Stenosis Shape Research Articles

Computational Fluid Dynamics Analysis of Pulsatile Blood Flow Behavior in Modelled Stenosed Vessels with Different Severities

This study focuses on the behavior of blood flow in the stenosed vessels. Blood is modelled as an incompressible non‐Newtonian fluid which is based on the power law viscosity model. A numerical technique based on the finite difference method is developed to simulate the blood flow taking into account the transient periodic behaviour of the blood flow in cardiac cycles. Also, pulsatile blood flow in the stenosed vessel is based on the Womersley model, and fluid flow in the lumen region is governed by the continuity equation and the Navier‐Stokes equations. In this study, the stenosis shape is cosine by using Tu and Devil model. Comparing the results obtained from three stenosed vessels with 30%, 50%, and 75% area severity, we find that higher percent‐area severity of stenosis leads to higher extrapressure jumps and higher blood speeds around the stenosis site. Also, we observe that the size of the stenosis in stenosed vessels does influence the blood flow. A little change on the cross‐sectional value makes vast change on the blood flow rate. This simulation helps the people working in the field of physiological fluid dynamics as well as the medical practitioners.

INFLUENCE OF HEAT AND CHEMICAL REACTIONS ON HYPERBOLIC TANGENT FLUID MODEL FOR BLOOD FLOW THROUGH A TAPERED ARTERY WITH A STENOSIS

In the present article, the blood flow through a tapered artery with a stenosis is analyzed by considering axially nonsymmetric but radially symmetric mild stenosis on blood flow characteristics in the presence of heat and mass transfer, assuming the flow is steady and blood is treated as hyperbolic tangent fluid. The solution of the nonlinear equations have been obtained by employing a regular perturbation technique. Perturbation solutions have been evaluated for velocity, temperature, concentration, resistive impedance, wall shear stress, and shearing stress at the stenosis throat. The quantitative behavior of the power law index m, Weissenberg number We, stenosis shape n, Brinkman number Br, Soret number Sr and maximum height of the stenosis δ for different types of tapered arteries (i.e., converging tapering, diverging tapering, nontapered artery) has been examined through graphs.

Two-fluid model for blood flow in stenosed arteries under periodic body acceleration: a mathematical model

This study analyses the pulsatile flow of blood through narrow arteries with mild asymmetric stenosis. Blood is modeled as a two-fluid model with the suspension of all the erythrocytes in the core region being treated as Casson fluid and the plasma in the peripheral layer being assumed as Newtonian fluid. Perturbation method is used to solve the resulting coupled implicit system of non-linear partial differential equations. The expressions for shear stress, velocity, wall shear stress, plug core radius, flow rate and resistance to flow are obtained. The effects of pulsatility, stenosis shape parameter, stenosis depth, peripheral layer thickness, body acceleration and non-Newtonian behavior of blood on these flow quantities are discussed. It is noted that the plug core radius and resistance to flow decrease with the increase of the body acceleration and pressure gradient. It is observed that the velocity and flow rate increase with the increase of the peripheral layer thickness and they decrease with the increase of the stenosis shape parameter. It is recorded that the estimates of the mean flow rate of the two-fluid blood flow model are considerably higher than that of the single-fluid blood flow model. It is also noticed that the presence of body acceleration and peripheral layer influences the mean flow rate by increasing their magnitude significantly in the arteries with different radii.

A validated predictive model of coronary fractional flow reserve

Myocardial fractional flow reserve (FFR), an important index of coronary stenosis, is measured by a pressure sensor guidewire. The determination of FFR, only based on the dimensions (lumen diameters and length) of stenosis and hyperaemic coronary flow with no other ad hoc parameters, is currently not possible. We propose an analytical model derived from conservation of energy, which considers various energy losses along the length of a stenosis, i.e. convective and diffusive energy losses as well as energy loss due to sudden constriction and expansion in lumen area. In vitro (constrictions were created in isolated arteries using symmetric and asymmetric tubes as well as an inflatable occluder cuff) and in vivo (constrictions were induced in coronary arteries of eight swine by an occluder cuff) experiments were used to validate the proposed analytical model. The proposed model agreed well with the experimental measurements. A least-squares fit showed a linear relation as (Δp or FFR)(experiment) = a(Δp or FFR)(theory) + b, where a and b were 1.08 and -1.15 mmHg (r(2) = 0.99) for in vitro Δp, 0.96 and 1.79 mmHg (r(2) = 0.75) for in vivo Δp, and 0.85 and 0.1 (r(2) = 0.7) for FFR. Flow pulsatility and stenosis shape (e.g. eccentricity, exit angle divergence, etc.) had a negligible effect on myocardial FFR, while the entrance effect in a coronary stenosis was found to contribute significantly to the pressure drop. We present a physics-based experimentally validated analytical model of coronary stenosis, which allows prediction of FFR based on stenosis dimensions and hyperaemic coronary flow with no empirical parameters.

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.

Influence of different bell-shaped stenoses on the progression of the disease, atherosclerosis

In the present paper, the effect of symmetrical and asymmetrical bell-shaped stenoses on wall pressure drop, streamline contour, and rise in wall shear stress for the progression of the disease, atherosclerosis has been investigated numerically. The governing equations have been solved by finite volume method. Both steady and pulsatile flow at inlet is considered in our study. It is revealed from the study that the impact of wall pressure and peak wall shear stress on progression of disease are always high for asymmetrical shaped stenosis for both steady and pulsatile flow. The impact of asymmetrical shape on plaque deposition zone is less, if the aggravation changes the shape of stenosis due to change in stricture length only keeping percentage of restriction same. Whereas, the impact of asymmetrical shape on plaque deposition zone will be high, if shape of stenosis changes by increasing both stricture length and percentage of restriction for both steady and pulsatile flow. Impact of pulsatile nature of flow on the aggravation of disease is higher at some timesteps in comparison to steady flow.

Effects of magnetic field, porosity, and wall properties for anisotropically elastic multi-stenosis arteries on blood flow characteristics

A mathematical model for blood flow through an elastic artery with multistenosis under the effect of a magnetic field in a porous medium is presented. The considered arterial segment is simulated by an anisotropically elastic cylindrical tube filled with a viscous incompressible electrically conducting fluid representing blood. An artery with mild local narrowing in its lumen forming a stenosis is analyzed. The effects of arterial wall parameters represent viscoelastic stresses along the longitudinal and circumferential directions Tt and Tθ, respectively. The degree of anisotropy of the vessel wall γ, total mass of the vessel, and surrounding tissues M and contributions of the viscous and elastic constraints to the total tethering C and K respectively on resistance impedance, wall shear stress distribution, and radial and axial velocities are illustrated. Also, the effects of the stenosis shape m, the constant of permeability X, the Hartmann number Hα and the maximum height of the stenosis size δ on the fluid flow characteristics are investigated. The results show that the flow is appreciably influenced by surrounding connective tissues of the arterial wall motion, and the degree of anisotropy of the vessel wall plays an important role in determining the material of the artery. Further, the wall shear stress distribution increases with increasing Tt and γ while decreases with increasing Tθ, M, C, and K. Transmission of the wall shear stress distribution and resistance impedance at the wall surface through a tethered tube are substantially lower than those through a free tube, while the shearing stress distribution at the stenosis throat has inverse characteristic through totally tethered and free tubes. The trapping bolus increases in size toward the line center of the tube as the permeability constant X increases and decreases with the Hartmann number Ha increased. Finally, the trapping bolus appears, gradually in the case of non-symmetric stenosis, and disappears in the case of symmetric stenosis. The size of trapped bolus for the stream lines in a free isotropic tube (i.e., a tube initially unstressed) is smaller than those in a tethered tube.

Clinical Significance of Aspirin on Blood Flow through Stenotic Blood Vessels

In this present study a two-phase model for the influence of aspirin on peripheral layer viscosity for physiological characteristics of blood flow through stenosed blood vessels using Casson’s fluid model has been obtained. Flow of blood with axially non-symmetric but radially symmetric stenosis geometry is considered. The non-linear pressure equations have been solved with help of boundary conditions and the results are displayed graphically for different flow characteristics. It was found that the resistance to flow decreases as stenosis shape parameter increases whereas the resistance to flow increases with increasing values of stenosis length, stenosis size and peripheral layer viscosity. The effects of stenosis severity and wall shear stress are discussed in the present computational analysis. Comparisons between the measured and computed peripheral layer viscosity profiles are favourable to the solutions. As a result it can be concluded that a regular dose of Asprin decreases the blood viscosity by diluting the blood of diabetic patients which ultimately decreases the blood pressure. For the validation of the numerical model, the computation results are compared with the experimental data and results from published literature.

Effects of shape of stenosis on arterial rheology under the influence of applied magnetic field

This study deals with the problem of blood flow through an axially non-symmetric but radially symmetric stenosis, when an externally uniform magnetic field is applied on the flow. The effect of magnetic field is considered in the transverse direction of blood flow and viscosity of blood is taken as radial coordinate dependent. The governing equations of motion have been solved with the help of boundary condition and series method and the expression for the dimensionless resistance to blood flow is derived. The effects of stenosis shape parameter m on the resistance to blood flow for the different magnetic fields are shown graphically. Finally, the significance of the present model over the existing published literature has been pointed out by comparing the results with other theories.

HEMODYNAMICS IN STENOSED ARTERIES — EFFECTS OF STENOSIS SHAPES

A numerical analysis has been carried out to investigate the hemodynamic flow through stenosed arteries having mild (S = 25%) to severe (S = 65%) occlusions and under different regimes of flow Reynolds numbers ( Re ) ranging from 50 to 400. Influence of different stenosis shapes (rectangular, trapezoidal, cosine, and Gaussian) on key hemodynamic parameters e.g., recirculation length, wall shear stress (WSS), pressure drop, and irreversible pressure loss coefficient (C I ) are studied. It has been observed that for S = 25%, no flow separation takes place with cosine and Gaussian shaped stenoses for all the Re values considered, while for rectangular or trapezoidal shapes the flow begins to separate at Re = 400. At higher degrees of stenosis, post-stenotic recirculation is noticed for all the shapes considered — the largest recirculation length being observed with the rectangular shape. The peak centerline velocity in the stenosed region is more sensitive to a change in the degree of occlusion for rectangular stenosis than the other shapes. From the study, it is also revealed that the irreversible pressure loss coefficient (C I ) is the maximum for rectangular shaped stenosis, while it is the least for Gaussian shape. It is observed that at high Re regime, C I becomes insensitive to Re values and can be approximated to be a function of the degree of stenosis (S) and the stenosis shape only.

SUSPENSION MODEL FOR BLOOD FLOW THROUGH ARTERIAL CATHETERIZATION

This article is concerned with the analysis of a dusty model for the axi-symmetric flow of blood through coaxial tubes such that the outer tube with an axially nonsymmetreic but radially symmetric mild stenosis and the inner tube have a balloon (assumed that is axi-symmetric in nature). The mild stenosis approximation is used to solve the problem. To estimate the effect of the stenosis shape, a suitable geometry has been considered such that the axial shape of the stenosis can be changed easily just by varying a parameter (referred to as the shape parameter). The model is also employed to study the effect of the volume fraction density of the particles C, the maximum height attained by the balloon δ2, the radius of the inner tube, which keeps the balloon in position κ, and the axial displacement of the balloon x d . Flow parameters such as velocity, the resistance to flow (the resistance impedance), the wall shear stress distribution in the stenotic region and its magnitude at the maximum height of the stenosis (stenosis throat) have been computed numerically for different shape parameters n, C, δ2, κ, and x d . It is shown that the resistance to flow decreases with increasing values of the parameter determining the stenosis shape n and the axial displacement of the balloon x d , while the resistance to flow increases with the volume fraction density of the particles C, the radius of the inner tube, which keeps the balloon in position κ, and the maximum height attained by the balloon δ2. The magnitudes of the resistance to flow are higher in the case of a dusty fluid model than in the case of a Newtonian fluid model. The wall shear stress distribution in the stenotic region and its magnitude at the maximum height of the stenosis possess a character similar to the resistance to flow with respect to C, δ2, κ, and x d . Finally, the effect of the volume fraction density of the particles C, δ2, and x d on the velocity profile are discussed.

Blood flow through a stenosed catheterized artery: Effects of hematocrit and stenosis shape

The problem of blood flow through a narrow catheterized artery with an axially nonsymmetrical stenosis has been investigated. Blood is represented by a two-phase macroscopic model, i.e., a suspension of erythrocytes (red cells) in plasma (Newtonian fluid). The coupled differential equations for both fluid (plasma) and particle (erythrocyte) phases have been solved and the expression for the flow characteristics, namely, the flow rate, the impedance (resistance to flow), the wall shear stress and the shear stress at the stenosis throat have been derived. It is found that the impedance increases with the catheter size, the hematocrit and the stenosis size (height and length) but decreases with the shape parameter. A significant increase in the magnitude of the impedance and the wall shear stress occurs even for a small increase in the catheter size. The flow resistance increases and the shear stress at the stenosis throat decreases with the increasing catheter size and assume an asymptotic value at about the catheter size half of the artery size.

A numerical model study of steady flow through bell-shaped stenoses with and without asymmetry

In the present paper, the effect of symmetrical and asymmetrical bell shaped stenoses on wall pressure drop, streamline contour, and rise in wall shear stress (WSS) for the progression of the disease, atherosclerosis has been investigated numerically. The governing equations have been solved by finite volume method. It is revealed from the study that the impact of wall pressure and peak WSS on progression of disease are always high for asymmetrical shaped stenosis. The impact of asymmetrical shape on plaque deposition zone is less, if the aggravation changes the shape of stenosis due to change in stricture length only keeping percentage of restriction same. Whereas, the impact of asymmetrical shape on plaque deposition zone will be high, if shape of stenosis changes by increasing both stricture length and percentage of restriction.

Effects of Magneto-Hydrodynamic and Hematocrit on Blood Flow in an artery with multiple mild stenosis

Fluid flow analysis of blood flow through multi stenosis arteries in the presence of magnetic field is investigated. In this paper the effect of magnetic field and shape of stenosis on the flow rate, pressure gradient, wall shear stress and resistance parameter is studied. The blood flowing through the artery is considered to be Newtonian. This model is consistent with the principles of Ferro hydrodynamics and magneto hydrodynamics (MHD). The results indicate that rise in systolic pressure and fall in diastolic pressure are very harmful for weak heart.

Direct numerical simulation of flow in stenotic channel to understand the effect of stenotic morphology on turbulence

A fundamental fluid dynamics study has been performed in order to understand the effect of shape of blockage in a stenotic channel on turbulence flow characteristics using direct numerical simulation (DNS) as a tool. DNS has been performed for four canonical types with identical degree of blockage (stenosis) but with varied morphological forms. The results revealed large-scale and small-scale features of the flow represented by the root mean square (rms) of velocity and vorticity statistics are type-dependent. The turbulent structures exhibited characteristic structures and mechanics very specific to the type of blockage. The analysis indicates that for given degree of stenosis, the turbulence characteristics are significantly dependent on the morphology of the blockage, and hence to quantify turbulence flow characteristics in stenosed channel, the stenosis shape is an important metric that needs to be considered. The results of this study are directly relevant to the flow dynamics in diseased stenotic coronary artery, in the context of the importance of stenotic morphology in addition to the height of the stenosis as an important indicator for the prediction of the flow dynamics in diseased coronary artery.

Flussuntersuchungen an Strömungsphantomen im Vor- und Nachlauf stenoseförmiger Verengungen mittels geschwindigkeitskodierter MRT und numerischer Simulation der Fluiddynamik / Fluid studies on flow behaviour in narrowing vessels with PC-velocimetry and numerical simulations

Fluid dynamics play an important role in arterial diseases. PC-velocimetry as a magnetic resonance (MR) method is a useful tool for the examination of blood vessels, in particular in haemodynamics and morphology. Due to signal loss caused by turbulent flow, classification of stenoses remains difficult. In the presence of metallic stents, susceptibility effects and RF-artefacts further deteriorate image quality. Regarding fluid dynamics, stenosis, stent and restenosis (i.e., re-closing of the vessel in areas with stents) have similar properties: the flow close to an obstacle is accelerated and after a specific length, the so-called reattachment length, it redevelops into its original flow profile. Depending on the shape of the obstacle and its reattachment length, a method is developed to classify stenosis using MR-imaging. Enlarged, simplified stenosis models (phantoms) were examined and were also modelled using computational fluid dynamics (CFD). MR- and CFD-measurements show influences of the stenosis shape, especially the diameter. In graphical analysis (streamline and vector plots), a reattachment length of 6.7xstep size could be determined under laminar conditions and nonpulsatile flow. Stenosis and other narrowing of vessels are classifiable more exactly using PC-velocimetry. From the flow behaviour in the area around the narrowing of the vessel wall, the character of the stenosis can be derived. But more parameters, as bended vessel shapes, pulsated flow, non-Newtonian flow behaviour as well as elastic properties of the vessels need to be incorporated.

Mathematical modeling of pulsatile flow of non-Newtonian fluid in stenosed arteries

The pulsatile flow of blood through mild stenosed artery is studied. The effects of pulsatility, stenosis and non-Newtonian behavior of blood, treating the blood as Herschel–Bulkley fluid, are simultaneously considered. A perturbation method is used to analyze the flow. The expressions for the shear stress, velocity, flow rate, wall shear stress, longitudinal impedance and the plug core radius have been obtained. The variations of these flow quantities with different parameters of the fluid have been analyzed. It is found that, the plug core radius, pressure drop and wall shear stress increase with the increase of yield stress or the stenosis height. The velocity and the wall shear stress increase considerably with the increase in the amplitude of the pressure drop. It is clear that for a given value of stenosis height and for the increasing values of the stenosis shape parameter from 3 to 6, there is a sharp increase in the impedance of the flow and also the plots are skewed to the right-hand side. It is observed that the estimates of the increase in the longitudinal impedance increase with the increase of the axial distance or with the increase of the stenosis height. The present study also brings out the effects of asymmetric of the stenosis on the flow quantities.

The micropolar fluid model for blood flow through a tapered artery with a stenosis

A micropolar model for axisymmetric blood flow through an axially nonsymmetreic but radially symmetric mild stenosis tapered artery is presented. To estimate the effect of the stenosis shape, a suitable geometry has been considered such that the axial shape of the stenosis can be changed easily just by varying a parameter (referred to as the shape parameter). The model is also used to study the effect of the taper angle \({\phi}\) . Flow parameters such as the velocity, the resistance to flow (the resistance impedance), the wall shear stress distribution in the stenotic region and its magnitude at the maximum height of the stenosis (stenosis throat) have been computed for different values of the shape parameter n, the taper angle \({\phi}\) , the coupling number N and the micropolar parameter m. It is shown that the resistance to flow decreases with increasing the shape parameter n and the micropolar parameter m while it increases with increasing the coupling number N. So, the magnitude of the resistance impedance is higher for a micropolar fluid than that for a Newtonian fluid model. Finally, the velocity profile, the wall shear stress distribution in the stenotic region and its magnitude at the maximum height of the stenosis are discussed for different values of the parameters involved on the problem.

Influence of magnetic field and Hall currents on blood flow through a stenotic artery

A micropolar model for blood simulating magnetohydrodynamic flow through a horizontally nonsymmetric but vertically symmetric artery with a mild stenosis is presented. To estimate the effect of the stenosis shape, a suitable geometry has been considered such that the horizontal shape of the stenosis can easily be changed just by varying a parameter referred to as the shape parameter. Flow parameters, such as velocity, the resistance to flow (the resistance impedance), the wall shear stress distribution in the stenotic region, and its magnitude at the maximum height of the stenosis (stenosis throat), have been computed for different shape parameters, the Hartmann number and the Hall parameter. This shows that the resistance to flow decreases with the increasing values of the parameter determining the stenosis shape and the Hall parameter, while it increases with the increasing Hartmann number. The wall shear stress and the shearing stress on the wall at the maximum height of the stenosis possess an inverse characteristic to the resistance to flow with respect to any given value of the Hartmann number and the Hall parameter. Finally, the effect of the Hartmann number and the Hall parameter on the horizontal velocity is examined.

CFD analysis of pulsatile blood flow in an atherosclerotic human artery with eccentric plaques

Atherosclerosis is a slow vascular degeneration. It thickens the internal walls of a blood vessel locally depositing an atherosclerotic plaque. Such reduced lumen increases the resistance to blood flow. Plaques can be punctual (eccentric, here considered) or circumferential (symmetrical). Stenoses do not have a typical shape: we hypothesised here a reference geometry (trapezium) with its possible evolutions (semi-ellipse, triangle). Two criteria (Equivalent Area and Equivalent Dimensions) were then defined to compare the results among the 35 case studies numerically analysed with a Computational Fluid Dynamics code (Comsol Multiphysics 3.3). Blood was considered a Cassonian fluid with modified viscosity equation. The artery was cylindrical, rigid and straight, interested by a pulsatile blood flow. Among the variables: shape and dimensions of the stenoses; number of stenoses (single or coupled pathologies); mutual locations (3 possibilities). The main results were that the length of the consequent flow disturbance is due to the stenotic shape and height; blood flow recirculation, downstream of the pathology, is due to the slope of the stenotic walls; and the peak velocities depend on the shape and height of stenosis. The differences from case to case diminish in diastole.