The study involved subjects (n = 34) undergoing coordinated angiography of the coronary vessels at the University Hospital (Favaloro Foundation, Buenos Aires, Argentina) (20, 31). A recent study of our group that focused on different hemodynamic issues used data from the same population (20). The exclusion criteria included heart valve diseases and cardiac arrhythmias. Prior to the evaluation, written informed consent was obtained from the subjects or their parents. If applicable, assent was also obtained. The protocol was approved by the Institutional Ethics Committee, and all procedures agreed with the Declaration of Helsinki.

The exposure of the subjects to cardiovascular risk factors (defined as previously described and following international recommendations) was determined from a clinical interview, biochemical analysis, echocardiographic studies, and anthropometric evaluation (32–36) (Table 1).

Invasive (catheterism) aoBP and bBP levels and waveforms were measured. In addition, aoBP levels and waveforms were non-invasively obtained from: (i)

CCA, BA, and RA applanation tonometry recordings (SphygmoCor device SCOR, v.9, AtCor Medical, Sydney, NSW, Australia),

Non-invasive data were obtained in random order to avoid potential bias associated with time intervals between non-invasive and invasive recordings.

While the subject was tested lying down on a catheterization table, intra-arterial aoBP and bBP levels and waveforms were recorded. After standard asepsis of the RA access area, lidocaine was subcutaneously injected, whereas soft sedation (1.5 mg of midazolam and 0.025 mg of fentanyl) was administered to minimize pain and discomfort. An intra-arterial introducer sheath was placed, and heparin was infused. A 0.035 in guide wire was moved forward and placed in the ascending aorta. Then a 5 French pigtail catheter (Cordis, Miami, USA) was introduced and positioned so that its tip remained always −4 cm away from the heart valve. The correct positioning of the catheter was confirmed (fluoroscopy, Allura Xper FD10 or Allura Clarity FD20/10, Philips Healthcare, Netherlands), and then the guide wire was removed, and the catheter was flushed with saline solution.

The fluid-filled catheter placed in the arterial lumen (aorta or BA) was connected to the external BP transducer (MX960, Medex, LogiCal, Smiths Medical ASD Inc., Minneapolis, USA) coupled to the Acist CVi system (Acist CVi, Medical System Inc., Germany). In turn, the Asist CVi system was synchronized with the x-ray imaging system Allura Xper FD10 or Allura Clarity FD20/10. The MX960 meets (or surpasses) the specifications of the Association for the Advancement of Medical Instrumentation/European Society of Hypertension/International Organization for Standardization (AAMI/ESH/ISO) collaboration.

The system (catheter, tubing, and external transducer) was flushed with saline solution, and the arterial pressure (aoBP or bBP) waveform was visually inspected for quality before each recording. The external transducer was calibrated following the built-in two-point calibration method of the system. First, the zero was assigned to the recording obtained with the sensor opened to the atmosphere (adjusting the baseline to zero or atmospheric pressure), and the second point was obtained by exposing the transducer to 100 mmHg (done by the device itself). The dynamic response of the system was adjusted to ensure a natural frequency of at least 20 Hz and a damping coefficient of at least 0.3. External transducers similar to the ones used in the present work (MX960, LogiCal) have high-quality, distortion-free frequency responses within the bandwidth of 0–30 Hz (37). This guarantees an adequate arrangement between the natural frequency and damping coefficient, ensuring that the measurement systems operate in areas of adequate dynamic responses (or in a somewhat underdamped region). The external transducer was always maintained at the cardiac level (midaxillary line). BP waveforms were visualized in the Allura Xper FD10 or Allura Clarity FD20/10 monitor.

Simultaneously, aoBP was invasively obtained and estimated using non-invasive ultrasound, oscillometry/plethysmography, and applanation tonometry recordings (see below) (Figure 1).

After recording aoBP, the catheter was moved to the BA opposite to that of the vascular access and positioned at the level where the pneumatic BA cuff for non-invasive BP measurement (MOG device) was located. Intra-arterial BP levels and waveforms were then measured, and non-invasive BP data were obtained (immediately before or after) using the oscillometric/plethysmographic technique (MOG device) (see below). After each bBP recording, the catheter was repositioned in the ascending aorta, and aoBP levels and waveforms were recorded, enabling hemodynamic stability to be confirmed.

The invasive recordings and data processing systems were used to determine heart rate (HR) and systolic, diastolic, and mean (i.e., from the pressure/time curve integral) BP levels.

After the evaluations, the subject was sent to the recovery area and discharged from the university hospital as appropriate considering his/her clinical situation.

At the same time, immediately before and/or after each invasive recording, bBP levels and waveforms were recorded by oscillometry/plethysmography (MOG device) through a pneumatic cuff positioned in the arm contralateral to the used for the vascular access (26, 38, 39). Non-invasive bBP values were used to calibrate CCA (vascular ultrasound), BA (applanation tonometry and oscillometry/plethysmography), and RA (applanation tonometry) pulse waveforms (see Figure 1).

The suffix “osc” was used to design data obtained with the oscillometric system (e.g., bSBPosc, bDBPosc, bPPosc, and HRosc). bMBP was directly obtained with oscillometry (bMBPosc). In addition, it was calculated from bSBPosc and bDBPosc considering two different form factors (33% and 41.2%), representing the percentage of the waveform amplitude added to the minimum (bDBPosc) to obtain the mean (bMBP) (20, 30): (i)

bMBP_0.412 mmHg = bDBPosc + 0.412 × bPPosc

The bMBP values obtained as stated above were used to calibrate the ultrasound-, tonometry-, and oscillometry/plethysmography-derived recordings used to obtain aoBP (Figure 1).

Non-invasive aoBP estimation involves three independent processes: (i) acquisition of a peripheral (e.g., CCA, RA, and BA) waveform, measured in voltage (e.g., mV) or mm; (ii) calibration with BP, to “convert” the waveform to one with pressure units (mmHg) instead of mm or mV; and (iii) estimation of aoBP (usually) via “mathematical filtering” of the recalibrated waveforms (22). In this work, calibration was done as follows. (1)

Invasive-derived (“Inv”): measured bMBP and bDBP were assigned, respectively, to the algebraic mean and minimum of the peripheral waveforms.

SBPA (SBPA = pSBP/aoSBP) and PPA (PPA = pPP/aoPP) were calculated from invasive and non-invasive aoSBP or aoPP data and from peripheral SBP and DBP (pSBP, pDBP; pPP = pSBP-pDBP) obtained at the BA (invasive and non-invasive recordings) or RA (Figure 2).

Two different approaches and devices were considered: one that allows obtaining different (new) peripheral BP values (e.g., SCOR) by using different schemes to calibrate the peripheral waveforms (a prior step to quantify aoBP) and another that does not (e.g., MOG). In this regard, the calibration of the SCOR-derived waveforms itself could result not only in different aoSBP and aoPP but also in new bSBP or radial SBP (rSBP) values. On the other hand, although MOG-derived bBP waveforms can be calibrated in three different ways to obtain the aoBP, the device does not give the new bSBP or bDBP values of the recalibrated waveforms, but only the bSBPosc and bDBPosc initially recorded are visible.

Finally, unlike methods using peripheral waveforms obtained from tonometry recordings that quantify aoBP after recalibration (resulting in new pSBP and pPP levels), when CCA waveforms (tonometry- or ultrasound-derived) are considered, the bSBP or bPP directly measured is used to calculate SBPA or PPA.

The variables related to augmented pressure (AP) were identified with a sequence of words (separated by underscores), which allows how they were obtained to be identified (Figure 1): (i)

The parameter to which it refers (i.e., pSBP/aoSBP, pPP/aoPP)

To illustrate this, “pSBP/aoSBP (MOG_GTF_sd)” refers to the SBPA (“pSBP/aoSBP”) recorded with the “MOG” by applying a transfer function (“GTF”) and obtained when calibrating using the systo-diastolic method (“sd”).

Peripheral and central BP (invasive and non-invasive) levels obtained with the different approaches are shown in Supplementary File S1 and Tables S1–S5. After analyzing the characteristics of the group, and peripheral and central BP data obtained with the different methods (Tables 1, 2; Supplementary File S1, Tables S1–S5), we analyzed the correlation (association) and agreement between invasive and non-invasive SBPA and PPA data. Concordance correlation coefficient (CCC) [Supplementary File S1, Table S6 (for SBPA) and Table S7 (for PPA)] and the Bland–Altman analysis were considered (Supplementary File S1, Tables S8–S9). The Bland–Altman analysis enabled us to determine the mean and proportional errors between SBPA (Figures 3–5) and PPA (Figures 6–8) data, obtained with the invasive and non-invasive methods. In all cases, the Bland–Altman test corresponded to the reference method (invasive SBPA or PPA data, x-axis) against “non-invasive and invasive difference” (non-invasive minus invasive data, y-axis). For each Bland–Altman test, linear regression equations were quantified. Systematic error was considered present if the mean error was significantly different from 0 mmHg, and proportional error was considered present if the slope of the linear regression was statistically significant. Considering the mean and proportional errors obtained from the Bland–Altman test, the mean difference between invasive and non-invasive-derived SBPA and PPA was calculated (and graphed) for different SBPA (Figures 4, 5) and PPA (Figures 7, 8) values.

Figure 5 (for SBPA) and Figure 8 (for PPA) show the pooled (aggregated) results (errors derived from the Bland–Altman analysis) when considering (i) the recording/analysis approach, (ii) the calibration method, and (iii) the arterial recording site.

According to the central limit theorem, considering the kurtosis and skewness distribution and the sample size (>25 subjects), a normal distribution was considered (51). Data analyses were performed with MedCalc (MedCalc Inc., Ostend, Belgium) and SPSS (IBM-SPSS Inc., Illinois, USA). A p < 0.05 was considered statistically significant.

The studied subjects were mostly middle-aged (61 ± 19 years) men (59%) with BMI in the overweight range (27.2 ± 4.4 kg/m²). In addition, most patients had a history of hypertension (70%) and dyslipidemia (61%) (Table 1). The above is in agreement with the expectations for the subjects sent to invasive coronary evaluation.

Data about hemodynamic variables are detailed in Table 2 and Supplementary File S1 (Tables S1–S5). The group was characterized by a wide age (range: 14–89 years) and BP range. Invasive aoSBP values were 6.5% < 100 mmHg, 58.1% between 100 and 139 mmHg, 19.4% between 140 and 159 mmHg, and 16.1% ≥ 160 mmHg. In turn, invasive aoDBP values were 19.4% < 60 mmHg, 70.9% between 60 and 84 mmHg, and 9.7% > 85 mmHg.

Figure 2 shows the SBPA and PPA values obtained from invasive (black bars) and non-invasive (gray bars) records. Similar scales were considered. Note the mean variability of the values. As expected, the SBPA and PPA values were generally above 1.0, although there were approaches that resulted in SBPA or PPA values below 1.0 (e.g., CCA_Echo_Exp_osc). In addition, note that for a given approach, the SBPA and PPA values were not the same.

CCC levels obtained for the association between invasive and non-invasive SBPA and PPA varied depending on the technique, site, and calibration scheme considered. In this regard, CCC levels ranged between −0.1 and 0.94 for SBPA and −0.1 and 0.91 for PPA. The highest CCC level for SBPA (or PPA) was achieved when calibrating to invasive bBP (Supplementary File S1, Tables S6–S7). However, even when calibrating to invasive bBP, only pSBP/aoSBP_SCOR_TC_NPROC_inv (CCC = 0.94, r = 0.96) and pPP/aoPP_SCOR_TC_NPROC_inv (CCC = 0.91, r = 0.94) reached satisfactory CCC or Pearson’s coefficient values.

When considering non-invasive bBP levels for calibration, “pSBP/aoSBP_Echo_Exponential_beat1_033HR” (CCC = 0.27, r = 0.41) and “pPP/aoPP_P2_SCOR_RT_GTF_033HR” (CCC = 0.35, r = 0.37) showed the maximum CCC and Pearson’s coefficient values. Then, even the maximum values were very low. In turn, the lowest CCC level (e.g., for SBPA, minimum CCC = −0.1, mean CCC = 0.01, and maximum CCC = 0.24) was obtained when considering the “SD” calibration.

The mean and proportional errors (bias) obtained when comparing invasive and non-invasive SBPA levels are detailed in Figures 3 and 4. In addition, Figure 5 shows pooled results of the mean errors when considering the (i) measuring and/analysis methodology, (ii) calibration method, and (iii) arterial measuring site.

The diverse approaches yielded a wide range of mean errors (−0.16 to 0.03). In general terms (61% = 34/56), the methods yielded negative errors. In 38% (21/56), the mean errors were statistically significant (Figure 3A; Supplementary File S1, Table S8). The pooled analysis of the records showed that overall, irrespective of the (i) recording method (Figure 5A), (ii) calibration method (Figure 5B), and (iii) recording site (Figure 5C), non-invasive measurements underestimated the SBPA levels.

Figures 6 and 7 show the mean and proportional errors obtained when comparing invasive and non-invasive PPA. Figure 8 shows the Bland–Altman derived errors when considering the (i) recording and/analysis methods, (ii) calibration scheme, and (iii) recording site. The different approaches yielded a wide range of mean errors (−0.25 to 0.26). Most of the approaches (73%, 41/56) achieved significant mean errors (Figure 6).

The main results of this work can be summarized in seven points.

First, regardless of the calibration scheme and whether invasive or non-invasive bBP was used to calibrate, the CCC levels and Pearson’s coefficients obtained were extremely low, except for SBPA and PPA obtained from CT, without using a GTF. Then, it could be said that, in general, SBPA and PPA levels obtained with non-invasive approaches are not associated with the recorded invasively. The lack of association did not depend on the recording site, the analysis methodology, not on the calibration scheme, indicating that the limitation to achieving non-invasively SBPA and PPA levels that resemble those measured invasively is not just due to a single factor. This could be considered a “wake-up call” for all those who quantify SBPA or PPA for clinical and/or research purposes.

These low (or even non-existent) levels of strength of association were consistent with that obtained by Nakagomi et al. (25), in 45 patients in whom SBPA was measured invasively (catheterization, elective coronary angiography) and non-invasively (MOG), using two calibration schemes (C1, bSBP/bDBP, and C2, bDBP/bMBP). The authors found that non-invasively measured SBPA was associated with invasively measured SBPA only in C1 calibration (r = 0.33, p = 0.03) (25).

Second, when considering SBPA, the different non-invasive approaches led to (extremely) dissimilar results. On the other hand, in general, irrespective of the (i) recording method, (ii) calibration scheme, and (iii) recording site, non-invasive measurements underestimated SBPA. In addition, the error depended on the SBPA levels considered: the higher the invasive SBPA, the greater the underestimation (Figure 5B).

The existence of proportional error found in our work is consistent with that reported by Bui et al. (52). In this regard, these authors compared SBPA (calculated as “bSBP—aoSBP”) and PPA (calculated as “bPP—aoPP”) levels obtained (i) invasively (catheterization, fluid column pressure transducer) and (ii) non-invasively (brachial cuff-based method), using the “SphygmoCor Xcel” device (model EM4C, Atcor Medical, Sydney, Australia) and the BP Plus device (version 2, Uscom, Sydney, Australia). The waveforms of both non-invasive devices were calibrated with the corresponding cuff bSBP and bDBP measured by each device, respectively, and proprietary methods were automatically applied to estimate the central aoBP waveforms. The authors reported that, for both devices, the Bland–Altman plots revealed that non-invasive SBPA overestimated invasive SBPA at lower SBPA levels and underestimated it at higher SBPA levels. The results were similar for PPA (52).

Similar to us (when analyzing the whole group), these authors reported low agreement between cuff-based and invasive SBPA in all quartiles of invasive SBPA, especially in the lowest and highest quartiles, due to significantly lower individual variability of cuff-based SBPA than of invasive measures. As the authors themselves discussed, we can also state that our finding does not support the previously held assumption that type I central aoBP devices always provide appropriate estimates of SBPA (9). Clearly, work needs to be done to improve SBPA and PPA detection using non-invasive methods. Unfortunately, the authors mentioned that it was not possible to evaluate the results using other calibration methods, as the non-invasive devices they used did not allow them to do so (52).

Third, none of the different calibration schemes that considered non-invasive bBP to estimate SBPA were clearly better (ensuring lower mean error) than the others. However, in terms of overall “mean error,” the best approach seemed to be to calibrate with bMBP₀₃₃.

Fourth, regardless of the calibration scheme, the pooled results showed that SBPA obtained from RA waveform analysis (applanation tonometry) minimized the mean errors (Figure 5A). In addition, SBPA levels derived from RA recordings showed the greatest homogeneity of bias when considering differences in the invasively recorded SBPA. In addition, there were no major differences in the results when applying different approaches to analyze RA waveforms (e.g., NPMA, GTF, P2) (Figure 5A). In contrast, SBPA data obtained from CCA waveforms showed the highest error (Figure 5A). Accordingly, a hierarchical order could be proposed to minimize the error in determining the SBPA: RA > BA > CCA. It is worth noting that in a recent work, we found that the lowest and highest mean errors in aoSBP estimation (non-invasive vs. invasive recordings) were achieved, respectively, from CCA and RA records (20). Thus, the best approaches to determine aoSBP and SBPA would differ.

This result shows that non-invasive estimation of SBPA (and PPA) is device- and technique-dependent and the results obtained with one technique do not apply to other devices. This is consistent with reports by other authors (52).

Fifth, when considering PPA levels, most approaches (73%, 41/56) achieved statistically significant mean errors (Figure 6). Compared to the observed for SBPA, the mean error levels when considering PPA were more homogeneously distributed, with approaches over- and underestimating invasive PPA. The higher the invasive PPA, the higher the underestimation obtained with the non-invasive approaches, and the opposite as well (existence of proportional error) (Figure 8B; Supplementary File S1, Table S9).

Sixth, in contrast to what was found for SBPA, when considering PPA regardless of the recording and/or analysis method, the pooled results showed that the calibration schemes “osc,” “033HR,” and “0412” ensured the lowest mean errors (Figure 8B), while the highest mean error level was obtained when calibrating with “033” (Figure 8B). Then, and surprisingly, the best calibration scheme when quantifying PPA could not be necessarily the best when quantifying SBPA.

Seventh, in contrast to what was reported for SBPA, regardless of the calibration scheme, the PPA levels obtained from CCA ultrasound recordings and BA waveform analysis (BT, GTF; MOG, and GTF) minimized the mean errors (Figure 8A). When quantifying PPA, data from RA waveforms resulted in PPA levels higher than those recorded invasively (positive mean error) (Figure 8A). The opposite was observed when considering CT:GTF and CT:NPROC recordings.

Altogether the findings above suggest that SBPA and PPA indices cannot be considered “synonymous.”

A significant part of our research work (and effort) has focused on identifying to what extent different non-invasive approaches that “in theory” enable us to assess the central (e.g., aortic) and/or peripheral (e.g., brachial) hemodynamics allow us to quantify intra-arterial BP levels. Recently, we focused on evaluating the level of agreement between aoSBP and aoPP recorded invasively and data obtained with more than 50 non-invasive approaches (20). To this end, simultaneous aoBP data were invasive and non-invasively obtained. However, at least in theory, an approach that allows an accurate non-invasive estimation of aoSBP or aoPP would not necessarily allow an adequate quantification of central-to-peripheral BP amplification (SBPA and PPA). In fact, in the “ARTERY Society task force consensus” (9), related to standardization of aoBP non-invasive records, measurement approaches (mainly devices) have been classified into two categories: (1) devices or systems that allow an adequate quantification of the (proportional) difference between aoBP and bBP (type I devices): in other words, such approaches allow an accurate assessment of the “degree of SBPA” enabling the monitoring of the effects of antihypertensive drugs whose responses may differ between bBP and aoBP (e.g., clinically relevant for hypertension management decisions); and (2) devices or systems that allow the derivation of accurate non-invasive aoSBP data (type II devices) (9): such approaches (type II devices) generally give aoSBP levels higher than bSBP (“reverse amplification”), which is likely to be non-physiological under normal (healthy) conditions and could be explained by the combination of underestimated bSBP (by the BA cuff), together with (in theory) the more accurate aoSBP estimation (9). Consequently, the more accurate non-invasive approach to quantify aoSBP or aoPP may be different from the more accurate method to quantify SBPA or PPA.

In this context, this study complements and deepens previous findings, focusing on the analysis of SBPA and PPA. To fulfill the aims of this work, it was necessary to measure not only invasive aoBP but also bBP (catheterization), as a way of knowing real central-to-peripheral BP amplification and being able to compare it with data obtained with several non-invasive approaches.

The results of this study add support to the hypothesis that the best approach (e.g., arterial recording site) for quantifying aoSBP (or aoPP) may not be the same for quantifying SBPA or PPA. For example, the findings show that regardless of the calibration scheme considered, the best approaches for determining aoSBP (or aoPP) were those based on CCA data (ultrasound or tonometry), followed by BA recordings since they resulted in aoSBP (or aoPP) values close to those recorded invasively (20). This was not the same for non-invasive SBPA and PPA quantification, since as stated above, regardless of the calibration scheme, the best approaches (ensuring lower mean errors) were those based on RA recordings and the least reliable were those based on CCA recordings. The above highlights the need for methodological accuracy and consensus to assess non-invasively SBPA (or PPA) and aoSBP (or aoPP). In addition, further research and development in this field is required.

The work was not conducted in healthy subjects, which is common to most of this kind of studies taking into account the indications (and contraindications) of invasive studies. However, the subjects evaluated are representative of those for whom it is important to know these hemodynamic variables for decision-making in clinical practice.

The sample size could be considered “borderline” (moderate), but it should be noted that it was adequate to detect statistical differences and, consequently, achieved satisfactory statistical power. In this context, it should be noted that most of the studies similar to this one considered sample sizes smaller, equal, or slightly larger than those included in this work (19, 53). The invasive recordings in the BA, opposite to that of the limb used for the vascular access, and the second invasive recording at the aortic root were part of the research protocol and not of the catheterization for diagnostic purposes. The same consideration applies to all non-invasive BP recordings. Those measurements increased the duration of invasive evaluations by at least 30 min, which limited the number of volunteers consenting to participate in the study. In this context, the number of subjects included represents an important sample size for a study that aims to demonstrate the relevance of several issues, but not necessarily to be conclusive on this important topic, which necessarily requires further evaluations.

The differences between invasive and non-invasive SBPA or PPA levels could vary in association with factors like age, sex, HR, and vascular reactivity (54, 55). In fact, our results (Bland–Altman test) showed that there is a “proportional error” between invasively and non-invasively obtained central-to-peripheral amplification values. This indicates that the differences between invasive and non-invasive values depend on the existing levels of BP amplification in each person, which in turn depend on different variables (e.g., HR) (56–58). However, our sample was not enough large and/or heterogeneous enough to allow defining subgroups (e.g., considering the age, sex, and/or exposure of the subjects to risk factors) and to be able to apply statistical tests with sufficient power. Future, multicentre studies, allowing for the inclusion of a large number of subjects will be necessary to assess the impact of covariates or confounding factors on the results.

Fluid column BP transducers, rather than solid-state pressure sensors, were used. Clearly, solid-state sensors are characterized by a major accuracy in obtaining BP waveform, mainly because they can detect high-frequency components. However, fluid column transducers are widely used in clinical practice to obtain BP levels and are used in our University Hospital. It should be noted that the ARTERY Society Task Force Consensus Statement on protocol standardization stated that although micromanometer-tipped catheters are the preferred instruments, meticulously managed fluid column catheters may also be acceptable to accurately measure intra-arterial BP (8). In addition, in a systematic review and meta-analysis, it was reported that mean errors in the non-invasive estimation of aoSBP were similar when comparing fluid-filled and catheter-tipped transducers (19).

Finally, one issue to mention is that the invasive recordings in the ascending aorta and BA were not obtained simultaneously, but sequentially. However, the stability in HR and diastolic BP, and the subsequent similarity between the initial and final invasive aortic recordings, performed before and after invasive BA measurements, respectively, allowed to confirm hemodynamic stability.