Disentangling Arterial Stiffness and Blood Pressure

Abstract

Vascular ageing refers to cellular and molecular mechanisms that eventually lead to vascular dysfunction, which may manifest in a variety of diseases [[1]Ungvari Z. Tarantini S. Donato A.J. Galvan V. Csiszar A. Mechanisms of Vascular Aging.Circ Res. 2018; 123: 849-867Crossref PubMed Scopus (258) Google Scholar]. One of these diseases is hypertension. Although hypertension is often interpreted as “high blood pressure”, it literally refers to the overstretching of the arteries, underscoring its close relationship to the vasculature. Indeed, (early) vascular ageing is commonly assessed by measuring arterial stiffness, often by means of the carotid-femoral pulse wave velocity (PWV) [[2]Boutouyrie P. Bruno R.M. The Clinical Significance and Application of Vascular Stiffness Measurements.Am J Hypertens. 2019; 32: 4-11Crossref PubMed Scopus (27) Google Scholar]. This PWV has shown prognostic value beyond traditional risk markers [[3]Ben-Shlomo Y. Spears M. Boustred C. May M. Anderson S.G. Benjamin E.J. et al.Aortic pulse wave velocity improves cardiovascular event prediction: an individual participant meta-analysis of prospective observational data from 17,635 subjects.J Am Coll Cardiol. 2014; 63: 636-646Crossref PubMed Scopus (1098) Google Scholar]. Regardless of whether hypertension and arterial stiffness are one another’s cause or consequence [[4]Humphrey J.D. Harrison D.G. Figueroa C.A. Lacolley P. Laurent S. Central artery stiffness in hypertension and aging: a problem with cause and consequence.Circ Res. 2016; 118: 379-381Crossref PubMed Scopus (104) Google Scholar], clinical studies remain essential to study and exploit their relationship. From an engineering point-of-view, PWV is known to acutely depend on blood pressure at the time of measurement [5Bramwell J.C. McDowall R.J.S. McSwiney B.A. The variation of arterial elasticity with blood pressure in man (part I).Proc R Soc Lond B. 1923; 94: 450-454Crossref Google Scholar, 6Gavish B. Izzo J.L. Arterial stiffness: going a step beyond.Am J Hypertens. 2016; 29: 1223-1233Crossref PubMed Scopus (50) Google Scholar, 7Spronck B. Heusinkveld M.H. Vanmolkot F.H. Roodt J.O. Hermeling E. Delhaas T. et al.Pressure-dependence of arterial stiffness: potential clinical implications.J Hypertens. 2015; 33: 330-338Crossref PubMed Scopus (87) Google Scholar]. This dependency may confound studies that aim to understand fundamentally how blood pressure affects vascular ageing. This brief editorial revisits the relationship between blood pressure and arterial stiffness, and aims to illustrate a potential pitfall in interpreting arterial stiffness measurements in relation to blood pressure.In the nineteenth century, Dutch physiologist Adriaan Isebree Moens [[8]Moens A.I. Die Pulscurve. E.J. Brill, Leiden1878Google Scholar] and mathematician Diederik Johannes Korteweg [[9]Korteweg D. Über die Fortpflanzungsgeschwindigkeit des Schalles in elastischen Röhren.Annalen der Physik. 1878; 241: 525-542Crossref Scopus (216) Google Scholar] independently showed that PWV relates to the incremental Young’s modulus (E, a material stiffness metric), wall thickness (h), inner radius (r) and blood mass density (ρ) [[10]Westerhof N. Noble M.I.M. Stergiopulos N. Westerhof B.E. Snapshots of Hemodynamics: an aid for clinical research and graduate education.3rd ed. Springer International Publishing AG, Cham, Switzerland2019Crossref Scopus (132) Google Scholar]:PWV=Eh2rρNote that, for a given artery, a sudden increase in pressure will increase radius r (distension) and decrease wall thickness h, both of which would decrease PWV with increasing pressure. However, it is the nonlinear, exponential increase in Young’s modulus E that is much stronger than these r and h changes, which causes PWV to change positively with pressure [[11]Hughes D.J. Babbs C.F. Geddes L.A. Bourland J.D. Measurements of Young's modulus of elasticity of the canine aorta with ultrasound.Ultrason Imaging. 1979; 1: 356-367Crossref PubMed Scopus (134) Google Scholar]. Importantly, this increase in PWV does not reflect a structural or material change in the artery, but rather is a consequence of its nonlinear mechanical behaviour.Besides the acute relationship between blood pressure and PWV, prolonged increased blood pressure (hypertension) may cause the arterial wall to remodel through deposition of additional wall material (increasing h) [[12]Laurent S. Boutouyrie P. The structural factor of hypertension: large and small artery alterations.Circ Res. 2015; 116: 1007-1021Crossref PubMed Scopus (263) Google Scholar] and potentially also by increasing material stiffness e.g., due to collagen cross-linking (increasing E) [[13]Aronson D. Cross-linking of glycated collagen in the pathogenesis of arterial and myocardial stiffening of aging and diabetes.J Hypertens. 2003; 21: 3-12Crossref PubMed Scopus (485) Google Scholar]. In this case, the artery per se has changed—it is now a different vessel.Note that, therefore, PWV can change 1) due to acute changes in blood pressure, as well as 2) due to long term remodelling (Figure 1A).Why is this important? Consider two imaginary cross-sectional studies on vascular ageing, in which PWV and blood pressure are measured in a range of normotensive to hypertensive subjects. In simulated study number one, the hypertension did not cause arterial remodelling; whereas in simulated study number two, it did. Figure 1C and F show simulated PWV measurements from both studies, plotted (cross-sectionally) versus blood pressure. 1Simulations are based on normally-distributed intrinsic stiffness index β0 among patients, which in study 2 was assumed to correlate with mean arterial pressure. PWV directly follows from β0 and blood pressure. Methodology and equations in Ref. [[14]Spronck B. Avolio A.P. Tan I. Butlin M. Reesink K.D. Delhaas T. Arterial stiffness index beta and cardio-ankle vascular index inherently depend on blood pressure but can be readily corrected.J Hypertens. 2017; 35: 98-104Crossref PubMed Scopus (79) Google Scholar]. Simulations are for illustration purpose only and do not contain patient data. From the resulting data, a regression model is constructed, and PWV is found to significantly and positively correlate with blood pressure (Figure 1C and F) in both studies. This correlation could be merely caused by the acute blood pressure dependency of PWV (Figure 1C), or by a combined effect of this acute dependency and arterial wall remodelling (Figure 1F). Without further information, these two interpretations cannot be distinguished, and from Figure 1C and F, one cannot tell whether the hypertensive subjects’ arteries intrinsically differ from normotensive arteries. A commonly used approach is to statistically correct PWV for blood pressure, which is illustrated in Figure 1D and G. However, this does not solve the problem, as the statistical correction will correct for (and eliminate) both acute and remodelling effects.The previous paragraph demonstrates that statistical correction of PWV for blood pressure may “throw the baby out with the bathwater”. If one is interested in whether intrinsic arterial remodelling has occurred in a patient, several options are available [[15]Spronck B. Delhaas T. Butlin M. Reesink K.D. Avolio A.P. Options for dealing with pressure dependence of pulse wave velocity as a measure of arterial stiffness: an update of Cardio-Ankle Vascular Index (CAVI) and CAVI0.Pulse (Basel). 2018; 5: 106-114Crossref PubMed Google Scholar]. Stiffness indices have been put forward that are not (or much less) acutely dependent on blood pressure. These include stiffness index β [[16]Kawasaki T. Sasayama S. Yagi S. Asakawa T. Hirai T. Non-invasive assessment of the age related changes in stiffness of major branches of the human arteries.Cardiovasc Res. 1987; 21: 678-687Crossref PubMed Scopus (549) Google Scholar] and β0 [[14]Spronck B. Avolio A.P. Tan I. Butlin M. Reesink K.D. Delhaas T. Arterial stiffness index beta and cardio-ankle vascular index inherently depend on blood pressure but can be readily corrected.J Hypertens. 2017; 35: 98-104Crossref PubMed Scopus (79) Google Scholar,[17]Hayashi K. Handa H. Nagasawa S. Okumura A. Moritake K. Stiffness and elastic behavior of human intracranial and extracranial arteries.J Biomech. 1980; 13: 175-184Crossref PubMed Scopus (470) Google Scholar], cardio-ankle vascular index (CAVI) [[18]Shirai K. Utino J. Otsuka K. Takata M. A novel blood pressure-independent arterial wall stiffness parameter; cardio-ankle vascular index (CAVI).J Atheroscler Thromb. 2006; 13: 101-107Crossref PubMed Scopus (648) Google Scholar], and CAVI0 [[14]Spronck B. Avolio A.P. Tan I. Butlin M. Reesink K.D. Delhaas T. Arterial stiffness index beta and cardio-ankle vascular index inherently depend on blood pressure but can be readily corrected.J Hypertens. 2017; 35: 98-104Crossref PubMed Scopus (79) Google Scholar]. Such indices use a mathematical model of arterial wall behaviour to capture the acute pressure dependency of PWV and correct for only this acute dependency. If in the preceding imaginary study, such a metric (β0) is used (Figure 1B), and a correlation between such metric and blood pressure is observed (Figure 1H), this can be interpreted as hypertension causing arterial remodelling. Similar mathematical models can also be used to correct PWV per se for (only) the acute blood pressure dependency, yielding a corrected PWV value (in metres per second, as opposed to a dimensionless index) [[7]Spronck B. Heusinkveld M.H. Vanmolkot F.H. Roodt J.O. Hermeling E. Delhaas T. et al.Pressure-dependence of arterial stiffness: potential clinical implications.J Hypertens. 2015; 33: 330-338Crossref PubMed Scopus (87) Google Scholar,[19]Van der Bruggen M.M. Spronck B. Bos S. Heusinkveld M.H.G. Taddei S. Ghiadoni L. et al.Pressure-corrected carotid stiffness and Young’s modulus: evaluation in an outpatient clinic setting.Am J Hypertens. 2021; ([accepted])Crossref PubMed Scopus (9) Google Scholar]. Alternatively, more experimental approaches have been used to estimate local arterial stiffness as a function of blood pressure throughout the cardiac cycle [[20]Laurent S. Caviezel B. Beck L. Girerd X. Billaud E. Boutouyrie P. et al.Carotid artery distensibility and distending pressure in hypertensive humans.Hypertension. 1994; 23: 878-883Crossref PubMed Scopus (211) Google Scholar,[21]Laurent S. Girerd X. Mourad J.J. Lacolley P. Beck L. Boutouyrie P. et al.Elastic modulus of the radial artery wall material is not increased in patients with essential hypertension.Arterioscler Thromb. 1994; 14: 1223-1231Crossref PubMed Scopus (199) Google Scholar]. Provided that the diastolic-to-systolic blood pressure ranges of all subjects at least partially overlap, a common blood pressure level can be chosen to evaluate arterial stiffness in all subjects in the study, without the need for a mathematical model. Finally, instead of using the cardiac cycle blood pressure variation, local variations in peripheral blood pressure induced by e.g., raising or lowering one’s hand have been used to characterise and subsequently correct for the blood pressure dependency of arterial stiffness [[22]Zieff G.H. Heffernan K. Stone K. Fryer S. Credeur D. Hanson E.D. et al.The pressure-dependency of local measures of arterial stiffness.J Hypertens. 2019; 37: 956-963Crossref PubMed Scopus (5) Google Scholar,[23]Chandran A. Brown D.W. Zieff G.H. Kerr Z.Y. Credeur D. Stoner L. Estimating local arterial stiffness using mixed-effects model-based residuals: a novel approach.Hypertens Res. 2021; Crossref PubMed Scopus (1) Google Scholar].In summary, in vascular ageing studies where both PWV and blood pressure differences are observed between subjects, care should be taken when interpreting results. Cross-sectional statistical regression results may suggest a relationship between arterial stiffness and blood pressure, but this may or may not be due to the acute blood pressure dependency of PWV. Distinguishing this blood pressure dependency from arterial remodelling may require more than just statistical methods.Funding SourcesThis work was supported by the European Union's Horizon 2020 research and innovation program (No 793805 ). Vascular ageing refers to cellular and molecular mechanisms that eventually lead to vascular dysfunction, which may manifest in a variety of diseases [[1]Ungvari Z. Tarantini S. Donato A.J. Galvan V. Csiszar A. Mechanisms of Vascular Aging.Circ Res. 2018; 123: 849-867Crossref PubMed Scopus (258) Google Scholar]. One of these diseases is hypertension. Although hypertension is often interpreted as “high blood pressure”, it literally refers to the overstretching of the arteries, underscoring its close relationship to the vasculature. Indeed, (early) vascular ageing is commonly assessed by measuring arterial stiffness, often by means of the carotid-femoral pulse wave velocity (PWV) [[2]Boutouyrie P. Bruno R.M. The Clinical Significance and Application of Vascular Stiffness Measurements.Am J Hypertens. 2019; 32: 4-11Crossref PubMed Scopus (27) Google Scholar]. This PWV has shown prognostic value beyond traditional risk markers [[3]Ben-Shlomo Y. Spears M. Boustred C. May M. Anderson S.G. Benjamin E.J. et al.Aortic pulse wave velocity improves cardiovascular event prediction: an individual participant meta-analysis of prospective observational data from 17,635 subjects.J Am Coll Cardiol. 2014; 63: 636-646Crossref PubMed Scopus (1098) Google Scholar]. Regardless of whether hypertension and arterial stiffness are one another’s cause or consequence [[4]Humphrey J.D. Harrison D.G. Figueroa C.A. Lacolley P. Laurent S. Central artery stiffness in hypertension and aging: a problem with cause and consequence.Circ Res. 2016; 118: 379-381Crossref PubMed Scopus (104) Google Scholar], clinical studies remain essential to study and exploit their relationship. From an engineering point-of-view, PWV is known to acutely depend on blood pressure at the time of measurement [5Bramwell J.C. McDowall R.J.S. McSwiney B.A. The variation of arterial elasticity with blood pressure in man (part I).Proc R Soc Lond B. 1923; 94: 450-454Crossref Google Scholar, 6Gavish B. Izzo J.L. Arterial stiffness: going a step beyond.Am J Hypertens. 2016; 29: 1223-1233Crossref PubMed Scopus (50) Google Scholar, 7Spronck B. Heusinkveld M.H. Vanmolkot F.H. Roodt J.O. Hermeling E. Delhaas T. et al.Pressure-dependence of arterial stiffness: potential clinical implications.J Hypertens. 2015; 33: 330-338Crossref PubMed Scopus (87) Google Scholar]. This dependency may confound studies that aim to understand fundamentally how blood pressure affects vascular ageing. This brief editorial revisits the relationship between blood pressure and arterial stiffness, and aims to illustrate a potential pitfall in interpreting arterial stiffness measurements in relation to blood pressure. In the nineteenth century, Dutch physiologist Adriaan Isebree Moens [[8]Moens A.I. Die Pulscurve. E.J. Brill, Leiden1878Google Scholar] and mathematician Diederik Johannes Korteweg [[9]Korteweg D. Über die Fortpflanzungsgeschwindigkeit des Schalles in elastischen Röhren.Annalen der Physik. 1878; 241: 525-542Crossref Scopus (216) Google Scholar] independently showed that PWV relates to the incremental Young’s modulus (E, a material stiffness metric), wall thickness (h), inner radius (r) and blood mass density (ρ) [[10]Westerhof N. Noble M.I.M. Stergiopulos N. Westerhof B.E. Snapshots of Hemodynamics: an aid for clinical research and graduate education.3rd ed. Springer International Publishing AG, Cham, Switzerland2019Crossref Scopus (132) Google Scholar]:PWV=Eh2rρ Note that, for a given artery, a sudden increase in pressure will increase radius r (distension) and decrease wall thickness h, both of which would decrease PWV with increasing pressure. However, it is the nonlinear, exponential increase in Young’s modulus E that is much stronger than these r and h changes, which causes PWV to change positively with pressure [[11]Hughes D.J. Babbs C.F. Geddes L.A. Bourland J.D. Measurements of Young's modulus of elasticity of the canine aorta with ultrasound.Ultrason Imaging. 1979; 1: 356-367Crossref PubMed Scopus (134) Google Scholar]. Importantly, this increase in PWV does not reflect a structural or material change in the artery, but rather is a consequence of its nonlinear mechanical behaviour. Besides the acute relationship between blood pressure and PWV, prolonged increased blood pressure (hypertension) may cause the arterial wall to remodel through deposition of additional wall material (increasing h) [[12]Laurent S. Boutouyrie P. The structural factor of hypertension: large and small artery alterations.Circ Res. 2015; 116: 1007-1021Crossref PubMed Scopus (263) Google Scholar] and potentially also by increasing material stiffness e.g., due to collagen cross-linking (increasing E) [[13]Aronson D. Cross-linking of glycated collagen in the pathogenesis of arterial and myocardial stiffening of aging and diabetes.J Hypertens. 2003; 21: 3-12Crossref PubMed Scopus (485) Google Scholar]. In this case, the artery per se has changed—it is now a different vessel. Note that, therefore, PWV can change 1) due to acute changes in blood pressure, as well as 2) due to long term remodelling (Figure 1A). Why is this important? Consider two imaginary cross-sectional studies on vascular ageing, in which PWV and blood pressure are measured in a range of normotensive to hypertensive subjects. In simulated study number one, the hypertension did not cause arterial remodelling; whereas in simulated study number two, it did. Figure 1C and F show simulated PWV measurements from both studies, plotted (cross-sectionally) versus blood pressure. 1Simulations are based on normally-distributed intrinsic stiffness index β0 among patients, which in study 2 was assumed to correlate with mean arterial pressure. PWV directly follows from β0 and blood pressure. Methodology and equations in Ref. [[14]Spronck B. Avolio A.P. Tan I. Butlin M. Reesink K.D. Delhaas T. Arterial stiffness index beta and cardio-ankle vascular index inherently depend on blood pressure but can be readily corrected.J Hypertens. 2017; 35: 98-104Crossref PubMed Scopus (79) Google Scholar]. Simulations are for illustration purpose only and do not contain patient data. From the resulting data, a regression model is constructed, and PWV is found to significantly and positively correlate with blood pressure (Figure 1C and F) in both studies. This correlation could be merely caused by the acute blood pressure dependency of PWV (Figure 1C), or by a combined effect of this acute dependency and arterial wall remodelling (Figure 1F). Without further information, these two interpretations cannot be distinguished, and from Figure 1C and F, one cannot tell whether the hypertensive subjects’ arteries intrinsically differ from normotensive arteries. A commonly used approach is to statistically correct PWV for blood pressure, which is illustrated in Figure 1D and G. However, this does not solve the problem, as the statistical correction will correct for (and eliminate) both acute and remodelling effects. The previous paragraph demonstrates that statistical correction of PWV for blood pressure may “throw the baby out with the bathwater”. If one is interested in whether intrinsic arterial remodelling has occurred in a patient, several options are available [[15]Spronck B. Delhaas T. Butlin M. Reesink K.D. Avolio A.P. Options for dealing with pressure dependence of pulse wave velocity as a measure of arterial stiffness: an update of Cardio-Ankle Vascular Index (CAVI) and CAVI0.Pulse (Basel). 2018; 5: 106-114Crossref PubMed Google Scholar]. Stiffness indices have been put forward that are not (or much less) acutely dependent on blood pressure. These include stiffness index β [[16]Kawasaki T. Sasayama S. Yagi S. Asakawa T. Hirai T. Non-invasive assessment of the age related changes in stiffness of major branches of the human arteries.Cardiovasc Res. 1987; 21: 678-687Crossref PubMed Scopus (549) Google Scholar] and β0 [[14]Spronck B. Avolio A.P. Tan I. Butlin M. Reesink K.D. Delhaas T. Arterial stiffness index beta and cardio-ankle vascular index inherently depend on blood pressure but can be readily corrected.J Hypertens. 2017; 35: 98-104Crossref PubMed Scopus (79) Google Scholar,[17]Hayashi K. Handa H. Nagasawa S. Okumura A. Moritake K. Stiffness and elastic behavior of human intracranial and extracranial arteries.J Biomech. 1980; 13: 175-184Crossref PubMed Scopus (470) Google Scholar], cardio-ankle vascular index (CAVI) [[18]Shirai K. Utino J. Otsuka K. Takata M. A novel blood pressure-independent arterial wall stiffness parameter; cardio-ankle vascular index (CAVI).J Atheroscler Thromb. 2006; 13: 101-107Crossref PubMed Scopus (648) Google Scholar], and CAVI0 [[14]Spronck B. Avolio A.P. Tan I. Butlin M. Reesink K.D. Delhaas T. Arterial stiffness index beta and cardio-ankle vascular index inherently depend on blood pressure but can be readily corrected.J Hypertens. 2017; 35: 98-104Crossref PubMed Scopus (79) Google Scholar]. Such indices use a mathematical model of arterial wall behaviour to capture the acute pressure dependency of PWV and correct for only this acute dependency. If in the preceding imaginary study, such a metric (β0) is used (Figure 1B), and a correlation between such metric and blood pressure is observed (Figure 1H), this can be interpreted as hypertension causing arterial remodelling. Similar mathematical models can also be used to correct PWV per se for (only) the acute blood pressure dependency, yielding a corrected PWV value (in metres per second, as opposed to a dimensionless index) [[7]Spronck B. Heusinkveld M.H. Vanmolkot F.H. Roodt J.O. Hermeling E. Delhaas T. et al.Pressure-dependence of arterial stiffness: potential clinical implications.J Hypertens. 2015; 33: 330-338Crossref PubMed Scopus (87) Google Scholar,[19]Van der Bruggen M.M. Spronck B. Bos S. Heusinkveld M.H.G. Taddei S. Ghiadoni L. et al.Pressure-corrected carotid stiffness and Young’s modulus: evaluation in an outpatient clinic setting.Am J Hypertens. 2021; ([accepted])Crossref PubMed Scopus (9) Google Scholar]. Alternatively, more experimental approaches have been used to estimate local arterial stiffness as a function of blood pressure throughout the cardiac cycle [[20]Laurent S. Caviezel B. Beck L. Girerd X. Billaud E. Boutouyrie P. et al.Carotid artery distensibility and distending pressure in hypertensive humans.Hypertension. 1994; 23: 878-883Crossref PubMed Scopus (211) Google Scholar,[21]Laurent S. Girerd X. Mourad J.J. Lacolley P. Beck L. Boutouyrie P. et al.Elastic modulus of the radial artery wall material is not increased in patients with essential hypertension.Arterioscler Thromb. 1994; 14: 1223-1231Crossref PubMed Scopus (199) Google Scholar]. Provided that the diastolic-to-systolic blood pressure ranges of all subjects at least partially overlap, a common blood pressure level can be chosen to evaluate arterial stiffness in all subjects in the study, without the need for a mathematical model. Finally, instead of using the cardiac cycle blood pressure variation, local variations in peripheral blood pressure induced by e.g., raising or lowering one’s hand have been used to characterise and subsequently correct for the blood pressure dependency of arterial stiffness [[22]Zieff G.H. Heffernan K. Stone K. Fryer S. Credeur D. Hanson E.D. et al.The pressure-dependency of local measures of arterial stiffness.J Hypertens. 2019; 37: 956-963Crossref PubMed Scopus (5) Google Scholar,[23]Chandran A. Brown D.W. Zieff G.H. Kerr Z.Y. Credeur D. Stoner L. Estimating local arterial stiffness using mixed-effects model-based residuals: a novel approach.Hypertens Res. 2021; Crossref PubMed Scopus (1) Google Scholar]. In summary, in vascular ageing studies where both PWV and blood pressure differences are observed between subjects, care should be taken when interpreting results. Cross-sectional statistical regression results may suggest a relationship between arterial stiffness and blood pressure, but this may or may not be due to the acute blood pressure dependency of PWV. Distinguishing this blood pressure dependency from arterial remodelling may require more than just statistical methods. Funding SourcesThis work was supported by the European Union's Horizon 2020 research and innovation program (No 793805 ).