Optimal lead subsets for reconstruction of QRS and ST-T in 35-lead precordial maps

METHODS

Optimal lead Subsets for Reconstruction of QRSand ST-T in 354ead Precordial Maps CHRISTOPHER D. McMANUS, MA, ALAN S. BERSON, PhD, JORGE C. RIOS, MD, EMIGDIO A. LOPEZ, MD, and HUBERT V. PIPBERGER, MD

Precordiai maps have been used for some 15 years to estimate the extent of myocardiai injury in patients with acute anterior or lateral wail infarction. Estimates have been based on various QRS- and ST-l-derived parameters, including amplitude sum of ST elevations. Application of the electrodes, commonly 35, is cumbersome and time-consuming with the crlticaiiy iii. A subset of 5 or 7 selected leads can be applied instead, and the remaining leads calculated from that subset with minimal loss of QRS and ST-T information. Maps were recorded from 100 patients within 72 hours of onset of anterior or lateral Infarct. Optimal lead subsets for QRS and ST-T feature extraction were found by the sequential selection method of Lux. Subsets numbering between 2 and 15 leads were derived, with their

A

new electrocardiographic technique to estimate the size of anterior wall myocardial infarcts was introduced in 1971 by Maroko,’ Reid2 and their co-workers. Arrays of electrodes are applied to the precordial area. The degree of ST-segment elevation in these leads is interpreted as an indicator for the extent of myocardial injury. In patients with acute myocardial infarction,

From the Veterans Administration Medical Center, Washington, DC, and The George Washington University School of Medicine, Washington, DC. This study was supported by the Medical Research Service of the Veterans Administration and by research grant HL 23715 from the National Heart, Lung, and Blood Institute, National Institutes of Health, Bethesda, Maryland. Manuscript received August 4, 1987; revised manuscript received and accepted December 17.1987. Dr. Berson’s present address: National Heart, Lung, and Blood Institute, National Institutes of Health, Bethesda, Maryland. Address for reprints: H.V. Pipberger, MD, Department of Computer Medicine, The George Washington University School of Medicine, 2300 K Street, Northwest, Washington, DC 20037.

lead-transform coefi icients. Measures to estimate goodness of fit for reconstructed leads included correlations, error-to-signal ratios and root-meansquare errors. These measures were calculated separately over the QRS and ST-T complexes. Reconstructions from a ‘I-lead subset had a mean 0.92 correlation with ST-T in the original leads and root-mean-square error of only 0.04 mV. Sum of ST elevation differed by only 2% between original leads and reconstructlons based on 5 or more leads. To confirm repeatability, lead-transform coefficients were also calculated from a training popuiation of 50 patients and applied to the maps of the other 50. (Am J Cardioi 1988;81:885-890)

serial precordial maps have also often been used to estimate increases or decreases of the injured myocardial area. Problems with the underlying assumptions have been reviewed in detail by Holland and Brooks.3 Nevertheless, the simplicity of the method and its noninvasive nature have led to its acceptance as a tool to estimate infarct size and to evaluate therapeutic interventions. In recent years, the number of leads was standardized to 35, based on the suggestion of Maroko et al4 Application of large arrays of electrodes over the precordium is cumbersome and time-consuming. Past studies suggest that the information in precordial maps is contained in subsets of many fewer leads, since neighboring leads contain much redundant information. Akiyama et al5 compared ST findings in precordial maps with those seen in Frank orthogonal &lead recordings. A correlation of 0.818 was found between maps and the Frank leads and the latter were considered adequate for ST-segment studies. In dog experiments, Foerster et al6 found an even higher correlation between ST changes in precordial maps and orthogo005

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nal leads (r = 0.921). These high correlations confirm more basic studies on the “dipolar” behavior of ST and T potentials7s8 In contrast to ST-T complexes, QRS potential distributions have not followed simple dipolar patterns in studies based on total body surface maps. Several precordial mapping studiesgr10have used QRS-derived parameters to estimate infarct size; thus, any study on lead reduction must also consider the QRS complex. We obtained complete precordial maps from patients with acute anterior and lateral infarcts, and applied data reduction techniques in order to identify a small subset of leads that would allow reconstruction of the QRS and ST-T complexes of the original 35 leads. Once such a subset has been identified from a sufficiently large base, only a small number of electrodes need to be applied to future patients with acute infarcts to derive full precordial maps.

Methods Patients with acute anterior or anterolateral infarcts were selected by staff physicians in the coronary care units of George Washington University Hospital, Washington, DC, and Brigham and Women’s Hospital, Boston, Massachusetts. Patients in this study from the latter hospital were selected from subjects in the Multicenter Investigation of the Limitation of Infarct Size study.11 Only patients with anterior or anterolateral infarcts were included because precordial mapping is thought to provide a measure of myocardial ischemia and injury of the myocardium underlying the anterior and lateral chest wall. Diagnosis was based on clinical history, enzyme elevations and acute ST elevations in anterior and lateral precordial leads of the standard l&lead electrocardiogram. Informed consent was obtained from patients and their attending physicians. Patients with other conditions that lead to ST elevations were excluded. The first record was taken as soon as possible after admission to the coronary care units, because ST abnormalities subside in some patients relatively soon after the acute event. Patients who did not exhibit ST abnormalities on admission were excluded from further study. The recording procedure was reduced to less than 15 minutes by use of a flexible plastic sheet with 35 holes set in 5 rows for the electrodes. Distances between electrodes were set to the specifications of Maroko et al4 The area covered by the precordial map extends from the left midaxillary line to a vertical line to the right of the sternum corresponding to the position of the conventional lead V1. In some patients the electrodes consisted of small disks of lithium chlorideimpregnated balsa wood cemented to the silver/silver-chloride surface of Becton Dickinson-type electrodes, The contact of the balsa wood with the skin eliminates the need for electrode paste, which usually prolongs and complicates the recording procedure.12 Maps were recorded using model 2001 mobile carts (Instruments for Cardiac Research). Cart features include: 500 sample/s recording and storage of 12 simultaneous potentials on magnetic tape cassette; input impedance from each patient lead to ground and be-

tween any z leads >50 megohms; right leg lead used as driven ground; leakage currents
If T represents the transformation that optimally estimates P2 from PI, then the mean-squared error J between the original and estimated lead values is minimized if T = K’12K;:. (21 The method of Lux secondly develops a recursive algorithm for selecting the m lead locations to derive the remaining leads with least error, for any number m. From equation 2, the mean-squared estimation error J due to the transformation T is: J = tr(K) - tr(Kil) - tr(K’12KiiK12) = tr(K) - tr(K;:L1& (3) where tr is the matrix trace operator and LI = KIIKII + KI&‘w (41

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TABLE I Mean Values of Goodness of Fit Measures to Assess Performance of Different Numbers of Optimal Leads for Reconstructing 35-Lead Maps (Optimal Leads Were Selected Separately for QRS and ST-T Complexes) Leads

2

3

5

7

9

12

15

Frank 3

Standard 12

QRS reconstruction Correlation coefficient Root-mean-square error (mV) Error-to-signal ratio

0.81 0.23 0.22

0.89 0.18 0.11

0.94 0.12 0.06

0.95 0.10 0.04

0.96 0.10 0.03

0.97 0.08 0.02

0.97 0.08 0.02

0.80 0.23 0.37

0.85 0.19 0.19

ST-T reconstruction Correlation coefficient Root-mean-square error (mV) Error-to-siqnal ratio

0.83 0.06 0.18

0.88 0.05 0.12

0.90 0.04 0.07

0.92 0.04 0.06

0.92 0.03 0.05

0.94 0.03 0.03

0.94 0.03 0.03

0.80 0.07 0.35

0.82 0.08 0.20

Since tr(K) cannot be changed, J is minimized when we maximize the “information index” I = tr(KiiL11). If the lead set P1 is a single site j, then K;: = l/SF Ln = ZiSfS+fj, and Ii = tr(K;:L11) = Nisi42ii, where si and rii are the standard deviation at site i and the correlation coefficient between sites i and j, respectively. This single-lead selection method is incorporated into a simple sequential selection algorithm, as follows. Having selected a best lead j, consider the remaining [n-l) lead sites as a vector P, and find the lead k with maximal information index Ik for that vector. Recursively, after each lead selection, consider the remaining leads as a vector P, and find the site 1 with maximal index It for that vector. This procedure provides at each step both a specific lead set and a measure of the information content of the selected leads, so that a limit on acceptable estimation error can be preset and used to terminate the procedure. The algorithm is optimal in the sense that no other set of m leads has smaller error, although the set is not necessarily unique; i.e., other lead sets might have equal error. The coefficients necessary to estimate or “reconstruct” the remaining leads from a chosen set are simply the entries of the transformation operator T from equation 2. Following Lux, the estimation error was expressed in 3 parameters: mean correlation coefficient, which characterizes similarity in lead patterns but not in amplitudes; ratio of error strength to signal strength, which characterizes both lead configuration and amplitude; and root-mean-square error. Their equations are, respectively: r = X’Y/IXJJYJ; ratio = IX - 12 / 1x12; ;:; andE=JX-YJ /n1/2* (7) where X and Y are the original and reconstructed time sequences of a lead site, and n is the sequence length. For each reconstruction, these 3 measures were calculated for each estimated lead, to get the average value of each measure over all estimated leads, Because QRS has been included in some estimates of infarct size,g*10the data reduction project was divided in 2 parts, one for QRS and one for ST-T. As expected, 2 sets of optimal leads resulted from this division of

TABLE ii Measures of Agreement Between Sum of R-Wave Amplitude (XR) in Original Precordiai Maps and Maps Reconstructed from Different Numbers of Optimal Leads

Mean difference between ZR of original and reconstructed maps (mV) Difference as percent of original ZR amplitude Correlation coefficient between original and reconstructed ZR Mean ZR in the original maps was 13.54 f

5-Lead Basis

7-Lead Basis

g-Lead Basis

-0.15

-0.08

0.17

0%

1%

0.97

0.98

-1% 0.97

1.11 mV (standard deviation).

the study, with comparable accuracy from a smaller subset for ST-T studies and a slightly larger one for QRS. For practical reasons, a common set was also determined for both QRS and ST-T.

Results Final study data were lead values from a single, computer-determined QRS-T complex, over 35 leads, for each of 100 acute infarct patients. Lead subsets numbering between 2 and 15 leads were selected for their power in reconstructing the original %-lead maps. In addition, the standard 12 leads and 3 orthogonal Frank leads were also tested for their power in reconstructing the total map. Using the aforementioned transformation method, the smaller lead sets served as bases for reconstruction of the original QRS and ST-T complexes. Typical results, separated for QRS and ST-T, are listed in Table I. Reconstructing the QRS complex from only 2 leads resulted in a mean correlation coefficient of 0.81 between the original and reconstructed leads. With an increasing number of leads, this correlation coefficient rose to 0.87 when 12 leads were used for the reconstruction. Mean correlation coefficients for Frank leads were close to those obtained from 2 optimized leads. For the standard 12 leads, correlations were found to be in between 2 and 3 optimized leads. The mean root-mean-square error decreased from 0.23 mV for reconstructions from 2 leads to 0.08 mV for 12 leads. Corresponding mean root-mean-

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TABLE III Measures of Agreement Between Sum of ST-T Elevations (EST) In Orlglnal Precordlal Maps and Maps Reconstructed from Different Numbers of Optimal Leads

Mean difference between ZST of original and reconstructed maps (mV) Difference as percentage of original ZST amplitude Mean difference between number of leads with ST elevation >O.l mV (& SD) Correlation coefficient between original and reconstructed ZST

&Lead Basis

C-Lead Basis

7-Lead Basis

g-Lead Basis

-0.34

-0.07

-0.10

-0.09

-0.06

-6%

-1%

-2%

-1%

-1%

-0.6 f4.4 0.95

0.1 f2.2 0.97

-0.3 f1.7 0.98

-0.2 f1.4 0.99

-0.5 f1.3 0.99

Mean ZST In the original map was 5.51 f 3.77 mV (standard deviation

1P-Lead Basis

[SD]) at 40 ms after the J point.

TABLE IV Mean Values of Goodness of Flt Measures to Assess Performance of Dlfferent Numbers of Optlmal Leads for Reconstructing 35-Lead Maps (Optlmal Leads Were Selected Separately for ORS and ST-T Reconatructlon, Based on a IO-Patlent Tralnlng Set; Reconstructlons from the Optlmal Lead Sets Were Then Applled to the other 50 Patlents as a Test Set) 5 Lead

7 Lead

Train set CRS reconstruction Correlation coefficient Root-mean-square error (mv) Error-to-slgnal ratio ST-T reconstruction Correlation coefficient Root-mean-square error (mV) Error-to-signal ratlo

Test set

0.90 0.04 0.07

0.90 0.04 0.08

9 Lead

Train set

Test set

Train Set

0.95

0.95

0.10 0.04

0.11 0.04

0.96 0.09

0.92 0.04 0.05

0.92 0.04 0.07

Test Set

0.96

0.03

0.10 0.04

0.92 0.03 0.04

0.92 0.04 0.05

TABLE V Mean Values of Goodness of Flt Measures That Assess Performance of Dlfferent Lead S&sets for ST-T Reconstructlon. Results In Columns Marked a Refer to Lead Bases Chosen from ST-T-Derlved Statlstlcs; Results In Columns b Refer to Lead Bases Chosen from QRS-Derived Statlstlcs (Optlmal Lead Bases Chosen from Elther QRS or ST-T Data Allow Reconstruction of ST-T Features Nearly Equally) 3 Lead ST-T Reconstruction Correlation coefficient Root-mean-square error (mV) Error-to-signal ratio

7 Lead

9 Lead

12 Lead

15 Lead

a

b

a

b

a

b

a

b

a

b

0.88 0.05 0.12

0.88 0.05 0.12

0.92 0.04 0.06

0.90 0.04 0.07

0.92 0.03 0.05

0.92 0.04 0.05

0.94 0.03 0.03

0.93 0.03 0.04

0.94 0.03 0.03

0.93 0.03 0.03

square errors for the Frank and standard 12 leads were 0.23 and 0.19, respectively. Mean error-to-signal ratio was 0.22 for 2 leads and decreased to 0.02 for reconstructions from 12 optimized leads. For the Frank leads and the standard 12 leads, corresponding error-to-signal ratios were 0.37 and 0.19. Reconstruction of the ST-T complex was slightly more efficient. The mean correlation coefficient increased from 0.83 to 0.94 when the number of leads was increased from 2 to 12. Mean root-mean-square error decreased from 0.06 mV with 2 leads to 0.03 mV when 9 leads were used. Mean error-to-signal ratio decreased from 0.18 for 2 leads to 0.03 with 12 leads. Reconstruction of the ST-T complex from Frank leads

or standard 12 leads gave results similar to those found in the QRS complex. Results were even slightly worse than reconstructions based on 2 optimal leads selected from the original 35 lead set. Comparisons between amplitude sums of original maps and reconstructed maps are listed in Tables II and III. For maps reconstructed from 5 or more optimal leads, the mean differences between R-wave voltage sums in original and reconstructed maps amounted to an insignificant 1% of the original R-wave amplitude sums. Correlation coefficients between original and reconstructed R-wave sums varied from 0.97 to 0.98. The sums of ST amplitudes were compared at 40 ms after the end of QRS. For maps reconstructed from

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5 leads or more, the mean differences between sums of ST amplitudes in original and reconstructed maps were only 1 to 2% of the original ST-amplitude sums. Correlation coefficients between original and reconstructed ST-segments sums were high, increasing from 9.95 to 9.99 when the number of leads was increased from 3 to 9. To test repeatability of results, the original 100 maps were divided into a training set of 50 maps and a test set of 50. Results from the training and test sets are listed for both QRS and ST-T in Table IV. A comparison of training and test sets shows results that are extremely stable with only very small differences. Optimal lead locations determined for QRS and ST-T reconstruction are clearly not unique. Due to the short distances between electrodes and consequent high degree of redundancy between neighboring electrodes, a shift from 1 location to an adjacent one may lead only to minute changes in reconstruction. This lead redundancy makes practical a common set of reduced leads for both QRS and ST-T reconstruction. To confirm this redundancy, the original optimized lead sets for QRS were replaced by those of ST-T. This was also done in reverse order. Results are listed in Table V. As can be seen, reconstruction of QRS and ST-T complexes results in almost identical records when optimized lead sets for QRS are replaced by optimized sets for ST-T. Only minute differences in the second decimal position could be found. This indicates that optimal lead sets for QRS can be safely replaced by those obtained for ST-T. Recommended lead locations for reduced lead sets are shown in Figure 1. Locations are valid for both QRS and ST-T reconstruction. Locations are widely spread with a slightly higher concentration of leads close to the sternum and a smaller number over the left precordium. Lead locations of the full precordial map are shown for comparison.

Discussion The performance of optimal lead sets of various sizes is shown in Table I. As shown, mean correlation coefficients, root-mean-square errors and error-to-signal ratios are all unchanged when the number of electrodes in the optimal lead subset is increased above 12. In fact, improvement is only minimal when the subset is increased above 5 or 7 leads. For practical purposes, these smaller sets appear adequate for reconstructions. Lux et all6 used, as error limits for recomputing total body surface maps of 192 leads from a reduced set of 30 leads, an average root-mean-square error of 32 pV, average correlation coefficient of 0.983 and an errorto-signal ratio of 3.5% in the presence of 20 PV-system noise. Our error limits for QRS and ST-T reconstruction (Tables I, IV and V) significantly exceed their limits. Comparisons are misleading, however, because their reconstruction involved total body surface maps while our study is restricted to chest leads, which are nearest the center of cardiac electrical changes. Also, their study measured reconstruction errors over the entire cardiac cycle, while our study measured error

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only in the QRS and ST-T complexes, where amplitude changes are greatest. In practical applications, the proper locations for the electrode subset can be easily determined. For the 7-lead optimal subset, for example, the first electrode is placed in the fourth intercostal space, on the right side of the sternum. On the left sternal border, 1 electrode is placed in the third intercostal space and 1 in the sixth. To determine the remaining locations, one must measure the horizontal distance between the left anterior axillary line and a vertical line following the left sternal border. One electrode each is placed at one-fourth of this measured distance, at the horizontal level of the second and of the fourth intercostal spaces. The next electrode is placed at three-fourths of the measured distance in the sixth intercostal space. The last electrode is placed in the left anterior axillary line, in the third intercostal space. When applying only 5 optimal leads, the same locations are used, but the 2 electrodes on the left sternal border are omitted. The present recording procedure, involving 35 electrode sites, is cumbersome and time-consuming. When interpreted by human observers, repeat variability is large. Our study has shown that QRS-T information in the 35 electrode array can be reconstructed from a smaller set of 5 to 7 leads, Coefficients to transform these lead subsets to signal values in the remain-

35LEAD

3-LEAD LOCATIONS

LOCATKINS 2nd ICS

5LEAD LOCATIONS

7-LEAD LOCATIONS

O-LEAD LOCATIONS

1 P-LEAD LOCATIONS

FIGURE 1. Optimal lead locatlons for reconstructlon of the QRS-T component of precurdlal maps. Top leff, the original 35 lead locatlons, wlth the sternum (S), left mid-axlllary line (LMAL) and second intercostal space (2nd CS) marked. The bottom row of thle map is the sixth intercostal space. The other 5 figures show the optimal lead locatlons for reconstructing the precardlal map from 3,5,7,9 and 12 leads, respectively. Lead locations were chosen by a sequential algorithm. Thus, larger lead sets Include the smaller sets.

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ing leads are available by writing the authors, It is hoped that this data reduction will result in a more practical clinical method for studies of myocardial infarct evolution and the effect of therapeutic interventions. Acknowledgment: We are deeply grateful for the assistance of Dr. Eugene Braunwald of Harvard University Medical School and Brigham and Women’s Hospital for providing the case material from the Multicenter Investigation of Limitation of Infarct Size study, which made our study possible. We thank also Drs. John Rutherford and Zoltan G. Turi, and Jeremy Poole, Harvard School of Public Health, who reviewed and selected study cases, and formatted and copied magnetic tape records for our analysis. The computer programs for optimal lead selection, calculation of transform coefficients and estimation of error measures were made available to us by the program designer, Dr. Robert L. Lux, and used with minor system adaptations. We are most grateful to him for his assistance, which saved us considerable time and facilitated comparisons of results.

References 1. Maroko PR, Kjekshus )K. Sobel BE, Watanabe T. Braunwald E. Factors influencing infarct size following experimental coronary artery occlusions. GircuJotion 1971;43:67-82. 2. Reid DS. Pelides Ll. Shillingford ]P. Surface mapping of RS-T segment in acute myocardial infbrction. Br Hem? / 1971;33:370-374. 3. Holland RP. Brooks H. TQ-STsegment mapping: critical review and analysis of current concepts. Am [ Cardiol 1977;40:110-129. 4. Maroko PR. Libby P, Cove11JW, Sobel BE, Ross] ]r, Braunwald E. Precordial S-T segment elevation mapping: an atraumatic method for assessingalterations in the extent of myocardial ischemic injury. Am 1 CardioJl972;29:223-

230. 5. Akiyama T. Hodges M, Biddle TL, Zawrotny B, Vangellow C. Measurement of ST segment elevation in acute myocardial infarction in man. Comparison of a precordial mapping technique and the Frank vector system. Am J Cardiof 1975;36:155-162. 6. Foerster )M. Vera Z, Janzen DA, Foerster SJ, Mason DT. Evaluation of precordial orthogonal vectorcordiographic lead ST-segment magnitude in the assessment of myocardial ischemic injury. Circulation 1977;55:728-732. 7. Brody DA, Mirvis DM, Ideker RE, Cox ]W, Keller FW. Larsen RA. Bandura JP.Relative dipolar behbvior of the equivalent T-wave generator: quantitative comparison with ventricular excitation in the rabbit heart. Circ Res 1977; 40:263-268. 8. Horacek BM. Eifler W], Gewirtz H, Helppi RK. Macauley PB, Sherwood JO, Smith ER, Tiberghien J, Rautahaju PM. An automated system for body surface potential mapping. In: Ostrow HG, Ripley KL. eds. Computers in Cardiology. Long Beach, California: IEEE Computer Society, 1977389-402. 9. Hillis LD, Askenazi J, Braunwald E. Radvany P, Muller JE, Fishbein MC, Maroko PR. Use of changes in the epicardial QRS complex to assessinterventions which modify the extent of myocardial necrosis following coronary artery occJusion. CircuJation 1976;54:591-598. 10. Henning H, Hardarson T, Francis G, O’Rourke RA, Ryan W, Ross ). Approach to the estimation of myocordial infarct size by analysis of precordial S-T segment and R-wave maps. Am J Cardiol 1978;41:1-8. 11.The MILIS Study Group. National Heart, Lang, and Blood Jnstitute Multicenter Investigation of the Limitation of Infarct Size (MILJS): design and methods of the clinical trial. Am Heart Association monograph no. 100, 1984. 12. Fischmann E). Seelye RN, Crutcher LR. Clinical trial of a balsa-lithium electrode for conventional electrocardiography. Am J Cardiol 1962;10:846851. 13. Pipberger HV, Arzbaecher RC, Berson AS, Briller SA, Brody DA, Flowers NC, Geselowitz DB, Lepeschkin E, Oliver GC, Schmitt OH, Spach M. Recommendations for standardization of leads and of specifications for instruments in electrocardiography and vectorcardiography. Report of the Committee on Electrocardiography. AHA. Circulation 1975;52:11-31. 14. Pipberger HV. The ECG computer analysis program developed in the U.S. Veterans Administration. In: van Bemmel /H, Willems JL, eds. Trends in Computer Processed Electrocardiograms. Amsterdam; North-Holland Publishing, 1977:125-132. 15. Ishikawa K. Batchlor C, Pipberger HV. Reduction of electrocardiographic beat-to-beat variation through computer wave recognition. Am Ijeart 1 1971;81:236-241. 16. Lux RL, Smith CR, Wyatt RF, Abildskov JA. Limited lead selection for estimation of body surface potential maps in electrocardiography. JEEE Trans Biomed Eng 1978;BME-25:270-276.