Wall shear stress revisited

Abstract

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.

Keywords

• Wall shear stress
• Wall shear rate
• Velocity profiles
• Non-invasive vascular ultrasound
• Glycocalyx
• Design arterial system