Analytical deduction of the instantaneous velocity distribution, wall shear stress and pressure gradient from transcutaneous measurements of the time-varying rate of blood flow

1981 ◽  
Vol 19 (4) ◽  
pp. 433-436
Author(s):  
M. F. Letelier S ◽  
H. J. Leutheusser
Keyword(s):  
Blood Flow ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Pressure Gradient ◽  
Velocity Distribution ◽  
Instantaneous Velocity ◽  
Time Varying ◽  
Wall Shear

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.

A Numerical Investigation on Pulsatile Blood Flow Through Consecutive Axi-Symmetric Stenosis in Coronary Artery

2010 ◽  
Author(s):  
Seyed Mohammad Javid Mahmoudzadeh Akherat ◽  
Morteza Kimiaghalam
Keyword(s):  
Blood Flow ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Velocity Distribution ◽  
Stress Gradient ◽  
Maximum Velocity ◽  
Distribution Patterns ◽  
Velocity Waveform ◽  
Area Reduction ◽  
Wall Shear

The objective of this research is the determination of the wall shear stress (WSS) and velocity distribution patterns in axi-symmetric single or repeated stenoses in coronary arteries. The blood flow is modeled as an incompressible laminar flow with Re = 500 and the analysis is performed for both Newtonian and non-Newtonian blood behaviors. For the single stenosis cases, the area reduction of 25%, 64% and 75% are considered, while for the consecutive stenosis cases two sets of 64%, 25%, and 75%, 64% for the first and second stenosis are examined numerically respectively. Single stenosis cases are also employed for validation purposes, since experimental data are available for them. Present results indicate that regions of high and low shear stress may play an important role in the rupture of atherosclerotic lesions. Both sides of the stenotic area with high WSS and intense WSSG (Wall Shear Stress Gradient) are the most vulnerable sites of plaques. For the cases of consecutive stenoses, results show that displacement of the secondary plauque does not have any effect on the flow pattern. Moreover, the effect of the progression and the area reduction percentage of the consecutive stenoses were studied numerically. It was concluded that the progression of the first and the second stenoses creates high alterations in WSS and velocity distribution and increases the vulnerability of creation of new plaques. Furthermore, the pulsatile property of blood was considered. An accurate velocity waveform was implemented to predict the pulsatile behavior of blood. Results significantly vary from those of the laminar analysis in terms of velocity distribution and the magnitude of the maximum velocity. The flow patterns are studied for several time sections in one period.

An Experiment on the Pulsatile Flow at Transitional Reynolds Numbers—The Fluid Dynamical Meaning of the Blood Flow Parameters in the Aorta

1993 ◽  
Vol 115 (4A) ◽  
pp. 412-417 ◽  
Author(s):  
Masahide Nakamura ◽  
Wataru Sugiyama ◽  
Manabu Haruna
Keyword(s):  
Blood Flow ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Pressure Gradient ◽  
Pulsatile Flow ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Human Aorta ◽  
Navier Stokes Equation ◽  
Wall Shear

An experiment on the fully developed sinusoidal pulsatile flow at transitional Reynolds numbers was performed to evaluate the basic characteristics of the wall shear stress. In this experiment, the wall shear stress was calculated from the measured section averaged axial velocity and the pressure gradient by using the section averaged Navier-Stokes equation. The experimental results showed that the ratio of the amplitude of the wall shear stress to the amplitude of the pressure gradient had the maximum value when the time averaged Reynolds number was about 4000 and the Womersley number was about 10. As this condition is close to the blood flow condition in the human aorta, it is suggested that the parameter of the aorta has an effect to increase the amplitude of the wall shear stress acting on the arterial wall.

Non-Newtonian Flow Patterns Associated With an Arterial Stenosis

1992 ◽  
Vol 114 (4) ◽  
pp. 512-514 ◽  
Author(s):  
X. Y. Luo ◽  
Z. B. Kuang
Keyword(s):  
Blood Flow ◽  
Shear Stress ◽  
Constitutive Equation ◽  
Wall Shear Stress ◽  
Velocity Profile ◽  
Pressure Gradient ◽  
Flow Patterns ◽  
Arterial Stenosis ◽  
Newtonian Flow ◽  
Wall Shear

A non-Newtonian constitutive equation for blood has been introduced in this paper. Using this equation, blood flow attributes such as velocity profiles, flowrate, pressure gradient, and wall shear stress in both straight and stenotic (constricted) tubes have been examined. Results showed that compared with Newtonian flow at the same flowrate, the non-Newtonian normally features larger pressure gradient, higher wall shear stress, and different velocity profile, especially in stenotic tube. In addition, the non-Newtonian stenotic flow appears to be more stable than Newtonian flow.

MATHEMATICAL MODELING OF BLOOD FLOW IN ARTERIES SUBJECT TO A VIBRATING ENVIRONMENT

2018 ◽  
Vol 18 (01) ◽  
pp. 1850001 ◽  
Author(s):  
J. C. MISRA ◽  
S. D. ADHIKARY ◽  
B. MALLICK ◽  
A. SINHA
Keyword(s):  
Blood Flow ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Pressure Gradient ◽  
Couple Stress ◽  
Harmonic Oscillation ◽  
External Pressure ◽  
Arterial Blood Flow ◽  
Arterial Blood ◽  
Wall Shear

A mathematical model has been developed in this paper with an aim to study arterial blood flow in a vibration environment. Blood is treated as a couple stress fluid. Oscillatory flow in a porous channel is considered in the study, when the flow takes place under the action of an external pressure gradient. The fluid flows between two porous plates lying parallel to each other. The fluid is considered to be injected on one plate with a constant velocity. The plates are considered to be oscillating with the same frequency in their own planes. However, the plate velocity of single-harmonic oscillation is not constant. The effects of various parameters representing couple stress, suction and magnitude of the oscillating pressure gradient on the velocity profile and wall shear stress are discussed. It is found that the presence of couple stress in the fluid enhances the velocity of the fluid in both axial and transverse directions, while a reverse phenomenon is observed for the wall shear stress.

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

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.

Alteration of Mean Wall Shear Stress Near an Oscillating Stagnation Point

1998 ◽  
Vol 120 (2) ◽  
pp. 227-237 ◽  
Author(s):  
A. L. Hazel ◽  
T. J. Pedley
Keyword(s):  
Blood Flow ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Stagnation Point ◽  
Intimal Hyperplasia ◽  
Bypass Surgery ◽  
Carotid Sinus ◽  
Time Varying ◽  
The Mean ◽  
Wall Shear

The site opposite an end-to-side anastomosis, resulting from femoral bypass surgery, and the carotid sinus are two regions well known to be prone to fibrous intimal hyperplasia or atherogenesis, respectively. The blood flow at these two sites features a stagnation point, which oscillates in strength and position. Mathematical models are used to determine some of the features of such a flow; in particular, the mean wall shear stress is calculated. The positional oscillations cause a significant change in the distribution and magnitude of the mean wall shear stress from that of the well-studied case of a stagnation point that oscillates only in strength. It is therefore proposed that the recorded effect of time dependence in the flow upon atherogenesis could still be a result of the distribution of the mean and not the time-varying components of the wall shear stress.

Basic study on estimation method of wall shear stress in common carotid artery using blood flow imaging

2020 ◽  
Vol 59 (SK) ◽  
pp. SKKE16 ◽  
Author(s):  
Ryo Nagaoka ◽  
Kazuma Ishikawa ◽  
Michiya Mozumi ◽  
Magnus Cinthio ◽  
Hideyuki Hasegawa
Keyword(s):  
Blood Flow ◽  
Shear Stress ◽  
Carotid Artery ◽  
Wall Shear Stress ◽  
Common Carotid Artery ◽  
Estimation Method ◽  
Flow Imaging ◽  
Basic Study ◽  
Blood Flow Imaging ◽  
Wall Shear

A Superposition Analysis of the Turbulent Boundary Layer in an Adverse Pressure Gradient

1951 ◽  
Vol 18 (1) ◽  
pp. 95-100
Author(s):  
Donald Ross ◽  
J. M. Robertson
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Turbulent Boundary Layer ◽  
Velocity Profile ◽  
Pressure Gradient ◽  
Adverse Pressure Gradient ◽  
Pressure Recovery ◽  
Stress Coefficient ◽  
Wall Shear

Abstract As an interim solution to the problem of the turbulent boundary layer in an adverse pressure gradient, a super-position method of analysis has been developed. In this method, the velocity profile is considered to be the result of two effects: the wall shear stress and the pressure recovery. These are superimposed, yielding an expression for the velocity profiles which approximate measured distributions. The theory also leads to a more reasonable expression for the wall shear-stress coefficient.

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