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Multidimensional Rhythm Disturbances as a Precursor of Sustained Ventricular Tachyarrhythmias Vladimir Shusterman, Benhur Aysin, Kelley P. Anderson, Anna Beigel Downloaded from http://circres.ahajournals.org/ by guest on June 16, 2017 Abstract—Cardiac cycle dynamics reflect underlying physiological changes that could predict imminent arrhythmias but are obscured by high complexity, nonstationarity, and large interindividual differences. To overcome these problems, we developed an adaptive technique, referred to as the modified Karhunen-Loeve transform (MKLT), that identifies an individual characteristic (“core”) pattern of cardiac cycles and then tracks the changes in the pattern by projecting the signal onto characteristic eigenvectors. We hypothesized that disturbances in the core pattern, indicating progressive destabilization of cardiac rhythm, would predict the onset of spontaneous sustained ventricular tachyarrhythmias (VTAs) better than previously reported methods. We analyzed serial ambulatory ECGs recorded in 57 patients at the time of VTA and non-VTA 24-hour periods. The disturbances in the pattern were found in 82% of the recordings before the onset of impending VTA, and their dimensionality, defined as the number of unstable orthogonal projections, increased gradually several hours before the onset. MKLT provided greater sensitivity and specificity (70% and 93%) compared with the best traditional method (68% and 67%, respectively). We present a theoretical analysis of MKLT and describe the effects of ectopy and slow changes in cardiac cycles on the disturbances in the pattern. We conclude that MKLT provides greater predictive accuracy than previously reported methods. The improvement is due to the use of individual patterns as a reference for tracking the changes. Because this approach is independent of the group reference values or the underlying clinical context, it should have substantial potential for predicting other forms of arrhythmic events in other populations. (Circ Res. 2001;88:705-712.) Key Words: ventricular arrhythmias 䡲 cardiac cycle dynamics 䡲 orthogonal decomposition A lthough substantial progress has been made in the understanding of arrhythmia mechanisms and identification of individuals at risk, short-term prediction of the timing of onset of sustained ventricular tachyarrhythmias (VTAs) has lagged, delaying development of preventive treatments.1 Because autonomic activity is thought to be an important trigger of VTA and because cardiac cycle lengths (CCLs) are modulated by autonomic tone, it has been assumed that the analysis of the changes in CCL could predict the timing as well as the triggers of VTA.2 This has been confirmed by studies that demonstrated heart rate increase before the VTA onset in many patients.2–5 However, the change in heart rate before the onset of VTA is usually small and indistinguishable from random daily variations.2,6 Descriptors of heart rate variability proved useful in general risk assessment but failed to predict the timing of VTA.5,7 Probable reasons for the failure include the high complexity of the interacting physiological influences and violation of the statistical assumptions that underlie traditional techniques.8 In addition, the attempts to summarize highly nonstationary and individually variable CCL dynamics in a few indices effectively resulted in non-uniform data compression and frequent oversight of individual changes that precede the onset of VTA.9 To overcome these problems, we sought a new approach that (1) automatically learns individual characteristic or “core” patterns of CCL (CPCCL); (2) accommodates the diversity of individual CPCCL, including the presence of ectopy and changes in neurohormonal activity; and (3) tracks the changes in CPCCL regardless of their linear or nonlinear properties. We used a pattern-recognition approach based on the modified KarhunenLoeve transform (MKLT) to develop a method that, in each individual, identifies CPCCL; we then tested the hypothesis that disturbances in CPCCL indicate destabilization of cardiac rhythm that precedes the onset of spontaneous, sustained VTA. To elucidate the origins of the disturbances, we examined the effects of ectopy and compared MKLT with other techniques using the identical data set. Materials and Methods Patient Characteristics Clinical and Holter ECG data were collected prospectively in a uniform fashion in the course of a NIH-sponsored clinical trial; protocols, methods, definitions, and patient characteristics have been Original received May 30, 2000; resubmission received December 13, 2000; revised resubmission received February 14, 2001; accepted February 14, 2001. From the University of Pittsburgh (V.S., B.A.), Pa; Marshfield Clinic (K.P.A.), Marshfield, Wis; and Biosonix, Ltd (A.B.), Hod-Hasharon, Israel. Correspondence to Vladimir Shusterman, University of Pittsburgh, 200 Lothrop St, Room B535, Pittsburgh, PA 15213. E-mail [email protected] © 2001 American Heart Association, Inc. Circulation Research is available at http://www.circresaha.org 705 706 Circulation Research April 13, 2001 described in detail.2,9 In brief, ambulatory 24-hour ECGs from 57 patients (87% male, age 64⫾10 years, 83% ischemic heart disease, and left ventricular ejection fraction of 0.36⫾0.15) with spontaneous sustained VTA (duration: ⱖ30 seconds; rate: ⱖ100 bpm) and with a minimum of 2 hours of ECG data preceding the onset of VTA were examined. In addition, 86 serial 24-hour ECG recordings without VTA events were obtained from the same patients and included into analysis. All patients had a history of cardiac arrest, documented ventricular fibrillation, sustained ventricular tachycardia, or syncope. Enrolled patients had to have at least 10 premature ventricular complexes per hour and VTA induced at electrophysiological study. None of the patients were receiving antiarrhythmic drugs at the time of the recordings. Patients with recent myocardial infarction, long-QT syndrome, hypertrophic cardiomyopathy, or arrhythmias due to transient or reversible disorders were excluded. Data Processing Downloaded from http://circres.ahajournals.org/ by guest on June 16, 2017 ECG data were digitized at 400 Hz, and the QRS complexes were classified using custom software and verified by a cardiologist.2 The effects of ectopy were estimated by analyzing an unfiltered series (all natural cycles included) and a filtered series that excluded ectopic beats and the 2 sinus beats that preceded and followed each ectopic beat. The effects of pauses, escape beats, and short-long-short sequences were eliminated by excluding intervals that differed by ⬎75 ms from the moving average of 5 cycles. Gaps in the time series resulting from noise or ectopic beats were interpolated with linear splines.10 The filtered series of RR intervals were regularly spaced and sampled at 2 Hz using a boxcar low-pass filter.11 Time Domain Analysis The mean and SD, square root of the mean of the squared differences between adjacent cardiac cycles (r-MSSD), and percentage of differences between adjacent cycles that are ⬎50 ms (pNN50) were estimated. Frequency Domain Analysis Power was integrated in the following frequency ranges: total power (TP), 0.01 to 0.4 Hz; high-frequency power (HFP), 0.15 to 0.4 Hz; low-frequency power (LFP), 0.04 to 0.15 Hz; and very-lowfrequency power (VLFP), 0.01 to 0.04 Hz. The ratio of low- to high-frequency power (LFP/HFP) was also calculated. Nonlinear Indices Approximate entropy (ApEn), a measure of regularity, was estimated as described by Pincus and Keefe.12 Briefly, ApEn measures the likelihood that the maximum distance between the scalar components of vectors in m dimensional space will remain similar in m⫹1 dimensions. Low values of ApEn signify that the m and m⫹1 dimensional patterns are similar. We used the same values of dimension and distance (2 and 20% of SD, respectively) as in the previous studies of the series of cardiac cycles.13,14 To calculate the ␣-1 and ␣-2 scaling exponents, first we computed the root-mean-square fluctuations of integrated and detrended time series.15 Then the relationship between the root-mean-square fluctuations and the segment length was obtained as a slope on a double-log graph for the segments that were shorter than 11 beats (␣-1) and those that were longer than 11 beats (␣-2). Pattern Recognition Analysis In this algorithm, the series of cardiac cycles is separated into 5-minute segments referred to as the unit vectors.16 Each unit vector has 600 points and can be represented as a vector with 600 components in a Hilbert space. The high dimensionality of this vector results in unwieldy complexity and obscures the detection of underlying pattern. The Karhunen-Loeve transform (or the principal component analysis), which was modified by the investigators for this application, allows simplifying the pattern and exposing its most significant features. The reduction of dimensionality of the unit vector is achieved by projecting it onto linearly independent basis vectors or eigenvectors, which represent the most characteristic features of the signal. To obtain the eigenvectors, first, a unit autocovariance matrix, U, is calculated for each unit vector (matrices appear in boldface type throughout this article). In this matrix, the strongest relationships between the data samples are magnified, whereas the weakest ones that are usually related to noise are reduced. Averaging the matrices U for all unit vectors yields an average autocovariance matrix, C, that represents the most characteristic components of the entire signal. Then, the characteristic eigenvectors are obtained by diagonalizing the matrix C. To reduce the dimensionality of the original data with a minimal information loss, we select the eigenvectors that correspond to the biggest eigenvalues.17 The quality of this reduction is controlled by the residual error of the signal reconstruction from its low-dimensional projection. MKLT coefficients are obtained by projecting the original series onto the corresponding eigenvectors; the time series of each MKLT coefficient represents temporal changes in the projection of the signal onto the corresponding eigenvector. Finally, because the time course of the changes does not correspond to the constant 5-minute length of the unit vectors, the window lengths are adjusted to separate the segments with different properties (see online data supplement available at http://www.circresaha.org for further description). Analysis of the Core Pattern of Cardiac Cycles The first 6 eigenvectors of the matrix C, which contain most of the information about the signal, were extracted, and their MLKT coefficients, ck, were obtained as described above. The time series of ck were used to estimate the SD of the series of each coefficient (k). A 3k threshold was established so that the probability of a random occurrence of the CCLs exceeding 3k would be ⬍0.0013 assuming a normal distribution. At the next step, the adaptive segmentation was applied to c1 through c6, and the number of coefficients exceeding the threshold (3k) was calculated in each window (see online data supplement available at http://www.circresaha.org). For each subject, the thresholds were determined using the training set and then applied to the recordings from the same subject in the test sets. Combined excursions of several ck values beyond the threshold reflect simultaneous instabilities in the orthogonal projections of the signal, which in turn signify complex and pronounced changes in the pattern of cardiac cycles. The CPCCL is said to be at a steady state when all 6 MKLT coefficients are within the limits of 3k. An excursion of 1 or more MKLT coefficients beyond the 3k threshold indicates disturbances of CPCCL. The dimensionality (Dm) of the disturbances is defined as the number of MKLT coefficients that simultaneously exceed the corresponding 3k thresholds. Thus, Dm shows the number of orthogonal projections in which the behavior of the series becomes unstable. The relationships between the variables were analyzed using a nonlinear Spearman correlation to eliminate the effects of the scaling differences between the studied variables. Results Steady-State Pattern of Cardiac Cycles The process of distinguishing the steady-state CPCCL and its disturbances is illustrated on a representative series of cardiac cycles beginning 16 hours before the onset of a spontaneous, sustained VTA in Figure 1. No clear pattern can be found in the plot of cardiac cycles (Figure 1A). However, the 6 MKLT coefficients plotted over the same time frame (Figures 1B through 1G) expose the transition from the steady-state pattern to the CPCCL disturbances. The shape and the magnitude of the autocovariance matrix C (see Materials and Methods) provide insight into the changes in CPCCL. Matrix representations of the steady-state CPCCL have smooth shape and low amplitudes of variations, indicating a regular but weakly correlated and nonperiodic Shusterman et al Downloaded from http://circres.ahajournals.org/ by guest on June 16, 2017 Figure 1. Cardiac cycle dynamics during 16 hours before onset of a sustained VTA. A, Red dots indicate original, unfiltered cardiac cycle series; blue dots, series filtered to eliminate ectopic beats, pauses, and outliers, as described in Materials and Methods. B through G, MKLT coefficients c1 through c6 (arbitrary units). Data are separated into 2 windows, W1 and W2, as described in the online data supplement available at http://www. circresaha.org. In the first window, the core pattern of cardiac cycles is at steady state, which is indicated by low variations in MKLT coefficients. None of the coefficients exceeds the 3 thresholds. In W2, there is a 5-fold increase in variations of c1 through c6 compared with W1, and 5 of 6 coefficients (c2 through c6) in both filtered and unfiltered series exceed the 3 thresholds, indicating simultaneous instabilities in the 5 orthogonal projections of the signal. VTA starts at the end of W2 after 7 hours of multidimensional (Dm⫽5) disturbances in the core pattern of cardiac cycles (see text for discussion). structure of the series (Figure 2, top and middle). An increase in the magnitude of the matrix elements and the number of spurious correlation spikes during the CPCCL disturbances shows that multiple nonstationarities and irregular sequences develop toward the onset of VTA (Figure 2, bottom). The most significant basis vectors that represent CPCCL and their frequency content are shown in Figure 3. Because the slow changes predominate, the spectral energy of all eigenvectors is concentrated in the low frequency range. Using our previous experiments, we chose the first 6 eigenvectors, which contain 88% of the information and represent CPCCL with a 12% residual error. The time series of the corresponding MKLT coefficients track the most significant changes in the structure of the signal over time, and multidimensional Multidimensional Rhythm Disturbances 707 Figure 2. Matrix representation of the steady-state pattern of cardiac cycles and its disturbances. Top, Average autocovariance matrix, C, for the entire 16-hour recording in Figure 1A. Amplitudes of variations are relatively small because averaging reduces the range of variability of matrix elements. This matrix represents a steady-state pattern of a stationary, nonperiodic, and weakly correlated structure of the signal. Note that for periodic and highly correlated signals, the matrix shape would show a clear periodic pattern. Middle, Matrix for the initial 5-hour period only. Compared with the entire recording (top), this matrix has similar amplitudes and shapes of variations along the z-axis. Both matrices have a smooth shape, and the amplitude of the nondiagonal elements is low. The similarity indicates that the series was at a steady state during the initial 5-hour period. Bottom, Matrix for the final 5-hour period that ended with the onset of VTA. The amplitude is 3 times higher than in the autocovariance matrix for the initial period. In addition, there are large and randomly distributed spikes of spurious correlations between cardiac cycles that reflect development of multiple nonstationarities and irregular sequences toward the onset of arrhythmia. (Dm⬎3) disturbances in CPCCL were detected in most patients before the initiation of spontaneous VTA (Figure 4). Of note, different combinations of MKLT coefficients exhibited disturbances equally often before the onset time. Therefore, the dimensionality of the disturbances Dm, rather than the specific combinations of MKLT coefficients, indicated an unstable trajectory of the cardiac rhythm that led to the initiation of arrhythmia. Influence of Heart Rate and Ectopy on the Pattern of Cardiac Cycles Average heart rate represents an envelope or slowly changing component of the cardiac cycle series. In most subjects, the 708 Circulation Research April 13, 2001 Figure 4. Progressive increase in the dimensionality of the CPCCL disturbances toward the onset time of VTA. Number of MKLT coefficients exceeding 3 thresholds increased before initiation of VTA, indicating accumulation of multidimensional instabilities in the series of cardiac cycles (P⫽0.03). Downloaded from http://circres.ahajournals.org/ by guest on June 16, 2017 Figure 3. Time domain (left column) and spectral (right column) representation of the first 6 eigenvectors that were obtained from the autocovariance matrix shown in Figure 2A. The eigenvectors i were ordered according to the corresponding eigenvalues of which the absolute values represent the amount of information in the corresponding eigenvectors. After this reordering, 1 represents the slowly changing envelope of the series, because the largest variations occur in the very-lowfrequency range of the spectrum. Spectral peaks of 2 to 6 gradually shift to the higher frequencies. This reflects the multicomponent structure of the signal in which the higher-frequency elements have lower amplitudes of variations. Eigenvectors are nonstationary and nonperiodic, reflecting nonstationarity of the series. If the series contained only 1 or 2 periodic components, it could be represented by 1 or 2 eigenvectors. In contrast, reconstruction of the series under consideration with 6 eigenvectors still gives a 12% error, which indicates the presence of multiple nonperiodic components. slow, minutes-to-hours variations of heart rate are predominant, and this envelope contains most of the information about the series.9 Therefore, the time series of the first MKLT coefficient c1 tracks the slow changes in the heart rate (Figure 1B). However, the fact that the changes occur simultaneously in several MKLT coefficients shows that, in addition to the slow changes in heart rate, CPCCL and its disturbances are linked to other independent dynamic processes. To investigate the effects of ectopy on the series of MKLT coefficients, the analysis was repeated after filtering out ventricular and supraventricular ectopy and outliers as described in Materials and Methods (Figure 1A). Because ectopic activity introduces ultrashort interbeat irregularities into the series of cardiac cycles, the processing effectively eliminated or reduced the high-frequency beat-to-beat oscil- lations. Although ectopy and short-term irregularities influence CPCCL, the filtering did not affect the detection of CPCCL disturbances that preceded the onset of VTA. This result shows that the impact of slow changes in the cardiac cycles on CPCCL is more important than the influence of ectopy and ultrashort interbeat irregularities. Note that measurements of the heart rate envelope (first MKLT coefficient) cannot adequately describe the complexity of these slow changes; at least 6 MKLT components are required for tracking the CPCCL disturbances. Because the eigenvectors are orthogonal, we examined the dynamics of the series with and without ectopy using 3-dimensional trajectories of the variances of the first 3 MKLT coefficients (Figure 5). The variations of the trajectories in the plane of the 2 most significant MKLT coefficients are similar, indicating that the disturbances in CPCCL are not eliminated by filtering of ectopy. However, the series without ectopy has lower amplitude of variation for the third MKLT coefficient, showing that ectopy and ultrashort irregularities mostly affect the higher-order MKLT coefficients. Multidimensional Disturbances in the Pattern of Cardiac Cycles and the Initiation of Ventricular Tachycardia The training data set comprised tapes from 30 patients with a single VTA during the 24 hours. Using the disturbances that had Dm⫽4 to 6, the initiation of VTA was predicted with 70% sensitivity and 93% specificity during the 6.8⫾4.4 hours before the onset (Table 1). The number of MKLT coefficients exceeding the threshold increased progressively over several hours before the event, indicating gradual increase in the dimensionality (complexity) of the disturbances and progressive destabilization of cardiac rhythm (Figure 4). The robustness of the method was validated in the 2 demanding test sets. The generality test set consisted of 27 ambulatory recordings from a different group of patients who had several VTAs during the 24-hour period. The longest VTA was chosen as the index event. Multiple disturbances that preceded the onset of each VTA enhanced the variance of MKLT coefficients and interfered with the analysis of the index event. This provided a naturally “noisy” environment for testing the robustness of MKLT on the most complicated perturbations of cardiac cycles. Predictably, the accuracy of the method decreased, but the expected decline of sensitivity and specificity was relatively modest (Table 1). The speci- Shusterman et al Multidimensional Rhythm Disturbances traditional linear and nonlinear methods (Table 2). Series of the time domain, spectral, and nonlinear indices were strongly correlated with the dynamics of cardiac cycles (P⬍10⫺4). The most prominent changes in all studied indices resulted from signal nonstationarities that elicit profound and complex perturbations in the basic structure of the series (Figure 6). However, the traditional indices could not distinguish among the changes in a singular property, in a multitude of properties, and in the entire structure of the series. The sensitivity of each index depended on a type of perturbation. Therefore, no single index could expose the complexity or the magnitude of multidimensional changes; some perturbations would be missed or underestimated with a single-index approach. In contrast, MKLT provides an accurate quantitative description of the magnitude and complexity (ie, dimensionality) of the changes, and therefore, it is more effective in detecting the transients that precede the onset of VTA (Table 2). Downloaded from http://circres.ahajournals.org/ by guest on June 16, 2017 Figure 5. Dynamics of the series shown in Figure 1A in the 3-dimensional space of the first 3 eigenvectors. Shown are trajectories of 60-minute variances of corresponding MKLT coefficients with (red line) and without (blue line) ectopy. At the beginning of the recording, both trajectories are close to the origin, indicating a steady state (shaded area). Eight hours later, the trajectories become unstable and make complex movements in all 3 directions. The 2 trajectories have similar amplitudes of variations in the c1,c2 plane, which represents most of the information about the signal. However, the filtered series has lower amplitude along the c3 axis, showing that filtering the ectopy reduces variations of ci for i⬎2. Discussion Main Results and Comparison With Previous Studies Multidimensional disturbances in the individual pattern of cardiac cycles provided more sensitive and specific prediction of the onset time of VTA than traditional linear and nonlinear methods (Tables 1 and 2). Although changes in heart rate, traditional time domain, spectral, and nonlinear estimators, including ApEn and scaling exponents, have been reported before the onset of VTA, their predictive value was not assessed.2–5,18 Data about the accuracy of prediction of the onset time are scarce. Skinner et al19 reported that changes in the correlation dimension, a nonlinear measure of signal complexity, identified 11 Holter ECGs with ventricular fibrillation (sensitivity, 91%; specificity, 85%). Mani et al20 found that changes in the spectral power in the 0.8 to 0.9 –Hz frequency range predicted the onset of VTA with 76% sensitivity and 76% specificity in 78 patients using 1024 CCLs. Because the training set and the test set were not separated in these studies, the generality of the results (ie, applicability to other groups) could not be confirmed.21 Furthermore, the specificity of the findings is ficity test set included 86 serial 24-hour VTA-free ECGs from the same patients who had VTAs in the training set. In this test set, a steady-state CPCCL was identified and the disturbances leading to the initiation of VTA were excluded, with a specificity of 73%. When the arrhythmia-free tape was recorded within 3 months from the time of the training recording, the specificity increased to 80% (n⫽40), which suggests that CPCCL remains unchanged for 3 months and then changes slowly over a longer period. Inclusion of ectopy into the analysis increased the sensitivity of the method but did not change the specificity as compared with the series of CCLs without ectopic beats and outliers (Table 1). Relationship Between the Changes in the Pattern of Cardiac Cycles and Traditional Linear and Nonlinear Indices The sensitivity and specificity of MKLT in predicting the onset time of VTA (Table 1) were higher than those of TABLE 1. Dimensionality of the Disturbances in the Pattern of Cardiac Cycles and the Effects of Ectopy on the Prediction of the Onset of Sustained VTAs Training Set With Ectopy Dm Generality Test Set Without Ectopy With Ectopy Without Ectopy SN SP SN SP SN SP SN SP 3 100 ⱖ5 50 100 䡠䡠䡠 27 䡠䡠䡠 90 䡠䡠䡠 30 䡠䡠䡠 83 䡠䡠䡠 40 䡠䡠䡠 83 ⱖ4 70 93 37 80 57 83 50 80 ⱖ3 70 80 43 77 70 80 67 77 ⱖ2 80 70 57 77 77 63 73 73 ⱖ1 83 67 67 70 80 60 73 63 6 709 SN indicates percentage sensitivity of prediction of the VTA onset; SP, percentage specificity of the prediction; with ectopy, series that include ectopic beats; and without ectopy, series that have ectopic beats and outliers removed as described in Materials and Methods. 710 Circulation Research April 13, 2001 TABLE 2. Traditional Linear and Nonlinear Techniques to Predict the Onset of VTAs: Results Are Shown for the Best-Performing Parameters (3 Thresholds and 8-Hour Windows) and for the Series That Include All Ectopic Beats Training Set Downloaded from http://circres.ahajournals.org/ by guest on June 16, 2017 Figure 6. Changes in CCLs and their SDs, r-MSSD, pNN50, LFP, ApEn, ␣-1, and ␣-2 for the original (unfiltered) series in Figure 1A. Series were normalized to eliminate scale differences and then distributed along the y-axis by adding a multiple of a small constant ⑀. LFP is shown because it exhibited the most pronounced change among the other spectral indices before onset of VTA.2 All series are highly correlated and exhibit pronounced changes in the second, nonstationary part of the recording because of the profound and complex perturbations in the structure of the original series of cardiac cycles. However, the traditional indices do not distinguish between the change in a singular property, a multitude of properties, and the entire structure of the series. Therefore, no single index can quantify the entire complexity or magnitude of the changes. Note that in this example, the sensitivity to the nonstationarity of the nonlinear indices, ApEn, ␣-1, and ␣-2, is less than that of the linear indices, r-MSSD, pNN50, SD, and LFP. Because responsiveness of any single index to different types of changes varies, some perturbations may be underestimated or missed if a single index is used. unclear because the analysis did not include serial recordings from the same patients during the VTA-free periods. Because comparative analysis of the methods applied to different groups is limited, we used an identical data set to compare the performance of MKLT with that of the traditional techniques (Table 2). The methods were initially applied to a training set, and then the sensitivity and specificity were tested on the other 2 test sets. The generality test set included 24-hour ECGs from a different group of patients who had multiple spontaneous VTAs. In contrast to the previous studies, the prediction was considered correct if and only if the onset occurred within the same time window, of which the length was determined by the algorithm (see online data supplement available at http://www.circresaha.org for details). The specificity test set included serial 24-hour VTA-free ECGs from the same patients who had VTAs in the training set. This set allowed us to assess specificity and temporal stability of MKLT. In all sets, the predictive accuracy of MKLT was similar, which confirms generality and reliability of the results (Table 1).21 The predictive accuracy did not change if the recordings were obtained within 3 months, which shows that CPCCL remains stable during this period. In agreement with previous studies, inclusion of ectopic beats into analysis improved the accuracy of the prediction.20 This shows that an increase in the number of ectopic beats and ultrashort irregularity plays an important role in the CPCCL disturbances in some patients. Still, the disturbances of the same dimensionality could be detected before VTAs in more than half of those patients who had them before filtering. This suggests that in most patients, the CPCCL and its disturbances Generality Test Set SN SP SN SP HR 29 83 20 77 TP 48 67 44 46 VLFP 61 61 60 46 LFP 61 61 52 46 HFP 65 67 56 46 LFP/HFP 68 67 52 31 SD 35 72 32 62 pNN50 52 67 36 54 r-MSSD 19 72 12 62 ApEn 26 61 28 46 ␣-1 13 67 16 62 ␣-2 23 50 16 62 SN indicates percentage sensitivity of the prediction of the VTA onset; SP, percentage specificity of the prediction; and HR, heart rate. are determined not by ectopy or ultrashort irregularities but by the more complex, longer-term relationships between the cardiac cycles. This observation is consistent with the predominant spectral energy concentration in the very-lowfrequency range, which has an important prognostic value.22 Our results, as well as other recent reports, provide new insights into the role of the very-low-frequency oscillations and their nonstationary behavior.23 Modified Karhunen-Loeve Transform Although the traditional methods detected some changes, the search for specific precursors of VTA was impeded by violation of the statistical assumptions that underlie the traditional techniques. The traditional methods assume (1) that the signal is stationary and (2) that the changes occur in a single, a priori– defined property, whereas all other properties remain unchanged. However, the series of CCL before the onset of VTA are highly nonstationary, have enormous structural individual variability, and have a large number of unstable properties that cannot be adequately described by single-valued techniques.8 MKLT can be considered as a generalization of the traditional methods that are limited by the assumptions of the stationarity of the signals and by the single-feature searching capabilities. Indeed, the Fourier transform can be considered as a special case of MKLT in which the basis functions are complex exponentials.17 If the series is periodic and stationary, the Fourier transform can project the signal onto a finite set of periodic basis functions and thus expose the corresponding frequency elements. However, stationarity and exact periodicity are not characteristics of the signals that precede VTA. The time domain indices, including SD, r-MSSD, and pNN50, also capture certain a priori– defined properties of the signal that may or may not represent the changes that occur before the onset of VTA.24 The nonlinear descriptors, ApEn and scaling exponents, also attempt to Shusterman et al Downloaded from http://circres.ahajournals.org/ by guest on June 16, 2017 summarize the complexity of the series using a single measure that is selectively sensitive to certain types of changes. ApEn, for example, does not respond to the changes in amplitude but reacts to the changes in variance and therefore can be used only on the series of which the variances are relatively stable.12 As Figure 6 clearly shows, changes in ApEn and scaling exponents before the onset of VTA reflect changes in the variance rather than specific changes in the complexity of the signal. In addition, interpretation of changes in ApEn is obscured by its sensitivity to ectopy, whereas MKLT analysis, as our results demonstrate, is relatively unaffected by ectopy.25 Semantic analysis, which has been proposed for characterizing short sequences of cardiac cycles, can also be considered as a special case of MKLT in which a small number of features are explicitly modeled using a limited set of parameters.26 The method is appropriate for simple patterns; however, complex and individually variable disturbances would require an enormous number of descriptors. In contrast, MKLT has an advantage of learning complex, highly variable individual patterns without the limitation of explicit modeling. Using a method similar to MKLT, Ivanov et al8 showed that a set of wavelet coefficients provides a better general assessment of the cardiac cycle complexity than singlevalued techniques. Motivated by the complexity of cardiac cycle dynamics and the inability of any single index to represent multidimensional changes, we used a set of MKLT coefficients to track the dynamics of the series. However, the method of Ivanov et al8 gives a general assessment of signal complexity, whereas MKLT was applied here to detect and quantify the complexity (dimensionality) of the short-term changes. In contrast to the constant, empirically defined wavelet function and analytic scales in the method of Ivanov et al,8 the MKLT basis vectors are directly derived from each individual series and represent a “fingerprint” or characteristic steady-state pattern. This adaptive property of MKLT makes it uniquely sensitive to the changes in the series regardless of interindividual differences. The traditional Karhunen-Loeve transform (KLT) has long been used for analysis of electrocardiographic waveforms and their spatial and temporal distribution.27,28 There are, however, important differences between the traditional applications of KLT and MKLT analysis. First, the traditional KLT requires the investigated pattern, eg, the QRS complex, to be deterministic and already identified. In contrast, MKLT is “blind” to the shape and location of the characteristic pattern and does not require any prerequisite classification of the series of cardiac cycles. Second, in the traditional KLT, the resulting “typical” pattern resembles individual waveforms, and their relationship can be examined by visual inspection or correlation analysis. In MKLT, the characteristic pattern is complex and nondeterministic; this requires examination of the variances of MKLT coefficients. Third, the time windows in the traditional KLT analysis are constant and a priori defined, whereas in MKLT, the time windows are automatically adjusted to separate the segments with different properties. Multidimensional Rhythm Disturbances 711 Future Research The idea that the dynamics of cardiac cycles may reveal hidden instabilities that precede the onset of arrhythmias is not new.29 Still, most events are unheralded, which has led to the perception that the initiation of malignant arrhythmias is the immediate consequence of a random event such as a critically timed premature beat. Unexplained is why the premature depolarizations that appear to initiate VTA have not been shown to have the features that clearly distinguish them from the thousands of premature beats that occur daily in patients with heart disease but do not initiate arrhythmias.1 In contrast, we detected disturbances in CPCCL several hours before the onset of VTA. The gradual increase in the dimensionality of the disturbances (Figure 4) could reflect changes in the milieu that transform an otherwise benign premature depolarization to a malignant trigger and may explain why spontaneous arrhythmias usually occur without the signs of intense stimulation (multiple tightly coupled extrastimuli, acute ischemia, or high concentrations of arrhythmogenic drugs) that is required for artificial initiation of arrhythmias.1 The slow development and continuance of a proarrhythmic vulnerable state could also explain why sustained arrhythmias often occur in clusters.30 On the other hand, low-dimensional disturbances do not necessarily progress but may resolve, followed by resumption of a steady state. Certain modes of stimulation are shown to prevent arrhythmias, suggesting that restoration of the steady-state CPCCL reverses the progression of electrophysiological changes and prevents arrhythmia.31 Disturbances in CPCCL have also been reported before the onset of paroxysmal atrial fibrillation.32 Description of the time course and dimensionality of the disturbances that precede the onset of different arrhythmias might lead to the development of clinically useful predictive algorithms. In summary, hours before the onset of sustained VTAs, there is evidence for progressive changes in the core pattern of cardiac cycles. Better understanding of these events could lead to methods of predicting and preventing arrhythmias and sudden cardiac death. Acknowledgments This study was supported by Scientist Development Grant 0030248N from the American Heart Association, by NIH Specialized Center of Research Grant P50 HL52338, and by a grant from Guidant Corporation of St. Paul, Minn. 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Conventional heart rate variability analysis of ambulatory electrocardiographic recordings fails to predict imminent ventricular fibrillation. J Am Coll Cardiol. 1993;22:557–565. Ivanov PC, Amaral LAN, Goldberger AL, Havlin S, Rosenblum MG, Struzik ZR, Stanley HE. Multifractality in human heartbeat dynamics. Nature. 1999;399:461– 465. Shusterman V, Aysin B, Weiss R, Brode S, Gottipaty V, Schwartzman D, Anderson KP. Dynamics of the low frequency RR-interval oscillations preceding spontaneous ventricular tachycardia. Am Heart J. 2000;139: 126 –133. Albrecht P, Cohen RJ. Estimation o heart rate power spectrum bands from real-world data: dealing with ectopic beats and noisy data. Comput Cardiol. 1988;15:311–314. Berger RD, Akselrod S, Gordon D, Cohen RJ. An efficient algorithm for spectral analysis of heart rate variability. IEEE Trans Biomed Eng. 1986; 33:900 –904. Pincus SM, Keefe DL. Quantification of hormone pulsatility via an approximate entropy algorithm. 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Osaka M, Saitoh H, Sasabe N, Atarashi H, Katoh T, Hayakawa H, Cohen RJ. Changes in autonomic activity preceding onset of nonsustained ventricular tachycardia. Ann Noninvasive Electrocardiol. 1996;1:3–11. 19. Skinner JE, Pratt CM, Vybiral T. A reduction in the correlation dimension of heartbeat intervals precedes imminent ventricular fibrillation in human subjects. Am Heart J. 1993;125:731–743. 20. Mani V, Wu X, Wood MA, Ellenbogen KA, Hsia PW. Variation of spectral power immediately prior to spontaneous onset of ventricular tachycardia/ventricular fibrillation in implantable cardioverter defibrillator patients. J Cardiovasc Electrophysiol. 1999;10:1586 –1596. 21. Eftestøl T, Sunde K, Aase SO, Husøy JH, Steen PA. Predicting outcome of defibrillation by spectral characterization and nonparametric classification of ventricular fibrillation in patients with out-of-hospital cardiac arrest. Circulation. 2000;102:1523–1529. 22. Lombardi F, Mortara A. 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Shusterman V, Aysin B, Weiss R, Gottipaty V, Anderson KP, Schwartzman DS. Changes in the pattern of cardiac cycle dynamics predict initiation of paroxysmal atrial fibrillation. Pacing Clin Electrophysiol. 2000;23:668. Abstract. Multidimensional Rhythm Disturbances as a Precursor of Sustained Ventricular Tachyarrhythmias Vladimir Shusterman, Benhur Aysin, Kelley P. Anderson and Anna Beigel Downloaded from http://circres.ahajournals.org/ by guest on June 16, 2017 Circ Res. 2001;88:705-712; originally published online March 30, 2001; doi: 10.1161/hh0701.088770 Circulation Research is published by the American Heart Association, 7272 Greenville Avenue, Dallas, TX 75231 Copyright © 2001 American Heart Association, Inc. All rights reserved. Print ISSN: 0009-7330. Online ISSN: 1524-4571 The online version of this article, along with updated information and services, is located on the World Wide Web at: http://circres.ahajournals.org/content/88/7/705 Data Supplement (unedited) at: http://circres.ahajournals.org/content/suppl/2001/04/03/hh0701.088770.DC1 Permissions: Requests for permissions to reproduce figures, tables, or portions of articles originally published in Circulation Research can be obtained via RightsLink, a service of the Copyright Clearance Center, not the Editorial Office. Once the online version of the published article for which permission is being requested is located, click Request Permissions in the middle column of the Web page under Services. Further information about this process is available in the Permissions and Rights Question and Answer document. Reprints: Information about reprints can be found online at: http://www.lww.com/reprints Subscriptions: Information about subscribing to Circulation Research is online at: http://circres.ahajournals.org//subscriptions/ MS #2183 / R1, Online Data Supplement Online Data Supplement The series is initially sampled at unequally spaced time points that correspond to the times of occurrence of the R-peaks. Then the series is re-sampled at the equally spaced, 500-ms intervals. The reason for the re-sampling is to convert the series from the function of the interval number into a function of time for the subsequent Fourier analysis and the spectral frequency representation in Hertz. Although the spectral analysis could be performed using the original time series, as a function of the interval number, this would provide only “relative” frequencies in cycles / beat which cannot be converted into Hertz. The frequency representation in Hertz is important because the spectral power integrated over the specific frequency ranges indicates physiological activity of the sympathetic and parasympathetic nervous system. 1 In particular, the power in the 0.15 – 0.4 Hz range represents parasympathetic activity, whereas the power in the 0.04 – 0.15 Hz range represents both sympathetic and parasympathetic effects.2,3 We used a linear interpolation, because it does not affect the low frequency components, which contain most of the energy of the series and may only cause a small reduction of the highfrequency elements.4 As Figure 1 shows, the interpolated series has slightly reduced amplitudes of the high-frequency spikes, but the envelope (i.e. the low frequency components) is unchanged. Figure 2 is a magnified plot of the cardiac cycle length series shown in Figure 1 of the manuscript. Each panel in Figure 2 from the Online Data Supplement is an hour-long segment of the interbeat intervals. The corresponding ECG waveforms are shown in Figures 3-10.5 1 MS #2183 / R1, Online Data Supplement Thus, the first six MKLT-coefficients are obtained for each 5-min segment and then the time series is constructed for each MKLT-coefficient by concatenating the corresponding coefficients for all consecutive data segments. Formally, MKLT can be described as follows. Step I. Initially, we assumed that the core pattern of cardiac cycles has M unit-length vectors x i , i = 1,2,..., M , and the length of each vector is equal to N points, to generate a covariance matrix Cx from the outer products of vectors x i : Cx ≅ 1 M M ∑x x i T i , (4) i =1 where i=1,2,…M. Step II. From the covariance matrix, one can obtain eigenvectors ψ k, i=1,2,…N and corresponding eigenvalues λk , i=1,2,…N. The eigenvalues are arranged in decreasing order so that λ 1 ≥ λ 2 ≥.... ≥ λ N . Then, the MKLT coefficients ci are obtained by multiplying a matrix of the eigenvectors ψ i by vector x i . Signal partition. To achieve an efficient compression of the 24-hour series of cardiac cycles, the series of the first MKLT coefficient, which contains most of the information about the signal, was used for segmentation. The partition of the signal was initially done using constant-length windows, w1i , which were obtained by dividing the series into equally spaced segments. These segments are referred to as the first level (L=1) windows. At the next step, the sum of entropies (λ) in the first two adjacent windows, λ( w11 )+λ( w12 ) was compared with the entropy, λ( w12 ) in the second level (L=1+1) window, w12 , which was obtained by combining windows w11 and w12 , i.e. λ( w12 )=λ( w11 + w12 ). If the latter entropy was smaller than the sum λ( w11 )+λ( w12 ), then the two 4 MS #2183 / R1, Online Data Supplement windows, w11 and w12 , were combined to form a wider window, w12 . After that, the sum of entropies in the combined window λ( w12 ) and the next window, λ( w13 ), was compared with the entropy in the combined window λ( w12 + w13 ) and, again, the windows were combined if the latter entropy was smaller than the sum λ( w12 ) +λ( w13 ) and so on. The entropy of the series of MKLT coefficients, c Lj , can be computed as L H (ci ) li =−∑ where ciL 2 ciL,k k =0 ciL 2 li 2 log ciL,k c iL 2 , (5) 2 = ∑ ciL,k , li is the number of MKLT coefficients in a given window, L is k= 0 the level of partition, and i denotes different windows at that level. 6,7 A straightforward computation shows that minimization of entropy, H, can be achieved by minimizing the following functional li 2 2 λ ( ciL ) = − ∑ ciL,k log ciL,k , k =1 (6) When the signal is stationary, entropy is relatively independent from the window length and the sum of entropies in shorter windows is bigger than the entropy in the combined, wider window. So, the windows are combined during stationary segments. However, when the signal is nonstationary, the variance and, therefore, the entropy in the wider window become bigger than the sum of entropies in the smaller windows. In this case, the windows are not combined which results in the shorter window lengths. This process leads to an optimal partition of the signal into windows whose lengths depend on the signal properties such that longer windows correspond to the stationary segments whereas shorter windows correspond to nonstationary segments. 5 MS #2183 / R1, Online Data Supplement The following two examples illustrate the segmentation procedure. The first example shows a simulated periodic signal that was obtained using the equation x ( t ) = sin( 0.6 * π ) + sin( 0.3 * π ) (7) for the first 70 points. To simulate nonstationarity of the signal, the last 30 points were obtained by multiplying the right hand side of the equation (4) by 3 (Figure 11, Panel A). First, we calculated the functional, λ, in the adjacent first-level windows, w11 and w12 according to equation (6). In both examples, the length of the windows at the first level was 22 points. λ( w11 )=-.0602e 3 , λ( w12 )=-.0685e 3 . Then, λ in the combined ( w11 + w12 ) window was compared with λ( w11 + w12 ). The sensitivity of this technique to the changes in signal properties can be modified by multiplying λ( w11 + w12 ) by a constant k. Using our preliminary results, we found that k=.985 gave the best segmentation sensitivity for the series of cardiac cycles. Since kλ( w11 + w12 )=-.1400e 3 is less than λ( w11 )+λ( w12 )=-.0602e3-.0685e3=-.1287e 3 , the two windows were combined into a second-level window w12 = ( w11 + w12 ). Next, the sum λ( w12 ) +λ( w13 ) was compared with kλ( w12 + w13 ). Since kλ( w12 + w13 )= -.2553e 3 is less than λ( w12 ) +λ( w13 )=-.1421e 3 -.0702e 3 =-.2102e 3 , the two windows are combined into a third-level window w13 =( w12 + w13 ). At the next step, the sum λ( w13 ) +λ( w14 ) was compared with kλ( w13 + w14 ). This time, kλ( w13 + w14 )=-.9718e 3 is bigger than λ( w13 )+λ( w14 )=-.2592e 3 -.9322e 3 =-1.1914e 3 . Therefore, the two windows remain separated. Note an almost four-fold increase in kλ( w13 + w14 ) compared to the previous combinations of windows which reflects a change in the structure of the series. The rest of the computations for this series is shown in Table 1. The second example (Figure 11, Panel B) shows the series of the first MKLT 6 MS #2183 / R1, Online Data Supplement coefficient obtained from a 500-min series of cardiac cycles. The computation of adaptive windows for this series is shown in Table 2. Although we used Shannon’s entropy to partition the series, other criteria including Kullback information and Kalman filter could be applied. 8,9 These computationally demanding techniques are capable of separating the segments with distinct spectral characteristics. Combining the entropies of several MKLT coefficients also could provide a better segmentation. However, the fundamental properties of MKLT are not affected by the specifics of the segmentation procedure and variations in the partion of the series would not affect the main results. 7 MS #2183 / R1, Online Data Supplement Table 1. Computation of adaptive windows for the series in Figure 11, Panel A (*e3). 1 st window 2 nd window Combined window λ1 + λ2 Decision w1 λ1 w2 λ2 w11 -.0602 w12 -.0685 -.1287 w11 + w12 -.1400 Combine w12 -.1421 w13 -.0702 -.2123 w12 + w13 -.2553 Combine w13 -.2592 w14 -.9322 -1.1914 w13 + w14 -.9718 Separate w14 -.9322 w15 -.4043 -1.3365 w14 + w15 -1.3521 Combine w1 + w2 kλ(1+2) Table 2. Computation of adaptive windows for the series in Figure 11, Panel B (*e9). 1 st window 2 nd window Combined window λ1 + λ2 Decision w1 λ1 w2 λ2 w11 -.5668 w12 -1.2479 -1.8147 w11 + w12 -1.8418 Combine w12 -1.8698 w13 -2.1245 -3.9943 w12 + w13 -4.0500 Combine w13 -4.1117 w14 -1.5913 -5.7030 w13 + w14 -5.6941 Separate w14 -1.5913 w15 -1.8308 -3.4221 w14 + w15 -3.4414 Combine w1 + w2 8 kλ(1+2) MS #2183 / R1, Online Data Supplement Figure legends Figure 1. Comparison of the original and interpolated series of interbeat intervals. The top panel shows the 16-hour series of the interbeat intervals in blue and the interpolated series in red. The arrows indicate the times of the two, short segments that are shown in the lower panels at higher magnification. The interpolation slightly reduces the amplitudes of the high-frequency spikes but preserves the envelope (i.e. the low frequency components) that contain most of the energy of the signal. Figure 2. Magnified plot of the cardiac cycle length series shown in Figure 1 of the manuscript. Each panel is an hour-long segment of the interbeat intervals. Figures 3-10. The 5-min ECGs obtained from the same patient whose cardiac cycle length series is shown in Figure 2. The ECGs in each two consecutive figures are separated by 55 minintervals. Thus, the eight figures cover an eight-hour period before the onset of sustained ventricular tachyarrhythmia. Figure 11. Segmentation of a simulated signal (Panel A) and a time series of the first MKLTcoefficient from the 500-min sequence of cardiac cycles. 9 MS #2183 / R1, Online Data Supplement REFERENCES 1. 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. 1996;93:1043-1065. 2. Akselrod S, Gordon D, Ubel FA, Shannon DC, Barger AC, Cohen RJ. 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