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Department of Physiology and Clinical Pharmacology, Faculty of Pharmacy, Centre National de la Recherche Scientifique, Unité Propre de Recherche de l'Enseignement Supérieur Associée 5014, Faculty of Pharmacy, 69373 Lyon Cedex 08, France
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ABSTRACT |
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Top
Abstract
Introduction
Methods
Results
Discussion
References
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A windkessel model was applied on a
beat-to-beat basis to evaluate the arterial mechanical characteristics
in seven conscious rats. Ascending aortic arterial pressure (AP) and
blood flow were recorded during steady-state in basal conditions,
during infusions of isoprenaline, sodium nitroprusside, and
phenylephrine, and after intravenous atenolol injection. For each
cardiac cycle the exponential decay time constant (
)
was estimated from the aortic AP curve, peripheral resistances
(R) were taken as the ratio of mean
AP to cardiac output, and systemic arterial compliance
(C) was calculated as
/R. In all conditions, mean
correlation coefficients of the exponential regression and ~70% of
values in each rat were >0.99, demonstrating the model validity. In
all conditions and C exhibited a
large spontaneous variability over time, and beat-to-beat correlations
were high between and C (0.83 ± 0.03). C was increased by sodium
nitroprusside, decreased by isoprenaline, but not significantly decreased by phenylephrine [5.1 ± 0.2, 3.2 ± 0.3, and 3.9 ± 0.2 µl/mmHg, respectively, vs. 4.2 ± 0.3 µl/mmHg
(baseline)]. In conclusion, the windkessel model
enables and C to be reliably
estimated in conscious rats during spontaneous and drug-induced
hemodynamic variations.
exponential decay time; aortic blood pressure; cardiac output
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INTRODUCTION |
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Top
Abstract
Introduction
Methods
Results
Discussion
References
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THE ARTERIAL TREE is a complex system not only because
of its geometry but also because of its nonlinear mechanical
properties. Thus biophysicists and physiologists have been trying to
develop simplified representations of this system to describe some of its functional aspects. Some characteristics of the mechanical properties of the whole arterial tree can be derived from the continuous measurements of aortic arterial pressure (AP) and blood flow. Among the parameters that can be estimated in the most
straightforward way for each cardiac cycle, the vascular resistance
(R), computed as the ratio of mean
AP (MAP) to mean aortic flow, and the time constant of the diastolic AP
decrease according to a monoexponential model () are the simplest
and the most interesting ones. According to Poiseuille's law with the
assumptions of a Newtonian fluid and a laminar flow in a cylindrical
tube, R contributes to the dissipation
of the circulatory energy in the arterial tree during each cardiac
cycle. The time constant signals the restoration of energy
stored by the arterial wall during the elastic distension due to
ventricular ejection. The determination of this time constant depends
on the accuracy of the exponential fit of the diastolic part of the AP
curve. Such a model based on the windkessel effect has been widely
used (13, 21, 24, 30) since Frank (6), and numerous studies have been
performed to improve it and to better estimate and interpret the model
parameters (3, 10, 15, 18, 20, 25, 27, 32).
In the simplest windkessel model made up of two elements, can be
considered as the product of R, as
previously defined, and the overall compliance of the arterial tree,
the so-called systemic arterial compliance
(C). Numerous works dealing with this topic and aiming at improving the quality of the models by increasing their complexity (4, 5) never approached the study of these
models over long periods of time, probably because of the lack of
computing resources, problems with signal acquisition, and
interpretation difficulties. Therefore, the interpretations of the
model parameters are essentially physical and do not sufficiently take
into account physiological regulations.
Many investigators are now interested in the study of local compliance obtained from the direct measurement of distensibility of a single arterial section. Several techniques for local estimation of arterial distensibility have been developed using ultrasonic techniques in humans (8, 26) and in anesthetized (7, 9, 17) or awake but restrained (28) animals. However, local compliance may differ from systemic compliance, which expresses the properties of the whole arterial tree, and the relationships between these two parameters are poorly documented (14).
The purposes of the present study were
1) to assess the quality of the
beat-to-beat estimation of using a two-element windkessel model
applied to the ascending aorta pressure curve in conscious unrestrained
rats over long periods in basal conditions and in various hemodynamic
situations induced pharmacologically, and 2) to study the spontaneous
variability over time of the classical hemodynamic parameters and of
the windkessel parameters , R, and
C.
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METHODS |
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Top
Abstract
Introduction
Methods
Results
Discussion
References
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Animals. Experiments were performed in seven male Sprague-Dawley rats (Iffa Credo, L'Arbresle, France) weighing 300-400 g and housed in controlled conditions (21 ± 1°C, 12:12-h light-dark cycle). The animals received standard rat chow (Usine d'Alimentation Rationnelle A03, Villemoisson-sur-Orge, France) containing <0.3% of sodium, and water ad libitum.
Chronic instrumentation. Rats were anesthetized with pentobarbital sodium (60 mg/kg ip) and were intubated. Body temperature was maintained at 37°C using an electric heating pad during and after surgery until rats awakened. A lateral thoracotomy was performed through the right third intercostal space (22), and the proximal aortic root was exposed by blunt dissection of the surrounding adipose and connective tissue. An ultrasonic transit-time flow probe (model 2.5 SB, Transonic Systems, Ithaca, NY) was then placed around the ascending aorta as proximal to the aortic valve as possible. The cable was passed through the thoracotomy and led subcutaneously to exit at the back of the neck and was left under the skin. The connector of the flow probe was exteriorized at the time of catheter implantation (see below). Rats were given penicillin G (100,000 IU ip) 3 days postoperatively. They were given 10-15 days to recover and to allow for fibrosis to develop around the probe. Two days before the study, rats were reanesthetized with halothane (2% in oxygen) for implantation of catheters. Polyethylene catheters were inserted via the left femoral vein into the inferior vena cava and via the right common carotid artery into the ascending aorta. The position of the ascending aortic catheter was verified by recording the waveform during the operation: the catheter was first inserted into the left ventricle and then withdrawn a few millimeters into the ascending aorta. Catheters were sutured to the vessels, filled with heparinized saline (50 IU/ml), and led subcutaneously to emerge between the scapulae. The connector end of the flow probe was protected in a small cap sewn to the skin. Antibiotic (neomycin sulfate) was applied topically. The anatomic location of the carotid arterial catheter tip was checked by postmortem dissection of the aortic wall. Signal recording. After cannulation, rats were placed in large cylindrical recording cages with food and water ad libitum. After 48 h, animals had regained their initial body weight. The aortic catheter was connected to a pressure transducer (Spectramed, Oxnard, CA) and was flushed (0.5 ml/h) with heparinized glucose (25 IU/ml) throughout the experiment to avoid blood diffusion and signal dampening. The cardiac flow probe cable was connected via a spring-guarded cable to an ultrasonic transit-time flowmeter (model T106, Transonic Systems). AP was amplified (model 13-4615-52, Gould, Cleveland, OH) and fed, simultaneously to aortic flow, to a chart recorder (model 8802, Gould). The analysis of the frequency response of the whole AP measurement system showed a slight underdamping and a resonance frequency of 36 ± 0.7 Hz, which did not affect the AP signal. Analog-to-digital conversions of both signals were simultaneously performed on-line at the sampling rate of 2,000 Hz with a PC 486 DX2/66 equipped with an acquisition board (AT-MIO16H-9, National Instruments, Austin, TX) and with software developed with LabVIEW 3.1.1 (National Instruments). Experimental protocol. The recording session began after a stabilization period of 15-30 min, when the animals were quiet and displayed normal activity. A baseline recording was taken over a period of 2.5 h. Animals then received intravenous administrations of four vasoactive drugs to produce various important hemodynamic changes. Infusion of isoprenaline (0.5 µg · kg
1 · min1)
was performed to induce an increase in cardiac output (CO) and rises in
pulse pressure of ~15 mmHg and in heart rate (HR) of ~15% through
-adrenoceptor stimulation. Infusions of sodium
nitroprusside (6.5 µg · kg1 · min1)
and of phenylephrine (13 µg · kg1 · min1)
were used to produce direct vasodilation (reducing AP by 15 mmHg) and
vasoconstriction (increasing AP by 20 mmHg), respectively. For each
infusion of a vasoactive agent, the steady state was reached in
5-10 min and the recording started at that time for a 15-min
duration. The administrations were separated by 45 min of recovery.
Finally, a bolus of atenolol (1 mg/kg iv) was used to induce a
bradycardia of >40 beats/min. The recording lasted 1 h after reaching
steady-state HR values.
Drugs. Isoprenaline HCl, sodium
nitroprusside, and phenylephrine HCl were obtained from Sigma Chemical
(St. Louis, MO), and atenolol was obtained from ICI
Pharma (Cergy, France).
Beat-to-beat computation of hemodynamic
parameters. Off-line data processing was performed on a
workstation (SPARC Station I, Sun Microsystems, Mountain View, CA). For
each cardiac cycle, MAP, HR, CO corresponding to mean aortic flow, and
R, defined as MAP/CO, were computed.
The time constant was estimated beat to beat using the exponential
decay time method previously described (13, 21, 25), with model
AP(t) = AP0et/
,
where t is time and
AP0 is the AP value at
time 0, the initial time for
application of the model. The model was applied to the last one-third
of the AP curve, the end points of which were computed after
determination of the cardiac cycle end points. When each cardiac beat was considered, it was verified that aortic flow was null
during the selected period, and a linear regression was performed after
logarithmic transformation of AP values, which yielded a correlation
coefficient
(r) that
expressed the quality of the exponential fit. The slope of the
regression line was 
1/, and systemic arterial compliance was
calculated using the windkessel relationship,
C = /R. The exponential fit and the
estimation of were performed during the baseline period, which
contained about 40,000 cardiac cycles, and during each of the
pharmacological situations, which each contained 4,000-7,000 cardiac cycles.
Statistics. For all parameters, the
overall variability was defined as the variation coefficient of all
values recorded during each experimental condition. Relationships
between hemodynamic parameters (,
R, and
C) were tested in each rat using
linear regression analysis applied to beat-to-beat values. These
analyses yielded one correlation coefficient for each rat in each
experimental condition.
Results are expressed as means ± SE. For comparisons of paired data
obtained in the different pharmacological conditions, a nonparametric
analysis of variance (Friedman test) was used, followed by the Wilcoxon
rank test in case of significance. Differences were considered
significant at P < 0.05. All
calculations were made using Systat 5.0 software (Systat, Evanston,
IL).
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RESULTS |
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Top
Abstract
Introduction
Methods
Results
Discussion
References
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Figure 1 shows three ascending aortic AP
curves and the corresponding aortic flow curves obtained in baseline
conditions and in two pharmacological situations. The segment of the AP
curve from which the monoexponential fit was calculated is shown. In all three cases, the aortic flow was null during this period. The first
part of the diastole, where reflected waves contribute to the AP
waveform, was excluded from the computations. The accuracy of the
linear fit after logarithmic transformation is demonstrated in each
condition by
r, which was
between 0.993 and 0.995. These values slightly differ from mean
r values given
in Table 1 because of the beat-to-beat
variability of
r. The distribution of
r values
obtained for all recorded beats gives the quality of the model used. An
example of a histogram of
r values
obtained in basal conditions in one rat is given in Fig.
2. Mean
r values and
percentages of
r values > 0.99 obtained in each experimental condition are given in Table 1. In
all conditions, mean
r was > 0.99. About 70% of cardiac beats had an
r value > 0.99 in baseline conditions, and this percentage was higher during
isoprenaline or phenylephrine infusions and after atenolol
administration.
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The steady state was tested by the differences in aortic pressure at
the start and at the end of each beat, which were evaluated in each rat
and at each experimental condition. Mean differences were 1.4 ± 0.1 mmHg in baseline conditions, 1.5 ± 0.2, 1.2 ± 0.1, and 1.9 ± 0.2 mmHg during isoprenaline, sodium nitroprusside, and
phenylephrine infusions, respectively, and 1.4 ± 0.2 mmHg after atenolol administration. In addition ~80% of the beats
exhibited pressure variation <2 mmHg in all conditions, except with
phenylephrine (65-70%). When beats with a pressure variation >2
mmHg were eliminated, mean values of MAP, HR,
R, ,
r, and
C were only slightly modified.
Differences in mean values obtained with all the beats and after
elimination only reached 0.6% as a maximum for HR and C. The analysis was thus
performed on all cardiac beats as steady state was verified.
Mean values of hemodynamic parameters obtained in all experimental
conditions are summarized in Table 2.
During infusions of vasoactive drugs, hemodynamic parameters varied in
the expected way. MAP varied moderately, from 13% with sodium
nitroprusside to +24% with phenylephrine. Variations of CO ranged from
14% with phenylephrine to +31% with isoprenaline, and those of
HR ranged from 22% with phenylephrine to +23% with
isoprenaline. Vascular resistances were modified from 29% with
isoprenaline to +44% with phenylephrine. The time constant was
decreased by isoprenaline (47%) and increased by phenylephrine
(+32%). C was significantly decreased
(24%) during isoprenaline and increased (+21%) during sodium
nitroprusside infusions. During phenylephrine infusion,
C tended to be reduced, but this did
not reach statistical significance (P = 0.063). Atenolol did not induce any significant change of the
windkessel parameters , R, and
C.
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An example of spontaneous evolution with time of cardiovascular
parameters over a period of 80 s in basal conditions is presented in
Fig. 3. All parameters, including and
C, show a marked variability due to
fast oscillations, obvious for CO and
R, and due to slower patterns lasting
up to 10 s. In addition, chronograms of and C exhibit a close visual
correspondence. Figure 4 shows variation coefficients of hemodynamic parameters obtained in all conditions. They
were <10% for MAP, HR, CO, and R,
whereas and C exhibited higher
values, between 10 and 18%, in basal and pharmacological conditions.
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Correlations between beat-to-beat values of and
C or
R are presented in Fig.
5. A strong linear correlation was found
between and C with mean
correlation coefficients of ~0.8 in basal conditions. On the
contrary, correlation coefficients between and
R were <0.5 in all experimental
conditions.
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Figure 6 presents an example of a
scatterplot of beat-to-beat values of MAP and
C obtained in one rat during the
baseline period. The strong dispersion of
C values makes it difficult to outline
a specific relationship between the two parameters. When each rat was
considered, no significant linear correlation between MAP and
C could be evidenced, either in basal
or in pharmacological conditions (0.3 < r < 0.2).
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DISCUSSION |
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Top
Abstract
Introduction
Methods
Results
Discussion
References
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The major finding of this study is the excellent accuracy of the
exponential AP decay time model in conscious unrestrained rats, applied
over long periods of baseline recording, as well as during various
pharmacological interventions. The results evidence spontaneous
variations over time of the windkessel parameters and their changes
after different pharmacological stimuli. The time constant and the
systemic arterial compliance C appear as hemodynamic variables spontaneously varying with time and with the
hemodynamic state. In addition, our results show that spontaneous variations of and C are linearly
related, therefore suggesting that may constitute an index of
C in basal conditions.
The diastolic AP decay reflects the mechanical behavior of the arterial
tree, and its analysis enables parameters to be numerically estimated.
The two-element windkessel model, including one resistive element and
one capacitive element, has long been used by many authors (13, 15, 21,
24). The estimation of the model parameters relies on the classical
decay time method. Arterial system modeling widely uses the
three-element windkessel model (3, 20, 21, 27, 32) and more complex
ones (4) that better depict AP and blood flow dynamics. In these
models, the aortic characteristic impedance and the systemic vascular
resistance are estimated from the aortic impedance spectrum (18), and
C is often obtained from the decay
time method (2, 5, 10, 20, 27, 32). Stergiopulos et al. (25) compared
classical and recently proposed compliance estimation methods and
showed that the classical exponential decay method was more accurate than new three-element windkessel-based methods and yielded errors of
usually <10%. In this work, the decay time method was applied to the
last one-third of the AP curve, and the relaxation time constant came
from the terminal stretch of the diastolic curve. For each cardiac
cycle, compliance was thus determined at end-diastolic pressures. The
different pharmacological administrations enabled the study of the
cardiovascular system in different hemodynamic states to evaluate the
power of the method in different conditions of steady state. In all
experimental situations, this part of the curve corresponded to null
flow, and the first part of the diastolic curve, where reflected waves
constrain the AP curve to deviate from exponential model (2, 25), was
excluded. In that way, the presence of wave reflections did not seem to affect the accuracy of the model in most of the cardiac cycles. The
validity of the model was proven by the correlation coefficient r of the
linear regression after logarithmic transformation of the data. This
coefficient was computed on a beat-to-beat basis, which is for
>40,000 cardiac cycles in basal conditions, and mean values were
>0.99 in all experimental conditions. Other studies using the same
method (10, 21, 25) reported similar
r values, but
they were obtained in anesthetized animals or from a few selected
cardiac beats in the case of human studies or still from numerical
simulation models. In the present study
r was slightly
lower for some rats, in which for a large number of cardiac beats the
part of the AP curve used for calculations might still contain
reflected waves, causing a deviation from exponential model. However,
in all the rats,
r was >0.99 for more than 50% of the cardiac beats.
Because R could also be estimated
using beat-to-beat CO measurement, C
was computed. However, we must keep in mind the limitations for using
these parameters, due to the assumption of Poiseuille's law for the
estimation of R and due to the
two-element windkessel model for . In addition, as already stressed
by some authors (27), beat-to-beat estimation of
R with the ratio MAP/CO should not be
applied during non-steady-state conditions because of the varying
amounts of blood stored in the compliant vessels. In this study we
verified that steady-state conditions were almost reached over the
whole selected recording sessions. In addition, mean values of all
parameters, including windkessel parameters, were almost unchanged
after a drastic selection of beats.
It was shown in rats (17) that an increase in HR resulted in a larger
inaccuracy of the method, but our data do not confirm this result. In
fact, during isoprenaline infusion, the correlation coefficients
remained elevated, even showing a trend to increase, despite the
tachycardia. In basal conditions and during sodium nitroprusside
infusion, the mean
r values were
the lowest. This may be explained by the fact that during large
systemic vasodilations, the pulse wave moves slowly and the wave
reflections may be superimposed on the diastolic part of the AP curve
considered for the estimation of .
As classically observed, spontaneous variability of MAP, HR, CO, and
R was evidenced by the representation
of their time course. The existence of a large variability over time of
and C also appeared on the
chronograms and moreover with the variation coefficients, which were
much higher for these parameters than for the classical ones. Although
these variation coefficients were computed over periods of different
durations in basal and pharmacological conditions, the differences
between and C and the other
parameters were maintained in all experimental conditions. When these
differences in data dispersion and the windkessel equality = R × C are considered, it clearly appears
that the variations of mainly reflect those of
C, and this is quantified by the
correlation coefficient between and
C. The visual correspondence of and C chronograms corroborates this
result. Therefore, this correlation seems to be related to the
difference between variation coefficients of and
R, which is particularly great in
basal conditions and during isoprenaline or sodium nitroprusside
infusions. In addition, it appears logical that beat-to-beat
variations were better related to C
than to R, inasmuch as vascular
resistance is smooth muscle dependent and varies more slowly. Indeed,
vascular smooth muscle responses to sympathetic nerve stimulation in
conscious rats were found to be significant up to 1 Hz (23), therefore
eliminating fast beat-to-beat variations of
R. Our beat-to-beat results do not confirm previous observations in humans and in anesthetized dogs (31),
which showed that 1-min averages of the time constant were well
correlated with R. When one considers
the relationship = R × C, the high linear correlation between
and C indicates that relationships
between and R and between
R and
C should also exist, but in a
nonlinear way. However, the strong linear relationship between
beat-to-beat values of R and 1/C, which was expected, was not found (data not shown). In addition, looking at
R and
C mean values during pharmacological
administrations, we cannot suggest any clear association of their
variations. Systemic arterial compliance is the result of complex
physiological adjustments involving all vascular beds and its
variations cannot be interpreted in so simplistic a way. A single
R value may be associated with various
C values, and because of various
regional distributions of blood flows, inverse variations of
R and compliance at the single-vessel
level cannot be evidenced at the systemic level. The high correlation
between and C in all the rats in
basal conditions suggests that may constitute an index of
C. However, although the regression
lines between and C nearly cross
the ordinate axis at the zero point in basal conditions, cannot be
considered as a true measure of C
because slopes of the linear regression exhibited large interindividual
variability and changes with the hemodynamic state (data not shown).
Recently, arterial compliance has often been determined at regional levels by measuring variations of arterial diameter in the course of the cardiac cycle as a function of AP changes (11, 17, 29) or from the pulse wave velocity along the aortic pathway with noninvasive Doppler ultrasonic technique (12). The role of vascular smooth muscle tone in the arterial stiffness (9) and the importance of pressure pulsatility (7) were demonstrated in rats. In humans, specific arterial alterations with aging and hypertension were found (11, 19, 29). However, relationships between regional compliance and C are poorly documented (14), and it is not known whether C better reflects carotid, aortic, or large-artery compliance.
It is now accepted that arterial compliance changes are due to
1) the mechanical effect of AP
variations, 2) functional
modifications of vascular tone (7, 14), and
3) structural changes of the arterial wall (9, 11, 16). In the present study the first two
mechanisms were taken into account in the conscious rat by studying
compliance variations induced by different pharmacological stimuli. No
clear relationship appeared between beat-to-beat
C and MAP values although the lowest
MAP observed under sodium nitroprusside and the highest MAP observed
under phenylephrine were associated with the highest and the lowest
C values, respectively. It was demonstrated in isolated vessels that graded increases in AP produced corresponding reductions of arterial compliance, following a nonlinear curve (3, 15, 16). As already suggested by other authors (7, 14), some
variations of C may be independent of
MAP variations but may be related to modifications of the vascular
smooth muscle tone. A drastic decrease of was found during
isoprenaline infusion, associated with a decrease of
C, which may be surprising according to the vasodilating properties of isoprenaline. Previous observations made on the isolated carotid artery (1) showed that the compliance was
unchanged after local administration of isoprenaline. The lack of
effect was explained by the absence of -adrenoceptor-mediated modulation of the carotid arterial compliance. As already described for
the carotid compliance calculated from the arterial diameter measurement (7), C was increased by
sodium nitroprusside, whereas no significant variation of was
noted. The differences between isoprenaline and sodium
nitroprusside may be due to the different vasodilating mechanisms:
vascular -adrenoceptor stimulation with isoprenaline, inducing
vasodilation preferentially in the skeletal muscle, and NO release with
sodium nitroprusside, inducing systemic vasodilation. Phenylephrine
induced a large increase in , which was associated with a slightly
lower C value, but the statistical test of difference did not allow us to conclude that there was a
significant decrease, although the probability was close to the
significance threshold. Previous observations made on carotid compliance showed a decrease with similar phenylephrine doses (7).
In conclusion, this work shows the validity of the two-element
windkessel model for beat-to-beat application in basal as well as in
pharmacological conditions. It appears that the relaxation time
constant presents an important spontaneous variability over time,
and it may constitute a valuable index of
C. The spontaneous variations over
time of probably signal variations of the hemodynamic state that
remain to be specified.
Perspectives. This study opens several areas of research. It would be first of interest to compare C with local compliances to clearly establish whether these two parameters are related and to specify the conditions in which they are linked. The determination of arterial compliance in regional circulations with simultaneous local measurements of AP and blood flow should then be examined to improve the physiological aspects of the study. Some hypotheses concerning C variations as a function of regional resistances and compliances, due to regional variations of blood flow, should be verified. In addition, one could compare young to aged normotensive rats, in which C is known to be lower for a similar AP level. Thus it would be possible to better explain the respective effects of AP and vascular muscle tone on C.
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ACKNOWLEDGEMENTS |
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This work was supported by a grant from the Fondation de France. P. Molino was supported by a grant from the Communauté de Travail des Alpes Occidentales and the Région Rhône-Alpes, France.
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FOOTNOTES |
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Address for reprint requests: C. Cerutti, Centre National de la Recherche Scientifique ESA 5014, Faculté de Pharmacie, 8 Ave. Rockefeller, 69373 Lyon Cedex 08, France.
Received 8 April 1997; accepted in final form 25 September 1997.
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Top
Abstract
Introduction
Methods
Results
Discussion
References
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