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Circulation Research
MARCH
1979
VOL. 44
NO. 3
An Official Journal of the American Heart Association
CONTROVERSIES IN CARDIOVASCULAR
RESEARCH*
How to Quantify Pump Function of the Heart
The Value of Variables Derived from Measurements on
Isolated Muscle
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Gus ELZINGA AND NICOLAAS WESTERHOF
TO DETERMINE cardiac performance, a comparison between the whole heart and isolated (skeletal)
muscle often has been made. Otto Frank (1895)
designed his beautiful experiments on the frog heart
following "the same pattern which Fick and Von
Kries used in their studies of skeletal muscle...."
A similar comparison between heart and muscle
can be found in Starling's formulation of, his "law of
the heart" (Patterson et al., 1914): "The law of the
heart is therefore the same as that of skeletal muscle
that the mechanical energy set free on passage from
the resting to the contracted state depends . . . on
the length of the muscle fibers." Presently, the same
line of thinking prevails, since variables derived
from studies on isolated muscle are determined for
the whole heart to establish its performance (Mason
et al., 1970).
The task of the heart is to transport arterial
blood to the various organs and venous blood to the
lungs. It does this by ejecting a sufficient amount of
blood at a given pressure against the resistance of
the arterial system. Although this pump function of
the heart has been fully recognized since Harvey
wrote his "de motu cordis" (1628), it is still not clear
how to quantify it. Cardiac output, stroke volume,
left ventricular function curves, peak systolic pressure, stroke work, peak wall stress, rate of rise of
left ventricular pressure, maximum velocity of
shortening, and many other variables all have been
put forward as a measure of the function or performance of the heart (Abel, 1976; Ahmed et al.,
1977; Baylen et al., 1977; Frank et al., 1965; Kreulen
et al., 1975; McDonald et al., 1972; Raphael et al.,
1977; Sonnenblick and Downing, 1963). However, a
From the Physiological Laboratory, Free University, Van der Boechoretstraat 7, Amsterdam, The Netherlands.
* This paper is the first part of a "Controversy" on The Value of
Instantaneously Measured Variables in Isolated Muscle to Quantify
Pumping Ability of the Heart. The paper taking the opposing view, by
Drs. Dean T. Mason and Edmund H. Sonnenblick, will be published in a
future issue of the Journal.
single universal quantitative description of the function of the cardiac pump is still lacking. Has the
comparison between isolated muscle and the whole
heart not been fruitful in this respect?
Pump Function of the Heart
How should the pump function of the heart be
characterized? To answer this question it is useful
to turn to fluid pumps, whose pump function is
given by a head-capacity curve. Such a graph relates, for a given setting of the pump, the amount
of fluid it can handle to the pressure head it has to
overcome. This is necessarily an inverse relationship, because for a certain head the pressure opposing flow is so high that output will be zero, whereas
at zero pressure, flow is at its maximum.
The pump function graph of a roller pump which
does not completely occlude the tubing is presented
in Figure 1. Pressure (head) is plotted as a function
of pump output (capacity). Three different settings
of the pump are studied: (1) control, (2) increased
speed of the roller pump, (3) speed of the roller
pump same as during control, but pressure exerted
by the rollers on the tubing is higher (more occlusive position). All three inverse relationships, obtained by varying the height of the outlet tubing
(see inset in Fig. 1), happen in this case to be
virtually linear. An increase in the speed of rotation
causes a more or less parallel shift of the line. A
better occlusion of the tubing results in an increased
ability to generate pressure while the output at zero
pressure remains constant.
The idea of characterizing pump function of the
heart by relating the amount of blood it can handle
per unit time to the pressure it has to overcome is
not new. Already in the last century, as reported by
Frank (1895), investigators had studied the effect of
an increased arterial pressure on cardiac output
(Blasius, 1872; Dreser, 1887-1888; Marey, 1881).
Unfortunately, as Frank correctly pointed out, car-
304
CIRCULATION RESEARCH
E
(D
c
a
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output (ml.seer'')
1 Pump function of an ordinary roller pump
measured at three settings of the pump: • control, A
increased roller speed, -k increased pressure on the
tubing at control roller speed (more occlusive).
FIGURE
diac pump function was in their experiments affected by the various arterial loading conditions
used, because end-diastolic volume was not kept
constant. A similar objection holds for the work of
Starling in which he studied the effect of arterial
pressure on cardiac output (Patterson et al., 1914).
As he himself admitted, he also allowed cardiac
enlargement at higher levels of arterial load. When
we want to determine the pump function of the
heart, it is an essential requirement to keep the
"setting" of the heart constant; i.e., changes in enddiastolic volume or inotropic state are not permitted.
A number of investigators (Von Anrep, 1912;
Muller, 1939; Sarnoff and Mitchell, 1962; Monroe et
al., 1974) have stated that a change in arterial
pressure, which is needed to obtain the graph describing cardiac pump function, is in itself an inotropic intervention (the Von Anrep effect). If this is
so, the setting of the cardiac pump would change
during the measurement of its function, rendering
the description invalid. Elzinga et al. (1977) tested
this possible error in experiments on isolated ejecting cat hearts and in intact dogs with denervated
hearts. They found the inotropic effect of an increase in aortic pressure to be negligible.
Sagawa (1967) was probably the first to relate
systematically left ventricular output to the pressure the left heart has to overcome. He used a
preparation in which mean left atrial pressure was
kept constant, and used mean aortic pressure as a
measure of ventricular load. Later, Herndon and
Sagawa (1969) studied pump function of the whole
heart (left and right in series) in the same way by
keeping right atrial pressure constant. However, the
VOL. 44, No. 3, March 1979
use of mean aortic pressure as a measure of the
pressure head the heart has to overcome has some
drawbacks, as will be explained below.
The use of left ventricular pressure instead of
aortic pressure to plot against left ventricular output for the determination of cardiac pump function
was advocated by Elzinga and Westerhof (1973).
They used mean values to obtain this relationship.
Buoncristiani et al. (1973) averaged the left ventricular pressure over the ejection period only and
plotted that value against mean flow, whereas
Weber et al. (1974) and McGregor et al. (1974)
made graphs of peak ventricular pressure against
stroke volume. Although different in a number of
experimental and theoretical details, all these studies had the same objective: the description of the
pump function of the heart by relating the amount
of blood it ejects to the pressure it has to overcome.
Mean aortic pressure ought not to be used in the
pump function graph, because force generated by
the myocardial fibers, the basic elements responsible for cardiac pump function, is related to the
pressure in the lumen of the ventricle. Experimental
results sustain this point of view. Figure 2 shows
data taken from an experiment in which the effects
of nine different arterial loads on an isolated ejecting cat heart were studied (Elzinga and Westerhof,
1973). These nine different loads were obtained by
combining three values of the arterial compliance
with three values of the peripheral resistance. The
three symbols used in the two plots indicate the
three compliance values. In Figure A, mean aortic
pressure is plotted against mean left ventricular
output, and three relationships are found (solid
lines). The slopes of the three dotted lines are equal
to the three values of the peripheral resistance. This
sensitivity to the differences in input impedance of
the arterial load in the nine situations is lost when
-
BO
-o- •
-
I
ifC ^ U l ' C L »
I
OLJCpUt
FIGURE 2 The effects of different arterial loads on the
output of an isolated, ejecting cat heart. Three values of
arterial compliance (•, V, O) were combined with three
values ofperipheral resistance (dotted lines in A). When
mean left ventricular pressure (B) instead of mean aortic
pressure (A) is plotted as a function of mean left ventricular output, a single relationship is obtained (data taken
from Elzinga and Westerhof, 1973).
HEART AS PUMP/Elzinga and Westerhof
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mean left ventricular pressure is used (Fig. 2B).
That graph therefore appears to be determined only
by the pump function of the left heart.
To obtain the left ventricular pump function
graph, we choose to analyze both aspects of cardiac
pump function (i.e., flow and pressure generation)
in a similar manner. Mean left ventricular output is
found by averaging stroke volume over the complete cycle. Therefore, we prefer averaging left ventricular pressure over the full period to taking (1)
pressure averaged over systole, (2) pressure averaged over the ejection period, or (3) peak left ventricular pressure. When values averaged over the
whole cardiac cycle (mean values) are used, changes
in heart rate affect the pump function curve in the
appropriate manner; i.e., an increase in heart rate
decreases the averaging period proportionally and
vice versa. This is in contrast to relationships obtained by using values averaged over systole, values
averaged over the ejection period, or peak values.
It has been shown that the behavior of the heart
can be approximated by a time-varying compliance
(Suga, 1971; Suga et al., 1973; Suga and Sagawa,
1974). We could demonstrate, for a model mimicking this behavior, that a very close relationship
exists between the compliance changes and the
pump function graph constructed from mean values
(Westerhof and Elzinga, 1978). Intercepts on both
axes and the slope of the line could be expressed in
terms of compliance changes. Another argument in
favor of mean ventricular pressure consists of its
close relationship to myocardial wall force. It has
been shown in papillary muscle and intact heart
that the integral of the systolic force is linearly
related to the energetic costs of contraction (Gibbs
and Gibson, 1970; Weber and Janicki, 1977).
What are the changes in cardiac pump function
produced by changes in initial muscle fiber length
and contractility (for definitions see Noble, 1972)?
The effects of these interventions on the pump
function graph of an isolated ejecting cat heart are
shown in Figure 3 (data taken from Elzinga and
Westerhof, 1978). The three relationships in this
figure are measured over a larger range than the
one shown in Figure 2B, due to differences in experimental technique. When ventricular filling is
increased, the pump function graph shifts in a parallel fashion. An enhancement in contractility results in a rotation of the curve such that the intercept at the mean output axis does not change. Two
multiplication factors, one for the mean pressure
and one for the mean output values, are needed to
describe the shift due to a certain increase in ventricular filling. Only one multiplication factor (for
the mean pressure values) can characterize the
change in pump function resulting from a given
enhancement in contractility (Elzinga and Westerhof, 1978). The similarity between the results obtained from the intact heart and the relationships
found for the roller pump is striking (compare Figs.
1 and 3).
mean (eft ventricular output
FIGURE 3 Pump function graphs of an
305
(ml sec
I
isolated ejecting feline heart determined for: T control, • increased
end-diastolic volume, • increased inotropic state (data
taken from Elzinga and Westerhof, 1978).
Pump Function and Contractility
There has been an extensive search for indices of
contractility of the heart. These measures have to
be, by definition, independent of the initial length
of the muscle fibers and should not be influenced
by changes of arterial load. A great many of the
attempts to find such an index were based on theory
derived from studies on isolated muscle. The forcevelocity relationship attracted particular interest,
because it has been suggested that velocity of
shortening of the contractile element at zero force
(VM,) is independent of initial muscle length in
isolated muscle (Noble, 1973).
However, measurement of (parts of) the forcevelocity relationship in the intact heart is complex.
The complications arise from a number of uncertainties, such as the unknown changes in active
state during the isovolumic contraction period,
what extrapolation procedure to use to obtain VnuX,
assumptions in the calculations, the model to be
used, etc. (Noble, 1972; Pollack, 1970; Sonnenblick
et al., 1969; Van den Bos et al., 1973). Apart from
the more theoretical problems, these indices appear
in experimental practice not to fulfill the criteria of
independence of initial muscle length and arterial
load (Moreno et al., 1976; Parmley et al., 1975;
Quinones et al., 1976; Van den Bos, 1973).
What is the value of these indices in quantifying
cardiac pump function? The majority of indices of
contractility are determined during the isovolumic
contraction period. During this time, dimensions of
the heart are approximately constant, and pressure
and force are linearly related. It is therefore the
period of choice to obtain information on the be-
306
CIRCULATION RESEARCH
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havior of the (average) muscle fiber in the ventricular wall. It is obvious that such indices cannot give
information about the amount of blood ejected at
a given pressure level. There is also no theoretical
reason to think that these indices are in any way
quantitatively related to the amount of blood the
heart can pump against various pressures. Nevertheless, we cannot yet exclude the existence of such
a relationship. Therefore we have compared the
change of the left ventricular pump function graph
due to a change in contractility (see Fig. 3), which
can be quantified by a single multiplication factor,
with the corresponding change in Vm»i,
[ (dP/dtJ/PJn^, and dP/dt™,*. We used for this comparison six experiments in which contractility of the
heart was altered by well-defined postextrasystolic
potentiation, keeping left ventricular end-diastolic
pressure constant (for details see Elzinga and Westerhof, 1978). The results of this comparison (Fig.
4) show that the change in pump function is not
reflected in a similar change in the contractility
indices. The points are not on the line of identity
and the relationships are nonlinear. Moreover dP/
dtm« seems to give an overestimation if used as a
measure of pumping ability, whereas V ^ and [ (dP/
dt)/P]mai are underestimating the effect of this
intervention. Therefore we conclude that changes
in pump function, due to augmented contractility,
are not reflected by changes in indices of contractility which have been derived from studies on
isolated muscle.
Pump Function and Initial Muscle Length
In the comparison between heart and muscle, the
length-tension relationship of skeletal muscle was
first taken into consideration. Frank (1895) stated
that "length and tension changes in skeletal muscle
correspond to changes in volume and pressure (in
the heart)." Even if one ignores such problems as
the existence of an activation sequence in the heart,
the distribution of sarcomere lengths in the wall,
fiber orientation, and the irregularities in geometry,
the transformation of the (isometric) length-tension
curve into the (isovolumic) volume-pressure relationship is complex. This can be demonstrated by
the very simple model shown in the inset of Figure
5 (Gabe, 1974). The muscle fibers in this cylindrical
thin-walled pump all run circumferentially. When
we assume a length-tension relationship for the
sarcomeres in the wall (solid line), we can calculate
the relationship between volume and pressure (dotted line). Because of Laplace's law, the shapes of
the two relationships differ in such a way that the
maximum for the volume-pressure curve is found at
shorter sarcomere lengths. A similar result can be
seen in an article by Monroe et aL (1970) in which
the measured volume-pressure relationship is compared with the volume-calculated stress relationship based on a thick-walled sphere as a ventricular
model.
Starling plotted cardiac output as a function of
VOL. 44, No. 3, March 1979
5O
BO
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dc
9O £ -
ao
7O
/
1
3O
increase
4O
in pump
\S
SO
1
BO
function (%)
4 The relation between the change in "contractility" and the change in pump function resulting
from well-defined potentiated beats. Three different indices of contractility are analyzed.
FIGURE
venous pressure on the right side of the heart (Patterson and Starling, 1914) and related this result to
the length-tension curve obtained from isometric
twitches in isolated muscle (Starling, 1918). This
comparison formed the basis for the formulation of
sarcomere length
1.6
2X3
(</m)
_ 2 A
end- diastolic volume
(cnvl
I
FIGURE 5 For a cylindrical thin-walled pump (inset),
the isovolumic pressure-volume relationship (dotted line)
is calculated from an assumed length-tension relationship (solid line).
HEART AS PUMP/Elzinga and Westerhof
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his "law of the heart" as quoted above. Two remarks can be made against the use of these socalled ventricular function curves as a quantitative
description of cardiac pump function, regardless of
whether stroke work or cardiac output is plotted on
the ordinate. First of all, ventricular end-diastolic
volume, or a closely related variable, is used as the
independent variable in these relationships. This
implies that the setting of the contractile machinery
of the heart at the start of the contraction is different along the horizontal axis because of the changes
in initial muscle fiber length in the wall of the heart.
According to our point of view, as presented above,
pump function of the heart should be determined
with end-diastolic volume and inotropic state of the
heart kept constant. The second objection against
the ventricular function curve as a description of
cardiac pump function is that the former relationship is not determined by the heart alone. It is also
affected by the arterial load. Different function
curves are found when peripheral resistance of the
arterial system is kept constant and when mean
aortic pressure is held at a given level (Elzinga and
Westerhof, 1976). Thus, since a description of cardiac pump function should reflect the performance
of the heart only, the ventricular function curve is
rendered unacceptable.
The question remains whether the similarity between the left ventricular function curve and the
length-tension relationship is indeed as great as
Starling thought it to be. He did his experiments
using a "Starling resistor." This device keeps aortic
pressure at almost a fixed level irrespective of the
amount of blood ejected by the heart. Recently it
has been reported (Mahler et al., 1975) that, in
conscious dogs, end-systolic diameter is hardly dependent on the resting fiber length and hence on
the amount of prior shortening, when systolic pressure is constant. Even in more isolated heart preparations, end-systolic volume at a given pressure
level seems to vary little with different degrees of
filling (Suga and Yamakoshi, 1977). These results
allow us to draw the schematic diagrams of Figure
6. In the top panel of Figure 6, the isovolumic
pressure-volume relation is shown, and diagrammatically drawn are a number of pressure-volume
loops taken at different degrees of ventricular filling,
but against the same ejection pressure. From this
figure a ventricular function curve can be constructed (bottom panel). The horizontal axes are
the same in the two diagrams but, in the function
curves, stroke volume instead of pressure is plotted
on the vertical axis. Instead of stroke volume, cardiac output or stroke work can be plotted equally
well, because heart rate and aortic pressure should
be constant. In Figure 6, stroke volumes can be
found from the horizontal parts of the pressurevolume loops. If end-systolic volume is the same at
all levels of ventricular filling, as is assumed in the
diagram, the function curve will be a straight line,
as is sometimes found (Kissling and Gallitelli, 1977),
even up to the extreme situation in which all valves
307
are open all the time. Since end-systolic volume is,
if anything, somewhat larger for bigger stroke volumes (Suga and Yamakoshi, 1977), a curvature will
occur as is often reported in the literature (Sarnoff
and Mitchell, 1962; Guyton et al., 1973). These
arguments suggest that the shape of the left ventricular function curve is not related to the shape of
the length-tension graph found in isolated muscle.
Conclusions
We show in this paper how pump function of the
heart can be quantified. Subsequently, a number of
quantities, determined in the intact heart but derived from the length-tension and force-velocity
relationships found in isolated muscle, are evaluated as descriptive of cardiac pump function. The
interest in these quantities results from the relevant
comparison between the function of heart and isolated muscle. Since so much basic information is
available on the behavior of isolated muscle, this
knowledge usually is taken as a basis for such a
comparison. However, we demonstrate for a number of variables derived in that way, that they
cannot give a quantitative description of the heart
as a pump.
It seems to us that the efforts to understand
cardiac pump function by applying muscle data and
theory to the whole heart have entered a phase of
diminishing returns. Another more fruitful possibility for bringing heart and muscle together seems to
loft
r o La
(•ft
vwicncuiBr
funcUun
1O
2O
CLTvoa
SO
left ventricular end-diastolic volume Ccrr>3)
FIGURE 6 Schematic representation of the relationship
between the pressure-volume graph of the left heart
(upper panel) and the left ventricular function curve
(lower panel). Two different contractile states are shown
(a and b).
CIRCULATION RESEARCH
308
orient research in the opposite direction, i.e., to
study isolated heart muscle as if it were part of the
ventricular wall.
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measurements on isolated muscle.
G Elzinga and N Westerhof
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Circ Res. 1979;44:303-308
doi: 10.1161/01.RES.44.3.303
Circulation Research is published by the American Heart Association, 7272 Greenville Avenue, Dallas, TX 75231
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