Two-dimensional blood flow through tapered arteries under stenotic conditions

A mathematical model of non-linear two-dimensional blood flow in tapered arteries in the presence of stenosis is developed. An improved shape of the time-variant overlapping stenosis present in the tapered arterial lumen is given mathematically in order to update resemblance to the in vivo situation,The vascular wall deformability is taken to be elastic while the flowing blood contained in it is treated to be Newtonian. The non-linear terms appearing in the Navier-Stokes equations governing blood flow and the instantaneous taper angle are accounted for. The present analytical treatment bears the potential to calculate both the axial and the radial velocity profiles with low computational complexity by exploiting the appropriate boundary conditions and the input pressure gradient arising from the normal functioning of the heart. The computed results are found to converge at a high rate with the tolerance of similar to 10(-14) and agree well with the corresponding existing data. An extensive quantitative analysis is performed through numerical computations of the desired quantities presented graphically at the end of the paper which help estimating the effects of tapering, the wall motion, the stenosis and the pulsatile pressure gradient on the flow characteristics of blood and thereby the applicability of the present model is established. (C) 2000 Elsevier Science Ltd. All rights reserved.