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Chapter 40
From Frank-Starling relationships to ventriculo-arterial
coupling
R. NAEIJE
Cardiovascular responses to volume loading are often described with reference to
Frank-Starling’s law of the heart. However, the exact formulation of this law, and
how it effectively applies to various haemodynamic conditions is not always clear.
It may therefore be useful to revisit the original observations by Otto Frank and
Ernest Starling, and discuss the different ventricular function curves that have been
derived from their pioneer experiments.
Otto Frank and the isolated frog heart preparation
In 1895, the German physiologist Otto Frank described the response of isolated frog
heart to progressively increased filling pressures [1]. As illustrated in Fig. 1, which
Fig. 1. Left ventricular pressure as a function of time at progressively increased filling
pressure (from 1 to 6) in the isolated frog ventricle. Increased filling pressure is associated
with an increased systolic ventricular pressure [1]
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represents the frog’s left ventricular pressure as a function of time recorded during
one of his experiments, the increase in initial tension, or the ventricular pressure
at the onset of contraction, was associated with an increase in the peak pressure
developed during systole. Frank recognised that such changes in the initial tension
were probably accompanied by changes in the resting fibre length. He proposed
that this behaviour of cardiac muscle was similar to that of skeletal muscle when it
is stretched progressively to greater initial lengths prior to contraction.
In 1898, Frank went further to characterise the contractions of the frog ventricle
in a pressure-volume diagram [2]. As shown in Fig. 2, the diagram was made of an
upper curve (“isomet maxima”) corresponding to the peak pressures produced by
the ventricle during isovolumic contractions at increasing resting volumes, thus
defining systolic elastance, and a lower curve (“isomet minima”) corresponding to
pressures passively increased at progressively increased resting volume, thus defining diastolic elastance. In the condition of an ejecting beat (stippled line), systolic
isotonic pressures (“isoton maxima”) fell below the systolic elastance curve, while
diastolic pressures were on the diastolic elastance curve, as one would expect.
However, end-systolic pressure remained below the systolic elastance curve, which
is surprising because end-systole is the only point of the ejecting beat pressure-volume curve with entirely isometric ventricular contraction. Frank attributed this to
history dependence, meaning that the same end-systolic elastance is obtained only
at pre-defined end-diastolic volume and time course of pressure-volume events.
Later studies demonstrated that such a history dependence is in fact trivial in
mammalian hearts. Therefore, end-systolic pressure at a given end-systolic volume
Fig. 2. Pressure-volume diagram of a frog ventricle, in non-ejecting and ejecting conditions.
The systolic elastance curve (isomet maxima) shows a maximum followed by a downsloping
portion. The diastolic elastance curve (isomet minima) shows a curvilinear increase in slope.
The end-systolic point of the ejecting ventricle pressure-volume loop (stippled line) falls on
a curve (unterstutz) that is below the systolic elastance curve, in keeping with a history-dependence phenomenon [2]
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can be used as an index of contractility as well as the quasi-linear portion of the
systolic elastance curve.
Ernest Starling and the canine heart-lung preparation
In 1914, Ernest Starling and his coworkers described the intrinsic response of the
heart to changes in venous return and arterial pressure in a canine heart-lung
preparation [3]. In that preparation, the right atrium was connected to a blood-filled reservoir allowing controlled changes in venous return, the right ventricle
pumped the blood through the pulmonary circulation with lung artificially ventilated to allow for normal oxygenation, the pulmonary venous return returned to
the left atrium and from there to the left ventricle, which pumped the blood into a
systemic blood pressure circuit returning the blood into the reservoir. Peripheral
resistance was adjusted by means of a pressure-limiting device made of a collapsible tube within a pressure chamber, since then called a “Starling resistor”. Cardiac
output was measured by temporarily diverting the flow returning to the venous
return reservoir. Atrial pressures and arterial pressure were measured using manometers. Ventricular volumes were measured using a cardiometer made of a glass
chamber connected to a volume recorder.
The effects of an isolated sudden change in venous return on the heart-lung
preparation are illustrated in Fig. 3. On these original tracings of ventricular
volume, aortic pressure and right atrial pressure as a function of time, it is apparent
Fig. 3. Effects of a sudden increase in venous return on ventricular volume, aortic pressure,
and right atrial pressure, in the canine heart-lung preparation. Both end-systolic and
end-diastolic volumes increase with an increase in stroke volume. Ventricular volumes are
decreased after venous return is back to baseline [3]
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that the sudden increase in venous return increased atrial pressure, while blood
pressure was maintained almost unchanged by manipulation of the Starling resistor. Both diastolic and systolic volumes increased rapidly, with an increase in
stroke volume that accommodated for the increase in venous return, and ejection
fraction was increased. Thus, stroke volume increased with the increase in end-diastolic volume. Since end-diastolic volume represents the maximum myocardial
fibre length before contraction, and can therefore be taken as an adequate estimate
of preload, a formulation of Starling’s law of the heart could be that stroke volume
increases with preload.
The effects of a rapid increase in blood pressure are illustrated in Fig. 4, which
also reproduces Starling’s original recordings. The increase in aortic pressure
induced by a manipulation of the Starling resistor was accompanied by a rapid
increase in right atrial pressure and in both systolic and diastolic ventricular
volumes. Stroke volume was maintained in the presence of increased blood pressure through an increase in ventricular volumes and a decrease in ejection fraction.
In this experiment, the formulation of a Starling’s law of the heart as proportional
changes in stroke volume and preload would not be valid anymore. However, the
product of stroke volume by blood pressure actually increased in proportion to
preload. Therefore, a more-adequate formulation of Starling’s law of the heart that
Fig. 4. Effects of a sudden increase in aortic pressure return on ventricular volume, aortic
pressure, and right atrial pressure, in the canine heart-lung preparation. Both end-systolic
and end-diastolic volumes increase with a maintained stroke volume [3]
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holds in the presence of changes in preload as well as in blood pressure is that stroke
work increases in proportion to preload.
This was recognised by Starling when he wrote: “Now here are two conditions
in which the work of the heart is increased and in which this organ adapts itself by
increasing the chemical changes in its muscle at each contraction to the increased
demands made upon it. It is evident that there is one factor, which is common to
both cases, and that is the increased volume of the heart when it begins to contract.
So we may make the following general statement. Within physiological limits, the
larger the volume of the heart, the greater are the energy of its contraction and the
amount of chemical change at each contraction” [4]. This is the most-advanced
formulation made by Starling himself of what would be called his law. It is interesting that he included the notion of “chemical changes”, which was premonitory
of major advances in the molecular understanding of myocardial mechanics that
occurred during the ensuing decades.
Ventricular function curves
The functional state of a skeletal muscle is best described by active and passive
tension-length relationships. This extrapolates to the intact ventricle as a pressure-volume diagram. As already mentioned, Frank used this diagram to describe the
functional state of frog ventricles. Isovolumic pressure-volume relationships illustrated the paper by Patterson et al. [3], but Starling never built such curves from
raw data generated by the canine heart-lung preparation. Ventricular pressure-volume curves were validated by Suga et al. in the late sixties [5, 6]. It is now well
established that instantaneous measurements of ventricular pressures and volumes allow for the definition of preload as end-diastolic volume and load-independent contractility as end-systolic or maximal elastance (Emax) [7]. The assumption that end-systolic pressure-volume coordinates are reasonably well described by a linear approximation has been verified to be correct over physiological
ranges of pressures and volumes. The approach has been demonstrated to be valid
for the right ventricle as well as for the left ventricle, although with pressure-volume
loops of different shapes. While the left ventricular pressure-volume loop is rectangular, with a well-defined upper left corner allowing for an accurate definition
of end-systolic elastance that coincides with Emax, the right ventricular pressurevolume loop has a triangular shape with a rounded upper left shoulder, and Emax
occurs before end-systole because of the normally low pulmonary arterial impedance [8].
Afterload can be defined by maximum wall stress, which is dependent on the
product of ventricular pressure and volume, corrected for wall thickness [7].
Afterload corresponds to the upper right corner of the pressure volume loop. Since
maximum wall stress is dependent on both volume and pressure, it is evident that
an increase in end-diastolic volume at unchanged mean blood pressure is associated with an increase in afterload. As any increase in afterload is quickly accompanied by an adaptative increase in ventricular volumes, it appears that, in intact
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ventricles, like demonstrated in isolated myocardial strips, preload and afterload
are necessarily interdependent.
Afterload can also be defined by arterial hydraulic load, calculated from a
spectral analysis of arterial pressure and flow waves, or more simply by arterial
elastance, that is mean arterial pressure divided by stroke volume [7].
Generating ventricular pressure-volume curves at the bedside is limited by the
technical difficulties of the measurements of instantaneous pressures and volumes.
Accordingly, surrogate cardiac, or ventricular function curves still called Starling
curves, can be built by plotting stroke volume or stroke work as a function of atrial
pressure, as introduced by Sarnoff et al. [9] (Fig. 5) or ventricular output as a
Fig. 5. Ventricular function curves expressed as ventricular stroke work versus atrial
pressure [9]
function of atrial pressure as introduced by Guyton et al. [10] (Fig. 6). Both
functional curves are easily generated from bedside haemodynamic measurements, and have been shown to be relatively sensitive to changes in preload,
afterload and contractility. The ventricular output curve is the less-accurate reflection of ventricular function changes, but the expression of cardiac output as a
function of right atrial pressure has the advantage of allowing a graphical analysis
of the coupling between cardiac function and systemic venous return [10].
Heterometric versus homeometric autoregulation of ventricular function
A close inspection of Starling’s original recordings of the effects of changes in
loading conditions on ventricular volumes shows a tendency for ventricles to
return to initial control volumes while increased loading is maintained, and a
marked decrease in ventricular volumes after return to the initial baseline loading
From Frank-Starling relationships to ventriculo-arterial coupling
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Fig. 6. Ventricular function curves expressed as ventricular output versus atrial pressure [10]
conditions (Fig. 3). In fact, later experiments showed that dimension-related autoregulation, or heterometric autoregulation, would reach a maximum after 20 to 30
s, with a progressive return to initial volumes within the next 5 minutes while
maintaining increased stroke work, indicating the existence of another dimensionindependent mechanism. This mechanism has been named “homeometric” autoregulation by Sarnoff et al. [11], and is also alluded to as the “Anrep effect” [12].
Homeometric autoregulation of the heart corresponds to an increase in contractility in the presence of afterload. The molecular mechanisms of stretch-induced
increase in contractility allowing for the heart to adapt to loading conditions with
limited dimension change remain incompletely understood. Heterometric autoregulation is important essentially for beat-by-beat ventricular adaptation to changes
in venous return and/or arterial impedance. However, homeometric autoregulation takes over most of the adaptative process after only a few minutes, and is
predominant in the longer term.
Ventriculo-arterial coupling
Ventricular function is coupled to venous return, and this coupling can be graphically analysed using ventricular function and venous return curves [10]. Ventricular function is also coupled to arterial hydraulic load. Sunagawa et al. showed
that this coupling can be graphically analysed on a pressure-volume diagram, as
shown in Fig. 7 [7, 13]. The diagram allows for the determination of Emax and of
arterial elastance (Ea), and the calculation of an Emax/Ea ratio. Complex mathematical modelling shows that the optimal matching of systolic ventricular and
arterial elastances occurs at an Emax/Ea ratio around 1.5. Isolated increase in Ea,
or decrease in Emax, reduce the Emax/Ea ratio, suggesting uncoupling of the
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Fig. 7. Calculations of maximum elastance (Emax) and arterial elastance (Ea) on pressurevolume diagrams, with effects of changes in afterload, preload, and contractility [7]
ventricle from its arterial system. Everything else being the same, a decrease in
Emax/Ea is necessarily accompanied by a decrease in stroke volume. On the other
hand, an isolated increase in preload is associated with an increase in stroke volume
with unaltered ventriculo-arterial coupling.
Application to the right ventricle: the single-beat method
The thin-walled right ventricle is sensitive to changes in loading conditions. Right
ventricular failure is associated with a poor prognosis whatever the initial aetiology.
However, the complex geometry of the right ventricle makes functional evaluations
with measurement of instantaneous volume changes technically difficult, and the
particular shape of the right ventricular pressure-volume loop makes single beat
determinations of Emax unreliable. This latter problem can be overcome by measuring pressure-volume loops at several levels of preload [7, 8], but bedside manipulations of venous return are too invasive to be ethically acceptable. In addition,
when applied to intact beings, changes in venous return are associated with reflex
sympathetic nervous system activation, which affects the ventricular function that
is measured. Accordingly, Brimioulle et al. designed a single beat method to study
the coupling of the right ventricle to the pulmonary circulation [14]. The approach
had been initially proposed for the left ventricle by Sunagawa et al. [15]. In its
principle, the method avoids absolute volume measurements and related technical
complexities, to calculate Emax and Ea from instantaneous right ventricular pressure and flow output measurements. As shown in Fig. 8, a Pmax is estimated from
a nonlinear extrapolation of the early and late systolic isovolumic portions of the
right ventricular pressure curve. This estimated Pmax has been shown to be tightly
correlated with Pmax directly measured during a non-ejecting beat [14]. A straight
line drawn from Pmax to the right ventricular pressure versus relative change in
From Frank-Starling relationships to ventriculo-arterial coupling
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Fig. 8. Determination of ventricular end-systolic elastance (Ees) and arterial effective elastance (Ea). Left. The end-systolic pressure of an isovolumic beat is computed by sine wave
extrapolation from the ejecting beat, using pressure values recorded before maximal dP/dt
and after minimal dP/dt. Right. This Pmax value is drawn on the RV pressure-volume
diagram. The ESPVR line is drawn from Pmax down and tangent to the pressure-volume
curve, i.e., from predicted isovolumic beat end-systole to actual ejecting beat end-systole.
The effective arterial elastance line is drawn from end-systole to end-diastole. Ees is the slope
of the ESPVR line, and Ea the absolute slope of the arterial elastance line [14].
volume curve allows for determination of Emax. A straight line drawn from the Emax
point to the end-diastolic relative volume point allows for determination of Ea.
Brimioulle et al. showed that the Emax/Ea ratio determined by this single-beat
method is between 1.5 and 2, which is similar to values reported for left ventricular-aortic coupling, and compatible with an optimal ratio of mechanical work to
oxygen consumption [16]. The Emax/Ea ratio was decreased by propranolol and
increased by dobutamine, and was maintained in the presence of increased Ea due
to hypoxic pulmonary vasoconstriction. In fact, Emax increased adaptedly to
increased Ea in hypoxia, even in the presence of adrenergic blockade, which is
compatible with the notion of homeometric adaptation of right ventricular contractility [14]. Further studies from the same group showed preserved Emax/Ea
ratio in the presence of acutely increased pulmonary artery pressure, in response
to hypoxia or pulmonary embolism, but a decoupling of the right ventricle from
the pulmonary circulation in the presence of excessive increases in afterload
produced by pulmonary arterial banding [17]. Also, the optimal values for the
Emax/Ea ratio were found not different in dogs, goats and in pigs [17]. Finally, right
ventriculo-arterial coupling as assessed by single-beat determinations of Emax/Ea
appeared to be well maintained in piglets with pulmonary arterial hypertension
induced by 3 months systemic to pulmonary shunting [18].
Practically, all that is needed to determine single-beat Emax/Ea ratios is instantaneous pulmonary blood flow and right ventricular pressures. This can be done
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non-invasively by Doppler echocardiography. Doppler pulmonary flow measurements synchronised to invasively measured pulmonary artery pressures has been
reported to allow for realistic pulmonary arterial impedance calculations [19].
Right ventricular pressure can be recalculated from the envelope of tricuspid
regurgitant jets and point-by-point application of the simplified form of the Bernoulli equation [20]. More work is needed to see whether this approach is really
applicable at the bedside. It will be interesting to correlate the findings to newlydeveloped tissue Doppler indices of right ventricular contractility. One of the most
fascinating aspect of the evolution of ideas on ventricular function since the pioneer
experiments of Otto Frank and Ernest Starling is that the basic concepts they put
forward remain essentially true, and may at last enter bedside reality thanks to
recent technological advances in non-invasive Doppler echocardiography.
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