## Abstract

The method used for pulse transit time (PTT) estimation critically affects the accuracy and precision of regional pulse wave velocity (PWV) measurements. Several methods of PTT estimation exist, often yielding substantially different PWV values. Since there is no analytic way to determine PTT in vivo, these methods cannot be validated except by using in silico or in vitro models of known PWV and PTT values. We aimed to validate and compare the most commonly used “foot-to-foot” algorithms, namely, the “ diastole-minimum,” “tangential,” “maximum first derivative,” and “maximum second derivative” methods. Also, we propose a new “diastole-patching” method aiming to increase the accuracy and precision in PWV measurements. We simulated 2,000 cases under different hemodynamic conditions using an accurate, validated, distributed, one-dimensional arterial model. The new algorithm detects and “matches” a specific region of the pressure wave foot between the proximal and distal waveforms instead of determining characteristic points. The diastole-minimum and diastole-patching methods showed excellent agreement compared with “real” PWV values of the model, as indicated by high values of the intraclass correlation coefficient (>0.86). The diastole-patching method resulted in low bias (absolute mean difference: 0.26 m/s). In contrast, PWV estimated by the maximum first derivative, maximum second derivative, and tangentia methods presented low to moderate agreement and poor accuracy (intraclass correlation coefficient: <0.79 and bias: >0.9 m/s). The diastole-patching method yielded PWV measurements with the highest agreement, accuracy, and precision and lowest variability.

- pulse wave velocity
- aortic stiffness
- wave reflection
- arterial pulse
- arterial model

the arterial pulse is the most broadly and frequently examined vital sign in clinical practice and research. Beyond maximum (systolic) and minimum (diastolic) blood pressure values, other pressure wave characteristics, which are directly related with arterial properties, yield valuable pathophysiological information. Pressure wave speed is one of the most important and clinically relevant properties of the arterial pulse because it is related to arterial stiffness and compliance.

The relationship between arterial stiffness and pulse wave velocity (PWV) was first described by Thomas Young in his Croonian lecture published in 1808 (38). However, in 1922, J. C. Bramwell and Nobel Laureate A. V. Hill set the basis for the measurement of transmission velocity of pulse waves in arteries (4) and established its analytic relation with arterial wall elasticity (5). Today, estimation of PWV is considered as the “gold standard” method for the assessment of arterial stiffness. A huge body of clinical evidence, gathered by use of simple, noninvasive, semiautomated technologies and methods (20), indicates that arterial stiffness (as assessed by PWV) is a strong, independent predictor of cardiovascular morbidity and mortality in several populations (19, 23, 25).

Regional (i.e., aortic) PWV is generally estimated by measuring the time that is required for the pulse wave to travel a given distance along the arterial tree. Most commonly, PWV is measured by recording pressure (or distension) waves at two arterial sites of known distance and estimating the time delay between the two recorded pulses. Thus, imprecise in vivo estimation of pulse transit time (PTT) and distance measurement may introduce considerable errors in PWV measurement. Several methods based on pressure wave analysis have been proposed for PTT estimation, mainly focusing on the determination of “characteristic points” located at the “foot” of the wave, namely, the end-diastolic or early systolic parts of the pressure wave, which are less affected by wave reflections (8, 35). However, substantial differences in PWV values estimated by different “foot-to-foot” methods have been previously reported (8, 22), even when PWV estimates are obtained from Federal Drug Administration-approved commercial apparatuses. Furthermore, it has been observed that a great variability exists among repeated PWV measurements on the same subject with a single device (26).

It is not yet possible to analytically and accurately determine PTT in vivo. For this reason, in vivo validation of different algorithms for PTT estimation and, consequently, PWV measurement is not currently feasible since the true PTT value is not known. In existing literature, only comparisons between different algorithms have been made in vivo, often limited to assessing the reproducibility/variability of multiple repeated estimates of PTT. Validation of different algorithms for the determination of PTT between two recording sites can be, however, performed experimentally or numerically using either in vitro or in silico arterial models of known elastic properties, where the true PWV can be derived analytically.

The aim of this study was to validate various existing algorithms of PTT estimation using an accurate, validated, distributed, one-dimensional (1-D) arterial model of the human circulation. The ultimate purpose was to quantify the accuracy and precision of different algorithms already used or/and incorporated in commercial devices for PWV measurement under a wide range of different simulated hemodynamic and vascular conditions that provide analytically known values of PWV and hence PTT. Finally, we proposed and tested a new algorithm for PTT estimation aiming to increase accuracy and precision in PWV estimation.

## METHODS

A great variety of pressure wave patterns were simulated for a wide range of different hemodynamic and cardiovascular conditions. For this purpose, we used a validated, 1-D mathematical distributed arterial model, which has been previously well described (24, 28, 29).

The governing equations of the model are obtained through integration of the longitudinal momentum and continuity Navier-Stokes equations over the arterial cross section. Pressure and flow waves throughout the arterial tree were obtained by solving the governing equations of the model with proper boundary conditions using an implicit finite-difference scheme. The arterial behavior was considered to be nonlinear and viscoelastic, according to the methodology of Holenstein et al. (15) and the data of Bergel (3). The arterial segments of the model were considered as long tapered tubes, and their compliance was defined by a nonlinear function of pressure as described by Langewouters (18). Left ventricular function was simulated by the varying elastance model proposed by Sagawa (30). Distal vessels were terminated with three-element Windkessel models. Intimal shear was modeled based on Witzig-Womersley theory. For further details on the 1-D model, the reader is referred to the original publications (28, 29).

The model is able to predict pressure and flow waves in good quantitative and qualitative agreement with in vivo measurements (28, 29), particularly with respect to shape and wave details, which are critical factors for the accuracy of foot-to-foot detection methods of PTT estimation. Different hemodyamic cases were simulated by altering key systemic parameters. Arterial compliance and total vascular resistance were altered by random scaling of their reference values (scale factor range: 0.1–1.0 and 1.0–3.0 for compliance and resistance, respectively). Heart rate and arterial segment volume were also altered with the cardiac period ranging from 0.6 to 1.2 s and volumetric change of −20% to +20%. Figure 1*A* shows an example of pressure waveforms calculated at two locations along the aorta.

The analyzed waveforms corresponded to the ascending aorta and iliac bifurcation. Pressure waves were up sampled to 1 kHz. The temporal resolution of the signal had no noticeable effect on our computations. Computational simulations, data processing, and pressure wave analysis were performed with Matlab (The Mathworks, Natick, MA).

#### Analytic computation of “real” PWV and transit time.

Aortic PWV was analytically calculated with the Bramwell-Hill equation (4), which relates PWV to compliance in straight elastic tubes. Accordingly, the “real” value of PWV was determined by the compliance of each arterial segment at the corresponding diastolic pressure level. PTT within each arterial segment was then defined by dividing the segment's length by the real PWV within the same segment. Total aortic PTT was defined as the summation of transit times in each arterial segment of the aorta. Also, total aortic length was determined by summation of the lengths of the aortic segments (Fig. 2) within the path of the pressure wave transmission (Fig. 1) Finally, the real value of aortic PWV was calculated by dividing total length by total PTT.

#### Foot-to-foot methods of PTT estimation.

Five different algorithms (four existing and one novel) were applied for the estimation of PTT: *1*) the “diastole-minimum” method, *2*) the “maximum first derivative” method, *3*) the “maximum second derivative” method, *4*) the “tangential” method, and *5*) a new algorithm herein called the “diastole-patching” method.

#### Minimum of the foot of the wave.

The diastole-minimum method searches for the point of minimum pressure, which coincides with the diastolic pressure and is often called the foot of the pressure wave, as the characteristic point for the calculation of time delay between the two waves. The foot of the wave is considered to be a reflectionless point of the pressure waveform, as this is the first point in the upcoming systolic cycle and is thus less prone to contamination by the backward running reflected waves (24).

#### Methods based on derivatives.

Methods based on derivatives use as characteristic points the points of maximum first or second derivative of the pressure wave. The first derivative of the pressure wave was calculated by a five-point central difference scheme and the second order derivative with a seven-point central difference formula. As described by Chiu et al. (8), the maximum first derivative was determined in a region extending from minimum pressure to 175 ms after diastole and the maximum second derivative in a region that extended from 10 ms before until 100 ms after the point of minimum pressure. The first and second derivatives of the pressure waves at the ascending aorta, close to the iliac arteries, are shown in Fig. 1, *B* and *C*.

#### Tangential method.

The tangential method, or “intersecting tangents method,” uses as the characteristic wave point the intersection of two tangents on the arterial pressure wave. The first tangent was defined as the line that passes tangentially through the maximum first derivative point. The second tangent line is the one passing through the minimum pressure point and is parallel to the time axis. Figure 3*A* shows how the characteristic point is determined in the tangential method.

#### Diastole-patching method.

We propose a new method, termed as the diastole-patching method, which determines PTT based on a characteristic “region” in the vicinity of the foot of the pressure waves instead of a characteristic point, as proposed by the other methods. The diastole-patching method was inspired by an image-processing method applied in texture synthesis, hole filling, and denoising (7, 11). The image-processing algorithm scans the image for all the picture elements (pixels) that resemble the pixel being restored. The level of resemblance is then evaluated by comparing a data “patch” around each pixel and not just the value of the pixel itself. In a similar way, a region in the foot of the proximal waveform (the “diastole patch”) is compared against equally sized, consecutively overlapping, regions in the foot of the distal wave (Fig. 3*C*). Figure 3*B* shows graphically how the window size is chosen based on the location of the minimum pressure and maximum first derivative. To quantify the difference between the patch and distal pressure waveform, we used the sum of square differences (SSD). As shown in Fig. 3*D*, the wave travel time is defined as the time point where SSD is minimized.

Foot-to-foot methods and the new diastole-patching method were also tested with waveforms from the carotid and femoral arteries. These arterial locations correspond to standard clinical practice where the pressure waveforms are recorded noninvasively via applanation tonometry.

Also, we further evaluated the diastole-patching method with noisy data. We examined the performance of the diastole-patching algorithm in estimating PWV from pressure waveforms that were artificially distorted with white Gaussian noise and baseline wander artifacts. The Gaussian noise was applied by substituting the pressure at each time point with a value drawn from a normal distribution. The mean of the distribution was equal to the pressure value at each time point and the SD was equal to a percentage of the SD of the total wave. We performed a comparison for five different levels of noise SD (1–5% of wave SD). The baseline wander artifact was generated by adding a linear positive offset in the pressure waves. The offset was equal to zero for the first time point and equal to a randomly generated value in the range of 1–5 mmHg for the last time point. The noisy signals were subsequently filtered with a low-pass filter, and the patching window was defined. PTT was estimated using the unfiltered, distorted waveforms.

#### Statistical analysis.

Agreement, accuracy, precision, variability, and the association between the model (real) and estimated PWV values were evaluated according to previously described methodology (27). In brief, we used Pearson's correlation coefficient (*r*), intraclass correlation coefficient (ICC), root mean square error (RMSE), coefficient of variation, bias (mean difference between test and reference measurements), SD of differences (SDD), limits of agreement, and Bland-Altman analysis. *r* was used to examine the relation between estimated and real PWV values of the model. The assessment of agreement between different PWV estimations, in the sense of consistency and conformity, was performed by using the ICC statistic parameter (2). ICC assesses measurement agreement by comparing the variability of different measures (e.g., estimated vs. real PWV) of the same case with the total variation across all measurements and all cases. ICC values range from −1 for perfect disagreement to 0 for random agreement and to + 1 for perfect agreement. Variability between different PWV estimates and the model's real values was evaluated by the between-measures coefficient of variation, which is defined by the ratio of SD to the mean value. RMSE is indicative of the accuracy between PWV values estimated by various foot-to-foot methods and the PWV values computed by the model, encompassing both random and systematic errors. RMSE can range from 0 to ∞ with lower values corresponding to better accuracy. Finally, we performed Bland-Altman analysis as previously described (1). By this method, the differences between two PWV values (estimated − real) are plotted against their mean value. The limits of agreement, which indicate the precision of the PWV estimation (compared with real values), is defined as mean difference − 2 × SDD and mean difference + 2 × SDD. *P* values of <0.01 were considered to indicate statistical significance. Statistical analysis was performed by SPSS 20 (SPSS).

## RESULTS

Descriptive values of the hemodynamic and vascular parameters derived from the 2,000 simulated cases are shown in Table 1. Mean values (±SD) of *1*) real PWV computed analytically and *2*) estimated PWV by different foot-to-foot methods for PTT determination are shown in Fig. 4.

Characteristic points were determined at the proximal and distal waveforms by each foot-to-foot algorithm, and the results were also visually inspected (Fig. 5). It was found that for all 2,000 simulations, the characteristic points were effectively detected by all methods.

#### Agreement between real and estimated PWV.

The diastole-minimum method and diastole-patching method gave estimates of PWV in excellent agreement with real PWV values, as indicated by the high ICC values (0.864 and 0.977 for the diastole-minimum method and diastole-patching method, respectively; Table 2). In contrast, PWV estimated by the maximum first derivative, maximum second derivative, and tangential methods presented a low to moderate agreement compared with real PWV (ICC: <0.7 for the maximum first derivative and maximum second derivative methods; Table 2).

#### Accuracy of PWV measurement by different algorithms of transit time estimation.

The accuracy of PWV calculation by the different methods (algorithms) for PTT estimation was evaluated by the mean difference (bias) of estimated versus real − analytic values of PWV. The diastole-patching method resulted in the lowest absolute bias (0.261), indicating high accuracy (Table 2). It was followed by the diastole-minimum method, with an absolute bias equal to 0.834. RMSE values for the diastole-patching method were also low (0.315 m/s). In line with the accuracy classification made by the ICC, the maximum first derivative, maximum second derivative, and tangential methods had the highest bias (>0.9 m/s) and RMSE values (>0.95), thus presenting lower accuracy in PWV estimation (Table 2). Bland-Altman plots showed that the bias of the diastole-minimum method had a trend to increase at higher levels of PWV (Fig. 6*A*). An inverse trend was observed for the bias of the tangential, maximum first derivative, and maximum second derivative methods (Fig. 6, *B–D*).

#### Precision of PWV measurement by different algorithms for PTT estimation.

The diastole-patching method provided PWV estimates with the highest precision compared with the other techniques. This observation was reflected by the low SDD and narrow limits of agreement (Fig. 6 and Table 2).

#### Variation between real and estimated PWV.

The variation between real PWV values and estimated PWV values by each different foot-to-foot method was assessed by the coefficient of variation. Once again, the diastole-patching method presented the lowest coefficient of variation value (<3%), whereas the respective coefficients of variation for the tangential, maximum first derivative, and maximum second derivative methods exceeded 10% and reached up to 21% (Table 2).

#### The patching method for PTT estimation.

Among all the examined methods for PTT estimation, the diastole-patching method yielded superior accuracy and precision while presenting the lowest variability in its estimates. The estimated PWV by this new technique had the greatest accuracy and agreement (with analytic, real PWV) compared with the other examined foot-to-foot methods. This was indicated by the smallest bias (−0.261 m/s), highest ICC (0.977), and lowest RMSE (0.315). Also, the diastole-patching method provided PWV measurements with the best precision, as indicated by the lowest SDD (0.176 m/s) and narrowest limits of agreement. Furthermore, this method for PTT estimation presented the lowest variability compared with reference PWV values (2.8%). For the patching method, there was no remarkable trend of the difference in PWV (estimated − real) to vary with the level of PWV, in contrast to PWV differences provided by all other PTT algorithms (Fig. 6*E*).

The four existing PTT methods and patching method were also assessed for waveforms that corresponded to carotid and femoral arteries. The results of the analysis of their accuracy, precision, agreement, and variability compared with real model values are shown in Table 3. Once again, the diastole-patching method resulted in very good accuracy, agreement, and precision.

The diastole-patching method yielded very good accuracy and precision even when aortic pressure waveforms were distorted with various levels of Gaussian noise and a randomly generated baseline wander. ICC was higher than 0.89 for all the levels of noise. Absolute bias was lower than 0.1 m/s and SDD and RMSE were lower than 0.75 and 0.8 m/s, respectively, even for the worst-case scenario of added noise and baseline artifact. The coefficient of variation was <4% in all cases.

## DISCUSSION

The present study validated, for the first time, various existing algorithms for PTT estimation, providing data regarding the accuracy, precision, and variability of current computational PTT-based methods for regional aortic PWV measurement. This was performed using an accurate, validated, distributed 1-D model of the arterial circulation. It was demonstrated that PTT estimation by some popular techniques provide PWV values that differ substantially from real PWV values of the model. To further advance the reliability of PWV measurement based on foot-to-foot pulse wave analysis, we proposed a new diastole-patching method, which exhibited an increased accuracy and precision compared with the examined existing algorithms of PTT estimation. The new method targets to detect and “match” a specifically defined region of the wave foot between the proximal and distal pulses rather than determine a single characteristic point at the two waves, based on which the transit time is estimated.

Although arterial stiffness estimation is now broadly used in clinical research, it is still struggling to be established as a diagnostic tool in clinical practice. PWV measurement is now suggested by the *European Society of Hypertension/European Society of Cardiology* as a tool for the assessment of subclinical target organ damage in arterial hypertension (21). In contrast, the guidelines for assessment of cardiovascular disease in asymptomatic adults published in 2010 by the American College of Cardiology Foundation and the American Heart Association raised several concerns that restrict, at the moment, the recommendation of arterial stiffness measurement for clinical research (12):
Although predictive information suggests a potential clinical role for measures of arterial stiffness, there are a number of technical problems that...restrict the applicability of measures of arterial stiffness predominantly to research settings at this time...the technical concerns make arterial stiffness tests less suitable for addition to the clinical practice of risk assessment in asymptomatic adults due to problems with measurement...

To date, the most widely and commonly used technique to measure PWV is the measurement of the travel time of the foot of a wave (pressure, flow/velocity, or diameter) over a known distance. The foot as well as the early part (upstroke) of the arterial pulse is less affected by wave reflections and, hence, maintains most of its features during its propagation along the arterial tree. For this reason, the majority of techniques for PTT estimation and commercial devices have relied on the identification of a characteristic point at the foot or at the wavefront of the arterial pulse.

The reliability of regional PWV measurement depends on the accuracy and precision of distance measurement (16, 31, 34) and PTT estimation; thus, imprecise in vivo estimation of both pulse distance measurement and PTT and may introduce considerable errors (32). The latter is a crucial factor affecting PWV accuracy. Currently, several algorithms are used, with no consensus or recommendation as to which one provides the most reliable measurement of PWV. Different algorithms applied on the same waveforms have been found to lead to substantial variance in measured PWV values of 5–15% (22). PWV measured by the SpygmoCor system, which uses the tangential method, was significantly higher than PWV measured by the Complior System, which uses the maximum systolic upstroke, with a mean difference of 0.91 ± 1.07 m/s (22). The aforementioned difference is in accordance with our findings, which reported a mean difference (0.61 m/s) in PWV measured by the tangential and maximum first derivative methods (Fig. 4). The observed differences in PWV between the tested algorithms for PTT estimation in our in silico study and the location of the estimated wave foots (Fig. 5) were also quite in line with the respective differences reported by Chiu et al. (8), who analyzed both invasive and noninvasive in vivo pressure waves (Fig. 5). As shown in Fig. 7, the diastole-minimum method provided the highest PWV, whereas the tangential, maximum first derivative, and maximum second derivative methods resulted in incrementally lower values of PWV. Markedly, PWV derived by the maximum first derivative method was greater than that estimated by the diastole-minimum method by 1 m/s, similar to our findings.

#### Physiological and clinical relevance of PWV measurement errors/differences.

To characterize and classify the absolute difference (bias) and SDD between estimated and real PWV values, we referred to a recent meta-analysis of 17 longitudinal studies that investigated aortic PWV and followed >12,000 subjects for an average of 7.7 yr (33); it was found that a PWV difference of 0.5 m/s corresponds to 7.5% change in the risk for cardiovascular mortality. In this respect, a difference >0.5 m/s between real and estimated PWV values can be considered as a clinically relevant “bias.” Moreover, according to recently published guidelines of the ARTERY Society regarding the validation of devices for the noninvasive measurement of arterial PWV (36), the accuracy of a measurement with a test device method (compared with a reference technique) is characterized as “excellent” when the mean difference is <0.5 m/s and SDD is <0.8 m/s, as “acceptable” when the mean difference is <1.0 m/s and SDD is <1.5 m/s, and as “poor” when the mean difference is >1.0 m/s or SDD is >1.5 m/s.

In view of the above evidence and recommendations, our findings indicate that for aortic waveforms, the diastole-minimum and tangential methods yielded acceptable PWV (with a mean difference of <1 m/s from real PWV values and SDD of <1.5 m/s), whereas only the diastole-patching method yielded excellent PWV values. The good performance of the diastole-patching method was sustained even when processing waves that have reduced similarities (carotid waves may differ significantly from femoral waves). This can be attributed to the fact that when searching for the time lag between the proximal and distal waveforms, we take into account a region of interest (which contains more information) instead of looking just for a single characteristic point in the signal. It should also be noted that in terms of precision, all methods except the maximum first derivative method had SDD values lower than 0.5 m/s. Interestingly, the tangential and maximum first derivative methods, which are the most popular methods for PTT estimation, yielded less accurate and precise PWV estimations compared with real PWV values. The maximum first derivative method underestimated PWV with a mean bias equal to 1.74 m/s and the tangential method underestimated PWV with a mean bias equal to 0.919 m/s.

#### Technical aspects and applicability of the diastole-patching method.

The diastole-patching method was inspired by techniques of pattern recognition and texture reconstruction where a small region of interest is matched to regions of a larger signal by minimizing a metric of mutual difference. To apply this concept in the estimation of PTT in the arterial tree, we proposed a method where the region of interest is a window located around the diastolic foot of proximal pressure wave and the target signal is the distal pressure wave. We tested different window widths and concluded that the maximum first derivative was the best compromise between really heuristic window values, especially since it is already used in some commercial systems for PWV measurement. Furthermore, we favored the sum of squared differences as a minimization criterion, since it has been shown to be robust in other applications of signal/pattern recognition (2, 6). In this study, a patch extracted from the proximal signal was overlaid on the distal signal. The accuracy and precision in the estimation of PWV by this approach was the same when a patch from the distal signal was overlaid on the proximal signal.

Since the common clinical practice is to noninvasively record pressure waveforms in the carotid and femoral artery, we compared foot-to-foot methods by applying them at the corresponding waves (carotid and femoral). The overall trend was the same. The diastole-patching method provided PWV estimation with very good accuracy, agreement, and precision (ICC: 0.96, RMSE: 0.467, and mean bias: −0.4).

A critical aspect in the development of a new method to estimate PTT is that it remains robust when processed pressure waveforms have reduced similarity in the region of the diastolic foot. This can occur as a result of the arterial tree dampening function. The unfavorable situation can be further deteriorated by measurement induced noise and artifacts. To address the absence of noise in the original simulated data, we examined the performance of the diastole-patching method in estimating PWV from distorted waveforms. We added five different levels of increasing Gaussian noise and randomly generated baseline wander. The method retained its good agreement compared with analytic PWV with ICC > 0.89 for all levels of added noise. Furthermore, the method remained accurate even at the worst simulated scenario with the maximum level of added white Gaussian noise and 5-mmHg baseline wander (RMSE < 0.8). The results showed that the diastole-patching method remained robust in PWV estimation.

#### Limitations.

Four existing algorithms and a novel algorithm for PTT estimation were validated in silico and not with in vivo pressure waveforms. It is true that the accuracy and precision for PWV measurement based on in vivo recordings could be affected by several physiological and technical factors, such as heart rate variability, respiratory or motion artifacts, preejection artifacts, arrhythmias, and operator-induced acquisition artifacts. However, although the precision of PWV measurement has been thoroughly examined in vivo, the accuracy of PTT estimation can be only assessed using in vitro or in silico models as they can provide analytically calculated real PWV and thus PTT values that cannot be directly measured in vivo. The ability of different algorithms to accurately determine PTT on realistic pressure waves generated by a model validated against human data (28, 29) is directly indicative of future comparative accuracy studies of different algorithms at in vivo settings.

It should be acknowledged that there is no simple way to describe all the important facets of accuracy, agreement, and precision. Some of the most popular methods in the medical literature, i.e., Pearson's correlation coefficient (*r* or *R*^{2}) and the slope from linear regression analysis, can be inappropriate since they measure association and not concordance (17). For example, one set of measurements may take systematically higher or lower values than another set and still providing very high but misleading *r* or *R*^{2} values. Thus, the correlation coefficient per se cannot indicate the level of accuracy, precision, and variability between a test and a reference method. To overcome this limitation, the use of other statistic metrics and methods have been proposed, such as ICC, RMSE, limits of agreement, SDD, and coefficients of variation.

Specific algorithms for PTT estimation were investigated in this study, although an increasing number of other methods can be found in the literature (10, 13, 14, 24, 37). Our choice was based on the fact that the examined techniques are the most well described and extensively used for PTT estimation. Based on a previous report (13) that published reference/normal values of PWV gathered from 16,867 subjects and patients from 13 different centers across 8 European countries, the most popular methods for PTT estimation are *1*) the intersecting tangent algorithm (SphygmoCor system) and *2*) the point of maximal upstroke during systole, namely, derivative-based methods (as used in the Complior system). Also, the four existing algorithms examined in our study have been previously investigated and compared with each other in vivo (8), thus allowing us to compare and extrapolate our findings to respective in vivo observations.

#### Conclusions and perspectives.

A great discrepancy and variability in PWV measurements have often been observed in vivo, mostly due to inconsistent and imprecise estimation of PTT and travel distance. This study demonstrated that current widely used algorithms for PTT estimation have inherent limitations in terms of accuracy and precision of PWV measurement. In an effort to further advance the reliability of PWV measurements, we developed and validated in silico a new foot-to-foot method for PTT estimation, which yielded superior accuracy and precision in PWV measurements compared with currently used algorithms. Future clinical studies should be undertaken to investigate the feasibility and reliability of the new diastole-patching method and the potential advancement of the diagnostic and prognostic value of PWV. It would be also interesting to compare and optimize different methods for PTT estimation based on the analysis of velocity waveforms that are typically recorded by phase-contrast magnetic resonance imaging (9). Concluding, a consensus regarding the optimal method for PTT estimation is quite demanding, since various current algorithms provide PWV estimates with substantial errors, which partially hinder the diagnostic and predictive effectiveness of PWV measurement in clinical practice.

## DISCLOSURES

No conflicts of interest, financial or otherwise, are declared by the author(s).

## AUTHOR CONTRIBUTIONS

Author contributions: O.V., T.G.P., and N.S. conception and design of research; O.V. performed experiments; O.V. and T.G.P. analyzed data; O.V., T.G.P., and N.S. interpreted results of experiments; O.V. prepared figures; O.V., T.G.P., and N.S. drafted manuscript; O.V., T.G.P., and N.S. edited and revised manuscript; O.V., T.G.P., and N.S. approved final version of manuscript.

## ACKNOWLEDGMENTS

The authors thank Dr. Stamatios Lefkimmiatis for the fruitful discussions on image and signal processing.

- Copyright © 2013 the American Physiological Society