Impact of arterial location, pressure wave indicators, and measurement devices on arterial form factor and mean and central arterial pressure

Mean arterial pressure (MAP) is often estimated from cuff systolic (S) and diastolic (D) blood pressure (BP) using a fixed arterial form factor (FF, usually 0.33). If MAP is measured directly, a true FF can be calculated: FF = [MAP–DBP]/[SBP–DBP]. Because waveform shapes vary, true FF should also vary and MAP accuracy will be affected. We studied factors affecting FF using radial tonography (SphygmoCor, n = 376) or brachial oscillometry (Mobil-O-Graph, n = 157) and to compare devices, 101 pairs were matched precisely for SBP and DBP. SphygmoCor brachioradial FF correlated strongly with central FF (r2 = 0.75), central augmentation index (cAI, r2 = 0.39), and inversely with pulse pressure amplification (PPA) ratio (r2 = 0.44) [all p < 0.000]; brachioradial FF was lower than central (c) FF (0.34 vs. 0.44, 95% CI’s [0.23,0.46] and [0.34,0.54], p < 0.000). On forward stepwise regression, brachioradial FF correlated with PPA ratio, age, heart rate, and cAI (multiple-r2 0.63, p < 0.000). With Mobil-O-Graph: brachial FF was fixed, lower than the corresponding cFF [mean(SD)] 0.46(0.00098) vs. 0.57(0.048), p < 0.000], and uncorrelated with clinical characteristics; MAP and cSBP were higher than SphygmoCor by 6.3 and 2.2 mmHg (p < 0.005) at the midpoint with systematic negative biases. We conclude that FF derived from radial tonometry (SphygmoCor) varies with pulse wave morphology within and between individuals and by measurement site, age, and heart rate. With oscillometry (Mobil-O-Graph), brachial FF was fixed and high and unrelated to other clinical variables; MAP and cSBP were higher than tonometry, with systematic negative biases.


INTRODUCTION
The estimation of mean arterial pressure (MAP) from cuff systolic (S) and diastolic (D) blood pressure (BP) usually involves the use of a constant form factor (FF, usually 0.33): MAP ≈ DBP + [0.33] [SBP -DBP] mmHg.In wave mechanics, however, FF is a pulsatile shape descriptor, so any variation in arterial waveform morphology should also affect FF (see Fig. 1, left panels).Arterial pressure waveforms vary with arterial size and structure and are influenced by local and systemic phenomena including augmentation index [AI], pulse pressure amplification [PPA], physiologic hemodynamic changes (e.g., vasoconstriction), and heart rate [1][2][3].It therefore follows that FF cannot be a universal constant and must vary within and between individuals.Any FF inaccuracy will directly influence MAP estimates and BP derivatives that are MAPdependent, including some central (c) SBP estimates [4].
A "true" FF can be easily calculated if BP and MAP are measured accurately and directly according to the formula FF = [MAP-DBP]/ [SBP-DBP].Accurate MAP measurement requires pulse wave analysis (PWA) with integration of a high-fidelity arterial pressure waveform, typically from an invasive catheter or applanation tonometry (e.g., SphygmoCor).More recent developments have suggested that PWA is also possible with oscillometry but validation studies have been limited by the proprietary shield oscillometric technology has been granted [5][6][7].Device or method-related differences may also influence the accuracy of estimates of MAP and related BP derivatives.
The present observational investigation was undertaken: (1) to identify and quantitate the within and between-subjects impact on FF of factors known to influence pulse wave morphology, including AI, PPA, heart rate, age, and demographic characteristics; and (2) to compare FF and derivative data between tonometric and oscillometric PWA methods.

General approach to the problem
We analyzed our existing PWA convenience cohorts obtained by radial tonometry (SphygmoCor, AtCor Medical) or oscillometry (Mobil-O-Graph, IEM).SphygmoCor uses applanation tonometry to generate a radial arterial waveform that is scaled to brachial cuff BP.Because of this admixture of forearm sites, we have used the term "brachioradial" to refer to data acquired in the arm with this technique.The SphygmoCor calculates MAP by integrating the radial arterial waveform.It is also capable of approximating a central (aortic) waveform and central BP through the use of a generalized transfer function [8]."Mobil-O-Graph uses oscillometry to yield brachial SBP and DBP; central (aortic) SBP and DBP are reportedly derived from PWA obtained during a 10 s pressure-hold at DBP. Subsequent application of a proprietary generalized transfer function allows estimation of central systolic BP, as described (in principle only) by the developer of the "ArcSolver" algorithm [9]; MAP is also reported but the methodology is not described.Mobil-O-Graph does not directly measure or report central or peripheral FF but these variables are easily derived from MAP and respective BP values at each site as already described.We have assumed that MAP is constant across major arterial sites (even though a gradient of 1-2 mmHg may be present; this deviation is systematic and minimal and does not affect our findings or interpretations in a meaningful way) [ Mobil-O-Graph generates a brachial waveform by holding cuff pressure constant at a value just above DBP.Both devices report MAP but neither reports FF (which is easily calculated from SBP, DBP, and MAP as already described).Within large arteries, MAP and DBP vary minimally [1] but SBP increases to a variable degree at distal sites due to varying degrees of apparent pulse pressure amplification (PPA, sometimes >40 mmHg in our experience).The location of the peripheral measurement site matters and there is additional PPA between the brachial and radial arteries (usually about 5-6 mmHg) [10,11].However, the usual difference in FF between the brachial and radial arteries is relatively small; in Fig. 1, the corresponding FF values are: brachial 0.33 and radial 0.32.
Initial attention was focused on identifying factors potentially correlated with brachioradial FF: aorta-to-brachioradial PPA ratio (PPA ratio = [ brachial pulse pressure/central pulse pressure]), central augmentation index (cAI = 100*[central SBP2/central SBP1]), heart rate, age, weight, race, and gender.We next created a stepwise multiple linear regression models for brachioradial and central FF.The second part of the investigation was to compare FF and other PWA-derived values from radial tonometry to those obtained by oscillometry, repeating steps used to assess tonometric FF.We were not able to compare devices by the standard method of simultaneous use of both devices in every individual but we were able to define sub-cohorts matched for SBP and DBP in which we could perform a novel matched-pairs Bland-Altman type analysis for MAP and central SBP.

Study subjects
We included all volunteers and patients who had PWA studies with either tonometry or oscillometry.The first cohort included volunteers who signed informed consent for a cross-sectional vascular function survey monitored by the Health Sciences IRB of the University at Buffalo; also included were hypertensive patients in a small clinical trial (NCT 05170061, n = 27).The second cohort included self-referred or physician-referred individuals who underwent 24 h ambulatory BP monitoring with a Mobil-O-Graph, which also performed oscillometric PWA studies.There was no selection for BP status but patients with heart failure or advanced renal disease were excluded from this analysis.Both cohorts included normotensives and hypertensives, either untreated or treated; in both cohorts, guidelinebased antihypertensive drugs included thiazide diuretics, renin-angiotensin blockers, and amlodipine (90% of treated subjects), with beta-blocker or spironolactone used sparingly (~5% each).

Statistical analysis
All analyses were performed on Microsoft Excel spreadsheets using IBM SPSS (Ver 24 and 27).To determine relationships between FF and other variables, we used standard Pearson linear regressions.Confidence intervals (95%) for each FF were also calculated.For comparison of MAP and central SBP values between devices, we identified pairs of subjects from each cohort by case-controlled matching using a fuzzy tolerance factor of 1.5 mmHg for both SBP and DBP.We constructed a Bland-Altman analysis against the mean of SphygmoCor and Mobil-O-Graph paired values.A secondary analysis of inter-device bias was performed with Pearson regressions; MAP and central SBP between devices were compared using paired t-tests.
Table 1 describes the clinical characteristics of patients studied with each technique.A large subset of the tonometry cohort was previously demonstrated to closely mimic the age-BP relationship observed in the general U.S. population [12].
Figure 1 (left panels) demonstrate a representative radial tonogram and the corresponding central waveform derived from a generalized transfer function [8].The respective central and brachioradial FF values [mean(SD)] for SphygmoCor were 0.44(0.048)and 0.34(0.056),p < 000.Right panels show scatterplots and regression equations for brachioradial FF against central augmentation index (cAI) and PPA ratio.The strong correlations demonstrate how closely factors affecting waveform shape are related to FF.  values, and about 34% higher than SphygmoCor brachioradial values (p < 0.000).
Table 2 describes the multiple linear regression analysis performed on the SphygmoCor cohort for central and brachioradial FF as dependent variables.PPA ratio explained 46% of the population variation in SphygmoCor brachioradial FF, while HR added another 13%; age and cAI together added an another 4% (total of 63%).For SphygmoCor central FF, HR explained 21% of central FF variation, age added another 10%, and pulse pressure explained another 2% (total 33%).HR was the most consistent influence on FF at both locations; each change in HR of 10 BPM was associated with a change in brachioradial or central FF of about 0.02 units.Height was significantly (p < 0.001) but very weakly correlated with FF, PPA and PPA ratio (R 2 = 0.049, 0.037, and 0.060, respectively) but this association did not affect the multiple regression models.Multiple regression analysis was not performed for Mobil-O-Graph because of the fixed bFF.
Table 3 demonstrates the clinical characteristics of the pairs selected for device comparison for MAP and central SBP between SphygmoCor and Mobil-O-Graph.Number of pairs (n = 101) and inter-device BP differences (mean SBP or DBP difference < 0.1 mmHg) were achieved with a fuzzy tolerance factor of 1.5 mmHg.Among the available characteristics, the cohorts differed only by age.
Figure 3 demonstrates the differences between MAP and central SBP between devices.Upper panel bar graphs represent means and SDs for SBP, DBP, MAP and central (c) SBP for each device.Middle panel shows the matched-pairs Bland-Altman analysis for MAP: solid horizontal line represents the mean interdevice difference and dotted horizontal lines represent 95% CI of the inter-device difference.Mobil-O-Graph MAP was 6.3 mmHg higher than SphygmoCor MAP but this calculation applied only to the mean MAP values because of the presence of a systematic decreasing bias at higher values; at MAP = 80 mmHg, Mobil-O-Graph MAP was about 8 mmHg higher than SphygmoCor but at MAP = 120 mmHg, Mobil-O-Lower panel shows the matched-pairs Bland-Altman analysis for central SBP; format is the same as middle panel.Mobil-O-Graph central SBP was 2.2 mmHg higher than SphygmoCor at the mean but as with MAP, the inter-device difference (MOB-SPG) decreased at higher values.In this case, below MAP = 120, Mobil-O-Graph central SBP exceeded SphygmoCor but above MAP = 120, SphygmoCor values were higher than Mobil-O-Graph.We estimated that the age difference between cohorts could account for no more than <2% of the inter-device differences we observed for MAP and central SBP.
Finally, we found SphygmoCor brachioradial FF to be correlated with central cSBP (cSBP = 203[brachioradial FF] + 56 [mmHg], r 2 = 0.17, p < 0.000) but this relationship was not sufficiently robust to suggest use of FF as a reliable surrogate for central SBP.

DISCUSSION
Present findings include several inter-related observations about arterial FFs and the influence of different measurement techniques.Our results are entirely consistent with the concept that a measured FF is a reliable arterial waveform shape indicator but most importantly, they also demonstrate that there is no universal FF.FF is lower in the aorta or carotid artery than the brachial or radial artery and the values reported here are in agreement with prior work [13].What we have emphasized is the general principle that FF decreases with distance from the heart, decreasing arterial caliber, and increased PPA.There is substantial between-individual variation in radial FF in the general population, with the dispersion related to individual characteristics including age and heart rate as well as pulse wave morphology.Our data also demonstrate that use of a "standard" fixed FF derived from a distal artery to estimate MAP will tend to yield artifactually low values.For example, if brachial BP is 140/80 mmHg and FF is =0.46 (Mobil-O-Graph), estimated MAP is 108 mmHg; in contrast, if brachial FF is 0.34 (SphygmoCor), estimated MAP is 100 mmHg.Further concern is added by our finding of widely divergent FF results between brachioradial tonometry (SphygmoCor) and brachial oscillometry (Mobil-O-Graph).These inaccuracies are further propagated when MAP is used in other calculations, including systemic vascular resistance (from MAP and cardiac output) and central BP (by generalized transfer function, especially if the scaling factor is (MAP -DBP) rather than (SBP -DBP).Artifactually low central SBP will also contribute to an overestimation of PPA.We did find a weak relationship between central SBP and radial FF but the association was not sufficiently robust to use a peripheral FF to approximate central SBP.We identified 3 major findings with conventional radial tonometry (SphygmoCor).Our data confirm that true measured FF values are influenced by familiar pulse wave morphology indicators: SphygmoCor brachioradial FF correlated strongly negatively with PPA ratio and positively with central AI.Second, FF is systematically higher in the aorta than in the forearm (0.44 ± 0.048 vs. 0.34 ± 0.056, p < 0.000), although central and brachioradial FF were strongly correlated (r 2 = 0.75, p « 0.000).Third, there was substantial between-individual variation in both brachioradial FF (95% CI: 0.23, 0.46) and central FF (95% CI: 0.34, 0.54).A stepwise multiple linear regression model revealed identifiable predictors of brachioradial FF: PPA ratio, heart rate, age, and central AI.Gender, height and race were noncontributory but it has been previously reported that FF is affected by age and gender [13].
Because PP increases with distance from the heart, FF must decrease as long as MAP remains constant.In our study, SphygmoCor central FF was 0.44 and brachioradial FF was 0.34 (p < 0.000).A related observation is that the central-to-peripheral FF ratio is very closely related to the corresponding central-toperipheral PP ratio: FF ratio = cFF/bFF = 0.90 [bPP/cPP] + 0.062, r 2 = 0.92, p < 0.000.A prior study by the developer of SphygmoCor found carotid FF to be 0.39 when brachioradial FF was 0.34 [14].This discrepancy was dismissed as a technical artifact of suboptimal carotid applanation tonometry but this explanation is unlikely because measurement error tends to increase dispersion rather than shift the mean.Two other SphygmoCor studies reported a mean carotid FF = 0.41 [15].All of these studies demonstrate that FF decreases with distance from the heart; carotid FF is intermediate between aortic and brachioradial FF, as would be expected [13][14][15].
Inter-individual FF variability has not been systematically investigated in prior studies but measured mean FF in other convenience cohorts also demonstrates a notable standard deviation [1,13,15].We identified some of the demographic and physical characteristics that contribute to FF variation in our stepwise multiple linear regression model.Brachioradial FF varied with age (r = 0.37, p < 0.000), heart rate (r = 0.25, p < 0.001), PPA ratio (r = −0.66,p < 0.000), and cAI (r = 0.62, p < 0.000); in the full model, these characteristics explained 63% of the population variation in FF.PPA and cAI were also closely related to age and HR, as found in other studies [16,17].Thus, If MAP, SBP and DBP are determined accurately, a low measured FF suggests a relatively high systolic peak (and a high PPA).
There were four major findings with oscillometric brachial PWA (Mobil-O-Graph).First, central and brachial FF values were much higher than SphygmoCor (0.57 ± 0.048 and 0.46 ± 0.00, respectively, p < 0.000 each).Second, Mobil-O-Graph brachial FF was fixed (i.e., it did not display inter-individual variation beyond a rounding error).Third, Mobil-O-Graph MAP was much higher than SphygmoCor MAP: 6.3 mmHg higher at the midpoint, with a negative systematic bias; below the midpoint, Mobil-O-Graph values were higher than SphygmoCor but the reverse was true above the midpoint.Fourth, Mobil-O-Graph central SBP was 2.2 mmHg higher than SphygmoCor at the midpoint, also with a negative systematic bias.
Overall, the assumptions underlying Mobil-O-Graph oscillometric PWA methodology remain unclear.In contrast, Fig. 2 Central and forearm form factors with different devices.Upper and lower scatterplots demonstrate marked differences in FF relationships at two different arterial sites for SphygmoCor and Mobil-O-Graph.With both devices, central FF was higher than forearm arterial FF.With SphygmoCor (upper panel), central and peripheral FF values were highly correlated (p < 0.000) and normally distributed (95% CI values included on scatterplots).With Mobil-O-Graph, brachial FF was fixed (0.46) and about 34% higher than SphygmoCor brachioradial FF (0.34, p < 0.000); Mobil-O-Graph central FF was about 26% higher than SphygmoCor.SphygmoCor MAP is determined by the preferred method of integrating the pulse area of high-fidelity waveform and an individual MAP is reported for each BP reading.When we calculated Mobil-O-Graph central and brachial FF, the central FF variation was similar to SphygmoCor, yet the Mobil-O-Graph brachial FF was simply a fixed value (0.46), probably derived empirically.Mobil-O-Graph methodology is proprietary; its developer has stated that MAP is "measured" [18] but present data argue strongly that Mobil-O-Graph MAP is not measured but rather derived empirically.We have previously demonstrated that the Mobil-O-Graph/ArcSolver methodology treats pulse wave velocity similarly and uses an empiric equation related to age (about 90%) and mean 24 h systolic BP (about 10%) [19].Additional speculation is also possible regarding Mobil-O-Graph methodology.Oscillometric BP detection theory was originally based on assumption that MAP is the pressure at which maximum pulse volume amplitude (and arterial wall motion) occurs.An "oscillometric envelope" is then observed if an external pressure gradient is applied to that peripheral artery; SBP and DBP are then determined from empirical studies as fixed fractions of the maximal cuff volume oscillation above and below MAP [20][21][22].The reliability of this methods is markedly compromised by various factors, especially arterial stiffness [22], so alternate approaches have been developed, especially the assertion that SBP and DBP occur at the points of maximal rate of increase and decrease in pulse volume that are seen at the edges of the oscillometric envelope.This approach seems to have been incorporated into the Mobil-O-Graph [22] because MAP is solely determined by the accompanying SBP and DBP values.At the same time, Mobil-O-Graph SBP and DBP have been validated against other methods with reasonable agreement [23].
The inter-device bias in MAP is complex and includes a standard bias plus a systematic negative bias.At MAP = 80 mmHg, Mobil-O-Graph MAP is predicted to be about 8 mmHg higher than SphygmoCor but at MAP = 120 mmHg, the bias would only be about 4 mmHg.We have previously identified that at a brachial BP of 140/80 mmHg, a FF of 0.42 yields a MAP value that is 6.3 mmHg higher than one derived from a FF of 0.33 [24].Other studies have shown that FF and PPA interact in determining MAP accuracy; when PPA is high, MAP is more accurately determined using FF = 0.33 and when PPA is low, MAP is more accurately determined using FF = 0.40 [1].With another proprietary oscillometric device, brachial FF was reported as 0.24 and the authors deemed the accompanying MAP estimates "too imprecise to be used for calibration."[25] It has been found that heart rate can affect MAP [26] but our cohorts did not differ in HR.
The developer of Mobil-O-Graph reported little difference between SphygmoCor and Mobil-O-Graph with respect to central SBP and AI values [6] and we found that central SBP values for the two devices were fairly highly correlated (r 2 = 0.88, p < 0.000).Overall, transfer-function-dependent methods tend to underestimate cSBP and overestimate aorta-to-radial PPA [27].However, on Bland-Altman type analysis of the matched pairs, we found that SphygmoCor central SBP was 2.2 mmHg lower than Mobil-O-Graph at the midpoint.This difference is consistent with prior studies given the systematic negative bias we found in the matched-pairs Bland-Altman type analysis.At a mean cSBP = 120 mmHg, our analysis predicts that there will be no appreciable difference between devices but for cSBP < 120 mmHg, Mobil-O-Graph values exceed SphygmoCor and for cSBP > 120 mmHg, SphygmoCor values exceed Mobil-O-Graph.Finally, we found that SphygmoCor brachioradial FF is correlated with central SBP according to the formula cSBP = 203 FF + 56 (mmHg).This relationship is highly significant (r 2 = 0.17, p < 000) but is not sufficiently precise to allow accurate approximation of central SBP from brachioradial BP and FF.
There are several limitations to this study but none is sufficient to negate the principal findings.The convenience samples we used are reasonably representative of the general adult population and include a wide range of age and BP.The small arterial pressure gradient between the aorta and radial artery (about 1.7 mmHg) [1] does not affect our conclusions.We identified a short list of factors that influence FF but our multiple regression FF model is constrained by the scope of the available clinical data and might differ if more variables were added to the model.We did not have full information on drug therapy in all hypertensive subjects but this is not likely to cause substantial bias because all drug classes other than beta-blockers tend to be quite neutral on pulse wave morphology and central AI [28]; in our cohorts, there was very limited use of beta blockers (<5%).It is not routine to use a Bland-Altman type of analysis in pairs of subjects matched for a different common characteristic (brachial BP) but our matching was extremely precise for SBP and DBP, the sample sizes and range values were more than adequate, and the cohort clinical characteristics were very similar.The only potentially meaningful difference was age, with the Mobil-O-Graph cohort 15 years older than the SphygmoCor cohort.However, based on our multiple regression modeling, this age difference would be predicted to account for little more than about 1% of the difference in bFF observed between the two cohorts.The MAP and cSBP biases we observed with Mobil-O-Graph are generally consistent with other studies, but the systematic negative biases we found have not been previously described.In summary, the present work was undertaken to provide a new perspective on arterial FF, a pulse shape indicator that is influenced by arterial location, pathophysiology, and methodology.Application of inaccurate FF values can result is substantial errors in estimation of MAP and MAP-dependent variables.Our data are pertinent to those interested in hemodynamics and PWA.3).Middle panel: matched pairs Bland-Altman-type analysis of MAP.Although MOB-MAP was 6.3 mmHg higher than SPG-MAP at the midpoint, the inter-device difference decreased at higher MAP values (negative systematic bias, regression equation on scatterplot).Lower panel: matched pairs Bland-Altman-type analysis of central (c) SBP.MOB-cSBP was higher than SPG-cSBP at the midpoint (2.2 mmHg).Due to negative systematic bias, for MAP values below 120 mmHg, MOB values were higher than SPG but for MAP values above 120 mmHg, SPG values were higher than MOB.

Figure 2
demonstrates the relationship between forearm and central FF values for SphygmoCor (upper panel) and Mobil-O-Graph (lower panel).With SphygmoCor, central and peripheral FF were closely correlated (r 2 = 0.75, p < 0.000) but this relationship was not present with Mobil-O-Graph.With SphygmoCor, there was a normal distribution of both central and brachioradial FF values but 95% confidence intervals were fairly wide ([0.23,0.46]and [0.34,0.54],respectively).With Mobil-O-Graph, brachial FF values were lower than central values, fixed (95% CI 0.457, 0.459), not correlated with corresponding Mobil-O-Graph central FF

Fig. 1
Fig. 1 Form factors and pulse wave shape: influence of arterial site, amplification, and augmentation (SphygmoCor).Left panels (dark background) taken from a random SphygmoCor study showing typical morphological differences between peripheral and central waveforms.The radial tonogram (left panel) was scaled to brachial SBP and DBP and subjected to a generalized transfer function to yield a central (aortic) pressure waveform (second panel).Morphological differences in arterial contour between arterial locations are typical as are the corresponding FF values.In this individual, PPA is 12 mmHg, PPA ratio is 1.17, and central augmentation index (AI) is 121%.Right panels are scatterplots showing close correlations between brachioradial FF and both PPA ratio and central AI (p < 0.000 each).

Fig. 3
Fig. 3 Matched pairs analysis of MAP and central SBP with SphygmoCor (SPG) and Mobil-O-Graph (MOB).Upper panel: means (bars) and SDs (verticals) for SBP, DBP, MAP and central (c) SBP by device (see Table3).Middle panel: matched pairs Bland-Altman-type analysis of MAP.Although MOB-MAP was 6.3 mmHg higher than SPG-MAP at the midpoint, the inter-device difference decreased at higher MAP values (negative systematic bias, regression equation on scatterplot).Lower panel: matched pairs Bland-Altman-type analysis of central (c) SBP.MOB-cSBP was higher than SPG-cSBP at the midpoint (2.2 mmHg).Due to negative systematic bias, for MAP values below 120 mmHg, MOB values were higher than SPG but for MAP values above 120 mmHg, SPG values were higher than MOB.

Table 1 .
Clinical characteristics of the full study cohorts.
P values are SphygmoCor compared to Mobil-O-Graph; t-tests for means; chi-squared for race and gender.Brachioradial refers to SphygmoCor technique.BMI body mass index, SBP systolic blood pressure, MAP mean arterial pressure, DBP diastolic blood pressure, PP pulse pressure, FF form factor.

Table 3 .
Clinical characteristics of the device comparison matched pairs.Abbreviations and footnotes as in Table1.Pairs matched for SBP and DBP with a fuzzy tolerance of 1.5 mmHg (see Fig.3); number with available data is reflected for each group (N).Comparison by paired t-test.