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
TOP
ABSTRACT
INTRODUCTION
PATIENTS AND METHODS
RESULTS
DISCUSSION
APPENDIX
REFERENCES

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
TOP
ABSTRACT
INTRODUCTION
PATIENTS AND METHODS
RESULTS
DISCUSSION
APPENDIX
REFERENCES

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
TOP
ABSTRACT
INTRODUCTION
PATIENTS AND METHODS
RESULTS
DISCUSSION
APPENDIX
REFERENCES

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.

                              
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Table 1.   Clinical and biochemical data for patients with cirrhosis and control groups

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 = (Sigma Ps)/n; where Ps is systolic pressure of a single cycle and n is number of cycles], and diastolic arterial blood pressure [DAP = (Sigma 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 = (Sigma 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 (Delta 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/<RAD><RCD><IT>T</IT></RCD></RAD>, 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; Delta 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
P(<IT>t</IT>)<IT>=</IT>P<SUB>o</SUB><IT>·e<SUP>−t/RC</SUP></IT> (1)
where Po is the start of diastolic pressure. The end of the diastolic pressure (Pd) is then
P<SUB>d</SUB><IT>=</IT>P<SUB>o</SUB><IT>·e</IT><SUP><IT>−t<SUB>1</SUB>/RC</IT></SUP> (2)
Isolation of C in Eq. 2 gives C1 with the corresponding time t1
C<SUB><IT>1</IT></SUB><IT>=</IT><FR><NU><IT>t<SUB>1</SUB></IT></NU><DE><IT>R·</IT>ln (P<SUB>o</SUB><IT>/</IT>P<SUB>d</SUB>)</DE></FR> (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
C<SUB><IT>1</IT></SUB><IT>=</IT><FR><NU>CO<SUB><IT>1</IT></SUB><IT>·t<SUB>1</SUB>·1,000/60</IT></NU><DE>(MAP<IT>−</IT>RAP)<IT>·</IT>ln (DAP<SUB>o</SUB><IT>/</IT>DAP)</DE></FR> (4)
In the entire interval of declining pressure, another estimate of arterial compliance, C2, can be obtained
C<SUB><IT>2</IT></SUB><IT>=</IT><FR><NU>CO<SUB><IT>1</IT></SUB><IT>·t<SUB>2</SUB>·1,000/60</IT></NU><DE>(MAP<IT>−</IT>RAP)<IT>·</IT>ln (SAP<IT>/</IT>DAP)</DE></FR> (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
C<IT>′<SUB>1</SUB>=</IT>[SV<SUB>I</SUB><IT>/</IT>(DAP<SUB><IT>o</IT></SUB><IT>−</IT>DAP)]<IT>·</IT>(<IT>t<SUB>1</SUB>/T</IT>) (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'
C<IT>′<SUB>2</SUB>=</IT>[SV<SUB>I</SUB><IT>/</IT>(SAP<IT>−</IT>DAP)]<IT>·</IT>(<IT>t<SUB>2</SUB>/T</IT>)<IT>=</IT>(SV<SUB>I</SUB><IT>/</IT>PP)<IT>·</IT>(<IT>t<SUB>2</SUB>/T</IT>) (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
TOP
ABSTRACT
INTRODUCTION
PATIENTS AND METHODS
RESULTS
DISCUSSION
APPENDIX
REFERENCES

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).

                              
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Table 2.   Hemodynamics in patients with cirrhosis and control groups

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.

                              
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Table 3.   Times and time relations of arterial pulse curve from patients with cirrhosis and control groups

C1 was directly related to the time from the start of the electrical systole to the start of the aortoiliac mechanical systole (Delta 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<UP><SUB>2</SUB><SUP>′</SUP></UP> (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 Delta t. , Control subjects; , cirrhosis patients (Child-Turcotte classes A, B, and C); open circle , all patients with cirrhosis.


                              
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Table 4.   Different determinations of arterial compliance in patients with cirrhosis and control groups



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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; triangle , 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

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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Table 6.   Relation between estimates of arterial compliance and clinical and hemodynamic variables



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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).

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
TOP
ABSTRACT
INTRODUCTION
PATIENTS AND METHODS
RESULTS
DISCUSSION
APPENDIX
REFERENCES

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
TOP
ABSTRACT
INTRODUCTION
PATIENTS AND METHODS
RESULTS
DISCUSSION
APPENDIX
REFERENCES

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 (V), and hemodynamic resistance (R) can be simplified as
P<IT>=R·</IT><A><AC>V</AC><AC>˙</AC></A> (A1)
or
<A><AC>V</AC><AC>˙</AC></A><IT>=</IT>P<IT>/R</IT> (A1a)
Power delivery (E) from the heart to the aorta is
E=P<IT>·</IT><A><AC>V</AC><AC>˙</AC></A><IT>+½</IT><A><AC>V</AC><AC>˙</AC></A><IT>·ϑ<SUP>2</SUP></IT> (A2)
simplified as
E=P<IT>·</IT><A><AC>V</AC><AC>˙</AC></A> (A2a)
because the contribution of acceleration (1/2 · V · theta 2) is small (<10%; if P = 120 mmHg and V = 10 l/min (~10 kg/min), then the product E = P · V = 160 J/min = 2.7 W, and if it is assumed that the linear velocity in the aorta is up to theta  = 1.5 m/s, then V · theta 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)
C<IT>=</IT>dV<IT>/</IT>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 V = dV/dt.

From Eq. A2a follows
E(t)=P(<IT>t</IT>)<IT>·</IT>dV<IT>/</IT>d<IT>t</IT> (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)
dV<IT>=</IT>dV<SUB>a</SUB><IT>+</IT>dV<SUB>b</SUB> (A5)
With this notation, Eqs. A3 and A1a can be rearranged.
dV<SUB>a</SUB><IT>=</IT>C<IT>·</IT>dP(<IT>t</IT>) (A6)

dV<SUB>b</SUB><IT>=</IT>(P(<IT>t</IT>)<IT>/R</IT>)<IT>·</IT>d<IT>t</IT> (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
E(t)=C<IT>·</IT>P(<IT>t</IT>)<IT>·</IT>dP(<IT>t</IT>)<IT>/</IT>d<IT>t+</IT>P(<IT>t</IT>)<SUP><IT>2</IT></SUP><IT>/R</IT> (A8)
and dividing by C · P(t)
<A><AC>V</AC><AC>˙</AC></A><IT>/</IT>C<IT>=</IT>dP(<IT>t</IT>)<IT>/</IT>d<IT>t+</IT>P(<IT>t</IT>)<IT>/</IT>(<IT>R·</IT>C) (A9)
During diastole, power and volume flow are zero [E(t) = 0 and V = 0]; consequently, Eqs. A8 and A9 can be reduced to
dP(<IT>t</IT>)<IT>/</IT>P(<IT>t</IT>)<IT>=</IT>−(<IT>1/</IT>RC)d<IT>t</IT> (A10)
and integrated from 0 to t
P(<IT>t</IT>)<IT>=</IT>P<SUB>o</SUB><IT>·e</IT><SUP><IT>−t/R</IT>C</SUP> (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
P<SUB>d</SUB><IT>=</IT>P<SUB>o</SUB><IT> · e</IT><SUP><IT>−t<SUB>1</SUB>/RC</IT></SUP> (A12)
and isolation of C, which in this time interval is termed C1, gives
C<SUB><IT>1</IT></SUB><IT>=</IT><FR><NU><IT>t<SUB>1</SUB></IT></NU><DE><IT>R·</IT>ln (P<SUB>o</SUB><IT>/</IT>P<SUB>d</SUB>)</DE></FR> (A13)
The hemodynamic resistance can be expressed as
R=p/<A><AC>V</AC><AC>˙</AC></A> (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
C<SUB><IT>1</IT></SUB><IT>=</IT><FR><NU><IT>t<SUB>1</SUB>·</IT><A><AC>V</AC><AC>˙</AC></A></NU><DE><IT>p·</IT>ln (P<SUB>o</SUB><IT>/</IT>P<SUB>d</SUB>)</DE></FR> (A13a)
or by applying the variables measured in the present study
C<SUB>1</SUB>=<FR><NU>t<SUB>1</SUB>·CO</NU><DE>(MAP<IT>−</IT>RAP)<IT>·</IT>ln (DAP<SUB>o</SUB><IT>/</IT>DAP)</DE></FR> (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
C<SUB>2</SUB>=<FR><NU>t<SUB>2</SUB>·CO</NU><DE>(MAP<IT>−</IT>RAP)<IT>·</IT>ln (SAP<IT>/</IT>DAP)</DE></FR> (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
R=(P<SUB>o</SUB><IT>−</IT>P<SUB>d</SUB>)<IT>/</IT>ln (P<SUB>o</SUB><IT>/</IT>P<SUB>d</SUB>)<IT>·</IT><A><AC>V</AC><AC>˙</AC></A> (A14a)
From Eqs. A13a and A14a an approximate compliance (C<UP><SUB>1</SUB><SUP>′</SUP></UP>) can be determined
C<IT>′<SUB>1</SUB>=</IT><A><AC>V</AC><AC>˙</AC></A><IT>·t<SUB>1</SUB>/</IT>(P<SUB>o</SUB><IT>−</IT>P<SUB>d</SUB>) (A14b)
and by directly measured values
C<IT>′<SUB>1</SUB>=</IT>CO<IT>·t<SUB>1</SUB>/</IT>(DAP<SUB>o</SUB><IT>−</IT>DAP) (A15)
or dividing by heart rate (HR)
C<IT>′<SUB>1</SUB>=</IT>[SV<IT>/</IT>(DAP<SUB>o</SUB><IT>−</IT>DAP)]<IT>·</IT>(<IT>t<SUB>1</SUB>/T</IT>) (A16)
where SV is stroke volume and T is the time of one heartbeat (= 1/HR).

Similarly, from Eqs. A13a, A13c, and A14a
C<IT>′<SUB>2</SUB>=</IT>CO<IT>·t<SUB>2</SUB>/</IT>(SAP<IT>−</IT>DAP) (A15a)
and
C′<SUB>2</SUB>=(SV<IT>/</IT>PP)<IT>·</IT>(<IT>t<SUB>2</SUB>/T</IT>) (A15b)
where PP is pulse pressure (i.e., SAP - DAP).

If t2/T is constant (Table 3), the simplified expression
SV<IT>/</IT>PP (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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ABSTRACT
INTRODUCTION
PATIENTS AND METHODS
RESULTS
DISCUSSION
APPENDIX
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