Dependence of arterial stiffness on pressure quantified in the realm of the cardiac cycle

The interaction of the structural and load-bearing components in the wall of arteries is a major determinant of the mechanical properties of the arterial vasculature [1]. At low strains, the load is borne by elastic fibres and becomes transferred to the stiffer collagen fibres with increasing strain. As the arterial wall is distended due to intravascular pressure, the inherent stiffness of the wall then becomes dependent on the distending pressure. This pressure-dependence of wall stiffness, due to the nonlinear stress-strain relationship, is an intrinsic property of all arteries. It is a fundamental evolutionary property of arterial design across all vertebrates and invertebrates with a closed circulatory system [2]. It enables the arteries to have a single value of wall tension to balance the distending pressure at all strains, as distinct from collapsible vessels wherein there may be more than a single operating point at different strains [2]. The measurement of intrinsic wall stiffness is not readily achievable in the intact circulation, and so, arterial pulse wave velocity (PWV) is generally used as a surrogate, due to the biophysical relationships between PWV and vessel stiffness and geometry [3]. Thus, when comparing measurements of arterial PWV across individuals, it is necessary to account for any difference in pressure for assessment of inherent differences in arterial stiffness. This has been important to differentiate age-related changes in populations with different risk profiles or environmental factors [4]. The large numbers of studies conducted in this field confirm repeatedly that the main factors affecting PWV, and so wall stiffness, in large conduits arteries are age and arterial blood pressure. In population studies, the age and pressure-dependence of arterial stiffness is accounted for by statistical means employing multiregression techniques, and much has been gained by these methods to suggest that arterial stiffness is a strong independent predictor of cardiovascular risk [5]. Consequently, there is an increasing research effort in establishing whether arterial stiffness per se could precede the development of hypertension [6–9] and whether early structural changes may be causally related to age-related increase in arterial pressure and associated risk factors [10–13], or could be reversed or attenuated by treatment [14,15]. Thus, the inter-relationship of age and blood pressure with arterial stiffness is a highly significant factor for the proper interpretation of measurements of arterial stiffness in relation to levels of cardiovascular risk, and to align arterial stiffness measurements with emerging guidelines incorporating normal population values of PWV as well as blood pressure [16,17]. However, although it is entirely feasible for this inter-relationship to be accounted for by statistical means in cohort studies, it does not necessarily follow that population normative values can always be extrapolated to individuals. The study by Spronck et al.[18] in the current issue of the Journal of Hypertension makes important advances in quantifying the degree of the pressure-dependence of arterial stiffness in individuals and can lead to important clinical applications of patient-specific assessment. In this study [18], arterial stiffness is measured as a regional parameter in the carotid artery by employing ultrasound measurement of arterial diameter and tonometric registration of the arterial pressure pulse. The study uses techniques developed in earlier studies by some of the same group of investigators [19,20], wherein pressure-area curves are used to determine the values of stiffness at three specific points in the cardiac cycle: diastole, peak systole and end systole. The pressure-area curves are modelled by a single exponential function and carotid PWV (cPWV) is determined using the established Bramwell–Hill relationship [cPWV = (ΔP.Ad/ΔA.ρ)1/2; where ΔP is pulse pressure; Ad: diastolic area; ΔA: change in area; ρ: blood density]. Spronck et al.[18] conducted the study in a small group of 23 hypertensive individuals. This was done essentially to demonstrate proof of principle and also to obtain ranges of variation of cPWV over the cardiac cycle with which to estimate broad values of pressure-dependence of cPWV. The overall conclusion is that in the human carotid artery, there is an average change of 1 m/s for a change of pressure of 10 mmHg. The implication of this is that PWV can vary markedly throughout the cardiac cycle, with changes of the order of 4–5 m/s (i.e. a two-fold change) over the range of normal pulse pressure of 40–50 mmHg. Thus, this high dependence of PWV on pressure is a manifestation of substantial effects of nonlinearity. However, this presents an apparent conceptual dilemma. The field of arterial haemodynamics, wherein pressure and flow are related in the frequency domain, is based on the existence of linearity manifest as a constant PWV throughout the excursion of the pressure change due to an input flow signal [3]. That is, a single frequency component of flow is related to a single frequency component of pressure. For nonlinear systems, a single frequency of flow is related to multiple frequencies of pressure, hence producing intermodulation frequencies. However, when the power of intermodulation frequencies is measured, it represents only some 2% of the total wave power [21], suggesting the haemodynamic effects of nonlinearities, although present, are relatively small, and a linear system is sufficient to describe the relationships of pressure and flow in conduit arteries [3]. The explanation for this lies in the fact that the measured (true) PWV is related to high frequencies, that is waves of short wavelength, and subjected to dissipation and dispersion [22,23], whereas most of the power in the arterial pulse is in the lower harmonics, and so of longer wavelengths, hence exhibiting less change in (apparent) PWV throughout the pressure range of the cardiac cycle [3]. A significant result in the study of Spronck et al.[18] is the high predictability of the effect of antihypertensive treatment using an invariant pressure-area curve obtained at baseline. In addition, the effect of treatment on change in PWV for similar changes in arterial pressure was age-dependent, with a greater pressure-dependence of PWV found in older individuals. Although an invariant pressure-area curve may be used for a relatively short-term treatment of 3 months, as employed in this study, it is not known to what extent this may be used for longer periods, as treatment and the change in blood pressure itself may result in structural modification, affecting the degree of pressure-dependence. Our recent studies in the rat aorta, including spontaneously hypertensive rats and models for arterial calcification, have shown a marked difference in pressure-dependence along the aortic trunk and with treatment of angiotensin-converting enzyme inhibition [24,25]. The three-point method for characterization of the pressure-area curve as proposed in the study by Spronck et al.[18] and in previous studies [19,20] is a potentially useful technique that can be readily applied in routine clinical assessment of vascular function wherein ultrasound methods for measurement of vascular geometry and noninvasive tonometric means of obtaining the arterial pressure pulse are employed. Using the pressure-area curve as a specific marker for the individual patient, it can be possible to estimate change in arterial stiffness that is not dependent on changes in blood pressure. Indeed, this becomes an important consideration in the interpretation of the effects of both blood pressure and arterial stiffness on assessment of cardiovascular risk. As the authors emphasize, this can eliminate the potential ‘double scoring’ of blood pressure values in cardiovascular risk computations according to guidelines [16] when there are changes in arterial stiffness as measured by PWV. This suggests that those with a higher PWV associated with higher blood pressure should be considered similar to those with a lower PWV associated with a lower pressure when assigning risk scores, particularly if the difference in PWV can be shown to be due only to the difference in blood pressure. This technique would then differentiate population values of arterial stiffness from individual values and so would improve stratification of cardiovascular risk. This potential patient-specific technique for assessment of arterial stiffness can be a significant complement to the patient-specific application of central aortic pressure in connection to guidelines of treatment of hypertension as determined from the conventional brachial cuff. Large population studies have shown a substantial overlap in central aortic systolic pressure across a range of brachial cuff systolic pressure values as specified by guidelines; some in the normotensive range as specified by hypertension guidelines have central systolic pressures similar to those in the hypertensive ranges [26]. These observations can have substantial implications on how to interpret hypertension guidelines [27] when assessing the efficacy of treatment in guiding therapy [28] and in monitoring effects of end-organ performance, such as in heart failure [29]. Similar considerations can be extended to the study by Spronck et al.[18] in relation to the potential benefits for patient-specific treatment and application of guidelines and population normative values [16,17]. In addition to the assumption of an invariant pressure-area curve used for the prediction of cPWV values with antihypertensive treatment, an additional caveat of the study is the lack of measurement of wall thickness. An inherent assumption when using PWV as a surrogate of stiffness of the wall material is that geometry does not change. As an extension of the Bramwell–Hill relationship (above), the Moens–Korteweg relationship expresses PWV in terms of wall elastic modulus (E), wall thickness (h), diameter (D) and blood density (ρ) [PWV = (E.h/D.ρ)1/2] [3]. Given the increase in diameter with age (as also seen in the study by Spronck et al. [18]), the marked age-related changes in PWV are predominantly due to changes in stiffness (E). However, marked pressure changes and/or treatment could also alter wall thickness, which would alter PWV and so overestimate the change in inherent wall stiffness (E). Further studies could attempt to obtain information on arterial geometric parameters so as to differentiate functional from structural changes as well as inherent differences in age-related changes in men and women that will determine the course of changes in blood pressure and age-related cardiovascular risk, particularly in longitudinal assessments of vascular function [30]. The study by Spronck et al.[18] has convincingly provided a demonstration of proof of principle that the use of a three-point characterization of the pressure-area relation of the carotid artery during the cardiac cycle can provide potentially useful information for improved assessment of the pressure-dependence of arterial stiffness. The technique has a real potential to advance the clinical applications for assessment of vascular function to quantify changes in fundamental vascular and haemodynamic parameters [31]. Specifically, the study highlights the important considerations of the application of population normative values of arterial pressure and PWV to individual patients when the variation of PWV is strongly related to the fundamental design property of the pressure-dependence of arterial stiffness. This technique promises to improve assessment of vascular function and can make a significant contribution to the overall approach of tailoring and optimizing patient-specific treatment, which will become a significant feature of the future of medicine. ACKNOWLEDGEMENTS Conflicts of interest There are no conflicts of interest.