Multidimensional Rhythm Disturbances as a Precursor of Sustained Ventricular Tachyarrhythmias
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.
Although 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 3 4 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 Karhunen-Loeve 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
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 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: ≥30 seconds; rate: ≥100 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.
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-low-frequency power (VLFP), 0.01 to 0.04 Hz. The ratio of low- to high-frequency power (LFP/HFP) was also calculated.
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 α-1 and α-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 (α-1) and those that were longer than 11 beats (α-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 (ςk). A 3ςk threshold was established so that the probability of a random occurrence of the CCLs exceeding 3ςk 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 (3ςk) 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 3ςk. An excursion of 1 or more MKLT coefficients beyond the 3ςk threshold indicates disturbances of CPCCL. The dimensionality (Dm) of the disturbances is defined as the number of MKLT coefficients that simultaneously exceed the corresponding 3ςk 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.
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 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 (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 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 oscillations. 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 specificity 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 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⇓).
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 3 4 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 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 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-low-frequency 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 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 single-valued 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.
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.
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.
Original received May 30, 2000; resubmission received December 13, 2000; revised resubmission received February 14, 2001; accepted February 14, 2001.
- © 2001 American Heart Association, Inc.
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