Wall Shear Stress Revisited

Abstract

Wall shear stress (WSS), the drag of the flowing blood exerted on the endothelial cells, is an important determinant of endothelial function, structure and gene expression. It also plays a role in atherogenesis. Based upon theory WSS is considered to be constant along the arterial tree and similar in a particular artery across species.

In vivo measurements in humans and animals, however, show that the theoretical assumptions regarding WSS and its calculation are far from valid. In humans mean WSS is higher in the common carotid artery (1.1–1.3 Pa) than in the brachial (0.4–0.5 Pa) and femoral (0.3–0.5 Pa) arteries; te latter values being substantially lower than the theoretically predicted value of 1.5 ± 50%. The lower mean WSS in these conduit arteries can be explained by the high peripheral resistance in these arteries, reducing mean volume flow and inducing reflections. In the femoral artery, adaptation of the peripheral resistance during vasodilatation results in mean WSS values close to those in the common carotid artery. Mean WSS also varies within the carotid and femoral artery bifurcations. Also in animals mean WSS varies along the arterial tree. Mean WSS was found to vary between 2.0 and 10.0 Pa in mesenteric arterioles and between 2.0 and 3.0 Pa in cremaster arterioles, the values being dependent on the site of measurement along the arteriolar tree. Across species mean WSS in a particular artery decreases linearly with increasing body mass. For example, in the descending aorta from 8.8 Pa in mice, to 7.0 Pa in rats and to 0.5 Pa in humans; the flow velocities in these artery being similar in these species.

The observation that mean WSS is far from constant along the arterial tree indicates that Murray’s cube law on flow-diameter relations in bifurcations cannot be applied to the whole arterial system. At the present state of the art, it may be concluded that the exponent of the power law varies along the arterial tree, from 2 in the major branches of the aortic arch to 3 in arterioles. The in vivo findings also imply that in in vitro investigations on endothelial gene expression and cellular adhesion the endothelial cells derived from different vascular areas or from the same artery from different species cannot be exposed to an average calculated shear stress value. The cells have to be studied under the shear stress conditions they are exposed to in real live.