Arterial stiffness as pulse wave velocity (PWV) is a powerful predictor of mortality and cardiovascular events in hypertensive patients, above and beyond traditional risk factors (Boutouyrie et al., 2002; Laurent et al., 2003; Cardoso et al., 2019). The arterial wall, however, presents a complex microstructure where different wall constituents, mainly collagen, elastin, and smooth muscle, play different but equally important roles in arterial function (Boutouyrie et al., 1998; Cruickshank et al., 2002; Krasny et al., 2017; Giudici et al., 2021e). The heterogeneous microstructure of the arterial wall makes its behavior highly nonlinear (Giudici et al., 2021b) so that arterial stiffness and, consequently, PWV are intrinsically blood pressure (BP)-dependent (Spronck et al., 2015b). This fact complicates distinguishing between chronic (i.e., actual BP-induced wall remodeling) and acute effects (i.e., transitional shift to a different working point in the nonlinear behavior of the arterial wall) of increased BP on arterial structure and mechanics. Most clinical studies address the issue of the BP-dependency of PWV via statistical methods, using BP as a confounding factor for PWV (Desamericq et al., 2015; Diaz et al., 2018; Valbusa et al., 2019). However, statistical methods suffer some limitations: (1) they lack subject specificity and, hence, are less likely to be used in clinical practice, (2) they may fail to discriminate between acute and chronic effects of increased BP on the wall stiffness (Spronck, 2021), and (3) the choice of the normalizing pressure, i.e., the subject-specific pressure level to be used as the confounder in multivariate analysis, is not trivial and largely affects the size of the correction itself (Giudici et al., 2021a). While, in clinical investigations, statistical adjustments for systolic BP (SBP) (Valbusa et al., 2019), mean BP (MBP) (Desamericq et al., 2015), and pulse pressure (PP) (Brandts et al., 2012) are often made, most regional PWV metrics (e.g., carotid-femoral and brachial-ankle PWV), use the foot of arterial waves as the fiducial point, suggesting that diastolic BP (DBP) likely represent a more appropriate choice for their pressure-normalization (Spronck et al., 2017b). As intergroup differences in SBP are typically larger than those in DBP, widely used SBP- and MBP-statistical adjustments likely lead to overcorrections of PWV and potentially limit our understanding of pressure-induced chronic vascular damage (Spronck et al., 2017b).

In the past two decades, researchers have attempted to address the BP-dependency of PWV using mechanistic approaches that rely chiefly on the assumption that, in the physiological pressure range, the pressure (P)-area (A)/diameter (D) relationship of arteries resembles an exponential function (Gavish and Izzo, 2016). If the fitting exponential function is opportunely formulated, its constant can be used as a BP-normalized index of arterial stiffness (Spronck et al., 2017a; Giudici et al., 2021a). In 2006, Shirai et al. introduced the cardio-ankle vascular index (CAVI) that uses the heart-to-ankle PWV (haPWV), a regional PWV metric quantifying the average properties of the entire heart-to-ankle arterial pathway, to estimate Kawasaki’s stiffness index β, defining the exponential relationship between P and D. A decade later, however, Spronck et al. (2017a) raised concerns related to the actual (in)dependency of CAVI from BP at the time of measurement, due to the inherent dependency of β from the subject-specific DBP. They proposed a revised metric CAVI₀ that relies on Hayashi’s stiffness index β₀, which, unlike β, is defined with respect to a standardized reference pressure (P_ref). Furthermore, CAVI and CAVI₀ differ also in the normalizing pressure used to estimate β from haPWV, raising once more the question of which is the most appropriate pressure level for the normalization of PWV metrics (Giudici et al., 2021a).

Similar methods have been devised to correct local PWV estimates, which, unlike regional PWVs, provide information on the stiffness of a specific location of the arterial tree. Spronck et al. (2015a) used the exponential P-A relationship proposed by Meinders and Hoeks (2004) to effectively predict the changes in local carotid PWV (cPWV), estimated via a linearized Bramwell-Hill equation (Bramwell et al., 1923), associated with the BP lowering achieved with 3-months of antihypertensive treatment in hypertensive patients. A considerably more complex approach was proposed by Ma et al. (2018) who used Fung’s exponential hyperelastic strain energy function to define the relationship between BP and local PWV. While undoubtedly elegant, this approach is unlikely to be used in clinical practice due to the difficulty in estimating subject-specific parameters for the mathematical model describing the artery behavior.

Using a similar mechanistic approach based on the exponential modeling of the P-A relationship of arteries (Spronck et al., 2015b,2017a), our current study analyzed differences in local cPWV between healthy controls and patients with hypertension, aiming to distinguish between acute and chronic effects of high BP on carotid function. We also aimed to compare mechanistic and statistical correction of cPWV, analyzing the impact of the choice of the normalizing pressure on the size of the correction and on inter-group differences.

The BP-dependency of arterial stiffness limits the ability of PWV to define changes in the mechanical properties of the arterial wall in response to cardiovascular pathologies and wall remodeling and damage (Spronck, 2021). This fact assumes particular relevance when evaluating changes in arterial mechanics in response to hypertension since elevated BP drives the short-term increase in PWV and potentially the long-term damage to the wall microstructure that, in turn, could result in a chronic increase in PWV. The BP-dependency of PWV has been typically addressed via statistical methods (Desamericq et al., 2015; Valbusa et al., 2019). More recently, methods that rely on the exponential modeling of the wall behavior have allowed to mathematically predict subject-specific changes in PWV in response to acute changes in BP (Shirai et al., 2006; Spronck et al., 2017a). Using a similar approach, we aimed to characterize differences in CCA stiffness between healthy controls and hypertensive patients, providing subject-specific BP-normalization of cPWV. Furthermore, we aimed to compare the mechanistic BP-normalization with that obtained using statistical methods, as well as investigate the impact of the choice of the normalizing pressure on the obtained correction. Our results indicated that BP alone accounted for 68% of the cPWV difference between groups.

The association between hypertension and increased PWV has long been known (The Reference Values for Arterial Stiffness’ Collaboration, 2010). However, understanding the causal relationships between the two is less trivial; on the one hand, studies have shown that PWV is an independent predictor of the longitudinal increase in SBP (Najjar et al., 2008), so that increased PWV drives the development of hypertension. On the other hand, PWV intrinsically depends on the BP level at the time of the data acquisition, and the subject-specific PWV can vary considerably in response to BP changes (Spronck et al., 2015b). This two-way relationship between PWV and BP complicates investigating the consequences of increased BP on arterial mechanics. Methods for the BP-normalization of PWV aim to address this issue, providing stiffness metrics that refer to a predefined reference pressure level and are, hence, independent from the BP level at the time of the measurement (Spronck et al., 2017a; Giudici et al., 2021a).

In this study, we analyzed differences in CCA PWV between normotensive and Grade 1–2 hypertensive individuals. In agreement with previous studies (Maritz et al., 2016; Park et al., 2020), our results indicated that the cPWV was, in fact, higher in hypertensives than in controls at their relative working pressure: 12% difference with a 13 and 12% difference in SBP and DBP, respectively. Notably, while age and sex are key determinants of arterial stiffness (The Reference Values for Arterial Stiffness’ Collaboration, 2010), our studied groups were well-matched, so that these factors unlikely played a role in inter-group differences in cPWV. Our finding is in agreement with previous work (Laurent et al., 1994) where distensibility of the CCA at MBP was reduced by ∼33% in hypertensive people compared to healthy controls but with a ∼30% difference in SBP/DBP. Similar results have also been reported for regional carotid-femoral PWV (The Reference Values for Arterial Stiffness’ Collaboration, 2010). However, the pressure-normalization of cPWV proposed here indicated that more than two-thirds of this difference had to be imputed to BP differences between the two groups (Figure 2) and that, in absolute terms, the CCA of hypertensive patients was not intrinsically stiffer than that of healthy people. Notably, as suggested by the Moens-Kortweg equation (Moens, 1878; Li et al., 2021), PWV quantifies the structural stiffness of an artery as a whole (i.e., including both wall material stiffness and geometrical features). As hypertensives here had a higher IMT and IMT/D_d ratio than controls, residual differences in PWV after pressure-normalization may, at least in part, be attributable to these structural differences, rather than pure differences in wall material properties. This finding was further confirmed by the exponential modeling of the P-A relationships, with the average hypertensive curve running almost parallel to that of controls, independently of pressure. Our findings are in agreement with seminal works of Laurent et al. (1994) and Armentano et al. (1995), who showed that CCA distensibility-pressure relationships of controls and hypertensives are almost superimposed. These results suggest that wall stiffening in response to increased BP is mild at the CCA. It is worth considering, however, that patients in our study presented only mild-to-moderate hypertension with a relatively short time between the diagnosis of the condition and the time of the examination (< 1 year). Therefore, it is possible that longer exposure to severely increased BP might trigger intensive remodeling and, consequently, intrinsic stiffening (i.e., BP-independent) of the carotid wall.

Whether accounting for the BP-dependency of PWV with statistical or mechanistic methods, the choice of the normalizing pressure has an important quantitative impact on the size of the correction. While the most widely adopted choices in clinical studies are SBP or MBP (Desamericq et al., 2015; Valbusa et al., 2019), it has been previously argued that the BP-dependency of most metrics pertaining to PWV, especially those relying on the foot-to-foot detection technique, is likely governed by DBP (i.e., the pressure at the foot of the wave) rather than either SBP or MBP (Spronck et al., 2015b,2017a; Giudici et al., 2021a). In this study, cPWV was estimated via linear regression of the P-D² relationship in late diastole, i.e., the diastolic decay after the dicrotic notch (Giudici et al., 2021c). Although this phase of the cardiac cycle spanned between DBP and ∼65% of the PP, our results indicated that, on average, P_c was determined for its 91.5% by DBP and only for its 8.5% by SBP (Figure 4). We obtained similar results when estimating cPWV via the lnDU-loop method, a linear regression between blood velocity (U) and the natural logarithm of the diameter distension (lnD) in early systole (Giudici et al., 2021d). These findings suggest that, as regional PWV, loop methods provide nearly diastolic measures of PWV and that DBP should be regarded as the main driver of their BP-dependency. Notably, however, in this study, DBP-adjustment provided the largest difference between statistical and mechanistic methods for the cPWV correction. This result warrants caution when performing statistical DBP-adjustment of all arterial stiffness metrics that are notably purely diastolic.

As other local techniques (Rabben et al., 2004; Khir and Parker, 2005; Feng and Khir, 2010; Campos Arias et al., 2019), the D²P-loop method (Alastruey, 2011) is based on the coupling of two arterial waveforms to provide an estimate of the wave speed at a single location of the arterial tree (i.e., local wave speed). In contrast, regional PWVs, such as the carotid-femoral PWV (Laurent et al., 2006), provide insights into the average arterial stiffness along a given wave path, which inevitably includes arteries with different wall structures. This is particularly relevant when considering that elastic and muscular arteries have shown to be affected differently by aging and disease (Borlotti et al., 2012). Furthermore, local methods are not affected by known limitations of regional PWVs, such as the possible inaccuracies in the estimation of the true arterial pathway length (Huybrechts et al., 2011; Giudici et al., 2021a). Finally, local arterial properties can be useful to predict damage of target organs located in the vicinity of the measurement site; for example, carotid stiffening and function have been associated with cognitive decline (Chiesa et al., 2019). For the aforementioned reasons, results reported here on differences in arterial wall stiffness between normotensives and hypertensives concern the carotid artery and should not be generalized to other locations or regions of the arterial tree.

In this study, we assumed the existence of an exponential P-A relationship for the CCA. While it is generally accepted that the P-A relationship of arteries closely resembles an exponential function in the physiological range of pressure (Gavish and Izzo, 2016), the subject-specific P-A relationships might not be exactly exponential, especially in young subjects at low pressures (Vande Geest et al., 2004). It is therefore possible that, for some subjects, the mechanistic method failed to accurately predict the relationship between BP and cPWV. It is, however, unlikely that this has significantly affected the cPWV-normalization since similar methods showed good ability in predicting changes in both local and regional PWV, given a BP change (Spronck et al., 2015b; Pucci et al., 2020).

We concluded that mild hypertension does not chronically affect the stiffness of the CCA wall, at least in the middle-aged subjects without target organ damage.

Assuming an exponential P-A relationship, we proposed a method that allows for determining arterial stiffness, as PWV, independently of BP. The proposed method is non-invasive and provides a subject-specific normalization of PWV which could be implemented in the clinical setting. The results warrant further investigations to establish the potential clinical utility of the method.

The raw data supporting the conclusions of this article will be made available by the authors, upon reasonable request.

The studies involving human participants were reviewed and approved by Comitato Etico di Area Vasta Nord Ovest (reference number: 3146/2010), Italy. The patients/participants provided their written informed consent to participate in this study.

AG contributed to the conceptualization, data analysis, manuscript drafting, and editing. AG and AK developed the analytical method. AK, CP, JC, and MK contributed to the conceptualization, manuscript editing, and project supervision. CM contributed to the data acquisition and management. All authors contributed to the article and approved the submitted version.

JC was a past president of the ARTERY (Association for Research into Arterial Structure and Physiology) society. MK was responsible for clinical studies at Esaote SpA (Genova, Italy). The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

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