METHODS

Patients.

Thirty-one patients (27 men and 4 women) were enrolled in our prospective study after informed consent was obtained. The investigation was approved by our institution. Patients were referred to our laboratory for diagnostic right and left heart catheterization for symptoms of chest pain, heart failure, or other cardiovascular symptoms. Patients with end-stage heart failure, rhythm disturbances, and aortic and mitral valve insufficiency were excluded from the study. Three groups were defined as follows: normal subjects (n = 7), idiopathic dilated cardiomyopathy (n = 10), and miscellaneous cardiac diseases (mainly coronary artery disease, hypertrophic cardiomyopathy, and right ventricular disease) (n = 14). Preliminary results have been published elsewhere (5).

Catheterization technique and protocol.

Patients were studied in the early morning in a basal state. They were unsedated and investigated ≥12 h after the last intake of their usual treatment. Routine right heart catheterization was performed using the Seldinger technique with an 8-Fr sheath from the femoral vein. The right heart catheter was a 7.5-Fr five-lumen thermodilution pressure-measuring tipped catheter with a high-fidelity transducer (Cordis/Sentron, Roden, The Netherlands) (4). The catheter was advanced into either the right or the left pulmonary artery to measure cardiac output. The left heart catheter was either an 8-Fr single-lumen catheter with a lateral high-fidelity transducer and a hole at the distal end or a closed 5-Fr catheter tipped with a high-fidelity transducer (Cordis/Sentron). The left heart catheter was advanced from the femoral artery to the aortic root in 28 of 31 patients. In three patients with peripheral arterial disease of the lower limbs, we used the percutaneous brachial artery approach (11). Pressure data were obtained at baseline after a 10-min equilibrium period. The data were computed on a Toshiba 3200SX with homemade software (sampling rate 500 Hz).

High-fidelity recordings at the aortic root level and cardiac output.

We measured systolic (SAoP), diastolic (DAoP), pulse (PP = SAoP − DAoP), and end-systolic aortic pressures (ESAoP). ESAoP was defined as the nadir of the incisura (dicrotic notch). We computed systolic (A_s) and diastolic (A_d) areas under the pressure curve. We measured heart period (T) as the time between two consecutive aortic pressure upstrokes. The time to SAoP was measured from the foot of the pressure upstroke to SAoP. Mean aortic pressure (MAoP) was calculated as the total area under the pressure curve (i.e.,A_s +A_d) divided byT. We calculated the ratio PP/MAoP. Cardiac output was measured in triplicate using the thermodilution technique in all patients. SV was calculated by dividing cardiac output by heart rate.

Wave reflection and augmentation index.

The human aortic pressure waveform exhibits an inflection point (P_i) indicating the end of the forward (or incident) wave and resulting from peak flow input into the vasculature previous to the effects of wave reflection. The relative increase in pressure amplitude above the inflection point (ΔP = SAoP − P_i) is an estimate of the magnitude of the reflected pressure wave. The ratio of ΔP to aortic pulse pressure defines a so-called augmentation index (ΔP/PP), thus allowing quantification of the extent of wave reflection in central arteries (24). The systolic inflection point was clearly defined in 25 of 31 subjects (81%). They were divided into three groups according to the classification previously proposed by Murgo et al. (24): type A (n = 21), ΔP/PP > 0.12; type B (n = 4), 0 < ΔP/PP < 0.12; type C (n = 0), ΔP/PP < 0. Thus, according to this classification, all our subjects were type A or type B. Given that all but three patients were older than 30 yr of age, this finding is consistent with earlier works (24, 26). In these 25 subjects, the time to SAoP (220 ± 39 ms) occurred during the second half of the systolic period and encompassed 75 ± 8% of left ventricular ejection time (LVET) (59–97%). In six subjects the inflection point could not be discerned; in these subjects, the time to SAoP (216 ± 58 ms) occurred during the second half of the systolic period and encompassed 74 ± 9% of LVET (58–83%).

Total arterial compliance estimated by the area method.

We assumed the windkessel model of systemic circulation. To ensure zero flow in diastole, we obtained pressure data at the aortic root level, and the patients with aortic insufficiency were excluded from the study. According to the area method (16) it can be derived that total arterial compliance is

Theoretical considerations and hypotheses tested.

The first hypothesis tested was the equality ofC_area and SV/PP, i.e.

Data analysis and statistics.

Results are expressed as means ± SD. Pressures, pressure areas, and time parameters were averaged over 10 consecutive cardiac cycles. Comparisons were performed using Student’st-test. Linear regressions were performed using the least-squares method. AP value <0.05 was considered statistically significant.

RESULTS

Characteristics of the study population are listed in Table1.

Compliance estimates.

In the overall population, SV/PP ranged from 0.34 to 2.80 ml/mmHg (mean ± SD: 1.46 ± 0.69 ml/mmHg) andC_area ranged from 0.31 to 2.74 ml/mmHg (mean ± SD: 1.43 ± 0.68 ml/mmHg) (Table 2).C_area was negatively related to age, MAoP, PP, and ΔP/PP and positively related to SV and body length (Table3). There was a positive linear relationship between PP and MAoP (r = 0.74, P < 0.001) and between PP and ΔP/PP (r = 0.67,P < 0.001).

In the overall population as well as in the three study groups, there was no significant difference betweenC_area and SV/PP (Table 2). There was a strong linear relationship betweenC_area and SV/PP (r = 0.99;P < 0.001;n = 31), and the slope and intercept of the regression lines did not differ from unity and zero, respectively (Fig. 1 and Table 2).

The equality betweenC_area and SV/PP (see Fig. 1 and Table 2) was partly explained by the close relationship between PP and the product of K times the difference between ESAoP and DAoP (see Eq.3) {PP = 0.82[K × (ESAoP − DAoP)] + 7.6 mmHg; n = 31;r = 0.97;P < 0.001}; the slope was different from unity (P < 0.05), whereas the intercept was not different from zero. There was also a close linear relationship between PP and (ESAoP − DAoP) (r = 0.91,P < 0.001). The equality between the two compliance estimates was independent of the pressure wave shape, given that 1) no relationship was found between PP and K(r = 0.30), and2) the difference between SV/PP andC_area was not related to ΔP/PP (r = 0.10) (Fig.2).

Relationship between PP/MAoP and T/RC_area.

In the study population (n = 31), PP/MAoP ranged from 0.33 to 0.78.T/RC_arearanged from 0.29 to 0.82.T/RC_areawas not significantly different from PP/MAoP (Table4). There was a strong linear relationship between the two ratios (r = 0.96,P < 0.001;n = 31) (Fig3). The intercept was not different from zero. The slope was different from unity (P < 0.05) such that the regression line progressively diverged from the identity line, especially for high PP/MAoP values (Fig. 3). As a result,T/RC_areawas equal to PP/MAoP in subjects with PP/MAoP < 0.50 (n = 17; mean difference ± SD = 0 ± 0.03), whereasT/RC_areaslightly overestimated PP/MAoP in subjects with PP/MAoP > 0.50 (n = 14; mean difference ± SD = 0.05 ± 0.06) (Fig. 3).

DISCUSSION

The main results of our study were as follows.1) On the basis of the windkessel model of systemic circulation, SV/PP was equal toC_area in humans at rest. 2) Our results may be explained by the fact that heart period normalized by the time constant of aortic pressure fall in diastole is proportionally related to PP/MAoP in humans at rest, a finding consistent with recent results in comparative physiology (39).

Relationship between SV/PP and total arterial compliance: comparison with previous results.

Since its validation by Remington et al. (32), SV/PP has been used to estimate arterial compliance (9, 28, 29, 34). Others have estimated arterial stiffness (or rigidity) by using PP/SV (1, 7, 21, 38). On the basis of theoretical and experimental arguments, recent studies have advised against the use of SV/PP as an estimate of total arterial compliance, such that alternative methods must be used (2, 13, 16, 36). Conversely, a previous study has shown that SV/PP is linearly related (r = 0.80) to total arterial compliance estimated by exponential fitting of diastolic pressure decay (9). Our study indicates that SV/PP was a simple, accurate estimate ofC_area in humans at rest. The results were obtained despite marked differences in cardiac status and over a wide range of aortic pressures, heart rates,C_area values, and extents of wave reflection.

Differences between our conclusions and others may be explained by the greater accuracy of the area method. This method avoids potential artifacts stemming from the choice of cutoff values for the onset and end of monoexponential analysis (16, 36). As this method does not depend on the exact form of the pressure wave, it is not influenced by deviations from a true exponential function (16). The mean value of the area coefficient K we reported (1.72;n = 31) is consistent with that of Liu et al. (1.68; n = 7) (16). Liu et al. (16) have predicted that SV/PP should be markedly larger thanC_area. However, the mean difference between SV/PP (calculated from Table 1 in Ref. 16) and total arterial compliance (C₁ in Table 2 of Ref. 16) is −0.07 ml/mmHg, which strengthens our findings. Importantly, SV/PP andC_area cannot be considered interchangeable estimates of “real” total arterial compliance. SV/PP determines compliance at MAoP, whereasC_area determines compliance at average diastolic pressure (which is known to be lower than MAoP). Because compliance normally decreases when arterial pressure increases (13, 16, 36), one can expect thatC_area was in fact lower than SV/PP in our patients.

PP, arterial compliance, and wave reflection.

Aortic PP is determined by the patterns of left ventricular ejection, aortic stiffness, and wave reflections (22, 27, 33). Cardiac ejection into a low-compliance system generates a wider PP than in a normally compliant system (30, 31, 37). Furthermore, reduced arterial compliance is associated with increased pulse wave velocity and wave reflection, and this also contributes to increased PP (12, 18, 24, 33). These mechanisms could account, at least in part, for the linear relationship observed in our study betweenC_area and SV/PP. Furthermore, in aged and hypertensive subjects, it is well documented that increased PP is associated with a shortening of theR ×C product (1, 9, 35). In these patients, both higher ESAoP and less compliant arterial vasculature contribute to this close link (17, 20, 26, 27).

The reflection of pressure waves leading to inflection point and the augmentation index result from wave transmission characteristics that are not contained in the windkessel models (24). Yet a good correlation between C_area and SV/PP was found. We feel it unlikely that the observed equality between SV/PP and C_areawas casual or related to the mutual canceling of the many assumptions and approximations on which the two compliance estimates were based. We suggest that this equality may furnish a basis for recent results in comparative physiology (39).

Relationship between PP/MAoP and T/T_c.

In a meta-analysis involving 36 major studies on windkessel parameters, Westerhof and Elzinga (39) have observed that both the diastolic time-to-arterial time constant ratio (T_d/T_c) andT/T_cwere independent of body mass in all mammalian species. These authors have hypothesized that the independence ofT/T_candT_d/T_crelative to body mass suggests that heart rate is compelled by the arterial tree to maintain similar diastolic and/or pulse pressure in all mammalian species, thus warranting coronary perfusion (8, 39). In our study, we have taken advantage of some redundancies in hemodynamic formulas to predict that the equality between SV/PP andC_area implies thatT/RC_area(i.e.,T/T_c) equals PP/MAoP (Eq. 6). This may furnish a basis for previous observations (39).T/RC_areawas equal to PP/MAoP in numerous subjects, especially those with PP/MAoP < 0.50 (see Fig. 3). Given thatT determines the frequency of blood spurts from the ventricle into the aorta and that both the resistive and viscoelastic properties of the arterial tree determine the value ofRC_area, the fact that the dimensionless ratio of two times (T/RC_area) was equal to that of two pressures (PP/MAoP) could be viewed as a contributory factor in ventricular-arterial coupling.

Importantly, however, our patients exhibited a wide range ofT/RC_areavalues, and this indicated thatT/T_cvalues could not be considered constants in humans, contrary to what has been hypothesized in comparative physiology (39). Furthermore, theT/RC_areavs. PP/MAoP regression line diverged from identity at high PP/MAoP values (Fig. 3), and this may testify to an uncoupling between the left ventricle and its load, a point that deserves further study. Finally, our study also strengthens the physiological relevance of PP/MAoP. Several studies have stressed the fact that PP depends on mean pressure: the higher the mean pressure, the higher the fluctuations around the mean (6, 18, 33). It has also been shown that PP/MAoP is linearly related to the characteristic impedance-to-R ratio in dogs with ascending aorta-abdominal aorta bypass (23).

Study limitations.

The windkessel model implies infinitely high wave speed in diastole and an absence of wave reflection (2, 22, 25), whereas wave reflections are known to occur in both health and disease (14, 15, 24). However, this model has been assumed to be applicable to humans, especially at low frequencies corresponding to normal ranges of heart rate (2, 13, 16,36). Other shortcomings of the area method need to be pointed out.1) No attempt was made to evaluate the runoff of blood forwarded into the peripheral circulation during systole. 2) It was assumed that the pressure asymptote is so small as to be negligible. The pressure dependence of compliance estimates (16, 36) was not tested in our study. The results pertain strictly to the study population, of which we had excluded patients with aortic and mitral valve insufficiency.3) We cannot exclude the possibility that our findings do not apply to subjects with negligible wave reflections (type C subjects) (24), and this deserves further studies focused on younger populations.

Implications.

From a practical point of view, two implications must be discussed. First, it is suggested that SV/PP furnishes a rapid, valuable estimate of C_area. We wish to emphasize that the purpose of our study was not to recommend that SV/PP replaceC_area, which remains the reference estimate of total arterial compliance in the time domain. However, the area method requires continuous pressure data recordings throughout the cardiac cycle, and this limits its clinical applications. Second, the SV-to-brachial PP ratio (SV/PP_b) has been previously used to estimate total arterial compliance. This approximation is likely to be accurate only in patients with no or minor amplification of pulse pressure from aorta to periphery; conversely, it must be used cautiously with subjects exhibiting physiological pulse wave amplification, given that SV/PP_bis likely to underestimate total arterial compliance in these subjects. From a physiological point of view, and to the best of our knowledge, this is the first study to have proposed a hemodynamic formula relating pulse pressure to the heart period of the corresponding beat (i.e., PP/MAoP =T/RC_area; see Eq. 6). Although pertaining strictly to the windkessel model, this new relationship could reasonably describe one aspect of the coupling between the left ventricle and its load. Further studies are needed to assess the relevance of this relationship in various populations and under dynamic conditions. Finally, from an epidemiological point of view, increased blood pressure and heart rate are considered major cardiovascular risk factors. Our results suggest that the changes in blood pressure (mean, pulse), heart period, and arterial time constant may well be coordinated (e.g., during aging or hypertension), and this point deserves further study.

Conclusion.

On the basis of the windkessel model of systemic circulation, SV/PP was equal to C_area in humans at rest. This implied that heart period normalized by the time constant of aortic pressure fall in diastole is proportionally related to PP/MAoP, a finding in keeping with recent results in comparative physiology.