A lesson in vigilance

The mechanical behaviour of arteries is complex due to their three-dimensional composite microstructure and the complex intrinsic mechanical properties of its constituents [1,2]. In addition, vascular smooth muscle tone can modulate the properties of vessels [3], which are also connected to the surrounding tissues (tethering), whereas side branches might anchor the vessel to organs. Experts in biomechanics have developed so-called constitutive models that can describe the anisotropic (i.e. material properties vary with direction) and nonlinear (the relation between stress and strain is nonlinear) behaviour of arteries [4–6]. Although these complex constitutive models are essential to fully understand the intrinsic biomechanics of arteries (and to understand, for instance, the growth and rupture of aneurysms or aortic dissection [7]), their practical use in the clinical setting is limited to date. It is simply impossible to measure in vivo all data that would be required to accurately assess the parameters of these constitutive models, requiring ex-vivo experiments with tissue samples exposed to controlled multiaxial loading. What is measurable in vivo, however, is the relation between the pressure (P) inside an artery and its diameter (D) or its cross-sectional area (A). This relation is nonlinear [8], an immediate consequence of the above described complex constitutive behaviour of arteries [9]. Progressive stretching of the arterial wall upon pressure inflation progressively stretches and recruits the initially wavy collagen fibres [10]. The result is that the stiffness of an artery is not constant, but depends on the degree to which the artery is stretched and thus on the intraluminal pressure (or more correct on the transmural pressure difference between the inside and outside of the vessel) [11]. As the vessel is loaded, it stiffens! The nonlinear relation between pressure and diameter is very well known, and there are a number of phenomenological models that can describe this relation fairly well (and that can be seen as reduced forms of the more advanced constitutive relations). When an artery is loaded over a wide pressure range, the model that probably best describes this behaviour is the arc-tangent model of Langewouters et al.[12] (Fig. 1, panel a). Defining compliance, CA, as dA/dP (the inverse of stiffness), CA is the slope of the local tangent to the A–P relation and is therefore a function of pressure (Fig. 1, panel b), with CA decreasing at higher pressure. It has been argued that arterial stiffening would represent a functionally more relevant aspect of arterial behaviour than arterial stiffness as such [13]. Analysing data from the Asklepios population, it has been shown that the change in carotid artery stiffness over the cardiac cycle, rather than diastolic stiffness, is independently associated with left ventricular mass index in healthy middle-aged individuals [14].FIGURE 1: Panel (a): illustration of the nonlinear relation between intra-arterial pressure and cross-sectional area assuming the arc-tangent model of Langewouters et al. for a vessel with a maximal diameter of 9 mm. Panel (b): compliance as a function of pressure. Panel (c): conversion of the same data in a physiological pressure range to pressure–diameter data. Panel (d): the slope of the relation between ln (P/P ref) and D/D ref yields β. The use of a different reference pressure yields different values of β.In vivo, however, pressure varies only between DBP and SBP, and over this pressure range (e.g. from 80 to 130 mmHg), the relation between pressure and area or, more frequently used, between pressure and diameter (D), may be described by an exponential relation P = Prefeβ[(D/Dref)-1], with Pref an arbitrarily chosen reference pressure and Dref the corresponding diameter [15]. Taking the logarithm and rearranging, one retrieves the so-called β stiffness index, quantifying arterial stiffness (or rather stiffening) in a pressure-independent way: β = ln(P/Pref)/[(D/Dref)-1]. It is common practice to substitute Pref and Dref by DBP and diastolic diameter, and P and D by the systolic values. Further expanding on this, and assuming that the pulse wave velocity measured over the heart-ankle trajectory can be converted into a single stiffness index via the Bramwell–Hill equation, the cardio-ankle vascular index (CAVI) can be derived [16,17]. Thanks to the availability of dedicated measuring equipment (Vasera; Fukuda Denshi, Tokyo, Japan), CAVI and the β stiffness index more and more find their way into (pre)clinical research [18]. It is fair to state that it is generally accepted by the scientific community that β (and, through extension, CAVI) indeed provides pressure-independent measures of arterial stiffness/stiffening. The current issue of the Journal of Hypertension, however, features an elegant and straightforward study with theoretical considerations on the presumption that β and CAVI are pressure-independent indices of arterial stiffness. Spronck et al.[19] demonstrate that the common practice of using DBP and diameter values as surrogate for the values at a reference pressure actually introduces pressure dependencies in the derived stiffness index β. When we use the same pressure–diameter data in Fig. 1 (over a 80–130 mmHg pressure range) and plot ln (P/Pref) as a function of D/Dref, the slope of the linear regression line yields β. It is indeed clear from the figure that the use of 80 mmHg (assumed DBP) or 100 mmHg as Pref yields two different slopes, and thus two different β values. Both choices are mathematically correct and describe the same pressure–diameter relation, though with slightly different parameter values. The choice of Pref is not important when considering a single pressure–diameter relation, but might become relevant when comparing data from individuals, or when analysing longitudinal data from a single individual when using different Pref. As discussed by Spronck et al., the nonlinear pressure–diameter relation leads to further pressure dependencies when deriving CAVI. To the best of my knowledge, this caveat went unnoticed until now, despite its obviousness. At a first glance, the effect appears relatively small and the actual impact is hard to assess from the article as the authors restrict themselves to a theoretical exercise. Nonetheless, in a realistic simulation of a blood pressure (BP) intervention trial in patients with hypertension, a reduction in BP from 160/111 to 120/79 mmHg would artificially yet significantly lower CAVI from 8.1 to 7.7 (when using DBP as reference pressure) despite the assumption of an unaltered pressure–diameter relation [19]. Although seemingly small in absolute number, the order of magnitude of change in CAVI is the same as reported in actual intervention studies [20]. Thus, where CAVI would have the theoretical benefit of assessing the impact of intervention on arterial stiffness independent of BP – this does not appear to be case (when DBP is used as reference pressure). The observation of Spronck et al. is therefore more than just a theoretical footnote and definitely has an impact on the current application and interpretation of β and CAVI. The good news, however, is that Spronck et al.[19] also propose a very simple way to correct β and CAVI for this pressure dependency. When using a fixed reference pressure (e.g. 100 mmHg), existing data from finalized studies are easily corrected for as demonstrated in their article, and the correction is easily implemented in manufacturer software. We hope that this will happen, even if this would lead to a reinterpretation of existing studies. The only assumption that remains to be made is that the relation between pressure and diameter is strictly exponential, which might only be so to a certain extent (as in the example shown in Fig. 1). In any case, the study by Spronck et al. is, by no means, a reason to discourage the use of the – corrected! – β stiffness index or derived indices. ACKNOWLEDGEMENTS Conflicts of interest There are no conflicts of interest.