Vol. 277, Issue 6, H2409-H2415, December 1999
SPECIAL COMMUNICATION
Novel method to estimate ventricular contractility using
intraventricular pulse wave velocity
Toshiaki
Shishido,
Masaru
Sugimachi,
Osamu
Kawaguchi,
Hiroshi
Miyano,
Toru
Kawada,
Wataru
Matsuura,
Yasuhiro
Ikeda, and
Kenji
Sunagawa
Department of Cardiovascular Dynamics, National Cardiovascular
Center Research Institute, Suita, Osaka 565-8565, Japan
 |
ABSTRACT |
We developed a novel technique for estimating
ventricular contractility using intraventricular pulse wave velocity
(PWV). In eight isolated, cross-circulated canine hearts, we used a
fast servo pump to inject a volume pulse into the base of the left ventricular chamber at late diastole and at late systole. We measured the transit time of the volume pulse wave as it traversed the distance
from base to apex and calculated the intraventricular PWV. The
intraventricular PWV increased from diastole (2.3 ± 0.4 m/s) to
systole (11.7 ± 2.4 m/s, P < 0.0001 vs. diastole). The square of the intraventricular PWV at late
systole correlated linearly with the left ventricular end-systolic
elastance (r = 0.939, P < 0.0001) and with the
end-systolic Young's modulus (r = 0.901, P < 0.0001). Moreover, the
intraventricular PWV was insensitive to preload. We conclude that the
intraventricular PWV at late systole reflects left ventricular
end-systolic elastance reasonably well. The fact that estimation of PWV
does not require volume measurement or load manipulation makes this
technique an attractive means of assessing ventricular contractility.
cardiac mechanics; ventricular elastance; hemodynamics; muscle
properties; stress-strain relationship
| |
INTRODUCTION |
THE SLOPE (end-systolic elastance,
Ees) of the
end-systolic pressure-volume relationship of the left ventricle (LV)
has been known to be a load-insensitive index of ventricular
contractility (16, 17). Despite the benefit of
Ees, its use has
been somewhat hampered by the fact that volume measurement is a
technically difficult task, particularly in clinical settings. Although
left ventriculography (6), echocardiography (20), radionuclide angiocardiography (9), and the conductance catheter technique (2) have
been used for volumetry in humans, evaluation of the accuracy of such
techniques itself is difficult because of the lack of any gold standard.
Pulse wave velocity (PWV) has been used as a quantitative measure to
indicate the degree of arterial sclerosis (1, 3), namely, arterial
stiffness. Theoretically, it has been demonstrated that the square of
PWV propagated in arteries is proportional to the arterial wall
stiffness expressed in terms of Young's modulus (10). Experimentally,
PWV has been found to correlate with the degree of arterial sclerosis.
By analogy, we hypothesized that PWV traveling within the LV chamber
similarly should reflect ventricular wall stiffness and thus be time
varying. To test this hypothesis, we examined the correlation between
intraventricular PWV and ventricular elastance in isolated,
blood-perfused canine hearts. The results indicate that PWV is closely
correlated with ventricular elastance and that this technique enables
us to develop a novel method to measure
Ees without
volume measurement.
| |
METHODS |
Surgical preparation.
The study was performed in eight excised, blood-perfused,
cross-circulated canine ventricles as previously described in detail (13, 18). Briefly, in each experiment two mongrel dogs [body wt
14.8 ± 3.4 (SD) kg] were anesthetized with pentobarbital
sodium (30 mg/kg iv) after premedication with ketamine hydrochloride (5 mg/kg im). Both dogs were heparinized (1,000 U/kg). The heart isolated
from the "donor" dog was metabolically supported by arterial blood from the second, "support" dog. A thin water-filled latex balloon, connected to a computer-controlled ventricular volume servo-pump system, was placed in the LV. LV pressure at base and apex
was measured using a catheter with two micromanometers (SPC-751, Millar
Instruments, Houston, TX) placed inside the latex balloon. The distance
between the two sensors was fixed at 3 cm. We considered the catheter
placement to be appropriate when the catheter was straight and the two
sensors were between the mitral adapter and the apex. LV volume was
measured with a linear variable-differential transformer. The systemic
arterial pressure of the support dog served as the coronary perfusion
pressure for the excised heart. The mean level of the systemic arterial
pressure of the support dog was reasonably stable and was >80 mmHg
throughout each experiment. The support dog was ventilated with room
air. Arterial blood was repeatedly sampled for measurements of pH,
PO2, and
PCO2. Supplemental oxygen and
intravenous sodium bicarbonate were given as necessary to maintain
these parameters within their physiological ranges throughout each
experiment. The temperature of the heart was monitored and maintained
at 37°C by means of a heater that warmed the coronary artery tubing.
Injection of volume pulse into LV.
We injected a narrow volume pulse into the LV by use of a linear pump
(Electrodynamic transducer ET-126, Labworks). We used a short (10 cm),
rigid stainless steel pipe (ID 2 mm) so as to minimize both the
attenuation and deformation of the pulse (Fig. 1). The flow within the pipe induced by the
pulse was monitored using an in-line type electromagnetic flow probe
placed at the end of the pipe and connected to a flowmeter (MFV-2100,
Nihon Koden, Tokyo, Japan). The infusion volume for the pulse was 1.2 ± 0.2 ml, with a duration of <14 ± 2 ms.
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Fig. 1.
A: schematic drawing of experimental
preparation. An isolated heart was perfused by arterial blood from a
support dog. Narrow volume pulse into ventricle was infused by use of a
pulse generator. Distance between the 2 pressure sensors inside
ventricle was 3 cm.
|
|
We examined the relationship between PWV and ventricular elastance in
isovolumic beats. Using isovolumic beats enabled us to exclude the
effect of changes in ventricular geometry on PWV, thus allowing
identification of the pure effects of changes in contractility on PWV.
To clamp LV volume at the various levels required, we used another
volume servo pump (VG-80CA, Vibration Test Systems). The heart was
paced via the left atrium at the rate of 143 ± 7 beats/min. When
the isolated heart beat steadily without arrhythmias, we injected a
narrow volume pulse into the ventricle either at late systole (end
systole ± 5 ms) or at late diastole (end diastole ± 5 ms) in
different beats. We estimated intraventricular PWV from the transit
time of this pulse.
Experimental protocol.
In each condition, we measured PWV by volume pulse injection and
determined LV elastance by slowly changing ventricular volume (in
1-2 min) until the peak isovolumic pressure became subatmospheric. After recording data under control conditions, we increased LV end-diastolic volume from 17.5 ± 5.6 to 23.3 ± 6.3 ml and
repeated the measurements. We then decreased LV volume to the same
level as that under control conditions and enhanced contractility by dobutamine infusion at the rate of 2-5 µg/min into the coronary perfusion tubing. The measurements were repeated, and the drug was
withheld. After contractility returned to baseline, we depressed contractility by administration of propranolol at an initial bolus dose
of 0.3 mg followed by a 15 µg/min continuous infusion and then
recorded data. After each protocol, and before proceeding to the next
protocol, we always confirmed that after withdrawal of drugs
contractility recovered to the initial control level.
Data analysis.
All data were recorded on a multichannel thermal array recorder
(Omnicorder 8M24, NEC San-Ei, Tokyo, Japan) and stored on a hard disk
after analog-to-digital conversion [AD12-16D(98)H, Contec,
Osaka, Japan] at 0.1-ms intervals with a personal computer system
(PC-9821Ap, NEC, Tokyo, Japan).
In this paper, we used the term "contractility" solely as the
systolic stiffness of the heart, and we did not include the deleterious
effect of diastolic dysfunction in this term. This definition is based
on the concept of the time-varying pressure-to-volume ratio described
by Suga and Sagawa (16) and Suga et al. (17).
Pressure-volume relationships were constructed from LV pressure and
volume data during whole cardiac cycles under each condition. Under
each condition, we varied the volume load from the volume at which PWV
was measured to the volume corresponding to a peak isovolumic pressure
of ~0. Given that the LV end-systolic pressure volume relation
(ESPVR) is practically linear (12, 16),
Ees could be
calculated from the linear regression of ESPVR as
|
(1)
|
where
Pes is LV end-systolic pressure, V
is LV isovolumic volume and V0 is
volume-axis intercept of ESPVR. In addition, we approximated the LV
end-diastolic pressure volume relation (EDPVR) according to the
relation
where
Ped is LV end-diastolic pressure,
Vu is volume-axis intercept of
EDPVR, and F is a coefficient that
characterizes the nonlinear diastolic properties (15). LV end-diastolic
elastance (Eed)
was defined as the slope of the tangent of the nonlinear EDPVR at the
volume where PWV was measured.
Intraventricular PWV was obtained as follows. For signals obtained at
each pressure sensor (at the base and apex), we subtracted unperturbed
LV pressure signals from their respective counterparts associated with
volume pulses to obtain the pure effects of the volume pulses. We used
the foot-to-foot time interval as a measure of transit time because the
foot of the pulse wave would seem to be least affected by wave
reflections. Although there are several automated ways to determine the
foot of the pressure rise, we selected manual determination instead
because the number of determinations was limited. Manual determination
is superior when the pulse waveform is not uniform. We actually did not
determine the time of the foot itself but only determined the pulse
transit time. To this end, using a custom-made software, we first
resampled the two pressure pulse responses every 0.01 ms (by linear
interpolation) and then superimposed these waves on the computer
display. One of the waves was shifted until the two waveforms at
pressure rise matched completely. This is basically the same method
employed by McDonald (10). We defined the pulse transit time as the
time shift needed to match these waveforms. Finally, PWV was calculated by dividing the distance between sensors by the transit time thus obtained. The pulse wave velocity (PWV) and the square of pulse wave
velocity (PWV2) were calculated,
because elastance is theoretically correlated with
PWV2.
We also performed a stress-strain analysis using a thick-walled
spherical ventricular model (see
APPENDIX). Because the end-systolic stress-strain relationship is nonlinear, we calculated the end-systolic incremental elastic modulus, i.e., incremental Young's modulus (Yinc, the
tangential slope) around the strain used for measuring PWV.
Yinc was
determined from the expression
|
(2)
|
where
d
is the change in stress induced by a small change in strain (d
)
around the operating strain value corresponding to the ventricular
volume at which PWV was measured. To obtain Yinc, the
end-systolic stress-strain relationship was fit to a linear function at
the operating strain ± 0.01. When d was within ±0.01, the
linear approximation was found to be reasonable.
Statistics.
Data are presented as means ± SD. Correlation analysis was
performed using a standard least-squares method, and goodness of fit
was expressed as Pearson's r-value.
Comparisons of PWV, PWV2, and
Ees between small
and large ventricular volumes were done by paired
t-tests (5). A value of
P < 0.05 was considered
statistically significant.
| |
RESULTS |
Ventricular pressure response to volume pulse at late systole and
late diastole.
Isovolumic LV pressure, with the pressure response to a volume pulse at
late systole from pressure sensors at base and apex, taken from a
typical experiment, are shown in Fig.
2A. The
pure pressure responses to volume pulses at late systole were obtained by subtracting relevant unperturbed from perturbed pressures at each
sensor and are shown in Fig. 2B. The
transit time in this case was 3.4 ms over the 3-cm distance, resulting
in a PWV at late systole of 8.8 m/s. The pure pressure responses to
volume pulse at late diastole in the same case are shown in Fig.
2C. Transit time was 16.5 ms and PWV
was 1.82 m/s at late diastole. Data from all dogs are summarized in
Fig. 3. Even in pooled data, there was a
characteristic increase in PWV from diastole (2.3 ± 0.4 m/s) to
systole (11.7 ± 2.4 m/s, P < 0.0001 vs. diastole) in accordance with the changes in elastance (0.8 ± 0.5 mmHg/ml at end diastole and 6.7 ± 3.7 mmHg/ml at end
systole).
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Fig. 2.
Example of simultaneously sampled and analyzed data. Isovolumic
pressure with pressure response to a volume pulse at late systole from
pressure sensors at apex and base of left ventricle are shown in
A. Pure pressure responses to volume
pulses were obtained by subtracting unperturbed from perturbed
pressures at late systole (B) and at
late diastole (C). In this case,
transit time at late systole was 3.40 ms over the 3-cm distance. As a
result, pulse wave velocity (PWV) was 8.8 m/s. At late diastole,
transit time was 16.52 ms and PWV was 1.8 m/s. Dotted lines indicate
zero pressure.
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Fig. 3.
Summary of changes in ventricular elastance
(A) and PWV
(B) at end diastole/late diastole
(left) and at end systole/late
systole (right) from all animals
during control conditions. Open symbols connected by line indicate data
from each animal, and closed symbols with error bars indicate means ± SD of all animals.
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Influence of changes in LV contractility on PWV.
The relationship between
Ees and PWV at
late systole (PWVs) as well as
that between Ees
and the square of PWVs
(PWV2s) at late systole under various
contractilities in each dog are shown in Table
1. The range of correlation coefficients
was 0.786-0.995 for
Ees and
PWVs and 0.824-0.990 for
Ees and
PWV2s. Both of these correlations were
reasonably linear and tight in each dog. Pooled data under various
contractile states were also used to construct a linear regression
(Fig. 4, A
and B). Although there was
intersubject variability of the slopes and intercepts of the regression
lines, both regressions were also reasonably linear, as shown in Fig.
4, A and
B. The point corresponding to the mean
value of Eed and
PWV at late diastole under control conditions is also plotted in Fig.
4, A and
B. The mean late diastolic point fitted better to the regression line between
Ees and
PWV2s than to that between
Ees and
PWVs. This is consistent with
theoretical considerations [Moens-Korteweg's equation (see Ref.
10)].
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Fig. 4.
A and
B: relationship between end-systolic
elastance (Ees)
and both PWV at late systole
(PWVs,  in
A) and
PWV2s ( in
B) for all animals for all
contractile conditions. Mean ± SD values of end-diastolic
elastance and PWV at late diastole under control conditions are also
plotted ( , SD smaller than marker size). Mean late diastolic point
fitted better to regression line between
Ees and
PWV2s than to that between
Ees and
PWVs.
C: relationship between
PWV2s and end-systolic incremental
elastic modulus
(Yinc) for all
animals for all contractile states. Dashed curves indicate 95%
confidence limits of regression, and error bars indicate SD.
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|
Relationship between PWV at late systole and end-systolic
Yinc.
Illustrated in Fig. 4C is the
relationship between PWV2s and
end-systolic
Yinc, derived
from the end-systolic pressure-volume relation using a spherical
ventricular model (see APPENDIX). As shown in Fig. 4C,
PWV2s also correlated well with
Yinc (r = 0.901, P < 0.0001).
Influence of volume loading on PWV at late systole.
When LV volume was increased from 17.5 ± 5.6 to 23.3 ± 6.3 ml at the control contractility state, neither
Ees [6.7 ± 3.7 and 6.7 ± 3.3 mmHg/ml, respectively; not significant
(NS)] nor PWVs (11.7 ± 2.4 and 11.7 ± 2.5 m/s, respectively; NS) changed. Figure 5 displays scatterplots of
PWV2s at control and increased volume
loading. This relation was highly linear
(r = 0.942, P < 0.0005), and the regression line
was not significantly different from the line of identity.
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Fig. 5.
Influence of volume loading conditions on
PWV2s under control contractility for all
animals. PWV2s was unchanged in response
to volume loading. Dashed curves indicate 95% confidence limits of
regression, and dotted line indicates line of identity.
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DISCUSSION |
Implication of results.
To our knowledge, this is the first study to demonstrate that
intraventricular PWV increases from diastole to systole in accordance with the increase in stiffness of the ventricular wall. This is analogous to the results of animal studies in which stiffening of the
aorta accelerated PWV (4) and is consistent with the results predicted
from transmission line theory (10). Because of the time-varying nature
of the LV, intraventricular PWV changes periodically even within a
cardiac cycle.
Besides the changes in stiffness within cardiac cycles, we have
demonstrated that intraventricular
PWVs reflected the changes in
end-systolic elastance (stiffness) that was induced by inotropic agents. Although both the relationship between
Ees and
PWVs and that between
Ees and
PWV2s were apparently linear, transmission line theory predicts that
Ees would be
proportional to PWV2s rather than to
PWVs itself
[Moens-Korteweg's equation (see Ref. 10)]. This was also
supported by experimental results. First, the relationship between
Ees and
PWVs had a large intercept (finite
PWVs for zero stiffness), which
seems unrealistic. Second, data obtained from end diastole fit much
better to the regression line obtained by
Ees and
PWV2s. Considering that both systolic and
diastolic PWV were governed by the common relationship, the linear
relationship between
Ees and
PWVs seems simply an apparent
linear fit obtained within the limited range to a potentially nonlinear relationship.
We also demonstrated that the intraventricular
PWVs was relatively insensitive to
changes in preload. Increasing LV volume by ~30% did not alter
PWVs. In contrast,
PWVs was highly sensitive to the
changes in contractility induced by infusion of positive and negative
inotropic agents. Therefore, PWVs
behaves in a manner at least similar to
Ees in terms of
its sensitivity to contractility and insensitivity to preload.
Advantages of method.
Ees has been
known to be a load-insensitive index of contractility. Two major
difficulties associated with the measurement of
Ees have been the
precise volumetry of the in situ heart and the requirement for load
manipulation. The fact that the measurement of intraventricular PWV
needed neither volumetry nor load manipulation represents a great
advantage of this method.
Although the recent development of the conductance catheter technique
(2) added to our armamentarium another method for measuring ventricular
volume, it has not been demonstrated to be better than other methods,
especially in the markedly dilated heart. The lack of a true gold
standard for volumetry of the in situ heart has made evaluation of
volumetry methods rather complicated. Even for the single-beat
estimation technique for
Ees (19), measurement of LV volume is still required. Load manipulation itself
might modify contractility through several mechanisms. Slinker and
Glantz (14) demonstrated that the behavior of the LV during transient
volume changes, e.g., by caval occlusion frequently used clinically and
experimentally, may differ from its behavior in steady-state
conditions. Nakano et al. (11) proposed a method to estimate myocardial
contractility (material property) based on the wall stress-logarithm of
reciprocal of wall thickness relationship. However, load manipulation
is still necessary. The present method does not require load
manipulation and is applicable on a single-beat basis. Although we
might need correction of PWV according to Moens-Korteweg's equation
based on ventricular geometry for ejecting beat, measurement of
ventricular dimension and wall thickness (e.g., by echocardiography) is
easier than volumetry itself.
Estimation of material properties and correlation with
Yinc obtained by
stress-strain relationship.
Theoretically, judging from Moens-Korteweg's equation,
intraventricular PWV reflects myocardial elastance (material property) rather than chamber elastance. The similar close relationships between
PWV2s and
Ees as well as
between PWV2s and
Yinc seem to have
resulted from the fact that differences in geometry among isolated
hearts in this study were small. These small differences in geometry
made it difficult for us to judge whether
PWV2s reflects mainly chamber elastance
or myocardial elastance only from this study. Although the slope of the
relationship between PWV2s and
Ees seems
different among animals, as shown in Table 1, the large confidence
interval of the estimated slope made the slope difference inconclusive. The question of whether under large changes in ventricular geometry intraventricular PWV (with and without the correction by ventricular volume and wall thickness) represents
Ees or
Yinc can only be answered by further studies.
Limitations.
There are some limitations in this study. First, dynamic changes in
ventricular geometry occurring in the naturally ejecting heart (such as
systolic wall thickening and systolic shortening of LV dimensions) are
likely to modify the relationship between PWV and elastance according
to Moens-Korteweg's equation. In this study, we selected the
isovolumic contraction mode to simplify the heart model. Further
investigation is necessary to examine whether this method can be used
to estimate elastance in ejecting hearts. Also, in the ejecting heart,
intraventricular PWV might be affected by inflow and outflow
velocities. The peak flow velocity is ~0.6-1.3 m/s in healthy
human adults (7). This would affect diastolic PWV to a considerable
extent but would affect late systolic PWV by only ~10%.
The second limitation has to do with the fact that myocardial
properties are time varying. Because a finite time is needed to measure
transit time, PWV might not be constant during measurements when
myocardial elastance increases or decreases sharply.
Indeed, low reproducibility prevented the precise determination of PWV at early systole and early diastole, even in the isovolumic contraction mode. Precise determination of the timing of end systole and end diastole and precise delivery of pulse in an intact heart are necessary
for clinical application. The development of a specialized servo-controlled device that operates in synchrony with cardiac cycle
might overcome this problem.
It is known that quick changes in LV volume deactivate the ventricle.
For example, Hunter et al. (8) reported that "steplike" changes
in ventricular volume reduced ventricular pressure. In this study, the
effect of volume pulse disappeared quickly in ~50 ms and pressure was
not different between perturbed and unperturbed beats thereafter. We
conjectured that the deactivation effect was small. This was probably
because we infused a smaller volume (1.2 ± 0.2 ml) than Hunter et
al. (2-3 ml).
Finally, we adopted a foot-to-foot basis as our measurement of choice
for PWV because the incident wave seems the fastest in the presence of
multiple reflections. During diastole, however, it might be difficult
to determine the foot of the pressure response to volume pulse. Other
investigators reported that the ratio of pressure change to small
volume change was small at the late diastolic phase because of low
myocardial elastance (8, 21). It seems that the amplitude of the
incident wave relative to that of the reflected waves became smaller
during diastole, making recognition of the foot more difficult.
In summary, we developed a novel technique for the estimation of
ventricular contractility using intraventricular PWV. The square of
intraventricular PWV at late systole showed a tight linear correlation
with LV Ees under
various contractile states. Intraventricular PWV was also insensitive
to preload. The fact that the estimation of PWV does not require volume
measurements or load manipulations makes this technique attractive for
the assessment of ventricular contractility.
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APPENDIX |
Model.
We used a thick-walled spherical model for the LV, where geometric
parameters may be estimated using the formulas
Vc = (4
/3)r3i and
Vc + Vw = (4/3)r3o, where
Vc and
Vw are cavity and wall volumes
(wall mass/1.05), respectively, and
ri and
ro are the inner
and outer radii, respectively.
Strain.
Instantaneous natural strain () for the midwall layer was determined
from instantaneous LV chamber volume and wall mass as
|
(A1)
|
where
rm = (ri + ro)/2 is the
midwall radius. The subscript ref means reference, and
rm,ref is the
midwall radius at reference volume. The operator ln denotes natural
logarithm. We chose the end-systolic unstressed volume
(V0) as the reference state.
Accordingly, Eq. A1 is also expressed
as follows
|
(A2)
|
where
Vm and
Vm,0 are volumes (cavity and inner
half wall) within the midwall for the actual and reference states.
Stress.
We used the balanced-force equation for a thick-walled spherical model
for calculation of stress as previously described (13, 22). Briefly, we
calculated instantaneous circumferential stress () as
|
(A3)
|
where
P is LV pressure, A is cross-sectional
area of the ventricular wall in the equatorial plane, and 1.332 × 103
dyn · cm
2 · mmHg1
is the constant for unit conversion. We defined
A as follows
|
(A4)
|
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ACKNOWLEDGEMENTS |
This study was supported by a grant from the Science and
Technology Agency, Encourage System of the Center of Excellence, by the
Health Sciences Research Grant on Advanced Medical Technology (FY1997),
and by a part of the Ground Research Announcement for Space Utilization
promoted by NASDA (National Space Development Agency of Japan) and
Japan Space Forum.
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FOOTNOTES |
The costs of publication of this
article were defrayed in part by the
payment of page charges. The article
must therefore be hereby marked
"advertisement"
in accordance with 18 U.S.C. §1734 solely to indicate this fact.
Address for reprint requests and other correspondence: T. Shishido,
Dept. of Cardiovascular Dynamics, National Cardiovascular Center
Research Inst., 5-7-1 Fujishirodai, Suita, Osaka 565-8565, Japan.
Received 4 December 1998; accepted in final form 9 July 1999.
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Am J Physiol Heart Circ Physiol 277(6):H2409-H2415
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