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A model expression for the ambulatory arterial stiffness index

Segers, Patricka; Kips, Jan G.a,b; Vermeersch, Sebastian J.a,b; Boutouyrie, Pierrec,d,e; Laurent, Stéphanec,d,e; Van Bortel, Luc M.b

doi: 10.1097/HJH.0b013e32835a927b

aIBiTech-bioMMeda, Gent University, Gent, Belgium

bHeymans Institute of Pharmacology, Gent University

cAssistance Publique, Hôpitaux de Paris, Hôpital Européen Georges Pompidou


eUniversité Paris, Descartes, Paris, France

Correspondence to Patrick Segers, Ghent University, IBiTech-bioMMeda, 5 Blok B, De Pintelaan 185, B-9000 Gent, Belgium. Tel: +32 9 332 3466; e-mail:

We thank Dr Gavish [1] for his insightful comments on our study in J Hypertens regarding the determinants of the Ambulatory Arterial Stiffness Index (AASI) in which we used a one-dimensional arterial network model for the generation of data simulating 24-h ambulatory blood pressure [2]. Dr Gavish is indeed correct that we used standard regression analysis to assess the slope of the relation between SBP and DBP and AASI [AASI calculated using standard regression (AASIstd)], as we believe this has been common practice in the literature up to today. Anyhow, using symmetric versus standard regression analysis indeed makes an important difference in the calculation of AASI.

Following the suggestion of Dr Gavish, we reanalyzed some of the data from our study, and transformed AASIstd into AASI calculated using symmetric regression (AASIsym) using the proposed expression: AASIsym = 1 – (1 – AASIstd)/R, with R being the correlation between SBP and DBP values. Results are summarized in Table 1 [2].



From these data, it follows that the use of symmetric regression analysis leads to lower absolute values of AASI and also lowers its sensitivity to changes in stiffness; excluding pressure-related arterial stiffening through linear model simulations reduces AASIstd from 0.42 to 0.18, and AASIsym from 0.36 to 0.11, suggesting that arterial stiffening indeed represents a (the) major component of AASI; symmetric regression analysis for the linear elastic case lowers AASI from 0.18 (AASIstd) to 0.11 (AASIsym), but it does not become zero.

These data, thus, demonstrate that AASIsym is less sensitive to the stiffness level assumed in the simulations than AASIstd but do not entirely confirm the hypothesis that AASI is solely a measure of arterial stiffening, which would predict AASIsym to become zero for the linear model.

The model used by Dr Gavish is based on an exponential relation between the SBP and DBP change and the associated change in volume, which is a valid description of the intrinsic mechanical behavior of soft tissues such as arteries wherein progressive collagen recruitment and stretching upon inflation cause a pressure-dependent stiffness under static testing. Also, when assuming a pure windkessel model, the relation between SBP and DBP is determined by the change in windkessel volume and windkessel compliance (which might be pressure dependent).

Although this windkessel component is the major determinant of the relation between SBP and DBP [3], arterial hemodynamics are also determined by inertial effects that, intertwined with the elasticity of the arteries, underlie pressure wave travel and reflection [4]. Changing resistance and compliance in the simulations undoubtedly affects change in volume, but it also affects arterial wave dynamics and the relation between SBP and DBP, and thus AASI, which we think explains why AASIsym was still different from zero for the linear model simulations.

The fact that the model [5] uses a quadratic relation between pressure and stiffness is, in our opinion, not critical. This expression and the assumed constants are based on measured data and is a valid way to describe the functional behavior of a vessel over a certain range of working pressures. As can be seen from our data, simulations were within the physiological pressure range wherein we assume this expression to be valid.

To conclude, we believe that the statistical issue raised by Dr Gavish is most relevant and important and should be considered when calculating AASI, as it is the more correct approach. Our data, however, do not confirm the hypothesis that AASI is fully explained by and quantifies arterial stiffening, although – as also discussed in the original article – it does make a major contribution to AASI.

Taken together, we believe that the above considerations further discourage the use of AASI – in whatever definition – as an index of arterial stiffness. Further in-depth analysis would be required to assess how accurate AASIsym reflects arterial stiffening, to identify the potential sources of error and variability and to explore its potential use as a diagnostic tool.

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Conflicts of interest

There are no conflicts of interest.

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1. Gavish B. A model expression for the ambulatory arterial stiffness index. J Hypertens 2013; 31:209–211.
2. Kips JG, Vermeersch SJ, Reymond P, Boutouyrie P, Stergiopulos N, Laurent S, et al. Ambulatory arterial stiffness index does not accurately assess arterial stiffness. J Hypertens 2012; 30:574–580.
3. Stergiopulos N, Meister JJ, Westerhof N. Determinants of stroke volume and systolic and diastolic aortic. Am J Physiol 1996; 270:H2050–H2059.
4. Milnor WR. Hemodynamics, 2nd ed. Baltimore, Maryland: Williams & Wilkins; 1989.
5. Reymond P, Merenda F, Perren F, Ruefenacht D, Stergiopulos N. Validation of a one-dimensional model of the systemic arterial tree. Am J Physiol 2009; 297:H208–H222.
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