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Optimizing the 12-lead electrocardiogram: a data driven approach to locating alternative recording sites
Journal of Electrocardiology 40 (2007) 292 – 299 www.jecgonline.com
Optimizing the 12-lead electrocardiogram: a data driven approach to locating alternative recording sites Dewar D. Finlay, PhD,a,4 Chris D. Nugent, DPhil,a Jan A. Kors, PhD,b Gerard van Herpen, MD, PhD,b Mark P. Donnelly, BSc,a Paul J. McCullagh, PhD,a Norman D. Black, PhDa a
School of Computing and Mathematics, Faculty of Engineering, University of Ulster, Belfast, Northern Ireland, UK b Department of Medical Informatics, Erasmus University Medical Centre, Rotterdam, The Netherlands Received 31 August 2006; accepted 14 December 2006
Abstract
Background: Despite its widespread use, the limitations of the 12-lead electrocardiogram (ECG) are undisputed. The main deficiency is that just a small area of the precordium is interrogated and for some abnormalities information may be transmitted to a region of the body surface where information is not recorded. In this study, we attempted to optimize the 12-lead ECG by using a datadriven approach to suggest alternate recording sites. Methods: A sequential lead selection algorithm was applied to a set of 744 body surface potential maps (BSPMs), consisting of recordings from subjects with myocardial infarction, left ventricular hypertrophy, and no apparent disease. A number of scenarios were investigated in which pairs of precordial leads were repositioned; these pairs were V3 and V5, V4 and V5, and V4 and V6. The algorithm was also used to find optimal positions for all 6 precordial leads. Result: Through estimation of entire surface potential distributions it was found that each of the scenarios, with 2 leads repositioned, captured more information than the standard 12-lead ECG. The scenario with V4 and V6 repositioned performed best with a root mean square error of 22.3 microvolts and a correlation coefficient of 0.967. This configuration also fared favorably when compared to the scenario where all 6 precordial leads were repositioned as optimizing all 6 leads offered no significant improvement. Conclusion: This study demonstrated the use of a lead selection algorithm in enhancing the 12-lead ECG. The results also indicated that repositioning just 2 precordial leads can provide the same level of information capture as that observed when all precordial leads are optimally placed. D 2007 Elsevier Inc. All rights reserved.
Introduction The main deficiency of the standard 12-lead electrocardiogram (ECG) is that the sampling region is constrained to a small area of the precordium. It is appreciated that for abnormalities such as true posterior infarcts diagnostic information may be transmitted to areas on the surface of the torso where the ECG information is not recorded.1-3 The most obvious and most effective way to address this problem would be to redesign the 12-lead ECG focusing specifically on the positions of the 6 precordial leads, because it has been shown that the current positions of these unipolar leads are not optimal for maximum information 4 Corresponding author. E-mail address: [email protected] 0022-0736/$ – see front matter D 2007 Elsevier Inc. All rights reserved. doi:10.1016/j.jelectrocard.2006.12.015
capture.4,5 In theory, this approach would be ideal; in practice, however, it is unlikely to succeed because the familiar format of the 12-lead ECG coupled with the considerable amount of diagnostic criteria accumulated in the literature mean that it is a tool with which most clinicians are extremely comfortable and which they are therefore unlikely to relinquish.6,7 A less radical approach that aims to enhance the current 12-lead ECG is to supplement the currently recorded information with information recorded from additional sites on the torso. This can mean anything from adding just a few extra recording sites on the right chest and posterior surface 3,8 to recording body surface potential maps (BSPMs).9 Although proven to yield superior diagnostic information, these approaches are seldom adopted because increasing the number of recording channels increases the
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the 12-lead ECG. A description of the basic operation of the algorithm and the studied data is given in the following paragraphs. Lead selection algorithm
Fig. 1. Schematic of 117 lead BSPMs. Also highlighted are the positions of the 6 precordial leads relative to this electrode array.
technical and practical complexity of the acquisition process. Bearing this in mind, the most efficient compromise would extend the diagnostic capability of the existing 12-lead approach, using the same hardware and number of electrodes, without sacrificing any of the information currently available for interpretation. This was the objective of the work previously undertaken by Kors and van Herpen.10 In this study, 2 of the 6 precordial leads were moved to alternate locations on the torso based on the assumption that the missing leads could be accurately synthesized. This meant that although the 12-lead ECG could still be displayed, there were 2 free electrodes that could be moved to alternative locations where the information presence was deemed greatest. The study concluded with the suggestion of 2 balteredQ lead systems relying on the relocation of V4 and V6, which exhibited better information capture than either the 12-lead ECG or the EASI Philips Medical Systems, Ander, MA lead system.11 In both of the altered systems, 1 electrode was moved to 2 intercostal spaces below V2 and the remaining electrode was placed either 2 intercostal spaces above V2, or 3 intercostal spaces above V4. As a measure of performance, the accuracy of the new lead configurations in estimating total body surface potential distributions (BSPMs) was assessed. In the work of Kors and van Herpen,10 the recording sites were chosen to record information from areas that were assumed to have best the signal information content and were not interrogated by the original electrode positions. The choice of the new recording sites was based on prior knowledge derived from the results of previous studies such as,12 where the objective was to establish where the most diagnostic information is projected onto the body’s surface. In the current study, an attempt is made to consolidate the work previously presented by Kors and van Herpen10; however, this time a lead selection algorithm is used to find the new recording sites. In addition, the data generated by the lead selection algorithm are used to provide a visual representation of the spatial distributions of electrocardiographic information on the body surface.
The algorithm uses a sequential forward selection approach to evaluate all available recording sites in the 117 lead BSPMs and chooses the best sites for capturing total body surface information. The process begins by evaluating how well each of the available sites can be used to estimate the potentials at all the remaining sites in the BSPM. Multiple linear regression is used to determine the transformation required to estimate the remaining ECG information. The individual site observed to perform best is chosen as the boptimalQ site. This constitutes the first iteration of the algorithm. On the next iteration, each of the remaining sites are evaluated in conjunction with the first chosen site. The site that performs best in conjunction with the first site is then chosen. At this point we have chosen 2 sites, and this process can be repeated for the desired number of iterations. In general, the algorithm can be used to select the first best site up to the nth site; this is exemplified in the application of the algorithm in the work of Finlay et al,4 where the top 32 sites were chosen. In the current study, the objective is to start off with some subset of the 6 precordial recording sites and build upon this. Highlighted in the discussion presented by Finlay et al,4 is the algorithm’s suitability to such an application because bpreselectedQ or benforcedQ recording sites can readily be incorporated in the selection process. Data set The data set consisted of 117 lead BSPMs that were recorded from 744 subjects. This was made up of approximately one third healthy subjects, one third subjects with myocardial infarction (MI), and one third subjects with left ventricular hypertrophy (LVH). The process for acquiring the data has been previously described in,13 and a schematic of the positions of the 117 recording sites is shown in Fig. 1. All isopotential map frames from the QRST of each subject were pooled, and to facilitate application of the algorithm a bselection setQ was extracted from this pool. This consisted of approximately 75% of the data set with an equal distribution of disease types. During the experiments, the selection algorithm further partitioned the selection set to test and evaluate each available recording site. Readers are directed to the in-depth discussion of the algorithm presented by Finlay et al4 for further information on the treatment of the data during the selection process. To obtain an independent measure of performance of the suggested lead systems, the remaining 25% of data was used to calculate performance metrics for each suggested lead configuration.
Methods
Investigated scenarios
In this study, a lead selection algorithm previously developed by the authors and described by Finlay et al,4 is applied. This algorithm analyzes a set of 117 lead BSPMs to determine which of the available leads best compliment
Regardless of the selection methodology, the feasibility of the entire study relies on the assumption that there is redundancy in the 12-lead ECG. This redundancy stems from the fact that the 6 precordial sites are close to each
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Fig. 2. Spatial distributions of RMS error when remaining precordial leads are evaluated with every available recording site in 117 lead BSPMs. Each plot corresponds with 1 of the 3 proposed lead subsets: (A) V3 and V5 dropped, (B) V4 and V5 dropped, (C) V4 and V6 dropped. In each of these plots, the locations of the remaining 4 precordial leads are indicated with white squares. The location of the next best recording site, which is that yielding the lowest RMS error, is indicated with a crossed square.
other. It has been shown that with the inclusion of the limb leads, missing information/leads can be reconstructed from as few as 2 of the 6 precordial leads.14-17 The accuracy of the reconstructed signals are of course dependent on how many recording sites have been eliminated, and in the current study the same assumption is used as in,10 where to ensure the integrity of the reconstructed signals, no more than 2 recording sites were removed. As well as deciding the maximum number of sites that should be removed to preserve integrity, a further consideration is determining the 2 most suitable recording sites for elimination. The most obvious criterion is to select recording sites based on how well the signals from those sites can be reconstructed. In the report of Nelwan et al,17 an
exhaustive search of all combinations of precordial sites showed that the best candidates for elimination were V4 and V6 when general reconstruction coefficients were used, and V3 and V5 when patient-specific coefficients were used. Although the current study does not consider patientspecific coefficients, it was decided that both these pairs of recording sites would be considered. In addition to selecting sites that can be accurately reconstructed, practical issues have also been taken into consideration. In their study, Kors and van Herpen10 also suggested V4 and V5 as desirable electrodes to relocate because these sites can be difficult to accurately locate in women due to breast obstruction. In the current study, these electrodes are also considered for relocation.
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Fig. 3. Spatial distributions of RMS error when remaining precordial leads and 1 optimally selected site are evaluated with every available recording site in 117 lead BSPM. Each plot corresponds with 1 of the 3 proposed lead subsets: (A) V3 and V5 dropped, (B) V4 and V5 dropped, (C) V4 and V6 dropped. In each of these plots, the locations of the remaining 4 precordial leads are indicated with white squares. Also indicated with a white-crossed square is the optimal recording site that was chosen on the previous iteration of the algorithm. The location of the next best recording site, which is that yielding the lowest RMS error, is indicated with a crossed square.
In addition to the 3 scenarios where only 2 precordial leads were repositioned, several other tests were conducted to facilitate discussion and comparison. These included finding optimal positions for all precordial leads, adding 2 further leads to the standard 6 precordial leads, and finding recording sites specific for each disease group in the data set. Performance evaluation To measure the performance of each recording site, during the selection process, spatial root mean square (RMS) voltage error was used. The selection algorithm uses this metric to quantify how well the remaining sites in a BSPM are estimated in comparison to actual measured
values. If P 1 and P 2 are the vectors of the measured and estimated potentials, respectively, and n is the number of sites at which potentials have been estimated, the spatial RMS error e can be determined by the equation; e¼
jP 1 P 2 j pffiffiffi n
ð1Þ
In addition to the spatial RMS error, used by the algorithm to guide the lead selection process, we used the correlation coefficient to provide a further metric of final performance. The correlation coefficient provides a measure of the similarity in BSPM patterns between measured and estimated BSPM frames independent of amplitude. If P is the
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pattern differences might be extreme. To establish final performance measures for each of the developed lead sets, RMS error and correlation coefficient were calculated for each individual isopotential map frame in the test set. From this, median values for each subject were calculated and final performance was expressed as the median of the medians for each subject. Wilcoxon’s signed rank test was used to determine the statistical significance of the differences in performance between lead sets. This test was applied to the paired differences in median RMS error values for each subject in the test set. Results The sequential selection algorithm was applied considering each of the 3 subsets of precordial leads (subsets resulting in the removal of V3 and V5, V4 and V5, and V4 and V6). To provide an insight into the spatial distributions of electrocardiographic information, Figs. 2 and 3 have been included. These plots depict the calculated RMS error as each recording site is being selected. In each of these figures there are 3 contour plots, each of which correspond with 1 of the studied scenarios. Considering Fig. 2, the performance of each of the precordial lead subsets in conjunction with every other available recording site is depicted. Thus, at each of the 117 available recording sites the RMS error has been plotted. This is the error obtained when that particular site is used, along with the existing 4 precordial sites, to estimate entire surface potential distributions. This exposes and clarifies the operation of the selection algorithm because the site that can be seen to exhibit the lowest RMS error is the first site that is selected. In each of the plots, this site is indicated with a crossed square. It is evident from the
Fig. 4. Final recording sites chosen using the algorithm. Plots a to c correspond with proposed lead subsets (A) V3 and V5 dropped, (B) V4 and V5 dropped, and (C) V4 and V6 dropped, respectively. Each plot shows the remaining precordial recording sites along with the 2 alternate recording sites that have been suggested. (D) Result of optimally repositioning all precordial leads.
original map frame and PV is the estimated map frame, the correlation coefficient q can be described as q¼
PPV jPjjPVj
ð2Þ
This measure is useful as small errors of amplitude on low amplitude map frames may appear to be insignificant, yet
Fig. 5. Positions of recording sites in the (A) Kors1 and (B) Kors2 systems.
D.D. Finlay et al. / Journal of Electrocardiology 40 (2007) 292 – 299 Table 1 Performance figures for each lead configuration Repositioned leads
RMS error (lV)
Correlation coefficient
12 lead V3 + V5 V4 + V5 V4 + V6 Six optimal Kors1 Kors2
28.3 23.3 23.4 22.3 22.3 23.2 23.4
0.952 0.966 0.965 0.967 0.967 0.965 0.964
(21.4-34.5) (19.3-28.8) (18.7-29.2) (18.1-28.7) (18.1-29.3) (18.5-28.9) (18.9-29.4)
(0.926-0.971) (0.948-0.978) (0.945-0.976) (0.950-0.978) (0.948-0.977) (0.949-0.977) (0.946-0.978)
Also included are the performance figures obtained from the 12-lead ECG and Kors1 and Kors2 systems. In each case, the median values, along with interquartile range (inside parentheses) are listed.
plot in Fig. 2 that in all 3 cases the lowest RMS error is in the region superior to the precordial electrodes V1 to V4. This, in turn, suggests that for the studied population there is significant information transmitted to this area that is not captured by the remaining precordial leads. This can be thought of as the bmissing information.Q It can also be seen that there are 2 further regions where there is relatively low, albeit to a lesser extent, RMS error. These are a small region approximately 1 intercostal space below V2 and a larger region on the posterior surface. If the locations that provide little information gain (high RMS error) are considered, it can be seen that obviously there is less information close to where the existing precordial leads are located, particularly the remaining precordial leads. In addition, in all of the contour plots it can be seen that little is gained through electrodes in the right sternum, close to the region that would be interrogated by right ventricular leads (to the right of V1).8 When the 3 plots in Fig. 2 are compared with each other, it can be seen that the distributions are very similar. This would indicate that, regardless of which 2 recording sites are removed, a similar pattern of missing information is observed. After the initial selection run, as indicated in Fig. 2, the positions of 5 recording sites were known (4 original precordial plus first optimal) and the next step was to establish where the next recording site should be positioned. This process involved taking the 5 current recording sites and trying all of the remaining available sites to find the best combination. In Fig. 3, where the second iteration of the algorithm is depicted, the observations are similar to that in the first selection in that the regions that are close to existing recording sites (4 precordial sites + 1 new site) are the regions where there is little to gain from placing a new recording site (high RMS error). The areas where the missing information is located (low RMS error) also resemble the 2 less dominant areas that were observed in the first pass of the algorithm. These are the region below V2 and a larger region on the posterior surface. Again, across all 3 plots the observed distributions are similar. In Fig. 4, each of the final electrode configurations is illustrated along with the configuration suggested when all 6 precordial leads are considered for relocation. For the sake of comparison, the recording sites originally proposed by Kors and van Herpen10 are illustrated in Fig. 5 (from here on, we refer to these as Kors1 and Kors2). Considering Fig. 4, it can be seen that although the first pass of the
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algorithm yields 3 similar spatial distributions, subtle variations mean that the same recording site is not chosen for each configuration. It can be seen that for the first configuration a recording site is chosen slightly to the right of and approximately 1 intercostal space above V2. In the 2 remaining configurations, it can be seen that the recording site is chosen approximately 2 intercostal spaces above and just to the right of V3. Although not exactly the same, these suggested recording sites bear similarity to the Kors2 system, where an electrode was proposed 2 intercostal spaces above V4. However, the choice of the second recording site (based on Fig. 3) introduces dissimilarities. This is particularly evident from the positioning of the second recording site for the scenarios where V4 and V5 and V4 and V6 are repositioned, as in this case a posterior recording site is chosen, something not considered by Kors and van Herpen.10 Table 1 shows that each of the 3 modified lead configurations yield greater information capture than the standard 12-lead ECG. In all 3 cases, the difference was found to be significant ( P b .001). Of the 3 scenarios investigated, the scenario with V4 and V6 removed exhibits the best performance, which is consistent with the results presented by Kors and van Herpen,10 where a final configuration with V4 and V6 removed was recommended. Also presented in this table are figures generated from the 2 configurations proposed in.10 It can be seen that in comparison to the results obtained from the same configuration (V4 and V6 removed) in this study, with the recording sites in different locations, an increase in performance is observed with the algorithm-based selection proposed here. This increase was found to be statistically significant ( P b .001). The improved performance may be due to the fact that in this study the suggested alternative leads include a posterior recording site. To further investigate the issue of considering only anterior sites and to allow a fairer comparison between this study and that of Kors and van Herpen,10 the algorithm was modified to only consider anterior sites when repositioning V4 and V6. The resulting lead configuration is illustrated in Fig. 6. Here it can be seen that the electrode configuration is now similar to that proposed in 10 (Kors1), and, with an RMS error of 23.1 microvolts and a correlation coefficient of 0.966, exhibits slightly better performance than both the Kors systems. This performance gain was not found to be statistically significant when compared to the Kors1
Fig. 6. Recording sites chosen when V4 and V6 are relocated to anterioronly locations.
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Fig. 7. Positions that were chosen as optimal for each disease group in the data set. The key indicates the positions of the sites for the various disease types. It should be noted that 2 of the chosen sites occupy the same location (indicated with a cross).
( P = .083) system, but was statistically significant when compared to the Kors2 system ( P b .001). In addition to the above experiments, we conducted several further tests for the sake of comparison. The first of these considered the relocation of all 6 precordial leads, as illustrated in Fig. 4D. It can be seen that all of the newly chosen sites except 1 are located in the precordial region with the remaining site located on the left posterior. Although 5 recording sites are chosen in the precordial region, just 1 of these occupies the location of an existing site (V4). Three other recording sites are chosen close to the precordial leads: 1 beneath V5, 1 beneath V1 and V2, and 1 between V2 and V3. The remaining site is located 2 intercostal spaces above where V2 would be situated. Despite the fact that 5 recording sites are chosen in the precordial region, 4 of which are quite close to the precordial leads, the system does exhibit better performance than the standard 6 precordial leads. This system also performed better than all of the other scenarios investigated with the exception of that which considered relocation of V4 and V6. When tested, the small difference between the performance of the 6 optimal leads vs that of the scenario where V4 and V6 were relocated was not found to be significant ( P = .551). We also set about establishing if there was any advantage, over our approach, in retaining all 6 precordial leads while adding 2 further leads. The selection algorithm was configured to retain all the conventional ECG leads and find positions for 2 further chest leads. It was found that the 2 suggested recording sites were identical to that proposed when we moved V 4 and V 6 (Fig. 4C). When the performance of these leads was evaluated, we found that there was a very slight improvement in performance (RMS error, 22.1 AV; correlation coefficient, 0.969). When compared to the lead system with V4 and V6 repositioned, the increase in performance, although seemingly small (0.2 AV), was deemed as statistically significant ( P b .001). To find optimal locations for bdisease-specificQ recording sites, we supplied the lead selection algorithm with 3 individual data sets taken from the original training set.
These 3 subsets were made up of healthy subjects, subjects with MI, and subjects with LVH, respectively. We focused these tests on the scenario where V4 and V6 were removed and the resulting lead configurations are illustrated in Fig. 7. In all 3 cases, the first site chosen was in the region above V3. Indeed, for the LVH and MI subsets the same site was chosen as that for the generic leads illustrated in Fig. 4C. The first normal lead was on a site diagonally adjacent to this. For the second chosen sites, the MI site was in the same location as that for the generic sites and the normal site was located just left of this. The main difference was the location of the second LVH recording site. This was not located on the posterior but was chosen 2 intercostal spaces below V2. We tested the accuracy of various combinations of diseasespecific recording sites and transformations on the various data subsets, and found that the bdisease-specificQ leads did not offer significant improvements in information capture over the generic leads types.
Discussion In the current study, we have illustrated that through the use of a lead selection algorithm and a representative data set we can suggest new lead locations that will enhance the information capture of the 12-lead ECG. We have shown that repositioning the leads used to record V4 and V6 provides the best opportunity for increasing information capture. This is consistent with the findings of previous investigators.17 There was, however, a discrepancy between the locations of the alternative recording sites from this and the previous study. In the previous study, posterior recording sites were not considered; however, the algorithmic approach used in this study showed that, although slight, a significant increase in performance could be attained through inclusion of a posterior lead. The trade-off can therefore be considered as an increase in information capture vs a sacrifice in practicality due to the requirement to record from the subject’s back. In additional experiments, we demonstrated that for the studied cohort, optimal placement of all 6 precordial leads did not a provide significant gain over what could be achieved by repositioning just V4 and V6. This infers that for optimal information capture, repositioning leads V4 and V6 should suffice, negating the need for more radical redesign of the entire precordial component of the standard 12 leads. We also assessed the merit of not altering the positions of the standard precordial leads but adding 2 further leads. It was observed that the optimal positions for the 2 new leads were identical to that when V4 and V6 were repositioned. The improvement in performance with this approach, which required 2 further recording channels, was found to be statistically significant. This approach may be favored by those who are reluctant to compromise on the standard positions of the 6 precordial leads. However, the major practical limitation is that new unconventional acquisition hardware must be used to record the additional channels. In assessing the effects of disease types on the lead selection process, it was noted that with the exception
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of the LVH-specific leads, the generic leads chosen in this study were similar to those optimal for the specific disease types. The current study has focused on just 1 aspect of current ECG sampling techniques, that is, the spatial distribution of recording sites. It is appreciated that this is not the only limitation and that other factors, such as temporal dynamics, may also be candidates for optimization. It is also appreciated that the ECG itself may remain a somewhat imprecise tool regardless of the extent of optimization because the intimate coupling of mechanical dysfunction and resulting electrical activity can often only be assumed. For this reason, the optimal, or complete, cardiac diagnosis may rely on other measures that are not part of the ECG, for example, blood enzyme levels. A further consideration in the current work relates to the distinction between electrocardiography and electrocardiology. In this study, we have focused on suggesting ways to obtain more information that should assist the cardiologist. We have done this by finding new recording sites that retrieve the most ECG signal information, effectively an exercise in optimal electrocardiography. What remains to be established is the impact of these new recording sites on diagnostic interpretation, and the question that we now must answer is: does capturing most ECG signal information translate to greater diagnostic yield? Currently, we can only speculate that this is the case. This speculation is based on comparisons of the lead sets chosen in this study with those chosen by Kornreich et al,12,18 where recording sites were chosen by evaluating how well very basic amplitude and integral measurements from each site could discriminate between disease types. We intend to extend our work in the future by first establishing a set of diagnostic criteria for the leads that we have chosen and then determining the use of these leads in complementing the conventional 12-lead ECG in diagnostic classification. References 1. Horwitz LI. Current clinical utility of body surface mapping. J Invasive Cardiol 1995;7:265.
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2. Mirvis D. Current status of body surface electrocardiographic mapping. Circulation 1987;75:684. 3. Carley SD. Beyond the 12 lead: review of the use of additional leads for early electrocardiographic diagnosis of acute myocardial infarction. Emerg Med 2003;15:143. 4. Finlay DD, Nugent CD, Donnelly MP, Lux RL, McCullagh PJ, Black ND. Selection of optimal recording sites for limited lead body surface potential mapping: a sequential selection based approach. BMC Med Inform Decis Mak 2006;6. 5. Finlay DD, Nugent CD, McCullagh PJ, Black ND. Mining for diagnostic information in body surface potential maps: a comparison of feature selection techniques. Biomed Engin Online 2005;4. 6. Kornreich F, Rautaharju PM. The missing information in the standard 12 lead electrocardiogram. J Electrocardiol 1981;14:341. 7. Lux RL. Leads: how many and where? J Electrocardiol 2002;35:213. 8. Somers MP, Brady WJ, Bateman DC, Mattu A, Perron AD. Additional electrocardiographic leads in the ED chest pain patient: right ventricular and posterior leads. Am J Emerg Med 2003;21:563. 9. Hoekema R, Uijen GJH, van Oosterom A. On selecting a body surface mapping procedure. J Electrocardiol 1999;32:93. 10. Kors JA, van Herpen G. How many electrodes and where: a bPoldermodelQ for electrocardiography. J Electrocardiol 2002;35:7. 11. Dower GE, Yakush A, Nazzal SB, Jutzy RV, Ruiz CE. Deriving the 12lead electrocardiogram from four (EASI) electrodes. J Electrocardiol 1988;21:182. 12. Kornreich F, Rautaharju PM, Warren J, Montague TJ, Horacek BM. Identification of best electrocardiographic leads for diagnosing myocardial infarction by statistical analysis of body surface potential maps. Am J Cardiol 1985;56:852. 13. Montague TJ, Smith ER, Cameron DA, et al. Isointegral analysis of body surface maps: surface distribution and temporal variability in normal subjects. Circulation 1981;63:1166. 14. Nelwan SP, Crater SW, Meij SH, et al. Simultaneous comparison of three derived 12-lead ECGs with standard ECG at rest and during percutaneous coronary occlusion. J Electrocardiol 2004;37:171. 15. Drew BJ, Pelter MM, Brodnick DE, Yadav AV, Dempel D, Adams MG. Comparison of a new reduced lead set ECG with the standard ECG for diagnosing cardiac arrhythmias and myocardial ischemia. J Electrocardiol 2002;35:13. 16. Wei D. Deriving the 12-lead electrocardiogram from four standard leads using information redundancy in the 12-lead system. Int J Bioelectromagn 2002;4:127. 17. Nelwan SP, Kors JA, Meij SH. Minimal lead sets for reconstruction of the 12-lead electrocardiogram. J Electrocardiol 2000;33:163. 18. Kornreich F. Optimal left ventricular hypertrophy classification and quantification: insights from body surface potential maps. Int J Bioelectromagn 2003;5:197.
Optimizing the 12-lead electrocardiogram: a data driven approach to locating alternative recording sites Dewar D. Finlay, PhD,a,4 Chris D. Nugent, DPhil,a Jan A. Kors, PhD,b Gerard van Herpen, MD, PhD,b Mark P. Donnelly, BSc,a Paul J. McCullagh, PhD,a Norman D. Black, PhDa a
School of Computing and Mathematics, Faculty of Engineering, University of Ulster, Belfast, Northern Ireland, UK b Department of Medical Informatics, Erasmus University Medical Centre, Rotterdam, The Netherlands Received 31 August 2006; accepted 14 December 2006
Abstract
Background: Despite its widespread use, the limitations of the 12-lead electrocardiogram (ECG) are undisputed. The main deficiency is that just a small area of the precordium is interrogated and for some abnormalities information may be transmitted to a region of the body surface where information is not recorded. In this study, we attempted to optimize the 12-lead ECG by using a datadriven approach to suggest alternate recording sites. Methods: A sequential lead selection algorithm was applied to a set of 744 body surface potential maps (BSPMs), consisting of recordings from subjects with myocardial infarction, left ventricular hypertrophy, and no apparent disease. A number of scenarios were investigated in which pairs of precordial leads were repositioned; these pairs were V3 and V5, V4 and V5, and V4 and V6. The algorithm was also used to find optimal positions for all 6 precordial leads. Result: Through estimation of entire surface potential distributions it was found that each of the scenarios, with 2 leads repositioned, captured more information than the standard 12-lead ECG. The scenario with V4 and V6 repositioned performed best with a root mean square error of 22.3 microvolts and a correlation coefficient of 0.967. This configuration also fared favorably when compared to the scenario where all 6 precordial leads were repositioned as optimizing all 6 leads offered no significant improvement. Conclusion: This study demonstrated the use of a lead selection algorithm in enhancing the 12-lead ECG. The results also indicated that repositioning just 2 precordial leads can provide the same level of information capture as that observed when all precordial leads are optimally placed. D 2007 Elsevier Inc. All rights reserved.
Introduction The main deficiency of the standard 12-lead electrocardiogram (ECG) is that the sampling region is constrained to a small area of the precordium. It is appreciated that for abnormalities such as true posterior infarcts diagnostic information may be transmitted to areas on the surface of the torso where the ECG information is not recorded.1-3 The most obvious and most effective way to address this problem would be to redesign the 12-lead ECG focusing specifically on the positions of the 6 precordial leads, because it has been shown that the current positions of these unipolar leads are not optimal for maximum information 4 Corresponding author. E-mail address: [email protected] 0022-0736/$ – see front matter D 2007 Elsevier Inc. All rights reserved. doi:10.1016/j.jelectrocard.2006.12.015
capture.4,5 In theory, this approach would be ideal; in practice, however, it is unlikely to succeed because the familiar format of the 12-lead ECG coupled with the considerable amount of diagnostic criteria accumulated in the literature mean that it is a tool with which most clinicians are extremely comfortable and which they are therefore unlikely to relinquish.6,7 A less radical approach that aims to enhance the current 12-lead ECG is to supplement the currently recorded information with information recorded from additional sites on the torso. This can mean anything from adding just a few extra recording sites on the right chest and posterior surface 3,8 to recording body surface potential maps (BSPMs).9 Although proven to yield superior diagnostic information, these approaches are seldom adopted because increasing the number of recording channels increases the
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the 12-lead ECG. A description of the basic operation of the algorithm and the studied data is given in the following paragraphs. Lead selection algorithm
Fig. 1. Schematic of 117 lead BSPMs. Also highlighted are the positions of the 6 precordial leads relative to this electrode array.
technical and practical complexity of the acquisition process. Bearing this in mind, the most efficient compromise would extend the diagnostic capability of the existing 12-lead approach, using the same hardware and number of electrodes, without sacrificing any of the information currently available for interpretation. This was the objective of the work previously undertaken by Kors and van Herpen.10 In this study, 2 of the 6 precordial leads were moved to alternate locations on the torso based on the assumption that the missing leads could be accurately synthesized. This meant that although the 12-lead ECG could still be displayed, there were 2 free electrodes that could be moved to alternative locations where the information presence was deemed greatest. The study concluded with the suggestion of 2 balteredQ lead systems relying on the relocation of V4 and V6, which exhibited better information capture than either the 12-lead ECG or the EASI Philips Medical Systems, Ander, MA lead system.11 In both of the altered systems, 1 electrode was moved to 2 intercostal spaces below V2 and the remaining electrode was placed either 2 intercostal spaces above V2, or 3 intercostal spaces above V4. As a measure of performance, the accuracy of the new lead configurations in estimating total body surface potential distributions (BSPMs) was assessed. In the work of Kors and van Herpen,10 the recording sites were chosen to record information from areas that were assumed to have best the signal information content and were not interrogated by the original electrode positions. The choice of the new recording sites was based on prior knowledge derived from the results of previous studies such as,12 where the objective was to establish where the most diagnostic information is projected onto the body’s surface. In the current study, an attempt is made to consolidate the work previously presented by Kors and van Herpen10; however, this time a lead selection algorithm is used to find the new recording sites. In addition, the data generated by the lead selection algorithm are used to provide a visual representation of the spatial distributions of electrocardiographic information on the body surface.
The algorithm uses a sequential forward selection approach to evaluate all available recording sites in the 117 lead BSPMs and chooses the best sites for capturing total body surface information. The process begins by evaluating how well each of the available sites can be used to estimate the potentials at all the remaining sites in the BSPM. Multiple linear regression is used to determine the transformation required to estimate the remaining ECG information. The individual site observed to perform best is chosen as the boptimalQ site. This constitutes the first iteration of the algorithm. On the next iteration, each of the remaining sites are evaluated in conjunction with the first chosen site. The site that performs best in conjunction with the first site is then chosen. At this point we have chosen 2 sites, and this process can be repeated for the desired number of iterations. In general, the algorithm can be used to select the first best site up to the nth site; this is exemplified in the application of the algorithm in the work of Finlay et al,4 where the top 32 sites were chosen. In the current study, the objective is to start off with some subset of the 6 precordial recording sites and build upon this. Highlighted in the discussion presented by Finlay et al,4 is the algorithm’s suitability to such an application because bpreselectedQ or benforcedQ recording sites can readily be incorporated in the selection process. Data set The data set consisted of 117 lead BSPMs that were recorded from 744 subjects. This was made up of approximately one third healthy subjects, one third subjects with myocardial infarction (MI), and one third subjects with left ventricular hypertrophy (LVH). The process for acquiring the data has been previously described in,13 and a schematic of the positions of the 117 recording sites is shown in Fig. 1. All isopotential map frames from the QRST of each subject were pooled, and to facilitate application of the algorithm a bselection setQ was extracted from this pool. This consisted of approximately 75% of the data set with an equal distribution of disease types. During the experiments, the selection algorithm further partitioned the selection set to test and evaluate each available recording site. Readers are directed to the in-depth discussion of the algorithm presented by Finlay et al4 for further information on the treatment of the data during the selection process. To obtain an independent measure of performance of the suggested lead systems, the remaining 25% of data was used to calculate performance metrics for each suggested lead configuration.
Methods
Investigated scenarios
In this study, a lead selection algorithm previously developed by the authors and described by Finlay et al,4 is applied. This algorithm analyzes a set of 117 lead BSPMs to determine which of the available leads best compliment
Regardless of the selection methodology, the feasibility of the entire study relies on the assumption that there is redundancy in the 12-lead ECG. This redundancy stems from the fact that the 6 precordial sites are close to each
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Fig. 2. Spatial distributions of RMS error when remaining precordial leads are evaluated with every available recording site in 117 lead BSPMs. Each plot corresponds with 1 of the 3 proposed lead subsets: (A) V3 and V5 dropped, (B) V4 and V5 dropped, (C) V4 and V6 dropped. In each of these plots, the locations of the remaining 4 precordial leads are indicated with white squares. The location of the next best recording site, which is that yielding the lowest RMS error, is indicated with a crossed square.
other. It has been shown that with the inclusion of the limb leads, missing information/leads can be reconstructed from as few as 2 of the 6 precordial leads.14-17 The accuracy of the reconstructed signals are of course dependent on how many recording sites have been eliminated, and in the current study the same assumption is used as in,10 where to ensure the integrity of the reconstructed signals, no more than 2 recording sites were removed. As well as deciding the maximum number of sites that should be removed to preserve integrity, a further consideration is determining the 2 most suitable recording sites for elimination. The most obvious criterion is to select recording sites based on how well the signals from those sites can be reconstructed. In the report of Nelwan et al,17 an
exhaustive search of all combinations of precordial sites showed that the best candidates for elimination were V4 and V6 when general reconstruction coefficients were used, and V3 and V5 when patient-specific coefficients were used. Although the current study does not consider patientspecific coefficients, it was decided that both these pairs of recording sites would be considered. In addition to selecting sites that can be accurately reconstructed, practical issues have also been taken into consideration. In their study, Kors and van Herpen10 also suggested V4 and V5 as desirable electrodes to relocate because these sites can be difficult to accurately locate in women due to breast obstruction. In the current study, these electrodes are also considered for relocation.
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Fig. 3. Spatial distributions of RMS error when remaining precordial leads and 1 optimally selected site are evaluated with every available recording site in 117 lead BSPM. Each plot corresponds with 1 of the 3 proposed lead subsets: (A) V3 and V5 dropped, (B) V4 and V5 dropped, (C) V4 and V6 dropped. In each of these plots, the locations of the remaining 4 precordial leads are indicated with white squares. Also indicated with a white-crossed square is the optimal recording site that was chosen on the previous iteration of the algorithm. The location of the next best recording site, which is that yielding the lowest RMS error, is indicated with a crossed square.
In addition to the 3 scenarios where only 2 precordial leads were repositioned, several other tests were conducted to facilitate discussion and comparison. These included finding optimal positions for all precordial leads, adding 2 further leads to the standard 6 precordial leads, and finding recording sites specific for each disease group in the data set. Performance evaluation To measure the performance of each recording site, during the selection process, spatial root mean square (RMS) voltage error was used. The selection algorithm uses this metric to quantify how well the remaining sites in a BSPM are estimated in comparison to actual measured
values. If P 1 and P 2 are the vectors of the measured and estimated potentials, respectively, and n is the number of sites at which potentials have been estimated, the spatial RMS error e can be determined by the equation; e¼
jP 1 P 2 j pffiffiffi n
ð1Þ
In addition to the spatial RMS error, used by the algorithm to guide the lead selection process, we used the correlation coefficient to provide a further metric of final performance. The correlation coefficient provides a measure of the similarity in BSPM patterns between measured and estimated BSPM frames independent of amplitude. If P is the
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pattern differences might be extreme. To establish final performance measures for each of the developed lead sets, RMS error and correlation coefficient were calculated for each individual isopotential map frame in the test set. From this, median values for each subject were calculated and final performance was expressed as the median of the medians for each subject. Wilcoxon’s signed rank test was used to determine the statistical significance of the differences in performance between lead sets. This test was applied to the paired differences in median RMS error values for each subject in the test set. Results The sequential selection algorithm was applied considering each of the 3 subsets of precordial leads (subsets resulting in the removal of V3 and V5, V4 and V5, and V4 and V6). To provide an insight into the spatial distributions of electrocardiographic information, Figs. 2 and 3 have been included. These plots depict the calculated RMS error as each recording site is being selected. In each of these figures there are 3 contour plots, each of which correspond with 1 of the studied scenarios. Considering Fig. 2, the performance of each of the precordial lead subsets in conjunction with every other available recording site is depicted. Thus, at each of the 117 available recording sites the RMS error has been plotted. This is the error obtained when that particular site is used, along with the existing 4 precordial sites, to estimate entire surface potential distributions. This exposes and clarifies the operation of the selection algorithm because the site that can be seen to exhibit the lowest RMS error is the first site that is selected. In each of the plots, this site is indicated with a crossed square. It is evident from the
Fig. 4. Final recording sites chosen using the algorithm. Plots a to c correspond with proposed lead subsets (A) V3 and V5 dropped, (B) V4 and V5 dropped, and (C) V4 and V6 dropped, respectively. Each plot shows the remaining precordial recording sites along with the 2 alternate recording sites that have been suggested. (D) Result of optimally repositioning all precordial leads.
original map frame and PV is the estimated map frame, the correlation coefficient q can be described as q¼
PPV jPjjPVj
ð2Þ
This measure is useful as small errors of amplitude on low amplitude map frames may appear to be insignificant, yet
Fig. 5. Positions of recording sites in the (A) Kors1 and (B) Kors2 systems.
D.D. Finlay et al. / Journal of Electrocardiology 40 (2007) 292 – 299 Table 1 Performance figures for each lead configuration Repositioned leads
RMS error (lV)
Correlation coefficient
12 lead V3 + V5 V4 + V5 V4 + V6 Six optimal Kors1 Kors2
28.3 23.3 23.4 22.3 22.3 23.2 23.4
0.952 0.966 0.965 0.967 0.967 0.965 0.964
(21.4-34.5) (19.3-28.8) (18.7-29.2) (18.1-28.7) (18.1-29.3) (18.5-28.9) (18.9-29.4)
(0.926-0.971) (0.948-0.978) (0.945-0.976) (0.950-0.978) (0.948-0.977) (0.949-0.977) (0.946-0.978)
Also included are the performance figures obtained from the 12-lead ECG and Kors1 and Kors2 systems. In each case, the median values, along with interquartile range (inside parentheses) are listed.
plot in Fig. 2 that in all 3 cases the lowest RMS error is in the region superior to the precordial electrodes V1 to V4. This, in turn, suggests that for the studied population there is significant information transmitted to this area that is not captured by the remaining precordial leads. This can be thought of as the bmissing information.Q It can also be seen that there are 2 further regions where there is relatively low, albeit to a lesser extent, RMS error. These are a small region approximately 1 intercostal space below V2 and a larger region on the posterior surface. If the locations that provide little information gain (high RMS error) are considered, it can be seen that obviously there is less information close to where the existing precordial leads are located, particularly the remaining precordial leads. In addition, in all of the contour plots it can be seen that little is gained through electrodes in the right sternum, close to the region that would be interrogated by right ventricular leads (to the right of V1).8 When the 3 plots in Fig. 2 are compared with each other, it can be seen that the distributions are very similar. This would indicate that, regardless of which 2 recording sites are removed, a similar pattern of missing information is observed. After the initial selection run, as indicated in Fig. 2, the positions of 5 recording sites were known (4 original precordial plus first optimal) and the next step was to establish where the next recording site should be positioned. This process involved taking the 5 current recording sites and trying all of the remaining available sites to find the best combination. In Fig. 3, where the second iteration of the algorithm is depicted, the observations are similar to that in the first selection in that the regions that are close to existing recording sites (4 precordial sites + 1 new site) are the regions where there is little to gain from placing a new recording site (high RMS error). The areas where the missing information is located (low RMS error) also resemble the 2 less dominant areas that were observed in the first pass of the algorithm. These are the region below V2 and a larger region on the posterior surface. Again, across all 3 plots the observed distributions are similar. In Fig. 4, each of the final electrode configurations is illustrated along with the configuration suggested when all 6 precordial leads are considered for relocation. For the sake of comparison, the recording sites originally proposed by Kors and van Herpen10 are illustrated in Fig. 5 (from here on, we refer to these as Kors1 and Kors2). Considering Fig. 4, it can be seen that although the first pass of the
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algorithm yields 3 similar spatial distributions, subtle variations mean that the same recording site is not chosen for each configuration. It can be seen that for the first configuration a recording site is chosen slightly to the right of and approximately 1 intercostal space above V2. In the 2 remaining configurations, it can be seen that the recording site is chosen approximately 2 intercostal spaces above and just to the right of V3. Although not exactly the same, these suggested recording sites bear similarity to the Kors2 system, where an electrode was proposed 2 intercostal spaces above V4. However, the choice of the second recording site (based on Fig. 3) introduces dissimilarities. This is particularly evident from the positioning of the second recording site for the scenarios where V4 and V5 and V4 and V6 are repositioned, as in this case a posterior recording site is chosen, something not considered by Kors and van Herpen.10 Table 1 shows that each of the 3 modified lead configurations yield greater information capture than the standard 12-lead ECG. In all 3 cases, the difference was found to be significant ( P b .001). Of the 3 scenarios investigated, the scenario with V4 and V6 removed exhibits the best performance, which is consistent with the results presented by Kors and van Herpen,10 where a final configuration with V4 and V6 removed was recommended. Also presented in this table are figures generated from the 2 configurations proposed in.10 It can be seen that in comparison to the results obtained from the same configuration (V4 and V6 removed) in this study, with the recording sites in different locations, an increase in performance is observed with the algorithm-based selection proposed here. This increase was found to be statistically significant ( P b .001). The improved performance may be due to the fact that in this study the suggested alternative leads include a posterior recording site. To further investigate the issue of considering only anterior sites and to allow a fairer comparison between this study and that of Kors and van Herpen,10 the algorithm was modified to only consider anterior sites when repositioning V4 and V6. The resulting lead configuration is illustrated in Fig. 6. Here it can be seen that the electrode configuration is now similar to that proposed in 10 (Kors1), and, with an RMS error of 23.1 microvolts and a correlation coefficient of 0.966, exhibits slightly better performance than both the Kors systems. This performance gain was not found to be statistically significant when compared to the Kors1
Fig. 6. Recording sites chosen when V4 and V6 are relocated to anterioronly locations.
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Fig. 7. Positions that were chosen as optimal for each disease group in the data set. The key indicates the positions of the sites for the various disease types. It should be noted that 2 of the chosen sites occupy the same location (indicated with a cross).
( P = .083) system, but was statistically significant when compared to the Kors2 system ( P b .001). In addition to the above experiments, we conducted several further tests for the sake of comparison. The first of these considered the relocation of all 6 precordial leads, as illustrated in Fig. 4D. It can be seen that all of the newly chosen sites except 1 are located in the precordial region with the remaining site located on the left posterior. Although 5 recording sites are chosen in the precordial region, just 1 of these occupies the location of an existing site (V4). Three other recording sites are chosen close to the precordial leads: 1 beneath V5, 1 beneath V1 and V2, and 1 between V2 and V3. The remaining site is located 2 intercostal spaces above where V2 would be situated. Despite the fact that 5 recording sites are chosen in the precordial region, 4 of which are quite close to the precordial leads, the system does exhibit better performance than the standard 6 precordial leads. This system also performed better than all of the other scenarios investigated with the exception of that which considered relocation of V4 and V6. When tested, the small difference between the performance of the 6 optimal leads vs that of the scenario where V4 and V6 were relocated was not found to be significant ( P = .551). We also set about establishing if there was any advantage, over our approach, in retaining all 6 precordial leads while adding 2 further leads. The selection algorithm was configured to retain all the conventional ECG leads and find positions for 2 further chest leads. It was found that the 2 suggested recording sites were identical to that proposed when we moved V 4 and V 6 (Fig. 4C). When the performance of these leads was evaluated, we found that there was a very slight improvement in performance (RMS error, 22.1 AV; correlation coefficient, 0.969). When compared to the lead system with V4 and V6 repositioned, the increase in performance, although seemingly small (0.2 AV), was deemed as statistically significant ( P b .001). To find optimal locations for bdisease-specificQ recording sites, we supplied the lead selection algorithm with 3 individual data sets taken from the original training set.
These 3 subsets were made up of healthy subjects, subjects with MI, and subjects with LVH, respectively. We focused these tests on the scenario where V4 and V6 were removed and the resulting lead configurations are illustrated in Fig. 7. In all 3 cases, the first site chosen was in the region above V3. Indeed, for the LVH and MI subsets the same site was chosen as that for the generic leads illustrated in Fig. 4C. The first normal lead was on a site diagonally adjacent to this. For the second chosen sites, the MI site was in the same location as that for the generic sites and the normal site was located just left of this. The main difference was the location of the second LVH recording site. This was not located on the posterior but was chosen 2 intercostal spaces below V2. We tested the accuracy of various combinations of diseasespecific recording sites and transformations on the various data subsets, and found that the bdisease-specificQ leads did not offer significant improvements in information capture over the generic leads types.
Discussion In the current study, we have illustrated that through the use of a lead selection algorithm and a representative data set we can suggest new lead locations that will enhance the information capture of the 12-lead ECG. We have shown that repositioning the leads used to record V4 and V6 provides the best opportunity for increasing information capture. This is consistent with the findings of previous investigators.17 There was, however, a discrepancy between the locations of the alternative recording sites from this and the previous study. In the previous study, posterior recording sites were not considered; however, the algorithmic approach used in this study showed that, although slight, a significant increase in performance could be attained through inclusion of a posterior lead. The trade-off can therefore be considered as an increase in information capture vs a sacrifice in practicality due to the requirement to record from the subject’s back. In additional experiments, we demonstrated that for the studied cohort, optimal placement of all 6 precordial leads did not a provide significant gain over what could be achieved by repositioning just V4 and V6. This infers that for optimal information capture, repositioning leads V4 and V6 should suffice, negating the need for more radical redesign of the entire precordial component of the standard 12 leads. We also assessed the merit of not altering the positions of the standard precordial leads but adding 2 further leads. It was observed that the optimal positions for the 2 new leads were identical to that when V4 and V6 were repositioned. The improvement in performance with this approach, which required 2 further recording channels, was found to be statistically significant. This approach may be favored by those who are reluctant to compromise on the standard positions of the 6 precordial leads. However, the major practical limitation is that new unconventional acquisition hardware must be used to record the additional channels. In assessing the effects of disease types on the lead selection process, it was noted that with the exception
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of the LVH-specific leads, the generic leads chosen in this study were similar to those optimal for the specific disease types. The current study has focused on just 1 aspect of current ECG sampling techniques, that is, the spatial distribution of recording sites. It is appreciated that this is not the only limitation and that other factors, such as temporal dynamics, may also be candidates for optimization. It is also appreciated that the ECG itself may remain a somewhat imprecise tool regardless of the extent of optimization because the intimate coupling of mechanical dysfunction and resulting electrical activity can often only be assumed. For this reason, the optimal, or complete, cardiac diagnosis may rely on other measures that are not part of the ECG, for example, blood enzyme levels. A further consideration in the current work relates to the distinction between electrocardiography and electrocardiology. In this study, we have focused on suggesting ways to obtain more information that should assist the cardiologist. We have done this by finding new recording sites that retrieve the most ECG signal information, effectively an exercise in optimal electrocardiography. What remains to be established is the impact of these new recording sites on diagnostic interpretation, and the question that we now must answer is: does capturing most ECG signal information translate to greater diagnostic yield? Currently, we can only speculate that this is the case. This speculation is based on comparisons of the lead sets chosen in this study with those chosen by Kornreich et al,12,18 where recording sites were chosen by evaluating how well very basic amplitude and integral measurements from each site could discriminate between disease types. We intend to extend our work in the future by first establishing a set of diagnostic criteria for the leads that we have chosen and then determining the use of these leads in complementing the conventional 12-lead ECG in diagnostic classification. References 1. Horwitz LI. Current clinical utility of body surface mapping. J Invasive Cardiol 1995;7:265.
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2. Mirvis D. Current status of body surface electrocardiographic mapping. Circulation 1987;75:684. 3. Carley SD. Beyond the 12 lead: review of the use of additional leads for early electrocardiographic diagnosis of acute myocardial infarction. Emerg Med 2003;15:143. 4. Finlay DD, Nugent CD, Donnelly MP, Lux RL, McCullagh PJ, Black ND. Selection of optimal recording sites for limited lead body surface potential mapping: a sequential selection based approach. BMC Med Inform Decis Mak 2006;6. 5. Finlay DD, Nugent CD, McCullagh PJ, Black ND. Mining for diagnostic information in body surface potential maps: a comparison of feature selection techniques. Biomed Engin Online 2005;4. 6. Kornreich F, Rautaharju PM. The missing information in the standard 12 lead electrocardiogram. J Electrocardiol 1981;14:341. 7. Lux RL. Leads: how many and where? J Electrocardiol 2002;35:213. 8. Somers MP, Brady WJ, Bateman DC, Mattu A, Perron AD. Additional electrocardiographic leads in the ED chest pain patient: right ventricular and posterior leads. Am J Emerg Med 2003;21:563. 9. Hoekema R, Uijen GJH, van Oosterom A. On selecting a body surface mapping procedure. J Electrocardiol 1999;32:93. 10. Kors JA, van Herpen G. How many electrodes and where: a bPoldermodelQ for electrocardiography. J Electrocardiol 2002;35:7. 11. Dower GE, Yakush A, Nazzal SB, Jutzy RV, Ruiz CE. Deriving the 12lead electrocardiogram from four (EASI) electrodes. J Electrocardiol 1988;21:182. 12. Kornreich F, Rautaharju PM, Warren J, Montague TJ, Horacek BM. Identification of best electrocardiographic leads for diagnosing myocardial infarction by statistical analysis of body surface potential maps. Am J Cardiol 1985;56:852. 13. Montague TJ, Smith ER, Cameron DA, et al. Isointegral analysis of body surface maps: surface distribution and temporal variability in normal subjects. Circulation 1981;63:1166. 14. Nelwan SP, Crater SW, Meij SH, et al. Simultaneous comparison of three derived 12-lead ECGs with standard ECG at rest and during percutaneous coronary occlusion. J Electrocardiol 2004;37:171. 15. Drew BJ, Pelter MM, Brodnick DE, Yadav AV, Dempel D, Adams MG. Comparison of a new reduced lead set ECG with the standard ECG for diagnosing cardiac arrhythmias and myocardial ischemia. J Electrocardiol 2002;35:13. 16. Wei D. Deriving the 12-lead electrocardiogram from four standard leads using information redundancy in the 12-lead system. Int J Bioelectromagn 2002;4:127. 17. Nelwan SP, Kors JA, Meij SH. Minimal lead sets for reconstruction of the 12-lead electrocardiogram. J Electrocardiol 2000;33:163. 18. Kornreich F. Optimal left ventricular hypertrophy classification and quantification: insights from body surface potential maps. Int J Bioelectromagn 2003;5:197.