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Body surface potential field representation fidelity: Analysis of map estimation procedures
Journal of Electrocardiology Vol. 32 No. 3 1999
Body Surface Potential Field Representation Fidelity: Analysis of Map Estimation Procedures
G y 6 r g y Sfindor, M S , G y 6 r g y K o z m a n n , P h D , Z s u z s a n n a Cserj~s, P h D , N o 6 r n i F a r k a s , MS,* a n d Istvfin P r d d a , M D , P h D t
Abstract: The first part of this study analyzed the spatiaI-temporal error distribution of the Lux-type limited lead system. Quantitative n e w evidence is reported that the 32-lead anterior subset estimates the further 160 leads with an average amplitude error less than 38.5 /xV. The spatial error distribution revealed 8 sites where the error is the highest, primarily on the anterior side, independent of the clinical classification. The second part of the study examined inter-lead-system conversion strategies for interpolating the Lux192 lead maps from the Montreal-63 data. The methodology based on the Laplacian interpolation yielded an average amplitude error of 143.7/zV and an average correlation of 0.87 for pattern fidelity. In this specific case a modified linear interpolation surpassed the Laplacian method. A presented example illustrates that even in cases w h e n the fidelity of the signal information is heavily compromised the diagnostic information m a y remain less influenced. K e y words: body surface potential maps, electrode grids, Laplacian interpolation, limited lead system, linear interpolation.
Body surface potential mapping (BSPM) is a technique for acquiring the entire diagnostic information available on the chest surface. Although BSPM technology has achieved a high standard because of the rapid development of computer technology, the answer for the basic issue concerning the amount of the additional diagnostic information in the map data is still obscure. Beyond
current evidence of the clinical utility of BSPM technology there is still a need for more rigorous statistical proof of the early findings. To accomplish these statistical studies, larger validated databases of BSPM are required than those currently available in most laboratories. Because no standardization has occurred in BSPM measurement, no direct routes are available for pooling the local databases. An inter-lead-system transformation, based on minimization of the surface Laplacian, has been elaborated within a European Union project called Noninvasive Evaluation of Myocardium (NEMY) and suggested as a vehicle for solving the pooling problem (1). Hoekema et al. (2) analyzed the accuracy of the transformation method for the 11 most frequently used lead systems and reported that when the input lead system contains more than 63
From the Research Institute for Technical Physics and Materials Science and the t Haynal Imre University of Health Sciences, Budapest, and the *University of Veszprdm, Veszprdm, Hungary.
Supported by grant F25618 from the Hungarian National Research Fund. Reprint requests: Dr. Gy6rgy Kozmann, MTA-MFA P.O.B. 49, Budapest 1525, Hungary. Copyright © I999 by Churchill Livingstone ®
0022-073619913203-0006510.00/0
253
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Journal of Electrocardiology Vol. 32 No. 3 July 1999
leads the average relative t r a n s f o r m a t i o n error is no larger t h a n 11%. The elaboration of a large validated BSPM database is a current p r o b l e m in our laboratory as well. Our group has compiled a BSPM data bank, with m o r e t h a n 2,000 items of n o r m a l and cardiacdiseased subjects (3). The data b a n k currently includes BSPM records that w e r e obtained b y three types of lead systems. Consequently we are highly interested in the quantitative accuracy of the different i n t e r - l e a d - s y s t e m transformations. Most of o u r files w e r e recorded by the Lux-32 (anterior-type) limited lead system. F r o m the m e a s u r e d 32 signals, 192-lead m a p s are calculated by m e a n s of a statistically derived estimation matrix (4). The second largest group of records was obtained by the M o n treal 63-lead system (5), a n d the third set, provided by the University of Parma, consists of 219-lead data (6). Unfortunately, the n u m b e r of leads in our input lead system is on the lower limit of the acceptance level. The objective of the present study was the detailed statistical characterization of the fidelity of our 192-lead BSPM representation with respect to (l) the use of the limited lead system a n d the statistical p r o c e d u r e for estimating potential values in the u n m e a s u r e d locations, and (2) the errors g e n e r a t e d as a consequence of data t r a n s f o r m a t i o n f r o m one lead system to another. Systematic amplitude a n d m o r p h o l o g i c error analysis was accomplished to assess the applicability of the m e t h o d s in our case. The estimation m e t h o d of the 192-lead BSPM, estimated f r o m the a n a t o m ically defined 32 limited lead set, was investigated. F u r t h e r m o r e , we evaluated the Laplacian transform a t i o n and a modified linear interpolation m e t h o d , w h i c h w e r e suggested for converting the M o n t r e a l 63-lead data into the Lux-32 limited lead systems. An e x a m p l e for the clinical utility of the data conversion is also outlined.
Materials and M e t h o d s Generation of Reference and Simulated Measurement Data Body surface potential m a p s f r o m 50 subjects (20 n o r m a l subjects, 15 w i t h ischemic heart disease, and 15 anterior myocardial infarction patients) were used as the e x p e r i m e n t a l data in the analysis. The c o m p u t a t i o n s w e r e confined to the QRS interval because it has the largest amplitudes and dyn a m i c change. The QRS segments w e r e t i m e - n o r -
219-lead original map
] Data Preprocesslng
[
Sele~ion of the normalized map instants
]
"~
/
192-lead reference map
Montreal 63-lead map
Lux-32 limited lead data ac, rttisition
Validation Process
/ Laplacian transformation
into 192-lead map
Modified linear interpolation into 32-lead map
Lux-type statistical estimation process to 192-lead map
Lux-type statistical estimation process to 192-1ead map
ERROR A N A L Y S I S A
B
] C
Fig. 1. Flowchart of validation in the Lux-type limited lead data acquisition philosophy (32---->I92, route A), Laplacian transformation method (63-->192, route B), and linear interpolation-based conversion of Montreal-63 data into the Budapest 192-lead database system (63--->192, route C).
malized a n d represented by 10 equally distant instantaneous maps. The test data w e r e recorded by the P a r m a system, w h i c h includes 219 leads in a nonequidistant a r r a n g e m e n t , w i t h a high electrode density in the precordial area. Figure 1 shows the flow chart of the analysis. In the following, we will refer to the three procedures as route A, route B, a n d route C. The database of our laboratory uses the 192-lead equidistant electrode layout as a standard, w i t h m e a s u r i n g point locations originally introduced b y the group of Salt Lake City. Our actual data acquisition is done by the Lux-type limited lead system containing 32 m e a s u r e m e n t locations, and the 192-1ead f o r m a t is calculated using the estimation p r o c e d u r e that is an i n h e r e n t part of the Lux approach. The first step of the analysis was the p r o d u c t i o n of 192-1ead reference m a p s f r o m 219-lead BSPM b y bilinear interpolation. In a similar w a y to the reference 192-lead maps, the simulated M o n t r e a l 63-lead and the Lux-32 limited lead m e a s u r e m e n t s w e r e derived f r o m the P a r m a data set. Subsequently, based on the simulated m e a s u r e m e n t , 192-lead m a p s were estimated (by the m e t h o d s described in the n e x t section). Because b o t h the Montreal and the Lux systems define the location of the electrode sites anatomically, before accomplishing the inter-leadsystem transformations the same average g e o m e t r y had to be assigned to all the P a r m a patients. The
Study of Map Estimation Procedures
relative position of the I 9 2 - a n d the 63-lead system m e a s u r i n g points in the P a r m a frame occurred on this hypothetical torso.
*
Sfndor et al.
255
w h e r e h is the distance b e t w e e n t w o adjacent sites. The linear interpolation was modified by missing the least significant sites. A predefined threshold
hi
Simulation of the Data Transformation Procedures For the first p r o b l e m of our study 192-lead BSPM was estimated f r o m the 32-lead simulated m e a s u r e m e n t data (route A), based on the estimation m a trix introduced b y Lux et al. The idea b e h i n d the Lux-type limited lead system is that BSPM is considered to be a sequence of r a n d o m potential vector distributions at s u b s e q u e n t time instants. Therefore, the r e d u n d a n c y of BSPM can be evaluated by a statistical m e t h o d . The covariance matrix of a training m a p set was used to find a n optimal t r a n s f o r m a t i o n matrix in least square sense. Detailed e x p l a n a t i o n can be f o u n d elsewhere (7). For the second p r o b l e m the 192-lead m a p data w e r e estimated directly f r o m the simulated M o n treal-63 m e a s u r e m e n t s (route B) by m e a n s of the Laplacian t r a n s f o r m a t i o n that was suggested by Oostendorp et al. (8). The second order derivatives (Laplacian) of the u n k n o w n potentials w e r e estim a t e d by m e a n s of a second degree Taylor expansion. Subsequently, the n o r m of the surface Laplaclan was m i n i m i z e d in order to find the missing potential values. Finally, in our third problem, the 192-lead data w e r e derived w i t h a modified linear interpolation m e t h o d developed b y the authors c o m b i n e d w i t h the L u x - t y p e estimation (route C) as an alternative w a y of route B. This latter p r o c e d u r e t o o k into consideration directly the geometric relations bet w e e n the Montreal-63 a n d Lux-32 lead set. Initially a w e i g h t e d average in the p r o p o r t i o n of the inverse distances of the four closest neighbors w e r e applied for d e t e r m i n i n g the potential values at the u n k n o w n sites:
was defined empirically as if a n y ~ is less t h a n 0.2 ( i = 1 . . . 4 , j = 1 . . . 4 ) t h e n the effect o f t h e j th neighbor is neglected. Thus a t r a n s f o r m a t i o n matrix was obtained w h o s e elements d e p e n d e d on the relative g e o m e t r y of the two lead sets.
Methodologies of the Error Analysis For characterization of the accuracy of the transf o r m a t i o n m e t h o d s various amplitude errors w e r e calculated. The average t e m p o r a l error (TE) in the ith time instant is defined as follows:
TEi=_~ ~
;.=
k=I
w h e r e N is the patient n u m b e r , M is n u m b e r of the estimated leads, and eij is the error of the jth lead. The relative (temporal) error (RTE) has b e e n defined at the ith instant as:
TEi RTEi - RMSi w h e r e RMS i is the root m e a n square of BSPM of N patients at the ith instant. The accuracy of the different m e t h o d s for each single lead has also b e e n calculated one by one. The spatial error (SE) is defined similarly to TE. SE of the j t h lead including the w h o l e QRS interval is defined as follows:
4
wiVi i=1 V j - - - 4
i=I
w h e r e Vj is to be interpolated, V i is an adjacent potential value, a n d w~ is the weighting coefficient defined as:
sfj = #
0 k=l
The relative spatial error (RSE) can be calculated f r o m SE like the RTE f r o m the TE, and the f o r m u l a can be written as:
st RSEj - RMSj Wi
z
.
-
-
4
k=l
w h e r e RMSj is the root m e a n square of the I0 time instants of N patients at the j t h lead.
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Journal of Electrocardiology Vol. 32 No. 3 July 1999
A global average amplitude error (AE) and relative error (RE) h a v e also b e e n introduced over the entire QRS interval:
M
1 NI EE]
xE=#E
-
-
RE
-
200
RMS
w h e r e root m e a n square c o m p u t a t i o n was confined to the QRS interval. The m a g n i t u d e of the transform a t i o n errors in each instant was c o m p a r e d with the w i t h i n - g r o u p variability c o m p u t e d in the v e r y same m o m e n t , at each clinical category. The average variance within the h o m o g e n e o u s groups at the ith instant is calculated, as follows:
(@iJl~9~iJ)2
1N k=i j=l
w h e r e o-i is the w i t h i n - g r o u p standard deviation in the ith instant, ~f is the potential m e a s u r e d at the jth site in the ith instant a n d &/j is the average potential of the ith instant group at the j t h site. A diagram f o r m a t was used for the purpose of representing TE and RTE, while for d e m o n s t r a t i n g SE and RSE m a p f o r m a t was the m o s t convenient. Morphologic similarity b e t w e e n the reference and the t r a n s f o r m e d m a p s was characterized by correlation coefficient. The m e a n correlation coefficients and the m a x i m u m values for all the m e t h o d s are represented.
Results First, the simulated data w e r e used for evaluating the amplitude error as a function of the n o r m a l i z e d QRS time instants for the three problems described in the previous section. Table 1 gives a global o v e r v i e w of the AE with standard deviation (SD), the m a x i m a l error (ME), and the RE, providing a quantitative c o m p a r i s o n b e t w e e n the m e t h o d s in a
Table 1. The Average Amplitude Error (AE) on the Entire QRS* and Standard Deviation (SD), the Relative Error (RE), and the Maximum Error (ME) Based on the Average of the I92-1ead BSPM
A E -+ SD (/,V) RE ( % ) M E (/,V)
400I 300
AE
and
k=l
2
500
A
B
C
3 8 . 5 -+ 2 8 16 71
143.7 ± 77 63 268
6 3 -+ 37 27 121
* M e a n v a l u e of t h e 10 t i m e i n s t a n t s .
I00 2
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Fig. 2. The temporal distribution of the amplitude error versus the QRS segment. The average temporal errors and standard deviations (in /,V) from the three procedures are shown, and for better comparison the root mean square (RMS) signal superposed by the withingroup variability (~r) is also plotted.
general sense. While the statistical estimation of Lux resulted in the best values, the modified linear interpolation yielded significantly less error t h a n the Laplacian interpolation despite that the error of route C includes the error of route A. In accordance with previously reported results (2), o u r analysis did not find significant difference a m o n g the three different patient subgroups, d e m o n s t r a t i n g that error values d e p e n d only w e a k l y on the m a p patterns d e t e r m i n e d by the clinical status of the patients. Therefore, the results w e r e obtained including all test data. Figure 2 shows the TE distribution a n d SDs for the three routes. For a better c o m p a r i s o n the root m e a n square values a n d the w i t h i n - m a p variability are represented. The error distributions resemble each other, but the linear interpolation results in roughly 50% lower values for all the calculated error parameters, and their SDs are also smaller. In each t r a n s f o r m a t i o n the MEs occurred at the sixth instant w h e n the b o d y surface root m e a n square value was also the largest. In unfavorable case of "B" the error can reach the average signal value not only in the first or the t e n t h time instant. Despite the increase of the TE, w h i c h is the error in absolute sense, the RTEs did not change significantly for the higher signal amplitudes. C o m p a r i n g RTEs (Fig. 3), the best result is 14%, f o u n d in the eighth instant of route A. For the interpolations the best values w e r e 52% at the sixth instant for route B and 26% at the fifth instant in the linear interpolation. While the AEs d e p e n d e d strongly on the position within the QRS, the REs w e r e rather stable. The fluctua-
Study of Map Estimation Procedures
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"rime Fig. 3. The relative error (in/xV) at the Lux-type estimation (route A), the Laplacian m e t h o d (route B), and the linear conversion (route C).
t i o n w a s b e l o w 1 0 % in r o u t e s B a n d C a n d 5 % i n r o u t e A. W e c h e c k e d t h e a c c u r a c y of t h e L a p l a d a n m e t h o d i n t w o f o r m s . First, t h e 63---~192 d i r e c t i n t e r p o l a t i o n w a s e x e c u t e d , r e s u l t i n g in o n l y a s l i g h t l y s m a l l e r e r r o r t h a n b y first a p p l y i n g t h e 63--->32 c o n v e r s i o n a n d s u b s e q u e n t l y a p p l y i n g t h e statistical e s t i m a t i o n of Lux. This o u t c o m e s u p p o r t s the hypothesis that in the Laplacian interpolation t h e n u m b e r of i n p u t l e a d s is e s s e n t i a l l y d e c i s i v e i n d e p e n d e n t of t h e o u t p u t l e a d n u m b e r . T h e s p a t i a l d i s t r i b u t i o n of t h e a m p l i t u d e e r r o r (the SE) w a s also i n v e s t i g a t e d . O n F i g u r e 4 b l a c k dots m a r k t h e L u x - 3 2 ( a n t e r i o r - t y p e ) l e a d s y s t e m a n d b l a c k s q u a r e d n u m b e r s d i s t i n g u i s h t h e sites where the statistically based estimation produced the largest absolute error. The figure reveals that t h e l a r g e s t e r r o r s o c c u r r e d at l o c a t i o n s close to t h e h e a r t . This f i n d i n g i m p l i e s t h a t a n y k i n d of l e a d s y s t e m m u s t h a v e e n o u g h d e n s e p r e c o r d i a l elect r o d e a r r a n g e m e n t for p r e s e r v i n g t h e signal i n f o r m a t i o n faithfully. S e c o n d , it p r o v e s t h e a d v a n t a g e of t h e n o n e q u i d i s t a n t s p a t i a l s a m p l i n g o n t h e t o r s o surface. T h e f i g u r e s h o w s t h e RSE d i s t r i b u t i o n o n t h e 1 9 2 - l e a d m a p (160 e s t i m a t e d l e a d ) . T h e h i g h RSE r e g i o n w a s o n t h e u p p e r h a l f of t h e t o r s o b o t h o n t h e p o s t e r i o r a n d o n t h e a n t e r i o r t h o r a c i c surfaces, a f i n d i n g t h a t p a r t l y s u p p o r t s t h e r e q u i r e m e n t for b a c k e l e c t r o d e s . T h e f i g u r e r e v e a l s t h a t in m o r e t h a n 7 5 % of t h e e s t i m a t e d sites t h e RSE w a s b e l o w 1 0 % . The RSEs w e r e b e y o n d 2 0 % in 5 % of t h e
5 5 13 4 6 15 3 2 3
5 8 15 4 8 13 1 2 3
•
Sandor et al. 257
8
7
3
6 • i10 25 7 - 9 11 15 121 6 12 • 5 7 8 61o 8 17 • 6 3 16 15 201 11 • i31 • 1168 5 [16 21 18 17 • 7 3 8 10 • 2 2 2 • • • • 20 • 15 20 1 1 2 • • • • • 14 3 7 4 5 1 3 4 2 • • 10 4 • 1 2 3 5 2 5 3 2 1 1 • 2 1 • 4 7 9 0 1 1 1 2i2 3 • 2 3 5 6 7
3 4
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9 5 6
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Fig. 4. The spatial relative error distribution for route A. The 8 boxed sites are those where the estimation produced the largest average amplitude error (3 of the 8 are on the back side). Black dots show the m e a s u r e m e n t location of the Lux-type limited lead system. The central dashed line represents the sternum; the dotted lines to the left and right correspond to the axillary lines.
sites, w h i c h w e r e m o s t l y o n t h e t o r s o side t h a t w a s closer to t h e h e a r t ( b o t h o n t h e f r o n t a n d t h e b a c k ) . F i g u r e 5 s h o w s t h e s p a t i a l d i s t r i b u t i o n of t h e error, b o t h for t h e L a p l a c i a n c o n v e r s i o n a n d t h e l i n e a r m e t h o d . I n b o t h cases t h e l a r g e s t e r r o r s a r e i n
:..,.
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Fig. 5. The spatial error distribution of the conversion based on linear interpolation with a m a x i m u m error of 327 ffV (A) and applying the Laplace transformation with a m a x i m u m error of 407/zV (B) produced by the Budapest system. In both cases the m a x i m u m error (marked with +) occurs close to tee heart region. (The difference between the contour lines is 50 /~V.)
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Journal of Electrocardiology Vol. 32 No. 3 July 1999
1 0,95
0.,9
0,85
0,8
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3
4
5
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Time Fig. 6. The correlation coefficients for the three methods (routes A, B, and C). For route A, the correlation coefficient is produced using the estimated and the reference i60 leads. For routes B and C the reference and the interpolated 192-lead maps were used. The average is calculated for each time instant.
the anterior, precordial sites. Qualitatively the error m a p s resemble each other m o r e t h a n was expected on the basis of the t e m p o r a l error distribution. F u r t h e r m o r e , the m a x i m a l values differ only slightly. The calculated correlation coefficients correspond to the REs. The m e a n values based on the three subgroups for the three m e t h o d s are s h o w n in Figure 6. The m e a n values, 0.95, 0.87, and 0.93 for routes A, B, and C, respectively, imply m o r e p r o m ising utilization of the m e t h o d s t h a n implied by the SE or AE distributions alone. The correlation coefficients diminish significantly at the low-voltage s e g m e n t of the heart cycle. In large amplitude m a p s the best values w e r e 0.99 for "A" a n d "C" and 0.95 for "B." This implies that some robust parameters, like the value and the trajectories of the e x t r e m e values, are well preserved.
Application of the Transformation Methods for a Clinical Example After the evaluation of the estimation and transf o r m a t i o n m e t h o d s by simulated data, modified linear and Laplacian conversion m e t h o d s (route B and C) w e r e tested using real data (Montreal-63) recorded in a clinical e n v i r o n m e n t . T h r o u g h an e x a m p l e we investigated the diagnostic utility of the c o n v e r t e d maps. To identify n o n - Q myocardial in-
farction (NQMI) or ischemic cardiac regions, we applied a n e w l y introduced m e t h o d for detecting a n d localizing "potential loss" (9). The classification was based on the m o s t robust spatial and t e m p o r a l i n f o r m a t i o n of BSPM, w h i c h are the amplitude a n d the location of the e x t r e m e values. The quotient of the absolute m a x i m u m a n d m i n i m u m values (measured within the QRS s e g m e n t on the whole b o d y surface) and the timeshift b e t w e e n their occurrences are considered to indicate potential loss connected with the injured heart region. These two p a r a m e t e r s w e r e quantitatively checked and compared. T w e n t y - o n e n o r m a l subjects and 17 patients with identified N Q M I w e r e involved in the test. Reference BSPM was recorded during sinus r h y t h m by the Montreal-63 lead system a n d the records w e r e processed and visualized by the C a r d i o m a p II syst e m of M o n t r e a l (5). Subsequently the conversion into the Budapest f o r m a t was executed in b o t h ways as described by routes B and C a n d BSPM was analyzed on the PC-based Budapest system (10). The diagnosis was originally d e t e r m i n e d f r o m the reference data of the Montreal-63 system. After the conversion, the original and the obtained p a r a m e ters w e r e statistically evaluated by m e a n s of a t w o - s a m p l e t test. F r o m the simulation study it was obvious that the i n t e r - e l e c t r o d e - s y s t e m transformations m i g h t result in a comparatively large error, especially in the amplitude values. This error m i g h t limit the chance of data transfer b e t w e e n different laboratories, m a i n l y for applications w h e r e high precision data are required. However, for some clinical studies only robust p a r a m e t e r s are used; consequently, in these applications, despite the significant deterioration of the signal information, the diagnostic inform a t i o n m a y r e m a i n intact. This was the m a i n m o t i v a t i o n of our p r e l i m i n a r y clinical test applying b o t h conversion methods. Figure 7 shows examples of isopotential m a p s f r o m selected instants in time for the results of the two methods. The figure shows the original maps, w h i c h w e r e p r o d u c e d by the original Montreal system, as well as the results of the linear interpolation and Laplacian t r a n s f o r m a t i o n - b a s e d conversion m e t h o d s (routes B a n d C). The m a p s p r o v e that Laplacian-based conversion is inaccurate for the small value regions, as RSEs are high. The topology of the m a p s confirms the results of the correlation study. Table 2 shows the m e a n values and the SDs of the two selected p a r a m e t e r s for the n o r m a l subjects a n d for the anterior a n d posterior N Q M I patients. C o m p a r i n g the data before and after the t r a n s f o r m a t i o n the results do not s h o w statistically
Study of Map Estimation Procedures
Fig. 7. S a m p l e i s o p o t e n t i a l m a p s at t w o t i m e i n s t a n t s : t o p panels, m a p s p r o d u c e d b y t h e original M o n t r e a l system; m i d d l e panels, t r a n s f o r m e d (linear interpolation) produced by the Budapest system; l o w e r panels, t r a n s f o r m e d (Laplacian i n t e r p o l a tion) m a p s p r o d u c e d b y t h e B u d a p e s t system. Despite t h e good morphologic agreem e n t , t h e errors, m a i n l y at small values, are relatively large. (For t h e M o n t r e a l system, maps include l0 equally spaced i s o c o n t o u r lines [zero line is thick]; i n t h e B u d a p e s t s y s t e m 15 i s o p o t e n t i a l cont o u r s are d r a w n , g r a d u a l l y inc r e m e n t e d f r o m m i n i m u m to maximum.)
24.0
M s e c Max:
42.0
. 8 1 i Min: - 0 . 2 3 3
•
PM 42 ms 2.00/-1.22 mV
• M 24 ms 0.80/-0.04 mV
PM 42 ms 2.011-1,49 mV
~
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"-I
Discussion
Two p r o b l e m s w e r e addressed in order to compile a large BSPM database, validation of the statistical extension of a limited lead system a n d validation of m e t h o d s for conversion of the 63-lead system into a I92-1ead format. The first one cannot be treated as a real t r a n s f o r m a t i o n m e t h o d because it has the restriction that the input lead system m u s t be a
Table 2. A n E x a m p l e for t h e D i a g n o s t i c U s e of t h e T r a n s f o r m e d B S P M Ratio of Absolute Maximum/Minimum
Montreal-63 (reference) Normal Anterior NQMI Posterior NQMI Budapest-192 Laplacian (route B) Normal Anterior NQMI Posterior NQMI Budapest-192 linear (route C) Normal Anterior NQMI Posterior NQMI
259
M.~ec~ax: 2 . 0 1 8 M i n : - l . 2 7 2
PM 24 ms 0.91/-0.18 mV
significant differences for a n y of the groups. F r o m this point of v i e w the utility of b o t h m e t h o d s are acceptable for medical experts. The large error in the signal i n f o r m a t i o n b e t w e e n the m e t h o d s is remarkable, but f r o m the standpoint of the diagnostic i n f o r m a t i o n these errors w e r e not significant in this specific example. The different pathological groups could be separated e v e n in the case of the use of the Laplacian-based conversion (P < .05).
Sandor et al.
Timeshift of the Extremes (ms)
Mean
SD
Mean
SD
1.05 0.88 1.73
0.25 0.32 0.38
3.65 10.3 18.4
3.9i 7.1 9.7
1.I5 0.86 1.64
0.35 0.34 0.32
2.73 10.1 16.8
4.18 8.2 7.9
1.09 0.89 1.68
0.28 0.37 0.35
3.42 9.65 18.32
3.68 7.43 8.59
Criteria are determined for identifying potential loss. The absolute value of the ratio between the maximum and the m i n i m u m value and, based on the entire QRS segment, the timeshift between their occurrence are calculated. The mean values and the standard deviations are summarized in the table calculated by using the original and the two transformed methods (routes B and C), respectively, for three subgroups (normals and anterior and posterior non-Q myocardial infarction).
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Journal of Electrocardiology Vol. 32 No. 3 July 1999
subset of the output. The error distribution is indep e n d e n t of the pathological classification of the test groups due to the correct sample selection for the transformation matrix. This study provided deeper insight into the error formation, which helps to clarify the possible limits of our simplified BSPM acquisition system. Concerning the accuracy parameters of the applied methods, our m e a s u r e m e n t s partly confirm recently published results (2,7). Specifically, the 38.5 /,V AE and the 0.95 average correlation coefficient for pattern fidelity do not differ significantly from the data of L u x et al., w h o reported 32 /xV for AE and 0.98 for correlation coefficient. The m e t h o d was found robust based o n the RE analysis. Assuming an extended version of the Lux-type system completed with leads m a r k e d by the squares in Figure 4, the error could be decreased from 38.5/,V to 31.4/xV, which is an 18.5% improvement. The RSE map revealed that the most significant RE occurs on the t r u n k above the level of V4-V 6 leads. Actually, in this part of the thorax the RE is three times greater than in the lower thorax. These results suggest that the error is influenced not only by the distance b e t w e e n the heart and the lead, but also by the underlying structure of the inhomogeneities (eg, large blood vessels). Obviously, the procedure minimizes the overall residual error but does not guarantee the uniform spatial distribution of the estimation errors in the different locations. The high average correlation coefficient b e t w e e n reference and estimated BSPM supports that the limited lead selection does not result in the acquisition of substantially different signal or diagnostic information than acquired using the original BSPM system. Obviously this characteristic applies to our clinical example, w h e r e the extracted features were rather robust. Our result for transforming the 63-lead Montreal system into a 192-lead system by the Laplacian m e t h o d clearly indicates that in this specific case the assumption behind the Laplacian procedure was not fulfilled satisfactorily. In fact, the error calculated by us is concordant with the results of MacLeod (11) and Hoekema (2). They reported an accelerated deterioration of the Laplacian interpolation accuracy as the lead system electrode density decreased. The low sampling density of the input potential field only partly explains the poor outcome. More emphasis should be on selecting the location of the electrodes, mainly on the precordial region, w h e r e the potential field changes rapidly. In such regions, the numerical estimation of the Laplacian by the first few members of the Taylor expansion fails. Inaccurate knowledge of the lead loca-
tions m a y also contribute to the failure of the method, since uniform thorax g e o m e t r y is used for the inter-lead-system transformation; consequently, only a rather vague knowledge of the geometric relationships is available. The geometric inaccuracy is further accentuated in regions w h e r e the surface cannot be unrolled into a plane. Whereas in the Laplacian m e t h o d the n u m b e r of leads in the input lead system is the important feature, in the modified linear interpolation the relative position of the two lead systems is the decisive characteristic. In our case 47 of the 63 leads were on the anterior region, which could result in a better accuracy level for the modified linear interpolation. Our results prove the necessity of detailed analysis before using methods described by general error characteristics for a specific lead system. These results provide detailed evidence that the measurements obtained by the Lux-type limited system are valid and acceptable; the RTE was b e t w e e n 15% and 20% after the first instant t h r o u g h o u t the QRS segment. As a byproduct of our analysis, the high error leads were also identified. A lead set incorporating 8 additional leads could diminish the average estimation error to 80% of the original error. The error in the Laplacian m e t h o d was f o u n d to be comparable with the SD within the groups. The modified linear interpolation considered as an alternative for the Montreal-to-Budapest lead system instead of the Laplacian approach is more satisfactory, but only w h e n rather robust parameters are extracted for statistical classification. Our study warns of the need for careful validation of i n t e r lead-system transformations before use. The following remarks must be made about the limitations of the study. A larger n u m b e r of the pathological cases involved in the analysis would increase the reliability of our results (12). The assumption of an average thoracic geometry, that is, relative positions of the electrodes in the electrode array are considered in the inter-electrodesystem transformation, purports an error source and decreases the accuracy of the analysis. Last, our study was confined to analyze the QRS segment and therefore the average errors were overestimated regarding the entire electrical heart cycle.
Acknowledgments The 219 lead maps were kindly provided by Prof. E. Musso, Parma University; the Laplacian transfor-
Study of Map Estimation Procedures
m a r i o n m a t r i c e s w e r e p r o v i d e d b y R. H o e k a m a , U n i v e r s i t y of N i j m e g e n . 7.
References 1. Monro DM (ed): The NEMY concerted action. Report Ref: ECISEINERMYID2-2. University of Bath, Bath, United Kingdom, 1996 2. Hoekema R, Uijen GJ, Stilli D, van Oosterom A: Lead system transformation of body surface map data. J Electrocardiol 31:2, 1998 3. Kozmann Gy, Lux RL, Tysler M: Multi-center attempt for validated body surface potential map database. p. 409. In Werner R, D'Amico C (eds): Computers in cardiology. IEEE Computer Society Press, Washington, 1994 4. Lux RL, Burgess MJ, Wyatt RF, et al: Clinically practical lead systems for improved electrocardiography: comparison with precordial grids and conventional lead systems. Circulation 59:2, 1979 5. Boneau G, Tremblay G, Savard P, et al: An integrated system for intraoperative cardiac activation mapping. IEEE Trans Biomed Eng 34:6, 1987 6. Stilli D, Musso E, Barone P, et al: Newer data on the
8.
9.
10.
ll.
12.
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configuration and variability ranges of body surface maps in a sample of normal subjects. J Electrocardiol 21:1, 1988 Lux RL, Smith CR, Wyatt RF, Abildskov JA: Limited lead selection for estimation of body surface potential maps in electrocardiography. IEEE Trans Biomed Eng 25:270, 1978 Oostendorp TF, van Oosterom A, Huiskamp GJ: Interpolation on triangulated 3D surface. J Comput Physics 80:331, 1989 Medvegy M, Pr~da I, Nadeau R, et al: Investigation of old non-Q wave myocardial infarction by body surface potential mapping. Circulation Suppl 94:731, 1996 Gross J, Sandor G: Body surface map processing system in windows environment. Cardiol Hungarica 24:4, 1995 Macleod RS, Lux RL, Taccardi B: Translation of body surface maps between different electrode configurations using a three-dimensional interpolation scheme, p. 30. In MacFarlane PW (ed): Electrocardiology '93. Word Scientific, Singapore, I993 Kozmann Gy, Lux RL, Scott M: Sample size and dimensionality in multivariate classification: implications for body surface potential mapping. Comput Biomed Res 24:170, 1991
Body Surface Potential Field Representation Fidelity: Analysis of Map Estimation Procedures
G y 6 r g y Sfindor, M S , G y 6 r g y K o z m a n n , P h D , Z s u z s a n n a Cserj~s, P h D , N o 6 r n i F a r k a s , MS,* a n d Istvfin P r d d a , M D , P h D t
Abstract: The first part of this study analyzed the spatiaI-temporal error distribution of the Lux-type limited lead system. Quantitative n e w evidence is reported that the 32-lead anterior subset estimates the further 160 leads with an average amplitude error less than 38.5 /xV. The spatial error distribution revealed 8 sites where the error is the highest, primarily on the anterior side, independent of the clinical classification. The second part of the study examined inter-lead-system conversion strategies for interpolating the Lux192 lead maps from the Montreal-63 data. The methodology based on the Laplacian interpolation yielded an average amplitude error of 143.7/zV and an average correlation of 0.87 for pattern fidelity. In this specific case a modified linear interpolation surpassed the Laplacian method. A presented example illustrates that even in cases w h e n the fidelity of the signal information is heavily compromised the diagnostic information m a y remain less influenced. K e y words: body surface potential maps, electrode grids, Laplacian interpolation, limited lead system, linear interpolation.
Body surface potential mapping (BSPM) is a technique for acquiring the entire diagnostic information available on the chest surface. Although BSPM technology has achieved a high standard because of the rapid development of computer technology, the answer for the basic issue concerning the amount of the additional diagnostic information in the map data is still obscure. Beyond
current evidence of the clinical utility of BSPM technology there is still a need for more rigorous statistical proof of the early findings. To accomplish these statistical studies, larger validated databases of BSPM are required than those currently available in most laboratories. Because no standardization has occurred in BSPM measurement, no direct routes are available for pooling the local databases. An inter-lead-system transformation, based on minimization of the surface Laplacian, has been elaborated within a European Union project called Noninvasive Evaluation of Myocardium (NEMY) and suggested as a vehicle for solving the pooling problem (1). Hoekema et al. (2) analyzed the accuracy of the transformation method for the 11 most frequently used lead systems and reported that when the input lead system contains more than 63
From the Research Institute for Technical Physics and Materials Science and the t Haynal Imre University of Health Sciences, Budapest, and the *University of Veszprdm, Veszprdm, Hungary.
Supported by grant F25618 from the Hungarian National Research Fund. Reprint requests: Dr. Gy6rgy Kozmann, MTA-MFA P.O.B. 49, Budapest 1525, Hungary. Copyright © I999 by Churchill Livingstone ®
0022-073619913203-0006510.00/0
253
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Journal of Electrocardiology Vol. 32 No. 3 July 1999
leads the average relative t r a n s f o r m a t i o n error is no larger t h a n 11%. The elaboration of a large validated BSPM database is a current p r o b l e m in our laboratory as well. Our group has compiled a BSPM data bank, with m o r e t h a n 2,000 items of n o r m a l and cardiacdiseased subjects (3). The data b a n k currently includes BSPM records that w e r e obtained b y three types of lead systems. Consequently we are highly interested in the quantitative accuracy of the different i n t e r - l e a d - s y s t e m transformations. Most of o u r files w e r e recorded by the Lux-32 (anterior-type) limited lead system. F r o m the m e a s u r e d 32 signals, 192-lead m a p s are calculated by m e a n s of a statistically derived estimation matrix (4). The second largest group of records was obtained by the M o n treal 63-lead system (5), a n d the third set, provided by the University of Parma, consists of 219-lead data (6). Unfortunately, the n u m b e r of leads in our input lead system is on the lower limit of the acceptance level. The objective of the present study was the detailed statistical characterization of the fidelity of our 192-lead BSPM representation with respect to (l) the use of the limited lead system a n d the statistical p r o c e d u r e for estimating potential values in the u n m e a s u r e d locations, and (2) the errors g e n e r a t e d as a consequence of data t r a n s f o r m a t i o n f r o m one lead system to another. Systematic amplitude a n d m o r p h o l o g i c error analysis was accomplished to assess the applicability of the m e t h o d s in our case. The estimation m e t h o d of the 192-lead BSPM, estimated f r o m the a n a t o m ically defined 32 limited lead set, was investigated. F u r t h e r m o r e , we evaluated the Laplacian transform a t i o n and a modified linear interpolation m e t h o d , w h i c h w e r e suggested for converting the M o n t r e a l 63-lead data into the Lux-32 limited lead systems. An e x a m p l e for the clinical utility of the data conversion is also outlined.
Materials and M e t h o d s Generation of Reference and Simulated Measurement Data Body surface potential m a p s f r o m 50 subjects (20 n o r m a l subjects, 15 w i t h ischemic heart disease, and 15 anterior myocardial infarction patients) were used as the e x p e r i m e n t a l data in the analysis. The c o m p u t a t i o n s w e r e confined to the QRS interval because it has the largest amplitudes and dyn a m i c change. The QRS segments w e r e t i m e - n o r -
219-lead original map
] Data Preprocesslng
[
Sele~ion of the normalized map instants
]
"~
/
192-lead reference map
Montreal 63-lead map
Lux-32 limited lead data ac, rttisition
Validation Process
/ Laplacian transformation
into 192-lead map
Modified linear interpolation into 32-lead map
Lux-type statistical estimation process to 192-lead map
Lux-type statistical estimation process to 192-1ead map
ERROR A N A L Y S I S A
B
] C
Fig. 1. Flowchart of validation in the Lux-type limited lead data acquisition philosophy (32---->I92, route A), Laplacian transformation method (63-->192, route B), and linear interpolation-based conversion of Montreal-63 data into the Budapest 192-lead database system (63--->192, route C).
malized a n d represented by 10 equally distant instantaneous maps. The test data w e r e recorded by the P a r m a system, w h i c h includes 219 leads in a nonequidistant a r r a n g e m e n t , w i t h a high electrode density in the precordial area. Figure 1 shows the flow chart of the analysis. In the following, we will refer to the three procedures as route A, route B, a n d route C. The database of our laboratory uses the 192-lead equidistant electrode layout as a standard, w i t h m e a s u r i n g point locations originally introduced b y the group of Salt Lake City. Our actual data acquisition is done by the Lux-type limited lead system containing 32 m e a s u r e m e n t locations, and the 192-1ead f o r m a t is calculated using the estimation p r o c e d u r e that is an i n h e r e n t part of the Lux approach. The first step of the analysis was the p r o d u c t i o n of 192-1ead reference m a p s f r o m 219-lead BSPM b y bilinear interpolation. In a similar w a y to the reference 192-lead maps, the simulated M o n t r e a l 63-lead and the Lux-32 limited lead m e a s u r e m e n t s w e r e derived f r o m the P a r m a data set. Subsequently, based on the simulated m e a s u r e m e n t , 192-lead m a p s were estimated (by the m e t h o d s described in the n e x t section). Because b o t h the Montreal and the Lux systems define the location of the electrode sites anatomically, before accomplishing the inter-leadsystem transformations the same average g e o m e t r y had to be assigned to all the P a r m a patients. The
Study of Map Estimation Procedures
relative position of the I 9 2 - a n d the 63-lead system m e a s u r i n g points in the P a r m a frame occurred on this hypothetical torso.
*
Sfndor et al.
255
w h e r e h is the distance b e t w e e n t w o adjacent sites. The linear interpolation was modified by missing the least significant sites. A predefined threshold
hi
Simulation of the Data Transformation Procedures For the first p r o b l e m of our study 192-lead BSPM was estimated f r o m the 32-lead simulated m e a s u r e m e n t data (route A), based on the estimation m a trix introduced b y Lux et al. The idea b e h i n d the Lux-type limited lead system is that BSPM is considered to be a sequence of r a n d o m potential vector distributions at s u b s e q u e n t time instants. Therefore, the r e d u n d a n c y of BSPM can be evaluated by a statistical m e t h o d . The covariance matrix of a training m a p set was used to find a n optimal t r a n s f o r m a t i o n matrix in least square sense. Detailed e x p l a n a t i o n can be f o u n d elsewhere (7). For the second p r o b l e m the 192-lead m a p data w e r e estimated directly f r o m the simulated M o n treal-63 m e a s u r e m e n t s (route B) by m e a n s of the Laplacian t r a n s f o r m a t i o n that was suggested by Oostendorp et al. (8). The second order derivatives (Laplacian) of the u n k n o w n potentials w e r e estim a t e d by m e a n s of a second degree Taylor expansion. Subsequently, the n o r m of the surface Laplaclan was m i n i m i z e d in order to find the missing potential values. Finally, in our third problem, the 192-lead data w e r e derived w i t h a modified linear interpolation m e t h o d developed b y the authors c o m b i n e d w i t h the L u x - t y p e estimation (route C) as an alternative w a y of route B. This latter p r o c e d u r e t o o k into consideration directly the geometric relations bet w e e n the Montreal-63 a n d Lux-32 lead set. Initially a w e i g h t e d average in the p r o p o r t i o n of the inverse distances of the four closest neighbors w e r e applied for d e t e r m i n i n g the potential values at the u n k n o w n sites:
was defined empirically as if a n y ~ is less t h a n 0.2 ( i = 1 . . . 4 , j = 1 . . . 4 ) t h e n the effect o f t h e j th neighbor is neglected. Thus a t r a n s f o r m a t i o n matrix was obtained w h o s e elements d e p e n d e d on the relative g e o m e t r y of the two lead sets.
Methodologies of the Error Analysis For characterization of the accuracy of the transf o r m a t i o n m e t h o d s various amplitude errors w e r e calculated. The average t e m p o r a l error (TE) in the ith time instant is defined as follows:
TEi=_~ ~
;.=
k=I
w h e r e N is the patient n u m b e r , M is n u m b e r of the estimated leads, and eij is the error of the jth lead. The relative (temporal) error (RTE) has b e e n defined at the ith instant as:
TEi RTEi - RMSi w h e r e RMS i is the root m e a n square of BSPM of N patients at the ith instant. The accuracy of the different m e t h o d s for each single lead has also b e e n calculated one by one. The spatial error (SE) is defined similarly to TE. SE of the j t h lead including the w h o l e QRS interval is defined as follows:
4
wiVi i=1 V j - - - 4
i=I
w h e r e Vj is to be interpolated, V i is an adjacent potential value, a n d w~ is the weighting coefficient defined as:
sfj = #
0 k=l
The relative spatial error (RSE) can be calculated f r o m SE like the RTE f r o m the TE, and the f o r m u l a can be written as:
st RSEj - RMSj Wi
z
.
-
-
4
k=l
w h e r e RMSj is the root m e a n square of the I0 time instants of N patients at the j t h lead.
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Journal of Electrocardiology Vol. 32 No. 3 July 1999
A global average amplitude error (AE) and relative error (RE) h a v e also b e e n introduced over the entire QRS interval:
M
1 NI EE]
xE=#E
-
-
RE
-
200
RMS
w h e r e root m e a n square c o m p u t a t i o n was confined to the QRS interval. The m a g n i t u d e of the transform a t i o n errors in each instant was c o m p a r e d with the w i t h i n - g r o u p variability c o m p u t e d in the v e r y same m o m e n t , at each clinical category. The average variance within the h o m o g e n e o u s groups at the ith instant is calculated, as follows:
(@iJl~9~iJ)2
1N k=i j=l
w h e r e o-i is the w i t h i n - g r o u p standard deviation in the ith instant, ~f is the potential m e a s u r e d at the jth site in the ith instant a n d &/j is the average potential of the ith instant group at the j t h site. A diagram f o r m a t was used for the purpose of representing TE and RTE, while for d e m o n s t r a t i n g SE and RSE m a p f o r m a t was the m o s t convenient. Morphologic similarity b e t w e e n the reference and the t r a n s f o r m e d m a p s was characterized by correlation coefficient. The m e a n correlation coefficients and the m a x i m u m values for all the m e t h o d s are represented.
Results First, the simulated data w e r e used for evaluating the amplitude error as a function of the n o r m a l i z e d QRS time instants for the three problems described in the previous section. Table 1 gives a global o v e r v i e w of the AE with standard deviation (SD), the m a x i m a l error (ME), and the RE, providing a quantitative c o m p a r i s o n b e t w e e n the m e t h o d s in a
Table 1. The Average Amplitude Error (AE) on the Entire QRS* and Standard Deviation (SD), the Relative Error (RE), and the Maximum Error (ME) Based on the Average of the I92-1ead BSPM
A E -+ SD (/,V) RE ( % ) M E (/,V)
400I 300
AE
and
k=l
2
500
A
B
C
3 8 . 5 -+ 2 8 16 71
143.7 ± 77 63 268
6 3 -+ 37 27 121
* M e a n v a l u e of t h e 10 t i m e i n s t a n t s .
I00 2
3
4
5
6
7
8
9
10
Time
Fig. 2. The temporal distribution of the amplitude error versus the QRS segment. The average temporal errors and standard deviations (in /,V) from the three procedures are shown, and for better comparison the root mean square (RMS) signal superposed by the withingroup variability (~r) is also plotted.
general sense. While the statistical estimation of Lux resulted in the best values, the modified linear interpolation yielded significantly less error t h a n the Laplacian interpolation despite that the error of route C includes the error of route A. In accordance with previously reported results (2), o u r analysis did not find significant difference a m o n g the three different patient subgroups, d e m o n s t r a t i n g that error values d e p e n d only w e a k l y on the m a p patterns d e t e r m i n e d by the clinical status of the patients. Therefore, the results w e r e obtained including all test data. Figure 2 shows the TE distribution a n d SDs for the three routes. For a better c o m p a r i s o n the root m e a n square values a n d the w i t h i n - m a p variability are represented. The error distributions resemble each other, but the linear interpolation results in roughly 50% lower values for all the calculated error parameters, and their SDs are also smaller. In each t r a n s f o r m a t i o n the MEs occurred at the sixth instant w h e n the b o d y surface root m e a n square value was also the largest. In unfavorable case of "B" the error can reach the average signal value not only in the first or the t e n t h time instant. Despite the increase of the TE, w h i c h is the error in absolute sense, the RTEs did not change significantly for the higher signal amplitudes. C o m p a r i n g RTEs (Fig. 3), the best result is 14%, f o u n d in the eighth instant of route A. For the interpolations the best values w e r e 52% at the sixth instant for route B and 26% at the fifth instant in the linear interpolation. While the AEs d e p e n d e d strongly on the position within the QRS, the REs w e r e rather stable. The fluctua-
Study of Map Estimation Procedures
.
'1\
6 7 15 19 7 [] 5 3 3
--,--Uadan
0,81-\
• linear
0,7
o,1 0
I
I
I
I
I
I
I
I
I
2
3
4
5
6
7
8
9
10
"rime Fig. 3. The relative error (in/xV) at the Lux-type estimation (route A), the Laplacian m e t h o d (route B), and the linear conversion (route C).
t i o n w a s b e l o w 1 0 % in r o u t e s B a n d C a n d 5 % i n r o u t e A. W e c h e c k e d t h e a c c u r a c y of t h e L a p l a d a n m e t h o d i n t w o f o r m s . First, t h e 63---~192 d i r e c t i n t e r p o l a t i o n w a s e x e c u t e d , r e s u l t i n g in o n l y a s l i g h t l y s m a l l e r e r r o r t h a n b y first a p p l y i n g t h e 63--->32 c o n v e r s i o n a n d s u b s e q u e n t l y a p p l y i n g t h e statistical e s t i m a t i o n of Lux. This o u t c o m e s u p p o r t s the hypothesis that in the Laplacian interpolation t h e n u m b e r of i n p u t l e a d s is e s s e n t i a l l y d e c i s i v e i n d e p e n d e n t of t h e o u t p u t l e a d n u m b e r . T h e s p a t i a l d i s t r i b u t i o n of t h e a m p l i t u d e e r r o r (the SE) w a s also i n v e s t i g a t e d . O n F i g u r e 4 b l a c k dots m a r k t h e L u x - 3 2 ( a n t e r i o r - t y p e ) l e a d s y s t e m a n d b l a c k s q u a r e d n u m b e r s d i s t i n g u i s h t h e sites where the statistically based estimation produced the largest absolute error. The figure reveals that t h e l a r g e s t e r r o r s o c c u r r e d at l o c a t i o n s close to t h e h e a r t . This f i n d i n g i m p l i e s t h a t a n y k i n d of l e a d s y s t e m m u s t h a v e e n o u g h d e n s e p r e c o r d i a l elect r o d e a r r a n g e m e n t for p r e s e r v i n g t h e signal i n f o r m a t i o n faithfully. S e c o n d , it p r o v e s t h e a d v a n t a g e of t h e n o n e q u i d i s t a n t s p a t i a l s a m p l i n g o n t h e t o r s o surface. T h e f i g u r e s h o w s t h e RSE d i s t r i b u t i o n o n t h e 1 9 2 - l e a d m a p (160 e s t i m a t e d l e a d ) . T h e h i g h RSE r e g i o n w a s o n t h e u p p e r h a l f of t h e t o r s o b o t h o n t h e p o s t e r i o r a n d o n t h e a n t e r i o r t h o r a c i c surfaces, a f i n d i n g t h a t p a r t l y s u p p o r t s t h e r e q u i r e m e n t for b a c k e l e c t r o d e s . T h e f i g u r e r e v e a l s t h a t in m o r e t h a n 7 5 % of t h e e s t i m a t e d sites t h e RSE w a s b e l o w 1 0 % . The RSEs w e r e b e y o n d 2 0 % in 5 % of t h e
5 5 13 4 6 15 3 2 3
5 8 15 4 8 13 1 2 3
•
Sandor et al. 257
8
7
3
6 • i10 25 7 - 9 11 15 121 6 12 • 5 7 8 61o 8 17 • 6 3 16 15 201 11 • i31 • 1168 5 [16 21 18 17 • 7 3 8 10 • 2 2 2 • • • • 20 • 15 20 1 1 2 • • • • • 14 3 7 4 5 1 3 4 2 • • 10 4 • 1 2 3 5 2 5 3 2 1 1 • 2 1 • 4 7 9 0 1 1 1 2i2 3 • 2 3 5 6 7
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Fig. 4. The spatial relative error distribution for route A. The 8 boxed sites are those where the estimation produced the largest average amplitude error (3 of the 8 are on the back side). Black dots show the m e a s u r e m e n t location of the Lux-type limited lead system. The central dashed line represents the sternum; the dotted lines to the left and right correspond to the axillary lines.
sites, w h i c h w e r e m o s t l y o n t h e t o r s o side t h a t w a s closer to t h e h e a r t ( b o t h o n t h e f r o n t a n d t h e b a c k ) . F i g u r e 5 s h o w s t h e s p a t i a l d i s t r i b u t i o n of t h e error, b o t h for t h e L a p l a c i a n c o n v e r s i o n a n d t h e l i n e a r m e t h o d . I n b o t h cases t h e l a r g e s t e r r o r s a r e i n
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Fig. 5. The spatial error distribution of the conversion based on linear interpolation with a m a x i m u m error of 327 ffV (A) and applying the Laplace transformation with a m a x i m u m error of 407/zV (B) produced by the Budapest system. In both cases the m a x i m u m error (marked with +) occurs close to tee heart region. (The difference between the contour lines is 50 /~V.)
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Journal of Electrocardiology Vol. 32 No. 3 July 1999
1 0,95
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Time Fig. 6. The correlation coefficients for the three methods (routes A, B, and C). For route A, the correlation coefficient is produced using the estimated and the reference i60 leads. For routes B and C the reference and the interpolated 192-lead maps were used. The average is calculated for each time instant.
the anterior, precordial sites. Qualitatively the error m a p s resemble each other m o r e t h a n was expected on the basis of the t e m p o r a l error distribution. F u r t h e r m o r e , the m a x i m a l values differ only slightly. The calculated correlation coefficients correspond to the REs. The m e a n values based on the three subgroups for the three m e t h o d s are s h o w n in Figure 6. The m e a n values, 0.95, 0.87, and 0.93 for routes A, B, and C, respectively, imply m o r e p r o m ising utilization of the m e t h o d s t h a n implied by the SE or AE distributions alone. The correlation coefficients diminish significantly at the low-voltage s e g m e n t of the heart cycle. In large amplitude m a p s the best values w e r e 0.99 for "A" a n d "C" and 0.95 for "B." This implies that some robust parameters, like the value and the trajectories of the e x t r e m e values, are well preserved.
Application of the Transformation Methods for a Clinical Example After the evaluation of the estimation and transf o r m a t i o n m e t h o d s by simulated data, modified linear and Laplacian conversion m e t h o d s (route B and C) w e r e tested using real data (Montreal-63) recorded in a clinical e n v i r o n m e n t . T h r o u g h an e x a m p l e we investigated the diagnostic utility of the c o n v e r t e d maps. To identify n o n - Q myocardial in-
farction (NQMI) or ischemic cardiac regions, we applied a n e w l y introduced m e t h o d for detecting a n d localizing "potential loss" (9). The classification was based on the m o s t robust spatial and t e m p o r a l i n f o r m a t i o n of BSPM, w h i c h are the amplitude a n d the location of the e x t r e m e values. The quotient of the absolute m a x i m u m a n d m i n i m u m values (measured within the QRS s e g m e n t on the whole b o d y surface) and the timeshift b e t w e e n their occurrences are considered to indicate potential loss connected with the injured heart region. These two p a r a m e t e r s w e r e quantitatively checked and compared. T w e n t y - o n e n o r m a l subjects and 17 patients with identified N Q M I w e r e involved in the test. Reference BSPM was recorded during sinus r h y t h m by the Montreal-63 lead system a n d the records w e r e processed and visualized by the C a r d i o m a p II syst e m of M o n t r e a l (5). Subsequently the conversion into the Budapest f o r m a t was executed in b o t h ways as described by routes B and C a n d BSPM was analyzed on the PC-based Budapest system (10). The diagnosis was originally d e t e r m i n e d f r o m the reference data of the Montreal-63 system. After the conversion, the original and the obtained p a r a m e ters w e r e statistically evaluated by m e a n s of a t w o - s a m p l e t test. F r o m the simulation study it was obvious that the i n t e r - e l e c t r o d e - s y s t e m transformations m i g h t result in a comparatively large error, especially in the amplitude values. This error m i g h t limit the chance of data transfer b e t w e e n different laboratories, m a i n l y for applications w h e r e high precision data are required. However, for some clinical studies only robust p a r a m e t e r s are used; consequently, in these applications, despite the significant deterioration of the signal information, the diagnostic inform a t i o n m a y r e m a i n intact. This was the m a i n m o t i v a t i o n of our p r e l i m i n a r y clinical test applying b o t h conversion methods. Figure 7 shows examples of isopotential m a p s f r o m selected instants in time for the results of the two methods. The figure shows the original maps, w h i c h w e r e p r o d u c e d by the original Montreal system, as well as the results of the linear interpolation and Laplacian t r a n s f o r m a t i o n - b a s e d conversion m e t h o d s (routes B a n d C). The m a p s p r o v e that Laplacian-based conversion is inaccurate for the small value regions, as RSEs are high. The topology of the m a p s confirms the results of the correlation study. Table 2 shows the m e a n values and the SDs of the two selected p a r a m e t e r s for the n o r m a l subjects a n d for the anterior a n d posterior N Q M I patients. C o m p a r i n g the data before and after the t r a n s f o r m a t i o n the results do not s h o w statistically
Study of Map Estimation Procedures
Fig. 7. S a m p l e i s o p o t e n t i a l m a p s at t w o t i m e i n s t a n t s : t o p panels, m a p s p r o d u c e d b y t h e original M o n t r e a l system; m i d d l e panels, t r a n s f o r m e d (linear interpolation) produced by the Budapest system; l o w e r panels, t r a n s f o r m e d (Laplacian i n t e r p o l a tion) m a p s p r o d u c e d b y t h e B u d a p e s t system. Despite t h e good morphologic agreem e n t , t h e errors, m a i n l y at small values, are relatively large. (For t h e M o n t r e a l system, maps include l0 equally spaced i s o c o n t o u r lines [zero line is thick]; i n t h e B u d a p e s t s y s t e m 15 i s o p o t e n t i a l cont o u r s are d r a w n , g r a d u a l l y inc r e m e n t e d f r o m m i n i m u m to maximum.)
24.0
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Discussion
Two p r o b l e m s w e r e addressed in order to compile a large BSPM database, validation of the statistical extension of a limited lead system a n d validation of m e t h o d s for conversion of the 63-lead system into a I92-1ead format. The first one cannot be treated as a real t r a n s f o r m a t i o n m e t h o d because it has the restriction that the input lead system m u s t be a
Table 2. A n E x a m p l e for t h e D i a g n o s t i c U s e of t h e T r a n s f o r m e d B S P M Ratio of Absolute Maximum/Minimum
Montreal-63 (reference) Normal Anterior NQMI Posterior NQMI Budapest-192 Laplacian (route B) Normal Anterior NQMI Posterior NQMI Budapest-192 linear (route C) Normal Anterior NQMI Posterior NQMI
259
M.~ec~ax: 2 . 0 1 8 M i n : - l . 2 7 2
PM 24 ms 0.91/-0.18 mV
significant differences for a n y of the groups. F r o m this point of v i e w the utility of b o t h m e t h o d s are acceptable for medical experts. The large error in the signal i n f o r m a t i o n b e t w e e n the m e t h o d s is remarkable, but f r o m the standpoint of the diagnostic i n f o r m a t i o n these errors w e r e not significant in this specific example. The different pathological groups could be separated e v e n in the case of the use of the Laplacian-based conversion (P < .05).
Sandor et al.
Timeshift of the Extremes (ms)
Mean
SD
Mean
SD
1.05 0.88 1.73
0.25 0.32 0.38
3.65 10.3 18.4
3.9i 7.1 9.7
1.I5 0.86 1.64
0.35 0.34 0.32
2.73 10.1 16.8
4.18 8.2 7.9
1.09 0.89 1.68
0.28 0.37 0.35
3.42 9.65 18.32
3.68 7.43 8.59
Criteria are determined for identifying potential loss. The absolute value of the ratio between the maximum and the m i n i m u m value and, based on the entire QRS segment, the timeshift between their occurrence are calculated. The mean values and the standard deviations are summarized in the table calculated by using the original and the two transformed methods (routes B and C), respectively, for three subgroups (normals and anterior and posterior non-Q myocardial infarction).
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Journal of Electrocardiology Vol. 32 No. 3 July 1999
subset of the output. The error distribution is indep e n d e n t of the pathological classification of the test groups due to the correct sample selection for the transformation matrix. This study provided deeper insight into the error formation, which helps to clarify the possible limits of our simplified BSPM acquisition system. Concerning the accuracy parameters of the applied methods, our m e a s u r e m e n t s partly confirm recently published results (2,7). Specifically, the 38.5 /,V AE and the 0.95 average correlation coefficient for pattern fidelity do not differ significantly from the data of L u x et al., w h o reported 32 /xV for AE and 0.98 for correlation coefficient. The m e t h o d was found robust based o n the RE analysis. Assuming an extended version of the Lux-type system completed with leads m a r k e d by the squares in Figure 4, the error could be decreased from 38.5/,V to 31.4/xV, which is an 18.5% improvement. The RSE map revealed that the most significant RE occurs on the t r u n k above the level of V4-V 6 leads. Actually, in this part of the thorax the RE is three times greater than in the lower thorax. These results suggest that the error is influenced not only by the distance b e t w e e n the heart and the lead, but also by the underlying structure of the inhomogeneities (eg, large blood vessels). Obviously, the procedure minimizes the overall residual error but does not guarantee the uniform spatial distribution of the estimation errors in the different locations. The high average correlation coefficient b e t w e e n reference and estimated BSPM supports that the limited lead selection does not result in the acquisition of substantially different signal or diagnostic information than acquired using the original BSPM system. Obviously this characteristic applies to our clinical example, w h e r e the extracted features were rather robust. Our result for transforming the 63-lead Montreal system into a 192-lead system by the Laplacian m e t h o d clearly indicates that in this specific case the assumption behind the Laplacian procedure was not fulfilled satisfactorily. In fact, the error calculated by us is concordant with the results of MacLeod (11) and Hoekema (2). They reported an accelerated deterioration of the Laplacian interpolation accuracy as the lead system electrode density decreased. The low sampling density of the input potential field only partly explains the poor outcome. More emphasis should be on selecting the location of the electrodes, mainly on the precordial region, w h e r e the potential field changes rapidly. In such regions, the numerical estimation of the Laplacian by the first few members of the Taylor expansion fails. Inaccurate knowledge of the lead loca-
tions m a y also contribute to the failure of the method, since uniform thorax g e o m e t r y is used for the inter-lead-system transformation; consequently, only a rather vague knowledge of the geometric relationships is available. The geometric inaccuracy is further accentuated in regions w h e r e the surface cannot be unrolled into a plane. Whereas in the Laplacian m e t h o d the n u m b e r of leads in the input lead system is the important feature, in the modified linear interpolation the relative position of the two lead systems is the decisive characteristic. In our case 47 of the 63 leads were on the anterior region, which could result in a better accuracy level for the modified linear interpolation. Our results prove the necessity of detailed analysis before using methods described by general error characteristics for a specific lead system. These results provide detailed evidence that the measurements obtained by the Lux-type limited system are valid and acceptable; the RTE was b e t w e e n 15% and 20% after the first instant t h r o u g h o u t the QRS segment. As a byproduct of our analysis, the high error leads were also identified. A lead set incorporating 8 additional leads could diminish the average estimation error to 80% of the original error. The error in the Laplacian m e t h o d was f o u n d to be comparable with the SD within the groups. The modified linear interpolation considered as an alternative for the Montreal-to-Budapest lead system instead of the Laplacian approach is more satisfactory, but only w h e n rather robust parameters are extracted for statistical classification. Our study warns of the need for careful validation of i n t e r lead-system transformations before use. The following remarks must be made about the limitations of the study. A larger n u m b e r of the pathological cases involved in the analysis would increase the reliability of our results (12). The assumption of an average thoracic geometry, that is, relative positions of the electrodes in the electrode array are considered in the inter-electrodesystem transformation, purports an error source and decreases the accuracy of the analysis. Last, our study was confined to analyze the QRS segment and therefore the average errors were overestimated regarding the entire electrical heart cycle.
Acknowledgments The 219 lead maps were kindly provided by Prof. E. Musso, Parma University; the Laplacian transfor-
Study of Map Estimation Procedures
m a r i o n m a t r i c e s w e r e p r o v i d e d b y R. H o e k a m a , U n i v e r s i t y of N i j m e g e n . 7.
References 1. Monro DM (ed): The NEMY concerted action. Report Ref: ECISEINERMYID2-2. University of Bath, Bath, United Kingdom, 1996 2. Hoekema R, Uijen GJ, Stilli D, van Oosterom A: Lead system transformation of body surface map data. J Electrocardiol 31:2, 1998 3. Kozmann Gy, Lux RL, Tysler M: Multi-center attempt for validated body surface potential map database. p. 409. In Werner R, D'Amico C (eds): Computers in cardiology. IEEE Computer Society Press, Washington, 1994 4. Lux RL, Burgess MJ, Wyatt RF, et al: Clinically practical lead systems for improved electrocardiography: comparison with precordial grids and conventional lead systems. Circulation 59:2, 1979 5. Boneau G, Tremblay G, Savard P, et al: An integrated system for intraoperative cardiac activation mapping. IEEE Trans Biomed Eng 34:6, 1987 6. Stilli D, Musso E, Barone P, et al: Newer data on the
8.
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configuration and variability ranges of body surface maps in a sample of normal subjects. J Electrocardiol 21:1, 1988 Lux RL, Smith CR, Wyatt RF, Abildskov JA: Limited lead selection for estimation of body surface potential maps in electrocardiography. IEEE Trans Biomed Eng 25:270, 1978 Oostendorp TF, van Oosterom A, Huiskamp GJ: Interpolation on triangulated 3D surface. J Comput Physics 80:331, 1989 Medvegy M, Pr~da I, Nadeau R, et al: Investigation of old non-Q wave myocardial infarction by body surface potential mapping. Circulation Suppl 94:731, 1996 Gross J, Sandor G: Body surface map processing system in windows environment. Cardiol Hungarica 24:4, 1995 Macleod RS, Lux RL, Taccardi B: Translation of body surface maps between different electrode configurations using a three-dimensional interpolation scheme, p. 30. In MacFarlane PW (ed): Electrocardiology '93. Word Scientific, Singapore, I993 Kozmann Gy, Lux RL, Scott M: Sample size and dimensionality in multivariate classification: implications for body surface potential mapping. Comput Biomed Res 24:170, 1991