Wall-shear-stress relaxation due to the compliant motion of arterial walls

Abstract

Our previous work demonstrated the fact that the pulsatile flow impinglng on a fixed wall could give rise to enormous wall shear stress for large frequencies. Hence it can be inferred that if the arterial blood flow includes turbulent motion at the sites of bifurcation, stenosis and bend of the vessel, high-frequency velocity components may injure the endothelial lining of the vessel and may be a possible cause of the atherogenesis at these sites. However, the actual vessel wall is by no means a fixed one, but moves, more or less, compliantly according to the intraluminal blood pressure. The present paper deals with this situation by solving the Navier-Stokes equation of motion, based on an idealized simple model, where two-dimensional pulsatile flow impinges obliquely on a plane wall oscillating normally to its own plane with common frequencies, First the solution for the unsteady flow induced by an oscillating plate on which steady flow is impinging is derived, Then, coordinate transformation of the result makes it possible to estimate the wall shear stress at the mean position of the stagnation point as a function of the common frequency, phase difference and ratio of the amplitudes of oscillation. The results are as follows: (a) The wall shear stress decreases monotonously and tends to the steady value as the frequency increases. This tendency is quite opposite to the case of an unmovable wall. (b) The wall shear stress increases monotonously with increasing phase difference and its amplitude attains a maximum at 180 degrees of difference. For 0 degree of difference which is the most compliant state, it attains a minimum. (c) The wall shear stress becomes larger as the ratio of the amplitudes of pulsating oncoming flow to oscillating wall increases. These conclusions have the physiological significance that the compliant motion of arterial walls may protect the endothelial cells from high-frequency components of turbulent motion.