Symmetric Stenosis Research Articles

The Effect of the Non-Newtonian Behavior of Blood on Capture Efficiency of Particles in a Vessel with a Local Symmetrical Stenosis

The Effect of the Non-Newtonian Behavior of Blood on Capture Efficiency of Particles in a Vessel with a Local Symmetrical Stenosis

Effects of stenosis and aneurysm on blood flow in stenotic-aneurysmal artery

Blood is indeed a suspension of the different type of cells along with shear thinning, yield stress and viscoelastic characteristics, which can be expressed by Newtonian and a lot of non-Newtonian models. Choosing Newtonian fluid as a sample, an unsteady solver for Newtonian fluid is constructed to determine the transient flow of blood in the obscure region. In this probe, the computational unsteady flow of blood in artery with aneurysm and symmetric stenosis has been considered, which is novelty of current research. The results of this investigation can be applied to detect stenotic-aneurysmal diseases and enhance knowledge of the stenotic-aneurysmal artery, which may increase the understanding of medical science. The blood artery is modeled as a circular tube having a 0.3-m radius and a 2-m length along the horizontal axis. The velocity of blood is taken at 0.12 ms−1 so that the geometry satisfies the characteristics of the blood vessel. The governing mass and momentum equations are then solved by finite difference technique of discretization. In this research, important variations in blood pressure and velocity at stenosis and aneurysms in the artery are found. The significant influences on blood flow of the stenotic-aneurysmal artery for pressure and velocity profiles of blood are displayed graphically for the Newtonian model.

Endoscopic balloon dilation of a stenosed artery stenting via cfd tool open-foam: Physiology of angioplasty and stent placement

The blood flow analysis inside an arterial segment of the left main coronary artery having stenosis is mathematically modeled. Numerical simulations are provided for the very first time for two considered cases that cover the thorough process of angioplasty and stent placement inside a coronary artery having symmetric stenosis. Firstly, the numerical simulations are disclosed for the section of a stenosed artery having a catheter placed inside it with a balloon plus stent over it. The second case covers the numerical simulations of blood flow inside the artery after a stent is placed that keeps the artery wide open and minimizes the effect of stenosis. Thus, the prime novelty of this work entertains the thorough mathematical modeling and FVM based numerical simulations for angioplasty of a coronary artery having a symmetric shape of stenosis. The current research work is modeled for the non-Newtonian Casson fluid to consider a more realistic approach of blood flow. This computational fluid dynamics (CFD) analysis is interpreted through the free source CFD C++ toolbox Open-FOAM. Numerical solutions are provided by using Open-FOAM that works on the principle of finite volume method. The detailed graphical results are disclosed for the process of angioplasty in addition to the simulation work obtained after completion of angioplasty and stent placement. The work provided is beneficial for surgical interpretations, detecting location of stenosis, place the balloon and stent at exact location via catheter, minimizing the effect of stenosis by placing a stent inside the artery, reducing the experimental cost by using simulations data. The catheter and balloon is removed after angioplasty, and the stent keeps the artery wide open to normalize the blood flow. Eventually, the coronary artery disease (CAD) is cured through this angioplasty and the risk of a heart attack is eliminated. A more developed and easily passing blood flow is revealed after the placement of stent.

Enhancing Heat Transfer in Blood Hybrid Nanofluid Flow with Ag–TiO2 Nanoparticles and Electrical Field in a Tilted Cylindrical W-Shape Stenosis Artery: A Finite Difference Approach

The present research examines the unsteady sensitivity analysis and entropy generation of blood-based silver–titanium dioxide flow in a tilted cylindrical W-shape symmetric stenosis artery. The study considers various factors such as the electric field, joule heating, viscous dissipation, and heat source, while taking into account a two-dimensional pulsatile blood flow and periodic body acceleration. The finite difference method is employed to solve the governing equations due to the highly nonlinear nature of the flow equations, which requires a robust numerical technique. The utilization of the response surface methodology is commonly observed in optimization procedures. Drawing inspiration from drug delivery techniques used in cardiovascular therapies, it has been proposed to infuse blood with a uniform distribution of biocompatible nanoparticles. The figures depict the effects of significant parameters on the flow field, such as the electric field, Hartmann number, nanoparticle volume fraction, body acceleration amplitude, Reynolds number, Grashof number, and thermal radiation, on velocity, temperature (nondimensional), entropy generation, flow rate, resistance to flow, wall shear stress, and Nusselt number. The velocity and temperature profiles improve with higher values of the wall slip parameter. The flow rate profiles increase with an increment in wall velocity but decrease with the Womersley number. Increasing the intensity of radiation and decreasing magnetic fields both result in a decrease in the rate of heat transfer. The blood temperature is higher with the inclusion of hybrid nanoparticles than the unitary nanoparticles. The total entropy generation profiles increase for higher values of the Brickman number and temperature difference parameters. Unitary nanoparticles exhibit a slightly higher total entropy generation than hybrid nanoparticles, particularly when positioned slightly away from the center of the artery. The total entropy production decreases by 17.97% when the thermal radiation is increased from absence to 3. In contrast, increasing the amplitude of body acceleration from 0.5 to 2 results in a significant enhancement of 76.14% in the total entropy production.

CFD analysis on blood flow inside a symmetric stenosed artery: Physiology of a coronary artery disease.

This research article interprets the computational fluid dynamics analysis on blood flow inside a symmetric stenosed artery. The current problem models the blood flow inside the left coronary artery as having a symmetric stenosis in the central region. A comprehensive physiological examination of coronary artery disease is numerically evaluated by using the computational fluid dynamics toolbox Open-Field Operation And Manipulation. There are no assumptions of mild stenosis taken into account since the considered stenosis has an exactly measured length, height and position, etc. The blood flow problem is modeled for the non-Newtonian Casson fluid with unsteady, laminar, and incompressible flow assumptions. The underlying problem is solved numerically in its dimensional form. A thorough graphical analysis is provided on the blood flow simulations, pressure profile, velocity line graphs, pressure line graphs, and streamlines for the left coronary artery having a symmetric stenosis formation. The considered artery is divided into three sections, i.e. pre-stenosis, post-stenosis, and stenosis region, and the velocity and pressure line graphs are plotted for these considered regions. The graphical illustrations provide a detailed analysis of how the blood flow is affected inside the left coronary artery due to coronary artery disease. These pre- and post-stenosis velocity line graphs reveal two intriguing results: In the pre-stenosis zone, the velocity increases with increasing axial coordinate length, whereas in the post-stenosis region, the velocity decreases with rising axial coordinate length. It is evident that as the flow moves toward the stenosis region, the flow profile rises; yet, after passing through the stenosis zone, the flow profile begins to fall as the flow moves away from the stenosis region.

Investigating the effect of injection rate on the capture efficiency of nanoparticles in different geometries of stenosed vessel

In this study, the effect of injection speed on the capture efficiency (CE) of nanoparticles under the influence of a magnetic field produced by a current-carrying wire is investigated. Three scenarios have been considered for the geometry of stenosis: (1) symmetrical stenosis, (2) upper wall stenosis, and (3) lower wall stenosis. The non-Newtonian behavior of blood has been modeled using the Carreau model. The effect of different parameters, including magnetic field, drag force, particle diameter, injection speed, blood velocity, and the shape of stenosis on the CE of nanoparticles, is investigated. Considering the injection speed along with non-Newtonian model in a vessel with stenosis is not addressed yet, and are investigated in the present study. The results show that blood velocity and particle diameter have a significant effect on the CE of nanoparticles. Besides, it was revealed that there is a threshold for current intensity (I = 0.009A). At the threshold, CE of nanoparticles is maximum (27.5%), and further increase in current intensity resulting in a dramatic reduction in CE. In all scenarios, as the injection speed increases, the CE of nanoparticles decreased. For example, for scenario 3, as the injection speed increased from 75 mm/s to 200 mm/s, the CE of nanoparticles reduced from 25% to 7.5%, respectively. Besides, for same injection speed, for example 75 mm/s, the CE of scenarios 1, 2, and 3 are 3%, 22.5%, and 25%, respectively. The upper wall stenosis is desired scenario in which the maximum carrier particles are captured at tumor site.

Mathematical modeling of non-Newtonian fluid in arterial blood flow through various stenoses

Since the stenosis geometry of some cardiovascular patients cannot be described by a vertically symmetric function throughout the stenosis, so it motivates us to study the blood flow through a vertically asymmetric stenosis. In addition, we compare the flow quantities in bothvertically symmetric and asymmetric stenoses. The vertically symmetric stenosis is explained by a vertically symmetric function such as an exponential function in bell shape and a cosine function in cosine shape. The vertically asymmetric stenosis is interpreted by a vertically asymmetric function such as the combination of two different stenosis shapes. Blood is treated as a non-Newtonian fluid which is represented in the power-law model. The finite difference scheme is used to solve governing equations for obtaining the flow quantities such as axial velocity, radial velocity, flow rate, resistance to flow, and skin friction. We investigated the way that the stenosis height, stenosis length, and non-Newtonian behavior affect the flow quantities through three various stenoses. The flow quantities in the bell shape and cosine shape of stenosis show significantly different behavior. Moreover, we found that the flow quantities in the single shape (bell shape or cosine shape) have the same behavior as the flow quantities in the combined shape in the first half part, but have a slightly different behavior in the last half part.

Computational simulations of hybrid mediated nano- hemodynamics (Ag-Au/Blood) through an irregular symmetric stenosis

This article examines theoretically and numerically the unsteady two-dimensional blood flow through a diseased artery featuring an irregular stenosis. An appropriate geometric model is adopted to simulate the irregular stenotic artery. Inspired by drug delivery applications for blood vessels, the impact of hybrid nanoparticles on blood flow using a modified Tiwari-Das model is discussed. The blood is examined to have a homogenous suspension of hybrid nanoparticles. Reynolds’ viscosity model is applied in the formulation to represent the temperature dependency of blood. The two-dimensional governing conservation equations for momentum and heat transfer with buoyancy effect are simplified by considering the mild stenotic approximation. A finite-difference technique is deployed to numerically discretize the transformed non-dimensional model. Extensive graphical results for blood flow characteristics are obtained by MATLAB code. Comprehensive visualization of the effects of hemodynamic, geometric and nanoscale parameters on transport characteristics is provided. The problem is conducted for silver and silver-gold hybrid mediated blood flow models, and experimental values of blood and these biocompatible metallic nanoparticles. A comparison between silver and hybrid nanofluid is obtained which promotes the use of hybrid nanoparticles in successfully achieving clinically more beneficial results associated with nano-drug delivery in diseased hemodynamics. Enhancement in viscosity parameter induces axial flow acceleration in the stenotic region while lower thermal conductivity decreases the temperature magnitudes. Furthermore, with time variation, the pressure gradient is found to be lower in coronary arteries comparatively to femoral arteries. The simulations are relevant to transport phenomenon in nano-drug targeted delivery in haematology.

Numerical study on flow topology and hemodynamics in tortuous coronary artery with symmetrical and asymmetrical stenosis

Tortuosity in coronary artery has been found to be greatly related to the potential sites of stenosis in these last years. Many investigations have been carried out based on the tool of Computational Fluid Dynamics (CFD) mainly focusing on the influences of curved artery in blood flow. Within the limited investigations of coupling between stenosis and tortuosity, the stenosis has been considered to be located at the tortuous segment. However, with recent clinical studies, the case of stenosis occurred at non-tortuous segment before tortuosities has been confirmed which has not been paid enough attention yet. Therefore, the present study aims to investigate the disturbed streamlines and hemodynamics in curved and spiral artery considering symmetrical and asymmetrical stenosis upstream these tortuosities. Different stenosis severities, pulse rates and distances between stenosis and tortuosity as controlling parameters have been studied. The distribution of time averaged wall shear stress (TAWSS) and streamlines through tortuous segment have been displayed in order to determine the potential disease sites. Artery surface of TAWSS below critical value has been quantified as well to evaluate the risks of atherosclerosis. The results reveal that larger artery surface of TAWSS below critical value generally goes with smaller pulse rate, larger stenosis severity and distance between stenosis and tortuosity both for curved and spiral artery. However, exceptions were found in the cases of distance of 6 mm in curved artery with symmetrical stenosis and stenosis severity of 50% in spiral artery. Moreover, the spiral tortuosity tends to suppress the potential risks of atherosclerosis compared to curved tortuosity.

Laparoscopic Approach of the Obstruction of the Lower Third of the Esophagus in Children.

Objective: To review the diagnostic methodology in pediatric patients with obstruction of the lower third of the esophagus as well as minimally invasive therapeutic options. Materials and Methods: Retrospective study carried out reviewing records of children with esophageal obstruction diagnostic, from 2000 to 2018. They were divided into Group I stenosis secondary to reflux; Group II achalasia; and Group III embryonic remnants. Results: Thirty-three patients. Group I: 7; esophageal barium swallow irregular stenosis of the distal third and endoscopy irregular stenosis in 7. Treated with laparoscopic fundoplication 2, Collis Nissen 5. Group II: 22 patients, age X = 11.55 years. All with dysphagia and symmetrical stenosis of esophagogastric junction. Fifteen underwent manometry and all underwent intraoperative endoscopy. All had laparoscopic myotomy, with 2 perforations and no conversions, 2 patients had subsequent dysphagia to solids, and they did not need esophageal dilatation. Group III: 4 patients, stenosis was above esophagogastric junction. On endoscopy, inflammation was present in all 3 with irregular esophagogastric junction and difficulty passing endoscope. Three patients underwent laparoscopic resection and anastomosis. One patient leaked and developed a fistula. One patient has not been operated upon as yet. Conclusions: In those patients, the best surgical option depends upon the diagnosis. Esophageal barium studies and endoscopy allow discerning among them.

A hemodynamic model with a seepage condition and fluid-structure interactions for blood flow in arteries with symmetric stenosis.

To strengthen the detailed understanding of arterial stenosis, we construct a novel hemodynamic model. Frequently used symmetric stenosis is employed in this work. Being different from a traditional model, this numerical model adopts microcirculation resistance as an outlet boundary condition, which is called a seepage condition. Meanwhile, fluid-structure interactions are used in the numerical simulation considering the interrelationship of blood and arterial wall. Our results indicate that (i) the region upstream of stenosis experiences very high pressures during cardiac cycles, (ii) pressure drops much faster as the flow moves into the stenotic region, and (iii) high flow velocities and high shear stresses occur in the post-stenosis region. This work provides evidence that there is a strong effect of the function of microcirculation on stenosis. This contributes to evaluating potential stenotic behavior in arteries and is pivotal in guiding disease treatment.

A MATHEMATICAL MODEL TO STUDY THE EFFECT OF POROUS PARAMETER ON BLOOD FLOW THROUGH AN ATHEROSCLEROTIC ARTERIAL SEGMENT HAVING SLIP VELOCITY

This theoretical investigation focusses on blood flow through a multiple stenosed human artery under porous effects. A mathematical model is developed for estimating the effect of porous parameter on blood flow taking Harschel-Bulkley fluid model (to account for the presence of erythrocytes in plasma) and artery as circular tube with an axially non-symmetric but radially symmetric mild stenosis. The mathematical expression for the geometry of the artery with stenoses is given by the polynomial function model. The velocity slip condition is also given due weightage in the investigation. It is necessary to study the blood flow through such type of stenosis to improve the arterial system. An extensive quantitative analysis is carried out by performing large scale numerical computations of the measurable flow variables having more physiological significance. The variations of velocity profile, volumetric flow rate and pressure gradient with porous parameter are calculated numerically by developing computer codes. Their graphical representations with appropriate scientific discussions are presented at the end of the paper.

Discrete-Phase Modelling of an Asymmetric Stenosis Artery Under Different Womersley Numbers

Understanding the hemodynamics in the post-stenotic region of an asymmetric stenosis is of paramount importance in the study of atherosclerosis progression. Numerically, the analysis becomes more complex when a discrete phase is added to the continuous phase in order to understand the behaviour of atherogenic particles in a pulsatile flow environment. In the present study, discrete-phase modelling (DPM) of an asymmetric and symmetric stenosed artery models has been carried out at different Womersley numbers. The objective is to understand the correlation between the discrete-phase (atherogenic) particle behaviour with the characteristics of continuous phase (blood) under varying pulse frequencies. Continuous phase is modelled by time-averaged Navier–Stokes equations and solved by means of pressure implicit splitting of operators algorithm. DPM has been carried out with one-way coupling. The transport equations are solved in the Eulerian frame of reference, and the discrete phase is simulated in Lagrangian frame of reference. The study brings out the importance of helicity in the atherosclerosis progression. Result shows that the asymmetric stenosis model exhibits less helical flow structure and the vortical structures are not getting transported to the downstream. Consequently, the average particle residence time (PRT) of the atherogenic particles is one order higher than the symmetric stenosis model. Low PRT leads to enhanced mass transport in the arterial flow and triggers further occlusion/plaque build-up at the post-stenotic region. The extent of asymmetry in a diseased artery may be considered as a useful parameter in understanding the rate of progression of atherosclerosis.

Pulsatile flow of non-Newtonian blood fluid inside stenosed arteries: Investigating the effects of viscoelastic and elastic walls, arteriosclerosis, and polycythemia diseases

Background and objectiveIn this study, the interaction of pulsatile blood flow with the viscoelastic walls of the axisymmetric artery is numerically investigated for different severities of stenosis. The geometry of artery is modeled by an axisymmetric cylindrical tube with a symmetric stenosis in a two-dimensional case. The effects of stenosis severity on the axial velocity profile, pressure distribution, streamlines, wall shear stress, and wall radial displacement for the viscoelastic artery are also compared to the elastics artery. Furthermore, the effects of atherosclerosis and polycythemia diseases on the hemodynamics and the mechanical behavior of arterial walls are investigated. MethodsThe pulsatile flow of non-Newtonian blood is simulated inside the viscoelastic artery using the COMSOL Multiphysics software (version 5) and by employing the fluid-structure interaction (FSI) method and the arbitrary Lagrangian-Eulerian (ALE) method. Moreover, finite element method (FEM) is used to solve the governing equations on the unstructured grids. For modeling the non-Newtonian blood fluid and the viscoelastic arterial wall, the modified Casson model, and generalized Maxwell model are used, respectively. ResultsAccording to the results, with stenosis severity increasing from 25% to 75% at the time of maximum volumetric flow rate, the maximum value of axial velocity and its gradient increase 7.9 and 19.6 times, and the maximum wall shear stress of viscoelastic wall increases 24.2 times in the constriction zone. With the progression of the atherosclerosis disease (fivefold growth of arterial elastic modulus), the wall radial displacement of viscoelastic arterial walls decreases nearly 40%. ConclusionsIn this study, axial velocity profile, pressure distribution, streamlines, wall radial displacement, and wall shear stress were examined for different percentages of stenosis (25%, 50%, and 75%). The atherosclerosis disease was investigated by the fivefold growth of viscoelastic arterial elastic modulus and polycythemia disease was examined by the 21-fold increase in the yield stress of the blood fluid. Furthermore, the comparison of results between the elastic and viscoelastic arterial walls shows that the wall radial displacement for viscoelastic artery is lower than that for the elastic artery as much as 21.7% for the severe stenosis of 75%.

A two-layered suspension (particle-fluid) model for non-Newtonian fluid flow in a catheterized arterial stenosis with slip condition at the wall of stenosed artery

The primary concern of the present investigation is to study blood flow in a porous catheterized artery with an axially asymmetric and radially symmetric stenosis (constriction). In the present study, blood is characterized as a two-fluid system containing a cell-rich zone of suspension of blood cells described to be a particle-fluid suspension (Jeffrey fluid) and a cell-free plasma (Newtonian fluid) layer near the wall. The systematic expressions for flow characteristics such as fluid phase and particle phase velocities, flow rate, wall shear stress, resistive force, and frictional forces on walls of arterial stenosis and catheter are derived. It is recorded that the wall shear stress, flow resistance, and frictional forces are found to be increased with catheter size, red cell concentration, and slip parameter. When blood obeys the law of constitutive equation of a Jeffrey fluid, the flowing blood experiences lesser wall shear stress, flow resistance and frictional forces as compared to the case of blood being categorized as a Newtonian fluid. The increase in Darcy number, blood rheology as Jeffrey fluid, and the presence of peripheral plasma layer near the wall serves to reduce substantially the values of the flow characteristics (wall shear stress, flow resistance and frictional forces).

Determination of pressure data from velocity data with a view towards its application in cardiovascular mechanics. Part 2. A study of aortic valve stenosis

This paper is Part 2 of a study of blood flow across cardiovascular stenoses. In Part 1, we developed a rigorous mathematical approach for deriving a pressure field from experimental data for a velocity field that can be obtained by direct measurement. In this Part, existing methods for quantifying stenoses, with specific reference to cardiac valves, are reviewed. Using the mathematically rigorous and physically reasonable approach that we developed in Part 1, for a pre-specified flow velocity field proximal to the stenosis and pressure waveform field distal to the stenosis, we ascertain the intra-stenosis and distal flow velocity field, pressure field proximal to and within the stenosis, and energy dissipation, all as functions of position and time. The computed dissipation, kinetic energy and pressure are then presented in an idealized geometry, but relevant to a realistic geometry, with a symmetric stenosis.

Determination of pressure data from velocity data with a view towards its application in cardiovascular mechanics. Part 2: A study of aortic valve stenosis

This paper is Part 2 of a study of blood flow across cardiovascular stenoses. In Part 1, we developed a rigorous mathematical approach for deriving a pressure field from experimental data for a velocity field that can be obtained by direct measurement. In this Part, existing methods for quantifying stenoses, with specific reference to cardiac valves, are reviewed. Using the mathematically rigorous and physically accurate approach that we developed in Part 1, for a pre-specified flow velocity field proximal to the stenosis and pressure waveform field distal to the stenosis, we ascertain the intro-stenosis and distal flow velocity field, pressure field proximal and within the stenosis, and energy dissipation, all as function of position and time. The computed dissipation, kinetic energy and pressure are then presented in an idealized geometry, but with realistic geometry, with a symmetric stenosis.

English

English

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

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.

A Two-Dimensional Numerical Investigation of Transport of Malaria-Infected Red Blood Cells in Stenotic Microchannels.

The malaria-infected red blood cells experience a significant decrease in cell deformability and increase in cell membrane adhesion. Blood hemodynamics in microvessels is significantly affected by the alteration of the mechanical property as well as the aggregation of parasitized red blood cells. In this study, we aim to numerically study the connection between cell-level mechanobiological properties of human red blood cells and related malaria disease state by investigating the transport of multiple red blood cell aggregates passing through microchannels with symmetric stenosis. Effects of stenosis magnitude, aggregation strength, and cell deformability on cell rheology and flow characteristics were studied by a two-dimensional model using the fictitious domain-immersed boundary method. The results indicated that the motion and dissociation of red blood cell aggregates were influenced by these factors and the flow resistance increases with the increase of aggregating strength and cell stiffness. Further, the roughness of the velocity profile was enhanced by cell aggregation, which considerably affected the blood flow characteristics. The study may assist us in understanding cellular-level mechanisms in disease development.