| HOME | HELP | FEEDBACK | SUBSCRIPTIONS | ARCHIVE | SEARCH | TABLE OF CONTENTS |
|
|
|
|||||||
|
|||||||||
1Service de Physiologie Cardio-Respiratoire, Centre Hospitalier Universitaire de Bicêtre, Assistance Publique-Hôpitaux de Paris, 94 275 Le Kremlin-Bicêtre; 2Unité Propre de l'Enseignement Supérieur 2705, Université Paris Sud 11, 92 141 Clamart; and 3Service de Physiologie et d'Explorations Fonctionnelles, Centre Hospitalier Universitaire Jean Verdier, Assistance Publique-Hôpitaux de Paris, Université Paris 13, 93 143 Bondy, France
Submitted 13 September 2002 ; accepted in final form 3 April 2003
 |
ABSTRACT |
|---|
 TOP ABSTRACT METHODSRESULTSDISCUSSIONREFERENCES |
|---|
rate-pressure product; cardiac index; ventriculoarterial coupling; pulse pressure; cardiac cycle length
Initial studies have suggested that Ea is poorly affected by changes in C and that Ea may be satisfactorily approximated by the R-to-T ratio (R/T ratio), where T is the cardiac cycle length (38–40). More recent studies have shown that the R/T ratio underestimates Ea in humans with stiff vasculature (e.g., hypertensive or aged subjects) (7, 8, 19). It is now widely accepted that Ea lumps the steady and pulsatile components of arterial load in a concise way, but the precise contribution of R and C to Ea remains to be established in humans.
Recently, Segers et al. (34) used a mathematical heart-arterial interaction model to study the effects of changes in R and C on Ea. They found that Ea was linearly related to R/T and 1/C and that R/T contributed about three times more to Ea than 1/C. The first aim of the present study was to test the hypothesis that Ea could also be described by a multilinear function of R/T and 1/C in humans and to document the respective contribution of R and C to Ea in normotensive and hypertensive adults.
In an attempt to simplify the assessment of Ea, the following aortic pressures have been used as surrogates for LVESP: mean aortic pressure (MAP) (38–40) and aortic notch pressure (2, 9, 15, 18), and empirical formulas based on systolic (SAP) and diastolic aortic pressures (DAP), namely, the (2SAP + DAP)/3 formula (19, 29) and the 0.9SAP formula (6, 19). The second aim of our study was to investigate which aortic pressure was the strongest hemodynamic correlate of LVESP. Our results indicated that LVESP was most strongly related to SAP, and the physiological implications for the Ea model are discussed.
|
METHODS |
|---|
|
TOPABSTRACTMETHODSRESULTSDISCUSSIONREFERENCES |
|---|
30% at coronary arteriography were included
in the study. Patients with valvular heart disease or diabetes mellitus were
excluded from the study. The characteristics of the study population are
listed in Table 1. All subjects
gave informed consent, and the study was approved by our institution.
|
Catheterization procedure. All patients were in the fasting state
for 
12 h before the procedure. All treatments were discontinued at least 3
wk before cardiac catheterization with the exception of short-acting nitrates.
No premedication was administered, and 1% lidocaine was used for local
anesthesia. A 15-min delay was observed after documentation of nonsignificant
coronary artery stenosis to eliminate the effects of contrast material.
Thereafter, simultaneous recordings of LV pressure and aortic pressure were
obtained using a 7-Fr double-tipped micromanometer angiographic catheter
(Sentron, Cordis Laboratory; Roden, The Netherlands)
(3), as previously described
(1,
25). The catheter was placed
through a femoral artery with a 7-Fr sheath. The distance between the two
high-fidelity transducers was 10 cm. Aortic pressure was recorded above the
aortic cusps. Heart rate (HR), aortic pressures, LV end-diastolic pressure,
and LVESP were calculated with the use of a catheterization data-analysis
computer system (Hewlett-Packard 5600 M; Andover, MA), which performed on-line
analysis on nine beats for averaging out respiratory variations. Aortic pulse
pressure (PP) was calculated as SAP minus DAP. MAP (range: 84–160 mmHg)
was automatically calculated as the area under the pressure curve divided by
T. Aortic end-ejection pressure was measured at the trough of the
incisura (dicrotic notch). Aortic mean ejection pressure was defined as the
systolic pressure area (from pressure upstroke to dicrotic notch) divided by
the LV ejection time. LV angiography (50 frames/s) was performed in a 30°
right anterior oblique projection (35 ml nonionic contrast medium, 12 ml/s)
with simultaneous recording of LV pressure (paper speed 200 mm/s) and a frame
marker.
Data analysis and calculations. LV end-diastolic volume and end-systolic volume (ESV) were calculated from monoplane angiograms by means of the area-length method (11). LV SV and ejection fraction were calculated using standard formulas. The LVESP was the pressure corresponding to the separation of the aortic and LV pressure curves recorded simultaneously. Ea was calculated as LVESP divided by SV (19). The SV-to-PP ratio was calculated as an estimate of C (5, 10, 13), and its reciprocal, i.e., the PP-to-SV ratio, was calculated as an estimate of total arterial stiffness (12, 42). R was calculated as MAP divided by cardiac output (SV x HR). For comparative purposes (biological scaling), SV was normalized for body surface area in the calculation of Ea, R, and C.
Effective arterial elastance: theoretical background. In the
two-element windkessel model, the governing equation in the frequency domain
is as follows
 |
, and 
is the circular frequency
(21). More simple, time-domain
indexes of systemic vascular load have been recently proposed. Assuming that
the systemic arteries can be considered an elastic chamber, the effective
volume elastance Ea is the slope of the linear
relationship between aortic end-systolic pressure and SV
(38–40).
If one assumes that end-systolic pressure can be approximated by end-ejection
pressure, that end-ejection pressure matches mean ejection pressure, and that
the intercept with the pressure axis is small enough to be negligible, the
three-element windkessel model of arterial circulation predicts the following
equations
(38–40)
 |
is the
diastolic pressure decay time constant ( = RC). With the use of
this approach, LVESP is uniquely determined by arterial properties, time
intervals, and SV, independently of how SV is generated, i.e., without the
need to take into account the preload and inotropic state
(30,
38–40).
In cases where is long compared with tD (
>> tD), then the denominator of the LVESP reduces to
tS + tD = T, and thus
Ea = RT/T
(19). The LV can also be considered as an elastic chamber, the end-systolic elastance (Ees) of which is the slope of the LVESP – (ESV – Vo) relationship, where Vo is the volume intercept (36, 37). Given similar dimensions for Ea and Ees (mmHg/ml), this framework allows rational analysis of the ventriculoarterial coupling in a concise way. Assuming similar LV and aortic pressure at end systole, the operating point of the coupled equilibrium between LV and arterial system is located at the intersection of the LVESP-ESV and LVESP-SV relationships in the pressure-volume plane (36–40).
In animals, previous studies have confirmed the linearity of the LVESP-SV
relationships obtained in various experimental conditions, thus allowing the
precise calculation of Ea. In humans, serial SV assessment
in various loading conditions is not easy to obtain without changing LV
contractility. Therefore, Ea is currently calculated as
the steady-state LVESP-over-SV ratio, assuming a linear LVESP-SV relationship
and negligible pressure intercept
(19)
 |
 |
 |
 |
represents the increment
of pressure above MAP at end systole divided by SV
 |
component is increased in
humans with stiff vasculature (i.e., aged and hypertensive subjets)
(7–9,
19), but no analytic model
relating Ea,
, and C has been yet
proposed in humans.
Very recently, Segers et al.
(34) used a mathematical
heart-arterial interaction model to precisely quantify the respective
contribution of R and C to Ea. Systemic
arterial load was described by a four-element windkessel model in which 121
possible combinations of R and C were simulated, together
with fixed values for total inertance and characteristic impedance
(34). The authors found that
Ea was linearly related (r2 = 0.99) to
R/T and 1/C according to the following equation
 |
Finally, in an attempt to simplify the calculation of Ea in humans, various LVESP estimates/surrogates have been used, namely, MAP (9, 39, 40), aortic notch pressure (2, 9, 15, 18), the (2SAP + DAP)/3 formula (19, 29), and the 0.9SAP formula (6, 19).
Statistical analysis. Data are expressed as means ± SD. ANOVA was used for overall comparisons between groups. Regressions were obtained using the least squares method. The following LVESP estimates were tested: MAP, aortic notch pressure, aortic mean ejection pressure, (2SAP + DAP)/3, and 0.9SAP. In each case, the bias (i.e., estimate – LVESP) ± SD was calculated. A P value of <0.05 was considered significant.
|
RESULTS |
|---|
|
TOPABSTRACTMETHODSRESULTSDISCUSSIONREFERENCES |
|---|
|
|
R/T as an estimate of Ea. The
R/T ratio significantly underestimated
Ea (Fig. 1,
left, and Table 4).
The (Ea – R/T) difference (i.e.,
) was higher in hypertensive
patients than in normotensive subjects (P < 0.001)
(Table 3). The steady,
R/T component of arterial load accounted for a lower
percentage of Ea in hypertensive patients (77 ± 5%)
than in controls (81 ± 5%) (P < 0.02;
Table 3). The unsteady,
component of arterial load
accounted for a higher percentage of Ea in hypertensive
patients (19 ± 5%) than in controls (23 ± 5%) (P <
0.02; Table 3). Among all the
clinical and hemodynamic variables studied, 1/C was the one most
strongly related to
(r2 = 0.82), such that R/T closely
approximated Ea for large C values only
(Fig. 1, right).
|
|
Respective contribution of R/T and 1/C to Ea
and to 
. After the inclusion of
1/C in the model, multiple linear regression analysis yielded the
following relation
 |
can be described by the
following equation in resting humans and over a wide MAP range
 |
|
Hemodynamic correlates of LVESP. The LVESP was strongly related to SAP (LVESP = 0.91SAP – 2 mmHg, r2 = 0.94, P < 0.001), and the equation line was close to the 0.9SAP empirical estimate of LVESP previously proposed (19). The LVESP was related to MAP (LVESP = 1.22MAP + 7 mmHg, r2 = 0.83, P < 0.001), to aortic notch pressure (LVESP = 0.67aortic notch pressure + 28 mmHg, r2 = 0.71, P < 0.001), and to aortic mean ejection pressure (LVESP = 1.07mean ejection pressure – 1 mmHg, r2 = 0.85, P < 0.001). The LVESP was also positively related to DAP (r2 = 0.41) and PP (r2 = 0.48) (each P < 0.001).
Empirical estimates of LVESP. The empirical formula (LVESP = 0.9SAP) gave an accurate estimate of LVESP [bias = 0 ± 5 mmHg, P = not significant (NS)], and the bias was similar in normotensive subjects (bias = 2 ± 5 mmHg) and in hypertensive patients (bias = 0 ± 6 mmHg; P = NS). All other empirical estimates significantly underestimated LVESP (each P < 0.001). The bias was higher in hypertensive patients than in normotensive subjects for MAP (–37 ± 9 vs. –23 ± 11 mmHg), aortic notch pressure (–26 ± 13 vs. –12 ± 5 mmHg), aortic mean ejection pressure (–12 ± 8 vs. 0 ± 6 mmHg), and the empirical formula LVESP = (2SAP + DAP)/3 (–13 ± 4 vs. –6 ± 7 mmHg) (each P < 0.001).
Implications for the Ea model. The
following estimate was shown to be accurate over a wide pressure range
 |
 |
 |
|
DISCUSSION |
|---|
|
TOPABSTRACTMETHODSRESULTSDISCUSSIONREFERENCES |
|---|
The R/T ratio significantly underestimates
Ea in hypertensive subjects because of an important
additional influence of pulsatile impedance load related to decreased arterial
compliance (7,
8,
19). The
(Ea – R/T) difference, namely,
, reflects the pulsatile
component of Ea
(7–9,
19). In hypertensive patients,
Cohen-Solal et al. (7) have
reported that is augmented
proportionally more than R/T, although the latter largely
predominates in determining Ea quantitatively, and our
findings are fairly consistent with their results
(Table 3). However,
partitioning Ea into a steady (R/T) and
a pulsatile () component does
not allow us to precisely quantify the respective contribution of R
and C to Ea.
Recently, using a mathematical heart-arterial interaction model in which the systemic circulation was described by a four-element windkessel model, Segers et al. (34) reported that Ea was linearly related to R/T and to 1/C according to the following equation: Ea = 1.023R/T + 0.314/C – 0.127 (r2 = 0.99). In our study, by use of a two-element windkessel model of the systemic arterial circulation in humans and over a wide MAP range (84–160 mmHg), Ea was accurately described according to the following equation: Ea = 1.00R/T + 0.42/C – 0.04 (in mmHg · m2 · ml–1, r2 = 0.97). The consistency between our clinical study and previous theoretical results (34) is thus excellent, and we feel that this strengthens the clinical relevance of the model.
Considering that aortic pressure is a continuous variable, we found that a
single multilinear function of R/T and 1/C
meaningfully described Ea in both normotensive and
hypertensive patients. Thus the sensitivity of Ea to a
change in R/T was 2.5 times higher than to similar change in
1/C whatever the prevailing MAP in humans. Assuming that the
(–0.04) factor was small enough to be negligible, we also found that
matched (0.42/C) in
both normotensive and hypertensive subjects. As C is lower (the
1/C ratio is higher) in hypertensives than in normotensive subjects,
our model was consistent with higher
and higher impedance load
related to decreased C in hypertensives (Refs.
7,
8, and
19 and
Table 3).
The two-element (RC) windkessel model is a linear model that does not incorporate the influences of wave transmission characteristics and implies an absence of wave reflection. This may be a limitation in hypertensive patients, in whom a weak but significant relationship has been previously reported between Ea and the extent of wave reflections (32). Conversely, a previous theoretical study (34) has shown that Ea is not necessarily related to the characteristics of wave reflections. Furthermore, the ability of the RC model to accurately describe the mechanical properties of the arterial system with a limited number of parameters and in various pathophysiological conditions has been stressed (24, 28, 35).
It is widely accepted that Ea mainly depends on MAP and SV, and thus the R/T ratio, given obvious redundancy in hemodynamic formulas. This implies that LVESP must be strongly related to MAP. However, in our study, LVESP was more strongly related to SAP (r2 = 0.94) than to MAP (r2 = 0.83). The advantage of relating arterial load to SAP rather than to MAP is that SAP incorporates the influences of peripheral resistance, arterial compliance, and wave reflections (27). Several studies, including the present one, have documented a strong linear relationship between MAP and SAP, thus suggesting the major role of increased peripheral resistance and small artery vascular tone on the increased SAP in hypertensive patients (14). Furthermore, in patients with stiff vasculature, both reduced arterial compliance and increased wave reflections result in a rise in late-peaking systolic pressure that may unfavorably load the still-ejecting LV (22, 27).
The LVESP-to-SV ratio is a hemodynamic parameter per se, and therefore Ea may not necessarily relate to the windkessel model. Thus we tested the possibility that an alternative model may be proposed to describe Ea. Taking advantage of certain redundancy in hemodynamic formulas, we demonstrated that Ea is proportional to the rate-pressure product-over-cardiac index ratio whatever the prevailing aortic pressure (Fig. 2, right). For a given level of cardiac contractility, the rate-pressure product reflects the myocardial oxygen demand (4, 16, 41), and our results thus argue in favor of a fixed relationship among the arterial load, cardiac index, and myocardial oxygen demand, a point that deserves confirmation.
Several aortic pressures have been proposed as surrogates for LVESP in an attempt to simplify the clinical assessment of Ea and Ees. To the best of our knowledge, our study is the first to critically evaluate these pressure surrogates in a significant number of subjects (n = 66) and over a wide pressure range. Mean pressure, notch pressure, mean ejection pressure, and the (2SAP + DAP)/3 formula significantly underestimated LVESP, the bias being higher in hypertensive patients than in normotensive subjects in all cases. Conversely, 0.9SAP gave a reliable estimate of LVESP whatever the prevailing aortic pressure. The 0.9SAP formula has been previously shown to give an accurate estimate of LVESP in four young normotensive and six older hypertensive subjects studied at rest and after preload reduction and pharmacological interventions (19). Given that the subjects in the present study were free of aortic stenosis and hypertrophic cardiomyopathy, our finding is also in keeping with previous results showing that 1) peak LV pressure is usually achieved close to the volume point of minimal LV volume (11, 37); 2) peak LV pressure and LVESP are close in magnitude, although they occur at different points in time (17, 31); and 3) LV peak systolic pressure can be used instead of LVESP to calculate LV Ees with reasonably good accuracy (20, 26).
The main clinical implication is that 0.9SAP may provide the most accurate estimate of LVESP, and this may improve the noninvasive calculation of Ea and Ees by using aplanation tonometry. Conversely, other empirical LVESP estimates must not be used, especially in hypertensive patients. Importantly, the 0.9SAP approximation applies strictly to central pressure recordings and not to brachial artery pressure, given the physiological increases in systolic pressure observed from the aorta to periphery (pulse wave amplification phenomenon) (27).
The limitations of our study must be discussed. Although some authors have suggested that the SV-to-PP ratio overestimates C (for a review, see Ref. 5), we (5) have recently reported that the bias between the SV-to-PP ratio and C (calculated using the so-called area method) was 0.03 ± 0.15 ml/mmHg in 31 subjects. In the present study, R, C, and Ea were calculated using widely used, standard formulas, in which the influences of downstream (zero flow) pressure were not taken into account. Further studies are needed to test the potential effects of changes in downstream pressure on the relationship among R, C, and Ea. For an invasive, high-fidelity pressure study, the number of normotensive and hypertensive subjects was likely to be sufficient to justify the conclusions drawn from the data. Finally, the results pertain strictly to the population under study, and data were obtained at rest. Improving our understanding of resting hemodynamics is an important goal of clinical research, because hypertension is a risk factor for increased morbidity and mortality (23). Further studies are needed to confirm our study in dynamic conditions and after pharmacological interventions.
In conclusion, in normotensive subjects and hypertensive patients, Ea can be precisely described by a multilinear function of R/T and 1/C. The sensitivity of Ea to a change in R/T was 2.5 times higher than to a similar change in 1/C. This confirms previous theoretical modeling and gives a valuable representation of the function of the arterial circulation as a mechanical load. Furthermore, the most accurate estimate of LVESP was 0.9SAP. This implies that a complementary aspect of the ventriculoarterial coupling might be proposed, in which Ea is proportional to the HR x SAP product-over-cardiac index ratio whatever the prevailing aortic pressure.
|
FOOTNOTES |
|---|
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.
|
REFERENCES |
|---|
|
TOPABSTRACTMETHODSRESULTSDISCUSSIONREFERENCES |
|---|
This article has been cited by other articles:
|
|
 |
|
  P. D. Chantler, E. G. Lakatta, and S. S. Najjar Arterial-ventricular coupling: mechanistic insights into cardiovascular performance at rest and during exercise J Appl Physiol, October 1, 2008; 105(4): 1342 - 1351. [Abstract] [Full Text] [PDF]
|
|
|
|
 |
|
 T. Otsuki, S. Maeda, M. Iemitsu, Y. Saito, Y. Tanimura, R. Ajisaka, and T. Miyauchi Systemic arterial compliance, systemic vascular resistance, and effective arterial elastance during exercise in endurance-trained men Am J Physiol Regulatory Integrative Comp Physiol, July 1, 2008; 295(1): R228 - R235. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
D. Chemla, I. Antony, K. Zamani, and A. Nitenberg Mean aortic pressure is the geometric mean of systolic and diastolic aortic pressure in resting humans J Appl Physiol, December 1, 2005; 99(6): 2278 - 2284. [Abstract] [Full Text] [PDF]
|
|
|
|
 |
|
 V. Muthurangu, D. Atkinson, M. Sermesant, M. E. Miquel, S. Hegde, R. Johnson, R. Andriantsimiavona, A. M. Taylor, E. Baker, R. Tulloh, et al. Measurement of total pulmonary arterial compliance using invasive pressure monitoring and MR flow quantification during MR-guided cardiac catheterization Am J Physiol Heart Circ Physiol, September 1, 2005; 289(3): H1301 - H1306. [Abstract] [Full Text] [PDF]
|
|
|
|
 |
|
 M. Briand, J. G. Dumesnil, L. Kadem, A. G. Tongue, R. Rieu, D. Garcia, and P. Pibarot Reduced Systemic Arterial Compliance Impacts Significantly on Left Ventricular Afterload and Function in Aortic Stenosis: Implications for Diagnosis and Treatment J. Am. Coll. Cardiol., July 19, 2005; 46(2): 291 - 298. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
K. L. Peterson Severe Calcific Aortic Stenosis: Left Ventricular Afterload and its Quantification J. Am. Coll. Cardiol., July 19, 2005; 46(2): 299 - 301. [Full Text] [PDF]
|
|
|
|
 |
|
 L Kadem, J G Dumesnil, R Rieu, L-G Durand, D Garcia, and P Pibarot Impact of systemic hypertension on the assessment of aortic stenosis Heart, March 1, 2005; 91(3): 354 - 361. [Abstract] [Full Text] [PDF]
|
|
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| HOME | HELP | FEEDBACK | SUBSCRIPTIONS | ARCHIVE | SEARCH | TABLE OF CONTENTS |
| Visit Other APS Journals Online |
