Download Multidimensional Rhythm Disturbances as a Precursor of Sustained

Multidimensional Rhythm Disturbances as a Precursor of
Sustained Ventricular Tachyarrhythmias
Vladimir Shusterman, Benhur Aysin, Kelley P. Anderson, Anna Beigel
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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
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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
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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 3␴k threshold was established so that the probability of a random
occurrence of the CCLs exceeding 3␴k 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 (3␴k) 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 3␴k. An excursion of 1 or more
MKLT coefficients beyond the 3␴k threshold indicates disturbances
of CPCCL. The dimensionality (Dm) of the disturbances is defined as
the number of MKLT coefficients that simultaneously exceed the
corresponding 3␴k 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
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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
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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
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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).
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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).
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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.
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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
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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
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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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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
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Copyright © 2001 American Heart Association, Inc. All rights reserved.
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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
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