INTRODUCTION

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THE WAY IN WHICH THE HEART and its load are coupled contributes to efficient blood flow delivery to the tissues. A complete description of arterial load requires the evaluation of aortic input impedance spectra defined in the frequency domain (22, 25). In current clinical practice, this approach is complex, and thus time-domain evaluations of arterial load are most often used. Total peripheral resistance (R) reflects the steady component of arterial load, whereas the pulsatile component of arterial load is quantified by estimating total arterial compliance (13, 16, 36) and the indexes of wave propagation and reflection (12, 14, 24). Aging and essential hypertension are associated with lowered arterial compliance (17, 20, 26), thus contributing to increased pulsatile load, which may in turn adversely affect the myocardial supply-demand balance and ventricular-arterial coupling. Total arterial compliance is an important determinant of the load on the heart, and therefore its determination is of major interest for physiologists and clinicians.

Although R is commonly calculated from the ratio of mean aortic pressure to cardiac output, time-domain measurements of total arterial compliance are more difficult and are based on the windkessel model of systemic circulation (10). Although the limitations of this model have been discussed (22, 25), its applicability has been widely demonstrated in humans (2, 13, 16). Recently, Liu et al. (16) have evaluated a method estimating total arterial compliance from systolic and diastolic areas under the aortic pressure wave. The so-called area method is now considered as the reference for time-domain estimation of total arterial compliance in humans (3, 19, 36). This method requires continuous pressure data recordings throughout the cardiac cycle, and this limits its clinical use and its diagnostic and therapeutic benefits (19).

The ratio of stroke volume to aortic pulse pressure (SV/PP) was initially proposed as an estimate of arterial compliance (32). Recent studies have questioned the accuracy of this approximation (2, 16). It has been stated that estimating total arterial compliance by SV/PP violates the fundamental concept of the windkessel model (2); others have predicted that SV/PP would be markedly larger than total arterial compliance (16). This contrasts with the results showing that SV/PP appears to be a relatively good estimate of total arterial compliance (calculated by using a monoexponential fit of aortic pressure decay) (9).

The aim of our study was to assess SV/PP as an estimate of total arterial compliance (area method; C_area) in humans at rest. If SV/PP is indeed an accurate estimate of C_area, one important implication is that the heart and its load could be coupled in such a way that the ratio of pulse pressure to mean aortic pressure equals the ratio of heart period to arterial decay time. We therefore investigated these ratios and their proportionality.

	METHODS

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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 by T. 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 (P = SAoP  P_i) is an estimate of the magnitude of the reflected pressure wave. The ratio of P to aortic pulse pressure defines a so-called augmentation index (P/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), P/PP > 0.12; type B (n = 4), 0 < P/PP < 0.12; type C (n = 0), P/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

(1)

with where K is the area coefficient.

Theoretical considerations and hypotheses tested. The first hypothesis tested was the equality of C_area and SV/PP, i.e.

(2)

This equality, in conjunction with Eq. 1, implies that

(3)

R is MAoP divided by mean flow, or MAoP divided by SV/T, i.e.

(4)

The time constant of aortic pressure decay in diastole (T_c) equals the product of R and total arterial compliance. Using C_area as a good approximation of total arterial compliance, and inserting Eqs. 2 and 4 in T_c, we obtain

(5)

or

(6)

Thus, if SV/PP is indeed an accurate estimate of C_area, one potentially important implication is the equality between two dimensionless ratios: the ratio of two pressures (PP/MAoP) and the ratio of two times (T/RC_area). Furthermore, Eq. 6 may be considered as an aspect of the coupling between the heart and its load. In the present study, we critically evaluated the accuracy of Eqs. 2, 3, and 6.

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's t-test. Linear regressions were performed using the least-squares method. A P value <0.05 was considered statistically significant.

	RESULTS

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Characteristics of the study population are listed in Table 1.

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) and C_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 P/PP and positively related to SV and body length (Table 3). There was a positive linear relationship between PP and MAoP (r = 0.74, P < 0.001) and between PP and P/PP (r = 0.67, P < 0.001).

View larger version (15K): [in this window] [in a new window]   Fig. 1.   Relationship between total arterial compliance estimated by using the area method (Carea) and the stroke volume-to-aortic pulse pressure ratio (SV/PP) in 31 patients: SV/PP = 0.99Carea + 0.05; r = 0.98; P < 0.001. Solid line, regression line; dashed line, identity line.

View larger version (14K): [in this window] [in a new window]   Fig. 2.   Relationship between SV/PP  Carea and augmentation index (n = 25). Augmentation index is the P-to-PP ratio, where P is late systolic pressure augmentation. The difference was not influenced by extent of wave reflections (r = 0.10; P = 0.6). In 6 subjects, inflection point could not be discerned and therefore P could not be calculated.

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_area ranged from 0.29 to 0.82. T/RC_area was not significantly different from PP/MAoP (Table 4). There was a strong linear relationship between the two ratios (r = 0.96, P < 0.001; n = 31) (Fig 3). 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_area was equal to PP/MAoP in subjects with PP/MAoP < 0.50 (n = 17; mean difference ± SD = 0 ± 0.03), whereas T/RC_area slightly overestimated PP/MAoP in subjects with PP/MAoP > 0.50 (n = 14; mean difference ± SD = 0.05 ± 0.06) (Fig. 3).

View larger version (18K): [in this window] [in a new window]   Fig. 3.   Relationship between aortic pulse pressure-to-mean aortic pressure ratio (PP/MAoP) and heart period-to RCarea ratio (T/RCarea), where R is total peripheral resistance. Solid line, regression line: T/RCarea = 1.18PP/MAoP  0.07; r = 0.96; P < 0.001; n = 31. Dashed line, identity line.

	DISCUSSION

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The main results of our study were as follows. 1) On the basis of the windkessel model of systemic circulation, SV/PP was equal to C_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 of C_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.

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 between C_area and SV/PP. Furthermore, in aged and hypertensive subjects, it is well documented that increased PP is associated with a shortening of the R × 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).

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) and T/T_c were independent of body mass in all mammalian species. These authors have hypothesized that the independence of T/T_c and T_d/T_c relative 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 and C_area implies that T/RC_area (i.e., T/T_c) equals PP/MAoP (Eq. 6). This may furnish a basis for previous observations (39). T/RC_area was equal to PP/MAoP in numerous subjects, especially those with PP/MAoP < 0.50 (see Fig. 3). Given that T 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 of RC_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.

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 replace C_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_b is 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.