(Circulation. 1995;92:1825-1838.)
© 1995 American Heart Association, Inc.
Articles |
Spatial Features in Body-Surface Potential Maps Can Identify Patients With a History of Sustained Ventricular Tachycardia
From the Faculty of Medicine, Dalhousie University and Victoria General Hospital, Halifax, Nova Scotia, Canada, and the Faculty of Medicine, University of Calgary and Foothills Hospital (L.B.M., E.R.S.), Calgary, Alberta, Canada.
Correspondence to B. Milan Horá
ek, 4-01 Sir Charles Tupper
Medical Bldg, Department of Physiology and Biophysics, Dalhousie University,
Halifax, Nova Scotia, Canada B3H 4H7. E-mail
mhoracek@biophy.bp.dal.ca.
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Abstract |
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 Top Abstract IntroductionMethods Results Discussion References |
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Background Regional disparities of ventricular primary-repolarization properties contribute to an electrophysiological substrate for arrhythmias. Such disparities can be assessed from body-surface distributions of ECG QRST areas. Our objective was to isolate and test those features of QRST-area distributions that would be suitable for identifying patients at risk for life-threatening ventricular arrhythmias.
Methods and Results We recorded ECGs simultaneously from 120 leads during sinus rhythm for 204 patients taking no antiarrhythmic drugs: half had had sustained ventricular tachycardia (VT); the other half, a myocardial infarction but no history of VT. For each patient, we calculated the QRST area in each lead and, using Karhunen-Loeve (K-L) expansion, reduced these data to 16 coefficients (each relating to one spatial feature, an eigenvector, derived from the total set of 204 QRST-area maps). Using stepwise discriminant analysis, we selected feature subsets that best discriminated between the two groups, and we estimated by a bootstrap procedure using 1000 trials how these subsets would perform on a prospective patient population. The mean diagnostic performance of the classifier for 1000 randomly selected training sets (n=102 in each, with both groups equally represented) increased monotonically with the number of features used for classification. The initial trend for the corresponding test sets (n=102 in each) was the same but reversed when the number of features exceeded eight. For an optimal set of eight spatial features, the sensitivity and specificity of the classifier for detecting patients with VT in 1000 test sets were (mean±SD) 90.3±4.3% and 78.0±6.1%, and its positive and negative predictive accuracies were 80.7±4.2% and 89.2±4.2%, respectively. Use of QRS duration as a supplementary feature to eight K-L coefficients can, in the test sets, increase specificity to 80.9±5.4% and positive predictive accuracy to 82.8±3.9% compared with the results for the optimal number of eight K-L features alone.
Conclusions Multiple body-surface ECGs contain valuable spatial features that can identify the presence of an arrhythmogenic substrate in the myocardium of patients at risk for ventricular arrhythmias. Our results compare very favorably with those achieved by any other known test, invasive or noninvasive, for arrhythmogenicity.
Key Words: diagnosis • electrocardiography • mapping • tachycardia
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Introduction |
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TopAbstractIntroductionMethods Results Discussion References |
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One of the prerequisites for reducing the incidence of sudden cardiac death1 is the identification of patients at risk for sustained ventricular tachycardia (VT) or ventricular fibrillation (VF). The search for clinically practical determinants of risk has yielded many candidates, among them clinical variables,2 the results of electrophysiological testing,3 and a host of ECG variables derived from exercise testing,4 ambulatory monitoring,5 heart rate variability analysis,6 signal-averaged ECGs,7 8 and body-surface potential mapping (BSPM).9 10 11 Clinical and ECG variables are often used in combinations.4 6 12 13 14 15
Among a plethora of approaches to detecting patients at risk of life-threatening ventricular arrhythmias, signal-averaged ECGs and BSPM are of particular interest because they provide a means of assessing the electrophysiological and anatomic substrate that is a precondition for these malignant arrhythmias from body-surface ECGs recorded during sinus rhythm. Signal-averaged ECGs currently are restricted to analyzing only a limited bandwidth of frequencies, only in certain leads, and only during the late phase of ventricular depolarization.7 16 The value of BSPM, which is admittedly still a rather cumbersome procedure, is that it can provide clues as to which diagnostically valuable spectral, temporal, and spatial features can be extracted from data recorded at judiciously chosen thoracic sites during judiciously chosen phases of the entire cardiac cycle.
The purpose of our study was to test the hypothesis that spatial features extracted from the entire cardiac cycle of multiple body-surface ECGs recorded during sinus rhythm are markers identifying patients at risk for ventricular arrhythmias. The underlying assumption was that spatial distributions of ECG QRST areas reflect the presence of a substrate for ventricular arrhythmias.9 17 18 19 20 21 Patients known to be at risk for ventricular arrhythmias have been found to have more complex, multipolar distributions of QRST areas on the body surface than do healthy subjects9 10 22 23 24 25 ; however, multipolar QRST-area maps have also been noted in postinfarction patients who have no history of VT.10 26 Accordingly, we addressed the problem of differentiating the ECG features in patients with a history of sustained VT and in patients with a healed myocardial infarction (MI) and no history of clinical arrhythmias. We used an orthogonal-expansion method to reduce the amount of data (without sacrificing any diagnostic information) and to identify principal spatial patterns in body-surface maps of QRST areas. We then carefully selected only those patterns that distinguish patients prone to ventricular arrhythmias and used them for diagnostic classification.
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Methods |
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TopAbstractIntroductionMethods Results Discussion References |
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Patient Population
The study sample consisted of 102 patients who had had ventricular tachyarrhythmia (VT group) and 102 who had had an MI but no history of ventricular arrhythmias (non-VT group). Those in the VT group presented at the Foothills Hospital, Calgary, Alberta, with ECG-documented spontaneous sustained VT in the absence of a reversible cause, such as electrolyte imbalance, proarrhythmic drug effect, or an MI within the previous 2 weeks. Of these, 70 had a healed MI; 6 suffered from atherosclerotic heart disease, 7 from congestive cardiomyopathy, 1 from hypertrophic cardiomyopathy, 2 from right ventricular dysplasia, and 1 from hypertension; and 15 had no apparent heart disease. Electrophysiological studies that used a programmed stimulation protocol described elsewhere27 that was performed while patients were receiving no antiarrhythmic drug therapy substantiated the vulnerability to VT in all but 9% of these subjects (see Table 1
). Members of the non-VT group, who were studied at the
Victoria General Hospital, Halifax, Nova Scotia, had all suffered an MI
at least 2 weeks before but had no history of ventricular
arrhythmias. They were matched for age and sex to members of
the VT group. Acute MI was diagnosed in both institutions from a
history of ischemic-type cardiac pain, diagnostic
serum cardiac enzyme elevations (peak creatine kinase more than twice
the upper limit of normal), and diagnostic 12-lead ECG
changes. All subjects were informed of the study procedures, in
accordance with the ethical guidelines approved by each hospital's
ethics committee.
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Table 1
summarizes the pertinent
clinical features of the VT and non-VT
groups and of two subgroups of the VT group.
Body-Surface Potential Mapping
Patients in both medical
centers underwent BSPM according to the
same protocol. Electrodes were applied to the chest in vertical strips;
each electrode (In Vivo Metric Systems) had an 8-mm-diameter Ag-AgCl
sensor embedded in an epoxy housing with a 2-mm-deep gel cavity. The
BSPM lead array (illustrated elsewhere28 ) had a total of
120 leads: 3 limb leads and 117 unipolar chest leads (76 were placed
anteriorly and 41 on the back). We made recordings from all the
leads simultaneously for 15 consecutive seconds while the
subjects were supine and had a normal sinus rhythm. Acquisition systems
with identical characteristics29 30 were used in both
medical centers. Analog signals were amplified, filtered (band pass
from 0.025 to 125 Hz), multiplexed, and converted at a rate of 500
samples per second per channel using 12-bit samples (2.5-µV
resolution for the least-significant bit). The digitized data were then
transferred to a PDP-11/24 computer (Digital Equipment Corp) and
recorded on magnetic tape. All subsequent data processing was
carried out on a MicroVAX 3400 computer (Digital Equipment Corp). From
the 15-second recordings, individual complexes were identified
and sorted into families based on QRS morphology. The beats in the
largest family were averaged, and the baseline was corrected (using the
UP segment as a reference) to yield a single
representative complex for each lead; the peak-to-peak
noise level of the averaged signal was <5 µV. We plotted the
averaged complexes in a format that resembled the layout of the
electrodes on the chest and then carefully edited these plots,
eliminating leads that we considered too noisy or that contained
artifacts. The QRS onset and T-wave offset were determined for the
entire set of 120 leads by computer algorithms based on the spatial
velocity calculated from the three orthogonal vectorcardiographic leads
(derived as a subset of BSPM leads); in addition, we then checked and
edited (which was seldom necessary) these fiducial points in the
magnified plots of those three leads and stored the edited values. To
replace rejected or missing leads, we performed a three-dimensional
interpolation31 based on a numerical torso
model.32
Integral Maps
We calculated QRST areas (hereafter called QRST
integrals) for
each lead as time integrals of ECG signal from the QRS onset to the
T-wave offset. The integration was performed as the algebraic sum of
sampled potentials (in microvolts) within integration limits multiplied
by the sampling interval of 0.002 second. The values of the QRST
integrals were thus in microvolt-seconds. To depict the distribution of
these values, we plotted contour maps called QRST-integral
maps.33 These contour maps were drawn with contour levels
chosen to span a decade in seven logarithmic steps based on the
standard sequence 1.0, 1.5, 2.2, 3.3, 4.7, 6.8, and 10. We plotted only
seven contours from the larger extremum (maximum or minimum) down
toward zero; these were complemented by "mirror" contours of
opposite polarity. For example, if the maximum of a QRST-integral map
were 75 µV · s and the minimum were -50 µV · s,
the
contour of 68 µV · s would be plotted, with no counterpart of
opposite polarity, followed by pairs of contours ±47, ±33 . . .
±0.68 µV · s.
Data Reduction
We used the Karhunen-Loeve (K-L) transform to
reduce the
dimensionality of the input data consisting of an ensemble (x) of
n m-dimensional random vectors (where n=204 and
m=117), each representing the set of
QRST-integral values for one subject. An eigenvalue and eigenvector
analysis of the sample covariance matrix (C)
yielded a square matrix (T) of m eigenvectors and a diagonal
matrix (
) of eigenvalues, so that
 | (1) |
where TT denotes a transpose of T (see Reference 34). For each subject, denoted by the subscript i, the K-L transform was defined by the relation35
 | (2) |
which assigned an output vector of K-L coefficients (yi) to an input vector of QRST-integral measurements (xi). We truncated vectors of K-L coefficients to k terms (k<<m) and then reconstructed the distributions of QRST integrals for each subject by a reverse transformation.
To choose k, we plotted the estimated average root-mean-square error of reconstruction against the number of basis vectors, expressing information contained in the first k basis vectors as a percent of the trace of the covariance matrix.35 We plotted the k eigenvectors as eigenmaps representing the principal patterns of the QRST-integral distributions on the body surface35 and plotted the measured, reconstructed, and difference maps for each subject. We evaluated the errors associated with the reconstruction based on k eigenvectors by three quantitative error measures (the root-mean-square, relative, and peak errors) for each map; then we calculated the mean and SD for each of the error measures for the constituent diagnostic groups and the total data set; in addition, we identified worst-case errors for each error measure and each group.
We computed the nondipolar content of the QRST-integral maps for each subject as the percentage of the total signal energy that is cumulatively contributed by the fourth through the kth eigenvectors.9 24 Computations involved in the data-reduction stage were programmed in FORTRAN; these programs made use of the NAG library routines (Numerical Algorithms Group Ltd).
Feature Selection and Diagnostic
Classification
To select features that contain the diagnostic
information for classifying the two constituent groups, we calculated
significance levels for each of the K-L coefficients by means of a
Student's t test36 ; we considered
P<.05 significant. Furthermore, subsets of K-L coefficients
that contain the diagnostic information for classifying the
two constituent groups were selected by a stepwise discriminant
analysis36 ; both forward and backward selection
was used. For each set of selected features, linear discriminant
functions were calculated.36
We then thoroughly tested the
classification performance
associated with different subsets of features by using the bootstrap
method37 38 to estimate the classification statistics
that
can be expected on a prospective population of patients. The bootstrap
method was used without replacement; ie, one half of the cases of each
group were randomly assigned to a training set and the rest to a test
set; the linear discriminant function was then computed for this
particular training set and applied to the corresponding test set. The
linear discriminant function assigned each patient to either the VT or
non-VT class; because the class to which each patient actually belonged
was known, the 2x2 contingency table was produced in which patients
were classified as true-positive (TP), false-negative (FN),
false-positive (FP), or true-negative (TN). Five measures of
classification performance were then calculated: sensitivity
(SE), specificity (SP), diagnostic performance
(DP), positive predictive value/accuracy (PV+), and
negative predictive value/accuracy (PV-); the last two
measures depend on the prevalence of VT (
) in the total patient
sample as follows:
PV+(%)=100SE/[SE+(100-)(100-SP)]
and
PV-
(%)=100(100-)SP/[(100-)SP+(100-SE)].
We
repeated this procedure 1000 times and calculated from the resulting
data estimates of classification performance, expressed as
mean±SD for these five measures, for all training and test sets.
Finally, we wanted to establish whether the results of our
QRST-integral analysis are independent of the other
variables listed in Table 1. We assessed this by calculating
with
CORRELATIONS39 the correlation matrix with
associated probability values for all K-L coefficients and the other
variables. To find out how these added variables rank in terms
of their ability to discriminate between VT and non-VT patients, we
followed the same approach as in the rest of this study: we entered the
new variables into the pool of features with the K-L coefficients,
chose the best features from this pool using stepwise discriminant
analysis, calculated linear discriminant functions for each set
of selected features, and tested their classification
performance with the bootstrap method using 1000 trials.
To calculate
predictive accuracies for the detection of risk for VT/VF
that can be expected in the real world, incidence40 of
VT/VF in post-MI patients during the first year after the acute event
was substituted for .
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Results |
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TopAbstractIntroductionMethods Results Discussion References |
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We first compared the clinical features of the constituent groups (Table 1
) and found some significant intergroup differences.
Subjects
in the VT group had a poorer left ventricular function
(P<.000001), longer QRS duration (P<.00001),
longer QTc interval (P<.0001), and higher heart
rate during sinus rhythm (P<.001) than did subjects in the
non-VT group. Within the VT group, patients in the subgroup with a
prior MI had poorer left ventricular function
(P<.00001) than did the remaining patients, and they were
older (P<.01).
We then proceeded with the analysis of spatial features
extracted from the QRST-integral maps (Fig 1). This entire
pattern space, comprising
117 QRST-integral values for each of the 204 patients, was reduced to
k=16 principal patterns, which are plotted as eigenvector
maps in Fig 2. The choice of k was based on
the percent trace, which was 99% for the 16 highest eigenvalues. The
first three eigenvectors in Fig 2 show smooth bipolar
distributions,
each with different locations of extrema; the eigenvectors beyond the
third have more complex distributions with multiple extrema. The
original QRST-integral distributions were then represented
in terms of principal patterns and plotted. The reconstructed maps
maintained the important spatial features, such as the locations and
number of extrema, of the original measured maps. This was
substantiated quantitatively, as shown in Table 2, which
summarizes reconstruction errors for the total patient set and the
individual diagnostic groups.
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The root-mean-square and peak errors were similar in the VT and non-VT groups; however, the VT group had a significantly higher (P<.05) relative error than the non-VT group.
The focus of our efforts was diagnostic classification. The
first attempt at classifying the two constituent groups was based on
the index of nondipolar content. This index was (mean±SD)
13.1±9.7%
for the VT group and 12.9±10.2% for the non-VT group; the difference
between them was not statistically significant (P
.05).
Because the index of nondipolar content, which estimates the lumped
relative contribution of the higher-order eigenvectors to the
QRST-integral maps, did not perform well in our patient population, we
examined how individual eigenvector patterns contribute to
QRST-integral maps in each group of patients. Table 3
lists the means and SDs of the coefficients relative to the first 16
eigenvectors in the two diagnostic groups. Significant
differences (P<.05) corrected for multiple comparisons were
found between the values of K-L coefficients in the VT and non-VT
groups for the 6th, 4th, 13th, 5th, 1st, 2nd, and 11th eigenvectors (in
the order of significance levels). As is apparent from Fig 2,
the 6th
eigenvector features a cloverleaf pattern of alternating maxima and
minima centered in the precordial area; the 4th eigenvector has
a distinct precordial maximum-minimum pair superimposed on
another, more diffuse bipolar distribution; and the 13th eigenvector
features a cluster of six extrema of alternating polarity that surround
a central minimum, all in the precordial area. Thus, all three
patterns that best separate the VT and non-VT groups represent
the precordial features of the QRST-integral maps, and they
have a regular appearance, whereas the 10th, 12th, 14th, 15th, and 16th
eigenvectors have a random-distribution appearance.
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A stepwise linear discriminant analysis confirmed that the
spatial features with the best ability to discriminate between the VT
and non-VT patients were drawn from eigenmaps 6, 4, 13, 5, 1, 2, 11,
14, 10, 15, and 9 (in that order) depicted in Fig 2. The
results of the
forward-selection process are summarized in the left half of Table
4, which shows the order in which the K-L coefficients
were entered into the discriminant analysis. To double-check
this feature selection, we also performed backward selection; the right
half of Table 4 shows in which order the K-L coefficients were
removed
from the discriminant analysis.
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To obtain a rigorous estimate of the discriminating potential of
various subsets of features on a prospective population of VT and
non-VT patients, we used the bootstrap method to calculate the means
and SDs of five classification indexes for the increasing number of
features, which were added in the order selected by the stepwise linear
discriminant analysis. The patient population consisted of the
VT (n=102) and non-VT groups (n=102); randomly selected training
and
test sets had 102 patients each, with both groups equally
represented. Fig 3 shows the results of this
analysis, and results for subsets of 3, 7, 8, and 16 features
are tabulated in Table 5. Fig 3 shows the means
and SDs
of the classification indexes for both the training and test sets as a
function of the number of features. The percentage of correctly
classified patients (diagnostic performance) for
both the training sets and the test sets increased monotonically as the
number of features in the discriminant analysis increased from
1 to 8. A further increase in the number of features from 8 to 16
increased the percentage of correctly classified patients for the
training sets, but there was a deterioration of diagnostic
performance for the test sets primarily because of decreased
sensitivity. Table 5 shows that classification based on the
discriminant analysis using 7 or 8 features was optimal (values
shown in boldface) for our particular data set. For a set of eight
features (y6, y4,
y13, y5, y1,
y2, y11, and y14),
the sensitivity and specificity of the classifier for detecting
patients with VT in the test sets were 90.3±4.3% and 78.0±6.1%,
respectively, and its positive and negative predictive accuracies were
80.7±4.2% and 89.2±4.2%, respectively.
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, mean of the
training sets (n=102, in which the two groups were equally
represented); 
, corresponding values for the test
sets of the remaining patients (n=102); and vertical bars,
SD.
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We then applied the same procedure of feature selection and feature
subset evaluation by the bootstrap method to the subpopulation of 172
post-MI patients with VT (n=70) and without VT (n=102); these
subgroups
are characterized in Table 1. Fig 4 shows the
results of
this analysis; results for subsets of 3, 6, 10, and 16 features
are tabulated in Table 6. The mean
diagnostic performance of the classifier for both
training and test sets (n=86 in each, with the VT and non-VT groups
represented by 35 and 51 patients, respectively) increased
monotonically until the number of features reached 10, and then it
declined. For an optimal subset of 10 features (y6,
y4, y2, y1,
y13, y5, y15,
y11, y14, and y9),
the sensitivity and specificity of the classifier for detecting
patients with VT in test sets were 90.0±5.2% and 82.4±5.3%,
respectively, and its positive and negative predictive accuracies were
83.9±4.0% and 89.3±4.9%, respectively. The latter two indexes
were
calculated for the VT prevalence of 50% in the post-MI population
tested to obtain predictive accuracies comparable to those in the
balanced sample. The prevalence of VT did not enter into the
calculation of the predictive accuracies for groups of equal size;
however, we had to consider it for the population of post-MI patients,
in which there is an unequal number of patients with and without VT. We
also calculated positive and negative predictive accuracies for the
detection of risk for VT/VF that can be expected in the real world,
assuming that the incidence of VT/VF in post-MI patients during the
first year after acute MI is approximately 5% (see Fig 4 and
Table 6).
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To test for possible differences in the arrhythmogenic substrate within
the VT group (n=102), we again applied the same procedure of feature
selection and feature subset evaluation by the bootstrap method to the
two subgroups of the entire VT group (characterized in Table
1). Fig 5 shows the bootstrap estimates of
classification
performance in a prospective patient population of a classifier
for distinguishing VT patients who had had a prior MI (n=70) from those
VT patients who had some other etiology (n=32) for an increasing number
of diagnostic features used in the classification. The
training and test sets were randomly selected (n=51 in each, with the
subgroups of VT patients represented by 35 and 16 patients,
respectively). It is apparent from Fig 5 that the total
percentage of
correctly classified patients and both predictive accuracies approach
50% (with the predictive accuracies calculated for the assumed
prevalence of VT patients in the total patient population being 50%).
This result demonstrates that the two subgroups of VT patients are
virtually indistinguishable.
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Finally, having found significant differences between the VT and non-VT
groups with respect to left ventricular ejection fraction
(LVEF), QRS duration, QTc interval, and heart rate during
sinus rhythm, we wanted to establish whether the results of our
QRST-integral analysis are independent of these other
variables. By calculating a complete correlation matrix of all K-L
coefficients and all variables listed in Table 1, we found that
the
variables correlate among themselves and correlate significantly
with some K-L coefficients (eg, LVEF correlates with
y1, y2, y7,
and y4; QRS duration correlates with y2,
y1, y4, and y7).
Using the same approach as in the rest of this study, we found that use
of LVEF as a supplementary feature with eight K-L coefficients
increases (in the test sets) mean specificity by 5.9% and mean
positive-predictive accuracy by 3.7%, but sensitivity drops by 2.5%
and negative-predictive accuracy drops by 1.7% compared with the
results for the optimal number of eight K-L features alone. Because
LVEF was not available for all 204 patients, both analyses,
that based on K-L features only and that based on the enlarged pool of
features, were performed on the reduced population of 149 patients.
Interestingly, use of QRS duration as a supplementary feature to eight
K-L coefficients can increase (in the test sets) specificity by 2.9%
and positive-predictive accuracy by 2.1%, whereas sensitivity and
negative-predictive accuracy drop only very slightly compared with the
results for the optimal number of eight K-L features alone (Table
5).
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Discussion |
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TopAbstractIntroductionMethods Results Discussion References |
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This study tested the hypothesis that patients at risk for ventricular arrhythmias can be identified noninvasively by means of spatial features extracted from body-surface ECG maps recorded during sinus rhythm. The underlying assumption was that spatial distributions of QRST integrals (ie, net areas of ECGs within the limits of the QT interval) reflect the presence of an electrophysiological and anatomic substrate for ventricular arrhythmias.19 21 We demonstrated that the QRST-integral distributions in patients prone to VT for various reasons differ quantitatively from those in patients who have had an MI but have no history of arrhythmias. We also showed that these groups of patients can be distinguished on the basis of such differences; a combination of spatial features is required to do so.
Systematic Selection of Spatial Features
In view of the
relatively small sample analyzed, it was
important for us to use a correspondingly small number of
parameters to describe each patient. This requirement
called for a drastic reduction of input data, which we achieved in
three major steps. The first was the time integration of ECGs, which
reduced for each lead several hundred samples into just one
QRST-integral value. The second was the transformation of the QRST
integrals for each patient into an orthogonal space by means of the K-L
transform. This procedure effectively eliminated the redundancy by
representing input data in terms of uncorrelated spatial
features (eigenvectors) and reducing 117 QRST-integral values into 16
K-L coefficients, each relating to one feature. The third consisted of
feature selection in which we used stepwise linear discriminant
analysis to isolate those features that had the best
discriminating potential. This systematic extraction of features
contrasts with, for instance, an ad hoc imposition of cutoff
frequencies in the spectral analysis of signal-averaged
ECGs.
The K-L transform, a mathematically sound method that allows data reduction without loss of diagnostic information, has been used in other ECG studies.9 24 35 41 Diagnostic classification based on features derived by means of the K-L transform from QRST-integral maps distinguished patients with ventricular arrhythmias from healthy subjects9 ; moreover, the 5-year follow-up study of post-MI patients indicated that this type of analysis can potentially detect patients at risk of sudden cardiac death from ECG body-surface maps recorded 7 to 14 days after infarction.9 42 Accordingly, the aim of the present study was to explore this approach by performing a larger-scale study and by refining the statistical analysis.
In concurrence with other
studies,24 35 we observed that
the percent trace, which is the measure of the adequacy of signal
representation, plateaued at 9 to 12 eigenvectors and that 99%
of the variability in the covariance matrix was accounted
for by 16 eigenvectors. We decided to include 16 eigenvectors in our
analysis—compared with, eg, the 9 eigenvectors used by De
Ambroggi et al24 or the 12 eigenvectors used by Lux et
al35 —in an attempt to keep the diagnostic
information that the eigenvectors beyond the 9th may contain, even
though they contribute only very small percentages to the
covariance matrix. The complexity of the spatial features
of the QRST-integral maps for the patient population included in this
study (Fig 1) was noted
previously.9 10 22 Our inclusion
of 16 eigenvectors assured that these complex features were
represented adequately. Table 3 shows that K-L coefficients
relating to the spatial features represented by 2
eigenvectors beyond the 9th differed significantly between the VT and
non-VT groups. Likewise, as is apparent from Table 4, the
forward-selection process of the stepwise linear discriminant
analysis included 3 eigenvectors beyond the 9th among the best
eight features for classification.
The spatial features represented by
the first 3
eigenvectors were dipolar (ie, they had one maximum and one minimum),
and those represented by the 4th to 16th eigenvectors were
nondipolar (Fig 2). This is consistent with the findings of
previous studies.24 35 Our relative errors of
reconstruction (Table 2) also compared favorably with those of
other
studies.35 41 This indicated that the K-L expansion
accurately represented the salient features of the maps,
which was a prerequisite to the statistical analysis of the
data.43
Rationale for Using Spatial Features as Markers of Vulnerability to
Ventricular Arrhythmias
The spatial features of the ECG body-surface
potential
distributions during both the depolarization and the repolarization of
ventricular myocardium are likely to reflect an
anatomic and electrophysiological substrate
for sustained ventricular
arrhythmias.7 44 We chose to assess the spatial
distribution of ventricular primary repolarization
properties whose disparities are known to be associated with
arrhythmogenesis.20 There are both
experimental18 and theoretical17 bases for
relating the QRST integral in ECGs to primary repolarization
properties. The distributions of QRST integrals on the cardiac surface
were related to a ventricular fibrillation
threshold19 and to vulnerability for
ventricular arrhythmias.21 The
body-surface mapping of QRST integrals provides a noninvasive
assessment of ventricular primary repolarization
properties.9 10 22 23 24 25
Current approaches to the analysis of signal-averaged ECGs use only X, Y, and Z leads. However, several studies indicated that the spatial distributions of abnormalities detected in body-surface ECGs provide valuable information regarding a patient's vulnerability to sustained ventricular arrhythmias. Berbari et al45 analyzed ECGs recorded from a 24-lead precordial array and reported that X, Y, and Z leads do not provide sufficient information for accurate measurement of the total QRS duration (including late potentials). Faugère et al,46 who analyzed high-pass filtered ECGs from 63 body-surface leads, noted that maps provide additional information that may be useful for identifying a mechanism of arrhythmia. Lacroix et al47 analyzed spatial distributions of the late ventricular potentials by comparing high-pass filtered ECGs from 63 body-surface leads with endocardial and epicardial recordings in patients undergoing surgery for VT and showed a close spatial correlation between the location and amplitude of extrema in intracardiac and body-surface potential distributions. Shibata et al,48 using 87-lead body-surface mapping of signal-averaged ECGs, analyzed the terminal portion of the QRS complex over a limited bandwidth of frequencies and isolated variables for the prediction of VT in post-MI patients. Ho et al49 achieved better sensitivity of diagnostic classification without loss of specificity when they used a 28-lead "optimal" array than when they used only X, Y, and Z leads. Arthur et al50 and Kavesh et al16 are proponents of a combined spatial and spectral analysis of the entire cardiac cycle.
Diagnostic Classification Based on Spatial
Features
We first tested the nondipolar content of QRST-integral
maps9 51 as a single lumped measure reflecting the
complexity of the map. Our method of calculating the nondipolar content
was the same as that used by Abildskov et al9 ; we are
aware of but did not explore alternative techniques, eg, subtraction of
body-surface distribution that is accounted for by a single equivalent
dipole.51 52 Our results showed considerable overlap
of
nondipolar content between our patient groups, and the ability to
discriminate between them based on this index was poor. This
observation of the present study was not previously well
established; in fact, previous studies of the nondipolar content of
QRST-integral maps9 42 51 obtained
results that appeared
very encouraging. For instance, the results of a follow-up study of
post-MI patients by Vincent et al42 (also reported in
Reference 9) showed that the mean nondipolar content of QRST-integral
maps obtained 7 to 14 days after infarction9 was
16.8±11.4% in the group of eventual 5-year survivors (n=24) and
38.0±11.0% in the nonsurvivor group (n=8). Likewise, Tsunakawa
et
al51 reported "nondipolar residues" of
22.7±6.7%
in post-MI patients without VT (n=29), 21.2±7.5% in patients who
had
VT only in the acute phase of MI (n=13), and 34.5±10.3% in
patients
tested >10 days after MI who had VT (n=17); a residue 25%
distinguished the last group from non-VT patients, with a sensitivity
of 82% and a specificity of 71%. Although our study in larger groups
could not confirm that the lumped nondipolarity index is a
robust-enough measure of the propensity to VT, it did confirm that the
quantitative assessment of the nondipolar content of QRST-integral maps
by other means yields valuable information for identifying such a
propensity.
Our diagnostic classification was based on the linear
discriminant analysis that used a combination of selected
spatial features extracted by systematic data reduction. The two
spatial features chosen by the stepwise linear discriminant
analysis as having the best discriminating potential
(y6 and y4 in Tables 5 and
6) were nondipolar.
This indicates that specific nondipolar spatial features differ between
the two groups and that the combination of these features has a
considerable discriminating potential (one that the nondipolarity index
uses less effectively by lumping all nondipolar features together). De
Ambroggi et al24 reported differences for specific
spatial features between a healthy control group and a group of
patients with long-QT syndrome, but they did not exploit them in a
discriminant analysis. The data in our Table 3 show that seven
coefficients (y6, y4,
y13, y5, y1,
y2, and y11) differed significantly
between the two groups; De Ambroggi et al24 found
significant differences only in y3 and y6.
When
we increased the number of features used in the discriminant
analysis, the diagnostic performance in the
training sets steadily improved until it reached a saturation level
(Figs 3 and 4), whereas in the test sets it
peaked for the classifier
based on the optimal number of features and then declined. The optimal
number of features was higher than that predicted by Kozmann et
al.53 Being aware of the results of these authors'
meta-analysis, we focused on the problem of the most efficient
data reduction with minimal loss of diagnostic information
and then carefully selected only those features that carried the
largest amount of diagnostic information (in
contradistinction to information necessary to merely reconstruct the
measured data). We expected that three features would be the largest
permissible number for our training and test set groups with 51
patients, which was a conservative but less pessimistic estimate than
that of Kozmann et al.53 One of the principal achievements
of this study was our demonstration that as many as eight orthogonal
features can be profitably used for a patient sample such as ours.
Diagnostic Classification Based on Spatial and
Supplementary Features
We also explored how other features, namely
LVEF, QRS
duration, QTc interval, and heart rate during sinus rhythm
(which were all significantly different in the VT and non-VT groups),
compared with the spatial features in terms of their ability to
discriminate between VT and non-VT patients. Only LVEF and QRS duration
ranked among the top 10 features: LVEF was the first feature selected,
and with LVEF removed, QRS duration was the second. This
analysis confirmed the status of LVEF as a powerful single
predictor of arrhythmic
events,2 12 15 54 and showed,
in
agreement with other studies,55 56 that temporal ECG
features (QRS duration and QTc interval) contain valuable
diagnostic information. However, although uncorrelated
spatial features (K-L coefficients) can be effectively added to enhance
the diagnostic performance of classifiers, LVEF,
QRS duration, QTc interval, and heart rate are so strongly
correlated among themselves that one of them suffices to supplement
diagnostic information provided by spatial features. When
available, LVEF is the best supplementary feature; using it can
increase specificity and positive-predictive accuracy compared with the
results for the optimal number of eight K-L features alone, albeit at
the cost of decreased sensitivity and negative-predictive
accuracy. QRS duration performs nearly as well as LVEF. We
found that using QRS duration as a supplementary feature to eight
K-L coefficients can increase specificity and positive-predictive
accuracy compared with the results for the optimal number of eight K-L
features alone. This welcome improvement of classification
performance can be obtained at no extra cost; thus, QRS
duration is a valuable supplementary feature.
Predictive Capabilities of the Classification
Estimates of
the classification performance of a given
classifier on a prospective population of patients can be misleadingly
optimistic when its predictive capabilities are not tested
properly.37 57 One must rigorously establish whether
a
classifier reflects just those differences between classes that are
specific to the particular sample from which it was derived or whether
it reflects differences inherent in the diagnostic classes
per se. We thoroughly evaluated the ability to classify future
observations for each of 16 subsets of selected features. Our 1000
bootstrap trials with randomized training and test sets yielded indexes
of classification performance that indicated how each subset of
features was likely to perform on a prospective population of patients.
The SD of these indexes for the training and test sets (Tables
5 and 6)
provides a measure of the variability that may be expected in
real-world applications of the classification procedure. The expected
errors in future classifications can be estimated from differences in
the diagnostic indexes for the training and test
sets.37 38 These differences appear to be very
stable,
particularly for sensitivity percentages, as can be judged from Figs
3 and 4.
Only a few other studies have reported estimated errors in future classification performance. One of those, which involved a linear regression model that incorporates both clinical variables and variables derived by signal averaging from the late QRS complex of the ECG,12 estimated sensitivity and specificity figures by the cross-validation method, which gives realistic values for the measures of classification performance in any prospective population of patients. This model achieved a sensitivity of 91% (with no SD or confidence limits reported) for predicting programmed-stimulation outcomes in a patient population similar to ours; however, it was typical for the signal-averaging of the late QRS complex that this high sensitivity was accompanied by a low specificity of 59%.
Conclusions
The results of this study indicate that spatial
features extracted
from QRST-integral maps provide diagnostic information from
which a patient's vulnerability to VT can be predicted. The
appropriately weighted combination of these features appears to
accurately reflect the
electrophysiological-anatomic substrate for
ventricular arrhythmias in members of the two
distinct diagnostic groups. We have therefore provided
empirical statistical evidence linking alterations in primary
repolarization properties measured from ECG QRST-integral maps and the
risk for sustained ventricular arrhythmias. The
bootstrap procedure provided estimates of the expected classification
performance of our test on a prospective population of
patients. The sensitivity for detecting patients at risk for VT can be
expected to be 
90%, and it should be accompanied by a specificity
of 80%. These results compare favorably with the
diagnostic performance achieved by
electrophysiological testing, but our test
is noninvasive and involves no additional risk to the patient.
Prospective assessments and long-term follow-up studies will ultimately
determine the clinical effectiveness of our classification
approach.
|
Acknowledgments |
|---|
This study was supported in part by grants from the Medical Research Council of Canada (MA-10413 and PG-11188), the Heart and Stroke Foundations of Nova Scotia and Alberta, the Whitaker Foundation, and the Alberta Heritage Foundation for Medical Research (AHFMR). Dr Mitchell received support from AHFMR as a medical scholar. We greatly appreciate the technical assistance of Brian Hoyt, Paul MacInnis, and Robert Potter; the painstaking collection of clinical data by Linda Ellis and Helen Tremayne, in the Foothills Hospital in Calgary and in the Victoria General Hospital in Halifax, respectively; and the editorial assistance of Peter King.
Received December 13, 1994; revision received April 19, 1995; accepted April 19, 1995.
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References |
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