Nonlinear analysis of arterial blood flow - steady streaming effect

摘要

Recent interest in the nonlinear analysis of oscillatory flow in an annular region has been motivated by the desire to apply the results of modelling to clinical medicine-especially to estimate the catheterinduced errors in blood pressure measurement. Insertion of catheters in the blood vessels brings in additional impedance or frictional resistance to flow and will alter the pressure distribution. The nonlinear analysis of Sarkar and Jayaraman (J. Biomech. 31 (1998) 781-791; Phys. Fluids 13(10) (2001) 2901-2912) provided a correction to the mean pressure drop predicted earlier by linear theory. A serious pathological condition is encountered when some blood constituents deposited on the artery wall get detached from the wall, join the blood stream again and form a clot. This can lead to partial or even complete blockage of the blood vessels. The seriousness can be very acute in the case of a stenotic artery. In this paper, the model experiment proposed by Doffin and Chagneau (J. Biomech. 14(3) (1981) 143-148) to understand such a serious situation and its repercussions in terms of vortices and separation in the flow of blood in the artery is analyzed in detail taking into account the nonlinear characteristic of the model. The mathematical treatment of the problem includes regular perturbation analysis when frequency parameter is small and matched asymptotic expansions magnifying the boundary layer characteristics near the walls when the frequency parameter is large. Important fluid dynamic parameters like wall shear stress, pressure drop and streamline patterns are discussed. (c) 2005 Published by Elsevier Ltd.