The problem of non-Newtonian and nonlinear blood flow through a stenosed artery is solved numerically where the non-Newtonian rheology of the flowing blood is characterised by the generalised Power-law model. An improved shape of the time-variant 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 (moving wall), however a comparison has been made with nonlinear visco-elastic wall motion. Finite difference scheme has been used to solve the unsteady nonlinear Navier–Stokes equations in cylindrical coordinates system governing flow assuming axial symmetry under laminar flow condition so that the problem effectively becomes two-dimensional. The present analytical treatment bears the potential to calculate the rate of flow, the resistive impedance and the wall shear stress with minor significance of computational complexity by exploiting the appropriate physically realistic prescribed conditions. The model is also employed to study the effects of the taper angle, wall deformation, severity of the stenosis within its fixed length, steeper stenosis of the same severity, nonlinearity and non-Newtonian rheology of the flowing blood on the flow field. An extensive quantitative analysis is performed through numerical computations of the desired quantities having physiological relevance through their graphical representations so as to validate the applicability of the present model.

An unsteady analysis of non-Newtonian blood flow through tapered arteries with a stenosis

HemeLB: A high performance parallel lattice-Boltzmann code for large scale fluid flow in complex geometries

Analysis of 3D transient blood flow passing through an artificial aortic valve by Lattice–Boltzmann methods

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 ∼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.

Kazuko Imaeda

Papers

Analysis of non-linear pulsatile blood flow in arteries.