Non-Newtonian Models for Blood Flow Through an Arterial Stenosis

2011 ◽  
Author(s):  
F. Kh. Tazyukov ◽  
H. A. Khalaf ◽  
Jafar M. Hassan
Keyword(s):  
Blood Flow ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Arterial Stenosis ◽  
Stenosed Artery ◽  
Two Dimensional Flow ◽  
Flow Through ◽  
Wall Shear ◽  
Volume Method

The problems of non-Newtonian blood flow through a stenosed artery are solved numerically using Finite Volume Method where the non-Newtonian rheology of the flowing blood is characterised by the Generalised Power-law, Carreau-Yasuda and Cross models. In view of the haemodynamical mechanisms related to atherosclerosis formation and the role of the wall shear stress in initiating and further developing of the disease, the investigation is focused on the two-dimensional flow field and in particular on the distribution of the wall shear stress in the vicinity of the stenosis. A comparison is made between the effects of each rheological model on the aforementioned parameters for different Re number.

scholarly journals Mathematical Modelling of Blood Flow through a Tapered Overlapping Stenosed Artery with Variable Viscosity

2014 ◽  
Vol 11 (4) ◽  
pp. 185-195 ◽  
Author(s):  
G. C. Shit ◽  
M. Roy ◽  
A. Sinha
Keyword(s):  
Magnetic Field ◽  
Blood Flow ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Pressure Gradient ◽  
Variable Viscosity ◽  
Stenosed Artery ◽  
Flow Through ◽  
Wall Shear ◽  
Analytical Expressions

This paper presents a theoretical study of blood flow through a tapered and overlapping stenosed artery under the action of an externally applied magnetic field. The fluid (blood) medium is assumed to be porous in nature. The variable viscosity of blood depending on hematocrit (percentage volume of erythrocytes) is taken into account in order to improve resemblance to the real situation. The governing equation for laminar, incompressible and Newtonian fluid subject to the boundary conditions is solved by using a well known Frobenius method. The analytical expressions for velocity component, volumetric flow rate, wall shear stress and pressure gradient are obtained. The numerical values are extracted from these analytical expressions and are presented graphically. It is observed that the influence of hematocrit, magnetic field and the shape of artery have important impact on the velocity profile, pressure gradient and wall shear stress. Moreover, the effect of primary stenosis on the secondary one has been significantly observed.

Computational Modeling of Non-Newtonian Blood Flow Through Stenosed Arteries in the Presence of Magnetic Field

2013 ◽  
Vol 135 (11) ◽  
Author(s):  
Aiman Alshare ◽  
Bourhan Tashtoush ◽  
Hossam H. El-Khalil
Keyword(s):  
Magnetic Field ◽  
Blood Flow ◽  
Shear Stress ◽  
Pressure Drop ◽  
Wall Shear Stress ◽  
Field Strength ◽  
Magnetic Field Strength ◽  
Stenosed Artery ◽  
Flow Through ◽  
Wall Shear

Steady flow simulations of blood flow in an axisymmetric stenosed artery, subjected to a static magnetic field, are performed to investigate the influence of artery size, magnetic field strength, and non-Newtonian behavior on artery wall shear stress and pressure drop in the stenosed section. It is found that wall shear stress and pressure drop increase by decreasing artery size, assuming non-Newtonian fluid, and increasing magnetic field strength. In the computations, the shear thinning behavior of blood is accounted for by the Carreau–Yasuda model. Computational results are compared and found to be inline with available experimental data.

Achievement of Pentoxifylline for Blood Flow through Stenosed Artery

2012 ◽  
Vol 13 ◽  
pp. 81-89
Author(s):  
Sapna Ratan Shah ◽  
S.U. Siddiqui
Keyword(s):  
Blood Flow ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Apparent Viscosity ◽  
Fluid Model ◽  
Plasma Viscosity ◽  
Diabetic Patients ◽  
Newtonian Viscosity ◽  
Stenosed Artery ◽  
Wall Shear

Blood-viscosity reducing drugs like “Pentoxifylline” improve blood flow by making the blood less viscous. The resistance to flow of blood in diabetic patients is higher than in non-diabetic patients. Thus diabetic patients with higher resistance to flow are more prone to high blood pressure. Therefore the resistance to blood flow in case of diabetic patients may be reduced by reducing viscosity of the plasma. Viscosity of plasma can be reducing by giving Pentoxifylline. In this paper an attempt has been made to investigate the blood flow behaviour and significance of non-Newtonian viscosity through a stenosed artery using Bingham Plastic fluid model. Numerical illustrations presented at the end of the paper provide the results for the resistance to flow, apparent viscosity and the wall shear stress through their graphical representations. It has been shown that the resistance to flow, apparent viscosity and wall shear stress increases with the size of the stenosis but these increases are comparatively small due to non-Newtonian behaviour of the blood indicating the usefulness of its rheological character in the functioning of the diseased arterial circulation.

Numerical Simulation of Blood Flow Through Stenosed Vessel

2004 ◽  
Author(s):  
Kimie Onogi ◽  
Kazuhiro Kohge ◽  
Kiyoshi Minemura
Keyword(s):  
Heart Rate ◽  
Blood Flow ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Flow Behavior ◽  
Pressure Change ◽  
Sinusoidal Waveform ◽  
Stenosed Vessel ◽  
Flow Through ◽  
Wall Shear

This article illustrates numerical results on pulsating blood flow through moderately stenosed blood vessel. Two kinds of waveform, that is, a purely sinusoidal waveform and a non-sinusoidal one just like human blood flow are calculated for two cases of heart rate as 60 and 160 (1/s), and resultant flow behavior such as flow velocities, secondary flow, wall shear stress and pressure change are discussed. The abrupt changes in the pressure and wall shear stress occur on the throat of the stenosis, suggesting that this part is easily damaged by the effects when the heart rate is increased.

scholarly journals Pulsatile Flow of a Two-Fluid Model for Blood Flow through Arterial Stenosis

2010 ◽  
Vol 2010 ◽  
pp. 1-26 ◽  
Author(s):  
D. S. Sankar
Keyword(s):  
Blood Flow ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Pulsatile Flow ◽  
Fluid Model ◽  
Core Radius ◽  
Flow Through ◽  
Wall Shear ◽  
Two Fluid Model ◽  
Two Fluid

Pulsatile flow of a two-fluid model for blood flow through stenosed narrow arteries is studied through a mathematical analysis. Blood is treated as two-phase fluid model with the suspension of all the erythrocytes in the as Herschel-Bulkley fluid and the plasma in the peripheral layer as a Newtonian fluid. Perturbation method is used to solve the system of nonlinear partial differential equations. The expressions for velocity, wall shear stress, plug core radius, flow rate and resistance to flow are obtained. The variations of these flow quantities with stenosis size, yield stress, axial distance, pulsatility and amplitude are analyzed. It is found that pressure drop, plug core radius, wall shear stress and resistance to flow increase as the yield stress or stenosis size increases while all other parameters held constant. It is observed that the percentage of increase in the magnitudes of the wall shear stress and resistance to flow over the uniform diameter tube is considerably very low for the present two-fluid model compared with that of the single-fluid model of the Herschel-Bulkley fluid. Thus, the presence of the peripheral layer helps in the functioning of the diseased arterial system.

scholarly journals Effects of Disturbed Flow on Vascular Endothelium: Pathophysiological Basis and Clinical Perspectives

2011 ◽  
Vol 91 (1) ◽  
pp. 327-387 ◽  
Author(s):  
Jeng-Jiann Chiu ◽  
Shu Chien
Keyword(s):  
Blood Flow ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Flow Patterns ◽  
Arterial Tree ◽  
Disturbed Flow ◽  
Hemodynamic Forces ◽  
Venous Diseases ◽  
Wall Shear

Vascular endothelial cells (ECs) are exposed to hemodynamic forces, which modulate EC functions and vascular biology/pathobiology in health and disease. The flow patterns and hemodynamic forces are not uniform in the vascular system. In straight parts of the arterial tree, blood flow is generally laminar and wall shear stress is high and directed; in branches and curvatures, blood flow is disturbed with nonuniform and irregular distribution of low wall shear stress. Sustained laminar flow with high shear stress upregulates expressions of EC genes and proteins that are protective against atherosclerosis, whereas disturbed flow with associated reciprocating, low shear stress generally upregulates the EC genes and proteins that promote atherogenesis. These findings have led to the concept that the disturbed flow pattern in branch points and curvatures causes the preferential localization of atherosclerotic lesions. Disturbed flow also results in postsurgical neointimal hyperplasia and contributes to pathophysiology of clinical conditions such as in-stent restenosis, vein bypass graft failure, and transplant vasculopathy, as well as aortic valve calcification. In the venous system, disturbed flow resulting from reflux, outflow obstruction, and/or stasis leads to venous inflammation and thrombosis, and hence the development of chronic venous diseases. Understanding of the effects of disturbed flow on ECs can provide mechanistic insights into the role of complex flow patterns in pathogenesis of vascular diseases and can help to elucidate the phenotypic and functional differences between quiescent (nonatherogenic/nonthrombogenic) and activated (atherogenic/thrombogenic) ECs. This review summarizes the current knowledge on the role of disturbed flow in EC physiology and pathophysiology, as well as its clinical implications. Such information can contribute to our understanding of the etiology of lesion development in vascular niches with disturbed flow and help to generate new approaches for therapeutic interventions.

scholarly journals A Physiologic Model for the Problem of Blood Flow through Diseased Blood Vessels

2016 ◽  
Vol 5 (2) ◽  
pp. 58
Author(s):  
Sapna Ratan Shah ◽  
S. U. Siddiqui
Keyword(s):  
Blood Flow ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Shape Parameter ◽  
Fluid Model ◽  
Porous Wall ◽  
Volumetric Flow Rate ◽  
Wall Model ◽  
Flow Through ◽  
Wall Shear

This study focuses on the behavior of blood flow through diseased artery in the presence of porous effects. The laminar, incompressible, fully developed, non-Newtonian in an artery having axially non-symmetric but radially symmetric stenosis is numerically studied. Here blood is represented as Herschel-Bulkley fluid model and flow model is shown by the Navier-Stokes and the continuity equations. Using appropriate boundary conditions, numerical expression for volumetric flow rate, pressure drop and wall shear stress have been derived. The expressions are computed numerically and results are presented graphically. The effects of porous parameter on wall shear stress, stenosis length, stenosis size and stenosis shape parameter are discussed. The wall shear stress increases as the porous parameter, stenosis size and stenosis length increases, but as the stenosis shape parameter increases, the wall shear stress decreases. The work shows that the results obtained from the porous wall model are significantly different from those obtained by the rigid wall model.

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