Arterial compliance in patients with cirrhosis:
stroke volume-pulse pressure ratio as simplified index
Jens H.
Henriksen,
Stefan
Fuglsang,
Flemming
Bendtsen,
Erik
Christensen, and
Søren
Møller
Departments of Clinical Physiology and Gastroenterology, Hvidovre
Hospital, University of Copenhagen, DK-2650 Hvidovre; and Clinic of
Internal Medicine I, Bispebjerg Hospital, University of Copenhagen,
DK-2400 Copenhagen, Denmark
 |
ABSTRACT |
Arterial function may be
altered in patients with cirrhosis. We determined compliance of the
arterial tree (C1) in relation to systemic and splanchnic
hemodynamic derangement and clinical variables. C1 and the
stroke volume-pulse pressure index (SV/PP) were significantly higher
(+62% and +40%, respectively; P < 0.001) in
cirrhotic patients (n = 49) than in control subjects
(n = 19), and a close correlation between
C1 and SV/PP was found in both cirrhotic patients
(r = 0.86, P < 0.001) and control
subjects (r = 0.96, P < 0.001).
Univariate analysis showed significant relations between C1
and SV/PP on one side and age, sex, body weight, portal pressure,
systemic hemodynamics, biochemical variables, and severity of disease
on the other. In the multiple-regression analysis, sex, age, mean
arterial blood pressure, systemic vascular resistance, and biochemical
variables were significant independent predictors of SV/PP
(P < 0.005-0.00001). In conclusion, arterial compliance is elevated in cirrhosis. A simplified SV/PP index seems to
reflect abnormalities in the arterial compliance of these patients.
cardiac output; circulatory regulation; hyperdynamic circulation.
 |
INTRODUCTION |
OVER THE LAST
DECADE, it has become apparent that abnormal distribution
of blood flow and volume in patients with cirrhosis is important for
the development of cardiovascular dysfunction, renal sodium-water
retention, and clinical outcome (5, 9, 11, 24, 25). In
addition to the presence of portal hypertension, these patients
typically present with a hyperdynamic systemic circulation with
increased heart rate, cardiac output, and plasma volume and low overall
vascular resistance (9, 33). The balance between
vasodilating and vasoconstricting forces is abnormal, especially in
decompensated patients (14, 26, 27). In addition to
changes in systemic vascular resistance, which is mainly located in
small arteries and arterioles, the function of larger arteries may also
be modulated in cirrhosis (2, 23).
Over the last decade attention has focused on the central vasculature
and, in particular, on assessing biophysical properties of the large
arteries, which have emerged as predictors of circulatory events
(34). Arterial compliance (i.e., change in luminal
arterial volume relative to change in transmural arterial blood
pressure) is largely unknown in cirrhosis, but recently in a
preliminary study (18) we found indications of elevated
arterial compliance in advanced disease that could indicate changes in
static composition of the arterial wall or dynamic changes in the
smooth muscle tone of the large arteries. Arterial compliance was
recently assessed in a simple way as stroke volume relative to pulse
pressure and was described in a large reference population
(4).
The present study was undertaken to measure the arterial compliance
from the arterial pressure curve and to evaluate the stroke volume-pulse pressure ratio (SV/PP) as an index of arterial compliance in patients with cirrhosis. In addition, we have determined its relation to systemic and splanchnic hemodynamics and clinical variables.
 |
PATIENTS AND METHODS |
Study population.
The study population comprised 49 patients with cirrhosis who were
referred for hemodynamic investigation to diagnose and quantify portal
hypertension. Of these, 44 patients had biopsy-verified cirrhosis. The
age range was 32-81 yr with an average of 50 yr. The etiology was
alcoholic in 43 and chronic hepatitis in 4, and no specific etiology
could be established in 2 patients. None of the patients had
experienced recent gastrointestinal bleeding or had encephalopathy
above grade I. All were abstaining from alcohol and had no signs of
withdrawal symptoms at the time of the study. None had signs of heart
failure, organic renal disease, diabetes, cancer, or any other major
disease. The patients were divided into three groups with increasing
severity of disease according to the modified Child-Turcotte criteria
(8). Fourteen patients belonged to class A, twenty to
class B, and fifteen to class C. Ultrasonography showed ascites in 15 patients, but none had signs of subacute spontaneous bacterial
peritonitis. The patients with ascites were prescribed a diet with 40 mmol of sodium a day. Twenty-five patients received diuretics
(100-400 mg spironolactone/day in 22, 2-4 mg bumetanide/day
in 6, 40-160 mg furosemide/day in 14, and 5 mg
bendroflumethiazide/day in 2). One patient was treated with a beta
blocker, one with a calcium antagonist, and one with a nitrate. The
clinical and biochemical characteristics are summarized in Table
1.
One control group comprised 19 patients without liver disease who were
referred for hemodynamic investigation to exclude circulatory disorders
(mainly intestinal ischemia), for which no evidence was found.
All had normal arterial blood pressure (i.e., diastolic pressure <90
mmHg). Five patients received diuretics (80 mg furosemide/day), one a
calcium antagonist, and one a nitrate. Clinical and biochemical data of
these normotensive controls are summarized in Table 1.
A second control group consisted of 16 patients with arterial
hypertension (i.e., untreated diastolic pressure >95 mmHg) referred for hemodynamic investigation to exclude renovascular hypertension with
unilateral renal generation of renin. None had signs of heart failure,
diabetes, cancer, or any other major disease. The final diagnosis was
essential hypertension in all 16 patients. Ten patients received
diuretics (40-160 mg furosemide/day in 3 and 5 mg
bendroflumethiazide/day in 7), four patients were treated with calcium
antagonists, and one was treated with a beta blocker. Clinical and
biochemical data are summarized in Table 1.
All the patients consented to participate in the study, which was
approved by the Ethics Committee for Medical Research in Copenhagen and
performed in accordance with the guidelines established in the Helsinki
Declaration II. No complications or side effects were encountered
during the study.
Catheterization.
Catheterization was performed to quantify arterial and portal
hypertension, to determine the response of food-induced splanchnic flow, and to collect elective renin samples. All the subjects were
studied in the morning after an overnight fast and at least 1 h in
the supine position, as described elsewhere (13, 25, 27).
In brief, a Cournand catheter (7 F) or a Swan-Ganz catheter (7 F) was
guided to the hepatic/renal veins through the femoral route under
fluoroscopic control with the patient under local analgesia. A small
indwelling polyethylene catheter (5 F) was introduced into the femoral
artery by the Seldinger technique with the tip of the catheter located
at the aortic bifurcation.
Pressures were measured with a capacitance transducer (Simonsen and
Weel, Copenhagen, Denmark), as previously described (27). Frequency characteristics and reliability of dynamic intravascular pressure measurement, including determination of systolic and diastolic
pressures, had been assessed earlier with this equipment (27). Systolic arterial blood pressure (SAP) was
determined as the average of the maximum blood pressure over 20-30
s [SAP = (
Ps)/n; where Ps
is systolic pressure of a single cycle and n is number of
cycles], and diastolic arterial blood pressure [DAP = (
Pd)/n; where Pd is diastolic
pressure] was determined as the average of the minimum blood pressure
in the same period. The start of the diastolic pressure was
determined at the dicrotic notch [DAPo = (
Po)/n]. Pulse pressure (PP, i.e., SAP
DAP) was determined as the average amplitude of the arterial
pressure over 20-30 s. The mean arterial pressure (MAP) was
determined independently by electronic integration of the pressure
signal. Right atrial pressure (RAP) was determined as the mean pressure
over 15 s. The hepatic venous pressure gradient (HVPG) was
determined as wedged minus free hepatic venous pressure. Zero reference
was the midaxillary level, and all pressures were measured in
millimeters of mercury. The time (
t) from the start of
the electrical systole [start of the R wave in the electrocardiogram
(ECG)] to the start of the aortoiliac mechanical systole was
determined from simultaneous registration of the ECG and pressure curve
(see Fig. 1). QT interval (in s) was
determined from the ECG, and the frequency was adjusted by standard
equation: QTc = QT/
,
where T (in s) is the time of the RR interval.

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Fig. 1.
Illustration of pressures and time relations.
P(t), arterial blood pressure as a function of time; SAP,
average systolic arterial pressure; DAP, average diastolic arterial
pressure; DAPo, average start of diastolic pressure;
Po, start of diastolic blood pressure; Pd, end
of diastolic blood pressure; MAP, mean arterial blood pressure;
t1, time from start to end of diastole;
t2, time from peak systole to end of diastole;
T, time of 1 cardiac cycle; t, time from start
of electrical systole to aortoiliac mechanical systole; ECG,
electrocardiogram.
|
|
Cardiac output (COI, in l/min) for the determination of
arterial compliance was measured by the indicator-dilution technique after a bolus injection of 150 KBq of 125I-labeled human
serum albumin (IFE IT.20S, Institute of Energy Technique, Kjeller,
Norway) into the right atrium, followed by arterial sampling as
previously described (13, 25).
Plasma volume (PVTc), blood volume (BVTc),
central circulation time, and additional measurement of cardiac output
(COTc) were determined by another indicator,
independent of the 125I indicator determination, as
described elsewhere (13). A quantitative injection of 0.5 MBq of 99mTc-labeled human serum albumin (Vasculocis, CIS
bio international, Grif-sur-Yvette, France) was given into the right
atrium, followed by automatic arterial sampling for 60 s and at 10 min as previously described (13, 25). Systemic vascular
resistance (SVR, dyn · s · cm
5) was
determined as SVRTc = 80 (MAP
RAP)/COTc.
Arterial compliance was estimated in different ways as outlined in the
APPENDIX. The compliance of the central arterial tree was
determined according to a two-element windkessel model (3, 20,
37) that assumes that compliance (C) and hemodynamic resistance (R) are constant during the measurement. An acceleration
component was ignored because it contributed <10% (see
APPENDIX).
Figure 1 illustrates arterial pressure over time [P(t)].
As shown in the APPENDIX, P(t) can be expressed
during diastole as
|
(1)
|
where Po is the start of diastolic pressure. The end
of the diastolic pressure (Pd) is then
|
(2)
|
Isolation of C in Eq. 2 gives
C1 with the corresponding time
t1
|
(3)
|
where t1 is the time from the start to
the end of diastole (in s).
Substitution of R, Po, and Pd in
Eq. 3 with the directly measured values gives
|
(4)
|
In the entire interval of declining pressure, another estimate
of arterial compliance, C2, can be obtained
|
(5)
|
(see APPENDIX), where t2 = time (in s) from the systolic maximum to the diastolic minimum pressure.
As described in the APPENDIX, arterial compliance can be
estimated in a more simple way (decay time principle) as
|
(6)
|
where SVI is stroke volume (in ml) determined by the
125I indicator as COI divided by heart rate
(HR) and T is the time (in s) of one heartbeat [i.e., 1/HR
(in s)].
Similarly, another simplified estimate is C2'
|
(7)
|
In the case in which t2/T is
relatively constant, a simplified index of arterial
compliance can be determined as SVI/PP (= SV/PP).
Statistical evaluation.
Data are presented as means ± SE. Statistical analysis was
performed by one-way ANOVA with Tukey's correction or by the
Kruskal-Wallis ANOVA on ranks with Dunn's correction or, in the case
of bivariate data, by unpaired/paired Student's t-test or
the Mann-Whitney and/or Wilcoxon rank tests. Correlations between
variables were performed with the Pearson regression test (method of
least squares) or by Spearman's rank correlation test.
Multiple-regression analysis was performed to evaluate the relation
between estimates of arterial compliance on the one hand and pertinent
clinical, biochemical, and hemodynamic variables on the other. All
variables were initially examined and included stepwise with the
forward selection method. P < 0.05 was considered to
be significant.
 |
RESULTS |
Hemodynamics, time intervals, and arterial compliance.
Table 2 summarizes the hemodynamics. As
expected, the cirrhotic patients were hyperdynamic with elevated CO
(+31%, P < 0.001), HR (+8%, P < 0.05) and SV (+22%, P < 0.001). The mean central circulation time shortened with the progression of the liver disease (
24%, P < 0.05). The arterial blood pressure was
slightly (
7%, P < 0.01) reduced or frankly (
16%,
P < 0.001) reduced in the patients with severe
disease. In the control subjects, MAP was close to DAPo but
significantly lower (104 ± 2.9 vs. 108 ± 3.2 mmHg,
difference 3.7 ± 1.1 mmHg, P < 0.001;
r = 0.94, P < 0.001). In the
patients with cirrhosis, MAP and DAPo were almost
identical: 89.4 ± 2.2 vs. 89.6 ± 2.0 mmHg (difference 0.2 ± 1.4 mmHg, not significant; r = 0.92, P < 0.001). PVTc and
BVTc were elevated [+35% (P < 0.001) and
+30% (P < 0.001)], and SVRTc was reduced (
28%, P < 0.001), especially in the patients with
severe disease (
34%, P < 0.01). RAP was normal, and
the splanchnic pressures, especially HVPG, were substantially increased
(+358%, P < 0.001). The differences between the
normotensive and hypertensive control subjects were solely related to
the higher arterial blood pressure in the latter group (MAP: 114 vs. 96 mmHg, P < 0.001).
Time intervals t1, t2,
T, t1/T, and
t2/T were remarkably similar in the
patients with cirrhosis and the control subjects, except for a slightly
higher t2/T in the patients with
severe cirrhosis (+3%, P < 0.05; see Table
3). The small differences could be
ascribed solely to the slight differences in HR of the cirrhotic
patients and controls.
C1 was directly related to the time from the start of the
electrical systole to the start of the aortoiliac mechanical systole (
t) (Fig. 2), which
indicates a direct relation between pulse propagation time and arterial
compliance. The different estimates of arterial compliance showed
the same trend in the different groups (Table
4). The lowest values of compliance were
found in the hypertensive control subjects. The cirrhotic patients had substantially higher values than both control groups either taken separately or together (40-79%, P < 0.001). In
the cirrhotic group, the compliance estimates in Child-Turcotte class A
patients were higher, although not significantly (14-26%,
P = 0.07-0.2), compared with the normotensive
control subjects. A significant increase was observed through
Child-Turcotte classes A to C, with the values in the class B and C
patients significantly above the control values (+74-76%,
P < 0.01). The C1 and
C1' values were significantly higher than all other
compliance estimates (P < 0.0001). C1 and C1' were not significantly different in the control
groups, but C1' was somewhat higher than
C1 in the patients with cirrhosis (+13.8%,
P < 0.001). In contrast, C2 and
C2' were not significantly different, either in the
cirrhotic patients or in the control subjects. The SV/PP values were
significantly higher than the C2 and
C2' values (P < 0.0001). A close
correlation was found between C1 on the one hand and
C1', C2, C2', and
SV/PP on the other, with the highest relation found among the
controls (Fig. 3). A somewhat smaller,
but still close and highly significant, relation was present in the
cirrhotic patients (Table 5 and Fig. 3).
The relationship between C1 and SV/PP revealed a somewhat lower slope in the patients with cirrhosis than in the control subjects
(0.54 vs. 0.82, P < 0.001), which means that the high values of SV/PP in patients with cirrhosis may underestimate the even
higher values of C1. This was also found with respect to the relation of C1 to C2 and
C
(see Table 5). C1 is in the main a
diastolic compliance, whereas C2 and SV/PP are both mixed
diastolic and systolic compliance estimates.

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Fig. 2.
Relation between arterial compliance (C1) and
t. , Control subjects; ,
cirrhosis patients (Child-Turcotte classes A, B, and C);
, all patients with cirrhosis.
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Fig. 3.
Different estimates of arterial compliance in patients with
cirrhosis and control subjects (C1,
C1', C2, C2') and
stroke volume-pulse pressure ratio (SV/PP) (see text and Table 4).
, Patients with cirrhosis; ,
normotensive control subjects; , hypertensive control
subjects. Correlations are summarized in Table 5.
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Table 5.
Slopes and correlations between different estimates of arterial
compliance in controls and patients with cirrhosis
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Relation of arterial compliance to clinical, biochemical, and
hemodynamic variables.
The univariate correlations are summarized in Table
6. SV/PP showed a significant correlation
to age, sex, body weight, Child-Turcotte score, coagulation factors 2, 7, and 10, MAP, SVRTc, PVTc, BVTc, and HVPG. SV/PP was determined independently of MAP, PVTc,
and SVRTc and can therefore be stochastically analyzed with
these and other variables. SV/PP was inversely related to MAP in both the cirrhotic patients and the control subjects (Fig.
4; cirrhotic patients: r =
0.44, P < 0.002 and control subjects:
r =
0.45, P < 0.01). A direct
relation was found between SV/PP and PVTc (Fig.
5; cirrhotic patients: r = 0.52, P < 0.005 and control subjects: r = 0.39, P = 0.05), and SV/PP was inversely related to
SVRTc (Fig. 6; cirrhotic
patients: r =
0.73, P < 0.0001 and
control subjects: r =
0.69, P < 0.001). SV/PP was directly related to HVPG (Fig.
7; cirrhotic patients: r = 0.31, P < 0.02). Higher SV/PP values were recorded
in men than in women (+46% in cirrhotic patients, P < 0.01; +31% in control subjects, P < 0.01), but this difference was not marked after adjustment for body size
(P = 0.05).

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Fig. 4.
Relations between SV/PP estimate of arterial compliance
and MAP. Symbols are as in Fig. 3 (cirrhosis patients:
r = 0.443, P < 0.002; control
subjects: r = 0.453, P < 0.01).
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Fig. 5.
Relation between SV/PP estimate of arterial compliance
and independent determination of plasma volume with technetium
indicator (PVTc). Symbols are as in Fig. 3 (cirrhosis
patients: r = 0.516, P < 0.01; control
subjects: r = 0.391, P = 0.05).
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Fig. 6.
Relation between SV/PP estimate of arterial compliance
and independent determination of systemic vascular resistance with
technetium indicator (SVRTc). Symbols are as in Fig. 3
(cirrhosis patients: r = 0.730, P < 0.00001; control subjects: r = 0.694,
P < 0.001).
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Fig. 7.
Relation between SV/PP estimate of arterial compliance
and portal pressure (hepatic venous pressure gradient: HVPG). Symbols
are as in Fig. 3 (cirrhosis patients: r = 0.31, P < 0.02; cirrhosis patients + normotensive
control subjects: r = 0.41, P < 0.01).
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In addition to the above-mentioned correlations, multiple-regression
analysis demonstrated that age, sex, coagulation factors 2, 7, and 10, MAP, and SVRTc were independent predictors of SV/PP. Body
weight, PVTc, and BVTc were borderline
significant (P = 0.1). The analysis identified the same
variables in separate analyses of patients with cirrhosis with and
without the inclusion of controls (see Table 6).
 |
DISCUSSION |
This study is the first to analyze in depth arterial compliance in
cirrhosis. We found that 1) arterial compliance is increased in patients with cirrhosis; 2) a simplified SV/PP index can
be applied as an estimate of arterial compliance in cirrhosis; and 3) in addition to a relation to demographic variables, the
increased arterial compliance in patients with cirrhosis is related to
hemodynamic derangement and indicators of severity of disease.
Determination of arterial compliance is complex (3, 20, 32,
37). The static and dynamic characteristics of the walls of
large and small arteries may be different, and a detailed investigation involves analysis of the relation between volume changes over time and
the arterial pressure curve. Accurate determination of arterial
compliance requires a definite stroke output-time relation and a blood
pressure-time relation at the aortic arch (41). Although
these complex registrations can be obtained with a combination of
several techniques in a highly experimental setup, in humans they are
made seldom or only during very invasive investigations of coronary
arteries (34, 37). An accurate blood pressure-time relation is most often combined with a more lumped registration of
output from the left ventricle (3, 18, 20, 37). Other clinical methods are measurements of pulse wave velocity, echo tracking, and volume oscillometry (20, 29, 30, 42).
Compliance may also be determined in a specific segment of the arterial
tree (20, 34, 35, 37).
SV/PP as an index of arterial compliance.
C1 is the average arterial compliance in diastole, as
determined by a catheterization technique with registration of the
pressure-time relationship in the aorta and mass-energy balance
equations (2-element windkessel model). It should be kept in mind that
the differential compliance (dV/dP) is dependent on the level of the
arterial pressure in a nonlinear, inverse relation. Thus systolic
compliance is smaller simply because of the higher pressure in this
part of the cardiac cycle. C1 and C'1
were close in the control group, thus indicating that the assumption of
an exponential decline in diastolic pressure is correct (Refs.
3, 20, and 41; see below). In the
patients with cirrhosis, C1 and C1'
were closely related but slightly higher values of
C1' were registered. The reason is most likely a
slight but systematic deviation from the exponential fall in pressure
in these patients, especially in those with advanced disease
(Child-Turcotte class C: r2 = 0.978, compared with r2 = 0.984, 0.986, 0.984, and
0.981 in class A, class B, normotensive control subjects, and
hypertensive control subjects, respectively). Propagation velocities of
the pressure pulse and its reflected wave in a compliant aorta are
reduced, thus moving the reflected wave from early diastole to late diastole.
C2 includes compliance in the systole and is, as expected,
below the C1 estimate in both patients and control subjects
but closely related to C1. The very close relation between
C2 and C2' illustrates that the
assumptions of constant time ratios (see Table 3) and an exponential
decline in pressure even when parts of systole are included are
reasonably correct. C2' and SV/PP only differ in
the factor t2/T. Thus SV/PP contains
components of both systolic and diastolic arterial compliance, and it
had a rather close relation to C1, but the numerical value
of SV/PP was somewhat lower than that of C1 (
15% in the
normotensive control group). However, in patients with cirrhosis this
discrepancy became somewhat larger, especially with very high values of
arterial compliance (
24%). Thus the true value of arterial
compliance in a patient with a high SV/PP index may be even higher than
the value estimated from this index. The reason may be that, although arterial blood pressure and pulse pressure are reduced in patients with
cirrhosis, especially in advanced disease, the ratio of PP to the fall
in pressure during diastole may be higher in patients with advanced
disease than in those with early disease and in control subjects.
However, the reason is not clear, and from a practical point of view
the difference is negligible.
The simplified SV/PP index of compliance of the arterial tree was
recently substantiated in a large population (4). Thus SV
measurements by echocardiography and PP measurements by arm cuff proved
to be adequate in large population studies (4, 32). In our
study, we determined PP and MAP directly and independently at the
aortic bifurcation/iliac arteries, which are taken to be representative
of the large arteries (40). SV is accurately determined by
HR and the indicator dilution flow over ~20 s (7), and
evaluations have shown a close similarity to values obtained by
echocardiography (4, 19). The reason for applying direct measurement and using the indicator-dilution technique is that these
methods are highly standardized (13, 16, 17). Owing to a
somewhat higher pulse amplitude found by direct measurement compared
with that by the cuff method (27), SV/PP values are somewhat lower in the control subjects in the present study than those
found by the indirect cuff method (4).
The time relation between maximal systolic blood pressure, the start of
diastolic blood pressure, and the end-diastolic blood pressure was
remarkably similar in the different groups, and when adjusted for the
small differences in heart rate any difference almost disappeared. A
low arterial compliance may contribute to early peripheral reflection
of the arterial pulse curve (owing to the fast rate of pulse
propagation) with a delayed and higher maximum of the systolic blood
pressure (29, 30, 42). This was not observed, probably
because our hypertensive controls had almost normal arterial compliance
and the patients with cirrhosis had elevated values (with a slow rate
of pulse propagation). The importance of the constancy of time ratios
and time-pressure relations is considered in the APPENDIX.
An increase in error has been reported when the duration of the
diastolic phase is reduced. This was the case with high heart rate and
mild exercise, in which the duration of the diastole was shortened from
0.63 s to 0.27 s. (37). In the present study
this figure was not problematic (0.44 s). A long QTc
(frequency-adjusted electric systole) has been reported in cirrhotic
patients with advanced disease (1). We did not find
significantly prolonged QTc or frequency-adjusted mechanic
systole (1
t1/T) in patients
with advanced disease, and T
t1 and QT were closely related and similar in
the different groups (Table 3). In addition to the isovolumetric time
interval, the registration of the arterial blood pressure curve at the
aortic bifurcation instead of the aortic arch may contribute to the
difference between T
t1 and QT.
Relation to gender, body size, and severity of disease.
As expected, estimates of arterial compliance increased with increasing
body size. Moreover, the difference in gender (higher values in males)
was less pronounced when values were adjusted for difference in body
size. SV/PP increased with increasing severity of the disease, and it
was shown earlier that patients with advanced cirrhosis, although
hyperkinetic, are hyporeactive at the arteriolar level (2, 22,
23, 28). In addition, a number of in vitro studies showed
decreased reactivity of medium-sized and large arteries to several
vasoconstrictors in experimental cirrhosis (2, 21, 23,
43). Changed dynamic and static functions of the arterial tree
may contribute to abnormal reactions of volume and baroreceptors
(30, 34). Elevated compliance may not only be confined to
the large and medium-sized arteries. All compliance estimation methods
are sensitive to compliance contributions from small peripheral vessels
(>1 mm in diameter) (37). It was shown earlier that
peripheral compliance represents only a small fraction (~20% of the
total compliance), and the bulk of the compliance in normal subjects
(~65%) is contained in the aortic trunk (ascending, descending,
thoracic, and abdominal aorta). Therefore, the compliance estimation
methods are sensitive not only to what happens in the aorta and large
proximal arteries but also to a lesser extent to the smaller arteries.
Thus, if present in the smaller arteries in the mesenteric tree,
increased compliance may contribute to splanchnic blood flow
abnormalities in cirrhosis (12). Increased vascular distensibility may, especially in areas with increased shear
stress, contribute to local dilatations and potentially to the
development of arteriovenous communications (40).
The level of coagulation factors 2, 7, and 10 contains major
prognostic information (the lower the level, the higher the mortality). Because arterial compliance was inversely related to coagulation factors 2, 7, and 10, in both the univariate and multiple-regression models, arterial compliance may contain prognostic information. However, this aspect needs further clarification.
Relation to arterial pressure and hemodynamic derangement.
One of the most important determinants of arterial compliance is the
level of the arterial pressure (3, 20, 32, 37). This holds
true both for the control groups and the patients with cirrhosis.
However, the regression analyses identified relations other than that
with the arterial pressure. A larger volume of blood and plasma was
related to increased arterial compliance. This is somewhat surprising
because most of the surplus blood and plasma in cirrhosis are contained
within the venous system (13). Another important relation
was to SVR. The latter reflects tonus in the arterioles. However, the
arteriolar tonus adjusts the level of arterial blood pressure and may
thereby also influence large artery compliance. In fact, arterial
compliance should depend on the properties of arterial intrinsic
elastic and smooth muscle, whereas arteriolar tone should result more
from the balance between vasoconstrictors and vasodilators. Recent data
suggest that the hyperdynamic circulation is mainly caused by
circulatory alterations in the splanchnic area (6, 10,
39). Thus arteriolar vasodilatation would be a more localized
event, whereas elevation in arterial compliance may be more
"systemic." Arterial compliance may be influenced by
vasoactive drugs, which potentially may be used for correction of the
circulatory derangement in cirrhosis (15). However, in the
present study only a few patients in the cirrhotic and control groups
received drugs with potential vasoactive effects. The discrimination of
static (relating to collagen, elastin, deposit) versus dynamic
(relating to smooth muscle cell tonus) compliance requires
manipulation, for instance, with vasoactive drugs, without changing the
mean arterial blood pressure (isobaric conditions). Thus a simplified
index of arterial compliance may be an integral variable for vascular
responsiveness, together with the systemic vascular resistance.
However, these aspects are for future studies.
In conclusion, arterial compliance is elevated in cirrhosis. Besides a
relation to age, body size, sex, and the level of the arterial blood
pressure, arterial compliance is directly related to the severity of
cirrhosis and the hyperdynamic circulatory derangement. A simplified
stroke volume/pulse pressure index reflects the arterial compliance and
thereby the cardiac load.
 |
APPENDIX |
Derivation of a simplified expression of arterial compliance.
All compliance estimation methods are based on either a two-element
windkessel model or a three-element windkessel model of the systemic
arterial tree. The fundamental relation between blood pressure (P),
volume flow (
), and hemodynamic resistance (R) can be simplified as
|
(A1)
|
or
|
(A1a)
|
Power delivery (E) from the heart to the aorta is
|
(A2)
|
simplified as
|
(A2a)
|
because the contribution of acceleration
(1/2 ·
·
2) is small
(<10%; if P = 120 mmHg and
= 10 l/min (~10
kg/min), then the product E = P ·
= 160 J/min = 2.7 W, and if it is
assumed that the linear velocity in the aorta is up to
= 1.5 m/s, then 2
·
2 = 11.3 J/min = 0.2 W).
Arterial compliance (C) is defined as a change in volume (dV) relative
to a change in transmural pressure (dP)
|
(A3)
|
In the following, it is assumed that R and C are
constant in time, whereas E and P are functions of time
[E(t) and P(t), respectively], and that
= dV/dt.
From Eq. A2a follows
|
(A4)
|
The volume displacement (dV) from the heart in systole can be
divided into a fraction retained in the arterial tree (dVa) and a fraction passing through arterioles (dVb)
|
(A5)
|
With this notation, Eqs. A3 and A1a can be
rearranged.
|
(A6)
|
|
(A7)
|
By multiplication with P(t)/dt on both
sides in Eq. A5 and substitution with Eqs. A6,
A7, and A2a, the following equations can be
derived
|
(A8)
|
and dividing by C · P(t)
|
(A9)
|
During diastole, power and volume flow are zero
[E(t) = 0 and
= 0]; consequently,
Eqs. A8 and A9 can be reduced to
|
(A10)
|
and integrated from 0 to t
|
(A11)
|
where Po is pressure at the start of diastole
(2-element windkessel model; Ref. 37).
By substitution in Eq. A11 of diastolic pressure
[Pd = P(t)], t becomes the
time (t1) from Po to Pd
|
(A12)
|
and isolation of C, which in this time interval is termed
C1, gives
|
(A13)
|
The hemodynamic resistance can be expressed as
|
(A14)
|
where p is the difference in mean pressure from the
arterial system to the right atrium. Substitution of Eq. A14
in Eq. A13 gives
|
(A13a)
|
or by applying the variables measured in the present study
|
(A13b)
|
where CO is cardiac output, MAP is mean arterial pressure, RAP
is right atrial pressure, DAPo is the start of diastolic
pressure, DAP is end-diastolic pressure, and t1
is the time from DAPo to DAP.
In a strict mathematical sense, the method is valid only when the
local flow is zero (i.e., ascending aorta during diastole). However,
the central arterial tree may be lumped and input may be considered
close to zero at peak systolic pressure. If t2
is the time from SAP to DAP, another expression of C in the time interval t2 (C2) can be derived from
Eq. A13a
|
(A13c)
|
Several studies have substantiated that the pressure decay from
Po to Pd can be approximated to a
monoexponential function in the resting condition (20,
37). In this case, p = (Po
Pd)/ln(Po/Pd), where p
is assumed to be equal to the temporal average between Po
and Pd and almost equal to the mean pressure gradient from
the arterial system to the right atrium. From Eq. A14
follows
|
(A14a)
|
From Eqs. A13a and A14a an approximate
compliance (C
) can be determined
|
(A14b)
|
and by directly measured values
|
(A15)
|
or dividing by heart rate (HR)
|
(A16)
|
where SV is stroke volume and T is the time of one
heartbeat (= 1/HR).
Similarly, from Eqs. A13a, A13c, and
A14a
|
(A15a)
|
and
|
(A15b)
|
where PP is pulse pressure (i.e., SAP
DAP).
If t2/T is constant (Table 3), the
simplified expression
|
(A17)
|
may be taken as an index of arterial compliance.
 |
FOOTNOTES |
Address for reprint requests and other correspondence: J. H. Henriksen, Dept. of Clinical Physiology, 239, Hvidovre Hospital, Univ. of Copenhagen, DK-2650 Hvidovre, Denmark (E-mail:
jens.h.henriksen{at}hh.hosp.dk).
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. Section 1734 solely to indicate this fact.
Received 25 September 2000; accepted in final form 25 October 2000.
 |
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