From the Biomedical Engineering Laboratory, Swiss Federal Institute of
Technology, Lausanne, Switzerland (N.S.); and Laboratory for Physiology,
Institute for Cardiovascular Research, Free University, Amsterdam, The
Netherlands (N.W.).
Correspondence to N. Stergiopulos, PhD, Biomedical Engineering Laboratory, Swiss Federal Institute of Technology, PSE-Ecublens, 1015 Lausanne, Switzerland. E-mail stergiopulos{at}eldp.epfl.ch
Abstract
Abstract—We have searched to define
the major arterial parameters that determine
aortic systolic (Ps) and diastolic
(Pd) pressure in the dog. Measured aortic flows were used
as input to the 2-element windkessel model of the arterial
system, with peripheral resistance calculated as mean
pressure divided by mean flow and total arterial compliance
calculated from the decay time in diastole. The windkessel
model yielded an aortic pressure wave from which we obtained the
predicted systolic (Ps,wk) and
diastolic (Pd,wk) pressures. These predicted
pressures were compared with the measured systolic and
diastolic pressures. The measurements and calculations were
performed for 7 dogs under control conditions during aortic occlusion
at 4 locations (the trifurcation, between the trifurcation and
diaphragm, the diaphragm, and the proximal descending thoracic aorta)
and during occlusion of both carotid arteries. Under all conditions
studied, the predicted systolic and diastolic
pressures matched the experimental ones very well:
Ps,wk=(1.000±0.0055) Ps with
r=0.958 and Pd,wk=(1.024±0.0035)
Pd with r=0.995. Linear regression for pulse
pressure (PP) resulted in PPwk=(0.99±0.016) PP with
r=0.911. We found the accuracy of prediction equally
good under control conditions and in the presence of aortic or carotid
artery occlusion. Multiple regression between pulse pressure and
arterial resistance and total arterial
compliance yielded a poor regression constant
(R2=0.19), suggesting that the 2
arterial parameters alone cannot explain pulse
pressure and that flow is an important determinant as well. We conclude
that for a given ejection pattern (aortic flow), 2 arterial
parameters, total arterial resistance and total
arterial compliance, are sufficient to accurately describe
systolic and diastolic aortic pressure.
Systolic and
diastolic pressure, and thus pulse pressure, are determined
by the complex interaction of the heart and the arterial
and venous systems. Studies in the isolated cat heart loaded with an
artificial arterial system showed that with a decrease in
compliance and leaving peripheral resistance and cardiac
parameters (diastolic filling, heart rate, and
contractility) constant, systolic pressure
increased very little but diastolic pressure decreased
considerably.1 In the intact dog, when
arterial compliance was decreased in such a way that
peripheral resistance and heart rate remained the same
while other cardiac parameters could vary, the increase in
systolic and decrease in diastolic pressures were
about the same.2 Comparison of these results
shows that cardiac parameters such as diastolic
filling and contractility do affect pulse pressure.
In an earlier theoretical model study,3 we
studied the contribution of major cardiac and arterial
parameters to systolic pressure,
diastolic pressure, and stroke volume. We found that the
characteristic impedance of the aorta contributes little to
systolic and diastolic aortic pressure.
Furthermore, using a distribution model of the arterial
tree,4 we have also shown that for a given
ejection pattern (aortic flow), systolic and
diastolic pressures were very accurately predicted by the
2-element windkessel. Therefore, total arterial compliance
and peripheral resistance seem to be the only 2 important
arterial parameters determining aortic pulse
pressure.5 6
We have therefore put forward the hypothesis that for a given ejection
pattern, pulse pressure depends solely on total arterial
compliance and peripheral resistance. We tested this
hypothesis using data from canine experiments.
Methods
Experimental Data
Determination of Parameters of 2-Element
Windkessel
Systolic and Diastolic Pressure Predicted From
Windkessel and Flow
The maximal and minimal values of Pwk were
designated as predicted systolic and diastolic
pressures. Systolic and diastolic pressures were
determined for a randomly selected cardiac cycle taken from series of
steady-state heart beats (approximate duration, 10 seconds) in all 7
dogs. One hundred twelve cycles were analyzed (n=112);
69 were for control conditions (including control measurements before
and after interventions) and the rest for occlusion at the aorta and
the carotid arteries.
Data Analysis
Results
Predictions of Systolic, Diastolic, and
Pulse Pressures
Bland and Altman8 plots for the entire set
(control and interventions) of measured and predicted systolic
and diastolic pressures are given in Figure 3
Effect of Occlusions
Discussion
Systolic and diastolic pressure are important
markers of cardiovascular function and disease.
Diastolic and systolic hypertension are known to be
precursors to a wide spectrum of cardiovascular
dysfunctions and diseases. Systolic pressure, which relates to
maximum wall stress (Laplace's law) and therefore determines heart
muscle load, has been shown to be a factor implicated in cardiac
hypertrophy.9 Also, systolic
pressure is an important determinant of myocardial oxygen
consumption.10 Recent studies have shown that
pulse pressure is one of the strongest predictors of coronary
heart disease and cardiovascular
mortality.11 12 It is therefore important to know
the major vascular and cardiac parameters that determine
systolic, diastolic, and pulse pressure.
We studied aortic pressures in the dog under control conditions
and under obstruction of the aorta and the carotids. Using aortic flow
as input, and thus accounting for the changes in the venous system
(preload) and in the heart (heart rate, contractility),
we could study the contribution of the arterial load on
systolic, diastolic, and pulse pressure. We found
that peripheral resistance and total compliance are the
only 2 arterial parameters that determine
systolic and diastolic pressure virtually
completely. The data show that systolic and
diastolic pressures are well predicted by the 2-element
windkessel, irrespective of the large changes in arterial
load and the distribution and topology of the reflection sites in the
arterial system. In our earlier study describing the pulse
pressure method, we attributed the good predictions of the pulse
pressure by the 2-element windkessel model to the fact that the
2-element windkessel matches well the true input impedance at low
frequencies.5 Because the first few harmonics
contain the major part of the information on the wave shape, these
harmonics mainly determine the systolic and
diastolic pressure.3 5
These findings have an important implication: systolic and
diastolic pressure do not depend on the distribution of the
wave reflection sites and are simply determined by the combined
properties (R and C) of the arterial system. The Table
In an earlier article, we derived analytically the dependence of aortic
systolic and diastolic pressure on the major
arterial and cardiac
parameters.3 We have shown that
cardiac parameters such as heart rate,
contractility, and venous pressure have a profound
effect on aortic pressure. This means that when analyzing the effects
of arterial parameters such as compliance and
peripheral resistance on pulse pressure, one needs to
consider also the modulating effect of cardiac parameters;
otherwise, the correlation between pulse pressure and
arterial parameters may be poor. To illustrate
this point, we performed a multiple regression analysis between
the pulse pressure (independent variable) and
peripheral resistance and compliance (dependent
variables) for the entire dog data set (n=112). Multiple regression
analysis yielded a result of
r2=0.19, suggesting that the 2
arterial system parameters alone cannot explain
all the variability in the data. This also explains the rather poor
correlation between pulse pressure and arterial compliance
reported from cross-sectional studies in
humans.13
We conclude that for a given aortic flow, systolic and
diastolic aortic pressures are determined by only 2
arterial parameters: peripheral
resistance and total arterial compliance. In general,
however, cardiac parameters such as heart rate,
contractility, and filling pressure also contribute and
therefore should always be taken into account.
Received January 29, 1998;
first decision February 8, 1998;
accepted April 7, 1998.
References
1.
Elzinga G, Westerhof N. Pressure and flow
generated by the left ventricle against different impedances.
Circ Res. 1973;32:178–186.
2.
Randal OS, van den Bos GC, Westerhof N. Systemic
compliance: does it play a role in the genesis of essential
hypertension? Cardiovasc Res. 1984;18:455–462.[Medline]
[Order article via Infotrieve]
3.
Stergiopulos N, Meister J-J, Westerhof N. Determinants
of stroke volume and systolic and diastolic aortic
pressure. Am J Physiol. 1996;270:H2050– H2059.
4.
Stergiopulos N, Young DF, Rogge TR. Computer
simulation of arterial flow with applications to
arterial and aortic stenoses. J
Biomech. 1992;25:1477–1488.[Medline]
[Order article via Infotrieve]
5.
Stergiopulos N, Meister J-J, Westerhof N. Simple and
accurate way for estimating total and segmental arterial
compliance: the pulse pressure method. Ann Biomed Eng. 1994;22:392–397.[Medline]
[Order article via Infotrieve]
6.
Stergiopulos N, Meister J-J, Westerhof N. Evaluation
of methods for the estimation of total arterial compliance.
Am J Physiol. 1995;268:H1540– H1548.
7.
Westerhof N, Elzinga G, Van den Bos GC. Influence of
central and peripheral changes on the input impedance of
the systemic arterial tree. Med Biol Eng. 1973;11:710–723.[Medline]
[Order article via Infotrieve]
8.
Bland JM, Altman DG. Statistical methods for assessing
agreement between two methods of clinical measurement.
Lancet. 1986;8:307–310.
9.
Krumholz HM, Larson M, Levy D. Sex differences in
cardiac adaptation to isolated systolic hypertension.
Am J Cardiol. 1993;72:310–313.[Medline]
[Order article via Infotrieve]
10.
Sarnoff SJ, Braunwald E, Welch GH, Case RB, Stainway
WH, Marcur R. Hemodynamic determinants of oxygen
consumption of the heart with special reference to tension-time index.
Am J Physiol. 1958;192:148–156.
11.
Mitchell GF, Moye LA, Braunwald E, Rouleau JL,
Bernstein V, Geltman EM, Flaker GJ, Pfeffer MA. Sphygmomanometrically
determined pulse pressure is a powerful independent predictor of
recurrent events after myocardial infarction in patients with impaired
left ventricular function. Circulation. 1997;96:4254–4260.
12.
Benetos A, Safar M, Rudnichi A, Smulyan H, Richard J-L,
Ducimetiere P, Guize L. Pulse pressure, a predictor of long-term
cardiovascular mortality in a French male population.
Hypertension. 1997;30:1410–1415.
13.
Blacher J, Guerin A, Pannier B, Safar ME, London GM.
Arterial remodeling and its impact on mortality in uremic
patients: structure and function of large arteries. In: Program and
abstracts of the Third International Workshop on Structure and Function
of Large Arteries; January 23–24, 1998; Versailles, France.
© 1998 American Heart Association, Inc.
Third Workshop on Structure and Function of Large
Arteries: Part III
Determinants of Pulse Pressure
Key Words: arterial compliance • vascular resistance • windkessel • cardiac output
Aortic pressure and flow waveforms were obtained earlier in
closed-chest anesthetized dogs.7 Flow was
measured with a previously implanted electromagnetic flow probe on the
ascending aorta. Pressure was measured with a catheter tip manometer
introduced into the femoral artery and moved to the same aortic
location as the flow probe at the day of the experiment. A typical set
of aortic pressure and flow recordings
simultaneously measured under control conditions is shown
in Figure 1
. Aortic pressure and flow
were also measured under several different conditions. Abdominal and
thoracic aortas were occluded totally by means of an inflatable balloon
at 4 locations: at the aortic trifurcation, between the trifurcation
and level of the diaphragm, at the diaphragm, and at the level of the
proximal descending thoracic aorta. A fifth intervention was the
occlusion of both carotid arteries. The location of the occlusions of
the aorta and the carotids is shown schematically in Figure 1, and the
interventions are designated by the letters A through E. The purpose of
the occlusions was to augment wave reflections and change the topology
of wave reflection sites (A through D) and to change aortic pressure
(E). Details regarding the experimental procedure have been published
previously.7
View larger version (15K):
[in a new window]
Figure 1. Typical simultaneous
recordings of flow and pressure in the dog ascending aorta.
Schematic diagram of the arterial tree indicating the
locations of aortic (balloon) and carotid (snare) occlusions.
From the measured ascending aortic pressures and flows,
peripheral resistance (R) was obtained as the ratio of mean
pressure and flow. Total arterial compliance (C) was
estimated by the decay time method, ie, fitting the
diastolic part of the pressure wave with a single RC time.
The time constant divided by peripheral resistance gave
total arterial compliance. From the same beats,
systolic and diastolic aortic pressures were
obtained.
Systolic and diastolic pressures were
determined as follows. Using measured flow (Q) as input to the
2-element windkessel, the output pressure, Pwk,
was calculated by integration of the governing equation
(dPwk/dt)+(Pwk/RC)=Q/C.
Linear regression was applied to determine the relation between
measured and predicted systolic, diastolic, and
pulse pressures. Paired t tests were performed to assess the
differences between predicted and measured pressures for control and
during interventions. Bland and Altman plots were used to check the
agreement between the measured and estimated systolic and
diastolic pressures. Multivariate
analysis was applied to assess the relation between pulse
pressure (dependent variable) and peripheral resistance
and total arterial compliance (independent
variables).
A cumulative graph showing the comparison between the measured and
predicted systolic and diastolic pressures for all
7 dogs and all cases (control, aortic and carotid occlusion) is shown
in Figure 2A. The dashed lines are the
lines of identity. Linear regression (slope±SEM) with intercept forced
to zero yielded Ps,wk=(1.000±0.0055)
Ps (r=0.958) for the systolic
pressure and Pd,wk=(1.024±0.0035)
Pd (r=0.995) for the
diastolic pressure. We conclude that both systolic
and diastolic pressures are accurately predicted for all
cases studied. Figure 2B shows a plot of the predicted versus the
measured pulse pressure (PP). Linear regression resulted in
PPwk=(0.99±0.016) PP (r=0.911).
Multiple regression analysis applied to the entire data set,
with peripheral resistance and compliance as independent
variables and pulse pressure as dependent, yielded
R2=0.19.
View larger version (22K):
[in a new window]
Figure 2. Global comparison of measured and predicted
systolic and diastolic pressures (A) and pulse
pressure (B) in 7 dogs under control conditions and during
interventions. . The mean of the difference between
measured and predicted pressures was 0.1 mm Hg and 1.4
mm Hg for the systolic and diastolic pressures,
respectively; the corresponding standard deviations were 7 mm Hg
and 2.7 mm Hg. Apart from a small, consistent positive
difference in the diastolic values, the differences are
clustered around the zero value, and no specific trends (ie, dependence
on pressure) in the distribution are observed.
View larger version (29K):
[in a new window]
Figure 3. Bland and Altman plots for the comparison of
measured and predicted systolic (A) and diastolic (B) pressures in 7
dogs under control conditions and during interventions.
Measured versus predicted systolic,
diastolic, and pulse pressure under control conditions (X);
with aortic occlusion at A, B, C, and D; with occlusion of the 2
carotids (E); and after deflation of the balloon occluding the aorta
(R) are plotted in Figure 4. Good
agreement between measured and predicted systolic,
diastolic, and pulse pressures is found for all conditions.
We observed an increase in pulse pressure with aortic occlusion, which
became progressively more important as the aortic occlusion site moved
closer to aorta (A through D). Data for the mean values and standard
deviation of hemodynamic parameters under
control conditions (groups X and R) and during interventions (groups A
through D and G) are given in the Table.
Paired t tests showed that for all groups, the difference
between measured and predicted pressures was not statistically
significant, except for the diastolic pressures under
control conditions (X and R), with the mean difference in
diastolic pressure for these 2 groups being <2
mm Hg.
View larger version (38K):
[in a new window]
Figure 4. Average values of measured versus predicted
pulse pressure. X indicates control; A through D, aortic occlusions; E,
occlusion of both carotid arteries; and R, release after deflation of
aortic balloon (see Figure 1 
). The numbers under the x
axis indicate the number of heart cycles analyzed for each type
of intervention.
View this table:
[in a new window]
Table 1. Hemodynamic Parameters Under Control Conditions and During
Interventions
shows that >60% of the total arterial compliance resides
in the ascending and descending aorta (compare C values under control
and total occlusion at D). Therefore, to further simplify the clinical
aspect of the problem, pulse pressure is determined mainly by the
periphery (R) and the elastic properties of the aorta (C).
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