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Entrainment of the natural pacemakers of the heart precedes atrial fibrillation
Computers in Biology and Medicine 36 (2006) 1204 – 1215 www.intl.elsevierhealth.com/journals/cobm
Entrainment of the natural pacemakers of the heart precedes atrial fibrillation Russell J. Fischer∗ Woodland Research Institute, 17 Woodland Rd, Bernardsville, NJ 07924, USA Received 9 February 2005; accepted 27 May 2005
Abstract A new measure of heart rate variability is proposed to investigate the interaction of the sino-atrial (SA) and atrioventricular (AV) pacemakers. Using electrocardiogram (ECG) fiduciary markers corresponding to the depolarization time of the SA and AV pacemakers, the variability of SA and AV depolarization rate is jointly analyzed by spectral analysis. The result of this joint analysis provides evidence of a distinct pattern of interaction between the SA and AV nodes prior to the onset of paroxysmal atrial fibrillation (PAF): frequency entrainment between the primary and secondary pacemakers of the heart, occurring at the respiratory frequency. We propose a measure of this entrainment as a diagnostic indicator for PAF, and compare it to standard diagnostic measures. The entrainment measure is found to have greater diagnostic power than five other common ECG-derived measures. 䉷 2005 Elsevier Ltd. All rights reserved. Keywords: Atrial fibrillation; Heart rate variability; Entrainment; Spectral analysis; Wavelet analysis; Singularity analysis
1. Introduction The normal human heartbeat is generated by the sino-atrial (SA) node pacemaker in the heart, but a continuously varying barrage of traffic from the sympathetic and parasympathetic nervous systems modulates its frequency. The resulting heart rate at any point in time is largely the net effect of these two systems; as a consequence, normal heart rate is not constant, varying even when the human body is at rest. ∗ Tel.: +1 908 337 3570.
E-mail address: russfi[email protected]. 0010-4825/$ - see front matter 䉷 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.compbiomed.2005.05.006
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The modulation of heart rate can be investigated noninvasively via heart rate variability (HRV) analysis, and this measurement has proven to be valuable in many clinical situations [1]. The analysis begins with the detection of a fiducial point in each cycle of the electrocardiogram (ECG). The reciprocal of the time difference between successive fiducial points is then used as an estimate of the time-varying heart rate. The R wave of the ECG is the fiducial point conventionally chosen to mark each cardiac cycle [2]; it typically has the largest magnitude, and is thus more easily detected and used as the basis of a rate measurement. The R wave is not the only ECG feature that may be used to derive a measure of heart rate. To understand the physiologic basis of the various ECG features and their connection to the cardiac cycle, it is useful to briefly review the process of cardiac electrical conduction. The electrical depolarization that triggers the heartbeat originates in the SA node, the primary pacemaker of the heart. It then spreads through the atria, stimulating them to contract. This yields a P wave on the ECG. The wave of depolarization then passes through the atrio-ventricular (AV) node, where its conduction speed is reduced to ensure that ventricular contraction does not begin before atrial contraction has ended. On the ECG, this corresponds to a brief pause following the P wave. The depolarization then proceeds rapidly through the bundle of His, the left and right branches and the Purkinje network, stimulating the ventricles to contract. This produces a feature called the QRS complex—normally the largest feature in the ECG—whose peak is the R wave. Ideally, the dynamics of the primary SA pacemaker would be characterized from a rate signal derived from the P wave. This is because the P wave is the closest temporal and physiologic correlate to SA depolarization in the ECG. The P wave is relatively low in magnitude however, and the R wave is typically used as proxy. It is then reasonable to ask whether a rate signal derived from the P wave is equivalent to one derived from the R wave. Under normal physiologic conditions there is a one-to-one correspondence between SA and AV depolarization, and either rate signal would yield the same value of mean heart rate. It is not clear, however, that the time-varying modulation of SA and AV depolarization frequency is the same, and thus it is possible that HRV analysis applied to the P wave and R wave rate signals will yield different results. Studies suggest that the SA and AV nodes have distinct paths of innervation from the vagus nerve [3] and that the SA and AV nodes may be independently modulated by the parasympathetic nervous system [4]; clearly it is possible that the rate signals associated with each node might show distinct patterns of modulation. In this research we propose a new approach to the analysis of heart rate variability called atrio-ventricular rate variability (AVRV) analysis, designed to characterize the interaction of the SA and AV pacemakers via a joint analysis of the P wave and R wave rate variability. This measure may be viewed as complementary to conventional HRV analysis in the following sense. Conventional HRV analysis (which is based on a rate signal derived from the R wave alone) is used to investigate extrinsic influences on the heart and its rate, such as the autonomic nervous system and respiration. The focus of AVRV analysis is to investigate intrinsic differences in the modulation of SA and AV depolarization rates. We apply the AVRV measure to the problem of noninvasive detection of the acute onset of paroxysmal atrial fibrillation (PAF). PAF is a short, self-terminating episode of atrial fibrillation (AF) that often precedes the onset of more sustained AF [5]. We were motivated to study AF because it represents a pathology for which there is a clear departure from normal SA pacing behavior. During an episode of AF, the ventricular rate is no longer under physiological control of the SA node, but instead is determined by interaction between the atrial rate and the filtering function of the AV node [6]. We hypothesized that if AF represents a departure from normal interaction of the SA and AV pacemakers, a joint analysis of the P and R wave rate variability signals might reveal early indication of impending AF.
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There is a clear clinical need for techniques to noninvasively predict AF—AF affects approximately 6% of the US population over the age of 65, and the prevalence is expected to rise as the population ages [5]. Currently, no reliable noninvasive markers predicting the onset of AF have been identified, although a number of ECG-derived markers have been investigated [7–9]. An accurate prediction of the acute onset of AF affords the possibility of early intervention via electrical atrial pacing to stabilize the heart and prevent the onset of fibrillation.
2. Methods In the AVRV approach, the occurrence time of the P wave is a proxy for the time of the SA node firing. Detection of the P wave is challenging from a signal processing perspective, however. The ECG is a non-stationary signal frequently contaminated by noise, artifacts and baseline drift. To detect the P wave we must not only overcome these signal impairments, but also the added challenge of detecting a relatively small feature in close proximity to the strong QRS complex. Fortunately, recent research exploring use of the wavelet transform as a tool for singularity detection simplifies this task [10]. The wavelet transform provides a multiscale expansion of a signal over a set of basis functions that are well localized in both the time and frequency domains. In this expansion, singularities of a signal are evident as local maxima/minima pairs that chain across scales of the wavelet transform. By treating the P, R, and T waves of the ECG as signal singularities, they may be detected by their distinct time and frequency characteristics. To illustrate, Fig. 1(A) depicts a short ECG segment and its wavelet transform. The P wave, R wave, and T wave singularities are seen as vertical maxima/minima bands in the “scale space” provided by the transform. These multiscale characteristics are then used in a detection process [11]. Only maxima/minima bands that persist across multiple wavelet scales are considered true singularities; signal noise and artifacts generally have less persistence across scale. Consider Fig. 1(B), the same data segment with an added baseline drift. In the corresponding wavelet transform, the distinction between baseline drift and an ECG singularity is apparent—the drift does not create a distinct maxima/minima band in the WT, and its energy is largely at lower frequencies. Noise contamination of the same data (in this example, Gaussian white noise) can be isolated in a similar manner by recognizing that it acts only at the higher frequencies of the transform and does not generate multi-scale maxima/minima bands (Fig. 1(C)). A singularity detection algorithm was implemented to identify the peaks of the P and R waves by their multiscale characteristics, in accordance with a previously described procedure [11]. We proceed by detecting the R waves in the ECG record first. R waves are selected by using three selection criteria for the maxima/minima chains: the length of the chain across scale, the relative magnitude of the maxima/minima in the chain, and the local regularity of the signal. These criteria are then thresholded to select the R wave. After the R wave has been detected, we determine the R wave occurrence time as the zero-crossing of the maxima/minima pair on scale 1, the wavelet scale with the highest time resolution. The accuracy of detection of the R wave occurrence time was approximately 0.18%. Once the locations of the R waves have been determined, we search for P waves, confining our search in two ways to improve the detection accuracy. First, we restrict our search to ECG sub-segments where the P wave is most likely to occur. Second, in these sub-segments, we search for a maxima/minima pair on the wavelet scale for which the P wave is most pronounced; this was empirically determined to be scale 4 for all subjects. The size of the sub-segment to be searched and its position relative to the R wave
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Fig. 1. Detection of ECG singularities with the wavelet transform. (A) Singularities associated with the P, R and T waves of the ECG are apparent as vertical bands corresponding to maxima/minima of the wavelet transform. (B) A baseline shift of the ECG is only apparent on the lower-frequency scales of the wavelet transform. (C) Noise contamination of the ECG (SNR = 10 dB) does not impede wavelet detection of the ECG singularities, as the noise only affects the higher-frequency scales.
are parameters that are empirically determined for each subject and fixed for the analysis of the ECG record. We took a number of measures to minimize the impact of common signal impairments such as ectopy, signal dropouts and amplifier saturation. These impairments were addressed prior to singularity analysis by visually reviewing each ECG record and noting the start and end times of impaired ECG segments. These segments were then removed from the record, and subsequent data time-shifted back to maintain a contiguous sequence. Singularity analysis was then performed on the edited ECG records to produce pairs of P and R wave occurrence times for each successive heartbeat. Artifacts may still be present in the record of P and R wave occurrence times due to undetected P waves and stray ectopic beats. The remaining ectopic beats were identified by comparing each P and R interbeat interval to a moving
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average of the previous interbeat values. When an ectopic beat occurs, both interbeat intervals will exceed a threshold value. Undetected P waves are easily found by referring to the R wave occurrence times: if two successive R waves are found without an intermediate P wave, the corresponding R wave is noted. When either type of defect was found, the occurrence times for that heartbeat were removed from the record, and the subsequent occurrence times were time-shifted back. Instantaneous rate signals for the P and R waves were then calculated as the inverse of the respective interbeat periods. Spectral analysis of the P and R wave variability signals was performed by Thomson’s multitaper method. The multitaper method is a nonparametric spectral analysis technique that provides spectral estimates with less variance than conventional techniques (e.g. Blackman–Tukey) and demonstrates superior mean squared error performance for the calculation of spectra with power-law behavior [12]. Adaptive weights were used for the multitaper analysis with a time-bandwidth product of 16. The length of the data record used for spectral analysis was approximately 1024 beats, varying slightly from case to case due to the artifact removal process. The sampling rate assumed in the spectral analysis was the reciprocal of the mean heart rate. The data used in this study were drawn from a set of public-domain ECG recordings of paroxysmal atrial fibrillation from the PhysioNet database (http://www.physionet.org/physiobank/database/afpdb/) [13]. The recordings consist of pairs of 30-min ECG segments, each pair drawn from a single 24-h recording. One record of the pair serves as a control, extracted at least 45 min distant from any episode of PAF. The other record of the pair ends just before the onset of PAF. There are 25 record pairs in the PhysioNet PAF database; we analyzed 21 of these record pairs, excluding four pairs due to poor signal quality.
3. Results Discernible changes to the P and R wave variability spectra were evident for many of the cases at the onset of PAF, as illustrated in Fig. 2. In this figure, the power spectral density (PSD) is shown for 3 of the 21 subjects (A,B,C, arranged row-wise). In the left panel the PSDs for the P and R wave variability signals are shown for the control period, at least 45 min prior to the episode of PAF. In the center panel the PSDs of the P and R variability signals are shown for the ECG segment immediately preceding the PAF episode. Comparing the control and PAF onset spectra, a strong, mutual harmonic component characterizes the P and R wave spectra at the onset of PAF. In many cases this mutual harmonic component was also observed in the control case; however, it typically increased in magnitude at the onset of PAF. This harmonic component is likely the respiratory sinus arrhythmia (RSA), a normal arrhythmia that occurs due to the influence of breathing on the vagal (parasympathetic) outflow to the sinoatrial node. We say this strong spectral component is “likely” the RSA because the breathing frequency was not recorded or controlled during these data recordings, so we cannot be certain that this spectral peak occurs at the breathing frequency. However, this component does occur in the frequency range typical of the RSA, 0.15–0.5 Hz. The RSA is often present in normal HRV; however, it is seldom as pronounced as it appears in the PAF onset data. Fig. 3 shows typical P and R wave variability spectra from normal subjects for reference. Contrasting the spectra for the normal data with that at PAF onset, we observed a pronounced entrainment of the P and R wave variability spectra at PAF onset at the RSA frequency. We use the term “entrainment”
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Fig. 2. Frequency entrainment of the P and R wave variability signals as paroxysmal atrial fibrillation approaches for three subjects. The plots for each subject (A, B, C) are arranged rowwise as follows: left column, the P and R wave variability power spectral densities (PSDs) under control conditions (at least 45 min distant from the PAF episode); center column, the P and R wave variability PSDs at PAF onset; right column the corresponding cross-spectral densities. For the PSD plots, the solid line is the spectra for the P wave variability signal and the dashed line is the spectra of the R wave variability signal. The records shown are from the Physionet PAF database, records p01, p43 and p25, respectively.
in the sense of Pikovsky et al. [14]: a coincidence of frequencies. However, this phenomenon is more than a coincidence of spectral content at the RSA frequency; it appears to be an equivalence of spectral power at this frequency at the onset of PAF. We propose that a useful diagnostic indication of the impending onset of PAF might be obtained by devising a measure to characterize the entrainment of the P and R wave variability spectra at the RSA frequency. A simple measure investigated here is the normalized cross spectrum [15]: CPR (f ) =
SP∗ (f )SR (f ) 1 (SPT (f )SR (f )) 2
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where SP (f ) and SR (f ) are the spectral density of the P and R wave variability signals, respectively, and * denotes the complex conjugate. The degree of entrainment was characterized by measuring the amplitude of the largest peak in the cross spectrum in the HF range (0.15–0.5 Hz). This value is then used
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Fig. 3. Spectral characteristics of the P and R wave variability signals for three typical normal subjects. The plots for each subject (A, B, C) are arranged rowwise, with the P and R wave variability power spectral densities (PSDs) for a given subject in the left column and the associated cross-spectral density plot in the right column. For the PSD plots, the solid line is the spectra for the P wave variability signal and the dashed line is the spectra of the R wave variability signal.
as the measure of AVRV entrainment. The right-most panels in Fig. 2 show the cross spectra for three subjects at PAF onset; strong peaks are present in the HF frequency range. Using the described procedure, P and R wave rate variability signals were calculated for the 21 subjects in this study, and PSD analysis applied to the variability signals. The AVRV entrainment measure was then calculated between the P and R wave rate variability spectra for the control and PAF onset data sets. An increase in AVRV entrainment was observed for 17 out of the 21 subjects (Fig. 4). 4. Discussion In this research, we have proposed a measure of the entrainment of the P and R wave variability signals as a diagnostic measure for the acute onset of PAF. To investigate the usefulness of such a measure, it is important to consider two issues: (1) the diagnostic power of the measure relative to other ECG-derived measures, (2) whether the measure provides an independent indication of the onset of PAF, or if it is somehow linked to previously described measures derived from the ECG.
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Fig. 4. A graphic representation of the change in cross-spectral peak height (relative to the control data) for the P and R wave variability signals at the onset of PAF. Each line segment represents a single subject in the study, terminated by a left endpoint corresponding to the cross-spectral peak height in the HF range at least 45 min from the episode of PAF, and a right endpoint corresponding to the cross-spectral peak height at the onset of PAF.
With this in mind, we compared a number of common ECG-derived diagnostic measures to the AVRV entrainment measure. Our approach was to compare the measures based on their performance as diagnostic tests for the acute onset of PAF using receiver operating characteristic (ROC) curves. The ROC curve is a plot of the true positive rate of a diagnostic test against the false positive rate as the discrimination threshold is swept. It requires no assumptions about the statistical nature of the data. The area under the ROC curve serves as a well-established index of diagnostic accuracy [16]; a value of 0.5 is equivalent to diagnostic assignment by chance whereas the maximum value (1.0) corresponds to perfect diagnostic assignment. Comparing the ROC curve for the AVRV entrainment measure to the other ECG-derived measures allows us to quantitatively assess the diagnostic power of the measures. We examined five ECG-derived diagnostic measures and compared their performance to the AVRV entrainment measure using ROC curves. The measures can be categorized as follows: measures of (1) sympathetic/parasympathetic balance, (2) dromotropic (conduction velocity) alteration, and (3) conventional measures of heart rate variability. 4.1. Sympathetic/parasympathetic balance The relationship between sympathetic and parasympathetic modulation of heart rate is often characterized from HRV with a measure called the LF/HF ratio [17]. The LF/HF measure is calculated as the ratio of total spectral power in the LF band (0.04–0.15 Hz) to the HF band (0.15–0.5 Hz). The LF/HF ratio for the 21 subjects in this study in both control and PAF onset conditions are listed in Table 1, calculated
Table 1 Standard measures of heart rate variability compared to the AVRV entrainment measure (shaded cells are the value of the measure at the onset of PAF, unshaded cells are the value of the measure for the control condition, 45 min distant from the episode of PAF)
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Fig. 5. Receiver operating characteristic (ROC) curves comparing the AVRV entrainment measure to the median P–R interval, median absolute deviation of P–R interval, SDNN, LF/HF, and DFA for prediction of an episode of PAF.
from the R wave variability data. In the table, the column of shaded cells are the values of the measure at the onset of PAF, while the unshaded cells are the values for the control condition, 45 min distant from the episode of PAF. The diagnostic power of the LF/HF measure as a predictor of PAF was then assessed and compared to the AVRV entrainment measure by ROC analysis (Fig. 5). The area under the ROC curve was 0.66 (95% CI: 0.46–0.83) for the AVRV entrainment measure and 0.43 (95% CI: 0.25–0.63) for the LF/HF measure. One conclusion we draw from this result is that the AVRV entrainment measure has greater diagnostic power for prediction of the acute onset of PAF. This result may also indicate that the phenomenon that forms the basis for the AVRV entrainment measure—entrainment of the P and R wave variability signals at the respiratory frequency—is not simply some consequence of an alteration to cardiac autonomic balance. 4.2. Dromotropic measures A dromotropic effect is one that affects conduction velocity. The inter-nodal conduction time is the interval between the onset of atrial depolarization and the onset of ventricular depolarization, and can be estimated from the ECG as the time interval between the P and R waves. AVRV analysis marks the occurrence time of the P and R waves; from these occurrence times, the P–R interval was calculated. We are interested in both the central tendency and dispersion of this measure and how it compares to the AVRV entrainment measure. The central value is of interest because decreased atrial conduction velocity is known to promote the initiation of atrial fibrillation [18]. The dispersion of the P–R interval is also of interest because to some extent it also characterizes the entrainment of the P and R wave variability spectra. Certainly for one extreme—P–R intervals with no beat-to-beat dispersion—we would expect complete spectral entrainment at all frequencies because the R wave would always occur a fixed time after the P wave.
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The values of the measures are listed in Table 1. The P–R interval times were prolonged (greater than 0.20 s) for 3 of the 21 subjects. We note that in a study of 125 subjects who developed sustained AFIB, approximately 38% had a P–R interval of 0.21 s or greater [19]. It is difficult to compare our results directly to this study, however, because (1) the number of subjects in the present study is relatively small, and (2) subjects in the present study had episodes of PAF, not sustained AF. The ROC curves comparing the AVRV entrainment measure to the dromotropic measures are shown in Fig. 5. We used the median and median absolute deviation to characterize the central tendency and dispersion of the P–R interval in an outlier-resistant manner. The median P–R interval was not effective as a diagnostic indicator (area under the ROC curve of 0.52 (95% CI: 0.32–0.71)), nor was the P–R dispersion measure (area under the ROC curve of 0.40 (95% CI: 0.23–0.60)).
4.3. Conventional HRV measures Heart rate variability measures are commonly used in the clinic and have been proposed as predictors of PAF. In one study, a measure of HRV achieved a 76% rate for detection of the onset of PAF [20]. We investigated two measures, one a common measure called SDNN, defined as the standard deviation of the time interval between normal R waves [1]. We also used a measure derived from a technique called detrended fluctuation analysis (DFA) [21]. For this technique, the root-mean-square fluctuation of an integrated and detrended version of the R–R interval time series is measured at a sequence of window sizes. The logarithmic relationship between the RMS fluctuation measurement and the window size is then characterized by linear regression. The slope of this linear relationship is used as an HRV measure. Neither measure was effective as a diagnostic indicator of PAF. The area under the ROC curve was 0.51 for the SDNN measure (95% CI: 0.33–0.70) and 0.50 for the DFA measure (95% CI: 0.31–0.68).
5. Conclusion We believe the results of this study have two important implications: (1) there is evidence of a distinct pattern of interaction between the SA and AV nodes prior to the onset of PAF: entrainment of the SA and AV rate variability at the frequency of respiration, (2) this interaction may be observed and characterized noninvasively using the ECG and may form the basis of a useful diagnostic indication of the impending onset of PAF. With regard to point 1 above, we hope the findings of this study will inspire further research to investigate the dynamics of cardiac pacemaker interaction and its role in the mechanism of arrhythmiogenesis. With regard to point 2, we found the diagnostic performance of the AVRV entrainment measure to be superior to all other measures used in this study, although the diagnostic performance was far from ideal. However, we note that the control records used in this study (ECG recordings made at least 45 min distant from the onset of PAF) contained evidence of SA/AV entrainment for a majority of the cases. In other words, the characteristic AVRV entrainment that we have observed in this study often develops earlier than 45 min prior to the onset of PAF. We anticipate that a better diagnostic result would likely be obtained in a study using normal subjects as control.
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Acknowledgements We are especially grateful to the creators of the PhysioNet database for the generosity they have shown in creating the public-domain physiological database used for this study. References [1] P.K. Stein, R.E. Kleiger, Insights from the study of heart rate variability, Annu. Rev. Med. 50 (1999) 249. [2] Task Force of the European Society of Cardiology and the North American Society of Pacing and Electrophysiology. Heart rate variability—standards of measurement, physiological interpretation, and clinical use, Circulation 93 (1996) 1043. [3] M.F. O’Toole, J.L. Ardell, W.C. Randall, Functional interdependence of discrete vagal projections to SA and AV nodes, Am. J. Physiol. Heart Circ. Physiol. 251 (1986) H398. [4] R. Shouldice, et al., PR and PP ECG intervals as indicators of autonomic nervous innervation of the cardiac sinoatrial and atrioventricular nodes, Proceedings of the First IEEE EMBS Conference on Neural Engineering, 2003. [5] S. McClennen, et al., Predicting Onset of Atrial Fibrillation (http://www.physionet.org/physiobank/database/ afpdb/paf.shtml). [6] S. Nattel, New ideas about atrial fibrillation 50 years on, Nature 415 (2002) 219. [7] P.E. Dilaveris, et al., Simple electrocardiographic markers for the prediction of paroxysmal idiopathic atrial fibrillation, Am. Heart J. 135 (1998) 733. [8] N. Ishimoto, M. Ito, M. Kinoshita, Signal-averaged P-wave abnormalities and atrial size in patients with and without idiopathic paroxysmal atrial fibrillation, Am. Heart J. 139 (2000) 684. [9] S. Vikman, et al., Altered complexity and correlation properties of R–R interval dynamics before the spontaneous onset of paroxysmal atrial fibrillation, Circulation 100 (1999) 2079. [10] S. Mallat, W.L. Hwang, Singularity detection and processing with wavelets, IEEE Trans. Inform. Theory 38 (1992) 617. [11] C. Li, Ch. Zheng, Ch. Tai, Detection of ECG characteristic points using wavelet transforms, IEEE Trans. Biomed. Eng. 42 (1995) 21. [12] E.J. McCoy, A.T. Walden, D.B. Percival, Multitaper spectral estimation of power law processes, IEEE Trans. Signal Process. 46 (1998) 655. [13] A.L. Goldberger, et al., PhysioBank, physiotoolkit, and physionet: components of a new research resource for complex physiologic signals, Circulation 101 (2000) e215. [14] A. Pikovsky, M. Rosenblum, J. Kurths, Synchronization: A Universal Concept in Nonlinear Sciences, Cambridge University Press, Cambridge, 2001. [15] J.S. Bendat, A.G. Piersol, Random Data: Analysis and Measurement Procedures, second ed., Wiley, New York, NY, 1990. [16] J.A. Swets, Measuring the accuracy of diagnostic systems, Science 240 (4857) (1988) 1285. [17] A. Malliani, et al., Physiology and clinical implications of variability of cardiovascular parameters with focus on heart rate and blood pressure, Am. J. Cardiol. 73 (1991) 3C. [18] American College of Cardiology/American Heart Association Task Force on Practice Guidelines and the European Society of Cardiology Committee for Practice Guidelines and Policy Conferences. ACC/AHA/ESC guidelines for the management of patients with atrial fibrillation, Eur. Heart J. 22 (2001) 1852. [19] B. Lown, Electrical reversion of cardiac arrhythmias, Brit. Heart J. 29 (4) (1967) 469. [20] C. Maier, M. Bauch, H. Dickhaus, Recognition and quantification of paroxysmal atrial fibrillation by analysis of heart rate variability parameters, Computers in Cardiology 2001, vol. 28, IEEE Press, New York, 2001, p. 129. [21] C.K. Peng, S. Havlin, H.E. Stanley, A.L. Goldberger, Quantification of scaling exponents and crossover phenomena in nonstationary heartbeat time series, Chaos 5 (1995) 82. Russell J. Fischer is a biomedical engineer with over 15 years experience in the research and development of medical devices, working for companies such as Datex-Ohmeda, Bellcore and Sarnoff Labs. He currently directs independent research in the areas of biomedical signal processing, and is developing a number of medical monitoring and diagnostic systems for corporate healthcare clients.
Entrainment of the natural pacemakers of the heart precedes atrial fibrillation Russell J. Fischer∗ Woodland Research Institute, 17 Woodland Rd, Bernardsville, NJ 07924, USA Received 9 February 2005; accepted 27 May 2005
Abstract A new measure of heart rate variability is proposed to investigate the interaction of the sino-atrial (SA) and atrioventricular (AV) pacemakers. Using electrocardiogram (ECG) fiduciary markers corresponding to the depolarization time of the SA and AV pacemakers, the variability of SA and AV depolarization rate is jointly analyzed by spectral analysis. The result of this joint analysis provides evidence of a distinct pattern of interaction between the SA and AV nodes prior to the onset of paroxysmal atrial fibrillation (PAF): frequency entrainment between the primary and secondary pacemakers of the heart, occurring at the respiratory frequency. We propose a measure of this entrainment as a diagnostic indicator for PAF, and compare it to standard diagnostic measures. The entrainment measure is found to have greater diagnostic power than five other common ECG-derived measures. 䉷 2005 Elsevier Ltd. All rights reserved. Keywords: Atrial fibrillation; Heart rate variability; Entrainment; Spectral analysis; Wavelet analysis; Singularity analysis
1. Introduction The normal human heartbeat is generated by the sino-atrial (SA) node pacemaker in the heart, but a continuously varying barrage of traffic from the sympathetic and parasympathetic nervous systems modulates its frequency. The resulting heart rate at any point in time is largely the net effect of these two systems; as a consequence, normal heart rate is not constant, varying even when the human body is at rest. ∗ Tel.: +1 908 337 3570.
E-mail address: russfi[email protected]. 0010-4825/$ - see front matter 䉷 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.compbiomed.2005.05.006
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The modulation of heart rate can be investigated noninvasively via heart rate variability (HRV) analysis, and this measurement has proven to be valuable in many clinical situations [1]. The analysis begins with the detection of a fiducial point in each cycle of the electrocardiogram (ECG). The reciprocal of the time difference between successive fiducial points is then used as an estimate of the time-varying heart rate. The R wave of the ECG is the fiducial point conventionally chosen to mark each cardiac cycle [2]; it typically has the largest magnitude, and is thus more easily detected and used as the basis of a rate measurement. The R wave is not the only ECG feature that may be used to derive a measure of heart rate. To understand the physiologic basis of the various ECG features and their connection to the cardiac cycle, it is useful to briefly review the process of cardiac electrical conduction. The electrical depolarization that triggers the heartbeat originates in the SA node, the primary pacemaker of the heart. It then spreads through the atria, stimulating them to contract. This yields a P wave on the ECG. The wave of depolarization then passes through the atrio-ventricular (AV) node, where its conduction speed is reduced to ensure that ventricular contraction does not begin before atrial contraction has ended. On the ECG, this corresponds to a brief pause following the P wave. The depolarization then proceeds rapidly through the bundle of His, the left and right branches and the Purkinje network, stimulating the ventricles to contract. This produces a feature called the QRS complex—normally the largest feature in the ECG—whose peak is the R wave. Ideally, the dynamics of the primary SA pacemaker would be characterized from a rate signal derived from the P wave. This is because the P wave is the closest temporal and physiologic correlate to SA depolarization in the ECG. The P wave is relatively low in magnitude however, and the R wave is typically used as proxy. It is then reasonable to ask whether a rate signal derived from the P wave is equivalent to one derived from the R wave. Under normal physiologic conditions there is a one-to-one correspondence between SA and AV depolarization, and either rate signal would yield the same value of mean heart rate. It is not clear, however, that the time-varying modulation of SA and AV depolarization frequency is the same, and thus it is possible that HRV analysis applied to the P wave and R wave rate signals will yield different results. Studies suggest that the SA and AV nodes have distinct paths of innervation from the vagus nerve [3] and that the SA and AV nodes may be independently modulated by the parasympathetic nervous system [4]; clearly it is possible that the rate signals associated with each node might show distinct patterns of modulation. In this research we propose a new approach to the analysis of heart rate variability called atrio-ventricular rate variability (AVRV) analysis, designed to characterize the interaction of the SA and AV pacemakers via a joint analysis of the P wave and R wave rate variability. This measure may be viewed as complementary to conventional HRV analysis in the following sense. Conventional HRV analysis (which is based on a rate signal derived from the R wave alone) is used to investigate extrinsic influences on the heart and its rate, such as the autonomic nervous system and respiration. The focus of AVRV analysis is to investigate intrinsic differences in the modulation of SA and AV depolarization rates. We apply the AVRV measure to the problem of noninvasive detection of the acute onset of paroxysmal atrial fibrillation (PAF). PAF is a short, self-terminating episode of atrial fibrillation (AF) that often precedes the onset of more sustained AF [5]. We were motivated to study AF because it represents a pathology for which there is a clear departure from normal SA pacing behavior. During an episode of AF, the ventricular rate is no longer under physiological control of the SA node, but instead is determined by interaction between the atrial rate and the filtering function of the AV node [6]. We hypothesized that if AF represents a departure from normal interaction of the SA and AV pacemakers, a joint analysis of the P and R wave rate variability signals might reveal early indication of impending AF.
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There is a clear clinical need for techniques to noninvasively predict AF—AF affects approximately 6% of the US population over the age of 65, and the prevalence is expected to rise as the population ages [5]. Currently, no reliable noninvasive markers predicting the onset of AF have been identified, although a number of ECG-derived markers have been investigated [7–9]. An accurate prediction of the acute onset of AF affords the possibility of early intervention via electrical atrial pacing to stabilize the heart and prevent the onset of fibrillation.
2. Methods In the AVRV approach, the occurrence time of the P wave is a proxy for the time of the SA node firing. Detection of the P wave is challenging from a signal processing perspective, however. The ECG is a non-stationary signal frequently contaminated by noise, artifacts and baseline drift. To detect the P wave we must not only overcome these signal impairments, but also the added challenge of detecting a relatively small feature in close proximity to the strong QRS complex. Fortunately, recent research exploring use of the wavelet transform as a tool for singularity detection simplifies this task [10]. The wavelet transform provides a multiscale expansion of a signal over a set of basis functions that are well localized in both the time and frequency domains. In this expansion, singularities of a signal are evident as local maxima/minima pairs that chain across scales of the wavelet transform. By treating the P, R, and T waves of the ECG as signal singularities, they may be detected by their distinct time and frequency characteristics. To illustrate, Fig. 1(A) depicts a short ECG segment and its wavelet transform. The P wave, R wave, and T wave singularities are seen as vertical maxima/minima bands in the “scale space” provided by the transform. These multiscale characteristics are then used in a detection process [11]. Only maxima/minima bands that persist across multiple wavelet scales are considered true singularities; signal noise and artifacts generally have less persistence across scale. Consider Fig. 1(B), the same data segment with an added baseline drift. In the corresponding wavelet transform, the distinction between baseline drift and an ECG singularity is apparent—the drift does not create a distinct maxima/minima band in the WT, and its energy is largely at lower frequencies. Noise contamination of the same data (in this example, Gaussian white noise) can be isolated in a similar manner by recognizing that it acts only at the higher frequencies of the transform and does not generate multi-scale maxima/minima bands (Fig. 1(C)). A singularity detection algorithm was implemented to identify the peaks of the P and R waves by their multiscale characteristics, in accordance with a previously described procedure [11]. We proceed by detecting the R waves in the ECG record first. R waves are selected by using three selection criteria for the maxima/minima chains: the length of the chain across scale, the relative magnitude of the maxima/minima in the chain, and the local regularity of the signal. These criteria are then thresholded to select the R wave. After the R wave has been detected, we determine the R wave occurrence time as the zero-crossing of the maxima/minima pair on scale 1, the wavelet scale with the highest time resolution. The accuracy of detection of the R wave occurrence time was approximately 0.18%. Once the locations of the R waves have been determined, we search for P waves, confining our search in two ways to improve the detection accuracy. First, we restrict our search to ECG sub-segments where the P wave is most likely to occur. Second, in these sub-segments, we search for a maxima/minima pair on the wavelet scale for which the P wave is most pronounced; this was empirically determined to be scale 4 for all subjects. The size of the sub-segment to be searched and its position relative to the R wave
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Fig. 1. Detection of ECG singularities with the wavelet transform. (A) Singularities associated with the P, R and T waves of the ECG are apparent as vertical bands corresponding to maxima/minima of the wavelet transform. (B) A baseline shift of the ECG is only apparent on the lower-frequency scales of the wavelet transform. (C) Noise contamination of the ECG (SNR = 10 dB) does not impede wavelet detection of the ECG singularities, as the noise only affects the higher-frequency scales.
are parameters that are empirically determined for each subject and fixed for the analysis of the ECG record. We took a number of measures to minimize the impact of common signal impairments such as ectopy, signal dropouts and amplifier saturation. These impairments were addressed prior to singularity analysis by visually reviewing each ECG record and noting the start and end times of impaired ECG segments. These segments were then removed from the record, and subsequent data time-shifted back to maintain a contiguous sequence. Singularity analysis was then performed on the edited ECG records to produce pairs of P and R wave occurrence times for each successive heartbeat. Artifacts may still be present in the record of P and R wave occurrence times due to undetected P waves and stray ectopic beats. The remaining ectopic beats were identified by comparing each P and R interbeat interval to a moving
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average of the previous interbeat values. When an ectopic beat occurs, both interbeat intervals will exceed a threshold value. Undetected P waves are easily found by referring to the R wave occurrence times: if two successive R waves are found without an intermediate P wave, the corresponding R wave is noted. When either type of defect was found, the occurrence times for that heartbeat were removed from the record, and the subsequent occurrence times were time-shifted back. Instantaneous rate signals for the P and R waves were then calculated as the inverse of the respective interbeat periods. Spectral analysis of the P and R wave variability signals was performed by Thomson’s multitaper method. The multitaper method is a nonparametric spectral analysis technique that provides spectral estimates with less variance than conventional techniques (e.g. Blackman–Tukey) and demonstrates superior mean squared error performance for the calculation of spectra with power-law behavior [12]. Adaptive weights were used for the multitaper analysis with a time-bandwidth product of 16. The length of the data record used for spectral analysis was approximately 1024 beats, varying slightly from case to case due to the artifact removal process. The sampling rate assumed in the spectral analysis was the reciprocal of the mean heart rate. The data used in this study were drawn from a set of public-domain ECG recordings of paroxysmal atrial fibrillation from the PhysioNet database (http://www.physionet.org/physiobank/database/afpdb/) [13]. The recordings consist of pairs of 30-min ECG segments, each pair drawn from a single 24-h recording. One record of the pair serves as a control, extracted at least 45 min distant from any episode of PAF. The other record of the pair ends just before the onset of PAF. There are 25 record pairs in the PhysioNet PAF database; we analyzed 21 of these record pairs, excluding four pairs due to poor signal quality.
3. Results Discernible changes to the P and R wave variability spectra were evident for many of the cases at the onset of PAF, as illustrated in Fig. 2. In this figure, the power spectral density (PSD) is shown for 3 of the 21 subjects (A,B,C, arranged row-wise). In the left panel the PSDs for the P and R wave variability signals are shown for the control period, at least 45 min prior to the episode of PAF. In the center panel the PSDs of the P and R variability signals are shown for the ECG segment immediately preceding the PAF episode. Comparing the control and PAF onset spectra, a strong, mutual harmonic component characterizes the P and R wave spectra at the onset of PAF. In many cases this mutual harmonic component was also observed in the control case; however, it typically increased in magnitude at the onset of PAF. This harmonic component is likely the respiratory sinus arrhythmia (RSA), a normal arrhythmia that occurs due to the influence of breathing on the vagal (parasympathetic) outflow to the sinoatrial node. We say this strong spectral component is “likely” the RSA because the breathing frequency was not recorded or controlled during these data recordings, so we cannot be certain that this spectral peak occurs at the breathing frequency. However, this component does occur in the frequency range typical of the RSA, 0.15–0.5 Hz. The RSA is often present in normal HRV; however, it is seldom as pronounced as it appears in the PAF onset data. Fig. 3 shows typical P and R wave variability spectra from normal subjects for reference. Contrasting the spectra for the normal data with that at PAF onset, we observed a pronounced entrainment of the P and R wave variability spectra at PAF onset at the RSA frequency. We use the term “entrainment”
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Fig. 2. Frequency entrainment of the P and R wave variability signals as paroxysmal atrial fibrillation approaches for three subjects. The plots for each subject (A, B, C) are arranged rowwise as follows: left column, the P and R wave variability power spectral densities (PSDs) under control conditions (at least 45 min distant from the PAF episode); center column, the P and R wave variability PSDs at PAF onset; right column the corresponding cross-spectral densities. For the PSD plots, the solid line is the spectra for the P wave variability signal and the dashed line is the spectra of the R wave variability signal. The records shown are from the Physionet PAF database, records p01, p43 and p25, respectively.
in the sense of Pikovsky et al. [14]: a coincidence of frequencies. However, this phenomenon is more than a coincidence of spectral content at the RSA frequency; it appears to be an equivalence of spectral power at this frequency at the onset of PAF. We propose that a useful diagnostic indication of the impending onset of PAF might be obtained by devising a measure to characterize the entrainment of the P and R wave variability spectra at the RSA frequency. A simple measure investigated here is the normalized cross spectrum [15]: CPR (f ) =
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Fig. 3. Spectral characteristics of the P and R wave variability signals for three typical normal subjects. The plots for each subject (A, B, C) are arranged rowwise, with the P and R wave variability power spectral densities (PSDs) for a given subject in the left column and the associated cross-spectral density plot in the right column. For the PSD plots, the solid line is the spectra for the P wave variability signal and the dashed line is the spectra of the R wave variability signal.
as the measure of AVRV entrainment. The right-most panels in Fig. 2 show the cross spectra for three subjects at PAF onset; strong peaks are present in the HF frequency range. Using the described procedure, P and R wave rate variability signals were calculated for the 21 subjects in this study, and PSD analysis applied to the variability signals. The AVRV entrainment measure was then calculated between the P and R wave rate variability spectra for the control and PAF onset data sets. An increase in AVRV entrainment was observed for 17 out of the 21 subjects (Fig. 4). 4. Discussion In this research, we have proposed a measure of the entrainment of the P and R wave variability signals as a diagnostic measure for the acute onset of PAF. To investigate the usefulness of such a measure, it is important to consider two issues: (1) the diagnostic power of the measure relative to other ECG-derived measures, (2) whether the measure provides an independent indication of the onset of PAF, or if it is somehow linked to previously described measures derived from the ECG.
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With this in mind, we compared a number of common ECG-derived diagnostic measures to the AVRV entrainment measure. Our approach was to compare the measures based on their performance as diagnostic tests for the acute onset of PAF using receiver operating characteristic (ROC) curves. The ROC curve is a plot of the true positive rate of a diagnostic test against the false positive rate as the discrimination threshold is swept. It requires no assumptions about the statistical nature of the data. The area under the ROC curve serves as a well-established index of diagnostic accuracy [16]; a value of 0.5 is equivalent to diagnostic assignment by chance whereas the maximum value (1.0) corresponds to perfect diagnostic assignment. Comparing the ROC curve for the AVRV entrainment measure to the other ECG-derived measures allows us to quantitatively assess the diagnostic power of the measures. We examined five ECG-derived diagnostic measures and compared their performance to the AVRV entrainment measure using ROC curves. The measures can be categorized as follows: measures of (1) sympathetic/parasympathetic balance, (2) dromotropic (conduction velocity) alteration, and (3) conventional measures of heart rate variability. 4.1. Sympathetic/parasympathetic balance The relationship between sympathetic and parasympathetic modulation of heart rate is often characterized from HRV with a measure called the LF/HF ratio [17]. The LF/HF measure is calculated as the ratio of total spectral power in the LF band (0.04–0.15 Hz) to the HF band (0.15–0.5 Hz). The LF/HF ratio for the 21 subjects in this study in both control and PAF onset conditions are listed in Table 1, calculated
Table 1 Standard measures of heart rate variability compared to the AVRV entrainment measure (shaded cells are the value of the measure at the onset of PAF, unshaded cells are the value of the measure for the control condition, 45 min distant from the episode of PAF)
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Fig. 5. Receiver operating characteristic (ROC) curves comparing the AVRV entrainment measure to the median P–R interval, median absolute deviation of P–R interval, SDNN, LF/HF, and DFA for prediction of an episode of PAF.
from the R wave variability data. In the table, the column of shaded cells are the values of the measure at the onset of PAF, while the unshaded cells are the values for the control condition, 45 min distant from the episode of PAF. The diagnostic power of the LF/HF measure as a predictor of PAF was then assessed and compared to the AVRV entrainment measure by ROC analysis (Fig. 5). The area under the ROC curve was 0.66 (95% CI: 0.46–0.83) for the AVRV entrainment measure and 0.43 (95% CI: 0.25–0.63) for the LF/HF measure. One conclusion we draw from this result is that the AVRV entrainment measure has greater diagnostic power for prediction of the acute onset of PAF. This result may also indicate that the phenomenon that forms the basis for the AVRV entrainment measure—entrainment of the P and R wave variability signals at the respiratory frequency—is not simply some consequence of an alteration to cardiac autonomic balance. 4.2. Dromotropic measures A dromotropic effect is one that affects conduction velocity. The inter-nodal conduction time is the interval between the onset of atrial depolarization and the onset of ventricular depolarization, and can be estimated from the ECG as the time interval between the P and R waves. AVRV analysis marks the occurrence time of the P and R waves; from these occurrence times, the P–R interval was calculated. We are interested in both the central tendency and dispersion of this measure and how it compares to the AVRV entrainment measure. The central value is of interest because decreased atrial conduction velocity is known to promote the initiation of atrial fibrillation [18]. The dispersion of the P–R interval is also of interest because to some extent it also characterizes the entrainment of the P and R wave variability spectra. Certainly for one extreme—P–R intervals with no beat-to-beat dispersion—we would expect complete spectral entrainment at all frequencies because the R wave would always occur a fixed time after the P wave.
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The values of the measures are listed in Table 1. The P–R interval times were prolonged (greater than 0.20 s) for 3 of the 21 subjects. We note that in a study of 125 subjects who developed sustained AFIB, approximately 38% had a P–R interval of 0.21 s or greater [19]. It is difficult to compare our results directly to this study, however, because (1) the number of subjects in the present study is relatively small, and (2) subjects in the present study had episodes of PAF, not sustained AF. The ROC curves comparing the AVRV entrainment measure to the dromotropic measures are shown in Fig. 5. We used the median and median absolute deviation to characterize the central tendency and dispersion of the P–R interval in an outlier-resistant manner. The median P–R interval was not effective as a diagnostic indicator (area under the ROC curve of 0.52 (95% CI: 0.32–0.71)), nor was the P–R dispersion measure (area under the ROC curve of 0.40 (95% CI: 0.23–0.60)).
4.3. Conventional HRV measures Heart rate variability measures are commonly used in the clinic and have been proposed as predictors of PAF. In one study, a measure of HRV achieved a 76% rate for detection of the onset of PAF [20]. We investigated two measures, one a common measure called SDNN, defined as the standard deviation of the time interval between normal R waves [1]. We also used a measure derived from a technique called detrended fluctuation analysis (DFA) [21]. For this technique, the root-mean-square fluctuation of an integrated and detrended version of the R–R interval time series is measured at a sequence of window sizes. The logarithmic relationship between the RMS fluctuation measurement and the window size is then characterized by linear regression. The slope of this linear relationship is used as an HRV measure. Neither measure was effective as a diagnostic indicator of PAF. The area under the ROC curve was 0.51 for the SDNN measure (95% CI: 0.33–0.70) and 0.50 for the DFA measure (95% CI: 0.31–0.68).
5. Conclusion We believe the results of this study have two important implications: (1) there is evidence of a distinct pattern of interaction between the SA and AV nodes prior to the onset of PAF: entrainment of the SA and AV rate variability at the frequency of respiration, (2) this interaction may be observed and characterized noninvasively using the ECG and may form the basis of a useful diagnostic indication of the impending onset of PAF. With regard to point 1 above, we hope the findings of this study will inspire further research to investigate the dynamics of cardiac pacemaker interaction and its role in the mechanism of arrhythmiogenesis. With regard to point 2, we found the diagnostic performance of the AVRV entrainment measure to be superior to all other measures used in this study, although the diagnostic performance was far from ideal. However, we note that the control records used in this study (ECG recordings made at least 45 min distant from the onset of PAF) contained evidence of SA/AV entrainment for a majority of the cases. In other words, the characteristic AVRV entrainment that we have observed in this study often develops earlier than 45 min prior to the onset of PAF. We anticipate that a better diagnostic result would likely be obtained in a study using normal subjects as control.
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Acknowledgements We are especially grateful to the creators of the PhysioNet database for the generosity they have shown in creating the public-domain physiological database used for this study. References [1] P.K. Stein, R.E. Kleiger, Insights from the study of heart rate variability, Annu. Rev. Med. 50 (1999) 249. [2] Task Force of the European Society of Cardiology and the North American Society of Pacing and Electrophysiology. Heart rate variability—standards of measurement, physiological interpretation, and clinical use, Circulation 93 (1996) 1043. [3] M.F. O’Toole, J.L. Ardell, W.C. Randall, Functional interdependence of discrete vagal projections to SA and AV nodes, Am. J. Physiol. Heart Circ. Physiol. 251 (1986) H398. [4] R. Shouldice, et al., PR and PP ECG intervals as indicators of autonomic nervous innervation of the cardiac sinoatrial and atrioventricular nodes, Proceedings of the First IEEE EMBS Conference on Neural Engineering, 2003. [5] S. McClennen, et al., Predicting Onset of Atrial Fibrillation (http://www.physionet.org/physiobank/database/ afpdb/paf.shtml). [6] S. Nattel, New ideas about atrial fibrillation 50 years on, Nature 415 (2002) 219. [7] P.E. Dilaveris, et al., Simple electrocardiographic markers for the prediction of paroxysmal idiopathic atrial fibrillation, Am. Heart J. 135 (1998) 733. [8] N. Ishimoto, M. Ito, M. Kinoshita, Signal-averaged P-wave abnormalities and atrial size in patients with and without idiopathic paroxysmal atrial fibrillation, Am. Heart J. 139 (2000) 684. [9] S. Vikman, et al., Altered complexity and correlation properties of R–R interval dynamics before the spontaneous onset of paroxysmal atrial fibrillation, Circulation 100 (1999) 2079. [10] S. Mallat, W.L. Hwang, Singularity detection and processing with wavelets, IEEE Trans. Inform. Theory 38 (1992) 617. [11] C. Li, Ch. Zheng, Ch. Tai, Detection of ECG characteristic points using wavelet transforms, IEEE Trans. Biomed. Eng. 42 (1995) 21. [12] E.J. McCoy, A.T. Walden, D.B. Percival, Multitaper spectral estimation of power law processes, IEEE Trans. Signal Process. 46 (1998) 655. [13] A.L. Goldberger, et al., PhysioBank, physiotoolkit, and physionet: components of a new research resource for complex physiologic signals, Circulation 101 (2000) e215. [14] A. Pikovsky, M. Rosenblum, J. Kurths, Synchronization: A Universal Concept in Nonlinear Sciences, Cambridge University Press, Cambridge, 2001. [15] J.S. Bendat, A.G. Piersol, Random Data: Analysis and Measurement Procedures, second ed., Wiley, New York, NY, 1990. [16] J.A. Swets, Measuring the accuracy of diagnostic systems, Science 240 (4857) (1988) 1285. [17] A. Malliani, et al., Physiology and clinical implications of variability of cardiovascular parameters with focus on heart rate and blood pressure, Am. J. Cardiol. 73 (1991) 3C. [18] American College of Cardiology/American Heart Association Task Force on Practice Guidelines and the European Society of Cardiology Committee for Practice Guidelines and Policy Conferences. ACC/AHA/ESC guidelines for the management of patients with atrial fibrillation, Eur. Heart J. 22 (2001) 1852. [19] B. Lown, Electrical reversion of cardiac arrhythmias, Brit. Heart J. 29 (4) (1967) 469. [20] C. Maier, M. Bauch, H. Dickhaus, Recognition and quantification of paroxysmal atrial fibrillation by analysis of heart rate variability parameters, Computers in Cardiology 2001, vol. 28, IEEE Press, New York, 2001, p. 129. [21] C.K. Peng, S. Havlin, H.E. Stanley, A.L. Goldberger, Quantification of scaling exponents and crossover phenomena in nonstationary heartbeat time series, Chaos 5 (1995) 82. Russell J. Fischer is a biomedical engineer with over 15 years experience in the research and development of medical devices, working for companies such as Datex-Ohmeda, Bellcore and Sarnoff Labs. He currently directs independent research in the areas of biomedical signal processing, and is developing a number of medical monitoring and diagnostic systems for corporate healthcare clients.