Effects of multiple stenoses and post-stenotic dilatation on non-Newtonian blood flow in a small arteries

Abstract

Fully-developed one-dimensional Casson flow through a single vessel of varying radius is proposed as a model of low Reynolds number blood flow in small stenosed coronary arteries. A formula for the resistance-to-flow ratio is derived, and results for yield stresses of τ0=0, 0.005 and 0.01 Nm-2, viscosities of μ=3.45×10−3, 4.00×10−3 and 4.55×10−3 Pa·s and fluxes of 2.73×10−6, ×10−5 and ×10−4 m3s−1 are determined for a segment of 0.45 mm radius and 45 mm length, with 15 mm abnormalities at each end where the radius varies by up to ±0.225 mm. When τ0=0.005 Nm-2, μ=4×10−3 Pa·s and Q=1, the numerical values of the resistance-to-flow ratio vary from[`(l)] = 0.525=0525, when the maximum radii of the two abnormal segments are both 0.675 mm, to[`(l)] = 3.06=306, when the minimum radii are both 0.225 mm. The resistance-to-flow ratio moves closer to unity as yield stress increases or as blood viscosity or flux decreases, and the magnitude of these alterations is greatest for yield stress and least for flux.