(Circulation. 1997;96:4415-4423.)
© 1997 American Heart Association, Inc.
Articles |
From the Institute for Surgical Research, the National Hospital, University of Oslo (Norway).
Correspondence to Harald Kjekshus, Institute for Surgical Research, The National Hospital, N-0027 Oslo, Norway.
| Abstract |
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Methods and Results In 8 anesthetized pigs we measured hepatic and systemic pressures and flows. Liver vascular volume was measured by sonomicrometry calibrated against integrated hepatic inflow during outflow occlusion. Pressure-volume (P-V) curves were constructed during outflow occlusion. Sonomicrometry accurately reflected hepatic blood volume (r=.99±.001), and hepatic P-V curves were highly reproducible. Norepinephrine (0.3 and 0.7 µg · kg body weight (bwt)-1 · min-1 intraportally) significantly reduced hepatic blood volume by 3.3±1 and 4.3±1 mL · kg bwt-1, respectively. Nitroprusside (8 and 18 µg · kg bwt-1 · min-1 intraportally) increased hepatic blood volume by 1.1±0.2 and 1.9±0.3 mL · kg bwt-1, respectively. Norepinephrine and nitroprusside parallel shifted the hepatic P-V curves, indicating reduced and increased unstressed blood volume, respectively. These curve shifts accounted for more than 90% of the respective blood volume changes. Compliance was unchanged. Phenylephrine but not isoprenaline yielded similar results as norepinephrine.
Conclusions The pig model used in this study, accurately
quantified hepatic capacitance.
-Adrenergic stimulation decreased
and nitroprusside increased capacitance by changing unstressed blood
volume. These changes in capacitance correspond to expulsion of 300 mL
and pooling of 130 mL of blood, respectively, in a 70-kg individual,
reflecting that the liver is not only a passive blood reservoir but can
respond actively and vigorously to pharmacological interventions.
Key Words: sodium nitroprusside catecholamines blood volume liver circulation veins
| Introduction |
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In this study, we introduce a modified sonomicrometric method in which integrated hepatic vascular inflow during brief occlusions of outflow is used for volumetric calibration, allowing in vivo calibrations without disturbing liver architecture. The method permits measurements of changes in hepatic blood volume as well as construction of vascular pressure-volume curves.
The aims of the present study were to determine the ability of this method to accurately measure liver blood volume and to evaluate the reproducibility of the method in assessing hepatic vascular pressure-volume curves. We have applied the method to investigate the mechanisms whereby hepatic blood volume is modulated by catecholamines and sodium nitroprusside. In particular, we wanted to determine to what extent these substances alter hepatic capacity by changing vascular compliance or unstressed blood volume.
| Methods |
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For pressure measurements (AE840 transducers, SensoNor) fluid-filled catheters (6F and 7F angiographic catheters, Cordis, except portal vein, 8F feeding tube, Pharma-Plast) with multiple side holes were positioned in the abdominal aorta, the right atrium, into the portal vein through a small side branch with the catheter tip palpable 1 cm from the liver, and into a right hepatic vein through a jugular vein under fluoroscopic guidance. The hepatic vein catheter was inserted gently until it wedged and then was withdrawn 1 to 2 cm to a free floating position. Injection of contrast during translumination confirmed a free floating position, with rapid clearance of contrast. A thermodilution catheter (Swan-Ganz 93A-131H-7F, American Edwards Laboratories, connected to a SAT-2 CO-computer, Baxter Healthcare Corp) for body temperature and cardiac output (CO) measurements was positioned in the pulmonary artery. Reference zero level for all pressures was set at the level of the right atrium. A separate catheter was inserted into a mesenteric vein and advanced toward the beginning of the portal vein for drug infusions. Liver blood flow was measured by ultrasound transit time with flowprobes on the hepatic artery and portal vein (4SB and 12SB, respectively, connected to a T201 flowmeter, Transonic Systems Inc). The flowprobes were mounted on straight portions of the vessels just before they entered the liver, and optimal placement was verified by checking of acoustical contact and zero flow with vascular occluders mounted on the hepatic artery and the portal vein (OC6 and OC12HD, respectively, In Vivo Metric) upstream from the flowprobes. To achieve sufficient space on the hepatic artery, the gastroduodenal artery was ligated and the flowprobe was positioned downstream and the occluder upstream from the branching. Liver thickness was measured by gluing (Histoacryl B, Braun Melsungen) ultrasonic transducers (ED3-2 connected to Sonomicrometer 120, Triton Technology) to the ventral and dorsal surfaces of the left lateral and the medial liver lobe in such a manner that the crystals were located at the thickest part of the lobe curvature. Transducer placement was optimized to achieve a high signal-to-noise ratio as viewed on the oscilloscope. An inflatable aortic balloon catheter with a fixed outer balloon diameter when inflated of 16.3 mm and a length of 269 mm (Datascope 50cc DL 9.5, Datascope Corp) was advanced under fluoroscopic guidance from a femoral vein to the intrahepatic portion of the inferior vena cava. In this position it completely blocked hepatic venous outflow when inflated with 60 mL of air. Outflow occlusion was considered adequate if there was no visible leakage of contrast (Omnipaque, Nyegaard) on translumination for 10 seconds after contrast had been injected into the hepatic vein during complete balloon inflation and if the liver dimensions remained stable through a 5-second period of simultaneous occlusion of hepatic vascular inflow and outflow.
All animal handling, experiments, and proceedings were approved by the local laboratory animal science specialist under the surveillance and registration of the Norwegian Experimental Animal Board, conforming with "Guiding Principles for Research Involving Animals and Human Beings."
Experimental Procedure
After completion of surgery, the pigs were allowed 30 minutes
for stabilization before baseline recordings were done. Each
set of measurements consisted of CO estimation (mean of three
injections of 10 mL of ice-cold 5% glucose after preflushing of the
right atrial catheter), followed by a 30-second continuous
recording of pressures, flows, dimensions, and ECG. The
recordings were done with the respirator off and consisted of
an initial 5- to 10-second period of stable pressures and flows,
followed by occlusion of hepatic vascular outflow and a 20-second
recording of the resulting pressure and blood volume increases.
Recordings were obtained on paper with a Gould ES2000
recorder (Gould Instrument System Inc) and were
simultaneously digitized and stored on a hard disk and
subsequently analyzed (CVSOFT version 2.2, Odessa Computer
Systems Ltd).
The following drugs and mean dosages were studied: norepinephrine 0.3 and 0.7 µg · kg-1 · min-1 (n=7), sodium nitroprusside 8 and 18 µg · kg-1 · min-1 (n=6), phenylephrine 1.0 and 2.8 µg · kg-1 · min-1 (n=4), and isoprenaline 0.2 and 0.8 µg · kg-1 · min-1 (n=4). All drugs were given as continuous intraportal infusions. Measurements were done 5 minutes after the start of every infusion or increase in dosage. Drug infusion was stopped immediately after the highest dosage was recorded, and a 30-minute washout period was allowed between drugs.
In four pigs, 10 repeated baseline recordings over a 3-hour period were done to evaluate reproducibility of the pressure-volume curves.
On completion of the experiments, the pigs were given an overdose of intravenous pentobarbital.
Calculations and Data Analysis
To assess hepatic blood volume, we measured two sets of liver
dimensions by sonomicrometry. Conversion from liver thickness to blood
volume was done by using integrated hepatic inflow during complete
outflow occlusions as reference blood volume. Volume-dimension (V-D)
curves were obtained by plotting each dimension as a function of the
flow integral during all the outflow occlusions performed in the pig.
Curve estimations with linear and cubic models were performed. Slope
was calculated by linear regression with the least-squares method (See
"Results" and "Discussion" for the rationale for this). The
mean slope in each pig was used as the conversion factor from
dimensional change in millimeters to blood volume change in
milliliters. On average, 18 occlusions were done in each pig at
differing liver volumes. In one pig, V-D curves from 5 of 18 occlusions
were not obtained because of incomplete outflow occlusion. Furthermore,
1% of the V-D curves were discarded due to interference from
respiratory movement.
To estimate changes in absolute blood volume, we assumed (on the basis
of personal washout studies and available literature3 13 )
that liver blood volume in the anesthetized pig at baseline was
35 mL · 100 g liver-1, which approximate 9.45
mL · kg-1 body weight (average liver to body weight
ratio of 0.027). Using this assumption, we computed blood volume
estimates at time x from each liver dimension by the
following formula:
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Hepatic pressure-volume curves were obtained during brief occlusions of liver outflow. Blood volume increase was plotted as a function of distending pressure as estimated by the pressure measured in the hepatic vein during complete outflow occlusion. Slope and intercept were calculated by linear regression analysis with the least-squares method and were used as estimates for hepatic vascular compliance and hepatic unstressed blood volume, respectively.
Transhepatic resistance was calculated as the difference between portal and hepatic venous pressures divided by the sum of portal vein and hepatic arterial blood flow.
Data are reported as mean±SEM unless otherwise specified. The variability of repeated baseline measurements was expressed as coefficient of variation (SD · 100/mean). Flows and blood volumes were divided by body weight for standardization. Effects of drug treatment were compared with the preceding baseline by repeated-measures ANOVA, with Student-Newman-Keuls post hoc test to isolate treatment effects. A value of P<.05 was considered statistically significant.
Definitions
Definitions are adapted from Rothe.14
| Results |
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Curve estimations of the individual volume-dimension curves from all the pigs were performed with linear and cubic models. Cubic fits were slightly better compared with linear fits, with mean r2 of .996 (range, .964 to 1.000) and .992 (range, .890 to .999), respectively. However, in their predictions of the observed volume-dimension curves in the study, the linear and cubic models differed by less than 2 mL for an observed blood volume change of 100 mL. Therefore, a linear model was used to determine the calibration factor, that is, the slope of the volume-dimension curves. The mean slope varied between pigs, with a range of .01 to .04 mm · mL-1, which partly reflected differences in measured baseline thickness which ranged from 8 to 19 mm. However, the slopes of the V-D curves from the individual liver dimensions within each pig had an average coefficient of variation of 10.6% (SD±3%). Drug intervention did not alter the calibration factor, as indicated by the ratio of the baseline-to-drug calibration factors of 1.04 (95% CI, 0.90 to 1.18) for norepinephrine, 1.11 (95% CI, 0.96 to 1.26) for phenylephrine, 1.02 (95% CI, 0.93 to 1.11) for isoprenaline, and 1.00 (95% CI, 0.95 to 1.04) for sodium nitroprusside.
The reproducibility of sonomicrometric blood volume estimates was tested in 10 repeated baseline recordings over a 3-hour period in four pigs and showed a coefficient of variation of 6±2%. Changes in the two liver dimensions closely paralleled each other, with an absolute difference in their respective blood volume estimates of 11±1%.
Representative examples of raw data recording are shown in Fig 2
.
Plotting hepatic blood volume as a function of hepatic venous pressure
from the point of complete vascular occlusion resulted in smooth and
near linear P-V curves with overall r2 values of
0.98±0.01 (range, .84 to 1.00). The P-V curves were reproducible at
repeated baseline recordings (Fig 3
), with a coefficient of variation of
10±1% for slope and of 17±3% for volume-axis intercept.
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Effects of Catecholamines
Norepinephrine caused dose-dependent reductions in
hepatic blood volume compared with baseline of 3.3±0.9
(P<.01) and 4.3±1.1 mL · kg-1
(P<.05) at the low and high dose, respectively, with a
parallel shift of the P-V curves toward the pressure axis (Fig 4
). Capacity at a distending pressure of
6 mm Hg was markedly reduced by 3.9±0.9 mL ·
kg-1 (P<.01) and 5.2±1.1 mL ·
kg-1 (P<.01), compared with baseline. This was
accounted for by a decrease in unstressed blood volume, whereas
apparent compliance was unchanged.
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Portal vein pressure increased by 2.3±1.0 (P<.01) and
3.5±0.9 mm Hg (P<.01), hepatic venous pressure
decreased by 1.0±0.3 (P<.05) and 0.8±0.3 mm Hg
(P<.05), and vascular inflow decreased by 2.1±1.4 (NS) and
4.3±1.3 mL · min-1 · kg-1
(P<.01) (absolute values in Table 1
).
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To evaluate the relative importance of
- and ß-adrenoceptor
activation as mediators of the effects of norepinephrine,
separate interventions with phenylephrine and isoprenaline
were performed in four pigs. Phenylephrine produced similar
responses as norepinephrine, but somewhat attenuated with
the dosages used (Table 2
, Fig 4
).
Isoprenaline increased hepatic venous pressure, portal vein pressure,
and hepatic blood volume but did not mimic the effects of
norepinephrine on hepatic P-V relations (Table 3
, Fig 5
).
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Effects of Sodium Nitroprusside
Sodium nitroprusside dose-dependently increased hepatic blood
volume by 1.1±0.2 (P<.01) and 1.9±0.4 mL ·
kg-1 (P<.01) at the low and high dose,
respectively, and caused parallel shifts of the P-V curves toward the
volume axis. Capacity at a distending pressure of 6 mm Hg was
increased by 1.3±0.4 mL · kg-1 (P<.01)
and 1.7±0.4 mL · kg-1 (P<.01) compared
with baseline. This was accounted for by an increase in unstressed
blood volume, whereas apparent compliance was unchanged. Right atrial
pressure was reduced, whereas changes in other systemic
hemodynamic parameters did not reach
statistical significance (Table 4
and Fig 4
).
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| Discussion |
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Norepinephrine infusion in dosages within the physiological range15 markedly decreased hepatic blood volume. This was accompanied by a parallel shift of the hepatic vascular pressure-volume curve toward the pressure axis, indicating a decrease in vascular capacitance and reflecting an active increase in vascular tone. Since norepinephrine also decreased hepatic blood flow, a passive mechanism could have contributed to the observed reduction in blood volume. Others have determined the contributions from passive mechanisms and have shown a linear relationship between hepatic blood flow and blood volume ranging from 0.07 to 0.11 mL of blood volume change for each mL/min change in flow.4 5 16 If we assume that a similar relationship applies to our model, this would account for only 7% to 12% of the blood volume decrease observed with norepinephrine infusion. Rothe and Gaddis17 found that 79% of total blood volume redistribution was attributable to passive elastic properties of the capacitance vasculature. This suggests that passive effects dominate in organs other than the liver.
Vascular capacitance can be reduced by decreasing compliance or by decreasing unstressed blood volume. In the present study we found no change in hepatic vascular compliance. This is consistent with the findings of Greenway et al5 and the baroreceptor study of Risoe et al11 but contrasts the findings of Bennett et al18 of decreased compliance with hepatic nerve stimulation or epinephrine infusion. However, Bennett et al calculated compliance from the blood volume change related to a step change in hepatic outflow pressure from 0 to 5 mm Hg in a pump-perfused dog model. Changes in outflow pressure in this low range may overestimate changes in hepatic distending pressure as others have found a discontinuity described as a critical closing pressure at 1 to 3 mm Hg,19 20 below which changes in hepatic outflow pressure will not be transmitted to the sinusoids. Furthermore, data from Greenway et al5 in cats suggest that norepinephrine alters the relationship between outflow pressure and hepatic lobar venous pressure in the low pressure range. They found that increasing hepatic venous outflow pressure from 0 to 5 mm Hg resulted in an increase in hepatic lobar venous pressure of 2.5 mm Hg at baseline compared with 1.6 mm Hg during norepinephrine infusion. If their data are applicable to the study of Bennett et al, this would explain the apparent decrease in compliance.
The ability of norepinephrine and hepatic nerves to
mobilize blood from the hepatic and splanchnic reservoirs has been well
documented.5 18 21 22 23 However, the relative importance of
- and ß-adrenergic receptors in mediating this effect is not
clear. We evaluated the individual effects of
- and ß-adrenoceptor
agonism on hepatic vascular capacitance and found that
phenylephrine produced active reductions in hepatic blood
volume through parallel shifting of the P-V curve, similar to what was
seen with norepinephrine. Isoprenaline, on the other hand,
did not mimic the effects of norepinephrine but caused a
slight increase in hepatic blood volume. This may be attributed to an
increase in hepatic venous pressure, possibly due to an increase in
hepatic blood flow, but the numbers are too small to conclude on these
minor changes. Taken together, these findings suggest that the effects
of norepinephrine on hepatic vascular capacitance are
mediated by the
-adrenergic receptor system. This conclusion is
supported by Greenway,24 who found that
-blockade with
phentolamine almost abolished the effect of hepatic nerve
stimulation on hepatic blood volume and portal pressure. Rothe et
al25 found that isoproterenol attenuated histamine-induced
increases in hepatic blood volume and portal pressure but did not
observe isoproterenol-induced reductions in hepatic blood volume during
basal conditions, and neither did others.26 27
Sodium nitroprusside increased hepatic blood volume in our study by
shifting the hepatic pressure-volume curve toward the volume axis
without changing the apparent compliance. This active change in
capacitance may seem in conflict with the study of Risoe et
al28 in humans, where sodium nitroprusside decreased
hepatic blood volume presumably by a passive mechanism, since hepatic
wedge pressure was decreased by 4.1 mm Hg. Fig 5
shows P-V
curves for a 70-kg individual constructed from the capacitance data
found in our present animal study. Moving from A to B in the figure
represents a pressure drop of 4.1 mm Hg and would
decrease hepatic blood volume by 101 mL or 11% of the starting value.
This compares very well with the observed 9% reduction in hepatic
blood volume found by Risoe et al. If the blood volume change had been
entirely passive, that is, a decrease along the same P-V curve from A
to C, the blood volume decrement would have been 224 mL or 24%. This
illustrates how alterations in flow and distending pressure may obscure
active capacitance changes if adequate P-V relations are not monitored.
Greenway24 found a small increase in hepatic blood volume
and a concomitant fall in portal pressure with sodium nitroprusside.
Although P-V curves were not reported, the data suggest an active
increase in hepatic vascular capacitance similar to our findings.
The present method represents a significant improvement relative to previous methods with sonomicrometry, as we could construct pressure-volume curves rather than pressure-dimension curves.10 29 Furthermore, in vivo volumetrical calibrations at different liver volumes were performed, avoiding postmortem calibrations with possible distortion of hepatic configuration.9 11 Our finding of a near linear relationship between hepatic ventero-dorsal thickness and hepatic blood volume is seemingly in conflict with the cubic properties of volume. However, the anatomy of the pig liver with four elongated lobes with a tendency for a larger relative change in the ventero-dorsal dimension10 contribute to reduce the curvilinearity of the cubic volume-dimensional relationship. In terms of estimated hepatic blood volume change, the difference between using a linear and a cubic model of the volume-dimension curves was trivial, thereby justifying the use of the mathematically simple linear regression analysis.
Changes in liver thickness measured at different lobes varied somewhat in magnitude between pigs and to a lesser degree within each pig, but each dimension always maintained a constant relationship to hepatic blood volume as reflected by the low variability of the slope of their respective volume-dimension curves. Thus the calculated volume estimates from each of the two liver dimensions were similar during all the interventions in every pig. Greenway and Rothe12 also found a variability in slope calculated from different liver thickness measurements. As the authors discussed in their report, the variability between the separate thickness measurements would have been reduced with individual volumetric calibration. The large variability not accounted for by volume changes in the study of Greenway and Rothe, as compared with ours, could be due to species differences in liver anatomy and size. The larger pig liver has four elongated lobes, making it easy to obtain stable and good-quality sonomicrometric recordings along the ventero-dorsal axis.
Dimensional measurements cannot distinguish between changes in intravascular and extravascular volumes. However, hematocrit studies of transsinusoidal filtration rates by Bennett et al18 indicate that a large fraction of the extravascular volume can be readily mobilized to the blood pool and thus contributes to blood volume regulation. This indicates that changes in total liver volume reflect changes in the liver's blood volume reservoir.
Estimation of appropriate hepatic vascular distending pressure is
essential for the computation of pressure-volume curves. In the
present study pressure-volume curves were constructed during
transient occlusion of hepatic outflow, and hepatic venous pressure was
used to represent hepatic distending pressure. During baseline
and during infusion of isoprenaline and nitroprusside, the occlusion
caused initially a rapid rise in hepatic venous pressure toward portal
pressure, and during the main part of the occlusion period the two
pressures were essentially similar and rose in parallel (Fig 2A
). This
implies that pressure was uniform throughout the liver, and hepatic
vein pressure as well as portal pressure could be used to
represent distending pressure. During
norepinephrine (Fig 2B
) and phenylephrine
administration, however, there was a substantial pressure difference
across the liver throughout the entire occlusion period, and it was not
obvious which pressure should be used to represent distending
pressure. One possible approximation could be to use the mean of
hepatic vein pressure and portal pressure to represent the
average distending pressure. This, however, would require assumptions
about the distribution of resistance and capacitance along the
vasculature between the portal and the hepatic vein. As an alternative,
one could use hepatic vascular pressure with zero flow after
equilibration of all pressures. Because of the complexity of the latter
approach only a limited number of pressure-volume coordinates could be
obtained. In additional experiments with norepinephrine
infusion, we have compared hepatic and portal pressures during outflow
occlusion with the equilibrium pressure with no flow. A
representative experiment is displayed in Fig 6
. These preliminary data demonstrate
that hepatic vein pressure as recorded in the present study
during outflow occlusion approximates the hepatic equilibrium pressure
after cessation of all flow. Portal pressure, however, exceeded the
equilibrium pressure. This relationship was confirmed at a range of
different liver volumes. These observations support the notion that in
the present pig model, hepatic vein pressure during outflow
occlusion is a reasonable representation of hepatic distending
pressure.
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Localization of hepatic resistance has been debated. Bohlen et al,30 who used a micropipette technique to measure hepatic venular pressure, found that norepinephrine increased portal pressure but not hepatic venular pressure in dogs, rats, and rabbits. They concluded that portal and sinusoidal vasculatures are the dominant but not exclusive resistance sites in the liver. In contrast, Lautt and coworkers31 32 33 34 found localized pressure drops in the hepatic veins and concluded that the major hepatic vascular resistance was located in the hepatic veins in both cats and dogs. During norepinephrine infusion or hepatic nerve stimulation they found a significant increase in sinusoidal or presinusoidal resistance, but of lesser magnitude than that of postsinusoidal resistance. Maass-Moreno and Rothe35 also found localized pressure drops in the hepatic veins, but the apparent resistance sites varied with catheter size. Through a mathematical model, the authors argued that the observed pressure drops were artifacts caused by catheter obstruction. In our pig model with the hepatic vein catheter placed freely floating 1 to 2 cm from a wedged position, we found no evidence for an outlet sphincter in the large hepatic veins, since hepatic venous pressure decreased with norepinephrine. We cannot exclude sphincters located in the hepatic veins or venules upstream from our catheter, but most likely the large transhepatic pressure gradient during norepinephrine reflects an increase in resistance predominantly at presinusoidal and sinusoidal levels as demonstrated by Bohlen et al.30 From a teleological point of view, presinusoidal and sinusoidal constriction would be a more efficient way to mobilize blood from the liver than postsinusoidal constriction, since the latter would increase the upstream distending pressure and tend to cause pooling of blood in the sinusoids similar to the outflow block observed during histamine infusion.36
P-V curves recorded during complete outflow occlusion constitute continuous, near-linear curves, obtained within 20 seconds, and provide an accurate basis for calculations of slope and intercept. A potential objection is that the rapid rise in pressure thus induced may have ignored the "stress relaxation" of the vessels that occurs when time is permitted for pressure equilibration. This would result in underestimation of compliance in our model. However, our compliance estimates of 25 to 33 mL · mm Hg-1 · kg liver-1 compare well with previously reported estimates of 20 to 30 mL · mm Hg-1 · kg liver-1 (References 4 and 54 5 ) calculated from static pressure-volume points.
Construction of dynamic P-V curves necessitates occlusion of the inferior vena cava, which markedly reduces venous return and activates cardiovascular reflexes. We found that there was an increase in heart rate that mainly occurred during the last 10 seconds of the occlusion. The degree of cardiovascular reflex activation as estimated by increases in heart rate was similar irrespective of drug interventions. Furthermore, pressure-volume relations calculated from the initial 10 seconds of outflow occlusion were similar to the values calculated from the entire recording period, suggesting that reflex activation due to caval occlusion did not significantly alter the P-V curve.
Conclusions
The present in vivo pig model enabled quantification of
changes in hepatic capacitance by construction of reproducible hepatic
vascular pressure-volume curves. Thereby we could determine the
contributions from active and passive mechanisms to changes in hepatic
blood volume. The vasoconstrictor norepinephrine through
-adrenoceptor activation decreased and the vasodilator sodium
nitroprusside increased hepatic vascular capacitance by changing
unstressed blood volume with no change in compliance. These active
changes in capacitance represented more than 90% of the
observed blood volume change and would correspond to expulsion of up to
300 mL and pooling of up to 130 mL of blood, respectively in a 70-kg
individual, reflecting that the liver is not only a passive blood
reservoir but can respond actively and vigorously to pharmacological
interventions in the pig.
| Acknowledgments |
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Received April 21, 1997; revision received August 15, 1997; accepted September 1, 1997.
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