Wall shear stress as measured in vivo: consequences for the design of the arterial system

Abstract

Based upon theory, wall shear stress (WSS), an important determinant of endothelial function and gene expression, has been assumed to be constant along the arterial tree and the same in a particular artery across species. In vivo measurements of WSS, however, have shown that these assumptions are far from valid. In this survey we will discuss the assessment of WSS in the arterial system in vivo and present the results obtained in large arteries and arterioles. In vivo WSS can be estimated from wall shear rate, as derived from non-invasively recorded velocity profiles, and whole blood viscosity in large arteries and plasma viscosity in arterioles, avoiding theoretical assumptions. In large arteries velocity profiles can be recorded by means of a specially designed ultrasound system and in arterioles via optical techniques using fluorescent flow velocity tracers. It is shown that in humans mean WSS is substantially higher in the carotid artery (1.1-1.3 Pa) than in the brachial (0.4-0.5 Pa) and femoral (0.3-0.5 Pa) arteries. Also in animals mean WSS varies substantially along the arterial tree. Mean WSS in arterioles varies between about 1.0 and 5.0 Pa in the various studies and is dependent on the site of measurement in these vessels. Across species mean WSS in a particular artery decreases linearly with body mass, e.g., 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 implies that Murray's cube law on flow-diameter relations cannot be applied to the whole arterial system. Because blood flow velocity is not constant along the arterial tree either, a square law also does not hold. The exponent in the power law likely varies along the arterial system, probably from 2 in large arteries near the heart to 3 in arterioles. The in vivo findings also imply that in in vitro studies no average shear stress value can be taken to study effects on endothelial cells derived from different vascular areas or from the same artery in different species. The cells have to be studied under the shear stress conditions they are exposed to in real life.

Fig. 1

Velocity distribution in the common carotid artery of a presumed healthy volunteer. The velocities are high in the center of the artery, especially during systole, and decrease nearly linearly toward the artery wall. Note the very small velocity gradient in the center of the artery during systole

Fig. 2

Shear rate distribution in the common carotid artery of a presumed healthy volunteer, as derived from the velocity profile in Fig. 1. The shear rate is substantially higher near the wall than in the center of the artery, especially during systole. The peaks near the wall represent the maximum dv/dr as measured 250–300 μm from the wall