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A Comparative Analysis of Several Corrected
Vectoreardiographic Leads
By DANIEL A. BRODY, M.D., AND ROBERT C. ARZBAECHER, PH.D.
With the technical assistance of Harry A. Phillips
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DURING the past decade a great deal of
attention has been devoted to the development and application of one or more
vectorcardiographic lead systems possessing
certain highly desirable physical characteristics. The overriding design consideration has
been that the lead system provide a truly
Cartesian frame of reference for the display
of cardiac vectors. Achievement of this goal
requires that the axes of the three component
leads be mutually orthogonal, that their individual electrocardiographic sensing abilities
be equally scaled, and that both of the preceding properties remain essentially invariant
throughout the cardiac region. Sets of electrocardiographic connections that attempt to
satisfy these basic requirements are frequently
referred to as corrected lead systems. They
appear to be gaining increasing acceptance in
vectorcardiographic practice.
The ultimate test of a vectorcardiographic
system lies in the demonstration of its reliability as a clinical diagnostic tool. Pending
such clinical testing and confirmation, however, the special merits of corrected lead
systems are predicated on their adherence to
the specific design principles referred to
above. Therefore it is of interest to examine
the physical properties of such leads in detail
and to determine how closely their parameters
approximate the ideal situation.
There is nothing basically new in the idea
of exploring the physical properties of lead
connections. Indeed, it was in this way that the
design of corrected lead systems was achieved.
The experimental methods applied to this
purpose, however, have been somewhat deficient in a number of technical and conceptual
respects. During the past 3 years we have
developed a method of measuring and analyzing the physical characteristics of lead connections in a manner that is designed to
eliminate or, at least, greatly minimize many
of the limitations of previously employed
methods.' Our new method embraces certain
fundamental concepts that were not comprehensively treated in earlier reports on corrected lead systems. An important technical
feature of the experimental method employed
in this study is its largely automatic mode of
data acquisition, and the extensive use of the
electronic digital computer in data processing and analysis.
In this present report we re-examine the
physical characteristics of three corrected lead
systems as determined by the newer experimental method. In addition, we shall deal
with three potentially valuable single leads
whose quantitative characteristics have not
previously been recorded in the electrophysiologic literature.
Theoretical Foundations
According to one of the newer concepts of
the interrelationships between leads and the
electromotive forces of the heart2' 3 the potential difference, V, which appears across the
terminals of a vectorcardiographic lead, can
be expressed mathematically as
(1)
V = FiMi + FijM!' + FijkMiik +
In this equation the successive F symbols are
covariant tensors of the first, second, third,
etc., rank, respectively. The corresponding M
symbols are contravariant tensors of like rank.
The contravariant tensors express the equiv-
From the Section of Cardiology, University of
Tennessee, Memphis, Tennessee.
Supported in part by Grants HE-0132-11, HE-K610432, FR-00001, National Institutes of Health, U. S.
Public Health Service; Grant GP-706 of the National
Science Foundation; and a grant from the West
Tennessee Heart Association.
Circulation, Volume XXIX, April 1 964
533
BRODY, ARZBAECHER
5-34
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alent cardiac generator behavior of the heart;
the covariant tensors express the intrinsic
characteristics of the given lead connection.
The form of the equation indicates that the
cardiac and lead parameters can be treated
as two experimentally independent sets even
though there is an inextricable conceptual
linkage between them. It is this ability to
divorce cardiac properties from lead characteristics that makes possible a comprehensive,
quantitative analysis of lead behavior.
Vectors are tensors of the first rank. Accordingly, the set, Mi: M 1, M 2-, M3, of equation 1 represents, respectively, the X, Y, and Z
components of the heart vector. By strict definition it is these components alone that the
vectorcardiogram is intended to display. Since
it is highly probable that heart tensor components above the first rank do exist,4- " the
desired purity of heart-vector display lies in
the development of registration systems in
which lead tensor components above the first
rank vanish. It is the achievement of this condition which is, in essence, the goal of most
corrected lead systems. Experimental evaluation of such systems in the biophysics laboratory requires not only determination of the
first rank parameters, but also verification that
the magnitudes of higher rank parameters
are acceptably small.
The F symbols of equation 1 are parameters
of the electrocardiographic lead field, which,
by definition, is the potential field generated
in the body when one unit of current from an
external electromotive source is caused to flow
from the positive to the negative terminal of a
given lead connection.7 The specific tensor
characteristics of the lead field, including
their relationship to the canonical or analytic
treatment of lead-field potentials, have been
described in detail elsewhere.'29 In devising
an experimental approach to lead-field analysis the analytic form has proved more rewarding. This is particularly true when the field is
treated as a series of spherical harmonics
components of the form
u1 = p.o( rn
(n1-7m)!
(n+m)!
P,'
/ P,"r
(y
(2)
cos mO \
sin m0/
p
Equations 2 are referred to conventional
spherical coordinates, r, 0, 0, with g = cos 0.
Other symbols indicate: u, the scalar potential of a given component; n and m, the degree
and order, respectively, of the component;
pllo Ppnm, and qnm, coefficients that characterize
the vectorcardiographic sensitivity of each
component; Pl1m ( pt), associated Legendre
functions of nth degree and mth order. In
ideal systems all sensitivity coefficients except
plo, pl, and q1l vanish. The appraisal of nonideal behavior, then, rests in large measure
upon quantitative evaluation of sensiti.vity
coefficients other than these three.
Experimental determination of the coefficients, Pnm and qtlIn, in torso models of the
human body does not require sampling of
lead-field potentials throughout the cardiac
region. WVhat is required, rather, is measurement at a number of spherically arrayed
sampling points that contain the cardiac
region.1 9 The sampling procedure should be
extensive enough to permit accurate interpolation of lead-field potentials at all intervening points. Having thus measured the potential function, us, over a spherical sampling
surface, the desired coefficients can be determined from the relationships,
1
2n+ 1
2r
J
u
usco mO
110()d
(3)
pno1
pniin
qnm /
_
'Sr
2n +- 1
2
J
1
u,
MO
</c.os
\sin > d0
m0
d1
0
Pill--" (
)
dp-
Methods and Materials
Three corrected vector systems, Frank's,1'(
Schmitt's SVEC-JII,"1 and McFee's 12 axial, were
studied in an electrolyte-filled torso model having
cross sectional dimensions of 20.8 by 35.7 cm. at
the midventricular transverse level, and measuring 50.9 cm. from the symphysis pubis to the
suprasternal notch. Either tap water or dilute
sodium chloride solution was employed as the
electrolyte. Precordial electrodes consisted of 30mm. diameter disks of pure silver foil temporarily
cemented to the internal surface of the model at
C,r(:;ulation. VolIz-)ne XXIX, April 1964
535
CORRECTED VECTORCARDIOGRAPHIC LEADS
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the appropriate locations. Larger rectangles of
the silver foil (approximately 5 by 8 cm.) were
cemented to the extremity stumps of the model
to serve as the right and left arm, and left leg
electrodes. The soldered connections of the lead
wires to the electrodes were carefully sealed with
Glyptal lacquer in order to minimize the possibility of unstable contact potential due to local
electrolytic effect.
Lead fields were generated within the model
by reciprocally energizing each connection with
1.000 cycle per second altemating current. By
means of the previously described device,' leadfield potentials were systematically and automatically measured at 425 spherically arrayed
sampling locations. Additional measurements were
made at the north and south poles of the sampling sphere, the radius of which was 8.52 cm.
Write-out of data observations was in both analog and digital (punch card) form at a rate of
six observations per minute. The individual sampling sites were located at 25 equiangular intervals of azimuth on 17 circles of latitude. The
sampling circles included the equator of the
spherical array and eight latitudes to either side
of the equator, arranged in equiangular steps of
7.2 degrees of elevation. The device that measured the lead-field potentials was essentially an
impedance bridge that balanced itself by means
of two servo mechanisms. The axis of rotation of
the sampling mechanism was parallel to the sagittal plane of the model. As viewed from the left
side, the vertical axis of the model was tilted forward 9.3 degrees in a counterclockwise direction
from the rotational axis of the mechanism. This
tilt permitted the center of the spherical sampling
pattern to be located at the centroid of the ventricular mass without the necessity of having an
excessively large port in the cervical region of
the model.
A computer program was employed that first
reduced the input data to millivolts of lead-field
potential, referred to a standard medium resistivity of 1,000 ohm-cm. Next, the Fourier coefficients of the potential function around each sampling circle were computed. This step amounted
to performance of the integration indicated in the
brackets of equation 3. Since the sampling circles
were disposed symmetrically to either side of the
equator, they were sorted into odd and even
functions of the spherical surface and thereafter
referred to the upper hemisphere alone. The 10
values of each odd and even set of the Fourier
coefficients in the upper hemisphere were smoothly
connected as ninth-degree polynomial functions
of g. By means of these polynomial functions
interpolated values of the Fourier coefficients
were determined for the argument, u taken
in steps of 0.02 from zero to one. At this
Circulation, Volume XXIX, April 1964
juncture pre-computed tables of associated Legendre functions for equal steps of argument were
read in, and the remaining integration indicated
in equation 3 was performed according to Simpson's rule. Due allowance was made for the fact
that the range of argument, g, had been limited
to the upper hemisphere.
In addition to the three complete systems the
properties of two anteroposterior grid-type of
lead connections were studied. In each case a
square array of 16 equally weighted, 1.0-cm.
diameter circular electrodes was applied to the
anterior and posterior walls of the model in the
region of the heart. In the first case, equivalent
to the MeFee-Johnston grid,7 the individual electrode centers were spaced 6.25 cm. apart as measured on the body surface of the model. In the
second case the electrodes were so relocated that
it was their projections on the frontal plane, rather
than the electrodes themselves, which formed the
square grid pattern.13
Two individual vertical leads were also studied.
One of these was lead aVI. The other was the
"<symmetrical" lead, which we proposed a few
years ago.14 It consists simply of two pairs of
equally weighted electrodes which are applied,
respectively, to the sides of the neck and the two
lower extremities.
Quantitative Results
In each case the lead vector components are
the first-degree coefficients, plo, pi,, and q1l,
divided by the factor, 8.52, which is the radius
in centimeters of the sampling sphere. Table 1
lists the lead vector magnitudes and their
direction cosines with respect to an anatomically oriented Cartesian coordinate system.
The axes of this reference frame are those
ordinarily employed in vectorcardiography:
X axis transverse and positive to the left; Y
axis vertical and positive toward the feet; Z
axis anteroposterior and positive toward the
back. The triple scalar product of the unit
base vectors was computed for each of the
complete lead systems studied. A geometric
interpretation of the triple scalar product is
that it is the volume of the parallelopiped the
sides of which correspond to the unit base
vectors. The departure of triple scalar product
from unity is one measure of non-orthogonality of the lead system.
The list of lead vector magnitudes in table 1
shows that the Frank system best meets the
desired condition of equal lead weights. The
BRODY, ARZBAECHER
536
Table 1
Summary of First-Degree Lead-Field Parameters
Lead
System
Lead
Magnitudes
(mv./cm.)
X
"Unit"
Y
"Unit"
z
"Unit"
or
type
Idceal
x
X
McFee axial
Y
z
Frank
Y
SVEC-III
z
X
Y
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Tetrahedron
Symmetric
McFee grid
Proj. grid
1.606
1.476
2.240
1.448
1.395
1.371
Angles between cooIrd.
planes, degrees
YZIZX
XY YZ
vectors
Direction cosines
-V
a
1.0000
.0000
.0000
.9990
.0256
.0637
.9897
.0753
.0450
.9595
z
1.286
1.048
1.545
aVF
1.527
.1479
(Y)
y
z
1.680
.0244
1.321
.0584
z
1.279
.0447
.0256
.0061
.0000
1.0000
.0000
.0000
.9996
.0528
.1217
.9804
.1766
.1894
.9996
.1376
.9890
.9997
.0394
.0550
.0000
.0000
1.0000
90.0
90.0
90.0
(TSP = 1.0000 )
.0440
.0092
.9966
.0752
.1823
.9833
.2087
.0092
.9905
88.9
(TSP
78.3
93.5
.9920)
91.3
110.3
.9165)
(TSP
79.1
(TSP
83.9
102.4
84.2
= .9434)
.0066
-.0014
.9975
.9975
Magnitudes and anatomic orientation of the lead vectors of the various connections studied. In the case of the
three complete lead systems the angles between the vectorcardiographic coordinate planes are also given. The
index of mutual orthogonality of the three axes, TSP, is the triple scalar product of each system's unit base
vectors.
direction cosines, angles between coordinate
plane, and triple scalar products show that the
axial lead system meets the conditions of
mutual orthogonality of axes and parallelism
with corresponding anatomic axes more satisfactorily than either of the other two systems.
On the other hand, the axial system is the
least satisfactory so far as scaling factors are
concerned. This is a readily correctible situation, however. The relative weights of the
SVEC-1IJ leads are also rather unsatisfactory.
They were somewhat better in their raw form,
before a specified correction multiplier of 0.75
was applied to the X lead, and a multiplier of
0.71 to the Y lead. The properties of the four
single leads listed in table 1 do not indicate
that they possess any unique merit so far as
their first-degree parameters are concerned.
It is anticipated that the higher degree leadfield components, p,,,,, and qMD, which are
computed according to the principles expressed in equation 3, will eventually serve
as a basis for determining the mtiltipolar
components of the equivalent cardiac generator. Pending such application, however,
find that the physical significance of these
coefficients is greatly clarified when each is
multiplied by a "normalizing factor," K. In
zeroth-order cases the normalizing factor is
we
(4a)
2n + 1
For coefficients above the zeroth order the
normalizing factor is
(r,
K= (-
(n
r2
inm)!
)"42n+ 1 (n+m)M!
(4b)
The r0 in equations 4 is the radius of the
spherical sampling pattern, which in the present study is 8.52 cm. The r1 is the radius of
a sphere that is large enough to contain the
cardiac mass. Somewhat arbitrarily we chose
a value of 7.5 cm.
The normalized p,,, and q,nm coefficients
derived from this study are presented through
(inraiiiifion, Voluime XXIX, April 1964
CORRECTED VECTORCARDIOGRAPHIC LEADS
537
Table 2
Dipolar and Non-Dipolar Lead-Field Parameters
Lead
n
pnO
Rect.
tank
z
Tetr.
1
2
2
3
1
2
.002
.048
.004
1.987
.201
.076
.049
.120
6.650
.019
.001
.261
.022
.057
3
1
2
3
1
2
3
1
2
3
1
2
3
1
2
3
1
2
3
1
2
3
1
2
3
1
2
3
1
2
3
1
2
3
.144
6.298
.363
.158
1.046
.008
.840
.678
.963
.026
5.668
.306
.071
.098
.275
.145
1.140
.819
.003
.155
.496
.239
6.462
.602
.069
7.181
.175
.079
.693
.062
.061
.586
.041
.093
.049
1.084
.358
.004
9.623
.292
.988
.588
.005
.152
2.037
.064
.101
5.931
.267
1.016
1.755
.018
.406
6.688
.422
.645
1.006
.168
.006
1.157
.097
.028
5.670
.007
.146
5.500
.056
.147
X
(I)
Axial
X
Axial
y
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Axial
z
Frank
X
Frank
y
Frank
z
SVECIII
X
SVECIII
z
Tetr.
y
(aVF)
Symmetr.
y
MeFee
grid
z
Proj.
grid
z
3
1
Pnl
.302
.011
Individual coefficients
pn2
qnl
.013
.022
.023
5.025
1.466
.159
6.948
.086
.045
.164
.313
.066
.618
.031
.209
6.207
.355
.585
.455
.046
.131
.267
.141
.010
7.124
.796
.568
.041
.039
.018
.978
.334
.025
.178
.112
.083
.334
.149
.027
.248
.066
.008
qn2
pn3
qn3
Lumped
coefficients
1.000
.005
.001
.001
.001
.084
.133
.103
.012
.033
.106
.688
.254
.168
.092
.037
.700
.166
.038
.044
.032
.044
.004
.214
.429
.627
.136
.869
.283
.503
.019
.082
.014
.158
.156
.491
.076
.241
.057
.087
.195
.134
.086
.710
.024
.016
.221
.286
.023
1.783
.051
.262
.234
.169
.117
.412
.162
.073
.021
.009
.006
.143
.039
.070
.021
.010
.036
.018
.156
.053
.437
.116
.068
.006
1.000
.086
.038
1.000
.054
.026
.343
.063
.026
.042
.065
.035
.002
.003
.008
.004
1.000
.275
.047
1.000
.104
.110
1.000
.097
.029
1.000
.075
.171
1.000
.183
.103
1.000
.105
.049
1.000
.140
.177
1.000
.677
.116
.288
.132
1.000
.567
.461
.108
.155
1.000
.124
.027
1.000
.038
Summary of lead-field components through the third degree and order. The individual components of nth degree and mth order, P,,m and q,5m. have been so normalized that the values given in the table show the root-meansquare contribution of each to the lead-field potential over an imaginary spherical surface, 7.5 cm. in radius,
which contains the heart. The relative lumped values for each degree are given in the right-hand column. These
numbers indicate the sensitivity of each lead connection to the dipolar, quadripolar, and octapolar fractions of the
equivalent cardiac generator.
Circulation, Volume XXIX, April 1964
538
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the third order and degree in table 2. In this
form each coefficient indicates the root-meansquare contribution from each component of
corresponding degree and order to the leadfield potential over an imaginary 7.5-cm.
radius spherical surface that contains the
heart. The peak magnitude of an individual
component contribution is roughly twice its
root-mean-square contribution. The total, or
lumped, contribution of components of a
given degree is the square root of the sum of
squares of all components of that degree. The
lumped contributions appear to be of considerable significance, since, when listed in
ascending degree, they respectively indicate
the sensitivity of the lead connection to dipolar, quadripolar, octapolar, etc., components
of the equivalent cardiac generator. The relative sensitivities of the various leads investigated in this study are presented in lumped
form in the right-hand column of table 2,
with the dipole sensing characteristics of each
lead arbitrarily taken as unity. The validity of
the experimental method is illustrated by
measurements of a uniform field generated in
a rectangular tank. The lumped second- and
third-degree components of the field were
determined as 0.8 and 0.4 per cent, respectively, as compared to theoretically ideal
values of zero.
Table 2 illustrates that several of the corrected vectorcardiographic leads possess sizable non-dipolar sensing characteristics. The
relative quadripolar sensitivity of the group is
greatest (28.8 per cent) in lead X of the
SVEC-III system. The greatest octapolar sensitivity occurs in the Z leads as a group, being
greatest in the axial and Frank systems and
somewhat less in the SVEC-III system. The X
connection of the SVEC-III system consists of
equally weighting the lead-I electrodes with
a supplementary pair of anteriorly located
thoracic electrodes. This synthesis from two
bipolar leads improves the anatomic orientation of the resultant lead axis, but it is interesting to note that it does not materially
reduce the quadripolar sensitivity of lead I,
and it increases the magnitude of octapolar
sensitivity.
BRODY, ARZBAECHER
Attainment of a satisfactory vertical lead
does not seem to offer any serious problems.
The best of the entire group that we studied
is the symmetrical Y configuration,'4 with a
lumped second-degree component of 3.8 per
cent and a third-degree component of 1.8 per
cent.
As remarked upon above, it is the anteroposterior connections of the three lead systems
that tend to deviate most widely from theoretically ideal conditions. It appears that this
undesirable situation can be improved by the
substitution of anteroposterior grid electrodes
as the Z lead. The quadripole sensing properties of both the McFee-Johnston and projected 13 grids are not significantly different
from the Frank Z, but somewhat better than
the SVEC-III and axial Z's. It is in the matter
of octapolar sensing content that the major
gain is achieved, since it is evident in table 2
that the lumped third-degree components of
either grid connection are quite small in comparison to the other three lead Z connections.
Graphic Analysis
Although accurate quantification of lead
parameters was the primary goal of this study,
we have found it quite illuminating to supplement such information with tle qualitative
information that can be derived from the
graphic method of lead-field mapping. The
computer was programmed to accept the coefficients that were derived from the sampling
sphere measurements, and from these data to
compute lead-field potentials at numerous,
systematically located points in three mutually
orthogonal planes passing through the cardiac
center of the torso model. The points were
arrayed in the form of a 12 by 12-cm. square
Cartesian grid, with a 1-cm. spacing between
the individual points. The planes in which this
process was performed were chosen respectively parallel to the frontal, sagittal, and
horizontal planes of the torso model. Interpolation to determine the location of the
desired whole-numbered values of potential
and automatic plotting of the lead-field isopotentials were done according to the principles of a previously described program."
(Circultion, Volumne XXIX, April 1964
539
CORRECTED VECTORCARDIOGRAPHIC LEADS
The metric scale of the plots was approximately 2.5 to 1, with a 0.1-inch resolution of
point location on the ordinates. Immediately
behind each automatically plotted point a
number was printed which indicated the next
order of resolution, giving a net equivalent
resolution of 0.1 mm. Those isopotential maps
of special interest were reproduced manually,
with the computer plots serving as a matrix
for the reproduction.
Back
HORIZ.
Figures 1 through 5 present a series of
particularly pertinent isopotential maps. Visual analysis of the maps is a fairly simple
matter. By definition the lead field of a perfect vectorcardiographic connection is uniform: that is, its flux lines are straight and
parallel, and its isopotential surfaces (which
are normal to the flux lines) are plane and mutually parallel. Therefore the traces of the isopotential surfaces in a plane parallel to the flux
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HORIZ.
Back
SAG IT.
Head
Front
FRONTAL
Head
-111 11T1' 111r 1 _1
i£ _, _ _ 111 11
CR
11
4-1
4-
14
c
ac
it-
0
0
Foot11
_
Foot
X
fo ot
AXIAL
Z
Figure 1
Axial lead system. Maps of the X and Z lead-field isopotential surfaces as they
intersect coordinate planes passing through the cardiac center. In this and the
other illustrations the equipotential interval is 2.0 mv., and the grid interval of the
Cartesian coordinates is 1.0 cm. The constant term of the lead field, po0 is so
chosen that the zero isopotential surface passes through the center of the grid,
which also coincides with the cardiac center. Lead X shows rather good symmetry
of its reciprocal field about the lead axis. This design goal is less well approximated
in lead Z, which shows proximity electrode distortion toward the frontal aspect
in both the horizontal and sagittal plane views.
Circulation, Volume XXIX, April 1964
BRODY, ARZBAECHER
540
Back
HORIZ.
Back
HORIZ.
W_
__
_i
c4a)
_J
Fr ont
Front
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Head
SAGIT.
y
1
\ 1
1
0
J)
_i
1
1
j 1
1
/
Y
U-
ir
A
1
1 1
1
1 1 o
1
'
0
1
11
/
1
"---1
1
Foot
Foot
X
1
1 L
A \ -1
j
FRANK
Z
Figure 2
Frank lead system. Same leads and views as figure 1. Both lead fields appear relatively uniform in the central portions of their horizontal plane views, with proximity
electrode distortion evident toward the margins. In both cases the tendency
toward central region uniformity is limited to the horizontal plane views. This is
a consequence of limiting electrode placement on the body surface to a single
transverse plane.
lines would form
of straight, parallel and
equally spaced lines. Departures from this
a
set
pattern are generally easy to recognize.
Although the illustrations speak rather well
for themselves, some aspects warrant specific
comment. The X and Z lead characteristics of
the three complete vector systems, axial,
Frank, and SVEC-III, are respectively displayed in figures 1, 2, and 3. As is to be expected from the quantitative determination of
coefficients (cf. table 2), none of these lead
fields closely approximates the ideal configura-
tion. The primary design consideration of the
axial system connections is that their lead
fields be symmetrically disposed about corresponding geometric axes passing through the
cardiac center. Figure 1 shows that this condition is met rather well in the case of the X
lead and somewhat less well in the case of
the Z lead. The horizontal plane maps of the
Frank X and Z leads indicate that a considerable degree of correction has been accomplished in the central region. Peripherally,
however, the X lead is distorted toward the
Circulation, Volume XXIX, April 1964
CORRECTED VECTORCARDIOGRAPHIC LEADS
left and the Z lead toward the front by electrode proximity effects. Both leads are less
well corrected out of the horizontal plane.
This is more or less to be expected, since the
leads are made up of body-surface electrodes
which lie only in the transverse plane which
passes through the cardiac center. Except for
some misalignment of orientation in the sagittal plane the Z lead of the SVEC-III system
shows a fair amount of straightening in the
central portion, with the expected electrode
proximity distortion toward the margins of
the maps. Misalignment and especially distorHORIZ.
541
tion are most conspicuous in lead X of the
SVEC-III connections. This appears to be the
least desirable of the various corrected leads.
The best vertical (symmetrical Y) and
second best anteroposterior (McFee-Johnston
grid) connections are shown in figure 4. It is
likely that the symmetrical Y lead does not
deviate in any clinically significant respect
from the theoretically ideal form. The grid
connection approximates the ideal configuration less satisfactorily but seems superior in
this respect to the other Z leads.
Figure 5 illustrates the characteristics of
HORIZ
Bock
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.T
/T /
_-A 11 _1l~~~~~~~~~~fY
M...
Front
Hea
_E _
Front
J
-
- Front
1 Mi-TT
£1 1 1\l 10
FRONTAL
Back
Head
'SAGIT.
Head
c
CE)a
0
i
Foot
X
Foot
SVECIm
z
Figure 3
SVEC-III lead system. Same leads and views as figures 1 and 2. The Z lead
displays about the same amount of distortion as the corresponding axial and
Frank leads (cf. text and table 2). Lead X shows striking proximity electrode
effects. It is the least well corrected connection of the three systems, and except
for anatomic axis orientation is inferior to the tetrahedral X.
Circulation, Volume XXIX, April 1964
BRODY, ARZBAECHER
542
FRONTAL
Ecc __~~~~~~~~~~~~~~~~~
._ _
-
He ad
SAGIT.
Head
__
4-
(0
_j
1
I
1
-I1
0
t __
-7~~Fo
__=
_
_
_
0
C)
_
m
_F_o_t
SYMMETRICAL Y
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H OR IZ .
Head
1I
_ __
_
e
SAGIT.
Back
--
1-11-___
a-0)-J
U
a
0
U-
-I
I
Front
Foot
McFEE-JOHNSTON GRID
Figure 4
Lead-field maps of two relatively wvell corrected derivations. The symmnetrical Y
lead probably does not deviate in a clinically significant nmanner from the theoretic
ideal. The grid type of anteroposterior connection is superior to the other types of
Z leads analyzed. It is likely that further improvemnent in the grid type of leadis feasible.
two other vertical leads, the Frank Y and lead
aV1. Distortion due to the use of a back electrode is evident in the first case, and the proximity effects of the left arm connection are apparent in the second case. In both cases deviation from the anatomic vertical axis is greater
than is necessary, since this kind of distortion
is virtually eliminated in the neck to left leg
and symmetrical Y type of electrode application.
Discussion
The resolution of lead fields into their
spherical harmonics components was first proposed by McFee and Johnston. The importance of their original proposal has increased
greatly with the development of newer knowledge regarding the tensor characteristics of
these components and their relationship to
the various multipolar components of the
equivalent cardiac generator. Now that instrumentation adequate for experimental implementation has been developed, the McFeeJohnston proposal appears to offer the most
systematic and thorough method of quantitaCirculation, Volumse
XXIX,
April 1964
543
CORRECTED VECTORCARDIOGRAPHIC LEADS
tively evaluating lead characteristics in the
biophysics laboratory.
Of the three corrected vectorcardiographic
lead systems analyzed by this advanced method, the axes of McFee's axial connections were
most nearly mutually orthogonal. The design
specifications of this system do not call for
uniform (i.e., distortion free) lead fields, but
simply for symmetry of the fields about the
lead axes. As described above, this design
condition is achieved reasonably well. As
judged from its lumped relative quadripole
Heod
FRONTAL
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1
=-
and octapole sensing characteristics, we find
the axial X lead somewhat better corrected
than the corresponding Frank lead, and considerably better than the SVEC-III lead.
Judged in the same way, the axial Y lead
(same as the SVEC-JJL Y lead except for
scaling factor) is rather superior to Frank's Y
connection. Second-degree distortion of the
axial Z lead is less than that of the other two
systems. Third-degree distortion is not significantly less than that of Frank's Z lead, and
is somewhat greater than in the SVEC-III sysHood
SAGIT.
I
APIWIm
=
£_
X C_==
4-
____
1- 1 t
c
0
LL
-J
TF
Foot
Foot
FRANK Y
FRONTAL
Head
SAGIT.
Head
L
.I
I
I1F
1ot
-
-
-
-1
__ ___
C~~~~~~~~~~
mL I~ -
e
04-
L
I- 1
T1 1 1
.~~.
1
= =-r--= =_-
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Foot
11
1
= 1
c
0
4-
---
1
1
cU
.X
l1l
Foot
TETRAHEDRAL Y
Figure
(AVF)
5
Lead-field maps illustrating two relatively unsatisfactory types of vertical derivation. The Frank Y lead appears fairly uniform in the frontal plane (upper left),
but distortion due to inclusion of a back electrode is evident in the sagittal plane
view (upper right). The frontal-plane view of lead aVF (lower left) shows the
distortion that is due to the proximity of the left-arm attachment.
Circulation, Volume XXIX1 April 1964
544
We find, therefore, that the Frank Z is
less well corrected than either of the other
two, but we can make little distinction between the SVEC-III and axial Z connections
except for the somewhat more satisfactory
lead axis orientation of the latter.
It thus appears that the axial system possesses several relatively favorable characteristics. Equalization of scale factors is poor, however. On the basis of our present information
it is our proposal that in using the axial
system the X channel be recorded at approximately 92 per cent and the Z channel at approximately 66 per cent of the Y channel sensitivity. These recommendations may have to
be modified somewhat after torso models representing other types of bodily habitus have
been similarly studied. The simplicity of constructing and accurately placing the axial
leads was a major consideration in the development of the system.12 Although such matters of clinical practicality are not directly
pertinent to the primary purpose of the present study they may be of some account in the
choice of lead system.
In principle, the grid type of anteroposterior
lead has much to commend it. XVe fail to find
any reports in the literature which indicate
that it has had extensive clinical trial. It might
be difficult or impossible to apply accurately
to female subjects because of the left breast
mass. As far as we are aware the lead vector
magnitude and orientation of the grid connections in the three-dimensional situation,
which are given in table 1, have not previously
been available.
The shape of the human torso is roughly
that of an ellipsoid with three unequal axes.
This goemetric configuration has a direct bearinig on the number of electrodes required to
produce various corrected leads. Because
leads representing the long-axis component of
vector forces (Y leads) may be formed from
remotely located electrodes little difficulty
has been encountered in developing a satisfactory connection. Contrariwise, short-axis
registration (Z leads) requires the use of
proximately located electrodes. The pitfalls
involved in relying on a highly limited num-
tem.
BRODY, ARZBAECHER
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ber of proximity electrodes for accurate vector
registration have been pointed out previously.15 The grid type of anteroposterior connection, although its characteristics can be improved, exemplifies the manner in which numerous proximity electrodes may be uised to
reduce distortion in the registration of shortaxis components. According to the same principles the difficulties involved in reducing the
distortion of X lead registration should be intermediate to those posed by the other two
connections.
In choosing a vectorcardiographic lead system the clinician faces a problem that is less
perplexing now than previously. Partly by
definition and partly by implication the vectorcardiogram is intended as an accurate display of the dipolar fraction of the equivalent
cardiac generator. It is now rather certain that
the equivalent generator exhibits significant
non-dipolar components during ventricular
depolarization.5 '; It is equally certain that the
older, uncorrected lead systems are deficient
in the desired properties of orthonormality
and insensitivity to non-dipolar components.
There is no need for the clinician to abandon
an uncorrected lead system if he believes
that it may possess singular merit. At the same
time, however, he would best serve the clinical science of vectorcardiography by employing in addition one of the better corrected
lead systems. In this way the desired conditions of standardization and distortion-free
technic can be approximated without necessarily eliminating the search for special virtue in other types of lead connections.
Summary
The sensitivity of several corrected vectorcardiographic leads to dipolar, quadripolar,
and octapolar components of the equivalent
cardiac generator was determined in an electrically homogeneous torso model of the human body. A new experimental method, which
insured that the desired parameters were determined for the entire cardiac region, was
employed.
Three complete vector systems were thus
studied: McFee's axial, Frank's, and the SVECCirculation, Volumne XXIX, April 1964
CORRECTED VECTORCARDIOGRAPHIC LEADS
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III. Individual leads also studied included the
tetrahedron X (lead I), the tetrahedron Y
(lead aVF), the "symmetrical Y," and two grid
types of anteroposterior connections.
Except for poor adjustment of scale factors
the axial leads were found to be the best corrected of the three complete systems. With
relative X, Y, and Z channel sensitivities of
0.92, 1.00, and 0.66, respectively, the axial lead
system can be recommended as the best of
the three. Of all the connections studied, we
found the X lead of the SVEC-III system to
be the most inadequately corrected. We
failed to confirm that the inclusion of weighted
back electrode potentials, as employed in
Frank's Y lead, improves the characteristics
of the neck to left leg connection as a vertical
lead.
We find the symmetrical Y lead superior to
both lead aVF and the neck to left leg connection. The grid type of anteroposterior connection is superior to the other types of corrected
Z leads that we investigated, but could probably be corrected further by improvements in
design.
The use of corrected leads is to be encouraged as a means of achieving standardization
and approximating the biophysical conditions
implicit in the basic concept and purpose of
3.
4.
5.
6.
7.
8.
9.
10.
11.
vectorcardiography.
Acknowledgment
We are greatly indebted to Dr. Elliot V. Newman
of Vanderbilt University for making available to us
the torso model used in this study. Mr. Charles
Eddlemon assisted in the preparation of illustrations.
References
1. ARZBAECHER, R. C., AND BRODY, D. A.: Electrocardiographic lead tensor measuring system.
IEEE Tr. Biomed. Electronics. In press.
2. BRODY, D. A., BRADSHAW, J. C., AND EVANS,
J. W.: The elements of an electrocardiographic
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13.
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BRODY, D. A.: The use of computers in electrophysiology. Circulation Research 11: 549,
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BRODY, D. A., AND BRADSHAW, J. C.: The equivalent generator components of uniform double
layers. Bull. Math. Biophys. 24: 183, 1962.
TACCARDI, B.: Distribution of heart potentials
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HORAN, L. G., FLOWERS, N. C., AND BRODY,
D. A.: Body surface potential distribution:
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MCFEE, R., AND JOHNSTON, F. D.: Electrocardiographic leads. I. Introduction; II. Analysis;
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BRODY, D. A., AND ROMANS, W. E.: A model
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J. W.: A theoretical basis for determining
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SCHMITT, 0. H., AND SIMONSON, E.: The present
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MCFEE, R., AND PARRUNGAO, A.: An orthogonal
lead system for clinical electrocardiography.
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BARBER, M. R., AND FISCHMANN, E. J.: A lead
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EVANS, J. W., ERB, B. D., AND BRODY, D. A.:
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BRODY, D. A.: Limited reliability of precordial
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A Comparative Analysis of Several Corrected Vectorcardiographic Leads
DANIEL A. BRODY, ROBERT C. ARZBAECHER and Harry A. Phillips
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Circulation. 1964;29:533-545
doi: 10.1161/01.CIR.29.4.533
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