- Research Article
- Open access
- Published:
Wall shear stress revisited
Artery Research volume 3, pages 73–78 (2009)
Summary
In vivo measurements of wall shear stress (WSS), a determinant of endothelial cell function and gene expression, have shown that theoretical assumptions regarding WSS in the arterial system and its calculation are invalid. In humans mean WSS varies along the arterial tree and is higher in the carotid artery (1.1 – 1.3 Pa; 1 Pa = 10 dyn cm–2) than in the brachial (0.4 – 0.5 Pa) and femoral (0.3 – 0.5 Pa) arteries. Also in animals mean WSS is not constant along the arterial tree. In arterioles mean WSS varies between 2.0 and 10.0 Pa and is dependent on the site of measurement. In both arteries and arterioles, velocity profiles are flattened rather than fully developed parabolas. Across species mean WSS in a particular artery decreases linearly with increasing body mass, in the infra-renal aorta from 8.8 Pa in mice to 0.5 Pa in humans. The observation that mean WSS is far from constant along the arterial tree indicates that Murray’s cube law on flow-diameter relations cannot be applied to the whole arterial system. The exponent of the power law varies from 2 in large arteries to 3 in arterioles. The in vivo findings imply that in in vitro investigations an average calculated shear stress value cannot be used to study effects on endothelial cells derived from different vascular areas or from the same artery in different species. Sensing and transduction of shear stress are in part mediated by the endothelial glycocalyx. Therefore, modulation of shear stress sensing and transduction by altered glycocalyx properties should be considered.
References
Furchgott RF. Role of endothelium in responses of vascular smooth muscle. Circ Res 1983;53:557–73.
Pohl U, Holtz J, Busse R, Bassenge E. Crucial role of endothe-lium in the vasodilator response to increased flow in vivo. Hypertension 1986;8:37–44.
Busse R, Fleming I. Pulsatile stretch and shear stress; physical stimuli determining the production of endothelium-derived relaxing factors. J Vasc Res 1998;35:73–84.
Koller A, Huang A. Development of nitric oxide and prosta-glandin mediation of shear stress-induced arteriolar dilation with aging and hypertension. Hypertension 1999;34:1073–9.
Koller A, Kaley G. Shear stress dependent regulation of vascular resistance in health and disease: role of endothelium. Endothelium 1996;4:247–72.
Davies PF, Tripathi SC. Mechanical stress mechanisms and the cell. An endothelial paradigm. Circ Res 1993;72:239–45.
Topper JN, Gimbrone MA. Blood flow and vascular gene expression: fluid shear stress as a modulator of endothelial phenotype. Mol Med Today 1999;5:40–6.
Chien S. Molecular and mechanical bases of focal lipid accumulation in arterial wall. Prog Biophys Mol Biol 2003;83: 131–51.
Gimbrone MA, Topper JN. Biology of the vessel wall. In: Chien KR, editor. Molecular basis of cardiovascular disease. Philadelphia: Saunders; 1999. p. 331–48.
Dekker RJ, Boon RA, Rondaij MG, Kragt A, Volger OL, Elderkamp YW, et al. KLF2 provokes a gene expression pattern that establishes functional quiescent differentiation of the endothelium. Blood 2006;107:4354–63.
Parmar KM, Larman HB, Dai G, Zhang Y, Wang ET, Moorthy SN, et al. Integration of flow-dependent endothelial phenotypes by Kruppel-like factor 2. J Clin Invest 2006;116:49–58.
Himburg HA, Dowd SE, Friedman MH. Frequency-dependent response of the vascular endothelium to pulsatile shear stress. Am J Physiol Heart Circ Physiol 2007;293:H645–53.
Murray CD. The physiological principle of minimum work: II. Oxygen exchange in capillaries. Proc Natl Acad Sci U S A 1926;12:299–304.
Murray CD. The physiological principle of minimum work: I. The vascular system and the cost of blood volume. Proc Natl Acad Sci U S A 1926;12:207–14.
Kamiya A, Bukhari R, Togawa T. Adaptive regulation of wall shear stress optimizing vascular tree function. Bull Math Biol 1984;46:127–37.
Reneman RS, Arts T, Hoeks AP. Wall shear stress – an important determinant of endothelial cell function and structure – in the arterial system in vivo. Discrepancies with theory. J Vasc Res 2006;43:251–69.
Cheng C, Helderman F, Tempel D, Segers D, Hierck B, Poelmann R, et al. Large variations in absolute wall shear stress levels within one species and between species. Atherosclerosis 2007;195:225–35.
Reneman RS, Hoeks AP. Wall shear stress as measured in vivo: consequences for the design of the arterial system. Med Biol Eng Comput 2008;46:499–507.
Lipowsky HH, Kovalcheck S, Zweifach BW. The distribution of blood rheological parameters in the microvasculature of cat mesentery. Circ Res 1978;43:738–49.
Pries AR, Secomb TW, Gaethgens P. Design principles of vascular beds. Circ Res 1995;77:1017–23.
Tangelder GJ, Slaaf DW, Muijtjens AM, Arts T, oude Egbrink MG, Reneman RS. Velocity profiles of blood platelets and red blood cells flowing in arterioles of the rabbit mesentery. Circ Res 1986;59:505–14.
Reneman RS, Woldhuis B, oude Egbrink MGA, Slaaf DW, Tangelder GJ. Concentration and velocity profiles of blood cells in the microcirculation. In: Hwang NHC, Turitto VT, Yen MRT, editors. Advances in cardiovascular engineering. New York: Plenum Press; 1992. p. 25–40.
Bakker EN, Versluis JP, Sipkema P, VanTeeffelen JW, Rolf TM, Spaan JA, et al. Differential structural adaptation to haemo-dynamics along single rat cremaster arterioles. J Physiol 2003;548:549–55.
Tangelder GJ, Slaaf DW, Arts T, Reneman RS. Wall shear rate in arterioles in vivo: least estimates from platelet velocity profiles. Am J Physiol 1988;254:H1059–64.
Long DS, Smith ML, Pries AR, Ley K, Damiano ER. Micro-viscometry reveals reduced blood viscosity and altered shear rate and shear stress profiles in microvessels after hemodilu-tion. Proc Natl Acad Sci U S A 2004;101:10060–5.
Vennemann P, Kiger KT, Lindken R, Groenendijk BC, Steke-lenburg-de Vos S, ten Hagen TL, et al. In vivo micro particle image velocimetry measurements of blood-plasma in the embryonic avian heart. J Biomech 2006;39:1191–200.
Groenendijk BC, Stekelenburg-de Vos S, Vennemann P, Wladimiroff JW, Nieuwstadt FT, Lindken R, et al. The endo-thelin-1 pathway and the development of cardiovascular defects in the haemodynamically challenged chicken embryo. J Vasc Res 2008;45:54–68.
Wazer JR. Viscosity and flow measurements, in a laboratory handbook of rheology. New York: Interscience Publishers; 1963.
Broeders MA, Tangelder GJ, Slaaf DW, Reneman RS, oude Egbrink MG. Endogenous nitric oxide protects against throm-boembolism in venules but not in arterioles. Arterioscler Thromb Vasc Biol 1998;18:139e45.
Brands PJ, Hoeks APG, Hofstra L, Reneman RS. A noninvasive method to estimate wall shear rate using ultrasound. Ultrasound Med Biol 1995;21:171–85.
Hoeks APG, Samijo SK, Brands PJ, Reneman RS. Assessment of wall shear rate in humans: an ultrasound study. J Vasc Invest 1995;1:108–17.
Brands PJ, Hoeks APG, Willigers J, Willekes C, Reneman RS. An integrated system for the non-invasive assessment of vessel wall and hemodynamic properties of large arteries by means of ultrasound. Eur J Ultrasound 1999;9:257–66.
Kornet L, Hoeks AP, Lambregts J, Reneman RS. Mean wall shear stress in the femoral arterial bifurcation is low and independent of age at rest. J Vasc Res 2000;37:112–22.
Samijo SK, Willigers JM, Barkhuysen R, Kitslaar PJEHM, Reneman RS, Hoeks APG. Wall shear stress in the common carotid artery as function of age and gender. Cardiovasc Res 1998;39:515–22.
Dammers R, Tordoir JHM, Hameleers JMM, Kitslaar PJEHM, Hoeks APG. Brachial artery shear stress is independent of gender or age and does not modify vessel wall mechanical properties. Ultrasound Med Biol 2002;28:1015–22.
Kornet L, Lambregts JAC, Hoeks APG, Reneman RS. Differences in near-wall shear rate in the carotid artery within subjects are associated with different intima-media thicknesses. Arterioscler Thromb Vasc Biol 1998;18:1877–84.
Kornet L, Hoeks APG, Lambregts J, Reneman RS. In the femoral artery bifurcation differences in mean wall shear stress within subjects are associated with different intima-media thicknesses. Arterioscler Thromb Vasc Biol 1999;19:2933–9.
Greve JM, Les AS, Tang BT, Draney Blomme MT, Wilson NM, Dalman RL, et al. Allometric scaling of wall shear stress from mice to humans: quantification using cine phase-contrast MRI and computational fluid dynamics. Am J Physiol Heart Circ Physiol 2006;291:H1700–8.
Zamir M, Sinclair P, Wonnacott TH. Relation between diameter and flow in major branches of the arch of the aorta. J Biomech 1992;25:1303–10.
Li YH, Reddy AK, Taffet GE, Michael LH, Entman ML, Hartley CJ. Doppler evaluation of peripheral vascular adaptations to transverse aortic banding in mice. Ultrasound Med Biol 2003;29:1281–9.
Reneman RS, Arts T, Hoeks APG. Wall shear stress in the arterial system in vivo – assessment, results and comparison with theory. In: Yim PJ, editor. Vascular hemodynamics rounds. New York: John Wiley & Sons; 2008.
Arts T, Kruger RT, van Gerven W, Lambregts JA, Reneman RS. Propagation velocity and reflection of pressure waves in the canine coronary artery. Am J Physiol 1979;237:H469–74.
Mayrovitz HN, Roy J. Microvascular blood flow: evidence indicating a cubic dependence on arteriolar diameter. Am J Physiol 1983;245:H1031–8.
Dammers R, Stifft F, Tordoir JH, Hameleers JM, Hoeks AP, Kitslaar PJ. Shear stress depends on vascular territory: comparison between common carotid and brachial artery. J Appl Physiol 2003;94:485–9.
Vink H, Duling BR. Identification of distinct luminal domains for macromolecules, erythrocytes, and leukocytes within mammalian capillaries. Circ Res 1996;79:581–9.
Gouverneur M, Spaan JA, Pannekoek H, Fontijn RD, Vink H. Fluid shear stress stimulates incorporation of hyaluronan into endothelial cell glycocalyx. Am J Physiol Heart Circ Physiol 2006;290:H452–H8.
Reitsma S, Slaaf DW, Vink H, van Zandvoort MA, oude Egbrink MG. The endothelial glycocalyx: composition, functions, and visualization. Pflugers Arch 2007;454:345–59.
Florian JA, Kosky JR, Ainslie K, Pang Z, Dull RO, Tarbell JM. Heparan sulfate proteoglycan is a mechanosensor on endo-thelial cells. Circ Res 2003;93:e136–42.
Moon JJ, Matsumoto M, Patel S, Lee L, Guan JL, Li S. Role of cell surface heparan sulfate proteoglycans in endothelial cell migration and mechanotransduction. J Cell Physiol 2005;203:166–76.
Tarbell JM, Pahakis MY. Mechanotransduction and the glyco-calyx. J Intern Med 2006;259:339–50.
Weinbaum S, Zhang X, Han Y, Vink H, Cowin SC. Mechano-transduction and flow across the endothelial glycocalyx. Proc Natl Acad Sci U S A 2003;100:7988–95.
Smith ML, Long DS, Damiano ER, Ley K. Near-wall micro-PIV reveals a hydrodynamically relevant endothelial surface layer in venules in vivo. Biophys J 2003;85:637–45.
van den Berg BM, Spaan JA, Rolf TM, Vink H. Atherogenic region and diet diminish glycocalyx dimension and increase intima-to-media ratios at murine carotid artery bifurcation. Am J Physiol Heart Circ Physiol 2006;290:H915–20.
Mochizuki S, Vink H, Hiramatsu O, Kajita T, Shigeto F, Spaan JA, et al. Role of hyaluronic acid glycosaminoglycans in shear-induced endothelium-derived nitric oxide release. Am J Physiol Heart Circ Physiol 2003;285:H722–6.
Yao Y, Rabodzey A, Dewey Jr CF. Glycocalyx modulates the motility and proliferative response of vascular endothelium to fluid shear stress. Am J Physiol Heart Circ Physiol 2007;293: H1023–30.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
This is an open access article distributed under the CC BY-NC license. https://doi.org/creativecommons.org/licenses/by/4.0/
About this article
Cite this article
Reneman, R.S., Vink, H. & Hoeks, A.P.G. Wall shear stress revisited. Artery Res 3, 73–78 (2009). https://doi.org/10.1016/j.artres.2009.02.005
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1016/j.artres.2009.02.005