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Articles in PresS. J Appl Physiol (July 28, 2005). doi:10.1152/japplphysiol.00713.2005 1 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. Downloaded from http://jap.physiology.org/ by 10.220.32.247 on June 16, 2017 From the Service de Physiologie Cardio-Respiratoire, CHU de Bicêtre, Université Paris 2 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. Downloaded from http://jap.physiology.org/ by 10.220.32.247 on June 16, 2017 diseases (n=108). The time-averaged MAP and the pulse pressure (PP=SAP-DAP) were 3 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 Downloaded from http://jap.physiology.org/ by 10.220.32.247 on June 16, 2017 significantly contributes to vascular load (9,21,34). Mean aortic pressure is adequately 4 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 Downloaded from http://jap.physiology.org/ by 10.220.32.247 on June 16, 2017 using either the geometric or the harmonic mean of SAP and DAP in the aorta of resting 5 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 Downloaded from http://jap.physiology.org/ by 10.220.32.247 on June 16, 2017 as observed with external pressure transducers (13). Pressure measured by a 6 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 Downloaded from http://jap.physiology.org/ by 10.220.32.247 on June 16, 2017 calculated as follows : 7 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 Downloaded from http://jap.physiology.org/ by 10.220.32.247 on June 16, 2017 formula currently used at the peripheral level underestimates central MAP by 5 mmHg 8 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. Downloaded from http://jap.physiology.org/ by 10.220.32.247 on June 16, 2017 values of G, FSP, and 1/FDP were calculated from published values of SAP, DAP, and 9 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 Downloaded from http://jap.physiology.org/ by 10.220.32.247 on June 16, 2017 furnished an accurate and precise estimate of the time-averaged MAP (Table 2 and 10 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 Downloaded from http://jap.physiology.org/ by 10.220.32.247 on June 16, 2017 population as well as in each subgroup. On average, the FSP and 1/FDP values were 11 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. Downloaded from http://jap.physiology.org/ by 10.220.32.247 on June 16, 2017 MAP = R x CO (Eq. 7) 12 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 Downloaded from http://jap.physiology.org/ by 10.220.32.247 on June 16, 2017 decreased buffering capacities of the proximal aorta and abnormalities in the traveling 13 (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. Downloaded from http://jap.physiology.org/ by 10.220.32.247 on June 16, 2017 systems, but it is not calculated in practice because it requires precise recordings of 14 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. Downloaded from http://jap.physiology.org/ by 10.220.32.247 on June 16, 2017 be avoided. 15 REFERENCES 1. An G. Mathematical modeling in medicine: a means, not an end. Crit Care Med 33: 253-254, 2005. 2. Berne RM, and Levy MN. The arterial system. In: Physiology. Berne RM and Levy MN eds. Mosby Inc. St Louis pp 415-428, 1998: 3. Bland JM, and Altman DG. Statistical methods for assessing agreement between two methods of clinical measurement. Lancet 8476: 307-310, 1986 vascular resistance and total arterial compliance to effective arterial elastance in humans. Am J Physiol Heart Circ Physiol 285: H614-H620, 2003 5. Chemla D, Hébert JL, Aptecar E, Mazoit JX, Zamani K, Frank R, Fontaine G, Nitenberg A, and Lecarpentier Y. 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Inflection point of ascending aortic waveform is a powerful predictor of restenosis after percutaneous transluminal coronary angioplasty. Am J Hypertens 15: 823-826, 2002. 38. Weisstein EW. Pythagorean means. From MathWorld-A Wolfram Web Ressource. http://mathworld.wolfram.com/PythagoreanMeans.html Wolfram Research Inc, 19992005 39. Wezler K, and Böger A. Die Dynamik des arteriellen Systems. In Ergebnisse der Physiologie (Asher L and Shapiro K eds) Verlag von JF Bergmann, München 292-606, 1939 40. Zieman SJ, Melenovsky V, Kass DA. Mechanisms, pathophysiology, and therapy of arterial stiffness. Arterioscler Thromb Vasc Biol 25: 932-943, 2005. Downloaded from http://jap.physiology.org/ by 10.220.32.247 on June 16, 2017 36. Stergiopulos N, Meister JJ, Westerhof N. Determinants of stroke volume and 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. Downloaded from http://jap.physiology.org/ by 10.220.32.247 on June 16, 2017 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. Downloaded from http://jap.physiology.org/ by 10.220.32.247 on June 16, 2017 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 Downloaded from http://jap.physiology.org/ by 10.220.32.247 on June 16, 2017 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). Downloaded from http://jap.physiology.org/ by 10.220.32.247 on June 16, 2017 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 Downloaded from http://jap.physiology.org/ by 10.220.32.247 on June 16, 2017 SAP 25 between diseased groups and the control group, only statistically significant differences are figured. Downloaded from http://jap.physiology.org/ by 10.220.32.247 on June 16, 2017 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 Downloaded from http://jap.physiology.org/ by 10.220.32.247 on June 16, 2017 (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. Downloaded from http://jap.physiology.org/ by 10.220.32.247 on June 16, 2017 28 Fig. 1 180 140 120 100 80 60 40 40 60 80 100 120 140 160 Mean aortic pressure (mmHg) 180 Downloaded from http://jap.physiology.org/ by 10.220.32.247 on June 16, 2017 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 Downloaded from http://jap.physiology.org/ by 10.220.32.247 on June 16, 2017 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 Downloaded from http://jap.physiology.org/ by 10.220.32.247 on June 16, 2017 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 Downloaded from http://jap.physiology.org/ by 10.220.32.247 on June 16, 2017 bias = (1/FDP) - FSP 0.50