Approximate Derivation for Stereoscopic
Vectorcardiograins with the Equilateral
Tetrahedron
An
By J. A. (CIRONVICH, M.S., J. A.
C. E. JACKSON, M.D., AND G.
ABILDSKOV, M.D.,
E.
BURCH, M.D.
A simple electrode arrangement, which permits the derivation of stereoscopic projections of the
spatial vectorcardiogram, eliminates the need for constructing models. The visual impression obtained from this method agrees satisfactorily with that from carefully constructed models.
method is simpler than that of using adjacent
electrodes employed by Schellong' and modified by Vastesaeger and Rochet.4 The shift of
these planes from the frontal plane is obtained
by means of the resistors connecting RA, LA
and B in the superior plane (see fig. 1). RA',
LA' and F are the apices of the plane whose
right apex is shifted backward along RA-B,
and RA", LA" and F are the apices of the
plane whose left apex is shifted backward along
LA-B. The frontal plane projection of the vectorcardiogram is obtained by using standard
Lead I connections to produce horizontal deflection on the oscilloscope and the unipolar
limb potential from the foot (VF) to produce
vertical deflection.' 2 Similarly, stereoscopic
views are obtained by using the potential difference between RA' and LA' in the plane
RA'-LA'-F to produce horizontal deflection on
the oscilloscope and VF to produce vertical
deflection. The recorded pattern from this oscilloscope is viewed with the left eye. In the
plane RA"-LA"-F the potential difference between RA" and LA" is used to produce horizontal deflection and VF to produce vertical
deflection. The recorded pattern from this oscilloscope is viewed with the right eye.
Ideally, vertical deflection in both RA'-LA'F and RA"-LA"-F should be obtained from
central terminal to foot derivations in each of
these planes. However, the error introduced
by our approximate derivation is probably
small compared with errors inherent in the use
of such an idealized reference frame as the
tetrahedron. Many refinements are obvious but
the stereoscopically obtained spatial vectorcar-
N THE study of spatial vectorcardiography in this laboratory it has been the
practice to construct wire models of the
spatial vectorcardiogram from its frontal and
sagittal projections which are presented on two
cathode-ray tubes.'' 2 These three-dimensional
models seemed necessary to facilitate visualization of the spatial characteristics of the vectorcardiogram, but their construction entailed
considerable time and care. To avoid the necessity of constructing such models, we have
recently developed a simple electrode arrangement which permits satisfactory stereoscopic
views of the spatial vectorcardiogram to be
photographed directly from two cathode-ray
tubes.
One plane is rotated by approximately three
degrees with respect to the frontal plane by
displacement of its right apex backward. The
other plane is rotated through an equal angle
by displacement of its left apex backward.
In the arrangement devised each cathoderay tube presents the projection of the vectorcardiogram onto a plane displaced slightly from
the frontal plane. Since the electrical derivation
of these planes involves the application of only
four electrodes, right arm (RA), left arm (LA),
left leg (F), and back (B), which form the
apices of the equilateral tetrahedron, this
I
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From the Department of Medicine, Tulane University. School of Medicine and Charity Hospital of
Louisiana at New Orleans, and the School of Electrical Engineering, Tulane University.
Aided by grants from a War Contract No. WD49-007-MD389, the Life Insurance Medical Research
Fund, the Mrs. E. J. Caire Fund for Research in
Heart Disease, and a Public Health Service grant.
126
Circulation, Volume II, July,
1950
J. A. CRONVICH, J. A. ABILDSKOV, C. E. JACKSON, AND G. E. BURCH
RA
127
LA
R= 22500 ohms
r= 1200 ohms
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E
FE
FiG. 1 Equilateral tetrahedra showing derived planes used in stereoscopic vectorcardiography.
ing the resistors used in the derivations. It may
be possible to obtain the last of these in a more
flexible manner if the electrodes are suitably
located on the surface of a homogeneous sphere
of resistive material.
A representative stereoscopic vectorcardiogram obtained by this method and stereoscopic
photographs of a wire model constructed from
the frontal and sagittal projections of the same
vectorcardiogram are shown in figure 2.
REFERENCES
FIG. 2A. (Above) Stereoscopic vectorcardiogram
recorded by the method presented in this paper. B.
(Below) Stereoscopic photograph of wire model constructed from frontal and sagittal projections of the
vectorcardiogram shown in A.
diograms appear to be similar to the wire
models carefully constructed from the frontal
and sagittal projections. Possible modifications
of this method include elimination of the 1200ohm resistors in the frontal plane so that RA"
coincides with RA and LA' coincides with LA,
use of separate central terminal deviations in
each plane for vertical deflection, and variation of the angles between the planes by chang-
1CONWAY, J. P., CRONVICH, J. A., AND BURCH,
G. E.: Observations on the spatial vectorcardiogram
in
man.
Am. Heart J. 38: 537, 1949.
2 PANTRIDGE, F. J., ABILDSKOV, J. A., AND BURCH,
G. E.: A study of the spatial vectorcardiogram
in left bundle branch block. Circulation 1: 893,
1950.
3SCHELLONG, F., HELLER, S., AND SCHWINGEL, G.:
Das Vektordiagramm; eine Untersuchungsmethode des Herzens. Ztschr. f. Kreislaufforsch.
29: 497, 1937.
4VASTESAEGER, M. M.
AND ROCHET, J.: La st6riovectocardiographie et la st6rdovectocardioscopie
mdthodes cliniques d'6tude de la rfpartition
spatiale des potentiels cardiaques. Travaux de
laboratoire de P'Institut Solvay de physiologie
29: 40, 1944.
An Approximate Derivation for Stereoscopic Vectorcardiograms with the Equilateral
Tetrahedron
J. A. CRONVICH, J. A. ABILDSKOV, C. E. JACKSON and G. E. BURCH
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Circulation. 1950;2:126-127
doi: 10.1161/01.CIR.2.1.126
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