Influence of pulsatile blood flow on allometry of aortic wall shear stress

Abstract

Shear stress plays an important role in the creation and evolution of atherosclerosis. An key element for in-vivo measurements and extrapolations is the dependence of shear stress on body mass. In the case of a Poiseuille modeling of the blood flow, P. Weinberg and C. Ethier have shown that shear stress on the aortic endothelium varies like body mass to the power $-\frac{3}{8}$, and is therefore 20-fold higher in mice than in men. However, by considering a more physiological oscillating Poiseuille + Womersley combinated flow in the aorta, we show that results differ notably: at larger masses ($M>10 \ kg$) shear stress varies as body mass to the power $-\frac{1}{8}$ and modifies the man to mouse ratio to 1:8. The allometry and values of temporal gradient of shear stress also change: $\partialτ/\partial t$ varies as $M^{-3/8}$ instead of $M^{-5/8}$ at larger masses, and the 1:150 ratio from man to mouse becomes 1:61. Lastly, we show that the unsteady component of blood flow does not influence the constant allometry of peak velocity on body mass: $u_{max} \propto M^{0}$. This work extends our knowledge on the dependence of hemodynamic parameters on body mass and paves the way for a more precise extrapolation of in-vivo measurements to humans and bigger mammals.