can robustly evaluate the organization of AA obtained from surface ECG recordings [14,15].
2.
Materials
In order to analyze the initial progressive deterioration of AA organization, 25 ECG recordings continuously registered during the first 5 min following paroxysmal AF onset were studied. On the other hand, to evaluate the increase of AA organization prior to AF termination, 20 ECGs registered 2 min before spontaneous AF termination were used. All signals were extracted from 24-h Holter recordings with two leads (II and V1) from 45 different patients and were available in Physionet [16]. They were digitized at 128 Hz with 16 bits/sample and 5 V resolution.
data [13]. It is defined as the negative natural logarithm of the conditional probability that two sequences of data values, that are similar for m points, will remain similar at the next point in the data set, within a tolerance r. Thus, it can be defined as SampEn(r,m) = −ln(A/B), where A and B are the total numbers of forward matches of length m + 1 and m, respectively [13]. No guidelines exist for the optimal selection of the parameters r and m, however, the most widely established parameters values are m = 1 and m = 2 and r between 0.1 and 0.25 times the standard deviation of the original time series {x(n)}, as suggested by Pincus [21]. Normalizing r in this manner gives to SampEn a translation and scale invariance, in the sense that it remains unchanged under uniform process magnification, reduction, or constant shift to higher or lower values [21]. These parameters produce a good statistical reproducibility in time series of length larger than 60 samples, as considered herein [22,23]. Because of in previous works, where SampEn was also applied to the main atrial wave (MAW), the best results were obtained with m = 2 and r = 0.25 times the standard deviation of the data [14,15], these m and r values were selected.
3.3.
3.
Methods
3.1.
Data preprocessing
The ECG recordings were preprocessed in order to improve later analysis. Firstly, baseline wander was removed making use of bidirectional high pass filtering with 0.5 Hz cut-off frequency [17]. Secondly, high frequency noise was reduced through an eight order IIR Chebyshev low pass bidirectional filtering, whose cut-off frequency was 70 Hz. Finally, powerline interference was removed through adaptive notch filtering, which preserves the ECG spectral information [18]. The recordings were upsampled to 1024 Hz. This preprocessing step was mainly useful in order to get a better alignment for QRST complex averaging and subtraction, which is necessary to extract the AA from surface ECGs [19], as will be described later in Section 3.3. Lead V1 was chosen for the analysis because previous works have shown that AF is dominant in this lead [20].
3.2.
Sample entropy as regularity estimator
The application of SampEn is justified for AF analysis because (i) the non-linearity, as necessary condition for a chaotic behavior, is present in the diseased heart with AF at cellular level and (ii) the electrical remodeling that takes place after AF onset is a far-from-linear process [5]. This phenomenon is described as the progressive shortening of effective atrial refractory periods, thus increasing the number of simultaneous reentries and, as a consequence, the perpetuation of AF [4]. Moreover, in previous works it has been shown that SampEn is a robust organization estimator of the AA obtained from surface ECG recordings [14,15]. SampEn examines time series for similar epochs and assigns a non-negative number to the sequence, with larger values corresponding to more complexity or irregularity in the
149
Organization variation assessment
Atrial activity analysis from the surface ECG is obstructed by the simultaneous presence of ventricular activity, which is of notably greater amplitude [20]. Whereby, cancellation of the QRS complex and the T wave (QRST) from the preprocessed ECG was firstly performed, such as Fig. 1 shows. Though a variety of QRST cancellation techniques exist, the average QRST template cancellation method was used, since only two leads were available [24]. Bearing in mind that the average beat cannot represent each individual beat accurately, since QRST morphology is affected by respiration, patient movement, etc., QRST residuals and noise are often present in the AA after ventricular cancellation [20], as can be appreciated in Fig. 1. These nuisance signals can degrade the AA organization estimation using non-linear regularity indexes and, consequently, unsuccessful results could be obtained. In fact, non-significative differences between terminating and non-terminating paroxysmal AF recordings were observed when SampEn was applied directly to the AA [11]. On the contrary, 93.33% of the same AF episodes were correctly classified after a proper conditioning of the atrial signal [14]. Hence, in order to reduce noise, ventricular residues and enhance the AA, the MAW, which can be considered as the fundamental atrial waveform, was analyzed. The MAW was obtained through selective filtering of the AA by tracking its dominant frequency, see Fig. 1. The dominant atrial frequency (DAF) was defined as the largest amplitude within the 3–9 Hz frequency range, that is the typical range of AA [19,25]. To obtain a robust tracking of this frequency, the AA power spectral density was computed. The Welch Periodogram was applied to non-overlapping AA segments of 10 s in length. A Hamming window of 2048 points in length, a 50% overlapping between adjacent windowed sections and a 4096-points Fast Fourier Transform (FFT) were used as computational parameters as suggested by previous works [26].
150
c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 9 3 ( 2 0 0 9 ) 148–154
Fig. 1 – Block diagram describing the strategy proposed to evaluate the AF organization variation assessment. Thin selective filter is applied to the atrial signal. The filter is tracking the dominant atrial frequency. Finally, SampEn is computed on the resulting signal.
Moreover, in order to prevent distortion, a linear phase FIR filter was used [27]. Chebyshev approximation was preferred because all the filter parameters can be suitably fitted and minimum ripple in the pass and stop bands was needed. Regarding the filter parameters, the bandwidth should be lower than 6 Hz because the typical AA frequency range is around 3–9 Hz [19,25], and a high order should be chosen to obtain such a selective filtering. Several bandwidth and order values were tested, but the best results were obtained with a 3-Hz bandwidth and 768 filter coefficients. Finally, the MAW organization was estimated in nonoverlapping segments of different time lengths through the application of SampEn, see Fig. 1. Overlapping between segments was discarded in order to not benefit the organization assessment, to obtain more consistent results and to increase the proposed strategy reliability. The best results were obtained by analyzing segments of 2 s in length and, hence, are reported in the next section. On the other hand, the DAF is a simple measure for AF characterization and, concretely, is directly related with atrial refractoriness. Subsequently, a lower DAF indicates a longer refractory period and, consequently, could reflect a more organized AF [19]. Thereby, the results obtained with the MAW organization analysis via SampEn were compared with those provided by the DAF analysis.
4.
Results
The Jarque–Bera test was applied to the samples and a test statistic value of 1.476 was obtained. This value corroborated that the data came from a normal distribution. Thereby, results are expressed as mean ± standard deviation and paired Student’s t-test was applied to the data in order to verify statistical differences. A two-tailed value of p < 0.05 was considered statistically significant.
The AA organization time course estimated over each ECG recording is presented in Figs. 2 and 3 for AF onset and AF termination, respectively. For easy visualization of all the analyzed recordings, the perspective representation has been preferred. As can be seen in Fig. 2a generalized organization decrease (SampEn increase) in the first 3 min after the onset takes place, specially within the first 40 s. On the other hand, a similar SampEn decrease (organization increase) can be observed in Fig. 3 for the last minute before AF termination. This common pattern can be easily assessed by plotting the averaged temporal evolution for all the patients, such as Fig. 4 shows. Finally, SampEn average values of the first 5 min after AF onset, computed in 1 min segments, are presented in Table 1. Note that the SampEn mean value after AF onset was progressively increasing from 0.0660 ± 0.0027 to 0.0703 ± 0.0016 (p < 0.00001). However, the largest variation (97.5%) took place within the first 180 s, since next, SampEn mean value was stabilized around 0.07 and non-significative differences between the fourth and fifth minute after AF onset were obtained (p = 0.3231). Regarding the last 2 min before AF termination, SampEn mean values during each minute were 0.0705 ± 0.0016 and 0.0679 ± 0.0025, respectively. Remark that non-significative differences between the fifth minute after AF onset and the last but 1 min before its termination were obtained (p = 0.1012). Moreover, SampEn values were progressively decreasing within the last 60 s, obtaining a notable statistical difference in comparison with the previous minute (p <0.001). On the other hand, Fig. 5 shows the averaged DAF temporal evolution for all the patients. The DAF mean values computed in non-overlapping segments of 1 min in length are presented in Table 2. As can been appreciated, the largest variation (95.75%) took place within the first 100 s, but nonstatistical differences between the first and second minutes were obtained (p = 0.2593). Regarding the 2 min prior to AF termination, the DAF mean value decreased in the last minute,
c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 9 3 ( 2 0 0 9 ) 148–154
151
Fig. 2 – Atrial activity organization time course of every analyzed ECG in the first 5 min after AF onset.
however, non-significative differences between both minutes were also reported (p = 0.4781).
5.
Discussion
This study has presented a quantitative and non-invasive analysis of the AA organization time course during the first and last minutes of paroxysmal AF. In previous works, other non-invasive methods were proposed to quantify AF organization [11,12], however, none of them presented an organization variation study. As a consequence, this work presents for the
first time the AA organization time course during the first and last minutes of paroxysmal AF patients and, in addition, from surface ECG recordings. The results obtained with the MAW organization analysis have demonstrated the existence of a certain AA organization degree in the first instants and a subsequent progressive organization deterioration within the first 3 min following the onset of AF. These findings are coincident with the conclusions obtained by Ravelli et al. [7], who performed a cycle length beat-to-beat analysis and computed atrial wave similarity making use of invasive recordings. The authors reported an AA organization decay within less than 3 min after AF
Fig. 3 – Atrial activity organization time course of every analyzed ECG in the last 2 min before AF termination.
152
c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 9 3 ( 2 0 0 9 ) 148–154
Fig. 4 – Atrial activity organization time course for all the analyzed recordings. (a) Average organization results for the first 5 min after AF onset. (b) Average results for the last 2 min before AF termination.
Table 1 – SampEn mean values during the first 5 min after AF onset computed in non-overlapping segments of 1 min in length Minute after AF onset
First
Second
Third
Fourth
Fifth
Mean value Standard deviation
0.0660 0.0027
0.0683 0.0025
0.0702 0.0020
0.0699 0.0020
0.0703 0.0016
onset. In addition, the presence of organized activity instances in AF onset is also consistent with the results reported by Israel et al. [28] and the progressive organization deterioration also agrees with other fibrillation observations reported by Huang et al. [29] and Konings et al. [30]. On the other hand, considering that it has been demonstrated that AF pacing success rate increased significantly in the presence of longer atrial cycles [31] and, consequently, higher levels of AF organization [28], the obtained results could be relevant in the treatment of AF by pacing techniques. Thus, these outcomes suggest that higher rates of success for the interruption of the arrhythmia could
Fig. 5 – The DAF time course for all the analyzed recordings. (a) Average DAF results for the first 5 min after AF onset. (b) Average results for the last 2 min before AF termination.
153
c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 9 3 ( 2 0 0 9 ) 148–154
Table 2 – DAF values during the first 5 min after AF onset and last 2 min prior to AF termination computed in non-overlapping segments of 1 min in length Minutes
Mean value (Hz) Standard deviation (Hz)
After AF onset First
Second
Third
Fourth
Fifth
4.720 0.557
4.940 0.785
4.942 0.883
4.967 0.821
4.943 0.815
be obtained through the early delivery of pacing, that is, when the episodes are more organized. Regarding AF termination, the MAW organization analysis showed a progressive AA organization increase during the last minute. In other studies, where AF termination was achieved by using different treatments, similar outcomes were reported. In this respect, Takahashi et al. [9] reported that a higher organization index of atrial electrograms is associated with termination of AF during limited ablation. In Hoekstra et al. [32] the non-linear analysis of unipolar epicardial electrograms revealed that cibenzoline produces an increases the atrial activation pattern global organization during pharmacological cardioversion. Regarding electrical cardioversion, invasive recordings analysis showed that the higher the level of AA organization, the higher the cardioversion success rates [6,33] and the lower the energy required for successful reversion to sinus rhythm [34]. On the other hand, considering that in previous works, where AA organization of persistent AF episodes was noninvasively evaluated by the application of SampEn to the MAW, higher SampEn mean values were obtained [14,15], it can be considered that paroxysmal AF presents a more organized AA than persistent AF [35]. Thus, this observation could be helpful for improving AF treatment, since useless therapeutic interventions in paroxysmal AF episodes could be avoided and the risk of AF patients could be minimized. Regarding the DAF analysis, the obtained results also showed a slight decrease and an increase in the refractory period within the first two and the last minute of the episode, respectively. However, non-significative differences between consecutive minutes were reported. Therefore, the AA organization evaluation obtained with the DAF analysis can be considered as poorer than the obtained with the MAW organization analysis. Consequently, SampEn could be considered as a suitable organization degree estimator of the AA obtained from surface ECG recordings. Finally, this study presents some limitations. Thus, the number of analyzed episodes was not very large and, therefore, the presented results must be considered with caution. A wider data set allowing a more rigorous statistical analysis should be required in order to provide confidence in the robustness of the MAW organization analysis. Moreover, the database should contain whole paroxysmal AF episodes in order to analyze accurately the AA organization time course within all the episode.
6.
Before AF termination
Conclusions
The present work has demonstrated for the first time that the organization variation within the first minutes after AF
Second 5.020 0.628
First 4.851 0.619
onset and last minutes before its spontaneous termination can be estimated from surface ECG recordings through the application of sample entropy to the main atrial wave. The reported findings are in agreement with invasive studies and, consequently, this non-linear regularity index can be considered as a reliable AA organization estimator from non-invasive recordings. Moreover, clinical relevant information related to the progressing nature of the arrhythmia can be extracted from the main atrial wave when the proper regularity estimators are used. Thus, an in depth analysis of this wave should improve the pathophysiological mechanisms understanding in the onset and termination of AF and may lead towards more effective therapies.
Acknowledgment This work was supported by the project TEC2007–64884 from the Spanish Ministry of Education and Science.
references
[1] W.B. Kannel, R.D. Abbott, D.D. Savage, P.M. McNamara, Epidemiologic features of chronic atrial fibrillation: the Framingham study, N. Engl. J. Med. 306 (17) (1982) 1018–1022. [2] C.D. Furberg, B.M. Psaty, T.A. Manolio, J.M. Gardin, V.E. Smith, P.M. Rautaharju, Prevalence of atrial fibrillation in elderly subjects (the Cardiovascular Health Study), Am. J. Cardiol. 74 (3) (1994) 236–241. [3] E.J. Benjamin, P.A. Wolf, R.B. D’Agostino, H. Silbershatz, W.B. Kannel, D. Levy, Impact of atrial fibrillation on the risk of death: the Framingham Heart Study, Circulation 98 (10) (1998) 946–952. [4] V. Fuster, L.E. Rydén, D.S. Cannom, H.J. Crijns, A.B. Curtis, K.A. Ellenbogen, et al., ACC/AHA/ESC 2006 guidelines for the management of patients with atrial fibrillation: a report of the American College of Cardiology/American Heart Association task force on practice guidelines and the European society of cardiology committee for practice guidelines (writing committee to revise the 2001 guidelines for the management of patients with atrial fibrillation): developed in collaboration with the European heart rhythm association and the heart rhythm society, Circulation 114 (7) (2006) e257–e354. [5] M. Allessie, J. Ausma, U. Schotten, Electrical, contractile and structural remodeling during atrial fibrillation, Cardiovasc. Res. 54 (2) (2002) 230–246. [6] H.J. Sih, D.P. Zipes, E.J. Berbari, J.E. Olgin, A high-temporal resolution algorithm for quantifying organization during atrial fibrillation, IEEE Trans. Biomed. Eng. 46 (4) (1999) 440–450. [7] F. Ravelli, M. Masé, M.D. Greco, L. Faes, M. Disertori, Deterioration of organization in the first minutes of atrial
154
[8] [9]
[10]
[11]
[12]
[13]
[14]
[15]
[16]
[17]
[18]
[19]
[20]
[21] [22]
c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 9 3 ( 2 0 0 9 ) 148–154
fibrillation: a beat-to-beat analysis of cycle length and wave similarity, J. Cardiovasc. Electrophysiol. 18 (1) (2007) 60–65. Z. Qu, J.N. Weiss, Dynamics and cardiac arrhythmias, J. Cardiovasc. Electrophysiol. 17 (9) (2006) 1042–1049. Y. Takahashi, P. Sanders, P. Jaïs, M. Hocini, R. Dubois, M. Rotter, et al., Organization of frequency spectra of atrial fibrillation: relevance to radiofrequency catheter ablation, J. Cardiovasc. Electrophysiol. 17 (4) (2006) 382–388. J. Kneller, J. Kalifa, R. Zou, A.V. Zaitsev, M. Warren, O. Berenfeld, E.J. Vigmond, L.J. Leon, S. Nattel, J. Jalife, Mechanisms of atrial fibrillation termination by pure sodium channel blockade in an ionically-realistic mathematical model, Circ. Res. 96 (5) (2005) e35–e47. F. Nilsson, M. Stridh, A. Bollmann, L. Sörnmo, Predicting spontaneous termination of atrial fibrillation using the surface ECG, Med. Eng. Phys. 28 (8) (2006) 802–808. F. Holmqvist, M. Stridh, J.E.P. Waktare, A. Roijer, L. Sörnmo, P.G. Platonov, C.J. Meurling, Atrial fibrillation signal organization predicts sinus rhythm maintenance in patients undergoing cardioversion of atrial fibrillation, Europace 8 (8) (2006) 559–565. J.S. Richman, J.R. Moorman, Physiological time series analysis using approximate entropy and sample entropy, Am. J. Physiol. 278 (6) (2000) H2039–H2049. R. Alcaraz, J.J. Rieta, Wavelet bidomain sample entropy analysis to predict spontaneous termination of atrial fibrillation, Physiol. Meas. 29 (1) (2008) 65–80. R. Alcaraz, J.J. Rieta, A non-invasive method to predict electrical cardioversion outcome of persistent atrial fibrillation, Med. Biol. Eng. Comput. 46 (7) (2008) 625–635. A.L. Goldberger, L.A. Amaral, L. Glass, J.M. Hausdorff, P.C. Ivanov, R.G. Mark, J.E. Mietus, G.B. Moody, C.K. Peng, H.E. Stanley, Physiobank, Physiotoolkit, and Physionet: components of a new research resource for complex physiologic signals, Circulation 101 (23) (2000) e215–e220. I. Dotsinsky, T. Stoyanov, Optimization of bi-directional digital filtering for drift suppression in electrocardiogram signals, J. Med. Eng. Technol. 28 (4) (2004) 178–180. M. Ferdjallah, R.E. Barr, Adaptive digital notch filter design on the unit-circle for the removal of powerline noise from biomedical signals, IEEE Trans. Biomed. Eng. 42 (6) (1994) 529–536. A. Bollmann, D. Husser, L. Mainardi, F. Lombardi, P. Langley, A. Murray, J.J. Rieta, J. Millet, S.B. Olsson, M. Stridh, L. Sörnmo, Analysis of surface electrocardiograms in atrial fibrillation: techniques, research, and clinical applications, Europace 8 (11) (2006) 911–926. S. Petrutiu, G.M. Nijm, H.A. Angari, S. Swiryn, A.V. Sahakian, Atrial fibrillation and waveform characterization—A time domain perspective in the surface ECG, IEEE Eng. Med. Biol. Mag. 25 (6) (2006) 24–30. S.M. Pincus, Assessing serial irregularity and its implications for health, Ann. N. Y. Acad. Sci. 954 (2001) 245–267. S.M. Pincus, Approximate entropy as a measure of system complexity, Proc. Natl. Acad. Sci. U.S.A. 88 (6) (1991) 2297–2301.
[23] S.M. Pincus, D.L. Keefe, Quantification of hormone pulsatility via an approximate entropy algorithm, Am. J. Physiol. 262 (5 Pt 1) (1992) E741–E754. [24] J. Slocum, A. Sahakian, S. Swiryn, Diagnosis of atrial fibrillation from surface electrocardiograms based on computer-detected atrial activity, J. Electrocardiol. 25 (1) (1992) 1–8. [25] M. Stridh, L. Sörnmo, C.J. Meurling, S.B. Olsson, Characterization of atrial fibrillation using the surface ECG: time-dependent spectral properties, IEEE Trans. Biomed. Eng. 48 (1) (2001) 19–27. [26] J.J. Rieta, F. Castells, C. Sánchez, V. Zarzoso, J. Millet, Atrial activity extraction for atrial fibrillation analysis using blind source separation, IEEE Trans. Biomed. Eng. 51 (7) (2004) 1176–1186. [27] L. Sörnmo, P. Laguna, Bioelectrical Signal Processing in Cardiac and Neurological Applications, Elsevier Academic Press, 2005. [28] C.W. Israel, J.R. Ehrlich, G. Grönefeld, A. Klesius, T. Lawo, B. Lemke, S.H. Hohnloser, Prevalence, characteristics and clinical implications of regular atrial tachyarrhythmias in patients with atrial fibrillation: insights from a study using a new implantable device, J. Am. Coll. Cardiol. 38 (2) (2001) 355–363. [29] J. Huang, J.M. Rogers, C.R. Killingsworth, K.P. Singh, W.M. Smith, R.E. Ideker, Evolution of activation patterns during long-duration ventricular fibrillation in dogs, Am. J. Physiol. Heart Circ. Physiol. 286 (3) (2004) H1193–H1200. [30] K.T. Konings, J.L. Smeets, O.C. Penn, H.J. Wellens, M.A. Allessie, Configuration of unipolar atrial electrograms during electrically induced atrial fibrillation in humans, Circulation 95 (5) (1997) 1231–1241. [31] R. Ricci, C. Pignalberi, M. Disertori, A. Capucci, L. Padeletti, G. Botto, S. Toscano, F. Miraglia, A. Grammatico, M. Santini, Efficacy of a dual chamber defibrillator with atrial antitachycardia functions in treating spontaneous atrial tachyarrhythmias in patients with life-threatening ventricular tachyarrhythmias, Eur. Heart J. 23 (18) (2002) 1471–1479. [32] B.P.T. Hoekstra, C.G.H. Diks, M.A. Allessie, J. DeGoede, Nonlinear analysis of the pharmacological conversion of sustained atrial fibrillation in conscious goats by the class Ic drug cibenzoline, Chaos 7 (3) (1997) 430–446. [33] T.H. Everett, L.C. Kok, R.H. Vaughn, J.R. Moorman, D.E. Haines, Frequency domain algorithm for quantifying atrial fibrillation organization to increase defibrillation efficacy, IEEE Trans. Biomed. Eng. 48 (9) (2001) 969–978. [34] G. Calcagnini, F. Censi, A. Michelucci, P. Bartolini, Descriptors of wavefront propagation. Endocardial mapping of atrial fibrillation with basket catheter, IEEE Eng. Med. Biol. Mag. 25 (6) (2006) 71–78. [35] S. Weber, G. Ndrepepa, M. Schneider, I. Deisenhofer, B. Zrenner, C. Schmitt, Electrophysiological differences of the spontaneous onset of paroxysmal and persistent atrial fibrillation, Pacing Clin. Electrophysiol. 30 (3) (2007) 295–303.
journal homepage: www.intl.elsevierhealth.com/journals/cmpb
Non-invasive organization variation assessment in the onset and termination of paroxysmal atrial fibrillation Raúl Alcaraz a,∗ , José Joaquín Rieta b a b
Innovation in Bioengineering Research Group, University of Castilla-La Mancha, Spain Biomedical Synergy, Valencia University of Technology, Spain
a r t i c l e
i n f o
a b s t r a c t
Article history:
Atrial Fibrillation (AF) is the most common supraventricular tachyarrhythmia. Recently, it
Received 12 February 2008
has been suggested that AF is partially organized on its onset and termination, thus being
Received in revised form
more suitable for antiarrhythmia and to avoid unnecessary therapy. Although several inva-
28 May 2008
sive and non-invasive AF organization estimators have been proposed, the organization
Accepted 1 September 2008
time course in the first and last minutes of AF has not been quantified yet. The aim of this work is to study non-invasively the organization variation within the first and last minutes
Keywords:
of paroxysmal AF. The organization was evaluated making use of sample entropy, which
Organization time course
can robustly estimate electrical atrial activity organization from surface ECG recordings.
Electrocardiogram analysis
This work proves an organization decrease in the first minutes of AF onset and an increase
Paroxysmal atrial fibrillation
within the last minute before spontaneous AF termination. These results are in agreement
Sample entropy
with the conclusions reported by other authors who made use of invasive recordings. © 2008 Elsevier Ireland Ltd. All rights reserved.
1.
Introduction
Atrial Fibrillation (AF) is a common arrhythmia being a significant public health problem worldwide. It affects up to 1% of the general population and nearly 1 out of 10 people over 80 years [1], thus, AF prevalence increases with advancing age [2]. Data from the Framingham Heart Study show that AF is associated with a 1.5- to 1.9-fold higher risk of death, which may be due to thromboembolic stroke [3]. Moreover, this arrhythmia considerably reduces the patient’s quality of life [4]. During the first minutes following the onset of AF, profound changes occur in the atrial tissue, provoking a progressive alteration of its electrophysiological properties [5]. Concretely, several instants after the onset, a progressive variation in atrial refractory period, conduction velocity and ion concentrations is started. Changes in these electrophysiological parameters cause variations in the number of simultaneous
reentries wandering the atrial tissue [4] and, as a consequence, in the organization degree of the atrial activity (AA) [6]. Thus, a recent study from invasive recordings has reported a progressive AA organization deterioration within the first 3 min [7]. In addition, several invasive studies have also demonstrated a decrease in the number of reentries prior to AF termination, thus producing a more organized AA [8–10]. Although several indices have been proposed to quantify non-invasively the AA organization degree, their performances are far from being optimal [11,12]. Moreover, no indices have been applied yet to evaluate the time course of AA organization during paroxysmal (spontaneously terminated) AF episodes from surface ECG recordings, which can be easily and cheaply obtained and could avoid the risks associated to invasive procedures. From a clinical point of view, this temporal evaluation of AA organization is interesting because useful information about AF mechanisms could be obtained
∗ Corresponding author at: E. U. Politecnica de Cuenca, Campus Universitario, 16071 Cuenca, Spain. Tel.: +34 969 179 100x4847/4768; fax: +34 969 179 119. E-mail address: [email protected] (R. Alcaraz). 0169-2607/$ – see front matter © 2008 Elsevier Ireland Ltd. All rights reserved. doi:10.1016/j.cmpb.2008.09.001
c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 9 3 ( 2 0 0 9 ) 148–154
and, consequently, AF treatment could be improved. Thereby, the aim of this work is to evaluate the AA organization variation both within the first minutes after AF onset and the last minutes prior to its spontaneous termination, from the surface ECG. Sample entropy (SampEn), that is a non-linear index for quantifying time series regularity [13], is used to estimate this organization because it has been recently demonstrated that this index can robustly evaluate the organization of AA obtained from surface ECG recordings [14,15].
2.
Materials
In order to analyze the initial progressive deterioration of AA organization, 25 ECG recordings continuously registered during the first 5 min following paroxysmal AF onset were studied. On the other hand, to evaluate the increase of AA organization prior to AF termination, 20 ECGs registered 2 min before spontaneous AF termination were used. All signals were extracted from 24-h Holter recordings with two leads (II and V1) from 45 different patients and were available in Physionet [16]. They were digitized at 128 Hz with 16 bits/sample and 5 V resolution.
data [13]. It is defined as the negative natural logarithm of the conditional probability that two sequences of data values, that are similar for m points, will remain similar at the next point in the data set, within a tolerance r. Thus, it can be defined as SampEn(r,m) = −ln(A/B), where A and B are the total numbers of forward matches of length m + 1 and m, respectively [13]. No guidelines exist for the optimal selection of the parameters r and m, however, the most widely established parameters values are m = 1 and m = 2 and r between 0.1 and 0.25 times the standard deviation of the original time series {x(n)}, as suggested by Pincus [21]. Normalizing r in this manner gives to SampEn a translation and scale invariance, in the sense that it remains unchanged under uniform process magnification, reduction, or constant shift to higher or lower values [21]. These parameters produce a good statistical reproducibility in time series of length larger than 60 samples, as considered herein [22,23]. Because of in previous works, where SampEn was also applied to the main atrial wave (MAW), the best results were obtained with m = 2 and r = 0.25 times the standard deviation of the data [14,15], these m and r values were selected.
3.3.
3.
Methods
3.1.
Data preprocessing
The ECG recordings were preprocessed in order to improve later analysis. Firstly, baseline wander was removed making use of bidirectional high pass filtering with 0.5 Hz cut-off frequency [17]. Secondly, high frequency noise was reduced through an eight order IIR Chebyshev low pass bidirectional filtering, whose cut-off frequency was 70 Hz. Finally, powerline interference was removed through adaptive notch filtering, which preserves the ECG spectral information [18]. The recordings were upsampled to 1024 Hz. This preprocessing step was mainly useful in order to get a better alignment for QRST complex averaging and subtraction, which is necessary to extract the AA from surface ECGs [19], as will be described later in Section 3.3. Lead V1 was chosen for the analysis because previous works have shown that AF is dominant in this lead [20].
3.2.
Sample entropy as regularity estimator
The application of SampEn is justified for AF analysis because (i) the non-linearity, as necessary condition for a chaotic behavior, is present in the diseased heart with AF at cellular level and (ii) the electrical remodeling that takes place after AF onset is a far-from-linear process [5]. This phenomenon is described as the progressive shortening of effective atrial refractory periods, thus increasing the number of simultaneous reentries and, as a consequence, the perpetuation of AF [4]. Moreover, in previous works it has been shown that SampEn is a robust organization estimator of the AA obtained from surface ECG recordings [14,15]. SampEn examines time series for similar epochs and assigns a non-negative number to the sequence, with larger values corresponding to more complexity or irregularity in the
149
Organization variation assessment
Atrial activity analysis from the surface ECG is obstructed by the simultaneous presence of ventricular activity, which is of notably greater amplitude [20]. Whereby, cancellation of the QRS complex and the T wave (QRST) from the preprocessed ECG was firstly performed, such as Fig. 1 shows. Though a variety of QRST cancellation techniques exist, the average QRST template cancellation method was used, since only two leads were available [24]. Bearing in mind that the average beat cannot represent each individual beat accurately, since QRST morphology is affected by respiration, patient movement, etc., QRST residuals and noise are often present in the AA after ventricular cancellation [20], as can be appreciated in Fig. 1. These nuisance signals can degrade the AA organization estimation using non-linear regularity indexes and, consequently, unsuccessful results could be obtained. In fact, non-significative differences between terminating and non-terminating paroxysmal AF recordings were observed when SampEn was applied directly to the AA [11]. On the contrary, 93.33% of the same AF episodes were correctly classified after a proper conditioning of the atrial signal [14]. Hence, in order to reduce noise, ventricular residues and enhance the AA, the MAW, which can be considered as the fundamental atrial waveform, was analyzed. The MAW was obtained through selective filtering of the AA by tracking its dominant frequency, see Fig. 1. The dominant atrial frequency (DAF) was defined as the largest amplitude within the 3–9 Hz frequency range, that is the typical range of AA [19,25]. To obtain a robust tracking of this frequency, the AA power spectral density was computed. The Welch Periodogram was applied to non-overlapping AA segments of 10 s in length. A Hamming window of 2048 points in length, a 50% overlapping between adjacent windowed sections and a 4096-points Fast Fourier Transform (FFT) were used as computational parameters as suggested by previous works [26].
150
c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 9 3 ( 2 0 0 9 ) 148–154
Fig. 1 – Block diagram describing the strategy proposed to evaluate the AF organization variation assessment. Thin selective filter is applied to the atrial signal. The filter is tracking the dominant atrial frequency. Finally, SampEn is computed on the resulting signal.
Moreover, in order to prevent distortion, a linear phase FIR filter was used [27]. Chebyshev approximation was preferred because all the filter parameters can be suitably fitted and minimum ripple in the pass and stop bands was needed. Regarding the filter parameters, the bandwidth should be lower than 6 Hz because the typical AA frequency range is around 3–9 Hz [19,25], and a high order should be chosen to obtain such a selective filtering. Several bandwidth and order values were tested, but the best results were obtained with a 3-Hz bandwidth and 768 filter coefficients. Finally, the MAW organization was estimated in nonoverlapping segments of different time lengths through the application of SampEn, see Fig. 1. Overlapping between segments was discarded in order to not benefit the organization assessment, to obtain more consistent results and to increase the proposed strategy reliability. The best results were obtained by analyzing segments of 2 s in length and, hence, are reported in the next section. On the other hand, the DAF is a simple measure for AF characterization and, concretely, is directly related with atrial refractoriness. Subsequently, a lower DAF indicates a longer refractory period and, consequently, could reflect a more organized AF [19]. Thereby, the results obtained with the MAW organization analysis via SampEn were compared with those provided by the DAF analysis.
4.
Results
The Jarque–Bera test was applied to the samples and a test statistic value of 1.476 was obtained. This value corroborated that the data came from a normal distribution. Thereby, results are expressed as mean ± standard deviation and paired Student’s t-test was applied to the data in order to verify statistical differences. A two-tailed value of p < 0.05 was considered statistically significant.
The AA organization time course estimated over each ECG recording is presented in Figs. 2 and 3 for AF onset and AF termination, respectively. For easy visualization of all the analyzed recordings, the perspective representation has been preferred. As can be seen in Fig. 2a generalized organization decrease (SampEn increase) in the first 3 min after the onset takes place, specially within the first 40 s. On the other hand, a similar SampEn decrease (organization increase) can be observed in Fig. 3 for the last minute before AF termination. This common pattern can be easily assessed by plotting the averaged temporal evolution for all the patients, such as Fig. 4 shows. Finally, SampEn average values of the first 5 min after AF onset, computed in 1 min segments, are presented in Table 1. Note that the SampEn mean value after AF onset was progressively increasing from 0.0660 ± 0.0027 to 0.0703 ± 0.0016 (p < 0.00001). However, the largest variation (97.5%) took place within the first 180 s, since next, SampEn mean value was stabilized around 0.07 and non-significative differences between the fourth and fifth minute after AF onset were obtained (p = 0.3231). Regarding the last 2 min before AF termination, SampEn mean values during each minute were 0.0705 ± 0.0016 and 0.0679 ± 0.0025, respectively. Remark that non-significative differences between the fifth minute after AF onset and the last but 1 min before its termination were obtained (p = 0.1012). Moreover, SampEn values were progressively decreasing within the last 60 s, obtaining a notable statistical difference in comparison with the previous minute (p <0.001). On the other hand, Fig. 5 shows the averaged DAF temporal evolution for all the patients. The DAF mean values computed in non-overlapping segments of 1 min in length are presented in Table 2. As can been appreciated, the largest variation (95.75%) took place within the first 100 s, but nonstatistical differences between the first and second minutes were obtained (p = 0.2593). Regarding the 2 min prior to AF termination, the DAF mean value decreased in the last minute,
c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 9 3 ( 2 0 0 9 ) 148–154
151
Fig. 2 – Atrial activity organization time course of every analyzed ECG in the first 5 min after AF onset.
however, non-significative differences between both minutes were also reported (p = 0.4781).
5.
Discussion
This study has presented a quantitative and non-invasive analysis of the AA organization time course during the first and last minutes of paroxysmal AF. In previous works, other non-invasive methods were proposed to quantify AF organization [11,12], however, none of them presented an organization variation study. As a consequence, this work presents for the
first time the AA organization time course during the first and last minutes of paroxysmal AF patients and, in addition, from surface ECG recordings. The results obtained with the MAW organization analysis have demonstrated the existence of a certain AA organization degree in the first instants and a subsequent progressive organization deterioration within the first 3 min following the onset of AF. These findings are coincident with the conclusions obtained by Ravelli et al. [7], who performed a cycle length beat-to-beat analysis and computed atrial wave similarity making use of invasive recordings. The authors reported an AA organization decay within less than 3 min after AF
Fig. 3 – Atrial activity organization time course of every analyzed ECG in the last 2 min before AF termination.
152
c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 9 3 ( 2 0 0 9 ) 148–154
Fig. 4 – Atrial activity organization time course for all the analyzed recordings. (a) Average organization results for the first 5 min after AF onset. (b) Average results for the last 2 min before AF termination.
Table 1 – SampEn mean values during the first 5 min after AF onset computed in non-overlapping segments of 1 min in length Minute after AF onset
First
Second
Third
Fourth
Fifth
Mean value Standard deviation
0.0660 0.0027
0.0683 0.0025
0.0702 0.0020
0.0699 0.0020
0.0703 0.0016
onset. In addition, the presence of organized activity instances in AF onset is also consistent with the results reported by Israel et al. [28] and the progressive organization deterioration also agrees with other fibrillation observations reported by Huang et al. [29] and Konings et al. [30]. On the other hand, considering that it has been demonstrated that AF pacing success rate increased significantly in the presence of longer atrial cycles [31] and, consequently, higher levels of AF organization [28], the obtained results could be relevant in the treatment of AF by pacing techniques. Thus, these outcomes suggest that higher rates of success for the interruption of the arrhythmia could
Fig. 5 – The DAF time course for all the analyzed recordings. (a) Average DAF results for the first 5 min after AF onset. (b) Average results for the last 2 min before AF termination.
153
c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 9 3 ( 2 0 0 9 ) 148–154
Table 2 – DAF values during the first 5 min after AF onset and last 2 min prior to AF termination computed in non-overlapping segments of 1 min in length Minutes
Mean value (Hz) Standard deviation (Hz)
After AF onset First
Second
Third
Fourth
Fifth
4.720 0.557
4.940 0.785
4.942 0.883
4.967 0.821
4.943 0.815
be obtained through the early delivery of pacing, that is, when the episodes are more organized. Regarding AF termination, the MAW organization analysis showed a progressive AA organization increase during the last minute. In other studies, where AF termination was achieved by using different treatments, similar outcomes were reported. In this respect, Takahashi et al. [9] reported that a higher organization index of atrial electrograms is associated with termination of AF during limited ablation. In Hoekstra et al. [32] the non-linear analysis of unipolar epicardial electrograms revealed that cibenzoline produces an increases the atrial activation pattern global organization during pharmacological cardioversion. Regarding electrical cardioversion, invasive recordings analysis showed that the higher the level of AA organization, the higher the cardioversion success rates [6,33] and the lower the energy required for successful reversion to sinus rhythm [34]. On the other hand, considering that in previous works, where AA organization of persistent AF episodes was noninvasively evaluated by the application of SampEn to the MAW, higher SampEn mean values were obtained [14,15], it can be considered that paroxysmal AF presents a more organized AA than persistent AF [35]. Thus, this observation could be helpful for improving AF treatment, since useless therapeutic interventions in paroxysmal AF episodes could be avoided and the risk of AF patients could be minimized. Regarding the DAF analysis, the obtained results also showed a slight decrease and an increase in the refractory period within the first two and the last minute of the episode, respectively. However, non-significative differences between consecutive minutes were reported. Therefore, the AA organization evaluation obtained with the DAF analysis can be considered as poorer than the obtained with the MAW organization analysis. Consequently, SampEn could be considered as a suitable organization degree estimator of the AA obtained from surface ECG recordings. Finally, this study presents some limitations. Thus, the number of analyzed episodes was not very large and, therefore, the presented results must be considered with caution. A wider data set allowing a more rigorous statistical analysis should be required in order to provide confidence in the robustness of the MAW organization analysis. Moreover, the database should contain whole paroxysmal AF episodes in order to analyze accurately the AA organization time course within all the episode.
6.
Before AF termination
Conclusions
The present work has demonstrated for the first time that the organization variation within the first minutes after AF
Second 5.020 0.628
First 4.851 0.619
onset and last minutes before its spontaneous termination can be estimated from surface ECG recordings through the application of sample entropy to the main atrial wave. The reported findings are in agreement with invasive studies and, consequently, this non-linear regularity index can be considered as a reliable AA organization estimator from non-invasive recordings. Moreover, clinical relevant information related to the progressing nature of the arrhythmia can be extracted from the main atrial wave when the proper regularity estimators are used. Thus, an in depth analysis of this wave should improve the pathophysiological mechanisms understanding in the onset and termination of AF and may lead towards more effective therapies.
Acknowledgment This work was supported by the project TEC2007–64884 from the Spanish Ministry of Education and Science.
references
[1] W.B. Kannel, R.D. Abbott, D.D. Savage, P.M. McNamara, Epidemiologic features of chronic atrial fibrillation: the Framingham study, N. Engl. J. Med. 306 (17) (1982) 1018–1022. [2] C.D. Furberg, B.M. Psaty, T.A. Manolio, J.M. Gardin, V.E. Smith, P.M. Rautaharju, Prevalence of atrial fibrillation in elderly subjects (the Cardiovascular Health Study), Am. J. Cardiol. 74 (3) (1994) 236–241. [3] E.J. Benjamin, P.A. Wolf, R.B. D’Agostino, H. Silbershatz, W.B. Kannel, D. Levy, Impact of atrial fibrillation on the risk of death: the Framingham Heart Study, Circulation 98 (10) (1998) 946–952. [4] V. Fuster, L.E. Rydén, D.S. Cannom, H.J. Crijns, A.B. Curtis, K.A. Ellenbogen, et al., ACC/AHA/ESC 2006 guidelines for the management of patients with atrial fibrillation: a report of the American College of Cardiology/American Heart Association task force on practice guidelines and the European society of cardiology committee for practice guidelines (writing committee to revise the 2001 guidelines for the management of patients with atrial fibrillation): developed in collaboration with the European heart rhythm association and the heart rhythm society, Circulation 114 (7) (2006) e257–e354. [5] M. Allessie, J. Ausma, U. Schotten, Electrical, contractile and structural remodeling during atrial fibrillation, Cardiovasc. Res. 54 (2) (2002) 230–246. [6] H.J. Sih, D.P. Zipes, E.J. Berbari, J.E. Olgin, A high-temporal resolution algorithm for quantifying organization during atrial fibrillation, IEEE Trans. Biomed. Eng. 46 (4) (1999) 440–450. [7] F. Ravelli, M. Masé, M.D. Greco, L. Faes, M. Disertori, Deterioration of organization in the first minutes of atrial
154
[8] [9]
[10]
[11]
[12]
[13]
[14]
[15]
[16]
[17]
[18]
[19]
[20]
[21] [22]
c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 9 3 ( 2 0 0 9 ) 148–154
fibrillation: a beat-to-beat analysis of cycle length and wave similarity, J. Cardiovasc. Electrophysiol. 18 (1) (2007) 60–65. Z. Qu, J.N. Weiss, Dynamics and cardiac arrhythmias, J. Cardiovasc. Electrophysiol. 17 (9) (2006) 1042–1049. Y. Takahashi, P. Sanders, P. Jaïs, M. Hocini, R. Dubois, M. Rotter, et al., Organization of frequency spectra of atrial fibrillation: relevance to radiofrequency catheter ablation, J. Cardiovasc. Electrophysiol. 17 (4) (2006) 382–388. J. Kneller, J. Kalifa, R. Zou, A.V. Zaitsev, M. Warren, O. Berenfeld, E.J. Vigmond, L.J. Leon, S. Nattel, J. Jalife, Mechanisms of atrial fibrillation termination by pure sodium channel blockade in an ionically-realistic mathematical model, Circ. Res. 96 (5) (2005) e35–e47. F. Nilsson, M. Stridh, A. Bollmann, L. Sörnmo, Predicting spontaneous termination of atrial fibrillation using the surface ECG, Med. Eng. Phys. 28 (8) (2006) 802–808. F. Holmqvist, M. Stridh, J.E.P. Waktare, A. Roijer, L. Sörnmo, P.G. Platonov, C.J. Meurling, Atrial fibrillation signal organization predicts sinus rhythm maintenance in patients undergoing cardioversion of atrial fibrillation, Europace 8 (8) (2006) 559–565. J.S. Richman, J.R. Moorman, Physiological time series analysis using approximate entropy and sample entropy, Am. J. Physiol. 278 (6) (2000) H2039–H2049. R. Alcaraz, J.J. Rieta, Wavelet bidomain sample entropy analysis to predict spontaneous termination of atrial fibrillation, Physiol. Meas. 29 (1) (2008) 65–80. R. Alcaraz, J.J. Rieta, A non-invasive method to predict electrical cardioversion outcome of persistent atrial fibrillation, Med. Biol. Eng. Comput. 46 (7) (2008) 625–635. A.L. Goldberger, L.A. Amaral, L. Glass, J.M. Hausdorff, P.C. Ivanov, R.G. Mark, J.E. Mietus, G.B. Moody, C.K. Peng, H.E. Stanley, Physiobank, Physiotoolkit, and Physionet: components of a new research resource for complex physiologic signals, Circulation 101 (23) (2000) e215–e220. I. Dotsinsky, T. Stoyanov, Optimization of bi-directional digital filtering for drift suppression in electrocardiogram signals, J. Med. Eng. Technol. 28 (4) (2004) 178–180. M. Ferdjallah, R.E. Barr, Adaptive digital notch filter design on the unit-circle for the removal of powerline noise from biomedical signals, IEEE Trans. Biomed. Eng. 42 (6) (1994) 529–536. A. Bollmann, D. Husser, L. Mainardi, F. Lombardi, P. Langley, A. Murray, J.J. Rieta, J. Millet, S.B. Olsson, M. Stridh, L. Sörnmo, Analysis of surface electrocardiograms in atrial fibrillation: techniques, research, and clinical applications, Europace 8 (11) (2006) 911–926. S. Petrutiu, G.M. Nijm, H.A. Angari, S. Swiryn, A.V. Sahakian, Atrial fibrillation and waveform characterization—A time domain perspective in the surface ECG, IEEE Eng. Med. Biol. Mag. 25 (6) (2006) 24–30. S.M. Pincus, Assessing serial irregularity and its implications for health, Ann. N. Y. Acad. Sci. 954 (2001) 245–267. S.M. Pincus, Approximate entropy as a measure of system complexity, Proc. Natl. Acad. Sci. U.S.A. 88 (6) (1991) 2297–2301.
[23] S.M. Pincus, D.L. Keefe, Quantification of hormone pulsatility via an approximate entropy algorithm, Am. J. Physiol. 262 (5 Pt 1) (1992) E741–E754. [24] J. Slocum, A. Sahakian, S. Swiryn, Diagnosis of atrial fibrillation from surface electrocardiograms based on computer-detected atrial activity, J. Electrocardiol. 25 (1) (1992) 1–8. [25] M. Stridh, L. Sörnmo, C.J. Meurling, S.B. Olsson, Characterization of atrial fibrillation using the surface ECG: time-dependent spectral properties, IEEE Trans. Biomed. Eng. 48 (1) (2001) 19–27. [26] J.J. Rieta, F. Castells, C. Sánchez, V. Zarzoso, J. Millet, Atrial activity extraction for atrial fibrillation analysis using blind source separation, IEEE Trans. Biomed. Eng. 51 (7) (2004) 1176–1186. [27] L. Sörnmo, P. Laguna, Bioelectrical Signal Processing in Cardiac and Neurological Applications, Elsevier Academic Press, 2005. [28] C.W. Israel, J.R. Ehrlich, G. Grönefeld, A. Klesius, T. Lawo, B. Lemke, S.H. Hohnloser, Prevalence, characteristics and clinical implications of regular atrial tachyarrhythmias in patients with atrial fibrillation: insights from a study using a new implantable device, J. Am. Coll. Cardiol. 38 (2) (2001) 355–363. [29] J. Huang, J.M. Rogers, C.R. Killingsworth, K.P. Singh, W.M. Smith, R.E. Ideker, Evolution of activation patterns during long-duration ventricular fibrillation in dogs, Am. J. Physiol. Heart Circ. Physiol. 286 (3) (2004) H1193–H1200. [30] K.T. Konings, J.L. Smeets, O.C. Penn, H.J. Wellens, M.A. Allessie, Configuration of unipolar atrial electrograms during electrically induced atrial fibrillation in humans, Circulation 95 (5) (1997) 1231–1241. [31] R. Ricci, C. Pignalberi, M. Disertori, A. Capucci, L. Padeletti, G. Botto, S. Toscano, F. Miraglia, A. Grammatico, M. Santini, Efficacy of a dual chamber defibrillator with atrial antitachycardia functions in treating spontaneous atrial tachyarrhythmias in patients with life-threatening ventricular tachyarrhythmias, Eur. Heart J. 23 (18) (2002) 1471–1479. [32] B.P.T. Hoekstra, C.G.H. Diks, M.A. Allessie, J. DeGoede, Nonlinear analysis of the pharmacological conversion of sustained atrial fibrillation in conscious goats by the class Ic drug cibenzoline, Chaos 7 (3) (1997) 430–446. [33] T.H. Everett, L.C. Kok, R.H. Vaughn, J.R. Moorman, D.E. Haines, Frequency domain algorithm for quantifying atrial fibrillation organization to increase defibrillation efficacy, IEEE Trans. Biomed. Eng. 48 (9) (2001) 969–978. [34] G. Calcagnini, F. Censi, A. Michelucci, P. Bartolini, Descriptors of wavefront propagation. Endocardial mapping of atrial fibrillation with basket catheter, IEEE Eng. Med. Biol. Mag. 25 (6) (2006) 71–78. [35] S. Weber, G. Ndrepepa, M. Schneider, I. Deisenhofer, B. Zrenner, C. Schmitt, Electrophysiological differences of the spontaneous onset of paroxysmal and persistent atrial fibrillation, Pacing Clin. Electrophysiol. 30 (3) (2007) 295–303.