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

Numerical investigation of the non-Newtonian blood flow in a bifurcation model with a non-planar branch.

Blood Flow Modeling in Carotid Arteries with Computational Fluid Dynamics and MR Imaging

Background
Many cardiovascular diseases, such as aortic dissection, frequently occur on the aortic arch and fluid-structure interactions play an important role in the cardiovascular system. Mechanical stress is crucial in the functioning of the cardiovascular system; therefore, stress analysis is a useful tool for understanding vascular pathophysiology. The present study is concerned with the stress distribution in a layered aortic arch model with interaction between pulsatile flow and the wall of the blood vessel.

http://www.jaist.ac.jp/jinzai/Paper18/BME-paper.pdf

Stress analysis in a layered aortic arch model under pulsatile blood flow

https://www.math.upatras.gr/~stratis/Papers/LT.pdf

M.S. Moayeri

Papers

Comparison of physiological and simple pulsatile flows through stenosed arteries.

Effects of elastic property of the wall on flow characteristics through arterial stenoses