Download Mean aortic pressure is the geometric mean of systolic and diastolic

Articles in PresS. J Appl Physiol (July 28, 2005). doi:10.1152/japplphysiol.00713.2005
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Mean aortic pressure is the geometric mean of systolic and
diastolic aortic pressure in resting humans
Denis Chemla, Isabelle Antony, Karen Zamani and Alain Nitenberg.
Affiliation
Sud 11, UPRES 2705, Assistance Publique - Hôpitaux de Paris, Le Kremlin-Bicêtre (DC,
KZ), and the Service de Physiologie et d’Explorations Fonctionnelles, CHU Jean Verdier,
Université Paris 13, Bondy (IA, AN), France.
Running head: Geometric mean aortic pressure.
Contact information: Prof. Denis CHEMLA, MD
Service d’Explorations Fonctionnelles Cardio-Respiratoires, Université de Paris Sud 11,
Hôpital de Bicêtre, 94 275 Le Kremlin-Bicêtre Cedex. FRANCE
Fax: (331) 45 21 37 78
Tel: (331) 45 21 25 63
E-mail: [email protected]
paris.fr
Part of this study has been presented at the 24th Meeting of the French Hypertension
Society and consequently appears as an abstract (J Hypertens 23 (8): A2-A3, 2005).
Copyright © 2005 by the American Physiological Society.
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From the Service de Physiologie Cardio-Respiratoire, CHU de Bicêtre, Université Paris
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ABSTRACT
The aim of our study was twofold: 1) to establish a mathematical link between mean
aortic pressure (MAP) and systolic (SAP) and diastolic (DAP) aortic pressures by testing
the hypothesis that either the geometric mean or the harmonic mean of SAP and DAP
were reliable MAP estimates; and 2) to critically evaluate three empirical formulas
recently proposed to estimate MAP. High-fidelity pressures were recorded at rest at the
aortic root level in controls (n=31) and in subjects with various forms of cardiovascular
calculated. The MAP ranged from 66 to160 mmHg (mean(SD) =107.9(18.2) mmHg). The
geometric mean, i.e., the square root of the product of SAP and DAP, furnished a reliable
estimate of MAP (mean bias(SD) = 0.3(2.7) mmHg). The harmonic mean was inaccurate.
The following MAP formulas were also tested: DAP+0.412 PP (Meaney et al. 2000);
DAP+0.33PP+5 mmHg (Chemla et al. 2002); and DAP+[(0.33 + (heart rate x 0.0012)]
PP (Razminia et al. 2004). They all provided accurate and precise estimates of MAP
(mean bias(SD) = -0.2(2.9); -0.3(2.7) and 0.1(2.9) mmHg respectively). The implications
of the geometric mean pressure strictly pertained to the central (not peripheral) level. It
was demonstrated that the fractional systolic (SAP/MAP) and diastolic (DAP/MAP)
pressures were reciprocal estimates of aortic pulsatility, and that the SAP times DAP
product matched the total systemic resistance times cardiac power output product. In
conclusion, although the previously described thumb-rules applied, the “geometric mean
aortic pressure” appears more valuable as it established a simple mathematical link
between the steady and pulsatile component of aortic pressure.
KEY WORDS. Pulse pressure, cardiac power, total peripheral resistance.
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diseases (n=108). The time-averaged MAP and the pulse pressure (PP=SAP-DAP) were
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An improved description of central aortic pressure is a key issue for
cardiovascular physiologists and clinicians because central aortic pressure is a major
determinant of myocardial oxygen consumption, coronary perfusion pressure and the
pressure for sinoartic baroreflex. Aortic pressure is currently analyzed according to both
its steady component (mean aortic pressure MAP) and pulsatile component (systolic
aortic pressure SAP; diastolic aortic pressure DAP; and pulse pressure PP = SAP –DAP).
The MAP accounts for more than 80% of the hydraulic load put on the left ventricle and
described by the cardiac output times total peripheral resistance product, and MAP is
considered as the perfusion pressure through each tissue bed. The overall strategy of the
cardiovascular system is to provide all organs with constant perfusion pressure, and MAP
is closely monitored via central and peripheral control mechanisms (2,31).
Mean aortic pressure is the time-averaged aortic pressure throughout cardiac cycle
length. Previous studies have established a link between the steady and pulsatile
component of aortic pressure by estimating MAP from SAP and DAP values using
various empirical formulas that rely on different physiological aspects of the human
circulation (5,20,30). The characterization of MAP by using empirical formulas is
focused on the amount of information contained in the pressure database and this may be
of interest for several reasons. First, mathematical solution for any system may be a step
for improving the rational modeling of the system (1), and a mathematical solution
relating the steady (MAP) and pulsatile (SAP, DAP) aortic pressures may be especially
valuable. Second, empirical formulas may help reduce the number of independent
variables. A properly defined collection of biological data must minimize redundancy,
because redundancy may hamper the understanding of pathophysiological processes and
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significantly contributes to vascular load (9,21,34). Mean aortic pressure is adequately
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the relevance of statistical analysis (15,17,22). Third, this approach may be utilitarian
with regard to precisely predicting one of the variable under study.
Although valuable, the previously proposed thumb-rules (5,20,30) do not belong
to the so called mathematical means (arithmetic, geometric, harmonic means). While it is
admitted that MAP is generally lower than the arithmetic mean of SAP and DAP (10,39),
the potential value of the geometric and harmonic mean remain to be established. The
aim of our study was to test the hypothesis that MAP could be accurately estimated by
humans. As we observed that the geometric mean (i.e., the square root of the product of
SAP and DAP) was an accurate and precise estimate of MAP, this new formula was
compared to the three empirical formulas recently proposed for estimating MAP
(5,20,30). Finally, because indices of aortic pressure pulsatility such as fractional systolic
pressure (SAP/MAP) and fractional diastolic pressure (DAP/MAP) could relate to the
risk of coronary heart diseases (16,23,26), the clinical implications of our results were
also discussed.
MATERIALS AND METHODS
Patients. Our study involved one hundred and thirty-nine patients (109 M / 30 F; 49 (12)
years). The subjects were referred to our laboratory for diagnostic left heart (n=66) and
left and right heart (n=73) catheterization for symptoms of chest pain, heart failure or
other cardiovascular symptoms. The final diagnosis was as follows: subjects with normal
cardiac function and coronary angiograms (n=31), hypertensive patients (n=46), grafted
hearts (n=18), idiopathic dilated cardiomyopathy (n=14) and miscellaneous cardiac
diseases, mainly coronary artery disease (n=30). Part of the study population has been
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using either the geometric or the harmonic mean of SAP and DAP in the aorta of resting
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described elsewhere (4,5). All investigations were approved by our institution and
informed consent was obtained for all patients.
Pressure recordings. Catheterization procedures and data analysis and calculations have
been previously described (4,5). In brief, pressures were recorded in resting subjects using
micromanometer tipped catheter (Sentron, Cordis Laboratory; Roden, The Netherlands).
Unlike fluid-filled catheters, micromanometer tipped catheters provide high-fidelity
pressure values without the errors stemming from differences in the reference zero level,
micromanometer catheter tip instrument depends on the vertical position of the catheter
tip in the chest given the hydrostatic pressure component. This was not a significant
problem in our study, as pressure was always recorded at the same site in the ascending
aorta in all supine patients, namely above the aortic cusp. Mean pressure was
automatically calculated as the area under the pressure curve divided by the cardiac cycle
length. Systolic, diastolic and mean pressures were averaged out over nine beats in 66
patients (4) and over a 15 sec period in 73 patients (5). Stroke volume was calculated
from monoplane angiograms using the area-length method (n=66) or by the triplicate
thermodilution method (n= 73). Cardiac index and total peripheral resistance were
calculated using standard formulas. Cardiac power output (W’) was calculated as the
MAP times cardiac index product (6,7,12).
Calculations of the mathematical means of SAP and DAP. The arithmetic, geometric and
harmonic means are traditionally thought to have been discovered by Pythagoras of
Samos and coworkers (38), from the Greek school of mathematicians around 500 BC,
and these means formed the basis of classical Greek theories of architecture, perspective,
music and processes of nature. Mathematical means have been largely used in medicine
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as observed with external pressure transducers (13). Pressure measured by a
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and physiology, as illustrated by the following examples in the cardiovascular field. The
arithmetic mean of systolic and diastolic brachial artery pressure has demonstrated great
value in predicting mortality risk (18). Geometric progression has been documented in the
distribution of coronary artery lesions in the human heart (11). If a circuit has two
resistors connected in parallel, the average resistance is the half of their harmonic mean
(2,21,31).
The following mathematical means of systolic and diastolic aortic pressures were
arithmetic mean (A) = (SAP+DAP) / 2
geometric mean (G) =
(SAP x DAP)
harmonic mean (H) = 2 (SAP x DAP) / (SAP + DAP).
From a mathematical point of view : A > G > H.
As far as G is concerned, Pythagoras of Samos and coworkers first noted that if a
rectangle is formed with side lengths x, and y, the geometric mean of x and y gives the
side length of a square with the same area. This appears a simple way to memorize the
mathematical formula of the geometric mean, which is often called mean proportional.
Finally, it must be noted that other mathematical means have been described (e.g.,
quadratic mean). The quadratic mean [Q = sqrt [(SAP2 + DAP2) / 2 ] was not tested
because Q > A.
Empirical formulas for estimating MAP. In peripheral systemic arteries, MAP can be
reasonably estimated by adding one third (0.33) of pulse pressure to diastolic pressure.
This very popular formula appears in all physiological and medical textbooks and is
currently used in clinical hypertension trials (2,8,9,10,31,33,39). In the aorta, three MAP
empirical formulas (E1, E2, and E3) have been recently proposed (5,20,30). Given the
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calculated as follows :
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sine-wave like pattern of aortic pressure, it has been suggested nearly one century ago that
the fraction of pulse pressure that must be added to DAP may be between 0.33 and 0.50
(10,39). Consistently, Meaney et al. (20) have recently documented the following
empirical formula in the ascending aorta of 150 patients (86M/64F) with various forms of
cardiac diseases :
MAPE1= DAP + 0.412 (SAP – DAP).
On the other hand, in 73 patients (45M/18F), we have observed that the classic empirical
such that the following formula applied (5) :
MAPE2 = DAP + 0.33 (SAP – DAP) + 5mmHg.
It was proposed (5) that the E2 formula is consistent with the classic empirical formula
currently used at the peripheral level if one considers that both MAP and DAP remain
nearly constant from central to peripheral arteries while there is a physiological
amplification of SAP from aorta to periphery (2,25,31), that amounts 15 mmHg on
average (28,35) (5 mmHg = 0.33 x 15 mmHg).
Finally, when the classic empirical formula currently used at the peripheral level was
corrected for the increasing time dominance of systole with increasing heart rates,
Razminia et al. have reported that the following heart-rate corrected MAP accurately
applied in 12 patients at increasing paced rates (30) :
MAPE3 = DAP + [(0.33 + (HR x 0.0012)] (SAP – DAP).
In the second part of our study, the accuracy and precision of E1, E2 and E3 were tested.
Fractional systolic and diastolic pressure. The aortic fractional systolic pressure (FSP =
SAP/MAP) and fractional diastolic pressure (FDP = DAP / MAP) were also calculated.
FSP and FDP have been recently proposed as valuable estimates of aortic pulsatility and
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formula currently used at the peripheral level underestimates central MAP by 5 mmHg
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could relate to the risk of coronary heart diseases (16,23,26). We tested the hypothesis
that FSP and 1/FDP were reciprocal estimates of aortic pulsatility.
Comparisons with studies using fluid-filled catheters. In the clinical setting, fluid-filled
catheter-manometer systems are used, not micromanometer tipped catheters. To
document how our analysis compares with fluid-filled catheter studies, we performed a
retrospective analysis of the main recent papers relating cardiovascular risk and aortic
pressures recorded by using fluid-filled catheters (for a review, see Ref 26). Average
MAP. Only studies in which the time-averaged MAP was documented entered the final
analysis (14,19,24,29,37), while papers using the classic empirical formula did not enter
the final analysis. Indeed, as previously discussed, the DAP + 0.33 (SAP - DAP) formula
underestimates the time-averaged aortic MAP by 5 mmHg (5).
Statistical analysis. Results are expressed as means (SD). For each estimate of mean
pressure, the mean bias (estimate minus the time-averaged mean pressure) and SD of the
bias were calculated. The mean bias and SD reflect the accuracy and the precision of the
estimate, respectively. Comparisons were performed using analysis of variance. The mean
pressure bias was plotted against the time averaged mean pressure and was also plotted
against the average of the time-averaged mean pressure and mean pressure estimate, as
previously recommended by Bland and Altman (3). The same statistical analysis was
performed for comparisons between FSP and 1/FDP and for comparisons of
hemodynamic formulas involving W’ (see Results). Between groups differences in
pressures were tested using analysis of variance followed by paired t test with Bonferroni
correction. Linear regressions were obtained using the least squares method. A P value <
0.05 was considered significant.
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values of G, FSP, and 1/FDP were calculated from published values of SAP, DAP, and
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RESULTS
Data were obtained over a 66 to 160 mmHg MAP range. Characteristics of the
study population are listed in Table 1. Amongst the three mathematical means of SAP
and DAP under study, the arithmetic mean A significantly overestimated the timeaveraged MAP, while the harmonic mean H significantly underestimated MAP (Table 2).
Only the geometric mean G , i.e., the square root of the product of SAP and DAP,
Figures 1 and 2).
The three empirical fomulas (E1, E2 and E3) were accurate and precise estimates
of the time-averaged MAP (Table 3). The E1formula proposed by Meany et al. (20)
applied in our subjects. The E2 formula proposed by our group (5) was also confirmed in
the present study on a larger number of subjects. The E3 formula proposed by Razminia
et al. at increasing pacing rates (30) also applied in our study in patients with markedly
different cardiac cycle duration at rest (from 506 to 1267 msec).
There was a significant influence of MAP on the biases for E2 and E3 and for the
arithmetic and harmonic means, but not for the geometric mean and E1 (Tables 2 and 3).
Similar results were obtained when the influence of the pressure level on the bias was
tested using Bland and Altman plots (X axis = the average between MAP and the
pressure estimate). Finally, resting heart rate was not related to the biases for G, H, E2
and E3, while there was a weak negative relationship between heart rate and the biases for
A (R2 = 0.032; P = 0.03) and E1 (R2 = 0.044; P = 0.01).
The practical implications of our results were studied. It was found that MAP,
SAP and DAP were related as follows
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furnished an accurate and precise estimate of the time-averaged MAP (Table 2 and
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MAP =
(SAP x DAP) (Eq. 1)
and thus that :
MAP2= SAP x DAP (Eq. 2)
Put differently, our findings implied that
SAP/MAP = MAP / DAP (Eq. 3)
FSP = 1/FDP (Eq. 4)
Given potential implications for risk stratification, this was tested in the overall
similar in the overall population (1.35 (0.12) vs 1.34 (0.12)). The bias appeared clinically
moderate and was not influenced by the mean (Figures 3 and 4). The FSP and 1/FDP
values were also similar within each subgroup, and the (1/FDP – FSP) bias appeared
small enough to be negligible (Table 4). Both FSP and 1/FDP were higher in
hypertensives than in controls. As compared to the values documented in controls, both
FSP and 1/FDP were lower in patients with grafted heart, idiopathic dilated
cardiomyopathy and miscellaneous cardiac diseases.
The applicability of our results to clinical conditions where fluid-filled catheters
are used was tested. Five studies having recently related FSP, FDP and cardiovascular
risk were selected (see Methods) and involved an overall population of 503 individuals
(Table 5). Our retrospective calculations confirmed that the geometric MAP matched the
time-averaged MAP in four studies (bias < or = 1 mmHg) (Refs 14,19,24,37). In one
study (Ref 29), G slightly overestimated MAP by 3-4 mmHg. The FSP vs 1/FDP
matching was essentially confirmed (Table 5).
The implications of our results for new developments of current hemodynamic
formulas were studied. The MAP can be precisely expressed as follows
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population as well as in each subgroup. On average, the FSP and 1/FDP values were
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MAP = (R x CO) + Pra (Eq. 5)
where R is systemic vascular resistance, CO is cardiac output and Pra is right atrial
pressure (which is often neglected). This equality, in conjunction with Eq. 1, implies that
(SAP x DAP) = (R x CO) + Pra (Eq. 6)
We further attempted to simplify Eq. 6 because the handling of square roots in
physiological equations is not intuitive. Assuming that right atrial pressure is small
enough vs MAP as to be negligible, Eq. 5 reduces as follows
where R is total peripheral resistance. Multiplying both sides of Eq. 7 by MAP, we obtain
MAP2 = R x W’ (Eq. 8)
where W’ is mean cardiac power (with W’ = MAP x CO). From Eqs. 2 and 8 we obtain
SAP x DAP = R x W’ (Eq. 9)
Thus, one physiological implication of our study is that the (SAP x DAP) product (12,052
(4,075) mmHg2) matched the product of total peripheral resistance times mean cardiac
power (12,016 (3,992) mmHg2, P = NS).
DISCUSSION
The square root of the product of SAP and DAP (geometric mean) matched the
time-averaged MAP in the aorta of resting humans. Although the previously described
empirical formulas (5,20,30) demonstrated essentially equivalent accuracy and precision
for MAP estimation, the “geometric mean aortic pressure” appears more valuable as it
established a simple mathematical link between the steady and pulsatile component of
aortic pressure.
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MAP = R x CO (Eq. 7)
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Physiological implications. While MAP is accurately described by CO, R and Pra,
the determinants of SAP and DAP are not quantitatively known (36). For a given ejection
pattern, SAP and DAP are mainly determined by peripheral vascular resistance and
arterial stiffness (8,9,25,27,32,36,40). In patients with normally compliant arteries
(younger individuals, normotensive subjects), SAP and DAP mainly depend upon R value
(and therefore upon MAP), with increasing R resulting in both SAP and DAP increases
(9). Conversely, in patients with stiff arteries (older individuals, hypertensives), the
arterial pressure/flow waves are responsible for the increased pulse pressure, with
opposite effects on SAP (increased) and DAP (decreased) (9,27,32,36). Indeed, ejection
into a stiff proximal aorta generates a wider pulse pressure than in a low-compliance
system. Furthermore, it is generally admitted that the increased backward-traveling wave
(increased wave reflection) results in a higher SAP by adding to the incident pressure
wave in systole, while it tends to decreases DAP given the loss of the physiological
boosting pressure effect in early diastole (27,32).The opposite contribution of arterial
stiffness to SAP and DAP may have been canceled when one multiplies SAP by DAP,
thus unmasking the remaining influence of R. Overall, the major role of R on SAP and
DAP values in patients with highly compliant arteries, and the opposite effects of arterial
stiffness on SAP and DAP in patients with stiff arteries, may furnish the physiological
basis of Equation 1.
Equation 9 was the axiomatic consequence of equation 1. Although essentially
phenomenological, Equation 9 established a simple relationship between the pulsatile
(SAP, DAP) and steady (R, W’) hemodynamical variables. Resistance is the only
component capable of extracting energy from a circuit by transforming it into heat
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decreased buffering capacities of the proximal aorta and abnormalities in the traveling
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(frictional loss) (21). The time-averaged mean power of the instantaneous pressure-flow
product is the total hydraulic power. Mean cardiac power (W’=MAP x CO) represents the
mean rate of energy input the systemic vasculature receives from the heart at the level of
the aortic root, i.e., the hydraulic power that would produce the same average flow in a
steady stream without pulsation (6,7,12,21). The total hydraulic power minus mean power
difference is the oscillatory power, which entails pulsatile pressure wave without
resulting in net forward flow. The pulsatile power proportionally increases in stiff arterial
instantaneous pressure and flow. Recent clinical works have demonstrated the interest in
studying W’ and the W’ / R relationship in the diagnosis, follow-up and prognosis of
heart failure (6) and cardiogenic shock (7).
Clinical implications. Aortic pressure determines the hemodynamic burden put on
the heart, coronary arteries, and carotid arteries (2,31), and this may impact on the risk of
heart failure, myocardial infarction and stroke (26,33). Indices that measure central
pressure are more directly related to cardiovascular events than measures of pressure in
peripheral arteries (26,27,32). Given that the higher the MAP, the higher the fluctuations
around the MAP (25,32), aortic FSP (SAP/MAP) and FDP (DAP/MAP) may be valuable
indices of aortic pressure pulsatility (16,23). After multivariable adjustments in 445
patients, Jankowski et al. have recently demonstrated that both FSP and FDP are related
to the risk of coronary heart disease (16). One implication of the matching between MAP
and the geometric mean was that FSP and FDP were essentially reciprocal estimates of
aortic pulsatility both in the overall population and in the various diseased subgroups.
This may have implications for simplifying the battery of indices used for risk
stratification.
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systems, but it is not calculated in practice because it requires precise recordings of
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Limitations and strengths of the study. Our results strictly pertain to pressures
recorded at the central aortic level, and do not apply to sphygmomanometer recordings.
Peripheral DAP measured by sphygmomanometer may be higher than pressures
determined invasively at the aortic root, and there is a physiological amplification of SAP
from the aorta to periphery. Overall, this could introduce some errors in estimating
peripheral pressure by means of any formula obtained at the central level. Thus, the
applications of our results to non-invasive peripheral blood pressure measurements must
Data were obtained over a 60 to160 mmHg MAP range and in a large high-fidelity
pressure data set (n=139), and consistent results were documented in the various
subgroups. Because micromanometer tipped catheters are not used in the clinical setting,
one may argue that the frequency-dependent amplitude distortion caused by fluid-filled
catheter may obscure the relationship we reported here. Although our results remain to be
confirmed with aortic pressure recorded by using fluid-filled catheter, the retrospective
analysis of previously published pressure data involving five hundred and three patients
(14,19,24,29,37) confirmed that our results remain essentially valid with fluid-filled
catheters.
In conclusion, in resting humans, the time-averaged mean aortic pressure can be
reliably estimated using the square root of the product of systolic and diastolic aortic
pressure. The “geometric mean aortic pressure” strictly applies to aortic root pressure and
not to peripheral blood pressure. This simple formula may offer a valuable mathematical
link between the steady and pulsatile component of central pressure.
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be avoided.
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20
Figure legends.
Figure 1. Linear relationship between the time-averaged mean aortic pressure (MAP) and
the geometric mean of the systolic x diastolic aortic pressure product
(G =
(SAP x DAP) ). The regression line was as follows : G = 1.00 MAP – 0.5 mmHg,
R2 = 0.98; P = 0.0001; n = 139.
Figure 2. Lack of influence of the aortic pressure level on the pressure bias (P = 0.14). X
axis = average of the sum of the time-averaged mean arterial pressure and the geometric
mean arterial pressure (bias). The mean bias (SD) = 0.3 (2.7) mmHg. The 95%
confidence interval for the bias is figured.
Figure 3. Linear relationship between the fractional systolic pressure (FSP) and 1/FDP,
where FDP is fractional diastolic pressure. The regression line was as follows : 1/FDP =
0.79 FSP + 0.27; R2 = 0.69; P = 0.0001; n = 139.
Figure 4. Lack of influence of the mean on the 1/FDP minus FSP bias (P = 0.32). The
mean bias (SD) = - 0.007 (0.070). The 95% confidence interval for the bias is figured.
The mean bias (SD) in each subgroup is presented in Table 4.
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mean arterial pressure (G). Y axis = difference between the g value and the time averaged
21
Table 1. Characteristics of the study population (n=139).
Range
Age, years
49 (12)
19-77
Body weight, kg
73 (13)
42-116
Body height, cm
169 (8)
145-197
Body surface area, m2
1.85 (0.18)
1.30-2.47
Heart period, msec
847 (147)
506-1267
SAP, mmHg
146.0 (31.1)
82.5-204.2
DAP, mmHg
80.8 (13.8)
49.8-133.0
MAP, mmHg
107.9 (18.2)
66.3-160.1
Cardiac index, L/min/m2
3.37 (1.00)
1.07-5.86
35 (12)
16-96
371 (142)
109-764
R, mmHg/L/min/m2
W’, mmHg x L/min/m2
SAP: systolic aortic pressure. DAP: diastolic aortic pressure. MAP: time-averaged mean
aortic pressure. R: total peripheral resistance. W’: mean cardiac power.
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Mean (SD)
22
Table 2. Various mathematical means of systolic (SAP) and diastolic (DAP) aortic
pressure (n=139).
Geometric
Arithmetic
(H)
(G)
(A)
103.3 *
108.2
113.4 *
(SD)
(17.2)
(18.6)
(20.5)
mean bias, mmHg
- 4.5
0.3
5.5
(SD)
(4.0)
(2.7)
(4.4)
- 0.36
0.05
0.41
< 0.001
0.54
< 0.001
mean value, mmHg
bias vs MAP
R value
P value
MAP = the reference, time-averaged mean aortic pressure = 107.9 (18.2) mmHg.
Note that only G the geometric mean of SAP and DAP, i.e., the square root of the (SAP x
DAP) product, gave a reliable estimate of MAP. * P < 0.001 vs MAP
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Harmonic
23
Table 3. The three empirical estimates (E1, E2 and E3) for estimating mean aortic
pressure (n=139).
DAP+0.33PP+5
DAP + [(0.33+ (HRx0.0012)] PP
(E1)
(E2)
(E3)
(Ref. 20)
(Ref. 5)
(Ref. 30)
mean value (SD),
107.7
107.5
107.9
mmHg
(18.8)
(17.5)
(19.0)
mean value (SD),
- 0.2
- 0.3
0.1
mmHg
(2.9)
(2.7)
(2.9)
R value
0.14
- 0.33
0.20
P value
0.10
< 0.001
< 0.05
bias vs MAP
DAP: diastolic aortic pressure. PP: aortic pulse pressure = systolic aortic pressure minus
DAP.
HR: heart rate. MAP = the reference, time-averaged mean aortic pressure = 107.9 (18.2)
mmHg. Bias = empirical estimate minus MAP. Note that the three empirical formulas
were reliable estimates of MAP and were of similar accuracy (when expressed in absolute
value) and precision than G (Table 2).
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DAP + 0.412 PP
24
Table 4. Aortic pressures and fractional pressures in the various patients’ subgroups
(n=139).
Controls
DAP
MAP
(SAP x DAP )
bias
FSP
1/FDP
1/FDP - FSP
mmHg
mmHg
mmHg
mmHg
mmHg
-
-
-
128 (12)
71 (7)
95 (7)
95(7)
0.1(3.2)
1.35 (0.10)
1.35 (0.10)
0.00 (0.09)
182 (12)*
90 (13)*
126 (10)*
127(9)
1.0(3.4)
1.44 (0.11)*
1.42 (0.13)*
-0.02 (0.08)
142 (20)+
90 (11)*
113 (14)*
113(14)
0.2(1.0)
1.26 (0.06)*
1.25 (0.05)*
-0.01 (0.02)
124 (20)
79 (10)*
99 (12)
99(13)
0.0(2.2)
1.25 (0.08)*
1.25 (0.06)*
0.00 (0.04)
123 (25)
73 (10)
94 (14)
94(15)
0.2(1.8)
1.29 (0.10)+ 1.30 (0.07)+
0.01 (0.05)
n=31
Hypertensives
n=46
Grafted heart
n=18
IDCM
n = 14
Miscellaneous
n=30
Values are means (SD). SAP: systolic aortic pressure. DAP: diastolic aortic pressure.
MAP: the reference, time averaged mean aortic pressure.
(SAP x DAP) : G, the
geometric mean of SAP and DAP. Bias: G minus MAP. FSP: fractional systolic aortic
pressure (SAP/MAP). FDP: fractional diastolic aortic pressure (DAP/MAP). IDCM =
idiopathic dilated cardiomyopathy. For sake of simplicity, the pressures have been
corrected to the nearest whole number. NS : not significant. * indicates P < 0.01 vs value
in the control group. + indicates P = 0.05 vs value in the control group. For comparisons
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SAP
25
between diseased groups and the control group, only statistically significant differences
are figured.
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26
Table 5. Retrospective analysis and pressure calculations from previously published
studies using fluid-filled catheters (n=503).
Ref.
patients
SAP
DAP
MAP
mmHg
mmHg
mmHg
(SAP x DAP)
mmHg
FSP
1/FDP
-
-
a
139.7
73.2
100.2
101.1
1.39
1.37
(14)
b
144.6
71.1
101.5
101.4
1.42
1.43
(19)
c
133.8
67.7
95.1
95.2
1.41
1.40
(19)
d
143.8
66.2
97.6
97.6
1.47
1.47
(24)
e
140
75
103
102
1.36
1.37
(24)
f
146
70
100
101
1.46
1.43
(29)
g
127
72
93
96
1.36
1.29
(29)
h
136
72
95
99
1.43
1.32
(29)
i
145
78
103
106
1.41
1.32
(37)
j
139
72
100
100
1.39
1.39
(37)
k
141
68
98
98
1.44
1.44
Values indicated are means. Ref: reference number, see Methods for inclusion criteria.
Patients with chest pain and without documented coronary heart disease (a, n=128) or
with documented coronary heart disease (b, n= 62). Patients > 60 years of age with stable
angina pectoris and without restenosis (c, n=48) or with restenosis (d, n=39). Patients
with coronary angiography performed 3 months after successful coronary angioplasty and
evidencing no restenosis (e, n=30) or restenosis (f, n=23). Patients with coronary artery
disease and one (g, n=41), two (h, n=32) and three (i, n= 26) diseased coronary vessels.
Patients with coronary angiography performed 3 months after successful coronary
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(14)
27
angioplasty and evidencing no restenosis (j, n=40) or restenosis (k, n=34). SAP: systolic
aortic pressure (as published in the corresponding reference). DAP: diastolic aortic
pressure (as published). MAP: the reference, time averaged mean aortic pressure (as
published).
(SAP x DAP) : calculated from published SAP and DAP values. FSP:
fractional systolic aortic pressure (SAP/MAP) and FDP: fractional diastolic aortic
pressure (DAP/MAP), both calculated from published SAP, DAP and MAP values.
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28
Fig. 1
180
140
120
100
80
60
40
40
60
80
100
120
140
160
Mean aortic pressure (mmHg)
180
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G = sqrt (SAP x DAP)
(mmHg)
160
29
Fig. 2
bias
(mmHg)
15
5
+ 2 SD
0
mean
-5
- 2 SD
-10
-15
40
60
80
100
120
140
160
(mean aortic pressure + G) / 2
(mmHg)
180
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10
30
Fig. 3
2.0
1.6
1 / FDP
1.4
1.2
1.0
1.0
1.2
1.4
1.6
FSP
1.8
2.0
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1.8
31
Fig. 4
0.25
+ 2 SD
mean
0
- 2 SD
- 0.25
- 0.50
1.0
1.2
1.4
1.6
1.8
mean = (FSP + 1/FDP) / 2
2.0
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bias = (1/FDP) - FSP
0.50