Effects of multiple stenoses and poststenotic dilatation on non-Newtonian blood flow in small arteries

Fully-developed one-dimensional Casson flow through a single vessel of vary ing radius is proposed as a model of low Reynolds number blood flow in smal l stenosed coronary arteries. A formula for the resistance-to-flow ratio is derived, and results for yield stresses of tau(0) = 0, 0.005 and 0.01 Nm(- 2), viscosities of mu = 3.45 x 10(-3), 4.00 x 10(-3) and 4.55 x 10(-3) Pa.s and fluxes of 2.73 x 10(-6), x 10(-5) and x 10(-4) m(3) s(-1) are determin ed for a segment of 0.45 mm radius and 45 mm length, with 15 mm abnormaliti es at each end where the radius varies by up to +/- 0.225 mm. When tau(0) = 0.005 N m(-2), mu = 4 x 10(-3) Pa.s and Q = 1, the numerical values of the resistance-to-flow ratio vary from <(lambda)over bar> = 0.525, when the ma ximum radii of the two abnormal segments are both 0.675 mm, to <(lambda)ove r bar> = 3.06, 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 visc osity or flux decreases, and the magnitude of these alterations is greatest for yield stress and least for flux.