Effects of peripheral layer viscosity on blood flow through the artery with mild stenosis

A theoretical model for diffusion through stenosis

Stenosis is caused by an abnormal growth in the artery's lumen. This undesirable growth can change the hemodynamic characteristics of the blood flow which could be injurious to normal health. Theoretical results obtained for specific geometrics are given for the velocity distribution, pressure, wall shearing stress, and other different phenomena. Flow resistance has been shown that the wall shear decreases with decreasing peripheral layer viscosity, but these properties increase with increasing stenosis size. A two-fluid blood model with a core of micro-polar fluid and a periphery of Newtonian blood has been researched in the presence of moderate stenosis. In terms of modified Bessels functions of zero and first order, analytical equations for flow resistance, wall shear stress, and diffusion via stenosis have been found. Therefore, understanding and preventing arterial illnesses need a thorough grasp of the specific flow characteristics of a channel with restriction. The results for wall shearing stress resistance to flow and concentration profiles have been obtained and discussed with the help of graphically.

Numerical and Analytical Study of Two-Layered Unsteady Blood Flow through Catheterized Artery

The pulsatile flow of blood in a catheterized blood vessel is analyzed. The flow of blood in vessel is modeled as the flow of two immiscible fluids. The fluid in the core region is characterized as a non-Newtonian viscoelastic fluid satisfying the constitutive equation of an Oldroyd-B fluid. The fluid in the peripheral region is treated as a Newtonian fluid. The catheter inside the vessel is modeled as a rigid tube of very small radius. The resulting differential system for velocity in each region is computed numerically by finite-difference scheme and analytically by Laplace transform. A comparison of numerical solution with Laplace transform solution is carried out. Various physical quantities of interest through the computed velocity are also analyzed.

ROLE OF SLIP VELOCITY IN BLOOD FLOW THROUGH STENOSED ARTERIES: A NON-NEWTONIAN MODEL

A mathematical model is developed in this paper for studying blood flow through a stenosed arterial segment by taking into account the slip velocity at the wall of the artery. Consideration of the non-Newtonian character of blood is made, where a constitutive relation of blood is described by the Herschel–Bulkley equation. The effect of slip at the arterial wall in the presence of mild, moderate, and severe stenosis growth at the lumen of an artery is investigated. Analytical expressions for skin friction, flow resistance, and the flow rate are derived by using the model. The derived expressions are computed numerically by considering an illustrative example. The study provides an insight into the effects of slip velocity on the volumetric flow rate of blood, flow resistance, and skin friction.

THEORETICAL ANALYSIS OF BLOOD FLOW THROUGH AN ARTERIAL SEGMENT HAVING MULTIPLE STENOSES

The present paper is concerned with the study of a mathematical model for the flow of blood through a multi-stenosed artery. Blood is considered here to consist of a peripheral plasma layer which is free from red cells, and a core region which is represented by a Casson fluid. A suitable generalized geometry of multiple stenoses existing in the arterial segment under consideration is taken for the study. A thorough quantitative analysis has been made through numerical computations of the variables involved in the analysis that are of special interest in the study. The computational results are presented graphically.

MATHEMATICAL MODELING OF BLOOD FLOW THROUGH STENOSED TUBE

In the present study, blood flow in a stenosed tube is modeled. Blood is assumed to be represented by couple stress fluid. The growth projects into the lumen of the artery and blood flow is disturbed; thus, a potential coupling develops between the growth and the blood flow through the artery. An analysis of the effect of an axially symmetric growth into the lumen of a tube of constant cross-section through which a Newtonian fluid is steadily flowing is presented. The importance of the effect of slip velocity in stenosed tube is highlighted.

MATHEMATICAL MODELING OF BLOOD FLOW IN A POROUS VESSEL HAVING DOUBLE STENOSES IN THE PRESENCE OF AN EXTERNAL MAGNETIC FIELD

In this paper, a mathematical model has been developed for studying blood flow through a porous vessel with a pair of stenoses under the action of an externally applied magnetic field. Blood flowing through the artery is considered to be Newtonian. This model is consistent with the principles of ferro-hydrodynamics and magnetohydrodynamics. Expressions for the velocity profile, volumetric flow rate, wall shear stress and pressure gradient have been derived analytically under the purview of the model. The above said quantities are computed for a specific set of values of the different parameters involved in the model analysis. This serves as an illustration of the validity of the mathematical model developed here. The results estimated on the basis of the computation are presented graphically. The obtained results for different values of the parameters involved in the problem under consideration, show that the flow is appreciably influenced by the presence of magnetic field and the rise in the hematocrit level.

Suspension model for blood flow through stenotic arteries with a cell-free plasma layer

The effects of the red cell concentration, the shape of the stenosis and a peripheral layer on blood flow characteristics due to the presence of a mild stenosis, are investigated. To account for the red cell concentration and the peripheral layer, blood is represented by a two-fluid model of particle-fluid suspension, and to estimate the effect of the stenosis shape, a suitable geometry has been considered such that the axial shape of the stenosis can be changed easily just by varying a parameter (referred to as the shape parameter). It is shown that the flow resistance increases with the cell concentration but decreases with increasing shape parameter. The existence of the peripheral layer causes significant reduction in the flow resistance. The wall shear stress distribution in the stenotic region and its magnitude at the maximum height of the stenosis (i.e., at stenosis throat) possess the variations similar to the resistance to flow with respect to any parameter except the shape parameter. The latter is independent of the shape whereas the former decreases in the converging zone as the shape parameter increases while it increases in the diverging zone in a similar situation. To discuss the physiological relevance, the analytical results are used to estimate the blood flow characteristics for different diseases using the experimental data and the present theoretical approach.

Two-phase model of blood flow through stenosed tubes in the presence of a peripheral layer: applications

The effects of red cell concentration and the peripheral layer on blood flow characteristics due to the presence of a mild stenosis, are studied. It is shown that the magnitudes of the flow characteristics significantly increase with cell concentration and the peripheral layer causes marked reduction in the magnitudes of the flow characteristics. Physiological relevance and the influence of various parameters are discussed.

Particle-fluid suspension model of blood flow through stenotic vessels with applications

The present study deals with the problem of blood flow through stenotic vessels when blood is represented by a particle-fluid suspension model, i.e. a suspension of red blood cells in plasma. The expression for the dimensionless resistance to flow, the wall shear stress, and the shearing stress on the wall at the maximum height of the stenosis are derived. The results obtained in the analysis are discussed in brief, both qualitatively and quantitatively by comparison with other theories. It is observed that the magnitudes of the blood flow characteristics significantly increase with an increase in the red cell concentration. The importance of the decreasing vessel diameter is also pointed out. Finally, to observe the biological relevance of the analysis, the results obtained are used to compute the blood flow characteristics for normal and diseased blood using the experimental data from published literature and results are compared with those computed using the present theoretical approach.

Two-layered model of Casson fluid flow through stenotic blood vessels: applications to the cardiovascular system

The effects of peripheral layer viscosity on physiological characteristics of blood flow through the artery with mild stenosis have been investigated. Blood has been represented by a two-fluid model, consisting of a core region of suspension of all the erythrocytes assumed to be a Casson fluid and a peripheral layer of plasma as a Newtonian fluid. The study is based on theoretical considerations and numerical evaluations and is restricted to the flow of blood through small arteries (130-1000 microns in diameter). It has been found that the resistance to flow and the wall shear stress decrease as the peripheral layer viscosity decreases. These characteristics are found to be decreasing as peripheral layer thickness increases. The numerical results show that the existence of the peripheral layer is helpful in functioning of the diseased arterial system. The analysis has been applied to calculate the resistance to flow and wall shear stress in different blood vessels.