# Spatial Features in Body-Surface Potential Maps Can Identify Patients With a History of Sustained Ventricular Tachycardia

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## Abstract

*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.

One of the prerequisites for reducing the incidence of sudden cardiac death^{1} 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 subjects^{9} ^{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.

## Methods

### 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 elsewhere^{27} 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.

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 elsewhere^{28} ) 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 characteristics^{29} ^{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 interpolation^{31} 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 (Λ) of eigenvalues, so that

where T^{T} denotes a transpose of T (see Reference 34). For each subject, denoted by the subscript *i*, the K-L transform was defined by the relation^{35}

which assigned an output vector of K-L coefficients (y_{i}) to an input vector of QRST-integral measurements (x_{i}). 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 surface^{35} 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 *k*th 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* test^{36} ; 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 analysis^{36} ; 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 method^{37} ^{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 2×2 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 (π) in the total patient sample as follows: PV^{+}(%)=100πSE/[πSE+(100−π)(100−SP)] and PV^{−} (%)=100(100−π)SP/[(100−π)SP+π(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 correlations^{39} 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, incidence^{40} of VT/VF in post-MI patients during the first year after the acute event was substituted for π.

## Results

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 QT_{c} 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.

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.

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.

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 (y_{6}, y_{4}, y_{13}, y_{5}, y_{1}, y_{2}, y_{11}, and y_{14}), 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.

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 (y_{6}, y_{4}, y_{2}, y_{1}, y_{13}, y_{5}, y_{15}, y_{11}, y_{14}, and y_{9}), 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⇓).

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.

Finally, having found significant differences between the VT and non-VT groups with respect to left ventricular ejection fraction (LVEF), QRS duration, QT_{c} 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 y_{1}, y_{2}, y_{7}, and y_{4}; QRS duration correlates with y_{2}, y_{1}, y_{4}, and y_{7}). 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⇑).

## Discussion

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 subjects^{9} ; 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 al^{24} or the 12 eigenvectors used by Lux et al^{35} —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 experimental^{18} and theoretical^{17} 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 threshold^{19} 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 al^{45} 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 al^{47} 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 al^{49} 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 al^{50} and Kavesh et al^{16} 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 maps^{9} ^{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 al^{9} ; 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 maps^{9} ^{42} ^{51} obtained results that appeared very encouraging. For instance, the results of a follow-up study of post-MI patients by Vincent et al^{42} (also reported in Reference 9) showed that the mean nondipolar content of QRST-integral maps obtained 7 to 14 days after infarction^{9} 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 al^{51} 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 (y_{6} and y_{4} 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 al^{24} 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 (y_{6}, y_{4}, y_{13}, y_{5}, y_{1}, y_{2}, and y_{11}) differed significantly between the two groups; De Ambroggi et al^{24} found significant differences only in y_{3} and y_{6}.

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, QT_{c} 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 QT_{c} 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, QT_{c} 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.

- Copyright © 1995 by American Heart Association

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- Spatial Features in Body-Surface Potential Maps Can Identify Patients With a History of Sustained Ventricular TachycardiaCheryl L. Hubley-Kozey, L. Brent Mitchell, Martin J. Gardner, James W. Warren, Cindy J. Penney, Eldon R. Smith and B. Milan HorácekCirculation. 1995;92:1825-1838, originally published October 1, 1995https://doi.org/10.1161/01.CIR.92.7.1825
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- Spatial Features in Body-Surface Potential Maps Can Identify Patients With a History of Sustained Ventricular TachycardiaCheryl L. Hubley-Kozey, L. Brent Mitchell, Martin J. Gardner, James W. Warren, Cindy J. Penney, Eldon R. Smith and B. Milan HorácekCirculation. 1995;92:1825-1838, originally published October 1, 1995https://doi.org/10.1161/01.CIR.92.7.1825