Analysis of Flow Fields in a Flexible Tube with Periodic Constriction

Numerical techniques based on pressure-velocity formulation have been adopted to solve approximately, the governing equations for viscous flows through a tube (simulating an artery) with a periodic constriction. The effect of the constriction as well as the rigid of the tube, on the flow characteristics, and its consequences for arterial disease is the focus of this investigation. The unsteady incompressible Navier-Stokes equations are solved by using the finite-difference technique in staggered grid distribution. The haemodynamic factors like wall shear stress, pressure and velocity are analyzed through their graphical representations. Maximum resistance is attained in case of rigid stenosed tube rather than the flexible one. The main result is to contribute that the recirculating region is larger in case of a rigid tube than that of flexible one

Numerical Modeling of a Stenosed Artery Using Mathematical Model of Variable Shape

The intention of the present work is to carry out a systematic analysis of flow behavior in a two-dimensional tube (modeled as artery) with a locally variable shaped constrictions. The simulated artery, containing a viscous incompressible fluid representing the flowing blood, is treated to be complaint as well as rigid tube. The shape of the stenosis in the arterial lumen is chosen to be symmetric as well as asymmetric about the middle cross section perpendicular to the axis of the tube in order to improve resemblance to the in-vivo situation. The constricted tube is transformed into a straight tube and the resulting governing equations are solved by a numerical method with Reynolds number and ‘n’, a number giving the shape of the constriction as parameters. The influences of these parameters on the haemodynamic factors like wall shear stress, pressure and velocity have been analyzed. The present findings demonstrate that the flow resistance decreases as the shape of a smooth stenosis changes and maximum resistance is attained in case of a symmetric stenosis. But the length of separation increases in case of asymmetric constrictions and the oscillation in the shear layer appears earlier in case of asymmetric constriction than that in the case of symmetric constriction. Maximum resistance is attained in case of rigid stenosed tube rather than the flexible one

The effects of gravitational acceleration on micropolar fluid model of blood flow in a bifurcated stenosed artery

Gravity is a fundamental force regulating the cardiovascular system in our body. However not many previous studies on bio-fluids take into consideration of the variation of gravitational acceleration. Besides, the geometry of the bifurcated artery is chosen to be investigated since it is significant in human cardiovascular networking, where stenoses tend to form around branching junctions. Blood flow in the segment of artery is assumed to be axisymmetric, unsteady, laminar, fully developed, and two-dimensional. This research investigates the effects of gravity on micropolar fluid model of blood flow along a bifurcated artery segment which consists of a single stenosis at the parent branch. Meanwhile, to proceed with this study, blood is initially modelled as Newtonian fluid and micropolar fluid respectively in a straight stenosed artery segment. Then, the effects of gravity on Newtonian blood flow in bifurcated artery are explored. Here, a non-dimensional parameter G is introduced to describe the condition of gravity, where G is directly proportional to gravitational acceleration. The governing equations are solved numerically using the explicit finite difference method with prescribed condition of pressure and the computational algorithms are developed in Matlab software. Generally, with consideration of gravity variation, increment of gravitational acceleration causes decrement of axial velocity and increment of wall shear stress. Thus the consideration of gravity term in fluid model is necessary so that results obtained are closer to realistic conditions. Further, flow abnormalities are noticed at the branching junction from graphs of wall shear stress. This can be a crucial cause of stenosis overlapping and restenosis, which means that the structures of artery is significant in influencing blood flow patterns

A Two-layered Non-Newtonian Arterial Blood Flow through an Overlapping Constriction

The problem of blood flow through an overlapping constriction in arteries is investigated in this work. To account for the non-Newtonian behavior and the peripheral layer, blood has been represented by a two-fluid model, consisting of a core region of suspension of all the erythrocytes assumed to be a Casson fluid and a peripheral layer of plasma (Newtonian fluid). The expression for the flow characteristics, namely, the impedance, the wall shear stress, the shear stress at the stenosis throats and at the critical height of the stenosis has been derived. Moreover, we present some results concerning the dependence of these quantities on the geometrical parameters

Effect of different types of stenosis on generalized power law model of blood flow in a bifurcated artery

This study is focus on generalized power law model of blood flow in a stenosed bifurcated artery under the effect of different types of stenosis. Stenosis can cause the narrowing of the artery that may reduce the flow of blood supply to the heart, and this may lead to the heart attacks. The geometry of the bifurcated artery with different classification of stenosis locations is considered in order to shows four possible morphologies formation of plaque from healthy artery to disease artery. The bifurcated artery is modelled as a two-dimensional rigid wall since the wall of a disease artery is reported to be less flexibility. Few assumptions are considered such as blood are incompressible, laminar, steady and characterized as the generalized power-law model. Simulation results are obtained using COMSOL Multiphysics 5.2, which is a software that based on the finite element method to solve this problem. Results concerning the effect of different locations of stenosis on generalized power law model of the blood flow characteristic such as streamlines pattern are discussed

Investigation of spiral blood flow in a model of arterial stenosis

The spiral component of blood flow has both beneficial and detrimental effects in human circulatory system [Stonebridge PA, Brophy CM. Spiral laminar flow in arteries? Lancet 1991; 338: 1360–1]. We investigate the effects of the spiral blood flow in a model of three-dimensional arterial stenosis with a 75% cross-sectional area reduction at the centre by means of computational fluid dynamics (CFD) techniques. The standard κ–ω model is employed for simulation of the blood flow for the Reynolds number of 500 and 1000. We find that for Re = 500 the spiral component of the blood flow increases both the total pressure and velocity of the blood, and some significant differences are found between the wall shear stresses of the spiral and non-spiral induced flow downstream of the stenosis. The turbulent kinetic energy is reduced by the spiral flow as it induces the rotational stabilities in the forward flow. For Re = 1000 the tangential component of the blood velocity is most influenced by the spiral speed, but the effect of the spiral flow on the centreline turbulent kinetic energy and shear stress is mild. The results of the effects of the spiral flow are discussed in the paper along with the relevant pathological issues

Influence of Primary Stenosis on Secondary One and Vice Versa in case of Double Stenoses

Numerical solutions of the steady viscous flow in the neighborhood of different double stenoses are obtained under laminar flow conditions with the motivation for modeling blood flow through stenosed artery formed due to arterial disease. The flowing blood is considered to be incompressible and Newtonian. A finite volume method has been employed to solve the governing equations. The dynamics of flow features have been studied by wall pressure, streamline contour, and wall shear stress distributions for all models. The results have demonstrated that when the shapes of stenosis change at primary stenosis keeping no change in the shape of secondary stenosis, the impact of changes in primary stenosis on secondary one is noted to be more, whereas, no impact of primary stenosis on secondary stenosis and vice versa is observed in case of changes in the shapes of secondary stenosis keeping no change in the shape of primary stenosis. When Reynolds number changes, the impact of changes in primary stenosis on secondary one is also noted to be higher

Pulsatile spiral blood flow through arterial stenosis

Pulsatile spiral blood flow in a modelled three-dimensional arterial stenosis, with a 75% cross-sectional area reduction, is investigated by using numerical fluid dynamics. Two-equation k-ω model is used for the simulation of the transitional flow with Reynolds numbers 500 and 1000. It is found that the spiral component increases the static pressure in the vessel during the deceleration phase of the flow pulse. In addition, the spiral component reduces the turbulence intensity and wall shear stress found in the post-stenosis region of the vessel in the early stages of the flow pulse. Hence, the findings agree with the results of Stonebridge et al. (2004). In addition, the results of the effects of a spiral component on time-varying flow are presented and discussed along with the relevant pathological issues

Generalized power-law model of magnetohydrodynamic blood flow in an inclined stenosed artery with body acceleration

This thesis focuses on the development of a mathematical model to investigate the effect of magnetic field and body acceleration on blood flow characteristics, heat and mass transfer from a stenosed artery, a condition due to the abnormal narrowing of a blood vessel. The arterial segment is assumed to be a cylindrical tube in an inclined position with oscillating boundary condition and the stenosis taking the shape of a cosine function. The momentum equation is based on the generalized power law model which is expected to handle the variations in blood rheology as blood flows through a different-sized vessel, with the index n 1 and n = 0 describing the shear-thinning, shear-thickening and Newtonian fluid respectively. The full governing equations comprising the generalized power-law equation, heat and mass equations are non-linear partial differential equations whose numerical procedure involves the discretization of the equations using the Marker and Cell (MAC) method, where pressure along the tube is calculated iteratively using the Successive-Over-Relaxation (SOR) technique. The results have been compared and validated with existing results in certain limiting cases. New results in terms of pressure, streamlines, heat and mass distribution are obtained for various parameter values of each of the external body forces. Specifically, for a stenosis with 48% occlusion, separation is seen to occur for Newtonian fluids at Re = 1000 and this region can be seen to increase in the case of shear thickening fluids, while the shear-thinning fluid is shown to be free of separation region. Moreover, blood velocity, wall shear stress and pressure drop decrease with increase n, while heat and mass transfer increase. It is also demonstrated through the simulations that under the influence of magnetic field, the velocity in the centre of the artery and the separation region are reduced with a sufficient strength of magnetic field, depending on the severity of stenosis. For a 75% and 84% occlusion, the separation zones entirely disappear with magnetic strength 8 and 12 Tesla respectively, while the pressure drop, wall shear stress, heat and mass transfer increase. On the other hand, increasing periodic body acceleration leads to increase velocity and the pressure drop while reducing heat and mass transfer. Inclination angle increases the velocity and wall shear stress but decreases the pressure drop and heat and mass transfer. Based on the results, patients with blood vessel disease are advised not to do a high-intensity exercise; it can put extra strain on the heart leading to a risk in chest pain or even cardiac arrest. Regular exercise and suitable intensity of magnetic field could enhance vascular health

Blood Flow through a Composite Stenosis in an Artery with Permeable Wall

The present work concerns the fluid mechanical study on the effects of the permeability of the wall through an artery with a composite stenosis. The expressions for the blood flow characteristics, the flow resistance, the wall shear stress, shearing stress at the stenosis throat have been derived. Results for the effect of permeability on these flow characteristics are shown graphically and discussed briefly