COMPUTERS
AND
BIOMEDICAL
RESEARCH
Reconstruction
L. EDENBRANDT,* “Department Science.
25, 538-546
(1992)
of the Electrocardiogram Heart Surgery
Z. R.ZENG,~ A. EDENBRANDT,~ L. S~RNMO,*+ AND S. B. OLSSON?
during
C.
MANSSON,*
of Clinicul Physiology, tDepurtrnent ~?f‘Curdiology. SDepartment and SDepcrrtment qf Signal Processing, Lund University, Lund,
Received
August
oj‘ Computer Snjrden
13, 1991
Electrocardiograms tECG) recorded during arrhythmia surgery are used for identification of arrhythmias of different morphology. However, the interpretation of an intraoperative ECG is difficult because some leads cannot be recorded and the signals of the remaining leads often differ from those of a preoperative recording because of the sternotomy. Therefore. a method for reconstruction of a complete intraoperative ECG. which resembles a preoperatively recorded ECG. was studied in 24 patients undergoing heart surgery. The reconstruction method involves calculating coefficients for a transformation matrix. using a preoperative ECG recording and a first intraoperative ECG recording. Once this matrix has been established, further intraoperative recordings can be transformed into an ECG which strongly resembles a preoperative ECG. The correlation between reconstructed intraoperative leads and the corresponding preoperative leads was high in the leads V, and V, (median correlation coefficient 0.98 and 0.97) and slightly smaller in lead V; (0.94). Further studies will prove if the method can be useful in arrhythmia surgery. L 1992 Acadsmlc Prers. Inc.
INTRODUCTION
Heart surgery is an established treatment in patients with certain types of cardiac arrhythmias. Ventricular tachycardia can, for example, be cured after excision of the structures responsible for the tachycardia. A crucial part of that procedure is to localize such structures as exactly as possible. The technique used includes intraoperative provocation of arrhythmias from different parts of the myocardium in order to identify the actual arrhythmia that is meant to be cured. A preoperative electrocardiogram (ECG) showing the arrhythmia is compared to intraoperative ECGs recorded during provoked arrhythmias. However, after the median sternotomy some of the precordial leads in the 12-lead ECG cannot be recorded. In the remaining leads, the QRS morphology can be affected in a clinically significant way. Therefore, the comparison of preoperative and intraoperative recordings becomes very difficult. Changes in QRS morphology have been studied by viewing the ECG after 538 0010-4809192 Copyright All rights
$5.00
0 1992 by Academic Press, Inc. of reproduction in any form reserved.
ECGDURINGHEARTSURGERY
539
median sternotomy as a linearly filtered version of the preoperative ECG (1). The gain and phase shift of the transfer function was estimated and analyzed, but a general transfer function did not prove to be the solution of the problem. Furthermore, only a subset of ECG leads were studied. The purpose of this study was to investigate a method for reconstruction of a complete intraoperative ECG, which closely resembles the preoperative ECG. Although the presented method was applied to orthogonal ECG recordings, it can also be used for nonorthogonal lead configurations. MATERIAL
ANDMETHODS
Patients Recordings were made in 24 patients (17 men and 7 women) between 46 and 81 years of age. The patients were undergoing coronary artery bypass surgery (18), heart valve surgery (2), or combined coronary artery bypass and heart valve surgery (4). Twenty-three patients had sinus rhythm and one had atria1 fibrillation. Recording
Technique
On each patient two orthogonal ECGs according to Frank (2) were recorded before surgery. Nine electrodes were used to record eight leads from which the three orthogonal leads V,. V,, and VZ could be calculated in accordance with the equations given by Frank (see the Appendix). The five chest electrodes, denoted A, C, E, I, and M, were positioned at the same horizontal level (fourth intercostal space). The electrodes A and I were positioned on the left and right lateral sides, respectively. The electrodes E, M, and C were positioned on the sternum, spine, and in a left-anterior oblique position between the electrodes A and E, respectively. The remaining four electrodes were positioned on the left arm (LA), right arm (RA), left leg (LL), and on the back of the neck (H). Before the median sternotomy the electrodes in position C and E had to be removed. The remaining seven electrodes were used to record two “incomplete” ECGs each consisting of the following six leads: I, (LA-RA), II, (LLRA), VA-CT,, VI-CT,, V,-CT,, and Vn-CT, (CT-central terminal) (LL + LA + RA)/3); ,-leads recorded during surgery). In the equations according to Frank, for the calculation of the leads V,, V,, and VZ, data from all eight leads is used. Consequently data from the six leads recorded during surgery is not sufficient for these equations to be used. Therefore, a reconstruction technique was developed for the calculation of leads V,, V,, and VZ during surgery. Two ECGs, one recorded before and one recorded after median sternotomy, were used for calculating a patient-specific reconstruction matrix (see below). The other two ECGs (also one recorded before and one recorded after median sternotomy) were used as a test set to analyze the performance of the reconstruction method. All recordings were made with a computerized ECG recorder (Sicard 740.
540
EDENBKANDT
ETA1
Siemens Elema AB, Solna, Sweden). The sampling rate was 250 Hz. Heart cycles were averaged and transferred to a computer for further analysis. Reconstruction
Technique
Let Lx denote the eight leads available before surgery and L” the six leads available during surgery. From the first preoperative ECG. Lx, the three orthogonal leads V = (V,, V>. VI) were calculated in the usual way, using the standard transformation matrix according to Frank, H, (see the Appendix): H,L*
= V.
Reconstruction meant finding a new patient-specific transformation matrix, H,, which could be employed to calculate orthogonal leads W = (W,, W,,, W,), but using only the six leads available after median sternotomy: HNL6 = W. Ideally, H, ought to be chosen so that V and W become identical, but in general this is not possible. Instead, we construct HN such that the difference between the vectors V, and W, is minimized, and similarly between the vectors V, , W, and V;, W;. To measure the difference between the vectors the Euclidean norm was used, that is, the sum of squares of differences between the elements of the vectors. The calculation of H, then becomes a standard minimization problem. known as the “least-squares problem”. This was solved using the normal equations algorithm (3). In summary, the coefficients of H, were calculated using the first preoperative ECG recording Ls and the first intraoperative recording L6. Once this matrix has been established, further intraoperative recordings could be transformed into the orthogonal components using H,. The reconstruction method was applied only to the QRST segment of the heart cycle. The performance of the transformation method was assessed using the second preoperative recording and the second intraoperative recording. The maximal amplitudes of the intraoperatively reconstructed leads V,. V, , and V; were compared to the corresponding amplitudes of the preoperative leads. The “overall” similarity in QRST waveform morphology was studied in terms of crosscorrelations for each pair of leads. RESULTS
The leads V,, V?,, and V;, reconstructed from intraoperative recordings of 24 patients, were compared to the corresponding preoperative leads. The absolute differences in maximal amplitudes were less than 0. I mV in 42 of the 72 leads. The absolute differences were on average 0.15 mV (SD 0.16), 0.07 mV (SD O.OS), and 0.14 mV (SD 0.11) in leads V,, V,., and V,, respectively. Thus the
ECG DURING
HEART
541
SURGERY
Y
.a. ..
. . . i!izl 0.0
. .
1.0
2.0
3.0
Max amp1[preop] (mV) FIG. I. Relationship between maximal intraoperative amplitudes and maximal preoperative amplitudes in the leads V,. V,, and V:.
absolute differences were on average smallest in lead VY, as were on average the maximal amplitudes. The opposite pattern was found in lead V, (Fig. 1). The best correlation was found in lead V,, with a median correlation coefficient of 0.98 and a range of 0.95-1.00. The corresponding values for leads V, and V, were 0.97 (range 0.74-1.00) and 0.94 (0.34-0.99), respectively. Small correlation coefficients were found in leads with small amplitudes (Fig. 2). The correlation coefficients were always greater than 0.94 when the peak-to-peak amplitudes were greater than 1.0 mV. In Fig. 3 the recordings from two patients are shown, one with a high correlation between the preoperative and intraoperative leads (0.99, 1.OO, and 0.98 in leads V,, V,, and Vz, respectively) and one with correlation coefficients close to the median values (0.99, 0.97, and 0.95 in leads V,, V,, and Vz respectively). An example where the resemblance between the preoperative and intraoperative leads was rather poor is shown in Fig. 4. The correlation coefficient in lead V, was 0.34, which was the lowest value of all 72. The corresponding values in leads V., and V, were 0.96 and 0.97, i.e., also one of the lowest values for lead V,. The original six leads from the two intraoperative recordings were studied
1 + +
o.o2o 0.0
1.0
.
.
Peak-to-peak amp1(mV) FIG. 2. Relationship between correlation coefficients and peak-to-peak amplitudes in the leads V,, V,, and V,.
542
EDENBRANDT
ET AL.
a Prew
b OP
prew
OP
FIG. 3. Recordings from (a) one patient where the correlations between the preoperative and intraoperative leads V,. V,. and V, were high (0.99. 1.00. and 0.98) and (b) from another patient where the correlation coefficients were close to the median values of the material (0.99. 0.97. and 0.95 in the leads V,, V,. and V;. respectively).
for this patient. The differences in lead I between these two recordings was substantial. Intraoperative recordings seems to vary more than preoperative recordings and in some cases cause significant differences. A comparison with the preoperatively recorded lead I illustrates the influence of median sternotomy on the potential differences between the left and right arm. The two preoperative recordings showed a good resemblance. DISCUSSION
Different methods to derive new ECG leads from recorded leads have been published in the literature. An orthogonal ECG can be derived from the 12-lead ECG and vice versa (4-6). These methods allow vectorcardiographic loops to be used in the interpretation while a conventional 12-lead ECG still can be recorded and/or presented. The 12-lead ECG could be impractical in a monitoring situation because of the number of required electrodes. Therefore. a method to derive a complete 12-lead ECG from a subset of the twelve leads has been presented (7). Neither of these methods are applicable for the reconstruction of ECG leads during heart surgery. After a median sternotomy neither a 12-lead ECG nor an orthogonal ECG can be recorded completely and changes of the electrical properties affect the QRS morphology in the remaining leads (I). The 12-lead ECG is the most widely used electrocardiographic investigation.
ECG DURING
HEART SURGERY
543
PreoP
1mV
I,
0.5s
I
FIG. 4. Preoperative and intraoperative leads V,, V,, and VL from the patient with the lowest correlation coefficient (0.34 in lead V,) in the material. Lead I from one of the two preoperative recordings and from both intraoperative recordings is also shown from the same patient.
However, this study is based on the orthogonal ECG according to Frank (2) because the three chest electrodes in position A, I, and M (positioned on the left and right lateral side, respectively, and on the spine) probably will give more information of the electric forces in the horizontal plane than will the ECG electrodes in position V, and V, (both positioned on the left lateral side of the chest). If a 12-lead ECG is preferred instead of three orthogonal ECG leads for the visual comparison of the pre- and intraoperative recordings, a 12-lead ECG can be derived using the reconstruction technique described above. In order to illustrate this, a 12-lead ECG and an orthogonal ECG from a healthy subject were used to calculate a reconstruction matrix. This matrix was used to derive a 12-lead ECG from a second orthogonal ECG recording. The derived 12-lead ECG was compared to a second “true” 12-lead ECG recording (Fig. 5). The correlation coefficients corresponding to the eight independent leads of these 12-lead ECGs ranged between 0.99 and 1.00. There was a good resemblance between preoperatively recorded leads and the corresponding leads reconstructed from intraoperative recordings. The absolute differences in maximal amplitudes between these leads were on average 0.15 and 0.07 mV in leads V, and V,, respectively. These differences are comparable to the normal daily variability for maximal amplitudes. Willems et al. (8) studied day-to-day variation of the orthogonal ECG and reported absolute changes in leads V, and V, of 0.14 and 0.06 mV, respectively. In lead V, the daily variability was slightly less than the differences between preoperative and intraoperative recordings (0.09 versus 0.14 mV). The correlation between preoperative and intraoperative recordings was also high in the leads V, and V,, but worse in lead VZ. However, it is not surprising that lead V, proved to be the most difficult lead to reconstruct. This lead reflects the potential differences in the anteroposterior direction. After the median sternotomy anteriorly positioned electrodes cannot be used.
244
EDENBRANDT
a
ET AL.
a
b
I,
IillV
02% v4
FIG. 5. Eight independent leads of two 124ead EC&, and (b) the other which is derived from an orthogonal
4 “I
AND
BIOMEDICAL
RESEARCH
Reconstruction
L. EDENBRANDT,* “Department Science.
25, 538-546
(1992)
of the Electrocardiogram Heart Surgery
Z. R.ZENG,~ A. EDENBRANDT,~ L. S~RNMO,*+ AND S. B. OLSSON?
during
C.
MANSSON,*
of Clinicul Physiology, tDepurtrnent ~?f‘Curdiology. SDepartment and SDepcrrtment qf Signal Processing, Lund University, Lund,
Received
August
oj‘ Computer Snjrden
13, 1991
Electrocardiograms tECG) recorded during arrhythmia surgery are used for identification of arrhythmias of different morphology. However, the interpretation of an intraoperative ECG is difficult because some leads cannot be recorded and the signals of the remaining leads often differ from those of a preoperative recording because of the sternotomy. Therefore. a method for reconstruction of a complete intraoperative ECG. which resembles a preoperatively recorded ECG. was studied in 24 patients undergoing heart surgery. The reconstruction method involves calculating coefficients for a transformation matrix. using a preoperative ECG recording and a first intraoperative ECG recording. Once this matrix has been established, further intraoperative recordings can be transformed into an ECG which strongly resembles a preoperative ECG. The correlation between reconstructed intraoperative leads and the corresponding preoperative leads was high in the leads V, and V, (median correlation coefficient 0.98 and 0.97) and slightly smaller in lead V; (0.94). Further studies will prove if the method can be useful in arrhythmia surgery. L 1992 Acadsmlc Prers. Inc.
INTRODUCTION
Heart surgery is an established treatment in patients with certain types of cardiac arrhythmias. Ventricular tachycardia can, for example, be cured after excision of the structures responsible for the tachycardia. A crucial part of that procedure is to localize such structures as exactly as possible. The technique used includes intraoperative provocation of arrhythmias from different parts of the myocardium in order to identify the actual arrhythmia that is meant to be cured. A preoperative electrocardiogram (ECG) showing the arrhythmia is compared to intraoperative ECGs recorded during provoked arrhythmias. However, after the median sternotomy some of the precordial leads in the 12-lead ECG cannot be recorded. In the remaining leads, the QRS morphology can be affected in a clinically significant way. Therefore, the comparison of preoperative and intraoperative recordings becomes very difficult. Changes in QRS morphology have been studied by viewing the ECG after 538 0010-4809192 Copyright All rights
$5.00
0 1992 by Academic Press, Inc. of reproduction in any form reserved.
ECGDURINGHEARTSURGERY
539
median sternotomy as a linearly filtered version of the preoperative ECG (1). The gain and phase shift of the transfer function was estimated and analyzed, but a general transfer function did not prove to be the solution of the problem. Furthermore, only a subset of ECG leads were studied. The purpose of this study was to investigate a method for reconstruction of a complete intraoperative ECG, which closely resembles the preoperative ECG. Although the presented method was applied to orthogonal ECG recordings, it can also be used for nonorthogonal lead configurations. MATERIAL
ANDMETHODS
Patients Recordings were made in 24 patients (17 men and 7 women) between 46 and 81 years of age. The patients were undergoing coronary artery bypass surgery (18), heart valve surgery (2), or combined coronary artery bypass and heart valve surgery (4). Twenty-three patients had sinus rhythm and one had atria1 fibrillation. Recording
Technique
On each patient two orthogonal ECGs according to Frank (2) were recorded before surgery. Nine electrodes were used to record eight leads from which the three orthogonal leads V,. V,, and VZ could be calculated in accordance with the equations given by Frank (see the Appendix). The five chest electrodes, denoted A, C, E, I, and M, were positioned at the same horizontal level (fourth intercostal space). The electrodes A and I were positioned on the left and right lateral sides, respectively. The electrodes E, M, and C were positioned on the sternum, spine, and in a left-anterior oblique position between the electrodes A and E, respectively. The remaining four electrodes were positioned on the left arm (LA), right arm (RA), left leg (LL), and on the back of the neck (H). Before the median sternotomy the electrodes in position C and E had to be removed. The remaining seven electrodes were used to record two “incomplete” ECGs each consisting of the following six leads: I, (LA-RA), II, (LLRA), VA-CT,, VI-CT,, V,-CT,, and Vn-CT, (CT-central terminal) (LL + LA + RA)/3); ,-leads recorded during surgery). In the equations according to Frank, for the calculation of the leads V,, V,, and VZ, data from all eight leads is used. Consequently data from the six leads recorded during surgery is not sufficient for these equations to be used. Therefore, a reconstruction technique was developed for the calculation of leads V,, V,, and VZ during surgery. Two ECGs, one recorded before and one recorded after median sternotomy, were used for calculating a patient-specific reconstruction matrix (see below). The other two ECGs (also one recorded before and one recorded after median sternotomy) were used as a test set to analyze the performance of the reconstruction method. All recordings were made with a computerized ECG recorder (Sicard 740.
540
EDENBKANDT
ETA1
Siemens Elema AB, Solna, Sweden). The sampling rate was 250 Hz. Heart cycles were averaged and transferred to a computer for further analysis. Reconstruction
Technique
Let Lx denote the eight leads available before surgery and L” the six leads available during surgery. From the first preoperative ECG. Lx, the three orthogonal leads V = (V,, V>. VI) were calculated in the usual way, using the standard transformation matrix according to Frank, H, (see the Appendix): H,L*
= V.
Reconstruction meant finding a new patient-specific transformation matrix, H,, which could be employed to calculate orthogonal leads W = (W,, W,,, W,), but using only the six leads available after median sternotomy: HNL6 = W. Ideally, H, ought to be chosen so that V and W become identical, but in general this is not possible. Instead, we construct HN such that the difference between the vectors V, and W, is minimized, and similarly between the vectors V, , W, and V;, W;. To measure the difference between the vectors the Euclidean norm was used, that is, the sum of squares of differences between the elements of the vectors. The calculation of H, then becomes a standard minimization problem. known as the “least-squares problem”. This was solved using the normal equations algorithm (3). In summary, the coefficients of H, were calculated using the first preoperative ECG recording Ls and the first intraoperative recording L6. Once this matrix has been established, further intraoperative recordings could be transformed into the orthogonal components using H,. The reconstruction method was applied only to the QRST segment of the heart cycle. The performance of the transformation method was assessed using the second preoperative recording and the second intraoperative recording. The maximal amplitudes of the intraoperatively reconstructed leads V,. V, , and V; were compared to the corresponding amplitudes of the preoperative leads. The “overall” similarity in QRST waveform morphology was studied in terms of crosscorrelations for each pair of leads. RESULTS
The leads V,, V?,, and V;, reconstructed from intraoperative recordings of 24 patients, were compared to the corresponding preoperative leads. The absolute differences in maximal amplitudes were less than 0. I mV in 42 of the 72 leads. The absolute differences were on average 0.15 mV (SD 0.16), 0.07 mV (SD O.OS), and 0.14 mV (SD 0.11) in leads V,, V,., and V,, respectively. Thus the
ECG DURING
HEART
541
SURGERY
Y
.a. ..
. . . i!izl 0.0
. .
1.0
2.0
3.0
Max amp1[preop] (mV) FIG. I. Relationship between maximal intraoperative amplitudes and maximal preoperative amplitudes in the leads V,. V,, and V:.
absolute differences were on average smallest in lead VY, as were on average the maximal amplitudes. The opposite pattern was found in lead V, (Fig. 1). The best correlation was found in lead V,, with a median correlation coefficient of 0.98 and a range of 0.95-1.00. The corresponding values for leads V, and V, were 0.97 (range 0.74-1.00) and 0.94 (0.34-0.99), respectively. Small correlation coefficients were found in leads with small amplitudes (Fig. 2). The correlation coefficients were always greater than 0.94 when the peak-to-peak amplitudes were greater than 1.0 mV. In Fig. 3 the recordings from two patients are shown, one with a high correlation between the preoperative and intraoperative leads (0.99, 1.OO, and 0.98 in leads V,, V,, and Vz, respectively) and one with correlation coefficients close to the median values (0.99, 0.97, and 0.95 in leads V,, V,, and Vz respectively). An example where the resemblance between the preoperative and intraoperative leads was rather poor is shown in Fig. 4. The correlation coefficient in lead V, was 0.34, which was the lowest value of all 72. The corresponding values in leads V., and V, were 0.96 and 0.97, i.e., also one of the lowest values for lead V,. The original six leads from the two intraoperative recordings were studied
1 + +
o.o2o 0.0
1.0
.
.
Peak-to-peak amp1(mV) FIG. 2. Relationship between correlation coefficients and peak-to-peak amplitudes in the leads V,, V,, and V,.
542
EDENBRANDT
ET AL.
a Prew
b OP
prew
OP
FIG. 3. Recordings from (a) one patient where the correlations between the preoperative and intraoperative leads V,. V,. and V, were high (0.99. 1.00. and 0.98) and (b) from another patient where the correlation coefficients were close to the median values of the material (0.99. 0.97. and 0.95 in the leads V,, V,. and V;. respectively).
for this patient. The differences in lead I between these two recordings was substantial. Intraoperative recordings seems to vary more than preoperative recordings and in some cases cause significant differences. A comparison with the preoperatively recorded lead I illustrates the influence of median sternotomy on the potential differences between the left and right arm. The two preoperative recordings showed a good resemblance. DISCUSSION
Different methods to derive new ECG leads from recorded leads have been published in the literature. An orthogonal ECG can be derived from the 12-lead ECG and vice versa (4-6). These methods allow vectorcardiographic loops to be used in the interpretation while a conventional 12-lead ECG still can be recorded and/or presented. The 12-lead ECG could be impractical in a monitoring situation because of the number of required electrodes. Therefore. a method to derive a complete 12-lead ECG from a subset of the twelve leads has been presented (7). Neither of these methods are applicable for the reconstruction of ECG leads during heart surgery. After a median sternotomy neither a 12-lead ECG nor an orthogonal ECG can be recorded completely and changes of the electrical properties affect the QRS morphology in the remaining leads (I). The 12-lead ECG is the most widely used electrocardiographic investigation.
ECG DURING
HEART SURGERY
543
PreoP
1mV
I,
0.5s
I
FIG. 4. Preoperative and intraoperative leads V,, V,, and VL from the patient with the lowest correlation coefficient (0.34 in lead V,) in the material. Lead I from one of the two preoperative recordings and from both intraoperative recordings is also shown from the same patient.
However, this study is based on the orthogonal ECG according to Frank (2) because the three chest electrodes in position A, I, and M (positioned on the left and right lateral side, respectively, and on the spine) probably will give more information of the electric forces in the horizontal plane than will the ECG electrodes in position V, and V, (both positioned on the left lateral side of the chest). If a 12-lead ECG is preferred instead of three orthogonal ECG leads for the visual comparison of the pre- and intraoperative recordings, a 12-lead ECG can be derived using the reconstruction technique described above. In order to illustrate this, a 12-lead ECG and an orthogonal ECG from a healthy subject were used to calculate a reconstruction matrix. This matrix was used to derive a 12-lead ECG from a second orthogonal ECG recording. The derived 12-lead ECG was compared to a second “true” 12-lead ECG recording (Fig. 5). The correlation coefficients corresponding to the eight independent leads of these 12-lead ECGs ranged between 0.99 and 1.00. There was a good resemblance between preoperatively recorded leads and the corresponding leads reconstructed from intraoperative recordings. The absolute differences in maximal amplitudes between these leads were on average 0.15 and 0.07 mV in leads V, and V,, respectively. These differences are comparable to the normal daily variability for maximal amplitudes. Willems et al. (8) studied day-to-day variation of the orthogonal ECG and reported absolute changes in leads V, and V, of 0.14 and 0.06 mV, respectively. In lead V, the daily variability was slightly less than the differences between preoperative and intraoperative recordings (0.09 versus 0.14 mV). The correlation between preoperative and intraoperative recordings was also high in the leads V, and V,, but worse in lead VZ. However, it is not surprising that lead V, proved to be the most difficult lead to reconstruct. This lead reflects the potential differences in the anteroposterior direction. After the median sternotomy anteriorly positioned electrodes cannot be used.
244
EDENBRANDT
a
ET AL.
a
b
I,
IillV
02% v4
FIG. 5. Eight independent leads of two 124ead EC&, and (b) the other which is derived from an orthogonal
4 “I
