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

2007 ◽  
Vol 07 (03) ◽  
pp. 337-353 ◽  
Author(s):  
J. C. MISRA ◽  
G. C. SHIT
Keyword(s):  
Blood Flow ◽  
Skin Friction ◽  
Flow Rate ◽  
Slip Velocity ◽  
Flow Resistance ◽  
Volumetric Flow Rate ◽  
Flow Through ◽  
Analytical Expressions ◽  
Insight Into

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.

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

2019 ◽  
Vol 24 (3) ◽  
pp. 645-659 ◽  
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.

INFLUENCE OF SLIP VELOCITY ON BLOOD FLOW THROUGH AN ARTERY WITH PERMEABLE WALL: A THEORETICAL STUDY

2012 ◽  
Vol 05 (05) ◽  
pp. 1250042 ◽  
Author(s):  
A. SINHA ◽  
J. C. MISRA
Keyword(s):  
Reynolds Number ◽  
Blood Flow ◽  
Shear Stress ◽  
Slip Velocity ◽  
Flow Resistance ◽  
Theoretical Study ◽  
Perturbation Technique ◽  
Volumetric Flow Rate ◽  
Arterial Segment ◽  
Flow Through

A theoretical investigation concerning the influence of slip velocity on the flow of blood through an artery having its wall permeable has been carried out. Here blood is treated as a homogeneous Newtonian fluid. The flow is characterized by three parameters: β the ratio of radius to length of the arterial segment, Re the characteristic Reynolds number associated with the pressure outside the arterial segment and ϵ the filtration coefficient. The problem has been solved by the use of a perturbation technique. ϵ is considered to be very small, ensuring the validity of the perturbation method. The computed numerical results are presented graphically to depict the variations in velocity, volumetric flow rate, wall shear stress and flow resistance.

Role of chemical factors in regulation of flow through kidney, hindlimb, and heart

1965 ◽  
Vol 208 (5) ◽  
pp. 813-824 ◽  
Author(s):  
J. B. Scott ◽  
R. M. Daugherty ◽  
J. M. Dabney ◽  
F. J. Haddy
Keyword(s):  
Blood Flow ◽  
Metabolic Rate ◽  
Flow Resistance ◽  
Reactive Hyperemia ◽  
Venous Outflow ◽  
Chemical Factors ◽  
Study Support ◽  
Dog Blood ◽  
Flow Through

In the anesthetized dog, blood flow or metabolic rate was varied in kidney, hindlimb, or heart (experimental organ) while simultaneously diverting a portion of the venous outflow through forelimb or kidney (bioassay organ). The resistance to blood flow through the experimental organ gradually rose in the first few minutes following a large increase in flow and gradually fell following a large decrease in flow. Resistance to blood flow through an experimental organ (hindlimb) fell following increase in metabolic rate. In each case, bioassay organ resistance changed in the same direction when the assay organ was the forelimb and in the opposite direction when the assay organ was the kidney. These findings suggest that active hyperemia, reactive hyperemia, and autoregulation of blood flow result, at least in part, from alteration in the chemical environment of the blood vessels. Other findings in this study support the possibility that adenosine triphosphate contributes to the change in environment.

The Effect of Stenotic Geometry and Non-newtonian Property of Blood Flow through Arterial Stenosis

2020 ◽  
Vol 20 (1) ◽  
pp. 16-30
Author(s):  
Somchai Sriyab
Keyword(s):  
Mathematical Model ◽  
Blood Flow ◽  
Skin Friction ◽  
Flow Rate ◽  
Flow Behavior ◽  
Blood Flow Rate ◽  
Stenosed Artery ◽  
Flow Through ◽  
Power Law Index ◽  
Newtonian Behavior

Background: A mathematical model of blood flow is a way to study the blood flow behavior. In this research work, a mathematical model of non-Newtonian blood flow through different stenosis, namely bell shape and cosine shape, is considered. The physiologically important flow quantities of blood flow behavior to describe the blood flow phenomena are obtained such as resistance to flow, skin friction and blood flow rate. Methods: Mathematical methods are used to analyze a mathematical model of blood flow through stenosed artery. The resistance to flow, skin friction and blood flow rate were obtained to describe the blood flow in stenosis. The resistance to flow is a relation between pressure and blood flow rate while the skin friction is the friction at the artery membrane. Results: The blood flow in cosine geometry exhibits higher resistance to flow and flow rate than in the bell geometry, while the blood flow in bell geometry gives a higher skin friction than in cosine geometry. Not only the effect of stenotic geometry was studied but also the effect of stenosis depth and stenosis height on the flow quantities Moreover, the power law index was adjusted to explore the non-Newtonian behavior. When blood exhibits Newtonian behavior, the resistance to flow and skin friction decrease but the blood flow rate increases. Conclusion: The stenosed artery geometry, the stenosis length, stenosis depth and the power law index (non-Newtonian behavior) are important factors affecting the blood flow through the stenosed artery. This work provides some potential aspects to further study the causes and development of cardiovascular diseases.

scholarly journals Quantitative Monitoring of Dynamic Blood Flows Using Coflowing Laminar Streams in a Sensorless Approach

2021 ◽  
Vol 11 (16) ◽  
pp. 7260
Author(s):  
Yang Jun Kang
Keyword(s):  
Blood Flow ◽  
Flow Rate ◽  
Blood Viscosity ◽  
Measurement Errors ◽  
Present Method ◽  
Test Fluid ◽  
Constant Flow Rate ◽  
Rbc Aggregation ◽  
Sinusoidal Flow ◽  
Analytical Expressions

Determination of blood viscosity requires consistent measurement of blood flow rates, which leads to measurement errors and presents several issues when there are continuous changes in hematocrit changes. Instead of blood viscosity, a coflowing channel as a pressure sensor is adopted to quantify the dynamic flow of blood. Information on blood (i.e., hematocrit, flow rate, and viscosity) is not provided in advance. Using a discrete circuit model for the coflowing streams, the analytical expressions for four properties (i.e., pressure, shear stress, and two types of work) are then derived to quantify the flow of the test fluid. The analytical expressions are validated through numerical simulations. To demonstrate the method, the four properties are obtained using the present method by varying the flow patterns (i.e., constant flow rate or sinusoidal flow rate) as well as test fluids (i.e., glycerin solutions and blood). Thereafter, the present method is applied to quantify the dynamic flows of RBC aggregation-enhanced blood with a peristaltic pump, where any information regarding the blood is not specific. The experimental results indicate that the present method can quantify dynamic blood flow consistently, where hematocrit changes continuously over time.

scholarly journals Computational Fluid Dynamic Accuracy in Mimicking Changes in Blood Hemodynamics in Patients with Acute Type IIIb Aortic Dissection Treated with TEVAR

2018 ◽  
Vol 8 (8) ◽  
pp. 1309 ◽  
Author(s):  
Andrzej Polanczyk ◽  
Aleksandra Piechota-Polanczyk ◽  
Christoph Domenig ◽  
Josif Nanobachvili ◽  
Ihor Huk ◽  
...  
Keyword(s):  
Blood Flow ◽  
Aortic Dissection ◽  
Flow Rate ◽  
Fluid Dynamic ◽  
3D Models ◽  
Renal Arteries ◽  
Acute Type ◽  
Type Iiib ◽  
Doppler Data ◽  
Flow Through

Background: We aimed to verify the accuracy of the Computational Fluid Dynamics (CFD) algorithm for blood flow reconstruction for type IIIb aortic dissection (TBAD) before and after thoracic endovascular aortic repair (TEVAR). Methods: We made 3D models of the aorta and its branches using pre- and post-operative CT data from five patients treated for TBAD. The CFD technique was used to quantify the displacement forces acting on the aortic wall in the areas of endograft, mass flow rate/velocity and wall shear stress (WSS). Calculated results were verified with ultrasonography (USG-Doppler) data. Results: CFD results indicated that the TEVAR procedure caused a 7-fold improvement in overall blood flow through the aorta (p = 0.0001), which is in line with USG-Doppler data. A comparison of CFD results and USG-Doppler data indicated no significant change in blood flow through the analysed arteries. CFD also showed a significant increase in flow rate for thoracic trunk and renal arteries, which was in accordance with USG-Doppler data (accuracy 90% and 99.9%). Moreover, we observed a significant decrease in WSS values within the whole aorta after TEVAR compared to pre-TEVAR (1.34 ± 0.20 Pa vs. 3.80 ± 0.59 Pa, respectively, p = 0.0001). This decrease was shown by a significant reduction in WSS and WSS contours in the thoracic aorta (from 3.10 ± 0.27 Pa to 1.34 ± 0.11Pa, p = 0.043) and renal arteries (from 4.40 ± 0.25 Pa to 1.50 ± 0.22 Pa p = 0.043). Conclusions: Post-operative remodelling of the aorta after TEVAR for TBAD improved hemodynamic patterns reflected by flow, velocity and WSS with an accuracy of 99%.

Pulsatile Blood Flow Through a Constricted Porous Artery

2020 ◽  
Vol 17 (2) ◽  
pp. 743-749
Author(s):  
Salah Uddin ◽  
Obaid Ullah Mehmood ◽  
Mahathir Mohamad ◽  
Mahmod Abd Hakim Mohmad ◽  
D. F. Jamil ◽  
...  
Keyword(s):  
Reynolds Number ◽  
Blood Flow ◽  
Flow Velocity ◽  
Nonlinear Differential Equations ◽  
Fluid Velocity ◽  
Volumetric Flow Rate ◽  
Physical Parameters ◽  
Porosity Parameter ◽  
Arterial Blood ◽  
Flow Through

In this paper a speculative study of an incompressible Newtonian blood flow through a constricted porous channel and pulsatile nature is inspected. Porosity parameter λ is incorporated in the momentum equation. Governing nonlinear differential equations are numerically evaluated by employing the perturbation method technique for a very small perturbation parameter ε 1 such that ε ≠ 0 and with conformable boundary conditions. Numerical results of the flow velocity profile and volumetric flow rate have been derived numerically and detailed graphical analysis for different physical parameters porosity, Reynolds number and stenosis has been presented. It is found that arterial blood velocity is dependent upon all of these factors and that the relationship of fluid velocity and flow is more complex and nonlinear than heretofore generally believe. Furthermore the flow velocity enhanced with Reynolds number, porosity parameter and at maximum position of the stenosis/constriction.

Effect of a Surgically Created Side-to-Side Arteriovenous Fistula on Heat Elimination from the Human Hand and Forearm: Evidence for a Critical Role of Venous Resistance in Determining Fistular Flow

1978 ◽  
Vol 55 (4) ◽  
pp. 349-353
Author(s):  
W. F. M. Wallace ◽  
J. P. Jamison
Keyword(s):  
Blood Flow ◽  
Cold Stress ◽  
Arteriovenous Fistula ◽  
Flow Rate ◽  
Temperature Regulation ◽  
Critical Role ◽  
Human Hand ◽  
Superficial Vein ◽  
Heat Elimination

1. In eight patients with a unilateral fistula between the radial artery and a nearby superficial vein, heat elimination from both hand and forearm, as measured by calorimetry, was always substantially greater on the side of the fistula (mean excess from hand-plus-forearm 889 J/min). 2. Fistular blood flow measured by hand-plus-forearm plethysmography in these patients averaged 431 ml/min. Correlation between fistular blood flow and heat elimination was poor (r = 0.70, P < 0.06), probably because heat elimination due to the fistula takes place mainly from veins, whose pattern varies from patient to patient. 3. Approximately half of the total increased heat elimination due to the fistula is from the hand. Occlusion of the circulation to the hand caused fistular flow rate to be reduced by about half. This suggests that the main resistance to fistular flow is venous, proximal veins offering a similar resistance to distal veins. 4. The obligatory heat loss due to the fistula is unlikely to embarrass temperature regulation, except in severe cold stress.

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

2011 ◽  
Vol 04 (02) ◽  
pp. 207-225 ◽  
Author(s):  
J. C. MISRA ◽  
A. SINHA ◽  
G. C. SHIT
Keyword(s):  
Mathematical Modeling ◽  
Magnetic Field ◽  
Mathematical Model ◽  
Blood Flow ◽  
Shear Stress ◽  
External Magnetic Field ◽  
Volumetric Flow Rate ◽  
Hematocrit Level ◽  
Flow Through ◽  
The Mathematical Model

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.

BLOOD FLOW THROUGH A CIRCULAR PIPE WITH AN IMPULSIVE PRESSURE GRADIENT

2000 ◽  
Vol 10 (02) ◽  
pp. 187-202 ◽  
Author(s):  
GIUSEPPE PONTRELLI
Keyword(s):  
Blood Flow ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Unsteady Flow ◽  
Pressure Gradient ◽  
Collocation Method ◽  
Difference Method ◽  
Flow Through ◽  
Impulsive Pressure

The unsteady flow of a viscoelastic fluid in a straight, long, rigid pipe, driven by a suddenly imposed pressure gradient is studied. The used model is the Oldroyd-B fluid modified with the use of a nonconstant viscosity, which includes the effect of the shear-thinning of many fluids. The main application considered is in blood flow. Two coupled nonlinear equations are solved by a spectral collocation method in space and the implicit trapezoidal finite difference method in time. The presented results show the role of the non-Newtonian terms in unsteady phenomena.

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