Analytical Study of Non-Newtonian Reiner–Rivlin Model for Blood flow through Tapered Stenotic Artery

Stenosis, the abnormal narrowing of artery, significantly affects dynamics of blood flow due to increasing resistance to flow of blood. Velocity of blood flow, arterial pressure distribution, wall shear stress and resistance impedance factors are altered at different degree of stenosis. Prior knowledge of flow parameters such as velocity, flow rate, pressure drop in diseased artery is acknowledged to be crucial for preventive and curative medical intervention. The present paper develops the solution of Navier–Stokes equations for conservation of mass and momentum for axis-symmetric steady state case considering constitutive relation for Reiner–Rivlin fluid. Reiner–Rivlin constitutive relation renders the conservation equations non-linear partial differential equations. Few semi-analytical and numerical solutions are found to be reported in literature but no analytical solution. This has motivated the present research to obtain a closed-form solution considering Reiner–Rivlin constitutive relation. Solution yields an expression for axial velocity, which is utilized to obtain pressure gradient, resistance impedance and wall shear stress by considering volumetric flow rate as initial condition. The effect of viscosity, cross viscosity, flow rate, taper angle of artery and degree of stenosis on axial velocity, resistance impedance and wall shear stress are studied.

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Numerical Simulation of Dispersed Particle-Blood Flow in the Stenosed Coronary Arteries

International Journal of Differential Equations ◽

10.1155/2018/2593425 ◽

2018 ◽

Vol 2018 ◽

pp. 1-16 ◽

Cited By ~ 2

Author(s):

Mongkol Kaewbumrung ◽

Somsak Orankitjaroen ◽

Pichit Boonkrong ◽

Buraskorn Nuntadilok ◽

Benchawan Wiwatanapataphee

Keyword(s):

Numerical Simulation ◽

Blood Flow ◽

Shear Stress ◽

Coronary Artery ◽

Pressure Drop ◽

Wall Shear Stress ◽

Stokes Equations ◽

Spherical Shape ◽

Shear Stresses ◽

Wall Shear

A mathematical model of dispersed bioparticle-blood flow through the stenosed coronary artery under the pulsatile boundary conditions is proposed. Blood is assumed to be an incompressible non-Newtonian fluid and its flow is considered as turbulence described by the Reynolds-averaged Navier-Stokes equations. Bioparticles are assumed to be spherical shape with the same density as blood, and their translation and rotational motions are governed by Newtonian equations. Impact of particle movement on the blood velocity, the pressure distribution, and the wall shear stress distribution in three different severity degrees of stenosis including 25%, 50%, and 75% are investigated through the numerical simulation using ANSYS 18.2. Increasing degree of stenosis severity results in higher values of the pressure drop and wall shear stresses. The higher level of bioparticle motion directly varies with the pressure drop and wall shear stress. The area of coronary artery with higher density of bioparticles also presents the higher wall shear stress.

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Analysis of Flow Characteristics of the Blood Flowing through an Inclined Tapered Porous Artery with Mild Stenosis under the Influence of an Inclined Magnetic Field

Journal of Biophysics ◽

10.1155/2014/797142 ◽

2014 ◽

Vol 2014 ◽

pp. 1-9 ◽

Cited By ~ 8

Author(s):

Neetu Srivastava

Keyword(s):

Magnetic Field ◽

Blood Flow ◽

Shear Stress ◽

Wall Shear Stress ◽

Flow Rate ◽

Flow Characteristics ◽

Volumetric Flow Rate ◽

Mhd Equations ◽

Inclined Magnetic Field ◽

Wall Shear

Analytical investigation of MHD blood flow in a porous inclined stenotic artery under the influence of the inclined magnetic field has been done. Blood is considered as an electrically conducting Newtonian fluid. The physics of the problem is described by the usual MHD equations along with appropriate boundary conditions. The flow governing equations are finally transformed to nonhomogeneous second-order ordinary differential equations. This model is consistent with the principles of magnetohydrodynamics. Analytical expressions for the velocity profile, volumetric flow rate, wall shear stress, and pressure gradient have been derived. Blood flow characteristics are computed for a specific set of values of the different parameters involved in the model analysis and are presented graphically. Some of the obtained results show that the flow patterns in converging region (ξ<0), diverging region (ξ>0), and nontapered region (ξ=0) are effectively influenced by the presence of magnetic field and change in inclination of artery as well as magnetic field. There is also a significant effect of permeability on the wall shear stress as well as volumetric flow rate.

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Blood flow rate and wall shear stress in seven major cephalic arteries of humans

Journal of Anatomy ◽

10.1111/joa.13119 ◽

2019 ◽

Vol 236 (3) ◽

pp. 522-530

Author(s):

Roger S. Seymour ◽

Qiaohui Hu ◽

Edward P. Snelling

Keyword(s):

Blood Flow ◽

Shear Stress ◽

Wall Shear Stress ◽

Flow Rate ◽

Blood Flow Rate ◽

Wall Shear

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Calculation of Unsteady Flows in Curved Pipes

Journal of Fluids Engineering ◽

10.1115/1.1400748 ◽

2001 ◽

Vol 123 (4) ◽

pp. 869-877 ◽

Cited By ~ 24

Author(s):

H. A. Dwyer ◽

A. Y. Cheer ◽

T. Rutaganira ◽

N. Shacheraghi

Keyword(s):

Shear Stress ◽

Wall Shear Stress ◽

Mass Flow ◽

Numerical Solutions ◽

Stokes Equations ◽

Velocity Profiles ◽

Frequency Parameter ◽

Detailed Knowledge ◽

Curved Pipes ◽

Wall Shear

Highly unsteady three-dimensional flows in curved pipes with significant variation of flow geometry and flow parameters are studied. Using improvements in computational efficiency, detailed knowledge concerning flow structures is obtained. The numerical solutions of the Navier-Stokes equations have been obtained with a variation of the projection method, and the numerical method was enhanced by new algorithms derived from the physics of the flow. These enhancements include a prediction of the flow unsteady pressure gradient based on fluid acceleration and global pressure field corrections based on mass flow. This new method yields an order of magnitude improvement in the calculation’s efficiency, allowing the study of complex flow problems. Numerical flow simulations for oscillating flow cycles show that the curved pipe flows have a significant inviscid-like nature at high values of the frequency parameter. The shape of the velocity profiles is strongly influenced by the frequency parameter, whereas the influence of variations on the pipe cross-sectional area is shown to be rather weak. For large values of the frequency parameter the flow history strongly influences the low mass flow part of the cycle leading to highly unusual velocity profiles. The wall shear stress is studied for all the flows calculated. Our results show that wall shear stress is sensitive to area constrictions, the frequency parameter, as well as the shape of the entrance profile.

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The Effect of Slip Velocity on Unsteady Peristalsis MHD Blood Flow through a Constricted Artery Experiencing Body Acceleration

International Journal of Applied Mechanics and Engineering ◽

10.2478/ijame-2019-0040 ◽

2019 ◽

Vol 24 (3) ◽

pp. 645-659 ◽

Cited By ~ 2

Author(s):

J. Nandal ◽

S. Kumari ◽

R. Rathee

Keyword(s):

Blood Flow ◽

Shear Stress ◽

Wall Shear Stress ◽

Flow Rate ◽

Axial Velocity ◽

Slip Velocity ◽

Volumetric Flow Rate ◽

Body Acceleration ◽

Stenosed Artery ◽

Flow Through

Abstract In this analysis, we present a theoretical study to examine the combined effect of both slip velocity and periodic body acceleration on an unsteady generalized non-Newtonian blood flow through a stenosed artery with permeable wall. A constant transverse magnetic field is applied on the peristaltic flow of blood, treating it as an elastico-viscous, electrically conducting and incompressible fluid. Appropriate transformation methods are adopted to solve the unsteady non-Newtonian axially symmetric momentum equation in the cylindrical polar coordinate system with suitably prescribed conditions. To validate the applicability of the proposed analysis, analytical expressions for the axial velocity, fluid acceleration, wall shear stress and volumetric flow rate are computed and for having an adequate insight to blood flow behavior through a stenosed artery, graphs have been plotted with varying values of flow variables, to analyse the influence of the axial velocity, wall shear stress and volumetric flow rate of streaming blood.

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Two-Dimensional Meshless Numerical Modeling of the Blood Flow Within Arterial End-to-Side Distal Anastomoses

Advances in Bioengineering, Biomedical and Safety Systems ◽

10.1115/imece2006-14900 ◽

2006 ◽

Author(s):

Zaher El Zahab ◽

Eduardo A. Divo ◽

Alain J. Kassab ◽

Eric A. Mitteff

Keyword(s):

Blood Flow ◽

Shear Stress ◽

Wall Shear Stress ◽

Meshless Method ◽

Stokes Equations ◽

Computational Domain ◽

Two Dimensional ◽

Point Distribution ◽

Direct Model ◽

Wall Shear

In the current paper we introduce the localized meshless method to resolve the two-dimensional blood flow in the vicinity of a peripheral bypass graft end-to-side distal anastomosis. The goal is to incorporate this new numerical technique in extracting the values of the fluid mechanics wall parameters, such as the wall shear stress and the wall shear stress gradients, which are suggested as contributory factors to the growth of post-operative intimal hyperplasia at the anastomosis. The localized meshless method depends on the Hardy Multiquadrics radial basis function to locally expand the flow variables over a set of nodes distributed in the computational domain. An explicit scheme is adapted for the meshless formulation of the laminar incompressible Navier Stokes equations. Our special interest in the localized meshless method arises from its automated point distribution feature that significantly facilitates the pre-processing of the solution. The blood flow is simulated in three different anastomosis model geometries; the conventional or direct model, the Miller Cuff model, and the Taylor Patch model. The results of the current localized meshless numerical method show a great agreement with the results provided by a well-established finite volume method commercial software.

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Domain decomposition modeling of carotid artery stenosis based on 3D rotational angiography

Advances in Mechanical Engineering ◽

10.1177/16878140211018069 ◽

2021 ◽

Vol 13 (5) ◽

pp. 168781402110180

Author(s):

Qinghe Yao ◽

Hongkun Zhu

Keyword(s):

Blood Flow ◽

Shear Stress ◽

Carotid Artery ◽

Wall Shear Stress ◽

Domain Decomposition ◽

Stokes Equations ◽

Computational Study ◽

Domain Decomposition Method ◽

Swine Model ◽

Wall Shear

An experiment-based computational study that helps analyze blood flow behavior and wall shear stress (WSS) distribution is reported in this work. Large scale numerical analysis of hemodynamics in swine-specific stenosed carotid artery based on in vivo surgery is presented. A pressure stabilized domain decomposition method is used to symmetrize the linear systems of Navier-Stokes equations and the convection-diffusion equation. A numerical expression of swine blood flow and a detailed swine carotid vessel model with stenosis are newly proposed, and the empirical function of WSS was validated for the swine model. Two wall models, a rigid and another elastic, are compared in precisely modelling for pathological analysis of vascular disease like carotid atherosclerosis and hemangioma. The flexible wall performs better in representing experimental conditions while the stern wall is much more efficient. Numerical results show that the stenosis has a great influence on the behavior and characters of blood and its subsequent affect the WSS of the vessel; further details show how stenosis affect the distribution and magnitude of wall shear stress in an artery which lay a foundation for further medical study.

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Mathematical Modelling of Pulsatile Flow of Non-Newtonian Fluid Through a Constricted Artery

Mathematical Modelling and Engineering Problems ◽

10.18280/mmep.080320 ◽

2021 ◽

Vol 8 (3) ◽

pp. 485-491

Author(s):

Saktipada Nanda ◽

Biswadip Basu Mallik ◽

Samarpan Deb Majumder ◽

Ramesh Kumar Karthick ◽

Sagar Suman ◽

...

Keyword(s):

Blood Flow ◽

Shear Stress ◽

Wall Shear Stress ◽

Pressure Gradient ◽

Power Law ◽

Flow Rate ◽

Computational Models ◽

Research Work ◽

Flow Parameters ◽

Wall Shear

The research work explores blood flow into a stenosed artery, or one with abnormal growth within it. At the throats and at the critical height of the stenosis, mathematical and computational models have been developed to calculate the various associated parameters such as flow rate, pressure gradient, impedance, and wall shear stress. Modeling blood as a power law fluid showed the dependency of these quantities on temporal and spatial variables, as well as the frequency of the flow oscillation in time and the key parameters of the flow mechanism. The exponential curve is the geometry of the stenosis studied in this analysis. Analytical expressions for axial velocity, volumetric flow rate, pressure gradient, blood flow resistance, and shear stress have been computed and simulated in ANSYS to generate useful results with respect to variation of flow parameters with power law indices and also for comparison between Newtonian and Non- Newtonian models of blood. Upon investigation, it was found that wall shear stress (WSS) increases with stenosis depth and therefore, plays a crucial role in affecting other flow parameters. At power law index 0.6, the highest shear stress and flow velocity were encountered at approximately 7 Pa and 0.5 m/s respectively.

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Inferior vena caval hemodynamics quantified in vivo at rest and during cycling exercise using magnetic resonance imaging

AJP Heart and Circulatory Physiology ◽

10.1152/ajpheart.00641.2002 ◽

2003 ◽

Vol 284 (4) ◽

pp. H1161-H1167 ◽

Cited By ~ 50

Author(s):

Christopher P. Cheng ◽

Robert J. Herfkens ◽

Charles A. Taylor

Keyword(s):

Magnetic Resonance Imaging ◽

Blood Flow ◽

Shear Stress ◽

Magnetic Resonance ◽

Wall Shear Stress ◽

Flow Rate ◽

Inferior Vena ◽

Resonance Imaging ◽

Cycling Exercise ◽

Wall Shear

Compared with the abdominal aorta, the hemodynamic environment in the inferior vena cava (IVC) is not well described. With the use of cine phase-contrast magnetic resonance imaging (MRI) and a custom MRI-compatible cycle in an open magnet, we quantified mean blood flow rate, wall shear stress, and cross-sectional lumen area in 11 young normal subjects at the supraceliac and infrarenal levels of the aorta and IVC at rest and during dynamic cycling exercise. Similar to the aorta, the IVC experienced significant increases in blood flow and wall shear stress as a result of exercise, with greater increases in the infrarenal level compared with the supraceliac level. At the infrarenal level during resting conditions, the IVC experienced higher mean flow rate than the aorta (1.2 ± 0.5 vs. 0.9 ± 0.4 l/min, P < 0.01) and higher mean wall shear stress than the aorta (2.0 ± 0.6 vs. 1.3 ± 0.6 dyn/cm2, P < 0.005). During exercise, wall shear stress remained higher in the IVC compared with the aorta, although not significantly. It was also observed that, whereas the aorta tapers inferiorly, the IVC tapers superiorly from the infrarenal to the supraceliac location. The hemodynamic and anatomic data of the IVC acquired in this study add to our understanding of the venous circulation and may be useful in a clinical setting.

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