A Study for Analyzing the Effect of Overlapping Stenosis and Dilatation on Non-Newtonian Blood Flow in an Inclined Artery

Mukesh Kumar Sharma,P R Sharma,Vinay Nasha

doi:10.4236/jbise.2016.912050

Abstract

The stenosis in the artery, which reduces the flow passage to blood, is a common cardiovascular disease that is responsible even for cardiac arrest sometimes. The hemodynaics reveals that the severe blockage in an artery due to stenosis generates pressure tangential stress that impacts adversely on the arterial wall downstream to stenosis and weakens the arterial wall. The site of weakened wall in the artery generates post stenotic dilatation. The objective of this paper is to study flow of blood, of non-Newtonian in nature described by Herschel-Bulkley model, in a diseased artery suffering with partly overlapped two stenoses and a dilatation distal to the stenoses. A mathematical model, describing the blood flow, has been derived using Navier-Stokes equations along with the prescribed geometry of the diseased artery. The expressions of velocity profile, resistive impedance to flow and wall shear stress (skin-friction) are derived. The effect of inclination of the vessel on the resistive impedance to flow is discussed along with the effect of rheological and geometrical parameters on the resistive impedance to flow and skin friction.

Highlights

The non-Newtonian effects in blood are depending on the magnitude of deformation rates; non-Newtonian effects may exist or be enhanced at low shear rates flow regimes
The objective of this paper is to study flow of blood, of non-Newtonian in nature described by Herschel-Bulkley model, in a diseased artery suffering with partly overlapped two stenoses and a dilatation distal to the stenoses
After the formation of aneurysm a gradual expansion might persist on the weakened arterial wall due to the hemodynamic forces exerted by the pulsatile flow of blood

Summary

Introduction

The non-Newtonian effects in blood are depending on the magnitude of deformation rates; non-Newtonian effects may exist or be enhanced at low shear rates flow regimes. For a given rheological model [2], the flow resistance and wall shear stress increase as the size of stenosis increases while the nonNewtonian nature of blood reduces the resistance and stress; it contributes to the body protection. The pulsatile flow of blood through partially occluded elastic arteries was discussed in [21] and observed that stenosis plays a critical role in plaque growth. The blood flow through tapered elastic artery with overlapping stenosis was studied by [22] and computed the expressions of impedance resistance to flow and wall shear stress. The aim of the present study is to investigate the effects of an overlapping stenoses and a dilatation on the flow properties and hemodynamic indicators for flow of non-Newtonian blood that described by Herschel-Bulkley model

Objectives

Results

Conclusion