378 Van Brummelen, Scarborough, and Josenhans

listocardiograms from ultralow-frequency
systems; studies of this kind have already
begun on a modest scale.

Summary

A hydrodynamic model of the systemic
circulatory system was mounted on
an ultralow-frequency ballistocardiograph
(ULF-BCG). The relationship between
stroke volume and _ballistocardiographic
amplitude was investigated for different
pulse wave velocities. It was found that
the amplitude of the displacement ballisto-
cardiogram, as used by Klensch (‘‘J‘‘M
minus “IJ), is strongly correlated to
stroke volume; however, the relationship
is highly dependent on pulse wave velocity.
Closer evaluation of the data showed that
there is a combination of amplitude meas-
urements that also gives a strong correla-
tion between amplitude and stroke volume
but is now independent of pulse wave ve-
locity.

REFERENCES

1. Haas, H. G.: Uber ein neues Verfahren der
Ballistokardiographie, Thesis, Bonn, 1955.
2, Josenhans, W. K, T.: Experimental analysis of
the ultra-low frequency ballistocardiogram by
means of a circulation model, Proceedings of
the Second European Symposium on Ballisto-

cardiography, Bonn, 1961.

3, Klensch, H., and Eger, W.: Ein neues Verfahren
der physikalischen Schlagvolumenbestimmung,
Pfliigers Arch. 263:459, 1956.

4, Klensch, H., Schade, A., Thurn, P., Caspari,
R., and Hilger, N.: Vergleichende Untersuchung

6.

10.

it.

. Talbot, S. A., and Harrison, W.

Am. Heart J.
‘March, 1964

des Minutenvolumens des Herzens mit der
ballistischen und der direkten Fickschen
Methode, Pfliigers Arch. 269:232, 1959.

. Nickerson, J. L.: Estimation of stroke volume

by means of the ballistocardiograph, Am. J.
Cardiol. 2:642, 1958.

Noordergraaf, A.: Physical basis of ballisto-
cardiography, Thesis, Department of Medical
Physics, University of Utrecht, Utrecht,
Netherlands, 1956.

. Rédenbeck, 'M.: Studies on the biophysics of

ballistocardiography, Thesis, Leipzig, 1959.
U. S. Joint Publications Research Service,
Washington, D. C. (available from Dr. Wm. R.
Scarborough).

Rédenbeck, M.: Voraussetzungen fiir die
Méglichkeit der Schlagvolumenbestimmung aus
dem Ballistocardiogramm, Proceedings of the
First Congress of the Society for Ballistocardio-
graphic Research, Zeist, 1960.

Rédenbeck, M.: Grenzen ballistokardiograph-
ischer Schlagvolumenbestimmungen, Ztschr.
Kreislaufforsch. 50:17, 1961.

. Starr, I., Rawson, A. J., Schroeder, H. A., and

Joseph, N. R.: Studies on the estimation of
cardiac output in man, and of abnormalities in
cardiac function from the heart’s recoil and
the blood’s impacts; the ballistocardiogram,
Am. J. Physiol. 127:1, 1939.

: Dynamic
comparison of current ballistocardiographic
methods. Part II, Circulation 12:845, 1955.
Burger, H. C., and van Brummelen, A. G. W.:
Proceedings of the Fourth European Sym-
posium on Ballistocardiography, Lille, 1963
(to be published and edited by Dr. J. F. Mer-
len).

Starr, I.: Studies made by simulating systole at
necropsy. VI. Estimation of cardiac stroke
volume from the ballistocardiogram, J. Appl.
Physiol. 8:315, 1955.



Kelumne 67 Pulse wave velocity in stroke volume determination from ULF-BCG

plotted against ‘‘stroke volume”; the cor-
relation coefficient, r, when all measured
points are included, was +0.74. However,
there is a striking dependence on pulse
wave velocity when this amplitude meas-
urement is employed, even though a high
correlation is present for any single pulse
wave velocity.

It has been known for some time that the
amplitude of the ‘“‘J-wave (b) decreases and
the ‘‘M (a) increases with increasing pulse
wave velocity.’ This phenomenon was also
found in our model experiments (Fig. 3).
It seemed logical, therefore, to determine
whether some linear combination of these
wave amplitudes might not be independent
of pulse wave velocity. As a first trial, we
intuitively took the linear combination
2b-+-a (or “1” J+ “J” M). This combination
makes the final results considerably less
sensitive to inaccurate placement of the
base line than are those calculated from
the formula of Klensch,‘ who uses only @ in
his formula. As an historical note it should
be remarked that Starr! employed a similar
relationship, viz., 21 + J, in one of his
formulas to calculate stroke volume from
the HF displacement record.

The results of this combination are given
in Fig. 5. There is still some dependence on
the pulse wave velocity but much less than
in Fig. 4 (correlation coefficient, 7, =
+0.989). A different linear combination
derived statistically from analog computer
measurements shows even less effect of the
pulse wave velocity. Using the method of
the least squares, and assuming a linear
relationship, the coefficients of 6 and a were
2.0 and 0.8, respectively. The correlation
coefficient was improved accordingly to
+0.994. A plot using these coefficients is
given in Fig. 6. It should be noted here that
these results give only the ratio between
the coefficients. The calibration. factor will
be introduced in later studies. Fig. 6 shows
that the influence of the pulse wave velocity
has been eliminated. Work of a similar
nature relating to the other three variables
(heart rate, peripheral resistance, systolic
ejection time) is now in progress, both in
model experiments and in patients.

This work should be looked upon as a
starting point, the results of which justify
further investigation since an_ essential
variable was eliminated by this method.

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‘STROKE VOLUME CM?

Fig. 5. Relation between the linear combination of
the “IJ and-“J‘M segment amplitudes (or 26-42)
and stroke volume for different pulse wave velocities,
Correlation coefficient is +-0.989.

PULSE
WAVE:
VEL,

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AMPLITUDE 0,80220b
8
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‘STROKE. VOLUME.

Fig. 6. Same as Fig. 5, but with a different linear
combination, 26+0.8a. Correlation coefficient is
+0.994. Dependence on pulse wave velocity is no
longer present under these experimental conditions,

However, the very high degree of correla-
tion found in this hydraulic-model work
between stroke volume and certain ampli-
tude measurements from ultralow fre-
quency displacement ballistocardiograms
should serve to stimulate immediate in-
vestigation of this relationship in human
beings by the simultaneous measurement of
mean stroke volume by indicator-dilution
or Fick techniques and displacement bal-




AM- 5-6

Reprinted from the AMERICAN HEART JOURNAL,
8, March 1964, published by the C. V.
any, St. Louis.

On the elimination of pulse wave velocity
in stroke volume determination from the

ultralow-frequency displacement bal!

A. G. W. van Brummelen, Ph.D.*

W. R. Scarborough, M.D.**

W. K.T. Josenhans, M.D.***
Utrecht, Netherlands

any formulas have been derived te

determine the stroke volume from
the ballistocardiogram (BCG). In the older
formulas the displacement record of a high-
frequency ballistocardiograph (HF-BCG)
was employed as the source of informa-
tion. A more recent attempt utilized the
low-frequency ballistocardiograph (LF-
BCG). In reality, when the high-frequency
ballistocardiograph was used for recording
the ballistocardiogram, the computation of
stroke volume was based on the accelera-
tion of the “internal” center of gravity; in
the case of the low-frequency ballisto-
cardiograph, it was based on motions of
the internal center of gravity, which were
hybrid mixtures of displacement and ve-
locity. In both cases, the external motions
were “impure” and distorted representa-
tions of the “true” internal driving mass-
motions.

The formulas used to derive the stroke
volume from tracings from the high-fre-
quency (Starr) bed involved a square root
relationship between quantities measured
from the BCG and the stroke volume.
However, it turned out that the statistically

tocardiogram

determined exponent was between 1 and
2, and only somewhat closer to 2 than to 1.

In the course of the development of
ballistocardiographic systems it has become
clear that the ultralow-frequency (ULF)
instrument is superior to the other types
of ballistocardiographs, for a number of
reasons, among which is the ease with
which displacement curves can be obtained.
It is only logical, therefore, that the modern
approach in computing stroke volume, or a
quantity proportional to it, from the
ballistocardiogram utilizes the ULF in-
strument only. The most logical attempt
to derive information about stroke volume
would seem to make use of the displace-
ment record, since this curve represents
the shift in the body’s center of gravity
caused by the ejection of blood from the
heart with each systole. Therefore, atten-
tion has recently been focused on the dis-
placement record.}*:*.7 Since there was no
strong evidence that quadratic relation-
ships should be assumed, every investigator
has started with the assumption that the
system is a linear one.

Fig. 1 shows a drawing of the displace-

From the Fysisch Laboratorium, Rijksuniversiteit, Utrecht, Netherlands.
‘This study was supported in part by the Canadian Heart Foundation, Grant X67B.

Received for publication May 6, 1963.

Department of Medical Physics, University of Utrecht, Utrecht, Netherlands.
**Cardiovascular Branch, Georgetown Clinical Research Institute, Aviation Medical Service, Federal Aviation Agency,

Washington, D.C.

‘***Department of Physiology, Dalhousie University, Halifax, Nova Scotia, Canada.



Volume 67

Number 3. Pulse wave velocity in stroke volume determination from ULF-BCG

Fig. 1, Schematic representation of an ultralow-
frequency displacement record.

ment record of a normal person. Haas,! in
his formula for stroke volume, used the
amplitude of the ‘“‘J-peak (6). However,
Klensch' utilized the amplitude of the ‘““M-
peak (a). Rédenbeck’s approach’ is dis-
tinctly different from that used by Haas
and Klensch. The latter use information
drawn from the systolic part of the BCG,
whereas Rédenbeck uses only information
from the diastolic part. Our preliminary
attempts to apply Rédenbeck’s formula
on model experiments were unsuccessful
because of the difficulty of drawing a
straight line through the diastolic part of

the curve. Thus far, only Klensch’s form-
ula‘ has been applied to the records from
human subjects, and he found good agree-
ment with stroke volume as determined
with the Fick method in normal young
subjects under “normal’’ conditions. In
patients, however, ‘normal’ conditions
may or may not exist; heart rate, peripheral
resistance, systolic ejection time, and pulse
wave velocity, for instance, may be quite
different from normal.!° A reliable formula
for stroke volume requires either that the
results be independent of these quantities
or there must be a correction in the formula
that allows for a change in these quantities.

Until now this problem has not been
clarified. It is, of course, a very complicated
one, and it can hardly be expected that all
these difficulties can be solved at the same
time. Therefore, this investigation was
begun by singling out one variable—in
this case, pulse wave velocity—and eval-
uating its effect while keeping the other ones
constant. In order to accomplish this aim,
we decided to use a hydrodynamic model
of the circulatory system, taking for
granted the shortcomings of such a model.

Methods

The model used in this work was devel-
oped by one of us? and is shown in Fig. 2.
It is mounted as a whole on a Schwarzer

i footwards

Fig. 2, Hydraulic circulatory pump.


Am. Heart J,

Van Brummelen, Scarborough, and Josenhans ‘March, 1964

Fig. 3. Samples of displacement “ballistocardio-
grams,” volume curves of the “heart,” and ‘“ven-
tricular” pressures recorded simultaneously using
the hydraulic circulatory analog. The stroke volume
is about the same for the different pulse wave ve~
locities. Calibrations: 0.1 mm. of BCG table de-
flection equals 13.8 small blocks in the records; 1
cm.’ of change in ventricular volume equals 1.07
small blocks; 100 mm. Hg equals 27.8 small blocks.
Heavy vertical time lines are 0.2 second apart.

ULF-BCG (J in Fig. 2), in such a way that
the relative movement between model and
BCG is negligible. It consists of a 1-liter
cylindrical glass jar (2) covered by a
rubber stopper (3) with perforations for a
funnel (4), two carbon rods (5), a pressure
release tube with stopcock (6), and an
air pressure line (7). The glass jar has a
134-inch outlet low on one side for the dual
purpose of (a) connecting the 134-inch
Gooch tube (aorta, &) to the heart, and
(b) housing a low-resistance rubber out-
flow valve (the “aortic valve’). The 134-
inch Gooch rubber tube* is laid out in a
fashion similar to that of the aorta, with a
shorter ascending and a lower descending
branch. The end of the Gooch tube is
connected to a 100-cm. long vertical glass
tube (9) with an open end (10) to prevent
syphoning in the backflow tube (/1). The
funnel (4) collects the returning water.
Between the funnel and jar is a low-pres-
sure valve (‘atrioventricular valve’’). The
electrical resistance between the carbon
rods (5) alters with the level of fluid in the
jar (2) and thus allows one to record the
time course of the volume. The ejection
of the fluid (myocardial contraction) is

‘*Canlab catalogue, 1963: No. 74-983

achieved by an air-pressure-operated truck
windshield wiper which opens and closes
two gas taps. One tap operates the air pres-
sure, and the other 1eleases the air pressure
in the jar. By arranging the opening and
closing times of the two taps and tap 6 in
Fig. 2, one can obtain a wide variation of
pressure contours and pressure maxima.
For this study a bell-shaped pressure con-
tour, beginning and ending at 0 pressure,
was used. To obtain different pulse wave
velocities a number of different colored
strings were wound helically around a
rubber tube which lies on the BCG in the
shape of the aorta. By systematically cut-
ting the strings (first, one string; then two,
three, etc.) it was possible to change the
pulse wave velocity in the range from 13.1
M. per second downward to 4.7 M. per
second in six steps. The volume of the
“heart” could be measured as a function
of time, which made it possible to calculate
the stroke volume. Samples of records are
reproduced in Fig. 3. Pulse wave velocity
was calculated from the time delay of two
pressure curves recorded simultaneously
from the beginning and the end of the
aorta.

Results

The results are represented in Figs. 4,
5, and 6. In Fig. 4 the amplitude of the
“M-peak (a in Klensch’s notation) is

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STROKE VOLUME cM?

Fig. 4. Relation between the height above the base
line of the ““M-peak of the BCG (or a) and stroke
volume for different pulse wave velocities. Correla-
tion coefficient computed using all points is +0.740.
High degree of dependence on pulse wave velocity is
apparent.