Introduction
In the recent years, there has been a growing interest toward improving cardiovascular risk estimation using central [aortic root] blood pressure [BP] [1, 2]. It is the central BP which loads the heart, and there is an anatomic proximity of the aorta to the brain and kidneys. Thus, end-organ damages due to pressure overload and cardiovascular complications may be more closely related to central than peripheral BP [3–6], although this point remains debated [7–9]. The peripheral systolic BP [SBP] is most often higher than central systolic BP [cSBP,] and this pressure amplification is mainly explained by the narrowing of arterial caliber and by arterial properties, especially arterial stiffness which affects the speed of the pressure pulse wave traveling down from the heart to periphery and back to the heart, thus impacting the amount of both pressure wave amplification and reflection [1, 2, 10–19]. As a result, peripheral SBP is considered an inaccurate substitute of cSBP. On the other hand, the mean BP [MBP] recorded in peripheral large arteries only slightly differ from central aortic value in a supine subject, and the same applies to diastolic BP [DBP] [1, 2, 10–20].
Invasive recordings at the central level provide the gold-standard measure of true aortic root cSBP, but they are limited to patients requiring catheterization and thus not ethically nor technically feasible in the general population. There has been an ongoing development of new devices to non-invasively estimate cSBP using various waveform acquisition techniques [tonometry, oscillometry, and echo-tracking] [20–27]. Some devices allow a calibration method based on brachial cuff SBP and DBP. However, studies carried out nowadays most often rely on the widely accepted assumption that peripheral MBP and DBP may be used as input values for central MBP and DBP [21, 22, 25]. A logical implication is that any empirical equation allowing the accurate and precise estimation of cSBP from central MBP and DBP would theoretically also allow the estimation of cSBP from peripheral MBP and DBP without the need for any supplemental device to record waveforms. In the remaining part of our manuscript, MBP and DBP will interchangeably refer to central or peripheral BP values, except where indicated.
Based on the basic principles of hemodynamics, here we propose a new formula for the direct central blood pressure estimation of cSBP, which is DCBP = MBP2/DBP [see Methods and Figure 1]. Our proof-of-concept and validation study tested the accuracy and precision of DCBP using invasive MBP and DBP values in an attempt to minimize BP measurement errors, as previously recommended [21–25].
Figure 1. Rationale of the DCBP formula. cSBP, central systolic blood pressure; DBP, diastolic blood pressure [either central or peripheral]; MBP, mean blood pressure [either central or peripheral]; DCBP, direct central blood pressure estimation of csBP.
Methods
Derivation of the DCBP Formula
Our group [28–30] and others [31] have proposed various empirical formulas relying on aortic SBP and DBP to estimate MBP at the aortic root level. In a previous high-fidelity aortic pressure study [28], we showed that the geometric mean of aortic SBP and DBP provides an accurate and precise estimate of the time-averaged aortic MBP:
Aortic MBP = aorticSBP×aorticDB P. This equation may be rewritten as follows:
Aortic MBP2 = aortic SBP × aortic DBP
A new empirical formula may thus be proposed to estimate central [aortic] SBP:
DCBP = aortic MBP2/aortic DBP
The first aim of our study was to establish the proof-of-concept by studying the accuracy and precision of this DCBP formula at the aortic root level.
The same DCBP formula may well also apply at the peripheral [brachial and radial] level, given that MBP and DBP values only slightly differ as pressure travels from aorta to brachial and radial artery:
DCBP = brachial MBP2/brachial DBP
DCBP = radial MBP2/radial DBP
The second aim of our study was to validate these DCBP formulas using MBP and DBP values that were invasively obtained at the brachial and radial artery level.
DCBP at the Aortic Root Level Using High-Fidelity Pressure Recordings [Proof of Concept, n = 139]
The DCBP formula was tested using a post-hoc analysis of our prospective high-fidelity aortic pressure database [28]. All investigations had been approved by our institution, and informed consent was obtained for all patients. The adult patients prospectively enrolled were free of aortic stenosis or left ventricular outflow tract obstruction. The underlying diagnosis was as follows: subjects with normal cardiac function and coronary angiograms [n = 31], subjects with known hypertension [n = 46], grafted hearts [n = 18], idiopathic dilated cardiomyopathy [n = 14], and miscellaneous cardiac diseases, mainly coronary artery disease [n = 30]. The invasive BP, namely the time-averaged MBP, cSBP, and DBP were automatically measured.
Validation of DCBP Using Invasive Peripheral BP
Invasive High-Fidelity Aortic and Brachial Pressures [n = 64]
A recent systematic review by our group [19] has documented that only two independent high-fidelity pressure studies have reported the full invasive BP data set [SBP, DBP, and MBP], either simultaneously or during the same overall procedure at both the aortic root and brachial artery level [10, 11]. These studies were used to test the accuracy and precision of the DCBP formula [n = 64]. As also previously discussed [19], two studies were excluded from the analysis because patients were given nitroglycerin [12] or because the data presented [13] have been subsequently upgraded [11], and four studies were excluded because they documented aortic/brachial SBP and DBP only, not MBP [14–17].
Carotid Tonometry Coupled With Invasive Fluid-Filled Radial BP [n = 30]
To prospectively validate the DCBP formula, we conducted an observational study in the 25-bed medical ICU of a University hospital. The study was approved by the Ethics Committee of the French Intensive Care Society [agreement 12-376]. All patients or their next of kin were informed and consented to participate. We included 30 consecutive spontaneously breathing patients who were hemodynamically stable and already equipped with a fluid-filled catheter in the radial artery. Only spontaneously breathing patients were included to ensure high-quality pressure signal of carotid tonometry [32]. Exclusion criteria were heart rate >120 bpm, aortic stenosis or obstructive cardiomyopathy, medical history of carotid occlusive diseases, or carotid murmur at auscultation. Carotid tonometry [Complior Analyse® ALAM Medical, Saint-Quentin-Fallavier, France] was performed, as previously described [23, 32, 33]. The advantage of using carotid tonometry relies on the fact that no transfer function or peripheral waveforms analysis is used to estimate cSBP [33]. Briefly, we obtained non-invasive carotid pressure on the same side as the arterial catheter, except in patients with a central venous catheter in the superior vena cava territory, in whom we studied the contralateral carotid to avoid any potential artifact. The carotid tonometer pressure signals were calibrated from the invasive radial DBP and the time-averaged radial MBP [input factors], assuming unchanged DBP and MBP from aorta to the peripheral arteries. Carotid SBP was used as a non-invasive estimate of cSBP, an assumption which is evidence-based [20, 34]. In all patients, non-invasive central BP [carotid tonometry] and invasive peripheral BP [radial artery catheter] were recorded simultaneously.
Sensitivity Analysis
The theoretical influences of isolated or combined [parallel or opposite] calibration errors in DBP or MBP on the DCBP-derived estimation of cSBP were studied. The following example illustrates the way calculations were performed: as compared to intra-arterial BP values, a +5% overestimation of MBP together with a +10% overestimation of DBP resulted in a +0.2% overestimation of cSBP by the formula DCBP [[1.05 × 1.05]/1.10 =1.0025]. The DCBP-derived estimates of cSBP were deemed reasonably acceptable from a clinical standpoint if the associated percentage error ranged from −10 to +10%.
Statistical Analysis
The normal distribution of data was checked by the Kolmogorov–Smirnov test. Continuous variables were summarized as mean ± standard deviation [SD] or median [interquartile range], and categorical variables as counts [percentages]. Correlations between variables were assessed by Pearson's correlation coefficient. Comparison between men and women were performed using Student's unpaired t-test. The error was calculated as the difference between DCBP and cSBP and was expressed in mmHg. The accuracy [mean error] and precision [SD] of DCBP estimate were calculated. As previously recommended [35], the difference was categorized into four bands according to its rounded absolute value: 0–5 mmHg which represent measurements considered to be very accurate [no error of clinical relevance]; 6–10 mmHg, which represent measurements considered to be slightly inaccurate; 11–15 mmHg, which represent measurements considered to be moderately inaccurate; and >15 mmHg which represent measurements considered to be very inaccurate. The final analysis was based on how values in these bands fall cumulatively into three zones: within 5 mmHg [this zone represents all values falling in the 0–5 mmHg band], within 10 mmHg [this zone represents all values falling in the 0–5 and 6–10 mmHg bands], and within 15 mmHg [this zone represents all values falling in the 0–5, 6–10, and 11–15 mmHg bands]. The error was also expressed as a percentage of cSBP given the high number of hypertensive patients in the study population. Statistical analysis was performed with MedCalc11.6.0 software [MedCalc, Mariakerke, Belgium], and a p-value < 0.05 was considered statistically significant.
Results
High-Fidelity Aortic Pressure Analysis [Proof of Concept, n = 139]
Patients were mostly men [78%] and were middle-aged [49 ± 12 years] [Table 1]. The cSBP varied across a wide range, from 82.5 to 204.0 mmHg. Six patients [4%] had their cSBP ≤ 100 mmHg, 13 patients [9%] had cSBP between 100 and 140 mmHg, 66 patients [47%] had cSBP between 140 and 160 mmHg, and 54 patients [39%] had cSBP ≥ 160 mmHg. Thus, 120/139 [86%] patients had their cSBP ≥ 140 mmHg at the time of the catheterization. Aortic DBP ranged from 49.8 to 133.0 mmHg. Six patients [4%] had their DBP ≤ 60 mmHg, 39 patients [28%] had their DBP ≥ 85 mmHg, and 14 patients [10%] had their DBP ≥ 100 mmHg.
Table 1. Demographic and hemodynamic characteristics of the patients from the invasive high-fidelity aortic pressure study.
There was a strong linear relationship between DCBP and cSBP [r2 = 0.95, p < 0.001 [Figure 2A]]. As compared to cSBP [146.0 ± 31.1 mmHg], the DCBP formula gave an accurate estimate of cSBP [mean error = −0.9 mmHg], the precision was 7.4 mmHg, and there was no bias across the range [r2= 0.01, p = 0.69] [Figure 2B]. The % error was −0.4 ± 5.0% of cSBP [range: from −16.9 to 11.3%] [Figure 2C]. The number of comparisons falling within the 5, 10, and 15 mmHg error bands was 86 [61.9%], 119 [85.6%], and 130 [93.5%], respectively. The error was similar in men and women [p = 0.67], it slightly increased with heart rate [r2 = 0.06, p < 0.05], and it slightly decreased with age [r2 = 0.10, p < 0.05].
Figure 2. Aortic high-fidelity pressures [n = 139]. [A] Linear relationship between central systolic blood pressure [cSBP] and the DCBP formula calculated from MBP and DBP. [B] Bland and Altman plots of the error [DCBP-cSBP] as a function of average [DCBP+cSBP]/2]. Dotted lines indicate 95% limits of agreement. [C] Influence of cSBP on the error [expressed as a percentage of cSBP].
Validation of DCBP Using Invasive Peripheral BP
Invasive High-Fidelity Brachial and Aortic Pressures [n = 64]
The invasive brachial pressures, the cSBP, and the DCBP calculated from brachial pressures are indicated in Table 2. In the two selected studies [10, 11], the weighed mean error [DCBP – cSBP] was 1.1 mmHg.
Table 2. Data from high-fidelity pressure studies reporting full data set of SBP, MBP, and DBP at both aortic and brachial level.
Carotid Tonometry Coupled With Invasive Fluid-Filled Radial BP [n = 30]
Patients were mostly men [77%], with a mean age of 62 ± 14 years and a median body mass index of 22 [19–26] kg/m2 [Table 3]. Two patients [7%] had atrial fibrillation and 10 patients [33%] received norepinephrine with a median dosage of 0.13 [0.11–0.30] μg/kg/min. The carotid cSBP ranged from 67 to 154 mmHg. Seven patients [23%] had their cSBP ≤ 100 mmHg, 21 patients [70%] had their cSBP between 100 and 140 mmHg, and two patients [7%] had their cSBP ≥ 140 mmHg. The carotid DBP ranged from 41 to 90 mmHg. Fifteen patients [50%] had their carotid DBP ≤ 60 mmHg, only one patient [3%] had carotid DBP ≥ 85 mmHg.
Table 3. Demographic and hemodynamic characteristics of the intensive care unit patients equipped with a fluid-filled catheter in the radial artery.
There was a strong linear relationship between DCBP and cSBP [r2 = 0.90, p < 0.001 [Figure 3A]]. As compared to cSBP [115.7 ± 18.2 mmHg], DCBP gave an accurate estimate of cSBP [mean error = −0.4 mmHg] [Figure 3B]. The precision was 5.8 mmHg and there was no bias across the range [r2 = 0.001, p = 0.8]. The % error was −0.2 ± 4.8% of cSBP [range: from −11.1 to 8.2%] [Figure 3C]. The number of comparisons falling within the 5, 10, and 15 mmHg error bands was 22 [73.3%], 28 [93.3%], and 29 [96.7%], respectively. The error was similar in men and women [p = 0.09], and was not influenced by heart rate [r2 = 0.11, p = 0.07] or by age [r2 = 0.06, p = 0.19].
Figure 3. Carotid tonometry study [n = 30]. [A] Linear relationship between the central systolic blood pressure [cSBP] estimated by carotid tonometry and DCBP calculated from radial MBP and DBP [fluid-filled catheter in the radial artery]. [B] Bland and Altman plots of the error [DCBP-cSBP] as a function of average [DCBP+cSBP]/2]. Dotted lines indicate 95% limits of agreement. [C] Influence of cSBP on the error [expressed as a percentage of cSBP].
Sensitivity Analysis
Results of the sensitivity analysis are given in Table 4. Assuming a perfectly accurate non-invasive measurement of peripheral MBP as compared with intraarterial MBP [the 0% error column in Table 4], a positive/negative % error in the estimation of peripheral DBP will translate into a negative/positive % error of essentially similar magnitude for the cSBP estimation by the DCBP formula. Assuming a perfectly accurate non-invasive measurement of peripheral DBP [the 0% error line in Table 4], positive/negative % error in the estimation of peripheral MBP will translate into a positive/negative % error of roughly doubled value. The theoretical influences of combined calibration errors on the DCBP-derived estimation of cSBP are summarized in Table 4, with green areas indicating reasonable accuracy from a clinical standpoint [-10% to +10% error of cSBP using DCBP].
Table 4. Sensitivity analysis indicating the % error in the estimation of central systolic blood pressure [cSBP] by using the DCBP formula.
Discussion
Our work showed that cSBP may be estimated from peripheral MBP and DBP values only. The cSBP estimation is based on our new formula: DCBP = MBP2/DBP. As compared with methods currently used, there is no need for any supplementary device or waveform recording.
To evaluate any new method, it is important to identify the sources of errors which might impact the accuracy of the results [21, 22]. For cSBP estimation, the potential sources of errors generally include the waveform acquisition technique [tonometry, oscillometry, and echo-tracking]. This is irrelevant in our case as we did not rely on pulse acquisition. The method used to calibrate pulse waves is another potential source of error. Here, we based our new method on the widely admitted recommendation that MBP and DBP may be used as input factors for central BPs [rather than SBP and DBP] [21, 22, 25]. The remaining sources of errors are: [1] the arterial site of pulse recording [radial, brachial, carotid, and aortic]; [2] the method for BP measurement [invasive, non-invasive]; and [3] the mathematical analysis used. For these reasons, we designed our study in three parts.
In the first part of our study, we focused on invasive high-fidelity aortic pressures, and the potential error due to mild differences between aortic and brachial MBP and DBP was excluded as only aortic BPs were considered. Thus, the main source of error tested was the mathematical analysis, i.e., the derivation of DCBP after having rearranged the geometric mean equation. We performed a post-hoc analysis of our previously published database [28]. Over a wide cSBP range, the DCBP formula was associated with a−0.9 mmHg mean error and 7.4 mmHg SD of error, both of which fall within the guidelines of the Association for the Advancement of Medical Instrumentation [AAMI], namely