Download Analog Computer Model of the Vectoreardiogram

Analog Computer Model of the
Vectoreardiogram
By RONALD H. SELvEsT1E, M.D., CLARENCE R. COLLIER, M.D.,
AND ROBERT B. PEARSON, M.D.
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THE formation of a model is an important phase of all scientific thinking
in that it serves to demonstrate or explain
the workings of an inherently complex natural system in terms that can be more readily
understood.
In electrocardiography, the Einthoven triangle' has been used for years as a relatively
simple geometric model of an essentially
complex volume conductor, the human torso.
From the Medical Science Service, Rancho Los
Amigos Hospital, Downey, California.
This model, in spite of many oversimplifications, has served for over 50 years as a useful
reference frame for a vast amount of data
and theory. More recently, the definitive
mapping study by Scher2 of the sequence of
myocardial depolarization in dogs, again a
simple model of a very complex phenomenon,
has served to illuminate and clarify a vast
body of empirical data. This model has added greatly to our understanding of previously
confusing findings in electrocardiography and
vectorcardiography.
The introduction of computer technics
MYOCARDIAL SEGMENTS
Figure 1
In the simulation the heart was pictured as consisting of 20 segments; this diagram gives an
approximation of the direction assigned to the vector representing each segment.
Circulation, Volume XXXI, January 1965
45
46
SELVESTER ET AL.
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(analog or digital) now makes it possible
easily and rapidly to study more sophisticated models, especially those that are nonlinear. These technics have had wide application in engineering and physical sciences and
are currently being utilized to an increasing
extent in biology and medicine. It seems conceivable, therefore, that such a model applied to the electric field of the heart might
enhance the contributions of Scher to our
understanding of the relationship between
myocardial pathology and observed electrocardiographic and vectorcardiographic changes.
Furthermore, the value of a good mathematical model of the heart and the surrounding volume conductor is clear-cut. If the simulation is adequate, then a large number of
experiments could be run mathematically and
the key experiments validated by observations either in animals or in human beings.
Such an approach may well eliminate vast
amounts of time in unproductive experimentation and pinpoint the areas of animal experimentation and human documentation
that are most likely to yield significant results.
The work reported here is a study of the
feasibility of simulating the vectorcardiogram
by means of a relatively simple analog computer model.
Methods and Materials
The approach used in this simulation is based
on concepts derived from Scher's work in the
sequence of ventricular myocardial depolarization
in dogs. Two obvious modifications were necessary to simulate the human vectorcardiogram.
The duration of depolarization was increased to
correspond with that observed in man and the
directional forces were chosen to allow for the
anatomic differences observed in the orientation
of the heart in the dog chest as compared to
the human. An additional liberty was taken by
SEGC MIENTAL FUNCTION
F2(t)
VOLTS
A
%.
-.
--.MP-
4
0
20
30
MLLISECON DS
10
40
5
so
y
Z
1
-
Y = R COS '
DERIVATION OF X ,Y & Z
OF A
SEPTAL
-
CONTR I3UTIONS
SEGMENT
Figure 2
Shown here is the time history of the field strength generated along the axis of a typical segment of the model. Segment 2 from the apex of the interventricular septum is shown with its
assigned direction in space. The contribution of this time varying vector to one of the orthogonal axes, here the Y axis, will be the strength of that vector (R) at a given instant, times
the cosine of the angle that the vector nwkes with the Y axis.
Circulation, Volume XXXI, January 1965
47
ANALOG COMPUTER
M. SEC.
0-- 10 20 30 40 50 60 70 s
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17+ 6q -.618 +.666
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Figure 3
The time history of the current field strength from each of the 20 segments is shown in the
central portion of this figure. To the right are the direction cosirres (L, M, and N) for each of
Circulation, Volume XXXI, January 1965
48
SELVESTER ET AL.
.TO F
FUNCTION
GENERATOR
TIME BASE
XFUNCTION
TIME
EX PASION
AM PLCITUDE
TO F3
ANALOG COMPUTER PRIOGRAM
-TO F4
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VECTORCARDIOGRAM
MODEL
K CHANNELS.
FROM
FK(t)
Figure 4
A diagram
of
the analog computer
program
used in this simulation.
increasing the disparity between the leftward
and rightward forces in the septum. Instead
of the ratio of 2/3 left to right and 1/3 right
to left, as would be suggested by Scher, the
left-to-right forces were assumed to be 80 per
cent of the total energy from the septum. These
changes were suggested by vectorcardiographic
findings in our laboratory, particularly in varying degrees of right ventricular hypertrophy.
In this simulation the heart was pictured as
consisting of 20 segments of myocardium; seven
for the septum, nine for the left ventricle, and
four for the right ventricle (fig. 1). The heart
was assumed to be in a purely resistive, homogeneous, conducting medium of infinite size. The
pickup electrodes were assumed to be on orthogonal axes at such distances that the effect of
the dimensions of the heart was negligible. These
are the same assumptions made in clinical vectorcardiography.
The current fields from each of the 20 segwere assigned as fixed direction vectors
ments
approximately perpendicular
to the
epicardial
surface of the center of each segment. These
directions were chosen to correspond to standard textbook anatomy of the heart. These current
fields were also assigned a magnitude that varied
with time during the passage of the depolarization wave through the segment. Because of the
rapid endocardial conduction of impulses as compared with the slower propagation of the wave
front through the myocardium, the wave front
will enter any given geometric segment somewhat obliquely and, therefore, the current buildup will always be somewhat gradual. The wave
front will leave the segment in the same manner
so that decay of the current field strength will
also be gradual. The value of the field strength
from moment to moment along the chosen vector
is assumed to be proportional to the effective
area of the wave front within that segment.
The duration of the current field from any given
segment will be a function of the thickness of
that segment. Figure 2 represents a typical segment showing the field strength as a function of
time that will be generated by this segment.
these segments. They represent the contribution to the X, Y, and Z orthogonal
of each segment.
axes
respectively
Circulation, Volume XXXI, January 1965
49
ANALOG COMPUTER
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The diagrams published by Scher were used
to assign the time of onset of each segment and
the duration of each segment. The published
time intervals were scaled upward to produce a
total QRS duration of 80 milliseconds. The 20
segments and their time of onset, duration, magnitude, wave form, and the direction cosines assigned are shown in figure 3. The size of the
segments in this simulation varied, and hence
the magnitude of the function representing that
segment varied proportional to the effective surface area that is perpendicular to its vector.
Since this model was to be viewed in an
orthogonal system, it was necessary to determine what the value of each segment would be
as seen in each of three axes (X, Y, Z). These
axis contributions were determined by the product of the scalar magnitude from that segment
and the cosine of the angle between each segment's force and the axis in question (fig. 2).
The simulation was performed on an EAI 231
R analog computer. In the computer (fig. 4),
each segment was embodied in the form of a
variable diode function generator. When driven
by a ramp voltage, it delivered the wave form
which had been previously stored in it. The rate
at which it scanned this wave form was determined by the slope of the ramp. All function
generators were driven by the ramp voltage from
a single ramp generator, whose role might be
considered roughly analogous to the AV node.
This ramp voltage was fed through each one
of 20 operational amplifiers to their corresponding variable diode function generators. These amplifiers acted as a conduction system in that a
bias voltage on the amplifier determined the time
of initiation of each segment. Following each
function generator, an attenuator determined the
scalar magnitude from each segment. This allowed for changes in the magnitude from any
NORMAL
HORIZON TAL
FRONTAL
SAGITTAL
7T
Figure 5
Three planar projections of the computer output. The horizontal plane was produced by
plotting the summed output from the computer for the X and Z axes, the frontal plane the
summed X and Y output, and the sagittal plane the summed Y and Z output.
Circulation, Volume XXXI, January 1965
50
SELVESTER ET AL.
HORIZONTAL PLANE
AX G.i
($1 S4uAweC RI)
SIMULATED
RVH
GAIN INCREASED ON ALL
RIGHT VENTRICULAR SEGMENTS
itV.
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Figure 6
The simulation of right ventricular hypertrophy was accomplished by increasing the output
from the four right ventricular segments by increments as shown. The computer's normal horizontal plane vectorcardiogram is shown in the upper left-hand corner for reference. The
middle figure at the bottom is an actual spatial vectorcardiogram recorded from a patient with
congenital pulmonary stenosis whose right ventricular systolic pressure was 75 per cent of
systemic pressure. The computer simulation resembles the reality in all significant aspects.
given segment. The signal was then fed into
three coefficient potentiometers which multiplied
the signal by the respective cosine for each of
the three orthogonal axes. Negative direction cosines required a sign inverting amplifier. Three
summing amplifiers then summed all the 20 individual X. Y, and Z axis voltages.
A record of each of the three usual projections
(horizontal, frontal, and sagittal) was obtained
by proper selection of the summed X, Y, and Z
voltages. An ink-writing X-Y plotter was used
instead of the more familiar oscilloscope. Because of the limited frequency response of such
recorders (and also so that we could keep up
with what was happening) the "ersatz" heart was
caused to perform at a rate 1/50 of normal.
In the work being reported, abnormalities were
produced only by changes in the magnitude of
one or more segments.
Results
When the summed outputs from the computer, representing each of the orthogonal
axes (X,Y,Z), were plotted in three planar
projections, as seen in figure 5, the summed
outputs did indeed resemble a normal vectorcardiogram.
Right ventricular hypertrophy was simulated by increasing the voltage from right ventricular segments in a stepwise fashion. Figure 6 demonstrates that a reasonable simulation of right ventricular hypertrophy was accomplished in this manner and that
the changes produced did indeed resemble
varying degrees of right ventricular hypertrophy. A clinical vectorcardiogram is shown
Circulatio,z, Volume XXXI, January 1965
ANALOG COMPUTER
51
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for comparison from a patient with valvular
pulmonary stenosis in whom the systolic right
ventricular pressure is 75 per cent of systolic
systemic pressures. Although varying in minor detail, it will be noted that the general
configuration as well as the amplitude and
direction of changes in the model are all quite
similar to that observed in pathologic right
ventricular overload.
Left ventricular hypertrophy was simulated by increasing the scalar magnitude of all
left ventricular segments in a stepwise fashion; this is recorded in the horizontal plane in
figure 7. A spatial vectorcardiogram from a
patient with moderately severe systemic hypertension for the past 10 years is included
for comparison.
A number of simulations of myocardial infarction were done by eliminating one or
more segments at a time. An example of such
a simulated infarct is given in figure 8, in
which three apical segments are removed,
one from the septum and two from the left
ventricular wall. For comparison, a clinical
vectorcardiogram is presented which was
taken from a patient who had an infarction
involving approximately the same mass and
location of myocardium. It should be noted
that the clinical material for comparison was
found after the computer work had been
done and the computer work was not based
on an attempt at curve fitting.
Discussion
This analog computer model of the electrical events of the heart has been based on experimental knowledge of ventricular depolarization. Not only did these results resemble
HORIZONTAL PLANE
c
Nomai/()
SIMULATED
LVH
GAIN INCREASED ON ALL 9
LEFT VENTRICULAR SEGMENTS
Figure 7
Left ventricular hypertrophy is simulated by increasing the output from all left ventricular
segments by increments. The lower right figure is a horizontal plane spatial vectorcardiogram
for comparison from a 72-year-old woman who had had systemic hypertension for at least
10 years.
Circulation, Volume XXXI, January 1965
52
SELVESTER ET AL.
S IMULATED
INFARCT
SEGMENTS
2,8.& 9 OUT
vcc;.
SPATIAL
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CLINICAL IN
AR 70Wd'
I
I
AUTOPSY 523 5
I
Figure 8
Myocardial infarction was simulated on the computer by reducing the output to zero from
certain segments. Here a lateral infarct was simulated. The lower right-hand figure is a spatial
vectorcardiogram from a patient with a large lateral myocardial infarct at autopsy.
normal vectorcardiographic loops, but also
changes based on concepts of pathologic
physiology produced configurations resembling abnormal clinical vectorcardiographic
findings.
When this model has been perfected, it
would seem feasible to introduce these 20
functions as dipoles into the electrolyte medium in either cadaver or artificial torso studies.
Although 20 dipoles is a rather small number,
it appears that a reasonable simulation can be
accomplished with this number. Such applications should greatly enhance our understanding of the validity of various lead systems, since we would have a physical and an
electrical model of the heart where the input
is entirely specified.
Furthermore, it appears quite likely that
most vectorcardiographic diagnostic '<pat-
terns" can be simulated with this simple model. Experimentation may allow us to detect
previously unrecognized alterations in wave
form, permitting diagnosis of infarction or
other processes not possible by present
knowledge and criteria.
The work to date leaves little doubt that a
more sophisticated model can be developed
with computer technics that simulates more
closely the electrical events of the cardiac
generator. It seems likely that a digital program can be written which will simulate the
direct propagation of a wave front as seen in
extrasystoles in addition to normal conduction. It would then be a simple matter to simulate a combination of normal conducton
and direct propagation as seen in bundlebranch block.
The simulation reported here was based on
Circulation, Volume XXXI, January 1965
ANALOG COMPUTER
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the assumption that the heart was small
(that is, all dipoles could be considered as
having a common origin and proximity effects
to any given electrode could be ignored). In
reality this obviously is not true. With digital
computer technics it appears possible to measure the contribution of each one of these dipoles located at differing distances from each
of the pickup electrodes and to test the actual
proximity effects of each. Wilson and Bayley3
have proposed analytical methods of measuring eccentric dipoles within a spherical conducting medium and Okada 4 has developed a
computational solution for a finite cylinder
with an eccentric dipole. A rather long iterative, digital, computational method has recently been developed by Gelernter and Swihart5
to simulate both the irregular boundary of the
thorax and irregular areas of tissue inhomogeneity. It must be confessed immediately
that this is a far cry from the simple analog
simulation reported here. With such a sophisticated model, many of the problems that
plague electrocardiography and vectorcardiography can certainly be evaluated and placed
on a rational foundation. It is our hope that the
further exploration of a combination of our
simulation of the cardiac generator and Gelernter-Swihart simulation of the volume conductor, will remove much of the empiricism and
dogmatism from the field of clinical electrocardiography and vectorcardiography and
place these studies on a more rational basis.
53
sembling known clinical vectorcardiographic
abnormalities.
It is expected that all known vectorcardiographic deviations can eventually be simulated on a rational basis, and, further, that previously unrecognized alterations may be
found permitting diagnosis of infarction or
other processes not possible by present
knowledge and criteria.
The present study strongly supports the
view that most, if not all, of the factors
known to influence the electrical field of the
heart can be simulated by computer technics.
When this is accomplished, it may be possible to remove much of the dogma and empiricism from traditional electrocardiographic
theory and place it on a more rational foundation. The need for further exploration in
this area seems imperative.
Acknowledgment
The authors express gratitude to Mr. Gilbert G.
Moser, for technical and engineering advice and assistance, and to Mr. Jon N. Mangnall for his donation of engineering and computer time at the EAI
Computation Center at Los Angeles.
1.
2.
Summary
This study demonstrates the feasibility of
developing an analog computer model of the
electrical events of the heart, based on a rational application of experimental knowledge
of ventricular depolarization.
Not only did the results resemble normal
vectorcardiographic loops, but also changes
were analogized from concepts of pathologic
physiology that produced configurations re-
Circulation, Volume XXXI, January 1965
3.
4.
5.
References
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Vber die Richtung und die manifeste Grosse
der Potentialschwankungen im menschlichen
Herzen und iuber den Einfluss der Herzlage
auf die Form des Elektrokardiogramms.
Pfluigers Arch. Ges. Physiol. 150: 275, 1913.
SCHER, A., AND YOUNG, A.: The pathway of
ventricular depolarization in the dog. Circulation Research 4: 461, 1956.
WILsoN, F. N., AND BAYLEY, R. H.: The electric
field of an eccentric dipole in a homogeneous
spherical conducting medium. Circulation 1:
84, 1950.
OKADA, R. H.: Potentials produced by an eccentric current dipole in a finite-length circular conducting cylinder. I.R.E. Trans. Med.
Elec. 7: 14, 1956.
GELERNTER, H. L., AND SWIHART, J. C.: A
mathematical-physical model of the genesis of
the electrocardiogram. IBM Research RC
999, 1963.
Analog Computer Model of the Vectorcardiogram
RONALD H. SELVESTER, CLARENCE R. COLLIER and ROBERT B. PEARSON
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Circulation. 1965;31:45-53
doi: 10.1161/01.CIR.31.1.45
Circulation is published by the American Heart Association, 7272 Greenville Avenue, Dallas, TX 75231
Copyright © 1965 American Heart Association, Inc. All rights reserved.
Print ISSN: 0009-7322. Online ISSN: 1524-4539
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