How Many Leads Are Necessary for a Reliable ... - IEEE Xplore

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IEEE TRANSACTIONS ON INFORMATION TECHNOLOGY IN BIOMEDICINE, VOL. 13, NO. 3, MAY 2009

How Many Leads Are Necessary for a Reliable Reconstruction of Surface Potentials During Atrial Fibrillation? Mar´ıa de la Salud Guillem, Andreas Bollmann, Andreu M. Climent, Daniela Husser, Jose Millet-Roig, and Francisco Castells

Abstract—In this study, we aimed at determining how many leads are necessary for accurately reconstructing ECG potentials during atrial fibrillation (AF) on the body surface. Although the standard ECG is appropriate for the detection of this arrhythmia, its accuracy for extracting other diagnostic features or constructing surface potential maps may not be optimal. We evaluated the suitability of the standard ECG in AF and proposed a new lead system for improving the information content of AF signals in limited lead systems. We made use of 64-lead body surface potential mapping recordings of 17 patients during AF and 18 healthy subjects. Lead selection was performed by making use of a lead selection algorithm proposed by Lux, and error curves were calculated for increasing number of selected leads for QRS complexes and P waves from healthy subjects and AF signals. From our results, at least 23 leads are needed in order to have the same degree of accuracy in the derivation of AF waves as the 12-lead ECG for a normal QRS complex (25% error). The 12-lead ECG allows a reconstruction of surface potentials with 53% error. If a limited lead set is to be chosen, a repositioning of only four electrodes from the standard ECG reduces reconstruction error in 11%. This repositioning of electrodes may include more right anterior electrodes and one posterior electrode. Index Terms—Atrial fibrillation (AF), body surface potential mapping (BSPM), ECG, lead systems.

I. INTRODUCTION TRIAL fibrillation (AF) is a supraventricular arrhythmia in which the electrical activation shows an uncoordinated pattern. The 12-lead ECG is the most extended noninvasive technique in the diagnosis of AF because of its capability to detect this arrhythmia in a simple and inexpensive manner. Despite the relatively large number of electrodes required to obtain the 12-lead ECG (nine electrodes), the total amount of information provided by all of them has been questioned [1]–[3]. Precordial leads V1 through V6 are positioned close to each other on the

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Manuscript received February 4, 2008; revised August 29, 2008 and December 1, 2008. Current version published May 6, 2009. This work was supported in part by Spanish Ministry of Education and Science under TEC200508401 and the Universidad Politécnica de Valencia through its research iniciative program. The work of D. Husser was supported by a Ministry of Education and Research Grant (01ZZ0407). M. S. Guillem, A. M. Climent, J. Millet-Roig, and F. Castells are with the Instituto de Aplicaciones de las Tecnolog´ıas de la Información y de las Comunicaciones Avanzadas (ITACA), Universidad Politécnica de Valencia, Valencia 46022, Spain (e-mail: [email protected]; [email protected]; [email protected]; [email protected]). A. Bollmann and D. Husser are with the Department of Electrophysiology, Heart Center, University Leipzig, Leipzig DE-04289, Germany (e-mail: [email protected]; [email protected]). Digital Object Identifier 10.1109/TITB.2008.2011894

body surface, and some of them are quite far from the atria. As a result, the standard leads are highly correlated and they exhibit a large amount of mutual information. In addition, the precordial leads were originally positioned for capturing the ventricular electrical activity, so the atrial activity may not be accurately reflected at these sites. Body surface potential mapping (BSPM) studies have shown that in some cases, there is diagnostic information that may be inadequately sampled by the standard 12-lead ECG, and thus, the diagnosis of some cardiac diseases would benefit from the use of a higher number of electrodes [4]–[14]. Benefit of the analysis of body surface maps is not only restricted to ventricular diseases but it has also been applied in the characterization of atrial activity in sinus rhythm and the localization of ectopic atrial activation [15]–[17]. Also, the utility of maps for the characterization of AF has been recently described [18]. Different electrical patterns were observed, such as single wavefronts propagating across the whole surface explored, wave breackages, wave splitting, and multiple simultaneous wavefronts. Practical use of BSPM systems is limited by the tedious recording procedure, and for this reason, some studies have proposed to use a limited number of nonstandard leads with the aim of improving the diagnostic information of the ECG. In fact, previous studies concerning the selection of leads from BSPM systems agree in considering that the total information content in multilead recordings is not as high as the number of electrodes used for recording ECG signals. Although the number and location of electrodes needed to contain most diagnostic information of the ECG vary among studies, it is generally accepted that 30–32 electrodes are sufficient [19]–[23]. These previous studies about the information content of multiple ECG leads have mainly been focused on optimizing the global information content of the whole ECG. In this case, the activity captured during the ventricular depolarization (i.e., the QRS complexes) predominates over any other cardiac activity. The nature of this electrical activity is much different from the AF signals for several reasons: 1) they have their origin in different parts of the heart; 2) the fibrillatory signals are consequence of a chaotic activation in contrast to the organized activation of a nonfibrillating ventricle; and 3) the fibrillatory signals exhibit a lower signal-to-noise ratio. Taking into account these considerations, it can be inferred that the model applicable to the whole ECG may not match the AF waves. The issue of information content of lone AF signals has not been addressed before. Previous studies have focused on proposing new reduced lead systems

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GUILLEM et al.: HOW MANY LEADS ARE NECESSARY FOR A RELIABLE RECONSTRUCTION OF SURFACE POTENTIALS DURING AF

for improving the diagnosis and therapy for AF [24], [25]. Furthermore, new electrode positions have been also investigated for minimizing errors in the reconstructed vectorcardiogram in AF [26]. A feasible approach for experimentally determining optimal electrode locations for any pathological or healthy condition is based on the selection of the leads with higher information content in BSPM recordings. This approach was proposed by Lux et al. [27] in an early study and is still being used by its authors [28]–[31] because it has shown a better performance than other methods proposed [32], [33]. The objective of this study is to evaluate the suitability of the standard ECG in AF and compare its performance to other limited lead systems. We made use of 64-lead BSPM recordings of patients during AF, and experimentally determined how many leads are necessary for accurately reconstructing the potentials on their whole body surface in terms of the rms error of reconstructed leads. The desired accuracy is limited by the noise level, and thus a perfect reconstruction cannot be achieved. A more reasonable objective is to achieve an accuracy in the reconstruction of AF waves as that achieved in the reconstruction of QRS complexes or P waves by using the standard 12-lead ECG. With this aim, we performed the same experiments over the QRS complex and P wave of healthy subjects in order to have a reference in the accuracy achievable for these waves in limited lead systems. Besides from measuring errors in reconstruction of nonselected leads, we evaluated the similarity of spectral features of reconstructed to recorded ECG signals as an independent diagnostic parameter that is frequently used in the study of AF. Also, new lead positionings will be evaluated aimed at improving the information content of AF signals recorded by limited lead systems. A nonstandard 12-lead ECG system will be proposed as a practical solution for improving the diagnosis of AF. In order to keep some coherence with the standard ECG, this lead system will include some of the standard leads and will allow a repositioning of four precordial leads. The performance of such a lead system will be evaluated. II. MATERIALS A. BSPM Recording System Our BSPM recording system has been described elsewhere [14]. Briefly, it consists of a commercial 64-lead recording system for biopotential measurement (Active One, Biosemi) adapted to our purposes. ECG signals were sampled at a sampling frequency (Fs) of 2048 Hz with a quantization of 1 µV/bit and stored on hard disk for its later processing. Electrodes were distributed nonuniformly upon the chest, with 16 posterior electrodes and 48 anterior electrodes, with a highest density at positions overlaying the heart (see Fig. 1). B. Population Under Study One-minute BSPM recordings were obtained from 17 patients admitted in the Otto-von-Guericke University Hospital (D.H., A.B.) and diagnosed with persistent AF. Also, 10-s recordings

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Fig. 1. Electrode positioning of the BSPM system. (Left) Front part of the thorax. (Right) Back. Each dot represents an electrode position.

of 18 healthy subjects were included in our study as control group. The protocol was approved by the institutional review board of the center, and all patients provided informed consent before taking part in the study. III. METHODS A. Preprocessing Signals were bandpass filtered with a passing band between 0.7 and 70 Hz in order to reject noise while preserving the signal content of ECG signals [34]. Then, QRS peaks were detected by using a modified version of Tompkins algorithm [35]. Detections were visually inspected in order to avoid incorrect detections of the algorithm. An averaged beat was calculated by template matching averaging, with a window size of 30% of the mean RR duration before the QRS peak and 70% of the mean RR duration after the QRS peak. Only beats with a correlation index with the median beat that exceeded the threshold of 0.97 were considered for averaging. Initial and final points of the QRS complex (QRSonset , QRSoffset ), T wave (Toffset ), and P wave (Ponset , Poffset ) were detected in the averaged beat when present in the recording by using a hop-along-based fiducial point detector. QRS complexes were defined as starting on the first QRSonset and ending on the last QRSoffset . Remaining baseline artefact was reduced by subtracting the mean value of each QRS complex in each lead. A total of six QRS complexes per patient was selected in order to have the same number of waves from each subject. These six QRS complexes were concatenated constituting the matrix (XQRS )64×6L , where L is the sample length of the QRS complex. The maximum amplitude value (Am ax ) of the matrix XQRS of each patient was calculated, and then, all the leads of that patient were divided by this Am ax value, thus constituting the normalized matrix XQRSnorm . P waves were defined as beginning on the first Ponset and ending on the last Poffset . P waves were again low-pass filtered with a cutoff frequency of 30 Hz. A total of six P waves of each healthy subject was concatenated and normalized as described for the QRS complexes, thus constituting the matrices XP , XPnorm . AF segments were defined as starting 25 ms after the last Toffset found in the 64 leads and ending 25 ms before the first

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QRSonset detected. Detections were performed in the averaged beat, and then applied before or after each QRS detection in the ECG signal. Considering the frequency content of AF signals [36], AF segments were again bandpass filtered between 2 and 30 Hz. All AF segments of every patient were concatenated and constituted the (XAF )64×6L matrix, where L is the summed duration of all AF segments defined for a given patient and is dependent on the heart rate and QT duration. AF segments were normalized as previously defined for QRS complexes or P waves, thus constituting the normalized matrix XAFnorm . B. P Wave and QRS Complex Datasets Patients belonging to the control group were divided into study and test datasets: the first half of patients constituted the study dataset while the second half of patients constituted the test dataset. Concatenation of normalized QRS complex potential matrices (XQRSnorm ) of the first nine patients resulted in XQRS,STUDY . Concatenation of P wave normalized potential matrices (XPnorm ) of the first nine patients resulted in XP,STUDY . C. AF Datasets AF signals were divided into study and test datasets considering two different scenarios: experiment 1: nine patients included in the study dataset and eight patients in the test dataset; experiment 2: the first 30 s of the recording constituted the study dataset and the last 30 s of the recording constituted the test dataset. Normalized potential matrices of patients belonging to the two defined study datasets were concatenated by taking the same number of samples from all patients. Concatenation of 7.5 s of XAFnorm matrices of the first nine patients resulted in (XAF,STUDY1 )64×L , where L = 9Fs × 7.5. Concatenation of 3 s of XAFnorm matrices belonging to the first 30 s of the recording of each patient resulted in the matrix (XAF,STUDY2 )64×L , where L = 17Fs × 3. D. Lead Selection Leads were selected according to the criteria previously established by Lux [27]. The criterion employed in the algorithm proposed in [27] is an iterative selection of leads that maximizes the information contained in each lead selection consisting of an increasing number of leads. First, a matrix M is initialized with the original BSPM data. Next, the iterative process begins, where an index based on the covariance of M that accounts for the new information (i.e., information not contained in the lead selection from the previous iteration) introduced by each of the nonselected leads is measured. Accordingly, the lead that exhibits the highest value for this index is added to the lead set. Finally, the nonselected leads are reconstructed from the selected leads according to a least mean squares criterion, and M is updated by excluding the row corresponding to the selected leads and subtracting from each of the nonselected leads the aforementioned reconstruction, which refers to the components of the signal already represented by the selected leads. This pro-

cess is iteratively repeated until all leads of the BSPM system are included in the lead set. This selection algorithm is indeed a suboptimal method, since in each iteration, the leads from the previous iterations are kept and just one more lead is added, whereas an optimal method should include all possible n lead combinations at the nth iteration. Although this algorithm was proposed in an early study, it has been recently shown to be still superior to other novel methods [32]. This algorithm was applied in previously defined study datasets that were constructed by concatenating normalized potential matrices, namely XAF,STUDY1 , XAF,STUDY2 , XP,STUDY , and XQRS,STUDY . In order to compare the reproducibility in the selection of leads in the case of AF, the same algorithm was applied to the test datasets, although the performance was computed only with the lead system derived from the study dataset. E. Proposal of a New 12-Lead System Optimized for AF A nonstandard 12-lead set optimized for AF was calculated by first selecting the limb leads plus two precordial leads, and then obtaining the remaining optimal four leads by using the method described before. This lead system would allow to use existing ECG machines by keeping the limb leads plus at least two standard precordial leads and changing the position of four electrodes. Two cases were considered: constraints 1 implied selecting V1 and V2 and constraints 2 implied selecting V1 and V4. F. Reconstruction of Body Surface Potentials Performance of a given lead set was quantified as the error in reconstruction of nonselected leads. Having the leads ordered as explained in Section III-D, we calculated derived leads from an increasing number of selected leads as a linear combination of them. The linear combination that optimizes the derivation is calculated by least squares optimization ˆ {i ,...,i } = T X{j ,...,j } X 1 N 1 M

(1)

where X{·} is a matrix containing the rows of X corresponding to the indices in {·}, {j1 , . . . , jM } are the indices of the selected ˆ is a matrix of estimated nonselected leads, {i1 , . . . , iN } leads, X are the indices of nonselected leads, and T is the transform that optimizes the estimation. T matrix is computed by using both selected leads and nonselected leads of the study dataset as follows: T = X{i 1 ,...,i N } X{j 1 ,...,j M } †

(2)

where X† is the Moore–Penrose pseudoinverse of matrix X. Normalized matrices for all study datasets XAF,STUDY1 , XAF,STUDY2 , XP,STUDY , and XQRS,STUDY were used for the computation of the transform matrices TAF1 , TAF2 , TP , and TQRS , respectively.


G. RMS Error in Reconstruction The derived leads were compared to true recorded leads by the mean root squared error 2 S ˆ i=1 X(j,i) − X(j,i) S εM =

(3) N where εM stands for the error produced by a lead set consisting of M leads, N is the total number of leads, and S is the number of samples in each row X. This error was normalized according to voltage amplitude present in the dataset, and so, a relative error was computed as follows: 2 S

N X(j ,i) i=1 j =1 S (4) A= N εR εR ,M = (5) A where εR ,M is the relative error of a lead set consisting of M leads. In order to evaluate the performance of the algorithms, we carried out two experiments corresponding to two different scenarios. The first scenario refers to an ideal situation where the lead selection and the transformation matrix T are applied over the same ECG signals, i.e., the study dataset. This would reflect the best performance that can be achieved by the lead selection algorithm because the optimal lead system and transformation matrix are available for the ECG signals under evaluation. The second scenario refers to a real situation where neither the optimal lead system nor the optimal transformation matrix for the ECG signals under test is available, i.e., the test dataset. In this case, the lead system and transformation matrix are computed for the study dataset, while the test dataset is used for evaluation. Absolute and relative errors were computed for all the datasets described before and for both real and ideal situations. Same evaluations were performed on a lead selection consisting only eight independent leads of the standard ECG in order compare their performance with the first eight leads selected with the algorithm proposed in [27]. Standard leads were ordered following the sequence: I, II, V1 , V3 , V5 , V2 , V6 , V4 . H. Spectral Analysis of Original and Derived AF Waves Derived leads were compared to true recorded leads in terms of their spectral content. In order to obtain the power spectral content of AF waves, AF signals were estimated from the surface ECG by canceling the ventricular activity from the subtraction of a matching QRS-T template in 10-s segments. This template was computed for each beat as a linear combination of the principal components previously obtained from the analysis of all beats in the ECG segment [37]. Welch’s periodogram was used to obtain the power spectral density (PAA ) of atrial signals (a hamming window of 2.5 s and 50% overlap). The dominant frequency (FAA ) was defined as the dominant peak in the power spectrum that accounts for at least 30% of the total power spectra. Power spectra of AF signals in which the cancelation

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process has not been successful present frequency components corresponding to the remaining ventricular activity, and thus, a dominant frequency cannot be determined. Accuracy in the estimation of AF frequency was evaluated for the 12-lead ECG and the proposed lead systems. Leads that did not belong to the lead system under study were used for evaluation. FAA and PAA were computed in the true recorded ECG signals and also in ECG signals reconstructed by using each lead set. Only leads in which a dominant frequency could be estimated in all lead systems under consideration were considered for comparison. Difference in the estimated FAA computed for the recorded signal and the estimated signal (∆FAA ), correlation among estimated FAA in the recorded and estimated signals (ρFAA ), and correlation of the power spectra of recorded and estimated signals (ρPAA ) were computed. I. Statistical Analysis Errors in reconstruction were computed for each patient and lead selection, and then, mean error values and standard deviations were computed. Comparisons between different lead selections evaluated for the same group of patients were conducted by a paired sample t-test. Comparisons between performances of lead selections applied to different groups of patients were obtained by an independent sample t-test. Two significance values were considered: p < 0.05 and p < 0.01. Differences of p value >0.05 were considered as nonsignificant (ns). J. Limitations Due to Low Signal-to-Noise Ratio When dealing with the information content of AF signals, it must be taken into account that the signal-to-noise ratio of the fibrillatory waves is much lower than that in QRS complexes. For this reason, the accuracy in the reconstruction of potentials can be limited by the noise level. Indeed, once the reconstruction error reaches the noise level, an improvement in the reconstructed potentials can not be expected if a new lead is added to the reduced lead set. In order to estimate the noise level present in our signals, we assumed that after having included almost all leads for the derivation on nonselected leads, the improvement due to the inclusion of a new lead is caused only by the inclusion of the noise of that lead. Therefore, the noise level is estimated as the tendency line of the error curve. The slope of this tendency line was calculated by using the last five points of the curve. An error of reconstruction of the maximum quantization error (0.5 µV) above the noise level will be considered to be the limit in the achievable information content. IV. RESULTS A. Leads Selected The first eight leads selected for the study and test datasets can be observed in Fig. 2, both for experiments 1 (division of patients into study and test groups) and 2 (seconds 0–30 of all patients constituted the study group while seconds 30–60 constituted the test group). Panel A shows different lead placements for the two groups of patients, while panel B shows no difference in the

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Fig. 2. First eight leads selected for the study and test datasets. Panel A shows the leads selected in experiment 1 (patient division). Panel B shows the leads selected in experiment 2 (time division). Plus sign represents leads selected for the study dataset. Circles represent leads selected for the test set.

Fig. 3. First 23 leads selected for the study dataset. The number of each lead positioning represents the order in which any given lead was selected.

selection of leads when applied to the same group of patients but in different time intervals. Fig. 3 shows the first 23 leads selected for the study dataset focused on the reconstruction of atrial potentials during AF. New 12 leads proposed for the study of AF can be observed in Fig. 4 both for constraints 1 (limb leads plus V1 and V2) and constraints 2 (limb leads plus V1 and V4). Lead placements obtained in the different experiments include a high density of electrodes around V1 and the right part of the anterior torso, some electrodes on the precordial area, and a few electrodes on the posterior torso. B. Performance of the Leads Selected Errors in reconstruction of the potentials on the whole body surface from a limited number of leads are depicted in Fig. 5. RMS errors for both ideal and real scenarios are represented.

Fig. 4. Twelve lead system proposed for AF. Panel A shows the leads selected with constraints 1 (selection of limb leads, V1, V2, and four calculated leads). Panel B shows the leads selected with constraints 2 (selection of limb leads, V1, V4 and four calculated leads). Plus sign represents leads selected for the study dataset. Circles represent leads selected for the test set.

Both absolute and relative errors obtained from the first eight leads selected, applied on the derivation of QRS complexes, P waves, and AF waves corresponding to experiment 1 (division of patients into study and test set) are summarized in Table I. Errors in wave derivation considering an ideal scenario in which the lead set and transformation matrix is computed for the same signals under test are lower than errors in a more realistic scenario in which both lead set and transformation matrices is computed for the study set and applied on the test set (32 µV versus 59 µV, p < 0.01, for the derivation of the QRS complex with the standard selected leads). This difference between results for real and ideal scenarios does not apply when the division of datasets is performed over time [see Fig. 5(d)]. Although error values are higher for waves with high amplitude than those for waves with low amplitude such as fibrillatory waves, relative errors in the derivation of AF waves are higher than those achieved in the derivation of other ECG waves (see Fig. 6). Errors in reconstruction from the standard ECG in a real scenario are comparatively higher for AF waves than for the QRS complex: 53% versus 25% (p < 0.01) or the P wave: 53% versus 39% (p = ns). This error in reconstruction of AF waves is reduced when the first eight leads selected are considered instead of the standard ECG: 42% versus 53% (p < 0.01). Improvement of the first eight leads selected over the standard ECG is less significant when applied to the QRS complex (22% versus 25%, p = ns) or the P wave (33% versus 39%, p = ns). According to the results from Fig. 6 and Table I, performance of reduced lead sets in AF is not as high as that in the QRS complex, and the number of leads needed to achieve a comparable performance needs to be increased. However, the amount of meaningful information in the case of AF signals has to be considered because a limited lead system cannot be expected


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Fig. 5. Errors for limited lead sets and standard ECG in the derivation of QRS complex, P wave, and AF waves. Solid line represents the results for the real case (leads and transfer matrices calculated for the study set and evaluation performed for the test dataset), while dashed line represents the results for the ideal case (leads and transfer matrices and calculated for the study set and errors calculated for the test dataset). Thick lines represents errors in reconstruction achieved with the standard 12-lead ECG, while thin lines represent errors in reconstruction achieved with computed optimized lead sets. Note that tracings corresponding to the 12-lead ECG stop at eight independent leads. Panel A presents errors in microvolts in the derivation of the QRS complex. Panel B presents errors in microvolts in the derivation of the P wave. Panel C presents errors in microvolts in the derivation of AF waves in experiment 1 (patient division). Panel D presents errors in microvolts in the derivation of AF waves in experiment 2 (time division). TABLE I ERRORS FOR THE STANDARD ECG AND FOR THE FIRST EIGHT SELECTED LEADS IN THE DERIVATION OF QRS COMPLEX, P WAVE, AND AF WAVES

to achieve a reconstruction error below the noise level. Fig. 7 shows the errors in reconstruction of AF signals compared to the estimated noise level. From Fig. 7, it can be observed that errors in reconstruction with more than 34 leads appear below the information content limit that we set, 0.5 µV above the noise level, which is the maximum quantification error. Consequently, inclusion of more than 34 leads does not increase the information content related to AF of a lead system. By computing this limit for the QRS complex and the P wave also, we observed that the noise level is reached with 56 leads for the QRS complex and 17 leads for the P wave.

Fig. 6. Relative errors for limited lead sets and standard ECG in the derivation of QRS complex, P wave, and AF waves. Solid line represents the results for AF, dashed line represents the results for the P wave, and dotted line represents the errors for the QRS complex.

Table II summarizes the number of leads required for reaching a given relative error threshold. While eight leads are enough for reaching an error lower than 25% in the QRS complex, 17 leads are needed for the P wave and 23 are needed for AF waves. If we lower this threshold down to 10%, 22 leads are needed for the reconstruction of the QRS complex while the number of leads required both for the reconstruction of the P wave and the QRS complex exceeded the number of leads with meaningful information given by the noise level present. An objective of

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6 µV or 42% (p = ns) and better results than those obtained for the 12-lead ECG: 8 µV or 53% (p < 0.05). Performance of any of these lead systems proposed for AF on the QRS complex is comparable to the performance of the standard 12-lead ECG: 22%–25% error versus 25% (p = ns) for the QRS complex and 34%–35% error versus 39% (p = ns). V. DISCUSSION

Fig. 7. Errors in the derivation of AF waves versus errors in reconstruction equal to a measured noise level. For AF, values correspond to experiment 1 (patient division) in the real case (leads and transfer matrices calculated for the study set and evaluation performed for the test dataset). TABLE II NUMBER OF LEADS NEEDED IN A REAL CASE TO ACHIEVE A GIVEN RELATIVE ERROR FOR THE QRS COMPLEX, P WAVE, AND AF WAVES

25% error is probably the most reasonable limit that we can set and 23 leads are needed to reach this limit in AF while 17 leads are needed for the P wave. Performance of the 12-lead ECG system and the proposed leads in the estimation of spectral features of nonrecorded signals is presented in Table III. A dominant frequency could not be estimated in 4.1 ± 7.1 true recorded leads. Additionally, a dominant frequency could not be estimated in 2.6 ± 4.6 leads for the standard ECG, 2.3 ± 3.4 leads for the first eight selected leads, and 1.5 ± 2.5 for the first 23 selected leads. Only leads in which a dominant frequency could be estimated in all lead systems were considered. Dominant frequency of derived AF signals showed a correlation (ρFAA ) with recorded AF signals of 0.57 (p < 0.01) for the standard 12-lead ECG, 0.67 (p < 0.01) for the first eight selected leads, and 0.76 (p < 0.01) for the first 23 selected leads. Difference in the estimated frequencies (∆FAA ) for leads derived from the 12-lead ECG was 0.60 Hz versus 0.47 Hz for the first eight selected leads (p < 0.01) and 0.33 Hz for the first 23 leads (p < 0.01). Correlation of the spectra (ρPAA ) was 0.95 for the 12-lead ECG versus 0.97 for the first eight selected leads (p < 0.01) and 0.98 for the first 23 selected leads (p < 0.01). C. Performance of a New 12-Lead System Optimized for AF Results on the performance of the two proposed 12-lead systems that include the limb leads plus two standard precordial leads are summarized in Table IV. Both lead sets (depicted in Fig. 4) achieve comparable errors to those obtained with the first eight selected leads: 6–7 µV or 43%–44% error against

The standard 12-lead ECG is not optimized for the reconstruction of body surface potentials during AF. In fact, its reconstruction errors are not negligible: 53% error from our results. Also, computation of lead sets optimized for the study of AF results in lead placements that differ from the standard lead placements. Our results agree with previous works [24]–[26] that suggested that the standard 12-lead ECG is not optimized for the study of AF signals. If we aim at defining a lead set optimized for AF, the first question that needs to be addressed is the number of leads that are necessary. Previous studies regarding the optimum number of leads using real BSPM data have dealt with the information content of nonfibrillating signals. Hoekema et al. [22] found that the number of independent signals in body surface maps is of the order of 10. However, these ten independent signals may not be appropriately sampled by ten electrodes according to the studies of Lux et al. [27], who reported that 32 leads could reconstruct body surface potentials with 5% error. From our results, only eight electrodes can reconstruct body surface potentials at 64 positions with 25% error for the QRS complex and 22 electrodes are needed in order to decrease this error down to 10%, which is consistent with the observations made by Hoekema and Lux. The number of independent signals in simulated AF was found to be of the order of 60 [25], which is sixfold the number of independent signals found in nonfibrillating BSPM recordings [22]. In order to determine experimentally the number of leads needed to reconstruct body surface potentials during AF, we applied the lead selection procedure proposed by Lux et al. [27] and computed errors in reconstruction of body surface potentials in two different scenarios: 1) a “real” scenario in which the lead selection and the transform used for the reconstruction of nonselected leads are performed on a study dataset and the evaluation is performed on a test dataset and 2) an “ideal” scenario in which the evaluation is performed on the same dataset used for the guidance of the lead selection procedure and the computation of transform matrices. In order to extract conclusions about the number of leads needed, we considered only the “real” scenario. However, we included this “ideal” scenario in order to separate two effects that have great influence in the evaluation of the performance of a lead set: 1) the nature of the signals under study, which is related to the number of independent signals and the signal-to-noise ratio and (2) interpatient variability that results in optimal lead placements and transform matrices that are different for every subject under study. In an ideal scenario, the effect of patient variability is reduced, and thus, we can obtain results that are less dependent on interpatient variability and reflect the effect of the inclusion of a


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TABLE III SPECTRAL MEASUREMENTS IN DERIVED AF SIGNALS COMPARED TO TRUE RECORDED AF SIGNALS

TABLE IV ERRORS FOR THE STANDARD ECG, FIRST EIGHT LEADS SELECTED FOR AF, AND THE PROPOSED REPLACEMENT OF THE STANDARD LEADS IN THE DERIVATION OF QRS COMPLEXES, P WAVES, AND AF WAVES

given number of leads on the global reconstruction error, which is primarily due to the nature of fibrillatory signals. However, in a real situation, these two effects are not separable, and we can interpret only the results arising from the “ideal” scenario as a limit of the best performance that can be achieved even if the transform matrix and lead selection could be performed by using patient-specific information. According to our results, 23 leads are needed in order to reconstruct body surface potentials during AF with 25% error, which is a larger number than the eight leads needed for the QRS complex for the same degree of accuracy. Although inclusion of more than 23 leads may reduce the reconstruction error in case of AF, inclusion of more than 34 leads adds information below the noise level, and thus, their information content is limited. Also, 23 leads are better in order to accurately estimate the spectral content of AF signals than a smaller subset of leads, allowing a better estimation of the spectrum and the dominant frequency in nonrecorded leads. This finding can be easily attributed to the nature of fibrillatory signals: electrical activity in fibrillating atria is far from being organized or explained by a dipolar model as opposed to the QRS complex that is mainly dipolar. In these circumstances, fibrillatory waves recorded in a given location are hardly reconstructed from electrodes located far away from this location. The location of these 23 leads may not be a crucial issue and many lead subsets—not all lead subsets-–with similar number of electrodes, and not necessarily 23, may present a similar performance. According to our experiment, our first 23 leads include right anterior electrodes and posterior electrodes. Two questions arose after we had computed this optimal lead set:

1) is this optimal lead set unique or does it vary among patients? and 2) is it stable over time or does it vary as AF signals do? In order to answer these two questions, we set up two different experiments: in experiment 1, we divided our patients into two groups, and in experiment 2, we put all patients together but studied separately two time intervals. We found that the optimum set of electrodes is not unique by observing the leads selected for our two subsets of patients in experiment 1. Also, we observed that the location of these electrodes is repeatable and stable: lead positioning is almost identical when ECG signals of the same patients acquired at different time instants are considered, as can be derived from our experiment 2. We want to emphasize that these electrode positions should not be taken as the only lead locations that would improve the reconstruction of body surface potentials during AF. Instead, it should be considered as a general guidance on how to arrange electrodes for performing BSPM mapping during AF. Also, it shall be cautious to extrapolate the present results considering the relatively short recording of our AF signals. Because of the well-known instability of the AF signals (due to nonstationary AF sources and continuously remodeling of AF substrates), further study is necessary to evaluate the true intrasubject stability. By stating that 23 leads are needed in order to reconstruct body surface potentials during AF, we do not mean to imply that AF cannot be diagnosed with a more reduced number of leads. In fact, the existence of AF can be diagnosed by using an even more reduced set of leads (e.g., standard ECG or Holter recordings). The potential application of this study is extraction of diagnostic features apart from the detection of AF. Preliminary studies [18]

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suggest that high-density surface mapping can be a valuable noninvasive tool for the study of the state of the atria in patients with AF. Although interpretation of body surface maps during AF is still an open research field, it is important to determine how many electrodes are necessary for constructing these maps. From our results, body surface potential maps during AF will only be at least as accurate as the 12-lead ECG for the QRS complex (25% error) if 23 leads are used. In case that only a small number of leads are available, a positioning of these leads that optimizes for the study of AF signals can improve the amount of information that is recorded both in terms of the rms error and the ability of estimating the dominant atrial frequency in nonrecorded leads. We present the results for different conditions: 1) no restrictions applied in the search procedure and 2) force the inclusion of limb leads plus two precordial leads in order to keep some ECG signals that the cardiologist is familiar with while using the same ECG machine that is available. In either case, selected leads include electrodes: 1) on the right side of the torso; 2) superior to V1; and 3) on the posterior torso. These results agree with lead placements previously proposed for the study of AF [24]–[26] although the exact location of the electrodes is not identical. Errors in reconstruction of AF waves from these limited lead sets are similar (42% to 44%) and always improve the 53% error achieved with the standard 12-lead ECG. Performance of the standard 12-lead ECG is more optimized for the study of the QRS complex or the P wave. In fact, improvement after lead repositioning (3% improvement for the QRS complex and 6% improvement for the P wave) is not significant. The standard ECG may be adequately sampling these nonfibrillating signals that can be represented with some accuracy with a dipolar model. Any of the proposed locations for lead sets limited to eight leads allows at least 9% less error in reconstruction than the standard 12-lead ECG without detriment to the performance on the QRS complex or P wave. The clinical relevance of this 9%–11% improvement is questionable, and an increase of the number of exploring electrodes is needed if a reasonable accuracy is desired, but if this is not possible, a change in the position of the standard 12-lead ECG may allow some improvement in the study of AF signals while the performance on other ECG waves is not altered. VI. STUDY LIMITATIONS We have computed optimal lead sets based on an information index and sequential search algorithm described by Lux et al. [27]. This method is based on an optimization of the error in reconstruction of leads not included in any lead set and not based in any clinical parameter. Also, this sequential search algorithm is suboptimal compared to exhaustive search algorithms that test all possible combination of leads for any number of leads [29]. This search strategy is computationally intensive and, as their authors in [29] reported, results are not more satisfactory than lead sets obtained by using Lux’s algorithm. The main limitation of our study is the limited number of patients enrolled and limited length of our recordings, especially in the case of AF signals that are variable in time. Consequently,

our results may not be valid for a different population of patients and are specific for our database. VII. CONCLUSION Limited lead sets allow the detection of AF but do not allow an accurate reconstruction of all the electrical information available on the body surface during this arrhythmia. At least 23 leads are needed in order to have the same degree of accuracy as the 12-lead ECG for a normal QRS complex, and thus construct surface maps with some reliability. All these results suggest that the fibrillatory waves are significantly more heterogeneous than P-waves and QRS complexes. Accordingly, in order to characterize and analyze the atrial signal during AF, our recommendation would be to employ as many leads as possible (with up to 34 leads instead of using a reduced lead system), also considering the possibility of employing a BSPM recording system. Nevertheless, if a limited lead set is to be chosen, a repositioning of only four electrodes from the standard ECG improves the accuracy of the characterization of AF waves, allowing a reconstruction of AF signals with 11% less error than the error achieved with the standard 12-lead ECG. This repositioning of electrodes may include more right anterior electrodes and one posterior electrode. REFERENCES [1] R. L. Lux, “Electrocardiographic body surface potential mapping,” Crit. Rev. Biomed. Eng., vol. 8, no. 3, pp. 253–279, 1982. [2] B. Taccardi, B. B. Punske, R. L. Lux, R. S. MacLeod, P. R. Ershler, T. J. Dustman, and Y. Vyhmeister, “Useful lessons from body surface mapping,” J. Cardiovasc. Electrophysiol., vol. 9, no. 7, pp. 773–786, 1998. [3] F. Kornreich, T. J. Montague, M. Kavadias, J. Segers, P. M. Rautaharju, M. B. Horacek, and B. Taccardi, “Qualitative and quantitative analysis of characteristic body surface potential map features in anterior and inferior myocardial infarction,” Amer. J. Cardiol., vol. 60, no. 16, pp. 1230–1238, 1987. [4] F. Kornreich, T. J. Montague, and P. M. Rautaharju, “Identification of first acute Q wave and non-Q wave myocardial infarction by multivariate analysis of body surface potential maps,” Circulation, vol. 84, no. 6, pp. 2442–2453, 1991. [5] S. F. Wung and B. Drew, “Comparison of 18-lead ECG and selected body surface potential mapping leads in determining maximally deviated ST lead and efficacy in detecting acute myocardial ischemia during coronary occlusion,” J. Electrocardiol., vol. 32, pp. 30–37, 1999. [6] K. Hisamatsu, K. F. Kusano, H. Morita, S. Takenaka, S. Nagase, K. Nakamura, T. Emori, H. Matsubara, and T. Ohe, “Usefulness of body surface mapping to differentiate patients with Brugada syndrome from patients with asymptomatic Brugada syndrome,” Acta Med. Okayama, vol. 58, no. 1, pp. 29–35, 2004. [7] M. Takagi, I. Toda, K. Takeuchi, and J. Yoshikawa, “Utility of right precordial leads at higher intercostal space positions to diagnose Brugada syndrome,” Pacing Clin. Electrophysiol., vol. 25, no. 2, pp. 241–242, 2002. [8] S. Sangwatanaroj, S. Prechawat, B. Sunsaneewitayakul, S. Sitthisook, P. Tosukhowong, and K. Tungsanga, “New electrocardiographic leads and the procainamide test for the detection of the Brugada sign in sudden unexplained death syndrome survivors and their relatives,” Eur. Heart J., vol. 22, no. 24, pp. 2290–2296, 2001. [9] H. J. Bruns, L. Eckardt, C. Vahlhaus, E. Schulze-Bahr, W. Haverkamp, M. Borggrefe, G. Breithardt, and T. Wichter, “Body surface potential mapping in patients with Brugada syndrome: Right precordial ST segment variations and reverse changes in left precordial leads,” Cardiovasc. Res., vol. 54, no. 1, pp. 58–66, 2002. [10] S. J. Maynard, I. B. Menown, G. Manoharan, J. Allen, A. J. McC, and A. A. Adgey, “Body surface mapping improves early diagnosis of acute


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Mar´ıa de la Salud Guillem was born in Valencia, Spain. She received the M.S. degree in telecommunications engineering from the Universidad Politécnica de Valencia (UPV), Valencia, Spain, in 2003, the M.S. degree in biomedical engineering from Northwestern University, Evanston, IL, in 2006, and the Ph.D. degree in electronics engineering from the UPV, in 2008. She is currently an Assistant Professor in the Electronical Engineering Department, and a Researcher at the Institute for Applications of Advanced Information and Communication Technologies (ITACA), UPV. Her research interests include biomedical signal processing with main interest in cardiac signals. Dr. Guillem is a Fulbright Fellow at Northwestern University.

Andreas Bollmann received the M.D. degree in 1995 from the Otto-von-Guericke University, Magdeburg, Germany. He is an Assistant Professor of medicine and clinical electrophysiologist at the University Leipzig Heart Center, Leipzig, Germany as well as a Visiting Professor at the Division of Clinical Pharmacology, Vanderbilt University, Nashville, TN. His clinical and research interests include atrial fibrillation, antiarrhythmic drugs, ablation, clinical genetics, implantable defibrillators and pacemakers, and ECG signal processing. Dr. Bollmann currently serves as the Co-Chair of the NordForsk research network “Electrocardiology of Atrial Fibrillation”.

Andreu M. Climent was born in Gandia, Spain. He received the M.S. degree in telecommunications engineering from the Universidad Politécnica de Valencia (UPV), Valencia, Spain, in 2006. He is currently working toward the Ph.D. degree at the Electronical Engineering Department, UPV. From 2005 to 2008, he has successfully completed research fellowships in Magdeburg, Milan, Lund, Leipzig, and Cleveland. He is a Fellow Researcher at the institute for Applications of Advanced Information and Communication Technologies (ITACA), UPV. His current research interests include atrioventricular conduction during supraventricular arrhythmias and biomedical signal processing.

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Daniela Husser received the M.D. degree in 2003 from the Otto-von-Guericke University, Magdeburg, Germany. Since 2007, she has been the Head of the Cardiac Arrhythmia Research Center and the Genetics Clinic of the Department of Electrophysiology, Heart Center Leipzig, Leipzig, Germany. From 2003 to 2006, she has successfully completed research fellowships in Los Angeles, Lund, and Nashville, where he focus on atrial fibrillation electrophysiology, signal processing, genetics, and ablation. Currently, she is a Coinvestigator of a research project “electrical signals as biomarkers in atrial fibrillation—from molecular determinants to clinical applications” sponsored by the Volkswagen Foundation, Germany. Dr. Husser is also a Guest Researcher at the Division of Clinical Pharmacology, Vanderbilt University, Nashville, TN.

Jose Millet-Roig was born in Valencia, Spain. He received the M.S. degree in physics from the University of Valencia (UV), Valencia, Spain, in 1991 and the Ph.D. degree in electrical and electronic engineering from the Universidad Politécnica de Valencia (UPV), Valencia, Spain, in 1997. He is currently a Full Professor in the Department of Electronic Engineering, UPV. Since 1997, he has been the Coordinator of the biomedical engineering branch, the Institute for Applications of Advanced Information and Communication Ttechnologies (ITACA), UPV. His professional research interests include biomedical signal processing, biomedical signal acquisition, and instrumentation, implantable devices for treatment of cardiac arrhythmias and Cardiac MRI.

Francisco Castells was born in Valencia, Spain, in 1976. He received the M.Eng. degree in telecommunications engineering from the Universidad Politécnica de Valencia (UPV), Valencia, Spain, in 2000, and the Ph.D. degree in electronics engineering from the UPV, in 2006. From 2000 to 2001, he was with Alcatel SEL AG, Stuttgart, Germany, where he was engaged in the telecommunications manufacturing industry. He is currently a Permanent Lecturer at the Electronics Engineering Department, UPV, where he is also a member of the Institute for Applications of Advanced Information and CommunicationTechnologies (ITACA). His research interests include statistical signal processing of biomedical signals, with special emphasis on the characterization, and analysis of atrial fibrillation.