Large variations in absolute wall shear stress levels within one species and between species

Abstract 

Wall shear stress (WSS), the frictional force between blood and endothelium, is an important determinant of vascular function. It is generally assumed that WSS remains constant at a reference value of 15dyn/cm². In a study of small rodents, we realized that this assumption could not be valid. This review presents an overview of recent studies in large and small animals where shear stress was measured, derived from velocity measurements or otherwise, in large vessels.

The data show that large variations exist within a single species (human: variation of 2–16N/m²). Moreover, when we compared different species at the same location within the arterial tree, an inverse relationship between animal size and wall shear stress was noted. When we related WSS to diameter, a unique relationship was derived for all species studied.

This relationship could not be described by the well-known r³ law of Murray, but by the r² law introduced by Zamir et al. in 1972.

In summary, by comparing data from the literature, we have shown that: (i) the assumption of a physiological WSS level of ∼15dyn/cm² for all straight vessels in the arterial tree is incorrect; (ii) WSS is not constant throughout the vascular tree; (iii) WSS varies between species; (iv) WSS is inversely related to the vessel diameter. These data support an “r² law” rather than Murray's r³ law for the larger vessels in the arterial tree.

Keywords: Wall shear stress, Animal, Clinical, Patients, Mice, Mouse, Rat, Rabbit, Dog, In vivo, Human, Doppler