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Geometrical factors affecting the interindividual variability of the ECG and the VCG
Journal of Electrocardiology Vol. 33 Supplement 2000
G e o m e t r i c a l Factors A f f e c t i n g t h e I n t e r i n d i v i d u a l Variability of t h e ECG a n d t h e VCG
A. v a n O o s t e r o m ,
P h D , R. H o e k e m a ,
P h D , a n d G. J. H . U i j e n , P h D
Abstract: Various measures for quantifying the interindividual variability of the electrocardiogram and the vectorcardiogram in healthy subjects are presented. An analysis of factors that may cause this variability is performed, in particular of the geometrical factors of body size, heart size, heart position, and orientation. The results indicate that the variations ~n t ee magnitude of the electrocardiogram as observed through leads placed on the anterior thorax are dominated by the solid angle at which the outline of ventricular mass is seen from points on the thorax. Heart size and body size as such play only a secondary role. The limited spatial sampling of the anterior thorax directly overlaying the heart causes the m e a n values of all measures of amplitudes in w o m e n to be lower than in men. The vectorcardiogram magnitude was found to be m u c h less dependent on overall geometry and heart position, and, hence, also to be less dependent on gender. Key words: ECG, VCG, scaling, constitutional factors.
of the depolarization and repolarization, a m a j o r source of variability can be attributed to differences in the geometrical relationships involved in heart position and orientation, torso shape as well as to lead p l a c e m e n t relative to h e a r t position (2-4). Moreover, it is a s s u m e d that the electrophysiological factors and the geometrical factors can be treated as contributing i n d e p e n d e n t l y to the variability of the ECG. A first step has b e e n to define a single m e a s u r e for quantifying the interindividual variability as observed in multilead ECG recordings. The m e a s u r e adopted, the relative variability, RelVar, was f o u n d to h a v e a value of 0.52. In a m o d e l study, b a s e d the individual g e o m e try of 25 h e a l t h y subjects, it was s h o w n t h a t a m a j o r p a r t of this variability, as high as 50%, can i n d e e d be a t t r i b u t e d to g e o m e t r i c a l factors. This suggests t h a t the physiologically based c o m p o -
The interindividual variability of electrocardiog r a m (ECG) (1) presents a limitation on the diagnostic accuracy of the ECG. Pathology w o u l d stand out m u c h m o r e clearly if interindividual variability in normals were lower. At present, we are engaged in the search for m e t h o d s to reduce this variability. The underlying hypothesis is that, n e x t to interindividual differences in the electrophysiology of the heart, timing
From the Department of Medical Physics and Biophysics, University of Nijmegen, Nzjmegen, The Netherlands'; Department of Clinical Neurophysiology, University Medical Center, Utrecht; and Department qf Experimenlal Cardiology, University Medical Centre~, Nijmegen, The Netherlands. Reprint requests: A. van Oosterom, PhD, Laboratory MedicaI Physics, Geert Grooteplein 21, 6525EZ, Nijmegen, The Netherlands; e-mail: [email protected] Copyright 9 2000 by Churchill Livingstone | 0022-0736/00/330S-0037535.00/0 doi: l 0.1054/jeic.2000.20356
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Journal of Electrocardiology Vol, 33 Supplement 2000
n e n t of the interindividual variability in normals is about 0.38 (4). Two attempts h a v e b e e n m a d e so far to reduce the geometrical factor in the variability. The first attempt, by m e r e l y adapting individual lead placem e n t to individual g e o m e t r y , failed. The second attempt, in w h i c h the orientation of the heart was also involved, has b e e n highly successful, but, u n fortunately, so far only in an application to simulated ECG data. The quality of the involved inverse p r o c e d u r e is at p r e s e n t insufficient (4). This article presents some further details on the variability observed in the group of 25 h e a l t h y subjects, of the ECG as well as of various g e o m e t rical factors, and discusses some of the findings in the light of general aspects of the effect of scaling. Moreover, the analysis is extended by including the vectorcardiogram (VCG), as welI as by discussing the factors gender a n d age. The analysis of the time signals is restricted to the QRS interval.
100 ms interval a r o u n d peak QRS w e r e used in the s u b s e q u e n t analysis. During this part of the heart cycle the heart is in end-diastole, in w h i c h state the MRI were also taken. G e o m e t r y changes of the heart are m i n i m a l during this period. The complete set of potentials recorded in any individual is represented by a matrix dO, of dimension 64 • IO0, the columns of w h i c h represent the instantaneous body surface potentials at all 100 s u b s e q u e n t time instances, w h e r e a s the rows represent the traditional time tracings of the 64 leads. We call this matrix a body surface potential movie, the sequence of columns representing the subseq u e n t frames of the movie. The distance b e t w e e n the location on the thorax w h e r e standard lead V 2 was placed, a i m e d to be the fourth intercostal space, and the supra-sternal n o t c h was d o c u m e n t e d .
Materials and Methods
The MRI data consisted of 32 axial, T l - w e i g h t e d , n o n - E C G - t r i g g e r e d and n o n - b r e a t h - h o l d spinecho images of the body, as well as 10 to 14 shorl axis T l - w e i g h t e d turbo-flash images of the heart, taken using ECG triggering at end-diastole and breath-hold. The contours of the torso, lungs, ven-tricular mass, as well as of the ventricular cavities, w e r e identified in the MRIs. The orientation of the heart was d o c u m e n t e d by identifying 4 l a n d m a r k s (6). These are LI: the top ol a h e m i s p h e r e fitted on top of the base of the heart; L2: the apex, L3: the position w h e r e the left descendent coronary artery (LAD) crosses the base of the heart; and L4: the position w h e r e the right circumflex (RCX) coronary artery crosses the base of the heart. L a n d m a r k s L1 and L2 w e r e used to specify the long axis direction of the heart. L a n d m a r k s L3 and L4 can be accurately identified in MR images and the vector pointing from L4 to L3 was t a k e n to represent the heart's short axis. The orientation of this axis signals a n y rotational variability around the long axis. The actual long-axis direction used was that of the vector pointing f r o m the middle of L3 and L4 towards L2. The position of the supra-sternal notch could be identified easily in the MR images. This landmark, together with the m e a s u r e d distances b e t w e e n this reference point and the location of lead V 2 during the potential recordings, was used to establish the location of the electrodes on the triangulated torso surface.
Twenty-five h e a l t h y patients were studied by using b o d y surface m a p p i n g (BSM) and magnetic resonance imaging (MRI) with a Siemens 1.5 Tesla M a g n e t o m SP (Siemens, Erlangen, Germany). The patients (15 m e n a n d l0 w o m e n ) ranged in age b e t w e e n 24 and 65. All patients u n d e r w e n t a brief e x a m i n a t i o n b e f o r e h a n d , including the m e a s u r e m e n t of blood pressure, analysis of the standard ECG, echocardiography, and anamnesis, on the basis of which no sign of cardiac disorder was found.
Recorded Potentials The BSMs w e r e recorded with the Arnsterdam lead system, having 64 electrodes (5). The sampling frequency was 1,000 Hz. Baseline correction was p e r f o r m e d by shifting each ECG such that its value during the PQ interval was zero, after which the data w e r e shifted to a z e r o - m e a n potential reference. The BSM signals of all subjects were time-aligned by first taking the BSM signals of one of the subject as a reference set. F r o m this set, the time interval of 100 ms centered a r o u n d p e a k QRS in standard lead V x was selected. Subsequently, for each of the other subjects, the entire data set was shifted in time until a m i n i m a l difference with the BSM signals of the reference set was achieved. The BSM signals in the
Recorded Geometry
Geometry and Scaling in EGG: and VCG
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T a b l e t, Basic Statistics; Means +_ SD Factor Ge~ader Weight Length vol(thorax) S(thorax) vol(llung) vol(rlung) vol(vemrmass) vol(LVC) vol(RVC) d~st(ebh) QRS_dur spa.t DIP,~• VCGm~,• .j Vma • Vma,, VI,~xp RMS SA(thorax) SA(el) Age
Labe[
Unit
0 1 2 3 4 5 6 7 8 9 l0 11 t2 13 14 15 16 17 18 19 20
kg cm ] m2 1 l ] mL mL cm ms mA.cm mV mV z:qV mV mV 2w 2rr Year
All
Women
Men
25 • I0 + 8.4 + 4.9 • 0.062 + 0.25 • 0.33 + 42 • 28 + 30 • 0.60 + 8.2 + 0.48 + 1.1 + 0.43 + 0.56 • 0.63 + 0.077 • 0.082 e 0.076 _+ 13
~O. 68.6 170 I9,3 0.420 0.995 1.32 19I 130 14?, 2.27 71.4 1.58 1.70 1.22 1.22 1.62 0.261 0.419 0.382 33.7
t5 80.1 182 23.6 0.469 1.27 1.71 248 138 162 2.31 79.7 1,95 2.11 1.65 1.75 2.36 0.356 0.420 0.400 40.3
75.5 I77 2] .9 0.459 1.16 1.55 225 135 155 2.29 76.4 1.80 1.95 1.48 1.53 2.06 0.312 0.419 0.392 37.7
Men/Women
t-value
1.16 1.07 1.22 1.12 1.28 1.30 1.30 1.06 1.13 1.02 1.12 1.24 1.25 1.40 1.43 1.46 1.32 1.00 1.05 1.19
3.2 4,9 2.3 2.0 3.0 3.5 4.5 0.7 1.5 0.2 2.9 2.0 0.9 2.8 (-)2.5 3.9 3.2 0.0 0.6 1.2
Constitutional Factors
(x) In addition to the detailed geometry as specified in the previous subsection, the factors: gender, weight, length and age of the subjects were documented. These factors are denoted as F0, F1, F2, and F20, respectively. Label n u m b e r s correspond to their ordering as used in Table 1.
M a t e r i a l s and M e t h o d s Measures for the Interindividual Variability There is no c o m m o n l y used measure to express the interindividuaI variability of BSMs. Measures used for comparing two individuals, such as correlation coefficient and relative difference cannot be used for this purpose in a straightforward m a n n e r . We use a variability measure derived from the variance (standard deviation squared) in the ECG signals of several subjects. Because any scaling effects should not come to expression in the measure, the measure is normalized by the overall p o w e r of the observed data. It is c o m p u t e d by first determining the variance of the ECG signal over all subjects for each lead and each time instant. These variances are subsequently added over all leads and all time instances. The resulting variance is divided by the p o w e r in all BSMs pooled together, after w h i c h the square root is taken. Accordingly,
telVar
= X/
I1 ,11
'
w h e r e RelVar is the interindividuaI relative variability, @ is tee m e a n value over alt subjects, i is the index to any of the patients (25) studied, and I1" IIF denotes the square root of the sum of squares of all matrix elements (the Frobenius norm of the matrix). Note that the equation expresses the variability of an entire signal matrix. In this article it is applied to recorded 64-1ead ECG data as well as to three-signal data derived from these potentials (VCG or equivalent dipole).
Derived VCG The lead system used includes the locations ot the Frank lead system (7). The ECG data recorded at these positions were used to derive the VCG of the individual subjects studied by means of the transfer matrix (Eqn. 2 of Frank's paper 171). The VCGs of the subjects i are denoted by VCG~, matrixes of dimension 3 • 100.
Triangulation of the Recorded Geometry Based on the measured MRI data triangulated representations were made of all surfaces mentioned in Sect. II-B. These surfaces are generally used :for computing the v o l u m e conduction aspects of the ECG. In this article they are included to assess
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their effect on the overall m a g n i t u d e of the potentials. By using this triangulation, surface areas a n d / o r volumes of the various c o m p a r t m e n t s were computed. In addition, the solid angles of the contours of the ventricular mass as seen f r o m points on the thorax w e r e c o m p u t e d . The following factors related to g e o m e t r y w e r e derived: F3, v o l u m e of the thorax; F4, surface area of the thorax; F5, v o l u m e of the left lung; F6, v o l u m e of the right lung; F7, v o l u m e of the ventricular mass; F8, v o l u m e of the left ventricular cavity (full diastole); F9, v o l u m e of the right ventricular cavity; F18, the m a x i m u m value of the solid angle of the contour of ventricular mass as seen by a n y point on the thorax; FI9, m a x i m u m value of the solid angle of the c o n t o u r of ventricular mass as seen f r o m a n y of the electrode locations; F 10, smallest distance b e t w e e n a n y point on the thorax and a n y point on the ventricular surface (closest distance b e t w e e n heart and thorax).
Equivalent Dipole For all subjects, the individual position of a stationary equivalent current dipole was c o m p u t e d f r o m the observed b o d y surface potentials and the m e a s u r e d g e o m e t r y of the thorax, as well as the time course of the strength of the dipole c o m p o nents t h r o u g h o u t the QRS interval. The m e t h o d used is the least squares procedure, described in reference (8), assuming a h o m o g e n e o u s torso. The latter a s s u m p t i o n allows a direct comparison of the matrix of resulting dipole strengths, d e n o t e d by DIP~, with the corresponding Frank data VCG~. The assumed overall electric conductivity of the thorax was 0.2 S.m -~.
Measures of Magnitude In the s u b s e q u e n t analysis the following m e a sures of overall m a g n i t u d e are used, extracted f r o m the recorded potentials: F14, Vmax. the highest positive reading a n y w h e r e in the movie; F15, Vm~• the highest negative reading a n y w h e r e in the movie; F16, v- - ]pap 9 the highest p e a k to p e a k value in ~]a x a n y of the time tracings; FI7, RMS: the root m e a n square value c o m p u t e d over all time instants and all leads; FI2, the highest value of the spatial magnitude of the equivalent dipole DIP; F13, the highest value of the spatial m a g n i t u d e of the VCG.
time interval b e t w e e n the m o m e n t s at w h i c h this curve passed the 5% threshold relative to its max.i m u m value w e r e taken as the QRS interval, labeled as F I I .
Statistical Methods The limited n u m b e r of subjects included in this study d e m a n d s a severe restriction on the n u m b e r of factors to be considered s i m u l t a n e o u s l y in the subsequent analysis. The tests used include: the t-value from the Student's t-test (two group [gen-. der] comparisons) and the linear correlation coefficient p b e t w e e n a n y pair of the factors studied. For N = 25, tcr for a two-sided test at the 95% confidence level is 2.06. The directional factors are specified t h r o u g h the a z i m u t h and the elevation of the vectors involved. The a z i m u t h was t a k e n to be the angle b e t w e e n the projection of the vector on the horizontal plane, and an axis pointing to the left part of the thorax, its sign was defined as positive for vectors pointing towards the back. The elevation was t a k e n as the angle b e t w e e n the vector a n d the horizontal plane, its sign defined as positive for vectors pointing towards the head. The statistics of these factors w e r e specified by c o m p u t i n g the preferential direction and the spatial precision (9). For the latter statistic, a value of 1 corresponds to a perfect clustering at the value of the preferential direction, a value of 0 corresponds to the directions f r o m the origin toward points scattered all over a sphere. For a spatial precision value close to 1 its inverse cosine is proportional to the geometric m e a n of the stano dard deviation of the a z i m u t h and the elevation values, in Table 4, this angle, a m e a s u r e for the dispersion a r o u n d the preferential direction, is s h o w n n e x t to the spatial precision.
Results Overall Statistics
9
QRS Duration The QRS duration as derived from the time course of the spatial m a g n i t u d e of the vector. The
An overview of the basic statistics of the factors considered is presented in Table 1. Separate entries are s h o w n for the entire group (N = 25), for the w o m e n (N - 10) and for the m e n (N - 15). Standard deviations for the gender-specific data are not shown. Instead, the ratios of the gender-specific m e a n s are shown, as well as the t-value for group comparisons based on gender. The (limited) precision with which the results are specified is t u n e d to
Geometry and Scaling in ECG and VCG
the limited accuracy of the values, which results from the small n u m b e r of subjects involved.
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223
T a b l e 3. D i s t a n c e s f r o m t h e L e v e l o f t h e H e a r t C e n t e r
DI D2
RelVar Values
M e a n (cm)
R a n g e (cm)
3.89 1.61
0-7.25 -0.75-5.5
D~: to that o{ V2; D2: to teat of the equivalent dipole
The expression for the relative variability (Equation 1), has been applied to the 64-lead ECG data as welt as to the 3-signal (dipole) data VCG and DIP. The results are listed in Table 2. Separate entries are s h o w n for the entire group (N = 25), for the w o m e n (N - 10) and for the m e n (N = 15). In addition, results are listed that were f o u n d by first normalizing the individual movies. Note that in this case the d e n o m i n a t o r of equation 1 loses its significance.
the wide range that was found. The a c c o m p a n y i n g RMS-based relative residual differences between recorded and dipole based potentials s h o w e d a m e a n value of 0.248 and a range of 0 . 1 4 9 - 0 . 4 2 8 .
Analysis Lead Placement The projection of the heart onto the frontal plane was marked. The plane transverse (horizontal) plane r u n n i n g half w a y b e t w e e n the c o n t o u r was taken to represent the level of the anatomical center of the heart. The distances D~ b e t w e e n this level and the level at which lead V2 had been placed were d o c u m e n t e d . Their statistics are included in Table 3. Note that the range of D t is even larger than that of D e .
Directional Data The basic statistics of directional data are presented in Table 4. In addition, the statistics of 6 are shown, ~bbeing the angle between the the long axis and the vector of maximal spatial VCG magnitude.
Over the years, the interindividual variability of the ECG and the VCG has been studied by several groups (10-14). These studies were based on observations made on large n u m b e r s of subjects. Impressive lists of (ranges of) normal values on just about any parameter used in the world of ECG and VCG can be found in the part III of the m o m e n t o u s series "Comprehensive Electrocardiology" (15). In fact so m a n y details are included that one m a y easily lose sight of the w o o d for the trees. This paper, which is based on just 25 subjects for w h i c h electric data as well as a u n i q u e set of matching geometry data was available, aims at presenting an overall view on some of the basic aspects of ECG variability in normals. The analysis builds on the major previous papers on this topic, the present material, as well as on some experience gathered over the years in our group on the topics of forward and inverse modeling of the ECG.
Equivalent Dipole The positions established for tEe stationary equivalent dipoles were mainly in the septal region. As s h o w n in Table 3, the positions were below the center of the heart defined in Lead Placement. Note
Table
2. R e l V a r V a l u e s ( E q u a t i o n
l)
All
Females
Males
64 Leads 64 Leads (norm)
0.52 0.48
0.44 0.42
0.5 I 0.48
VCG VCG (norm)
0.46 0.4I
0.36 0.32
0.46 0.41
DIP DIP (norm)
0.47 0.41
0.45 0.34
0.45 0.42
T a b l e 4. S t a t i s t i c s o f D i r e c t i o n a l D a t a : P r e f e r e n t i a l Direction and Precision Vector Long-axis azhn e|ev prec VCGma~ azim elev prec
Unit
All
Women
Men
degr degr (degr)
52,8 -34.5 0.986 (9)
-55,4 358 0.992 (7)
51.1 -33.7 0.983 (10)
degr degr (degr)
14.2 -33.7 0.918 (23)
10.7 37.0 0.932 (21)
16.4 31.6 0.910 (24)
degr degr (degr) degr (degr)
43.9 54.7 0.973 (13) 54.0 0.973 (13)
50.2 56.5 0.980 (11) 52.7 0,971 (13)
39.9 53.5 0.970 (14) 54.9 0.974 (13)
short-axis
azim elev prec ~ prec
--
azim, azimuth; prec, predsion; elev, elevation.; degr, degrees.
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Journal of Electrocardiology Vol. 33 Supplement 2000
Relvar The RelVar values listed in Table 2 indicate that the overall variability of the normal ECG and VCG data is quite considerable. Clear gender based differences were found. This fact has been noticed before in the literature (eg, [14]). As stated in the introduction, a major part of this variability arises from geometrical factors, and we are searching to reduce this contribution. As is also clear from Table 2, for the VCG RelVar has a smaller value than for the ECG. This is a result of the fact that at most 3 independent signals are present in the VCG, whereas the ECG m a y contain more i n d e p e n d e n t c o m p o n e n t s (at most 8 in the standard-12 lead ECG; about 11 in the 64-lead BSPM data; see [16]), each contributing to the overall variability.
Magnitude Table 2 indicates that a part of the variability disappears alter normalizing the individual movies (matrixes). This t h e n brings us to the major topic of lhe present paper: what determines the overall size of the ECG and of the VCG and h o w does this relate to body size, gender, and age? In Measures of Magnitude, the measures of magnitude used are described. In Table 1 these are listed as "factors" 12-17. As can be seen, even these crude indicators of m a g n i t u d e exhibit a large variation.
points are inversely proportional to the square o[ the distance R between source and field points~ These potentials are also proportional to the surface area S of the depolarized tissue. More precisely, it is the solid angle i'l subtended by the wave front at the observation point that is a main d e t e r m i n a n t for the electric potential (17). By scaling a subject by a linear factor L, a procedure practiced with great enthusiasm in the d o m a i n of allometry (see re! [18]), we see that both S and R 2 are proportional to L 2 and as a consequence i~ is invariant to scaling. From the m o u s e and the elephant we, hence, learn that the double layer strength of ventricular depolarization must be invariant to scaling.
Solving the Riddle The remaining part of this article is aimed at explaining the observed gender-related differences in the magnitude measures, and, in passing, to relate several of the observations to the general problem of magnitude and scaling. We will use Figure 1 to see if any of the proposed ideas might be contradicted by the observations made in this study.
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G e n d e r . Five of these 6 measures of magnitude show clear gender differences, the m a x i m u m spatial m a g n i t u d e of the VCG being the odd one out. Is this significant, w h a t causes these differences anyway2 Is the female cardiac electric generalor intrinsically less "powerful" than the male version?
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The riddle posed by the mouse and the elephant led us to consider the w e l l - k n o w n equivalent generator of the cardiac generator during ventricular depolarization: the double layer. This generator seems to have all the properties for the present discussion. The potentials that it generates at distant
x
+
Size. A simple answer to the question posed above is an affirmative: nren generally are taller, have larger hearts and hence, have more a more powerful cardiac generator. However, both mice and elephants have ECG values on their body surface of about 1 mV of magnitude, yet their size is "somewhat" different.
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Fig. 1. Matrix of linear correlation coefficients p observed between factors. Row and column indexes correspond to the labels used in Table 1; The symbols used (% + and - ) denote p v a I u e s > 0.507, > 0.337 and < -0.337, respectively. Blank entries denote -0.337 < p < -.337. The values 0.337 and 0.507 are the critical values for testing p - 0 at confidence levels 5% and 0.5%, respectively. The partitioning shown is used in the Analysis.
Geometry and Scaling in ECG and VCG
The format in which these correlations are presented is s o m e w h a t similar to the one s h o w n in reference (19). The partitioning s h o w n for the rows follows the nature of the factors: F1-F10 all relate to size, F1 l relates to time, F I 2 - F 1 7 relate to electric data, and F20 is age. The partitioning of the cohtmns follows the d e p e n d e n c y of the factors on scaling. Factors F1-F10 as well as F11 and F12 depend, as will be argued, on scaling. Factors F13-F19 are independent of scaling. T h e VCG. For the ideal VCG lead system, any difference in heart position w o u l d not have any effect on the observed vector. By assuming the female cardiac generator to be identical to the male variant, the maximal spatial magnitude of the VCGvector should be expected to be i n d e p e n d e n t of gender. Indeed, as s h o w n in Table 1 the m a g n i t u d e of the VCG-vector was found to be i n d e p e n d e n t of gender. In some of the literature, based on a greater n u m b e r of subjects, m i n o r magnitude differences are suggested. These small differences can be easily explained of the basis that, in w o m e n , the contribution of potentials as seen by left precordial electrode C of the Frank system, contributing to the vector c o m p o n e n t s in the horizontal plane, are smaller in w o m e n , related to anatomical differences that yield greater distances b e t w e e n the heart and electrodes. Perhaps less well k n o w n is the fact that the VCG is also i n d e p e n d e n t on scaling. The basis for this statement is directly linked to the observation on the m o u s e and the elephant. The Frank leads perform a fixed linear weighting of potentials on the body surface. With the potentials on the body surface being invariant to scaling, so is the o u t c o m e of the weighting procedure. In spite of this some of the correlation coefficients s h o w n on r o w 13 s h o w e d values for which P < 5% for some of the size-iinked factors. We attribute this at this stage, awaiting further analysis, to imperfections in the lead placement (see Table 3). T h e E q u i v a l e n t D i p o l e . The results on the equivalent dipole seem to contradict the above theory. However, the contrary holds true and it is for this reason that the equivalent dipole data are included in this paper. The equivalent dipole is easily confused with Frank's VCG. Its nature is that of a true current dipole, having a dimension of current • distance, expressed in units, say, mA.cm. After the Gabor-Nelson equations (20) the equivalent current dipole I) can be c o m p u t e d from the full body surface potential distribution as
(2)
9 van Oosterom et al,
225
fl=~f ad~,
with o~the conductivity of the m e d i u m (assumed to be h o m o g e n e o u s ) , (I~ the potential distribution on the thorax, and dS the (directed} surface elements of the thorax. If we n o w apply the idea of the invariance of the potential to scaling we see that the magnitude of the equivalent dipole is proportional to the surface area of the thorax. As seen from Table 1 the m e a n value the thorax surface was about 0.46 m x. After scaling the individual ~olp; ~ ' ~pat .... values by the corresponding S(thorax) values the result no longer showed a n y d e p e n d e n c y on gender or scaling. Summarizing, the proportionality factor bet w e e n VCG and the true equivalent dipole I) depends on the surface area involved and on the assumed electric conductivity. The strength of the equivalent dipole scales as L 2.
M a x i m u m N e g a t i v i t y . V..... (El 5), the highest negative reading a n y w h e r e in the movie can be expected to be in the area of Vx. The d o m i n a n t single factor in this situation was found to be the solid angle subtended by the heart as seen from any of the electrodes: F19, for w h i c h p = - 0 . 6 5 . Inclusion of neither of the other factors did not significantly increase p. M a x i m u m P o s i t i v i t y . V,~• (FI4), the highest positive reading a n y w h e r e in the movie can be expected to be in the area of V4. The d o m i n a n t single factor in this situation was found to be heart size (F6), with p - 0.58. This corresponds to the fact that any d e p e n d e n c y on the solid angle subtended by the heart as seen from any of the electrodes (F19), for which p - 0.41, is dominated by genderrelated differences at this part of the thorax. After harmonizing the potential readings for gender, the solid angle based factor again clearly dominated (p - 0.64). M a x i m u m P e a k - t o - P e a k Value. F16, the highest peak to peak value in any of the time tracings, showed a d e p e n d e n c y similar to that reported on for El4. There was, as also s h o w n in Table l, a clear d e p e n d e n c y on gender. However, after h a r m o n i z i n g the m a g n i t u d e values such that equal means for both sexes resulted the m a x i m u m solid angles dominated and the results were indep e n d e n t of heart size per se. RMS. The b e h a v i o u r of the root m e a n square value c o m p u t e d over all time instants and all leads (F12) showed a similar b e h a v i o u r as F16.
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Gender All of the gender-based differences in the ECG m e a s u r e s of m a g n i t u d e can be explained by genderrelated geometric differences. For the RMS values, a reduced value over a part of the t h o r a x (left precordium) having large potential values, cannot b u t lead to smaller RMS values in w o m e n . Moreover, female hearts being smaller, the fixed vertical spacing of the electrodes (3.8 cm), again will result in smaIler values in females because of a relatively cruder spatial sampling. The latter also affects the m i n i m u m negativity observed (F15). For the m a x i m u m potential (V14) it is the greater distance to the heart that counts, showing indeed a higher gender-based ratio in Table 1.
Directional Results The directional data s h o w n in Table 4 are in a g r e e m e n t with literature data [I] in so far these are avaiiable. A large m e a n value of q~ was observed, m a i n l y involving the azimuth. The individual shifts were of a n o n - s y s t e m a t i c nature. Slight gender-based differences were Observed, consistent with ideas f o u n d in the literature. Interestingly, the slightly m o r e anterior direction of the long-axis found in females together w i t h the gender i n d e p e n d e n t value of the m e a n 4) shift is consistent with VCGm~x pointing m o r e to the left in w o m e n . This leads to smaller potentials o n the frontal part of the thorax. The g e n d e r - b a s e d differences in the short-axes direction w e r e e v e n larger, but again, significance remains to be shown.
Duration QRS Slight but significant gender-based differences in QRS duration were observed (see row 11 of Fig. 1) (/9 = 0.51). However, the largest correlation (p 0.55) was f o u n d b e t w e e n QRS duration and length. The latter seems to be the direct factor involved (Iinked to h e a r t size), gender being an indirect factor. This is in a g r e e m e n t with the general theory of scaling which states that any time interval r scales like r -- L.
Age The n u m b e r of cases included in this study is too small to draw a n y firm conclusions. Yet all of the entries s h o w n in the b o t t o m row of Figure 1 are
consistent with the fact that, with advancing age, at least in the range included here, people tend to b e c o m e m o r e obese. The distance b e t w e e n heart and electrodes increases, the solid angles decrease, and as a result the potentials decrease. Moreover, a slight angular shift of the long axis (azimuth only) was observed. All these factors are quite sufficient to account for the decrease of the m a g n i t u d e s with age that have previously b e e n reported on in the literature.
Body Indexes Several of the b o d y indexes f o u n d for expressing individual obesity were tried in the present study. None of these w e r e found to reduce the residual variance a n y further b e y o n d that already achieved by incorporating the solid angle only. W h e n studying the b e h a v i o u r of these different indexes it was f o u n d that over the range of weights of 50 kg to 100 kg and for lengths f r o m 150 to 200 cm all of these indexes are in fact equivalent, only differing by a factor (the slope of the curve). If we take for example Rohrer's index m.1 3, or the p o n d e r a l index m~/3.1-1, w h e n used consistently, the results for the present application are identical. The use of such indexes should be restricted to those that are invariant to scaling. Because of this, the use of the Quetelet index m.1-2 should be avoided on theoretical grounds. A l t h o u g h in practice, it does not m a k e m u c h difference.
The Other Factors The analysis of the other factors listed in Table I did not result in a n y significant reduction of the variance of the m e a s u r e s of m a g n i t u d e .
Conclusion This p a p e r has s h o w e d that a c o h e r e n t view on the cause of a p p a r e n t gender and size-related differences in overall m a g n i t u d e of cardiographic signals as observed on the thorax can be derived from considerations of g e o m e t r y only. The implications for VCG are: the spatial magnitudes are scale and gender i n d e p e n d e n t . The small g e n d e r - b a s e d differences found are caused by the m a x i m a l spatial vector being directed slightly m o r e in parallel to the frontal part of the thorax in females, as well as to the fact of Frank's lead C being m o r e r e m o t e f r o m the heart in w o m e n . The ideal
Geometry and Scaling in ECG and VCG
v e c t o r l e a d s y s t e m w o u l d also be i n d e p e n d e n t of the actual heart position. F o r t h e ECG t h e implications are t h a t overall differences in size (scaling) are u n i m p o r t a n t : p o t e n t i a l is i n v a r i a n t to scaIing. QRS d u r a t i o n scales l i n e a r l y w i t h L, w i t h h e a r t a n d b o d y mass b o t h scaling as L 3. Based o n t h e solid angle a p p r o a c h , g e n d e r - r e l a t e d differences s h o u l d c o m e to e x p r e s s i o n m a i n l y in the a n t e rior leads, a n d m u c h less in t h e e x t r e m i t y leads. This can in fact be clearly o b s e r v e d in t h e Tables A 1 9 - A 2 0 s h o w n in r e f e r e n c e (1). The large d i f f e r e n c e s b e t w e e n t h e o b j e c t i v e l e a d p l a c e m e n t a n d t h e a c t u a l p l a c e m e n t w i t h r e s p e c t to t h e h e a r t (see Table 3), s u g g e s t t h a t a m e t h o d n e e d s to b e d e v e l o p e d for p l a c i n g t h e a n t e r i o r e l e c t r o d e s in m a n n e r t h a t is t u n e d to t h e a c t u a l h e a r t p o s i t i o n r a t h e r t h a n to s o m e i n t e r c o s t a l space.
References 1. Macfarlane PW: Normal limits, in Macfarlane PW,
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Lawrie TTV, (eds): Comprehensive Electrocardiology (vol 3). Oxford, Pergamon Press, 1989, p 1441 Hoekema R, Uijen G, van Oosterom A: Normalization of the electrocardiogram by standardization of Heart Position and Orientation, in Murray, Arzbeacher R, (eds): Computers in Cardiology. Piscataway, N J, IEEE Computer Society Press, 1996, p 717 Hoekema R, Uijen G, van Erning, et al: Interindividual variability of mulilead ECG recording. J Electrocardiol 32:137, 1999 Hoekema R, Uijen G, van Oosterom A: Geometrical aspects of inter-individual variability mulilead ECG recordings, in Murray A, Swerin S (eds): Computers in Cardiology. Piscataway, N J, IEEE Computer Society Press, 2000, p 499 Sippens Groenwegen A, Spekhorst H, Hauer RNW, et ah A radiotransparent carbon electrode array [or body surface mapping during cardiac catherization. Proceedings frorn the 9th Annual IEEE-EMBS Conference, Boston, MA, November 1987, p 178 Hoekema R, Uijen G, van Oosterom: An elasticized net modeling the pericardium. Proceedings from the 19th Annual IEEE-EMBS Conference, 1997, p 113
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7. Frank E: An accurate, clinically practical syslem [or spatial vectorcardiography. Circulation 13:737, 1956 8. Oostendorp TF, van Oosterom A: Source parameter estimation in inhomeogenoues vohune conductors of arbitrary shape. IEEE Trans Biomed Eng 36:382, 1989 9. Liebman J: Linear and directional statistics, in Macfarlane PW, Lawrie TTV, (eds): Comprehensive Electrocardiology. Oxford, Pergamon Press, 1989, p 1522 10. Simonson E: Differentiation between Normal and Abnormal in Electrocardiography, St Louis, MO, Mosby, 1961 11. Draper H, Peffer C, Stallmann F, et al: The corrected orthogonai electrocardiogram and vectorcardiogram in 510 normal m e n (Frank lead system). Circulation 30:853, 1964 I2. Pipberger H, Goldmann M, Littman D, et ah Effect of conductivity interfaces in clectrocardiography. Circu~ Iation 35:536, 1967 13. Nemati M, Doyle J, McCaughan D, et ah The orthogona] electrocardiogram in normal women. Implications of sex differences in diagnostic electrocardiography. Am Heart J 95:12, 1978 14. Green LS, Lux RL, Haws CW, et ah Effects of age, sex and body habitus on qrs and st-t potential maps of 1100 normal subjects. Circulation 85:244, 1985 I5. Macfarlane PW, Lawrie TTV (eds): Comprehensive Electrocardiology. Oxford, Pergamon Press, 1989 16. Hoekema R, Uijen G, van Oosterom A: The n u m b e r if independent signals in body surface maps. Meth Inform Med 38:119, 1999 17. van Oosterom A: Cell models-Macroscopic source descriptions, Macfarlane PW, Lawrie TTV, (eds): Comprehensive Electrocardiology (vol 1). Oxford, Pergamon Press, 1989, p 155 18. Schmidt-Nielsen K: Why is Animal Size so Important? Cambridge University Press, 1984 19. Matthes T, Gottsch G, Zywietz C: Interactive analysis of statistical ECG diagnosis on an intelligent electrocardiograph--An expert system approach, Willems J, van Bemmel J, Zywietz C, (eds): Computer ECG Analysis: Toward Standardization. Amsterdanq, Elsevier Science, I986, p 215 20. Gabor D, Nelson CV: The determination of resultant dipole of the heart from measurements on the body surface. J Appl Phys 25:413, 1954
G e o m e t r i c a l Factors A f f e c t i n g t h e I n t e r i n d i v i d u a l Variability of t h e ECG a n d t h e VCG
A. v a n O o s t e r o m ,
P h D , R. H o e k e m a ,
P h D , a n d G. J. H . U i j e n , P h D
Abstract: Various measures for quantifying the interindividual variability of the electrocardiogram and the vectorcardiogram in healthy subjects are presented. An analysis of factors that may cause this variability is performed, in particular of the geometrical factors of body size, heart size, heart position, and orientation. The results indicate that the variations ~n t ee magnitude of the electrocardiogram as observed through leads placed on the anterior thorax are dominated by the solid angle at which the outline of ventricular mass is seen from points on the thorax. Heart size and body size as such play only a secondary role. The limited spatial sampling of the anterior thorax directly overlaying the heart causes the m e a n values of all measures of amplitudes in w o m e n to be lower than in men. The vectorcardiogram magnitude was found to be m u c h less dependent on overall geometry and heart position, and, hence, also to be less dependent on gender. Key words: ECG, VCG, scaling, constitutional factors.
of the depolarization and repolarization, a m a j o r source of variability can be attributed to differences in the geometrical relationships involved in heart position and orientation, torso shape as well as to lead p l a c e m e n t relative to h e a r t position (2-4). Moreover, it is a s s u m e d that the electrophysiological factors and the geometrical factors can be treated as contributing i n d e p e n d e n t l y to the variability of the ECG. A first step has b e e n to define a single m e a s u r e for quantifying the interindividual variability as observed in multilead ECG recordings. The m e a s u r e adopted, the relative variability, RelVar, was f o u n d to h a v e a value of 0.52. In a m o d e l study, b a s e d the individual g e o m e try of 25 h e a l t h y subjects, it was s h o w n t h a t a m a j o r p a r t of this variability, as high as 50%, can i n d e e d be a t t r i b u t e d to g e o m e t r i c a l factors. This suggests t h a t the physiologically based c o m p o -
The interindividual variability of electrocardiog r a m (ECG) (1) presents a limitation on the diagnostic accuracy of the ECG. Pathology w o u l d stand out m u c h m o r e clearly if interindividual variability in normals were lower. At present, we are engaged in the search for m e t h o d s to reduce this variability. The underlying hypothesis is that, n e x t to interindividual differences in the electrophysiology of the heart, timing
From the Department of Medical Physics and Biophysics, University of Nijmegen, Nzjmegen, The Netherlands'; Department of Clinical Neurophysiology, University Medical Center, Utrecht; and Department qf Experimenlal Cardiology, University Medical Centre~, Nijmegen, The Netherlands. Reprint requests: A. van Oosterom, PhD, Laboratory MedicaI Physics, Geert Grooteplein 21, 6525EZ, Nijmegen, The Netherlands; e-mail: [email protected] Copyright 9 2000 by Churchill Livingstone | 0022-0736/00/330S-0037535.00/0 doi: l 0.1054/jeic.2000.20356
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n e n t of the interindividual variability in normals is about 0.38 (4). Two attempts h a v e b e e n m a d e so far to reduce the geometrical factor in the variability. The first attempt, by m e r e l y adapting individual lead placem e n t to individual g e o m e t r y , failed. The second attempt, in w h i c h the orientation of the heart was also involved, has b e e n highly successful, but, u n fortunately, so far only in an application to simulated ECG data. The quality of the involved inverse p r o c e d u r e is at p r e s e n t insufficient (4). This article presents some further details on the variability observed in the group of 25 h e a l t h y subjects, of the ECG as well as of various g e o m e t rical factors, and discusses some of the findings in the light of general aspects of the effect of scaling. Moreover, the analysis is extended by including the vectorcardiogram (VCG), as welI as by discussing the factors gender a n d age. The analysis of the time signals is restricted to the QRS interval.
100 ms interval a r o u n d peak QRS w e r e used in the s u b s e q u e n t analysis. During this part of the heart cycle the heart is in end-diastole, in w h i c h state the MRI were also taken. G e o m e t r y changes of the heart are m i n i m a l during this period. The complete set of potentials recorded in any individual is represented by a matrix dO, of dimension 64 • IO0, the columns of w h i c h represent the instantaneous body surface potentials at all 100 s u b s e q u e n t time instances, w h e r e a s the rows represent the traditional time tracings of the 64 leads. We call this matrix a body surface potential movie, the sequence of columns representing the subseq u e n t frames of the movie. The distance b e t w e e n the location on the thorax w h e r e standard lead V 2 was placed, a i m e d to be the fourth intercostal space, and the supra-sternal n o t c h was d o c u m e n t e d .
Materials and Methods
The MRI data consisted of 32 axial, T l - w e i g h t e d , n o n - E C G - t r i g g e r e d and n o n - b r e a t h - h o l d spinecho images of the body, as well as 10 to 14 shorl axis T l - w e i g h t e d turbo-flash images of the heart, taken using ECG triggering at end-diastole and breath-hold. The contours of the torso, lungs, ven-tricular mass, as well as of the ventricular cavities, w e r e identified in the MRIs. The orientation of the heart was d o c u m e n t e d by identifying 4 l a n d m a r k s (6). These are LI: the top ol a h e m i s p h e r e fitted on top of the base of the heart; L2: the apex, L3: the position w h e r e the left descendent coronary artery (LAD) crosses the base of the heart; and L4: the position w h e r e the right circumflex (RCX) coronary artery crosses the base of the heart. L a n d m a r k s L1 and L2 w e r e used to specify the long axis direction of the heart. L a n d m a r k s L3 and L4 can be accurately identified in MR images and the vector pointing from L4 to L3 was t a k e n to represent the heart's short axis. The orientation of this axis signals a n y rotational variability around the long axis. The actual long-axis direction used was that of the vector pointing f r o m the middle of L3 and L4 towards L2. The position of the supra-sternal notch could be identified easily in the MR images. This landmark, together with the m e a s u r e d distances b e t w e e n this reference point and the location of lead V 2 during the potential recordings, was used to establish the location of the electrodes on the triangulated torso surface.
Twenty-five h e a l t h y patients were studied by using b o d y surface m a p p i n g (BSM) and magnetic resonance imaging (MRI) with a Siemens 1.5 Tesla M a g n e t o m SP (Siemens, Erlangen, Germany). The patients (15 m e n a n d l0 w o m e n ) ranged in age b e t w e e n 24 and 65. All patients u n d e r w e n t a brief e x a m i n a t i o n b e f o r e h a n d , including the m e a s u r e m e n t of blood pressure, analysis of the standard ECG, echocardiography, and anamnesis, on the basis of which no sign of cardiac disorder was found.
Recorded Potentials The BSMs w e r e recorded with the Arnsterdam lead system, having 64 electrodes (5). The sampling frequency was 1,000 Hz. Baseline correction was p e r f o r m e d by shifting each ECG such that its value during the PQ interval was zero, after which the data w e r e shifted to a z e r o - m e a n potential reference. The BSM signals of all subjects were time-aligned by first taking the BSM signals of one of the subject as a reference set. F r o m this set, the time interval of 100 ms centered a r o u n d p e a k QRS in standard lead V x was selected. Subsequently, for each of the other subjects, the entire data set was shifted in time until a m i n i m a l difference with the BSM signals of the reference set was achieved. The BSM signals in the
Recorded Geometry
Geometry and Scaling in EGG: and VCG
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T a b l e t, Basic Statistics; Means +_ SD Factor Ge~ader Weight Length vol(thorax) S(thorax) vol(llung) vol(rlung) vol(vemrmass) vol(LVC) vol(RVC) d~st(ebh) QRS_dur spa.t DIP,~• VCGm~,• .j Vma • Vma,, VI,~xp RMS SA(thorax) SA(el) Age
Labe[
Unit
0 1 2 3 4 5 6 7 8 9 l0 11 t2 13 14 15 16 17 18 19 20
kg cm ] m2 1 l ] mL mL cm ms mA.cm mV mV z:qV mV mV 2w 2rr Year
All
Women
Men
25 • I0 + 8.4 + 4.9 • 0.062 + 0.25 • 0.33 + 42 • 28 + 30 • 0.60 + 8.2 + 0.48 + 1.1 + 0.43 + 0.56 • 0.63 + 0.077 • 0.082 e 0.076 _+ 13
~O. 68.6 170 I9,3 0.420 0.995 1.32 19I 130 14?, 2.27 71.4 1.58 1.70 1.22 1.22 1.62 0.261 0.419 0.382 33.7
t5 80.1 182 23.6 0.469 1.27 1.71 248 138 162 2.31 79.7 1,95 2.11 1.65 1.75 2.36 0.356 0.420 0.400 40.3
75.5 I77 2] .9 0.459 1.16 1.55 225 135 155 2.29 76.4 1.80 1.95 1.48 1.53 2.06 0.312 0.419 0.392 37.7
Men/Women
t-value
1.16 1.07 1.22 1.12 1.28 1.30 1.30 1.06 1.13 1.02 1.12 1.24 1.25 1.40 1.43 1.46 1.32 1.00 1.05 1.19
3.2 4,9 2.3 2.0 3.0 3.5 4.5 0.7 1.5 0.2 2.9 2.0 0.9 2.8 (-)2.5 3.9 3.2 0.0 0.6 1.2
Constitutional Factors
(x) In addition to the detailed geometry as specified in the previous subsection, the factors: gender, weight, length and age of the subjects were documented. These factors are denoted as F0, F1, F2, and F20, respectively. Label n u m b e r s correspond to their ordering as used in Table 1.
M a t e r i a l s and M e t h o d s Measures for the Interindividual Variability There is no c o m m o n l y used measure to express the interindividuaI variability of BSMs. Measures used for comparing two individuals, such as correlation coefficient and relative difference cannot be used for this purpose in a straightforward m a n n e r . We use a variability measure derived from the variance (standard deviation squared) in the ECG signals of several subjects. Because any scaling effects should not come to expression in the measure, the measure is normalized by the overall p o w e r of the observed data. It is c o m p u t e d by first determining the variance of the ECG signal over all subjects for each lead and each time instant. These variances are subsequently added over all leads and all time instances. The resulting variance is divided by the p o w e r in all BSMs pooled together, after w h i c h the square root is taken. Accordingly,
telVar
= X/
I1 ,11
'
w h e r e RelVar is the interindividuaI relative variability, @ is tee m e a n value over alt subjects, i is the index to any of the patients (25) studied, and I1" IIF denotes the square root of the sum of squares of all matrix elements (the Frobenius norm of the matrix). Note that the equation expresses the variability of an entire signal matrix. In this article it is applied to recorded 64-1ead ECG data as well as to three-signal data derived from these potentials (VCG or equivalent dipole).
Derived VCG The lead system used includes the locations ot the Frank lead system (7). The ECG data recorded at these positions were used to derive the VCG of the individual subjects studied by means of the transfer matrix (Eqn. 2 of Frank's paper 171). The VCGs of the subjects i are denoted by VCG~, matrixes of dimension 3 • 100.
Triangulation of the Recorded Geometry Based on the measured MRI data triangulated representations were made of all surfaces mentioned in Sect. II-B. These surfaces are generally used :for computing the v o l u m e conduction aspects of the ECG. In this article they are included to assess
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their effect on the overall m a g n i t u d e of the potentials. By using this triangulation, surface areas a n d / o r volumes of the various c o m p a r t m e n t s were computed. In addition, the solid angles of the contours of the ventricular mass as seen f r o m points on the thorax w e r e c o m p u t e d . The following factors related to g e o m e t r y w e r e derived: F3, v o l u m e of the thorax; F4, surface area of the thorax; F5, v o l u m e of the left lung; F6, v o l u m e of the right lung; F7, v o l u m e of the ventricular mass; F8, v o l u m e of the left ventricular cavity (full diastole); F9, v o l u m e of the right ventricular cavity; F18, the m a x i m u m value of the solid angle of the contour of ventricular mass as seen by a n y point on the thorax; FI9, m a x i m u m value of the solid angle of the c o n t o u r of ventricular mass as seen f r o m a n y of the electrode locations; F 10, smallest distance b e t w e e n a n y point on the thorax and a n y point on the ventricular surface (closest distance b e t w e e n heart and thorax).
Equivalent Dipole For all subjects, the individual position of a stationary equivalent current dipole was c o m p u t e d f r o m the observed b o d y surface potentials and the m e a s u r e d g e o m e t r y of the thorax, as well as the time course of the strength of the dipole c o m p o nents t h r o u g h o u t the QRS interval. The m e t h o d used is the least squares procedure, described in reference (8), assuming a h o m o g e n e o u s torso. The latter a s s u m p t i o n allows a direct comparison of the matrix of resulting dipole strengths, d e n o t e d by DIP~, with the corresponding Frank data VCG~. The assumed overall electric conductivity of the thorax was 0.2 S.m -~.
Measures of Magnitude In the s u b s e q u e n t analysis the following m e a sures of overall m a g n i t u d e are used, extracted f r o m the recorded potentials: F14, Vmax. the highest positive reading a n y w h e r e in the movie; F15, Vm~• the highest negative reading a n y w h e r e in the movie; F16, v- - ]pap 9 the highest p e a k to p e a k value in ~]a x a n y of the time tracings; FI7, RMS: the root m e a n square value c o m p u t e d over all time instants and all leads; FI2, the highest value of the spatial magnitude of the equivalent dipole DIP; F13, the highest value of the spatial m a g n i t u d e of the VCG.
time interval b e t w e e n the m o m e n t s at w h i c h this curve passed the 5% threshold relative to its max.i m u m value w e r e taken as the QRS interval, labeled as F I I .
Statistical Methods The limited n u m b e r of subjects included in this study d e m a n d s a severe restriction on the n u m b e r of factors to be considered s i m u l t a n e o u s l y in the subsequent analysis. The tests used include: the t-value from the Student's t-test (two group [gen-. der] comparisons) and the linear correlation coefficient p b e t w e e n a n y pair of the factors studied. For N = 25, tcr for a two-sided test at the 95% confidence level is 2.06. The directional factors are specified t h r o u g h the a z i m u t h and the elevation of the vectors involved. The a z i m u t h was t a k e n to be the angle b e t w e e n the projection of the vector on the horizontal plane, and an axis pointing to the left part of the thorax, its sign was defined as positive for vectors pointing towards the back. The elevation was t a k e n as the angle b e t w e e n the vector a n d the horizontal plane, its sign defined as positive for vectors pointing towards the head. The statistics of these factors w e r e specified by c o m p u t i n g the preferential direction and the spatial precision (9). For the latter statistic, a value of 1 corresponds to a perfect clustering at the value of the preferential direction, a value of 0 corresponds to the directions f r o m the origin toward points scattered all over a sphere. For a spatial precision value close to 1 its inverse cosine is proportional to the geometric m e a n of the stano dard deviation of the a z i m u t h and the elevation values, in Table 4, this angle, a m e a s u r e for the dispersion a r o u n d the preferential direction, is s h o w n n e x t to the spatial precision.
Results Overall Statistics
9
QRS Duration The QRS duration as derived from the time course of the spatial m a g n i t u d e of the vector. The
An overview of the basic statistics of the factors considered is presented in Table 1. Separate entries are s h o w n for the entire group (N = 25), for the w o m e n (N - 10) and for the m e n (N - 15). Standard deviations for the gender-specific data are not shown. Instead, the ratios of the gender-specific m e a n s are shown, as well as the t-value for group comparisons based on gender. The (limited) precision with which the results are specified is t u n e d to
Geometry and Scaling in ECG and VCG
the limited accuracy of the values, which results from the small n u m b e r of subjects involved.
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T a b l e 3. D i s t a n c e s f r o m t h e L e v e l o f t h e H e a r t C e n t e r
DI D2
RelVar Values
M e a n (cm)
R a n g e (cm)
3.89 1.61
0-7.25 -0.75-5.5
D~: to that o{ V2; D2: to teat of the equivalent dipole
The expression for the relative variability (Equation 1), has been applied to the 64-lead ECG data as welt as to the 3-signal (dipole) data VCG and DIP. The results are listed in Table 2. Separate entries are s h o w n for the entire group (N = 25), for the w o m e n (N - 10) and for the m e n (N = 15). In addition, results are listed that were f o u n d by first normalizing the individual movies. Note that in this case the d e n o m i n a t o r of equation 1 loses its significance.
the wide range that was found. The a c c o m p a n y i n g RMS-based relative residual differences between recorded and dipole based potentials s h o w e d a m e a n value of 0.248 and a range of 0 . 1 4 9 - 0 . 4 2 8 .
Analysis Lead Placement The projection of the heart onto the frontal plane was marked. The plane transverse (horizontal) plane r u n n i n g half w a y b e t w e e n the c o n t o u r was taken to represent the level of the anatomical center of the heart. The distances D~ b e t w e e n this level and the level at which lead V2 had been placed were d o c u m e n t e d . Their statistics are included in Table 3. Note that the range of D t is even larger than that of D e .
Directional Data The basic statistics of directional data are presented in Table 4. In addition, the statistics of 6 are shown, ~bbeing the angle between the the long axis and the vector of maximal spatial VCG magnitude.
Over the years, the interindividual variability of the ECG and the VCG has been studied by several groups (10-14). These studies were based on observations made on large n u m b e r s of subjects. Impressive lists of (ranges of) normal values on just about any parameter used in the world of ECG and VCG can be found in the part III of the m o m e n t o u s series "Comprehensive Electrocardiology" (15). In fact so m a n y details are included that one m a y easily lose sight of the w o o d for the trees. This paper, which is based on just 25 subjects for w h i c h electric data as well as a u n i q u e set of matching geometry data was available, aims at presenting an overall view on some of the basic aspects of ECG variability in normals. The analysis builds on the major previous papers on this topic, the present material, as well as on some experience gathered over the years in our group on the topics of forward and inverse modeling of the ECG.
Equivalent Dipole The positions established for tEe stationary equivalent dipoles were mainly in the septal region. As s h o w n in Table 3, the positions were below the center of the heart defined in Lead Placement. Note
Table
2. R e l V a r V a l u e s ( E q u a t i o n
l)
All
Females
Males
64 Leads 64 Leads (norm)
0.52 0.48
0.44 0.42
0.5 I 0.48
VCG VCG (norm)
0.46 0.4I
0.36 0.32
0.46 0.41
DIP DIP (norm)
0.47 0.41
0.45 0.34
0.45 0.42
T a b l e 4. S t a t i s t i c s o f D i r e c t i o n a l D a t a : P r e f e r e n t i a l Direction and Precision Vector Long-axis azhn e|ev prec VCGma~ azim elev prec
Unit
All
Women
Men
degr degr (degr)
52,8 -34.5 0.986 (9)
-55,4 358 0.992 (7)
51.1 -33.7 0.983 (10)
degr degr (degr)
14.2 -33.7 0.918 (23)
10.7 37.0 0.932 (21)
16.4 31.6 0.910 (24)
degr degr (degr) degr (degr)
43.9 54.7 0.973 (13) 54.0 0.973 (13)
50.2 56.5 0.980 (11) 52.7 0,971 (13)
39.9 53.5 0.970 (14) 54.9 0.974 (13)
short-axis
azim elev prec ~ prec
--
azim, azimuth; prec, predsion; elev, elevation.; degr, degrees.
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Journal of Electrocardiology Vol. 33 Supplement 2000
Relvar The RelVar values listed in Table 2 indicate that the overall variability of the normal ECG and VCG data is quite considerable. Clear gender based differences were found. This fact has been noticed before in the literature (eg, [14]). As stated in the introduction, a major part of this variability arises from geometrical factors, and we are searching to reduce this contribution. As is also clear from Table 2, for the VCG RelVar has a smaller value than for the ECG. This is a result of the fact that at most 3 independent signals are present in the VCG, whereas the ECG m a y contain more i n d e p e n d e n t c o m p o n e n t s (at most 8 in the standard-12 lead ECG; about 11 in the 64-lead BSPM data; see [16]), each contributing to the overall variability.
Magnitude Table 2 indicates that a part of the variability disappears alter normalizing the individual movies (matrixes). This t h e n brings us to the major topic of lhe present paper: what determines the overall size of the ECG and of the VCG and h o w does this relate to body size, gender, and age? In Measures of Magnitude, the measures of magnitude used are described. In Table 1 these are listed as "factors" 12-17. As can be seen, even these crude indicators of m a g n i t u d e exhibit a large variation.
points are inversely proportional to the square o[ the distance R between source and field points~ These potentials are also proportional to the surface area S of the depolarized tissue. More precisely, it is the solid angle i'l subtended by the wave front at the observation point that is a main d e t e r m i n a n t for the electric potential (17). By scaling a subject by a linear factor L, a procedure practiced with great enthusiasm in the d o m a i n of allometry (see re! [18]), we see that both S and R 2 are proportional to L 2 and as a consequence i~ is invariant to scaling. From the m o u s e and the elephant we, hence, learn that the double layer strength of ventricular depolarization must be invariant to scaling.
Solving the Riddle The remaining part of this article is aimed at explaining the observed gender-related differences in the magnitude measures, and, in passing, to relate several of the observations to the general problem of magnitude and scaling. We will use Figure 1 to see if any of the proposed ideas might be contradicted by the observations made in this study.
0
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+
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G e n d e r . Five of these 6 measures of magnitude show clear gender differences, the m a x i m u m spatial m a g n i t u d e of the VCG being the odd one out. Is this significant, w h a t causes these differences anyway2 Is the female cardiac electric generalor intrinsically less "powerful" than the male version?
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The riddle posed by the mouse and the elephant led us to consider the w e l l - k n o w n equivalent generator of the cardiac generator during ventricular depolarization: the double layer. This generator seems to have all the properties for the present discussion. The potentials that it generates at distant
x
+
Size. A simple answer to the question posed above is an affirmative: nren generally are taller, have larger hearts and hence, have more a more powerful cardiac generator. However, both mice and elephants have ECG values on their body surface of about 1 mV of magnitude, yet their size is "somewhat" different.
Scaling
.
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Fig. 1. Matrix of linear correlation coefficients p observed between factors. Row and column indexes correspond to the labels used in Table 1; The symbols used (% + and - ) denote p v a I u e s > 0.507, > 0.337 and < -0.337, respectively. Blank entries denote -0.337 < p < -.337. The values 0.337 and 0.507 are the critical values for testing p - 0 at confidence levels 5% and 0.5%, respectively. The partitioning shown is used in the Analysis.
Geometry and Scaling in ECG and VCG
The format in which these correlations are presented is s o m e w h a t similar to the one s h o w n in reference (19). The partitioning s h o w n for the rows follows the nature of the factors: F1-F10 all relate to size, F1 l relates to time, F I 2 - F 1 7 relate to electric data, and F20 is age. The partitioning of the cohtmns follows the d e p e n d e n c y of the factors on scaling. Factors F1-F10 as well as F11 and F12 depend, as will be argued, on scaling. Factors F13-F19 are independent of scaling. T h e VCG. For the ideal VCG lead system, any difference in heart position w o u l d not have any effect on the observed vector. By assuming the female cardiac generator to be identical to the male variant, the maximal spatial magnitude of the VCGvector should be expected to be i n d e p e n d e n t of gender. Indeed, as s h o w n in Table 1 the m a g n i t u d e of the VCG-vector was found to be i n d e p e n d e n t of gender. In some of the literature, based on a greater n u m b e r of subjects, m i n o r magnitude differences are suggested. These small differences can be easily explained of the basis that, in w o m e n , the contribution of potentials as seen by left precordial electrode C of the Frank system, contributing to the vector c o m p o n e n t s in the horizontal plane, are smaller in w o m e n , related to anatomical differences that yield greater distances b e t w e e n the heart and electrodes. Perhaps less well k n o w n is the fact that the VCG is also i n d e p e n d e n t on scaling. The basis for this statement is directly linked to the observation on the m o u s e and the elephant. The Frank leads perform a fixed linear weighting of potentials on the body surface. With the potentials on the body surface being invariant to scaling, so is the o u t c o m e of the weighting procedure. In spite of this some of the correlation coefficients s h o w n on r o w 13 s h o w e d values for which P < 5% for some of the size-iinked factors. We attribute this at this stage, awaiting further analysis, to imperfections in the lead placement (see Table 3). T h e E q u i v a l e n t D i p o l e . The results on the equivalent dipole seem to contradict the above theory. However, the contrary holds true and it is for this reason that the equivalent dipole data are included in this paper. The equivalent dipole is easily confused with Frank's VCG. Its nature is that of a true current dipole, having a dimension of current • distance, expressed in units, say, mA.cm. After the Gabor-Nelson equations (20) the equivalent current dipole I) can be c o m p u t e d from the full body surface potential distribution as
(2)
9 van Oosterom et al,
225
fl=~f ad~,
with o~the conductivity of the m e d i u m (assumed to be h o m o g e n e o u s ) , (I~ the potential distribution on the thorax, and dS the (directed} surface elements of the thorax. If we n o w apply the idea of the invariance of the potential to scaling we see that the magnitude of the equivalent dipole is proportional to the surface area of the thorax. As seen from Table 1 the m e a n value the thorax surface was about 0.46 m x. After scaling the individual ~olp; ~ ' ~pat .... values by the corresponding S(thorax) values the result no longer showed a n y d e p e n d e n c y on gender or scaling. Summarizing, the proportionality factor bet w e e n VCG and the true equivalent dipole I) depends on the surface area involved and on the assumed electric conductivity. The strength of the equivalent dipole scales as L 2.
M a x i m u m N e g a t i v i t y . V..... (El 5), the highest negative reading a n y w h e r e in the movie can be expected to be in the area of Vx. The d o m i n a n t single factor in this situation was found to be the solid angle subtended by the heart as seen from any of the electrodes: F19, for w h i c h p = - 0 . 6 5 . Inclusion of neither of the other factors did not significantly increase p. M a x i m u m P o s i t i v i t y . V,~• (FI4), the highest positive reading a n y w h e r e in the movie can be expected to be in the area of V4. The d o m i n a n t single factor in this situation was found to be heart size (F6), with p - 0.58. This corresponds to the fact that any d e p e n d e n c y on the solid angle subtended by the heart as seen from any of the electrodes (F19), for which p - 0.41, is dominated by genderrelated differences at this part of the thorax. After harmonizing the potential readings for gender, the solid angle based factor again clearly dominated (p - 0.64). M a x i m u m P e a k - t o - P e a k Value. F16, the highest peak to peak value in any of the time tracings, showed a d e p e n d e n c y similar to that reported on for El4. There was, as also s h o w n in Table l, a clear d e p e n d e n c y on gender. However, after h a r m o n i z i n g the m a g n i t u d e values such that equal means for both sexes resulted the m a x i m u m solid angles dominated and the results were indep e n d e n t of heart size per se. RMS. The b e h a v i o u r of the root m e a n square value c o m p u t e d over all time instants and all leads (F12) showed a similar b e h a v i o u r as F16.
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Journal of Electrocardioiogy Vol. 33 Supplement 2000
Gender All of the gender-based differences in the ECG m e a s u r e s of m a g n i t u d e can be explained by genderrelated geometric differences. For the RMS values, a reduced value over a part of the t h o r a x (left precordium) having large potential values, cannot b u t lead to smaller RMS values in w o m e n . Moreover, female hearts being smaller, the fixed vertical spacing of the electrodes (3.8 cm), again will result in smaIler values in females because of a relatively cruder spatial sampling. The latter also affects the m i n i m u m negativity observed (F15). For the m a x i m u m potential (V14) it is the greater distance to the heart that counts, showing indeed a higher gender-based ratio in Table 1.
Directional Results The directional data s h o w n in Table 4 are in a g r e e m e n t with literature data [I] in so far these are avaiiable. A large m e a n value of q~ was observed, m a i n l y involving the azimuth. The individual shifts were of a n o n - s y s t e m a t i c nature. Slight gender-based differences were Observed, consistent with ideas f o u n d in the literature. Interestingly, the slightly m o r e anterior direction of the long-axis found in females together w i t h the gender i n d e p e n d e n t value of the m e a n 4) shift is consistent with VCGm~x pointing m o r e to the left in w o m e n . This leads to smaller potentials o n the frontal part of the thorax. The g e n d e r - b a s e d differences in the short-axes direction w e r e e v e n larger, but again, significance remains to be shown.
Duration QRS Slight but significant gender-based differences in QRS duration were observed (see row 11 of Fig. 1) (/9 = 0.51). However, the largest correlation (p 0.55) was f o u n d b e t w e e n QRS duration and length. The latter seems to be the direct factor involved (Iinked to h e a r t size), gender being an indirect factor. This is in a g r e e m e n t with the general theory of scaling which states that any time interval r scales like r -- L.
Age The n u m b e r of cases included in this study is too small to draw a n y firm conclusions. Yet all of the entries s h o w n in the b o t t o m row of Figure 1 are
consistent with the fact that, with advancing age, at least in the range included here, people tend to b e c o m e m o r e obese. The distance b e t w e e n heart and electrodes increases, the solid angles decrease, and as a result the potentials decrease. Moreover, a slight angular shift of the long axis (azimuth only) was observed. All these factors are quite sufficient to account for the decrease of the m a g n i t u d e s with age that have previously b e e n reported on in the literature.
Body Indexes Several of the b o d y indexes f o u n d for expressing individual obesity were tried in the present study. None of these w e r e found to reduce the residual variance a n y further b e y o n d that already achieved by incorporating the solid angle only. W h e n studying the b e h a v i o u r of these different indexes it was f o u n d that over the range of weights of 50 kg to 100 kg and for lengths f r o m 150 to 200 cm all of these indexes are in fact equivalent, only differing by a factor (the slope of the curve). If we take for example Rohrer's index m.1 3, or the p o n d e r a l index m~/3.1-1, w h e n used consistently, the results for the present application are identical. The use of such indexes should be restricted to those that are invariant to scaling. Because of this, the use of the Quetelet index m.1-2 should be avoided on theoretical grounds. A l t h o u g h in practice, it does not m a k e m u c h difference.
The Other Factors The analysis of the other factors listed in Table I did not result in a n y significant reduction of the variance of the m e a s u r e s of m a g n i t u d e .
Conclusion This p a p e r has s h o w e d that a c o h e r e n t view on the cause of a p p a r e n t gender and size-related differences in overall m a g n i t u d e of cardiographic signals as observed on the thorax can be derived from considerations of g e o m e t r y only. The implications for VCG are: the spatial magnitudes are scale and gender i n d e p e n d e n t . The small g e n d e r - b a s e d differences found are caused by the m a x i m a l spatial vector being directed slightly m o r e in parallel to the frontal part of the thorax in females, as well as to the fact of Frank's lead C being m o r e r e m o t e f r o m the heart in w o m e n . The ideal
Geometry and Scaling in ECG and VCG
v e c t o r l e a d s y s t e m w o u l d also be i n d e p e n d e n t of the actual heart position. F o r t h e ECG t h e implications are t h a t overall differences in size (scaling) are u n i m p o r t a n t : p o t e n t i a l is i n v a r i a n t to scaIing. QRS d u r a t i o n scales l i n e a r l y w i t h L, w i t h h e a r t a n d b o d y mass b o t h scaling as L 3. Based o n t h e solid angle a p p r o a c h , g e n d e r - r e l a t e d differences s h o u l d c o m e to e x p r e s s i o n m a i n l y in the a n t e rior leads, a n d m u c h less in t h e e x t r e m i t y leads. This can in fact be clearly o b s e r v e d in t h e Tables A 1 9 - A 2 0 s h o w n in r e f e r e n c e (1). The large d i f f e r e n c e s b e t w e e n t h e o b j e c t i v e l e a d p l a c e m e n t a n d t h e a c t u a l p l a c e m e n t w i t h r e s p e c t to t h e h e a r t (see Table 3), s u g g e s t t h a t a m e t h o d n e e d s to b e d e v e l o p e d for p l a c i n g t h e a n t e r i o r e l e c t r o d e s in m a n n e r t h a t is t u n e d to t h e a c t u a l h e a r t p o s i t i o n r a t h e r t h a n to s o m e i n t e r c o s t a l space.
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