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PULMONARY VASCULAR FUNCTION
R NAEIJE, MD, PhD
Department of Physiology
Erasme Campus of the Free University of Brussels, CP 604
Department of Cardiology
Erasme Academic Hospital of the Free University of Brussels
808, Lennik road
B-1070 Brussels
BELGIUM
Phone +32 2 5553322
Fax +32 2 5554124
Email [email protected]
N WESTERHOF, PhD
Department of Pulmonary Diseases,
VU University Medical Center,
De Boelelaan 1117
P.O. Box 7057, 1007 MB Amsterdam,
THE NETHERLANDS
Phone +31-20 4441887
Fax +31-20 4444328
E-mail: [email protected]
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The pulmonary circulation is a low pressure and high flow circuit. The low
pressure prevents fluid moving out of the pulmonary vessels into the interstitial space,
and allows the right ventricle to operate at a low energy cost. The flow is matched to
ventilation for pulmonary gas exchange. As a low pressure system, the pulmonary
circulation is very sensitive to mechanical influences, and the thin-walled right
ventricle is poorly prepared for rapidly increased loading conditions.
The pulmonary circulation is functionally coupled to the right ventricle.
Pulmonary pressure-flow relationships are determined by a dynamic interaction
between ventricular pump function and mechanical properties of the pulmonary
arterial tree. In this respect, it is always important to remember that the pulsatility of
the pulmonary circulation is greater than in the systemic bed. The ratio of pulse
pressure over mean pressure in the pulmonary artery is about unity (1), while in the
aorta, pulse pressure is about 40% of mean pressure (2) implying that pulsatile
energy to be generated by the right heart is relatively more important.
1. Steady flow pulmonary hemodynamics
Pulmonary vascular resistance
The function of a vascular system is defined pressure difference-flow
relationships.
In the “steady-flow” hemodynamic approach, pressure and flow waves are
summarized by their mean values, and a single point pressure difference-flow
relationship is calculated as a resistance. This provides a single-number description of
the resistive properties, or “function” of the vascular system under consideration.
The functional state of the pulmonary circulation can thus be defined by a
pulmonary vascular resistance (PVR) calculated as the difference between mean
pulmonary artery pressure (PAP), taken as an inflow pressure, and mean left atrial
pressure (LAP) taken as the outflow pressure, divided by a mean flow (Q):
PVR = (PAP – LAP)/Q
This is most often implemented in clinical practice by fluid-filled thermodilution
catheters. These catheters are balloon-tipped, allowing for an estimate of LAP by an
occluded PAP (PAOP).
Sometimes a measurement of LAP or PAOP cannot be obtained, and a total PVR
(TPVR) is calculated as
TPVR = PAP/Q
Since the LAP is not negligible with respect to PAP, TPVR is larger than PVR
and flow-dependent. Thus TPVR is not a correct characterization of the resistive
properties of the pulmonary circulation.
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A resistance calculation derives from Ohm’s law first derived for electric circuits.
The resistance is determined by vessel and fluid properties. A law that governs
laminar flows of Newtonian fluids through non distensible, circular tubes was
originally proposed by the French doctor Poiseuille and later put in mathematical
equation by the German physicist Hagen. The law states that resistance R to flow of a
single tube, is equal to the product of the length l of the tube by a viscosity constant 
divided by the product of fourth power of the internal radius r by , and can be
calculated as a pressure drop P to flow Q ratio:
R = 8 l · / · r4 = P/Q
The ratio of pressure drop and flow of an entire vascular bed accounts for the
resistances in series and in parallel of the individual vessels The fact that r in the
equation is at the fourth power explains why R is mainly located in the smallest
arteries and arterioles (the resistance vessels) and is exquisitely sensitive to small
changes in caliber of these small vessels (a 10% change in radius results in almost
50% change in resistance) Accordingly, PVR is a good indicator of the state of
constriction or dilatation of pulmonary resistive vessels and helpful to monitor
disease-induced pulmonary vascular remodeling and/or changes in tone.
The limits of normal of resting pulmonary vascular pressures and flows as derived
from measurements obtained in a total of 55 healthy resting supine young adult
healthy volunteers (3-5) are shown in Table 1. In that study population, Q was lower
in women, who are smaller than men, and thus PVR calculated to be higher. However,
there were no gender differences in pulmonary hemodynamics after correction body
dimensions.
Earlier studies have shown that aging is associated with a slight increase in PAP
and a decrease in Q, leading to a doubling of PVR over a five decades life span (6-9).
Pressure-flow relationships
The inherent assumption of a PVR calculation is that the PAP-Q relationship is
linear and crosses the pressure axis at a value equal to LAP, allowing PVR to be
constant whatever the absolute level of pressure of flow. While the relationship
between (PAP - LAP) and Q has indeed been shown to be reasonably well described
by a linear approximation over a limited range of physiological flows, the zero
crossing assumption may be true only in case of well oxygenated lungs in supine
resting subjects, suggesting complete recruitment and minimal distension. Hypoxia,
and a number of cardiac and respiratory diseases increase both the slope and the
extrapolated intercepts of multipoint (PAP - LAP)-Q plots (10).
While an increase in the slope of a PAP-Q plot is easily understood as being
caused by a, generally, decreased radius and thus cross-sectional area of pulmonary
resistive vessels, the positive extrapolated pressure intercept has inspired various
explanatory models. Permutt et al conceived a vascular waterfall model made of
parallel collapsible vessels with a distribution of closing pressures (11). At low flow,
these vessels would be progressively de-recruited, accounting for a low flow PAP-Q
curve that is concave to the flow axis, and intercepts the pressure axis at the lowest
closing pressure to be overcome to generate a flow. At higher flow, completed vessel
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recruitment and negligible distension account for a linear PAP-Q curve with an
extrapolated pressure intercept representing a weighted mean of closing pressures. In
this model, the mean closing pressure is the effective outflow pressure of the
pulmonary circulation. If LAP is lower than the mean closing pressure, it is irrelevant
to flow as is the height distal to a waterfall. In that situation, a PVR calculation
becomes misleading because of flow-dependency: increased or decreased flow
necessarily decrease or increase PVR respectively, without change in the functional
state in the pulmonary circulation taking place. These concepts are illustrated in
Figure 1, which represents pulmonary vessels as collapsible with tone or due to
chamber pressure within a device called “Starling resistor”. This device had been
conceived by Starling and his coworkers to control systemic arterial pressure in their
heart-lung preparation. The “waterfall model” of Permutt is also called the “Starling
resistor” model.
However, distensible vessel models have been developed which explain the shape
PAP-Q curves by changes in resistance and compliance (12,13). In fact, as illustrated
in Figure 2, PAP-Q curves can always be shown to be curvilinear with concavity to
flow axis provided a large enough number of PAP-Q coordinates are generated and
submitted to adequate fitting procedure.
However, a de-recruitment can be directly observed at low pressures and flows
(14). Therefore, it seems reasonable to assume that both recruitment and distension
probably explain most PAP-Q curves (15). According to this integrated view, at low
inflow pressure, many pulmonary vessels are closed as an effect of their intrinsic tone
and surrounding alveolar pressure, and those that are open are relatively narrow. As
inflow pressure increases, previously closed vessels progressively open (recruitment),
and previously narrow vessels progressively dilate (distension). Both mechanisms
explain a progressive decrease in the slope of pulmonary vascular pressure/flow
relationships with increasing flow or pressure.
Whatever the model, PVR determinations are better replaced by multi-point
pressure-flow relationships for the evaluation of the functional state of the pulmonary
circulation at variable flow. The problem of in vivo pressure-flow relationships in
intact animals is to alter flow without affecting vascular tone. Exercise to increase
flow may spuriously increase slopes of PAP-Q plots, in normal subjects (16) as well
as in patients with cardiac or pulmonary diseases, leading to linear fitting of PAP-Q
plots with negative extrapolated pressure intercepts (17,18). An infusion of low-dose
dobutamine to increase flow might be preferable (18), although it is always difficult to
exclude a possible flow-induced or β- or -adrenergic receptor mediated changes in
tone, depending on dose and pre-existing functional state.
Most often only a single PVR determination can be obtained for every given
functional state of pathophysiological condition. It is then advised to reason on a
pressure-flow diagram as illustrated in Figure 3. This diagram shows four possible
combinations of flow and pressure changes, with certainties about true changes in
structure- or tone-determined resistance in only 2 of them: decreased pressure with
increased flow as a true decrease in PVR, and increased pressure with decreased flow
as a true increase in PVR, the other combinations remaining in an uncertainty domain.
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2. Effects of exercise
Supine exercise is associated with proportional increases in cardiac output and
pulmonary vascular pressure gradient, with slight to moderate decrease in PVR.
Upright exercise is associated with a marked initial hyperbolic decrease in PVR. At
high levels of exercise, PVR at any given load that is independent on body position.
The sharp curvilinear decrease in PVR at low levels of upright exercise may be
explained by a vascular de-recruitment, together with inherent slight curvi-linearity of
pressure-flow relationships (19).
High levels of exercise markedly increase pulmonary vascular pressures. In
athletes able to increase their cardiac output to 25-35 L/min, PAP may increase to 4045 mmHg, together PAOP increased to 25-35 mmHg (19).
None of previously reported pulmonary hemodynamic measurements at
exercise in normal subjects have included direct measurements of LAP through a left
heart catheterization. However, PAOP at exercise is unlikely to overestimate LAP.
High levels of cardiac output are associated with a complete recruitment of the
pulmonary capillary network, which is the condition for the valid estimation of LAP
by a PAOP. On the other hand, the filling pressures of both ventricles, as assessed by
directly measured right atrial pressure (RAP) and indirectly measured LAP, rise at
exercise in relation to stroke volume and exercise capacity (20). This suggests that the
left ventricle tends to over-use the Frank Starling mechanism (increase stroke volume
by an increased preload, or end-diastolic ventricular volume/pressure) to maximize
cardiac output at the highest levels of exercise (19).
As mentioned above, PVR increases with aging, so that the average slope of
PAP-Q plots during exercise is 1 mmHg/L/min in young adults, but more than
doubles, up to 2.5 mmHg/L/min, in old subjects. Much of the slope of PAP-Q is
caused by an increase in PAOP (or LAP) (7,8,19). Earlier and more important
increase in LAP in older subjects at exercise could be explained by age-related
decreased diastolic compliance of the left ventricle (8).
While PAP-Q relationships at exercise are generally best described by a linear
approximation (19), a sufficient number of measurements at high levels of exercise,
above the anaerobic threshold, may disclose an increased slope as a cause of a
biphasic “take-off” pattern on logPAP-logVO2 (16). Because of the tight relationship
between Q and VO2, this is to be interpreted as an high level of exercise-induced
pulmonary vasoconstriction, caused by sympathetic nervous system activation,
acidosis and decreased mixed venous oxygenation. Increased slope of PAP-Q plots
above the anaerobic threshold may also be related to an increase in LAP. It is
intriguing that the take-off pattern of PAP-VO2 plots at exercise is not observed in
patients pulmonary vascular disease, who rather show a “plateau” pattern (16). The
reason for decreased slope of PAP-VO2 relationships at high levels of exercise in
patients with pulmonary vascular diseases is not clearly understood.
3. Passive regulation of steady-flow pulmonary hemodynamics
Left atrial pressure
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At a given Q, an increase in LAP is transmitted upstream to PAP in a less than one
for one proportion, depending on the state of arterial distension and the presence or
not of a closing pressure higher than LAP (10,15). In a fully distended and recruited
pulmonary circulation, a PAP/LAP is close to unity.
Lung volume
An increase in lung volume above functional residual capacity increases the
resistance of alveolar vessels, that are the vessels exposed to alveolar pressure, but
decreases the resistance of extra-alveolar vessels, that are the vessels exposed to
interstitial pressure. A decrease in lung volume below functional residual capacity has
the opposite effects. As a consequence, the lowest resultant PVR is observed at
functional residual capacity (21).
Gravity
Pulmonary blood flow increases almost linearly from non-dependent to dependent
lung regions. This inequality of pulmonary perfusion is best demonstrated in an
upright lung (22) The vertical height of a lung is on average about 30 cm. The
difference in pressure between the extremities of a vertical column of blood of the
same size amounts to 23 mmHg, which is quite large compared to the mean perfusion
pressure of the pulmonary circulation. Accordingly, the physiologic inequality of the
distribution of perfusion of a normal lung can be explained by a gravity-dependent
interplay between arterial, venous and alveolar pressures. At the top of the lung,
alveolar pressure (PA) is higher than mean PAP and pulmonary venous pressure
(PVP). In this zone 1, flow may be present only during systole, or not at all. Zone 1 is
extended in clinical situations of low flow, such as hypovolemic shock, or increased
alveolar pressure such as during ventilation with a positive end expiratory pressure.
Further down the lung there is a zone 2 where PAP > PA > PVP. In this zone 2,
alveolar pressure is an effective closing pressure, and the driving pressure for flow is
the gradient between mean PAP and PA. As mentioned above, such a flow condition
can be likened to a waterfall since PVP, the apparent outflow pressure, is irrelevant to
flow as is the height of a waterfall. In zone 3, PVP is higher than PA, so that the
driving pressure for flow is PAP – PVP.
At the most dependent regions of the upright lung, there is an additional region
where flow decreases, defining an additional zone 4 (23). This zone 4 has been
attributed to an increase in the resistance of extra-alveolar vessels, because it expands
when lung volume is reduced or in the presence of lung edema. Active tone may be an
additional explanation for zone 4 as it is also reduced by the administration of
vasodilators.
The vertical height of lung tissue in a supine subject is of course much reduced
compared to the upright position, and accordingly, the lung is then normally almost
completely in zone 3, with however persistence of a still measurable increase in flow
from non dependent to dependent lung regions.
Three dimensional reconstructions using single-photon-emission computed
tomography have shown that there is also a decrease in blood flow from the center of
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the lung to the periphery (24). High resolution methods and fractal modeling of the
pulmonary circulation have actually led to the suggestion that the distribution of
pulmonary blood flow would be determined as a consequence of the fractal structure
of the pulmonary arterial tree, with only secondary minor gravity-dependent
adjustments (25). Subtle differences in arterial branching ratios may indeed influence
flow distribution with increased heterogeneity as the scale of the inquiry narrows,
corresponding to the “what is the length of the coastline” effect. However, the
overwhelming evidence remains in favor of the thesis that gravity is the single most
important determinant of pulmonary blood flow distribution (26). Vascular geometry
related small unit heterogeneity of pulmonary blood flow distribution has not been
shown to be relevant to gas exchange.
4. Active hypoxic regulation of steady-flow pulmonary hemodynamics
There is an active intrapulmonary control mechanism able to some extent to
correct the passive gravity-dependent distribution of pulmonary blood flow: a
decrease in PO2 increases pulmonary vascular tone. Hypoxic pulmonary
vasoconstriction was first reported by von Euler and Liljestrand (27), who proposed a
functional interpretation that can still be considered valid. In lung tissue, PO2 is
determined by a ratio between O2 carried to the lung by alveolar ventilation (VA) and
O2 carried away from the lung by blood flow (Q):
PO2 = VA/Q
In contrast with hypoxic vasodilation in systemic tissue, where local PO2 is
accordingly determined by a ratio flow of O2 carried to the tissues (Q) and local O2
consumption (VO2):
PO2 = Q/VO2
The hypoxic pulmonary pressor response is universal in mammals and in birds,
but with considerable inter-species and inter-individual variability. The attributes of
hypoxic pulmonary vasoconstriction can be summarized as follows (28). The
response is turned on in a few seconds, fully developed after 1 to 3 minutes, and more
or less stable thereafter according to the experimental conditions. It is reversed in less
than a minute. It is observed in lungs devoid of nervous connections, and indeed also
in isolated pulmonary arterial smooth muscle cells. Hypoxic pulmonary
vasoconstriction is enhanced by acidosis, a decrease in mixed venous PO2, repeated
hypoxic exposure (in some experimental models), perinatal hypoxia, decreased lung
segment size, cyclooxygenase inhibition, nitric oxide inhibition, and certain drugs or
mediators which include almitrine and low dose serotonin. Hypoxic pulmonary
vasoconstriction is inhibited by alkalosis, hypercapnia, an increase in pulmonary
vascular or alveolar pressures, vasodilating prostaglandins, nitric oxide, complement
activation, low dose endotoxin, calcium channel blockers, 2 stimulants,
nitroprusside, and, paradoxically, by peripheral chemoreceptor stimulation. The
hypoxic pressor response is biphasic, with a progressive increase as PO2 is
progressively decreased to approximately 35 to 40 mmHg, followed by a decrease
(“hypoxic vasodilatation”) in more profound hypoxia.
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The hypoxia-induced increase in PVR is mainly caused by a constriction of precapillary small arterioles (28). Small pulmonary veins also constrict in response to
hypoxia, but this should not normally contribute to more than 20-30 % of the total
change in PVR (29). An exaggerated hypoxic constriction of small pulmonary veins
could explain the development of pulmonary edema which is observed in a small
proportion, in the order of 1-2 %, of subjects rapidly taken to high altitudes (5).
Grant et al (30) used the equations of the control theory and the linear
relationships between lobar blood flow and alveolar PO2 (PAO2) found in the
coatimundi, an animal with a strong hypoxic pressor response, to calculate the
efficiency of hypoxic vasoconstriction as a mechanism to stabilize PAO2. They found a
gain due to feedback (Gfb) of a maximum of 0.9 at a PAO2 between 60 and 80 mmHg,
falling rapidly off outside these values. A Gfb of 0.9 represents an active correction of
47 % of the decrease in PAO2 that would occur in a passive system without hypoxic
vasoconstriction. Mélot et al used the same equations and linear relationships between
compartmental blood flow and PAO2 derived from inert gases elimination data obtained
in healthy volunteers, and found a Gfb of a maximum of 0.63 at a PAO2 of 60 mmHg,
also falling rapidly off at lower and at higher PAO2 (4) A Gfb of 0.63 represents an
active correction by 39 % of a decrease in PAO2 that would occur in a passive system
without hypoxic vasoconstriction. These studies suggested that the hypoxic pressor
response is an only moderately efficient feedback mechanism, acting essentially at
PAO2 values higher than known to occur in severe lung diseases. However, more recent
evaluations of the efficiency of hypoxic pressor rersponse using multicompartment lung
models (31) fed by real data biphasic stimulus-response curves (32) led to the
conclusions that hypoxic vasoconstriction is really effective in improving gas exchange
in severe respiratory insufficiency.
A quantification of the efficiency of hypoxic pulmonary vasoconstriction in
terms of correction of arterial hypoxemia in chronic obstructive pulmonary disease
(COPD) is presented in Figure 4 (32). Patients with COPD are hypoxemic because of
increased dispersion of the distributions of perfusion and ventilation, with increased
perfusion to lung units with a lower than normal VA/Q. Thus, in these patients, altered
pulmonary gas exchange can be quantified by the logarithm of the standard deviation
of VA/Q dispersion. On the other hand, the strength of hypoxic vasoconstriction can
be expressed as PAP in hypoxia divided by PAP in hyperoxia at constant flow. The
magnitude of hypoxic vasoconstriction ranges normally from 1 to 4 in the canine and
in the human species. It can be seen that, in COPD, arterial PO2 may increase by up to
20 mmHg through the effects of vigorous hypoxic vasoconstriction. The
same
analysis was performed in patients with ARDS, who are hypoxemic mainly because
of an increased shunt (32). Thus, in these patients, altered gas exchange can be
quantified by intrapulmonary shunt, expressed in % of cardiac output. In ARDS,
arterial PO2 could increase by as much as 20 mmHg owing to vigorous hypoxic
vasoconstriction. All these predictions are in keeping with the magnitude of decreases
in arterial oxygenation observed in patients with ARDS or COPD due to the
administration of vasodilating drugs that inhibit hypoxic pulmonary vasoconstriction
(32).
The biochemical mechanism of hypoxic pulmonary vasoconstriction remains
incompletely understood (28,33). Current thought is that a decrease in PO2 inhibits
smooth muscle cell voltage-gated potassium channels, resulting in membrane
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depolarization, influx of calcium, and cell shortening. However, the nature of the low
PO2 sensing mechanism remains elusive. Mitochondria and nicotinamide adenine
dinucleotide phosphate oxidases are discussed as oxygen sensors. Reactive oxygen
species, redox couples and adenosine monophosphate-activated kinases are candidate
mediators. The reversal of hypoxic vasoconstriction by profound hypoxia is due to an
activation of ATP-dependent potassium channels (28).
The normal as well as the abnormal pulmonary vascular tone has been shown to
be modulated by a series of endothelium-derived and circulating mediators.
Endothelium-derived relaxing factors include nitric oxide, prostacyclin, and the
endothelium-derived hyperpolarizing factor. The major endothelium derived
contracting factor is endothelin. These observations have been at the basis of efficient
treatments of pulmonary arterial hypertension with prostacyclin derivatives,
phosphodiesterase-5 inhibitors to enhance nitric oxide signaling and endothelin
receptor blockers (34).
The pulmonary circulation is richly innerved by the autonomic nervous system,
which includes adrenergic, cholinergic, and non-adrenergic non-cholinergic (NANC)
(35) However, role played by the autonomic nervous system in the control of
pulmonary vascular tone appears to be minor. The autonomic innervation of the
pulmonary arterial tree is predominantly proximal, suggesting a more important effect
in the modulation of proximal compliance.
5. Pulsatile flow pulmonary hemodynamics
Pulmonary vascular impedance
As already mentioned, the study of the pulmonary circulation as a steady flow
system is a simplification, since pulmonary arterial pulse pressure, or the difference
between systolic and diastolic PAP is in the order of 40 to 50 % of mean pressure, and
instantaneous flow varies from a maximum at mid-systole to around zero in diastole.
Since pressure and flow depend on the heart and arterial load, analysis of wave
shapes alone is of limited use in the characterization of the pulmonary arterial tree.
However, calculation of the relation between pulsatile pressure and flow allows for a
more detailed characterization of the arterial load, than by resistance only. Pulmonary
vascular resistance characterizes the small vasculature, i.e. the resistance vessels,
only. A complete description of pulmonary arterial function requires consideration of
pulsatile pressure-flow relationships, or pulmonary vascular impedance (PVZ).
A PVZ can be calculated from a spectral analysis of the pulmonary arterial
pressure and flow waves (36). This analysis is possible because the pulmonary
circulation behaves close to a linear system, i.e., a purely sinusoidal flow oscillation
produces a purely sinusoidal pressure oscillation of the same frequency. The
sinusoidal pressure and flow waves can be related by the ratio of their amplitudes
(modulus) and the difference in their phases (phase angle). Thus both pressure and
flow are decomposed into a series of sine waves with frequencies 1, 2, 3, etc times the
heart rate, each with its amplitude and phase angle. PVZ is now the ratio of
amplitudes of the sine waves of pressure and flow (modulus) and their phase
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differences, and is graphically represented as modulus and phase angle, both as a
function of frequency. A typical PVZ spectrum is illustrated in Figure 5.
Pulmonary arterial impedance at zero Hz (ratio of mean pressure and mean flow,
PAP/Q = Zo) corresponds to TPVR. Normally, the modulus of the impedance,
decreases rapidly to a first minimum at 2-3 Hz and then oscillates about a constant
value. At low frequencies, the phase angle is negative, indicating that flow leads
pressure and at higher frequencies the phase hovers around zero degrees. The
precipitous fall in modulus and the negative phase of the impedance are a measure of
total arterial compliance. At high frequencies the rather constant modulus and
negligible phase is the so-called characteristic impedance, Zc, of the proximal
pulmonary artery.
The notion of impedance can be explained as follows. For mean pressure and flow
and for low frequencies impedance is mainly determined by the small resistance
vessels, and at zero frequency equal to TPVR. For intermediate frequencies the
impedance is strongly affected by the elasticity (compliance) of the large arteries. For
high frequencies the characteristic impedance of the proximal arteries determines the
input impedance. Together one can say that the higher the frequency the closer you
‘look’ into the arterial tree.
Characteristic impedance is the input impedance without wave reflections. It is
measured as the average modulus at higher frequencies (usually 4-8 Hz). It can also
be measured as the slope of the early systolic pulmonary artery pressure/flow
relationship (Figure 5).
The oscillations of the input impedance about its mean value result from distinct
reflections of waves. Increased magnitude of the oscillations implies increased
reflections. A shift of the first minimum and maximum to higher frequencies indicates
an increased wave velocity or a decreased distance of the dominant reflection site.
Characteristic impedance is depends on the ratio of inertia and compliance of the
pulmonary circulation, and can be approximated by the equation:
Zc = [Inertance/Area Compliance]½ =[Inertia/(A/P)]½ = [(/A)/(A/P)]½
= [(/r2)/(2rr/P)]½
Where  is the density of blood, r the mean internal radius, /A = /r2 the
Inertance and r2/P = 2rr/P the Area Compliance of the proximal pulmonary
arterial tree.
The extent of the oscillations of the input impedance around Zc can be used to
estimate the degree of arterial wave reflection (2), with Rc, an index of wave
reflection, calculated as
Rc = (1 – Δ/Zc)/(1 + Δ/Zc)
There have been reports on PVZ in normal subjects (40) and in patients with
pulmonary hypertension secondary to mitral stenosis, congenital cardiac defects,
congestive heart failure and COPD, and idiopathic pulmonary arterial hypertension
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(37). The general pattern has been that of an upwards shift of PVZ spectra (higher
TPVR and higher Zc) with the first minima and maxima of impedance moduli shifted
to higher frequencies (higher pulse wave velocity thus decreased arterial compliance).
The limited number of available data has not allowed to identify specific patterns, and
even less so the effects of therapeutic interventions. Semi-invasive approaches for the
determination of PVZ with fluid-filled catheters and trans-thoracic Doppler have been
reported in patients with idiopathic pulmonary arterial hypertension (38) and the
results agree with those reported using high-fidelity technology (39).
Pulmonary arterial input impedance is little affected by normal breathing (40), or
by disease processes limited to alveolar or juxta-alveolar vessels (41-42). In contrast,
proximal pulmonary arterial obstruction markedly affects pressure and flow wave
morphology, the PVZ spectrum, and at any given PVR, has more important
depressant effect on right ventricular output (41-43).
The time constant of the pulmonary circulation
As mentioned above the arterial input impedance is a comprehensive and
quantitative description of the pulmonary arterial system. However, the method has
not gained acceptance because of perceived mathematical complexity and difficulty to
interpret data in the frequency-domain domain.
Accordingly, Lankhaar et al modeled PVZ as being determined by a dynamic
interaction between PVR, total arterial compliance Ca and Zc (1,43,44). A practical
application of this approach was in the quantification of the effects of therapeutic
interventions on small and large arteries. These studies also showed that the product
of PVR and Ca, i.e. the time constant of the pulmonary circulation, remained constant
at approximately 0.7 seconds in all circumstances. This is illustrated in Figure 6,
which shows PVR and Ca values from patients with pulmonary vascular diseases of
various severities and origins. The hyperbolic relationship between compliance and
resistance of the pulmonary arterial circulation explains that mild increases in PVR
may already markedly increase right ventricular (RV) afterload because of associated
decrease in compliance. Pharmacological decrease of only mildly increased PVR may
markedly improve RV flow output because of proportionally larger increase in
compliance.
A lately discovered characteristic of pulmonary vascular function has been the
tight correlation between systolic, diastolic and mean PAP, which persists in
pulmonary hypertension of all possible etiologies (45,46). Accordingly, mean PAP
(MPAP) can be calculated from systolic PAP (SPAP) using a simple formula:
MPAP = 0.6 x SPAP + 2 (45) Remarque: en début de texte PAP = MPAP 
conserver la même abréviation au fil du texte ?
and inversely
DPAP = 0.71 MPAP - 0.66 mmHg, and SPAP = 1.50 MPAP + 0.46 mmHg (46).
This notion is of practical relevance as non-invasive evaluations of the pulmonary
circulation in clinical practice often rely on the measurement of a maximum velocity
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of tricuspid regurgitation (TR) to calculate a SPAP using the simplified form of the
Bernouilli equation and a measurement of right atrial pressure (RAP) (47):
SPAP = (TR2 + 4) + RAP
The tight relationships between pulmonary arterial pressures imply that the
response of the pulmonary circulation to insults and diseases is more monotonous
than previously assumed.
Pressure and flow wave morphology
Pressure and flow can also be analyzed by wave form analysis as shown in Figure
10 (48,49). The pressure and flow wave consist of a part that travels from heart to
periphery (forward or initial pressure and flow wave, Pf and Qf) and waves that return
towards the heart (backward or reflected pressure and flow waves, Pb and Qb). The
derivation of forward and backward waves requires measurement of pressure and
flow as a function of time (measured pressure and flow (Pm and Qm) and
determination of characteristic impedance. The mathematical relations are:
P f = (P m + Zc Q m)/2
and
Q f = + P f/Zc
and
Qb = - P b/Zc
and
P b = (P m - Zc Q m)/2
It should be realized that the value of the characteristic impedance is at the site of
measurement of pressure and flow, thus the proximal pulmonary artery. Reflections
and forward and backward waves only certain to oscillatory parts of the pressure and
flow. The analysis does not give information on relations between mean pressure and
flow. Figure 7 shows wave separation in the pulmonary artery of the dog (48).
Increased reflection is obtained by vasoconstriction.
Wave form analysis, separation into forward and backward waves has not been
often attempted in the pulmonary circulation. Furuno et al reported high fidelity
pressure and flow measurements in dogs with pulmonary arterial obstruction either
proximal, by arterial banding, mimicking pulmonary embolism, or distal, by injection
of small glass beads, mimicking ARDS (41). They were able to explain the typical
aspects of late systolic peaking of pulmonary arterial pressure waves and mid-systolic
deceleration, or notching seen in embolic pulmonary hypertension by wave reflection,
i.e. addition of reflected pressure wave and substraction of reflected flow wave on
respective forward waves (41). Nakayama et al reported higher pulmonary arterial
pulse pressures in chronic thrombo-embolic as compared to idiopathic pulmonary
arterial hypertension, with the assumption that this would be explained by wave
reflection, and proposed this as a help to the differential diagnosis between the two
conditions (50). Castelain et al could not confirm this finding, even though some
effect of wave reflection could be identified on pressure wave morphology analysis in
chronic thromboembolic pulmonary hypertension patients (51). The same idea but
focused on flow waves was reported by Hardziyenka et al, who showed shortened
time to notching in patients with proximal obstruction due to thromboembolic
pulmonary hypertension (52).
13
The morphology of pulmonary artery pressure and flow waves in normal subjects
and in pulmonary hypertension is based on the increase in pulmonary vascular
resistance and the decreases in pulmonary arterial compliance and the change in
characteristic impedance. These changes in the arterial system explain the altered
relation between pressure and flow but cannot explain the whole change in wave
shape. Wave shape is also determined by cardiac pump function. It has been shown
experimentally that right ventricular output decreases with an increased afterload thus
if resistance increases and/or compliance decreases (44). The same was recently
reported in patients with pulmonary hypertension associated to systemic sclereosis:
lower cardiac output in these patients as compared to patients with the idiopathic
form of pulmonary hypertension is likely explained by altered right ventricular pump
function (53).
6. Right ventriculo-arterial coupling
Blood pressure and flow depend on the pump (the right ventricle) and the load on
the pump (the arterial system). Therefore in the study of pulmonary arterial
hypertension knowledge of the arterial system alone is not sufficient. It is of special
interest to study the power transfer from pump to arterial load, because it has been
shown that power transfer and ventricular efficiency are near maximal in normal
subjects. A simplified approach to test this has been given by Sunagawa et al (54).
These authors proposed a graphical analysis based on the ventricular pressure-volume
diagram (55,56) of the right ventricle and characterizing the arterial system by means
of its arterial elastance (Figure 8). The diagram allows for the determination of
maximal ventricular elastance (Emax), which is the best possible load-independent
measurement of contractility, and of arterial elastance Ea ≈ PVR/T (with T the R-R
interval), as a measurement of afterload as it is “seen” by the ventricle. The ratio
Emax/Ea ratio is a measure of the coupling of the ventricle and the arterial load. The
optimal matching of heart and load, i.e. where power transfer and cardiac efficiency
are close to maximal, is found when the Emax/Ea ratio is about 1.5. An isolated
increase in Ea (increased vascular resistance), or decrease in Emax (decreased cardiac
contractility), decrease the Emax/Ea ratio, indicating uncoupling of the ventricle from
its arterial system, i.e. lower cardiac efficiency. 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.
However, while Ea equals the ratio of end-systolic pressure, Pes, and Stroke
Volume and can be found from standard RV catheterization, the Emax requires
measurement of at least two end-systolic pressures and volumes, since the endsystolic pressure volume relation does not go through the origin. The common
approach is to reduce RV diastolic filling and measure a series of pressure-volume
loops (55,56), 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. This problem was first approached by
Sunagawa for the left ventricle (57). This so-called single beat method was recently
applied to the coupling of the RV to the pulmonary circulation (58). As shown in
Figure 8, an ‘isovolumic’, i.e. the pressure of a not ejecting beat with pressure Pmax is
14
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 (58). A
straight line drawn from Pmax to the RV end-systolic pressure of the ejecting beat
versus change in volume change (Stroke Volume) allows for the determination of
Emax. A straight line drawn from the end-systolic pressure point to the end-diastolic
volume point determines Ea.
This method avoids absolute volume measurements and related technical
complexities. The Emax is now calculated as Emax = (Pmax – Pes)/SV. With Ea= Pes/SV,
the ratio Emax/Ea = (Pmax – Pes)/Pes = Pmax/Pes – 1. The Emax/Ea ratio determined by this
single beat method is normally around 1.5, which is similar to values reported for left
ventricular-aortic coupling, and compatible with an optimal ratio of mechanical work
to oxygen consumption (54).
The Emax/Ea ratio is decreased by propranolol and increased by dobutamine, and
maintained in the presence of increased Ea due to hypoxic pulmonary
vasoconstriction. In fact, Emax increases 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. On the other hand, the
approach allows for the demonstration that clinically relevant doses of dobutamine do
not affect pulmonary arterial hydraulic load (58).
The single beat approach has been used to show the profound decoupling effects
of inhaled anesthetics in the same setting (59), this being due to the devastating
effects of both negative inotropy and pulmonary vasoconstriction. The method also
showed that prostacyclin, at clinically relevant doses, has no intrinsic positive
inotropic effect on the right ventricle (60).
Most recently, Kuehne et al used magnetic resonance imaging (MRI) together
with RV pressure measurements to generate pressure-volume loops and Emax and Ea
determinations in patients with pulmonary arterial hypertension (61). As compared to
controls, RV Emax was increased from 5.2  0.9 to 9.2  1.2 mmHg/ml/100 g, P <
0.05, but RV Emax/Ea was decreased from 1.9  0.4 to 1.1  0.3, P < 0.05, indicating
an increased RV contractility in response to increased afterload that was however
insufficiently coupled to its hydraulic load, with inefficient mechanical work
production.
15
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19
Figure legends
Figure 1. Starling resistor model to explain the concept of closing pressure within a
circulatory system. Flow (Q) is determined by the gradient between an inflow
pressure, or mean pulmonary artery pressure (PAP), and an outflow pressure which is
either closing pressure (CP) or left atrial pressure (LAP). When LAP > CP, the (PAP
– LAP)/Q relationship crosses the origin (A curve) and PVR is constant. When CP >
LAP, the (PAP - LAP)/Q relationship has a positive pressure intercept (B curve), and
PVR decreases curvilinearly with increasing Q. Also shown are possible misleading
PVR calculations: PVR, the slope of (PAP - LAP)/Q may remain unchanged in the
presence of a vasoconstriction (from 1 to 2) or decrease (from 1 to 3) with no change
in the functional state of the pulmonary circulation (unchanged pressure/flow line).
After reference 10.
Figure 2. Pulmonary artery pressure versus flow at two levels of pulmonary
hypertension are correctly described by a linear approximation over a physiological
range of flows (3-5 L/min). The linearized pressure/flow relationships (dashed lines)
have extrapolated pressure intercepts (open squares) that are positive, suggesting a
closing pressure higher than left atrial pressure PAOP. However, the pressure/flow
relations are better described by a curvilinear fit (fully drawn lines), which takes into
account the distensibility of the pulmonary vessels. In the curvilinear relations as well
as the linear relations over the physiological range, pulmonary vascular resistance
(PVR) calculations are misleading: from A to B, PVR does not seem change, and
from C to B and from D to E, i.e. running over single relation the PVR decreases, and
in the presence of aggravated pulmonary hypertension as assessed by higher pressures
at a given flow range the slope, and thus resistance, may differ little (Arrows).
Figure 3. Pressure/flow diagram for the interpretation of pulmonary hemodynamic
measurements. The central point C corresponds to initial mean pulmonary artery
pressure (PAP), left atrial pressure (LAP) and flow (Q) measurements. A decrease in
(PAP - LAP) at increased Q can only be explained by pulmonary vasodilatation. An
increase in (PAP - LAP) at decreased Q can only be explained by pulmonary
vasoconstriction. Rectangles of certainty are extended to adjacent triangles because
negative slopes or pressure intercepts of (PAO - LAP)/Q lines are impossible. Arrows
indicate changes in measured (PAP - LAP) and Q, (1) vasodilatation, (2)
vasoconstriction. After reference 10.
Figure 4. Effects of hypoxic pulmonary vasoconstriction (HPV) in chronic obstructive
pulmonary disease (COPD), a lung disease characterized by VA/Q mismatching. LSD,
logarithmic standard deviation of log-normal VA/Q ratio distribution. The fraction of
inspired O2 (FIO2) was set to 0.30; other variables were set to normal values and
remained unchanged during calculations (barometric pressure = 760 Torr,
temperature = 37°C, hemoglobin = 15 g/dl, base excess = 0 mmol/l, P50 = 26.8 Torr,
O2 consumption = 300 ml/min, CO2 production = 240 ml/min, cardiac output = 6.00
L/min, ventilation = 7.20 L/min, shunt = 0%, dead space = 30%). A: HPV
significantly improved PaO2 at all LSD values and improved SaO2 when it was most
decreased. B: at PaO2 of 40 Torr (LSD = 2.2), HPV decreased blood flow by 30% in
hypoxic lung units (VA/Q ratio < 0.3, alveolar PO2 < 45 Torr) and increased blood
flow by 76% in normoxic lung units (VA/Q ratio > 0.5, alveolar PO2 > 60 Torr).
20
LogSD VA/Q: logarithmic standard deviation of log-normal VA/Q distribution. From
reference 32.
Figure 5. Légende manquante.
Figure 6. Hyperbolic relationship between pulmonary arterial resistance and
compliance in patients with a normal pulmonary circulation (NONPH), with chronic
thrombo-embolic pulmonary hypertension (CTEPH) and with idiopathic pulmonary
arterial hypertension (IPAH). From reference 43.
Figure 7. Pressure and flow in common pulmonary artery are broken down in their
forward and backward components. Thick lines are measured waves, Pm and Qm,
thin lines are forward waves Pf and Qf, and dotted lines are backward running waves.
With vasoconstriction reflection, given by Pb/Pf =Qb/Qf, is increased. Redrawn from
reference 49.
Figure 8. Single beat method to measure right ventriculo-arterial coupling. A
maximum pressure (Pmax) is calculated from nonlinear extrapolation of early and late
isovolemic portions of the right ventricular pressure curve. A straight line is drawn
from the Pmax and end-diastolic volume (EDV) to Pes and end-systolic volume, thus
Emax = (Pmax - Pes)/SV, with SV = Stroke Volume. The arterial elastance Ea = Pes/SV.
21
Table 1. Limits of normal of pulmonary blood flow and vascular pressures
Variables
Mean
Limits of normal
Q L/min
Heart rate, bpm
PAP systolic, mmHg
PAP diastolic, mmHg
PAP, mean, mmHg
PAOP, mmHg
PCP, mmHg
RAP, mmHg
PVR, dyne.s.cm-5
SAP, mean, mmHg
6.4
67
19
10
13
9
10
5
55
91
4.4 - 8.4
41 - 93
13 - 26
6 - 16
7 - 19
5 - 13
8 - 12
1-9
11 – 99
71 - 110
Legend: Q: cardiac output; PAP: pulmonary artery pressure; PAOP: occluded PAP;
PCP: pulmonary capillary pressure (measured by single occlusion); RAP: right atrial
pressure; PVR: pulmonary vascular resistance; SAP: systemic arterial pressure; limits
of normal: from mean – 2 SD to mean + 2 SD; n = 55 healthy resting volunteers (n = 14
for the measurement of PCP), from references 3-5.