Effects of the shape of stenosis on the resistance to blood flow through an artery

Performance of Blood Flow with Suspension of Nanoparticles Through Tapered Stenosed Artery for Jeferey Fluid Model

This paper presents the effect of heat and mass transfer on the blood flow through a tapered stenosed artery assuming blood as a Jeffrey fluid model. The equations governing the blood flow are modeled in cylindrical coordinates. Analytical solutions are constructed for the velocity, temperature, concentration and flux by solving flow governing nonlinear coupled equations using Homotopy Perturbation Method. The important characteristics of blood flow such as concentration and temperature are found by using Homotopy Perturbation Method and these solutions are used to find exact solution for velocity profile. Variation in velocity, temperature, concentration and flux profiles for different values of thermophoresis and Brownian motion parameter are discussed. Homotopy Perturbation Method technique is used to calculate these expressions and Matlab programming is used to find computational results. And then computational results are presented graphically. The significance of the present model over the existing models has been pointed out by comparing the result with other theories both analytically and numerically. Here, in this paper, we have discussed some important phenomena raised in biotechnology and medicine at the nanoscale. So, this paper about nanoparticles behavior could be useful in the development of new diagnosis tools for many diseases in medical field, biotechnology as well as in medicine at the nanoscale.

Modeling and analysis of biomagnetic blood Carreau fluid flow through a stenosis artery with magnetic heat transfer: A transient study

We present a numerical investigation of tapered arteries that addresses the transient simulation of non-Newtonian bio-magnetic fluid dynamics (BFD) of blood through a stenosis artery in the presence of a transverse magnetic field. The current model is consistent with ferro-hydrodynamic (FHD) and magneto-hydrodynamic (MHD) principles. In the present work, blood in small arteries is analyzed using the Carreau-Yasuda model. The arterial wall is assumed to be fixed with cosine geometry for the stenosis. A parametric study was conducted to reveal the effects of the stenosis intensity and the Hartman number on a wide range of flow parameters, such as the flow velocity, temperature, and wall shear stress. Current findings are in a good agreement with recent findings in previous research studies. The results show that wall temperature control can keep the blood in its ideal blood temperature range (below 40°C) and that a severe pressure drop occurs for blockages of more than 60 percent. Additionally, with an increase in the Ha number, a velocity drop in the blood vessel is experienced.

Mathematical modelling of blood-brain barrier failure and oedema

Injuries such as traumatic brain injury and stroke can result in increased blood-brain barrier (BBB) permeability. This increase may lead to water accumulation in the brain tissue resulting in vasogenic oedema. Although the initial injury may be localized, the resulting oedema causes mechanical damage and compression of the vasculature beyond the original injury site. We employ a biphasic mixture model to investigate the consequences of BBB permeability changes within a region of brain tissue and the onset of vasogenic oedema. We find that such localized changes can indeed result in brain tissue swelling and suggest that the type of damage that results (stress damage or strain damage) depends on the ability of the brain to clear oedema fluid.

Numerical Investigation of Oxygenated and Deoxygenated Blood Flow through a Tapered Stenosed Arteries in Magnetic Field

Current paper is focused on transient modeling of blood flow through a tapered stenosed arteries surrounded a by solenoid under the presence of heat transfer. The oxygenated and deoxygenated blood are considered here by the Newtonian and Non-Newtonian fluid (power law and Carreau-Yasuda) models. The governing equations of bio magnetic fluid flow for an incompressible, laminar, homogeneous, non-Newtonian are solved by finite volume method with SIMPLE algorithm for structured grid. Both magnetization and electric current source terms are well thought-out in momentum and energy equations. The effects of fluid viscosity model, Hartmann number, and magnetic number on wall shear stress, shearing stress at the stenosis throat and maximum temperature of the system are investigated and are optimized. The current study results are in agreement with some of the existing findings in the literature and are useful in thermal and mechanical design of spatially varying magnets to control the drug delivery and biomagnetic fluid flows through tapered arteries.

Cu-blood flow model through a catheterized mild stenotic artery with a thrombosis

Copper nanoparticles blood flow analysis through a catheterized mild stenotic artery with a thrombosis is presented. The system of coupled governing equations are prescribed and then simplified under mild stenosis assumptions. The governing equations are solved exactly, and then expressions for temperature, axial velocity, stream function, wall shear stress and resistance impedance are obtained generally for metallic nanoparticles blood flow. Due to the importance of copper nanoparticles in biomedicine, the results for Cu-blood flow model are introduced. The effect of various pertinent flow and geometric parameters on copper-blood flow features in the stenotic region are illustrated and discussed through graphs for catheter and tube models. Blood trapping is introduced graphically for numerous flow parameters.

MECHANICS OF BIOLOGICAL BLOOD FLOW ANALYSIS THROUGH CURVED ARTERY WITH STENOSIS

The viscous fluid model is considered in this article for the study of blood flow through an axis-symmetric stenosis with the effect of three distinct types of arteries i.e., diverging tapering arteries, converging tapering arteries and nontapered arteries. The Cauchy–Euler method has been used for the solution to velocity profile, resistance impedance to flow and the pressure gradient. The characteristics of viscous blood flow on velocity profile, impedance resistance to flow and pressure gradient have been discussed by plotting the graphs of various flow parameters and finally it is found that stenosis dominantes the curvature of curved artery.

The Polar Fluid Model for Blood Flow through a Tapered Artery with Overlapping Stenosis: Effects of Catheter and Velocity Slip

The blood flow through an overlapping clogged tapered artery in the presence of catheter is discussed. Since cholesterol deposition is resulting in the stenosis formation, velocity slip at the arterial wall is considered. The equations governing the fluid flow have been solved analytically under the assumption of the mild stenosis. The analysis with respect to various parameters arising out of fluid and geometry considered, on physiological parameters such as impedance and wall shear stress at the maximum height of the stenosis as well as across the entire length of the stenosis has been reported. A table summarizing the locations of extreme heights and the corresponding annular radii is provided. It is observed that the wall shear stress is the same at both the locations corresponding to the maximum height of the stenosis in case of nontapered artery while it varies in case of tapered artery. It is also observed that slip velocity and diverging tapered artery facilitate the fluid flow. Shear stress at the wall is increasing as micropolar parameter is decreasing and the trend is reversed in case of coupling number. The results obtained are validated by comparing them with the experimental and theoretical results.

NUMERICAL MODELING OF PULSATILE FLOW OF BLOOD THROUGH A STENOSED TAPERED ARTERY UNDER PERIODIC BODY ACCELERATION

A mathematical model is developed for the pulsatile flow of blood through a stenosed tapered artery under the influence of externally imposed body acceleration. The artery is assumed as a cylindrical tube with time-dependent radius having mild stenosis and the non-Newtonian behavior of blood is characterized by generalized Power-law model. The governing equations are transformed by using a radial transformation and solved numerically by a suitable finite difference scheme in order to obtain the velocity, fluid acceleration, wall shear stress, and flow rate. The effect of stenosis severity, tapering, and externally imposed body acceleration on the blood flow in artery is discussed with the help of graph. It is found that all flow characteristics are affected by the stenosis severity, tapering, and periodic acceleration applied on the body.

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.

Effects of surface irregularities on flow resistance in differently shaped arterial stenoses

The combined influence of an asymmetric shape and surface irregularities has been explored in a computational study of flow through arterial stenoses with 48% areal occlusion. Contrary to the conclusion of an earlier investigation, namely that the resistance to laminar flow through a stenosed artery is being reduced in the presence of surface irregularities, the present predictions demonstrate that the flow resistance is practically unaffected by surface irregularities at low Reynolds numbers, whereas an excess pressure drop up to 10% above that for a smooth stenosis is observed for higher Reynolds numbers. For a given areal occlusion, the flow resistance is reduced with increasing degree of stenosis asymmetry and this effect may more than outweigh the influence of surface irregularities. This effect is moreover prevailing throughout the entire range of Reynolds numbers considered.

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.

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.