Download An Experimental Study of Burger Triangles Constructed From Toad

An Experimental Study of Burger Triangles
Constructed From Toad Hearts in Situ
By
ZANG Z. ZAO,
M.D.
The present paper presents a method of constructing Burger triangles directly from living toud
hearts in situ. Depolarization and repolarization Burger triangles from same toads were almost
identical. It was shown, that the Burger triangle is more accurate than the Einthoven triangle.
The two expedients of Brody, which simplify the use of the Burger triangle, are illustrated. Burger
triangular shapes from toads approximate those of Wilson, constructed from human subjects
with a current dipole on thorax.
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B
URGER and van Milaan 1 demonstrated
with vector mathematics that the deflection written in an electrocardiographic lead is the scalar product of two vectors,
one of which represents that lead and the other
the dipole moments produced by the cardiac
electric activity. From their human phantom,
they constructued a scalene triangle for the
RLF plane, which practically summarized all
the information concerning the nature of the
electric field within it and that obtainable from
potential differences between electrodes corresponding in location to the limb electrodes
used in clinical electrocardiography. The various aspects of this triangle have been investigated in subsequent studies. t 8 All results suggest, that it is superior to the Einthoven
triangle.
So far an electric dipole has been used as the
source of the cardiac vector. In the present
study living toad (Bufo marinus) hearts in
situ were used. This study included: (1) Construction of Burger triangles of R and T peaks
in various cardiac positions, (2) uses of Burger
triangles and comparison of Burger and Einthoven triangles and (3) simplification of the
use of Burger triangles.
2. Place the toad in a recumbent position on a
cork board. Fix each leg with a German silver needle
electrode on the board. Connect each electrode to a
proper limb cable of a direct writing electrocardiograph*.
3. Open the thorax, expose the heart and mobilize
the two aortas. Fix the heart in different positions
by the rod over the aortic bifurcation.
4. Place a twine ligature around apex. Allow 5 to
10 minutes for the injury current to disappear.
5. Fix the heart vertically toward +90 degrees
by means of the twine (fig. 1 A). Take standard
limb leads (tracing v) with normal speed and standardization.
6. Fix the heart horizontally toward 0 degree
(fig. 1 B). Again take standard limb leads (tracing
h) with same norm.
It should be noted that ventricular configuration
of the toad is symmetrical on each side. It was assumed that its anatomical axis is practically identical in direction with the electrical axis in the RLF
plane.
RESULTS
The standard limb leads from three illustrative cases (toads A, B, C) is shown in figure
2. It should be noted that the tracing h from
toad C was taken when the heart had been
turned horizontally toward ±180 degrees.
The deviation of the S-T segment in various
leads was the consequence of apex ligature.
The heart position was normal in A, slightly
toward left in B, and toward right in C. The
tracing bearing +110 degrees was taken at an
anatomic heart axis of +110 degrees.
The R and T peaks in each lead were measured in millivolts (table 1). Values in paren-
METHODS
Each experiment (fig. 1) was performed as follows:
1. Destroy the central nervous system of the
toad as usual.
Experiments performed at R. Preto Medical
School, Siio Paulo, Brazil.
Presented at 7th Annual Meeting, Brazilian Association for the Advancement of Science, 1955
Received for publication November 11, 1955.
* Helligo, Direct-Electrocardiograph Type 9S00,
Fritz Hellige & Co., Freiburg, Germany.
211
Circulation Research, Volume IV, March 195$
212
BURGER TRIANGLE FROM TOADS' HEARTS
Fio. 1. Experimental arrangement. A, the heart axis was toward +90 degrees, B, toward 0 degrees.
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Burger triangles of R, T peaks, their construction, use, etc,: A Burger triangle may be
constructed graphically according to the
method given by Wilson, Bryant and Johnston.1
This may be described using R peaks from
toad A (table 1):
Lead vector I.—Draw a horizontal segment 14
cm. in length, which represents Ri (10 cm. represents
1 millivolt) from tracing h. Since Ri is positive from
tracing h and negative from tracing v, draw a vertical segment through the right of the horizontal
segment and extend upward 2.5 cm. to represent Hi
from tracing v. Draw the hypotenuse of the right
triangle of which these two segments are the perpendicular sides. This hypotenuse is the positive
direction of lead vector I. It is from the beginning
of its horizontal to the end of its vertical component, 14.3 cm. long and directed toward —10 degrees in the RLF plane.
Lead vector II. Draw a horizontal segment 5 cm.
in length to represent Ri in tracing h. Since Rj is
positive in tracings h and v, extend a vertical segment
1—R and T Peak Potentials in Millivolts from
Toad Standard Limb Leads Electrocardiograms
TABLE
Toads
Ri
A
-0.25
+ 1.6 (+1.4)
-0.6
+2.8 (+3.0)
+0.5
-2.05
-0.15
B
FIG. 2. The classic limb leads electrocardiogram
from toads A, B and C.
theses are corrected to the actual measurement
in order to have the Einthoven law, Li + L3 =
Lj, valid. They differ only slightly from actual
measurements, and in most instances this is
not necessary.
c
Ti
+0.1
-0.7
-0.1
R.
+0.7
+0.5
+ 1.9
+0.7
+2.2
-1.15
+1.7
R<
V
+0.9 (+0. 95)
h
-0.9
V
+2.4 (+2. 5)
ll
-2.4 (-2. 3)
V
+ 1.7
h
+0.9
+ 110°
+ 1.8.5
T,
Tt
+0.7
-0.4
+0.6
Tracing!
+0.6
+0.3
+0.7
V
h
+ 110°
213
ZAO
of 7 em. downward through the right of above
segment. The hypotenuse of this right triangle is the
positive direction of lead vector II. It is 8.6 cm. long
and directed toward +54 degrees in the RLF plane.
Lead vector III.—Draw a horizontal segment 9
cm. long, to represent Rj in tracing h. Since Rj is
negative in tracing h but positive in tracing v, extend a vertical segment 9.5 cm. long downward
through the left of the horizontal segment. The hypotenuse of this right triangle is the positive direction
of lead vector III. It is 13.1 cm. long and directed
toward +133 degrees in the RLF plane.
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The above three lead vectors may be connected to form a Burger triangle for the R
peak, toad A. But it is more convenient to construct a Burger triangle directly on a single
graph, as also described by Wilson. As shown
in the top row of figure 3 both methods give
same results. From left to right there are the
Burger triangles of R peaks from toads A, B,
C and of T peak from toad C. Each graph also
gives six corresponding measurements from
table 1 at proper sides, so that the construction
becomes selfevident. These graphs demonstrate
also the necessity of having the Einthoven law
valid in order to obtain a closed system. I t
should be noted, that the polarities of R and T
in tracing h from toad C were reversed. This
is necessary, because the heart was directed
toward ±180 degrees instead toward 0 degrees
in this case. The lowest common denominator
and positive direction of each lead vector are
summarized in table 2.
For convenience a Burger triangle may be
transformed to a triaxial reference system. 8
The above four Burger triangles were so transformed in mid row of figure 3. Dash lines represent horizon. Each scale mark indicates 0.1
unit. The lead vectors are designated at their
positive sides.
To plot the projection of the heart vector
upon a lead vector it is necessary, before beginning the usual procedure, to divide recorded lead deflections by the length of their
corresponding lead vectors. A major part of the
measurements from table 1 was divided by
corresponding lowest common denominators
from table 2. The results are listed in table 3.
The values shown in this table were used to
plot the vectorial directions in corresponding
triaxial reference systems in the middle row
Fia. 3. Top row, the graphic construction of Burger triangles from left to right that of R peaks
from IOIICIH A, B and C and T peak from toad C. Middle row, corresponding trinxiiil reference systems with calculated cardiac vectorial directions, bottom row, triaxial reference system of Buylcy
with calculated vectorial directions.
BURGER TRIANGLE FROM TOADS' HEARTS
214
TABLE 2—Lowest Common Demoninaton ami Positive
Directions of Lead Vectors.
Lead Vector I
I.e.dJ
R
R
R
T
peak, A
peak, B
penk, C
poiik, C
p.d.
1.43] -10°
1.53;
1.05 + 14°
1.41
Lend Vector II Lead Vector III
Led.
p.d.
0.S6 +54°
1.01 +69.5C
1.24 +62°
1.61 +60°
l.c.d.1
P.d.
1.31 +133°
1.70+132.5°
0.96+118°
1.33 + 116°
Led. ~ lowest common denominator,
p.d. = ponitive direction.
TABLE 3—Quotients of Lead Deflections and Corresponding Lead Vector Lengths.
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Toads
'R'l
'R'l
'R'i
Tracings
A
-0.174
+0.980
-0.39
+ 1.96
-0.071
+0.S14
+0.5S2
+ 1.9
+0.69
+0.68
+0.725
-0.6S7
+ 1.47
-1.35
+0.96
V
h
B
c
li
+ 110°
T,
T'I
-0.07
V
+0.37
+0.52
+ 110°
of figure 3. Then from measurements in table 1
corresponding vectorial directions were plotted
in the Bay ley system (lower row). The results
of three methods are given in table 4.
In this Table it may be observed, that the
R and T axes are practically identical in
direction with corresponding anatomical axes
when the calculation was made in the Burger
triangle. They deviate from each other, when
the Einthoven triangle was used.
Figure 4, A is the triaxial reference system
of T peak from toad C. From this the direction
of R axis of the same toad was plotted when
the anatomic axis was +110. The value obtained was +103 degrees. Figure 4 B is the
triaxial reference system of R peak from toad
C. By plotting direction of the T axis under
same condition as above, it was found to be
+ 111 degrees. Figure 4, C is the triaxial reference system of peak R from toad A. Using
the direction of R axis from toad C, when the
anatomical axis was +110 degrees, the value
obtained (+82 degrees) deviates even more
from the anatomical axis than the value obtained by use of the Einthoven triangle (+94
degrees). The significance of figure 4 is given
below.
Simplification of the use of Burger triangle:
Brody9 transformed a hypothetic Burger triangle into a triangular coordinate plot, which
(1) obeys the Einthoven law, (2) synthesizes
a set of instantaneous scalar lead data into a
unique, directed line segment within the triangle or, conversely, (3) projects the representation of the cardiac dipole moments as a single
vector quantity on the sides of the triangle so
as to yield a set of scalar extremity leads. The
total number of divisions on each side should
be proportional to the square of the length of
the sides. Construction involves drawing perpendicular lines to the sides of the Burger
triangle from each of the scale marks to cover
that figure. With a slightly modified technic
such a triangular coordinate plot was constructed for peak R from toad C (fig. 5A).
The following technic wns used:
1. Divide lead vector I into equal parts (for
example 5) with 4 points on it. From these points
TABLE 4—Correlation between Anatomic Heart Axes
and Electric Axes, Calculated in Einthoven Triangle and
Burger Triangles.
Toads
R Axis
(Burger)
(Einlhoven)
Anatomic Heart
Axia
A
+90°
0°
+90°
0°
+ 108°
+ 104°
-10°
+ 114°
-18°
+94°
vertical
horizontal
vertical
horizontal
+ 110°
+98°
+ 110°
B
C
T Axis
+ 106°
Fio. 4. A and B illustrate that in the Burger
triangles, R and T peaks from a same toad may be
interchanged with practically the same accuracy. C
illustrates that a "normal" Burger triangle may not
be used for a dextrocardiac subject, because tho
result is even more inaccurate than that obtained
from the Einthoven triangle.
215
ZAO
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FIG. 5. A, triangular coordinate plot of Brody from It peak, toad C. B, Corresponding triaxiul
reference syHtem with unequal Brody divisions on lead vectors, and vectorial directions, which
were plotted from deflections as usual.
draw perpendicular lines to lead vector II. Cover
the triangle completely with parallel lines of equal
inter-spacing. The length between any two neighbouring perpendicular lines on lead vector II equals
one division of lead vector II.
2. Divide lead vector II also into 5 equal parts
with 4 points on it. From these points draw perpendicular lines to lead vector I. The length between
any two neighbouring perpendicular lines on lead
vector I equals one division of lead vector I.
3. Draw perpendicular lines to lead vector III in
such a way that they intersect the meeting points
of perpendicular lines to lead vectors I and II. The
length between any two neighbouring perpendicular
lines on lead vector III equals one division of lead
vector III.
The Brody division is of unequal length on
the three lead vectors. In present case the
lowest common denominators of them on lead
vectors were I, 1.G5; II, 1.40; III, 1.8.
The same author suggested the transformation of the triangular coordinate plot into an
axial reference system. In the case of bipolar
limb leads this may be accomplished by plotting
the positive sides of lead vectors I, II, and III,
and their proper scale divisions, as arising from
a single point of origin. For the sake of completeness the negative of each lead vector, together with corresponding divisions, may also
be plotted. Such a system is shown in figure
5B. It is transformed from figure 5.4 and has
the same significance. Therefore, it can be used
as usual, without at first dividing each deflection by the corresponding lead vector length.
Using the measurements given in table 1 the
directions of the R axis from toad C were
plotted in three instances: when the anatomical
heart axis was vertical, horizontal, and toward
+ 110 degrees (fig. 5). In each instance, the
direction of the R axis was practically identical
with the anatomic axis in the RLF plane.
DISCUSSION
During the inscription of R and T peaks in
electrocardiograms of toads, the cardiac dipole
has practically the same direction as the anatomic heart axis in the RLF plane, when the
Burger triangle is used. This does not necessarily mean that the electric axis and anatomic
axis coincide.
Triangles of R and T peaks of a same toad
are very similar; they can be interchanged
with practically same accuracy (figure 4A and
B). Their non-identity could be within the
limits of experimental errors. If Schaefer's
hypothesis that QRS and T dipoles are different
and occupy different regions in heart10 is correct and applicable to toads, then triangles of
R and T peaks of a same toad ought be different.
Burger triangles in these experiments resemble those of Wilson and associates.2 When
the toad heart was at its original position, the
triangle was usually slightly scalene, lead
vector III was larger than lead vector II, and
the angle between lead vector I and the horizontal was negative. When the heart was fixed
to the left of its original position at the same
horizontal level, the triangle was of the same
general configuration except that it was more
216
BURGER TRIANGLE FROM TOADS' HEARTS
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scalene; the more the heart was shifted to the
left the more the accentuation. When the heart
was fixed to the right of its original position at
the same horizontal level, lead vector II was
larger than lead vector III and the angle which
defines the direction of lead vector I was positive.
They differ in that triangles of the toad are
broader. This is not surprising, when one considers such differences in shape as nonhomogeneity of tissues, sources of dipoles, cardiac
rotation and spread of impulses.
The influence of the spread of the dipole
moments of the heart, i.e., the effective size
of the cluster of individual dipoles and the
mobility of the assumed resultant dipole is by
no means negligible. The difficulty remains
of dealing practically with such spread in
bundle branch block and premature beats.
If, incidentally, a "normal" Burger triangle is
used for a dextro-cardiac subject, results will
be even more inaccurate than if the Einthoven
triangle is used (fig. 4C). Despite these factors,
it may be said that the Burger triangle is
superior to the Einthoven triangle, because it
gives accurate experimental results, regardless
of thorax form, tissue non-homogeneity and
eccentricity of the assumed heart dipole.
SUMMARY AND CONCLUSIONS
Burger triangles were constructed for R and
T peaks from standard limb leads of toads
whose hearts were placed in various positions.
The method is described in detail.
The triangles for R and T peaks of a same
toad were very similar to each other, though
not quite identical. It can not yet be said
whether this is within the limits of experimental errors or whether this supports the
hypothesis of Schaefer.
Triangles from toads were similar to those
described by Wilson and associates, except
that they were broader. It is shown that the
Einthoven triangle does not give accurate results and that the Burger triangle eliminates
potential errors. Brody's simplification of the
Burger triangle was found valid for the toad's
heart.
SUMMARIO IN INTERLINGUA
Triangulos de Burger esseva construite pro
culmines de R e T ab derivationes de extremitate standard in bufones con cordes in varie
positiones. Le methodo es describite in detalio.
Le triangulos pro culmines R e T de un sol
bufon esseva similissime ben que non integremente identic. II es non ancora possibile decider
si isto cade intra le limites de errores experimental o si illo supporta le hypothese de
Schaefer.
Le triangulos ab bufones esseva simile a illos
describite per Wilson e associates, excepte que
illos esseva plus large. Es demonstrate que
le triangulo de Einthoven non produce resultatos accurate e que le triangulo de Burger
elimina errores potential. Le simplification del
triangulo de Burger introducite per Brody se
provava valide in le caso del corde de bufon.
1
1
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vector and leads, I. Brit. Heart .7. 8: 157, 1946.
II. Brit. Heart J. 9: 154, 1947. III. Brit. Heart
J. 10: 229, 1948.
WILSON, F. N., BRYANT, J. M. AND JOHNSTON,
F. D.: On the possibility of constructing an
Einthoven triangle for a given subject, Am.
Heart J. 37: 493, 1949.
3
BECKING, A. G. TH., BURGER, H. C. AND VAN
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Brit. Heart J. 12: 339, 1950.
* MCFEE, R., STOW, R. AND JOHNSTON, F. D.: Ex-
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leads using fluid mappers. Circulation 6: 21,
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BRODY, D. A. AND ROMANS, W. E.: A model which
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FRANK, E. AND KAY, C. F.: Frontal plane studies
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ZAO, Z. Z.: Beitrag zum Burgerschen Dreieckschema. Ztschr. f. Kreislaufforech. 44: 593,
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-—: Burger triangle as a method for correcting
inaccuracies of Einthoven triangle. Science 122:
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9
BRODY, D. A.: The meaning of lead vector and the
Burger triangle. Am. Heart J. 48: 730, 1954.
10
SCHAEFER, H.: Das Elektrokardiogramm, Theorie und Klinik. Berlin-Gottingen-Heidelberg,
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An Experimental Study of Burger Triangles Constructed From Toad Hearts in Situ
ZANG Z. ZAO
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Circ Res. 1956;4:211-216
doi: 10.1161/01.RES.4.2.211
Circulation Research is published by the American Heart Association, 7272 Greenville Avenue, Dallas, TX 75231
Copyright © 1956 American Heart Association, Inc. All rights reserved.
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