Stenosis Shape Research Articles

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.

Mechanics of non-Newtonian blood flow in an artery having multiple stenosis and electroosmotic effects.

The electro-osmotically modulated hemodynamic across an artery with multiple stenosis is mathematically evaluated. The non-Newtonian behaviour of blood flow is tackled by utilizing Casson fluid model for this flow problem. The blood flow is confined in such arteries due to the presence of stenosis and this theoretical analysis provides the electro-osmotic effects for blood flow through such arteries. The mathematical equations that govern this flow problem are converted into their dimensionless form by using appropriate transformations and then exact mathematical computations are performed by utilizing Mathematica software. The range of the considered parameters is given as . The graphical results involve combine study of symmetric and non-symmetric structure for multiple stenosis. Joule heating effects are also incorporated in energy equation together with viscous effects. Streamlines are plotted for electro-kinetic parameter and flow rate . The trapping declines in size with incrementing , for symmetric shape of stenosis. But the size of trapping increases for the non-symmetric case.

Entropy generation for the blood flow in an artery with multiple stenosis having a catheter

This article explicates the blood flow across an artery with multiple stenosis at outer wall and a thrombus at the centre. The symmetric multiple stenosis and non-symmetric multiple stenosis shapes are both considered in this study. Entropy analysis is also taken into account for a detailed study of irreversibility. The governing equations are interpreted with provided boundary conditions and exact mathematical solutions are developed. Further, these exact solutions are elucidated graphically. Streamlines show that the closed contours are symmetric in shape for symmetric multiple stenosis but non-symmetric in shape for non-symmetric multiple stenosis shape. The increase in multiple stenosis heights, increases the shear stress at wall having multiple stenosis.

Bio-mathematical analysis of electro-osmotically modulated hemodynamic blood flow inside a symmetric and nonsymmetric stenosed artery with joule heating

This is the first paper that explains electro-osmotically modulated hemodynamic inside a stenosed artery, considering both cases of symmetric and nonsymmetric shapes of stenosis. Blood is treated as an aqueous ionic solution. The energy equation incorporates viscous dissipation as well as Joule heating effects. Exact solutions are calculated for governing equations subject to “no slip” boundary conditions. These solutions are further discussed through graphical results. The flow pattern for symmetric and nonsymmetric stenosis is visualized by plotting streamlines for this flow problem.

Newtonian and Non-Newtonian Blood Rheology Inside a Model of Stenosis

In order to imitate the atherosclerosis artery disease and determine the key issues, Computational Fluid Dynamics (CFD) is able to play a leading rule in the analysis of flow physics within the clogged arteries, in particular the stenosis artery. The problem of blood flow blockage through the blood vessel has been investigated numerically within a stenosis artery. In this work, a CFD technique was employed to solve the three-dimensional, steady, laminar and non-Newtonian Carreau model blood flow through a stenosis artery using Star-CCM+ software. The shape of stenosis that has been selected is a trapezoidal with two cases (70% and 90% blockage). Shear rate, streamlines, vorticity and importance factor are examined to assess the influence of non-Newtonian model through the test section, the Carreau model was compared with Newtonian model. The clinical significance of the shear rate is reported for the examined cases, observing that the levels of non-Newtonian model are predicted to be higher in the 90% blockage than that observed within the 70%; the same finding as related with the axial velocity and vorticity. The levels of re-circulation areas and vorticity are showed to be enlarged in the Carreau model compared with the case of Newtonian.

Roll of stenosis severity, artery radius and blood fluid behavior on the flow velocity in the arteries: Application in biomedical engineering

In this work, the Sisko model is involved for blood flow simulation in the arteries with triangular shapes of stenosis, which is different in severities of 20%, 30%, and 40%, respectively. Firstly, the effects of different severity of stenosis as much as 20%, 30%, and 40% are investigated in the velocity of blood while artery radius of 0.002 m and Sisko parameters of n = 0.639 and b = 0.1735 are constant. Then, stenosis with the severity of 40% remains, and the radius of the artery is varied from 0.002 m to 0.0035 m to investigate the effects of artery radius on the blood velocity. Finally, different types of blood fluids are employed by manipulation of Sisko parameters, and influences of blood fluid behaviors are investigated in velocity profiles. It is reported that influences of increasing severity of stenosis and reducing the radius of the artery cause blood velocity to be augmented due to the role of stenosis as an obstacle against blood flow and influences of artery radius in reducing cross-section area of the vessel. Maximum velocities are roundabout 0.15 m/s, 0.185 m/s of 0.235 m/s in order of stenosis of 20%, 30% and 40% respectively. Also, investigation in the effects of the behavior of different blood showed that blood fluid types could change maximum flow velocity as much as 0.025 m/s. Despite of roll of stenosis severity, artery radius, and blood fluid behavior in exacerbation of velocity deviation, it was concluded that their consequences for the human body healthy can be ignorable in the range of studied.

Numerical study for blood rheology inside an artery: The effects of stenosis and radius on the flow behavior

Background and objectiveIn this work, using Sisko model, blood flow is simulated inside an artery which have cone shape of stenosis with different angles of φ = 0.25, φ = 0.5, φ = 0.75, φ = 1 and φ = 1.25 degree, respectively. MethodsIn the first step, an artery radius of 0.002 m is fixed to study the effects of cone shape of arterial stenosis on the flow behavior. Then, stenosis angle of φ = 0.5 degree is fixed to study the effects of different Artery radii of 0.002 m, 0.0025 m, 0.003m, and 0.0035 m orderly on the flow behavior. For simulation the blood flow, Sisko model is used. Afterward, stenosis angle of φ = 0.5 degrees with a radius of 0.002m is fixed for investigating the influences of different behavior of blood fluid by manipulation of constant parameters of the Sisko model. ResultsIt is reported that with increasing arterial stenosis angle, maximum blood flow velocity is sharply increased in central region of artery from 0.12 m/s to 0.16 m/s, 0.25 m/s, 0.36 m/s and 0.56 m/s in order of increasing stenosis angles from φ = 0.25 to φ = 0.5, φ = 0.75, φ = 1 and φ = 1.25 degree, respectively. Also, maximum shear stress of artery wall are as much as 64 Pa, 42 Pa, 24 Pa, 18 Pa and 16Pa respectively in order of stenosis angles of φ = 0.25, φ = 0.5, φ = 0.75, φ = 1 and φ = 1.25 degree. On the other side, the effect of increasing artery radius is against the influences of stenosis angle, and contradiction of these parameters is affected by the stress tension and viscosity of blood. ConclusionsVariations of blood behavior from non-Newtonian to Newtonian shows that shear stress in blood stream in the stenosis artery with non-Newtonian blood is higher than that of Newtonian blood due to differences in their viscous behaviors and reactions in exposure of stenosis and artery wall effects.

The analysis of a sudden death caused by the unusual shape of the foramen magnum stenosis

Introduction. The anomalies of the size and shape of the foramen magnum (FM), followed by its stenosis, take a special place in clinical and forensic practice. The clinical picture of FM stenosis is variable, but it is not specific, which is why these anomalies are sometimes not recognized in time and are only detected by autopsy. Case report. This paper analyzes the case of a sudden death caused by the unusual shape of the FM stenosis. On autopsy, we found exostoses on the front and rear edges of the FM with their prominence into the FM. The exostoses reduced the sagittal diameter of the FM and practically divided it into two asymmetric semicircles, which is why we called this stenosis the "keyhole" stenosis of the FM. This form of the FM stenosis pushes the medulla oblongata aside, resulting in its incarceration into one of the FM semicircles. Conclusion. A stenosis of the FM can represent a threat to life, especially when combined with its unusual shape, as in our case. In this way, the critical stenosis of the FM becomes clinically clearly manifested, and there is a loss of consciousness that can also end with a sudden death, as in our case.

Numerical investigation of non-Newtonian blood flow within an artery with cone shape of stenosis in various stenosis angles

Background and objectiveIn this work, a numerical study is done on the blood flow inside an artery with a cone shape of stenosis. An artery has different stenosis angles. Also, blood flow is energized by constant heat flux which is applied on the wall. The finite volume method is employed to determine blood properties on the basis of a Sisko fluid model with different constant parameters. MethodsFirstly, the effects of applying constant heat flux of q'' = 4 W/m2 are studied on the velocity profile of blood flow inside an artery with stenosis angles of φ = 0.5°. Afterward, effects of different stenosis angles of φ = 0.25, φ = 0.5, φ = 0.75, φ = 1 and φ = 1.25 is studied on blood flow temperature profile. Then, different values of the Sisko model are employed to investigate influences of Newtonian and non-Newtonian behaviors of blood fluid on the temperature profiles of blood flow inside an artery with stenosis angle of φ = 0.5°. ResultsIt is reported that with increasing stenosis angles, blood flow temperature is decreased due to velocity enhancement. This phenomenon is convinced by non-slip condition and sticking non-Newtonian blood fluid to the internal surface of artery wall which reduce velocity from wall surface region to central region of vessel. Also, it is concluded that changing behavior of blood fluid from non-Newtonian to Newtonian behaviors can empower the capability of blood in thermal energy transfer inside human body vessels. ConclusionsAny treatment by balloon angioplasty, percutaneous transluminal angioplasty, and serum injection, which changes the behavior of blood flow inside body veins, can be effective on blood flow temperature.

An experimental model for pressure drop evaluation in a stenosed coronary artery

Non-invasive measurement of pressure drop has great clinical significance for the treatment of coronary artery diseases. The objective of this study is to develop a relationship that can estimate pressure drop in a stenosed coronary artery model as a function of different parameters such as blood viscosity, artery length and diameter, flow rate and flow profile, and shape and degrees of stenosis. Experimental pressure measurements from a wide range of degrees of stenosis and critical simplified geometries of stenosis along with different unsteady flow profiles are employed to evaluate the pressure drop equation. To calculate the blockage term of the pressure drop, several experimental cases are investigated, and the results show that the blockage factor is strongly dependent on the shape and degree of stenosis. Furthermore, different unsteady flow profiles are applied to calculate the pulsatile pressure drop term, and it is found that the pulsatility parameter is not a function of the flow profile or the shape of the stenosis. However, it is only a function of the degree of stenosis. To test the validity of the developed equation, pressure drops through stenosed coronary artery models with the real physiological flow profile of the left and right coronary arteries were predicted and compared with the experimental measurements. The proposed equation is able to determine the pressure drop inside a stenosed coronary artery non-invasively using the measurement of the flow profile inside the artery as well as the images of the stenosed coronary artery obtained based on the non-invasive methods.

Effect of stenosis shape on the sound emitted from a constricted blood vessel.

Effect of stenosis shape on the post-stenotic pressure fluctuations and the sound emitted from a constricted blood vessel is studied numerically. Large eddy simulations are performed using OpenFOAM under pulsatile flow conditions with a non-Newtonian fluid model. Findings indicate that the high slope at the stenosis entrance and overlap of more than one stenosis shorten the length of the flow jet, trigger turbulence, and increase vortical activity, turbulent kinetic energy, and magnitude of pressure fluctuations at the post-stenotic region. Also, these morphological parameters strengthen the audible signal especially in the systolic phase of the pulsatile flow. On the other hand, asymmetry of the stenosis creates an opposite effect. Based on the wall pressure data, it is shown that the stenosis shape affects the intensity and the pattern of the murmurs generated. Stenosis shape is found to be an essential factor for the acoustic-based non-invasive diagnosis of stenosis. Graphical abstract Wall pressure content of the elliptic stenosis shape.

Numerical investigation of wall pressure fluctuations downstream of concentric and eccentric blunt stenosis models.

Pressure fluctuations that cause acoustic radiation from vessel models with concentric and eccentric blunt stenoses are investigated. Large eddy simulations of non-pulsatile flow condition are performed using OpenFOAM. Calculated amplitude and spatial-spectral distribution of acoustic pressures at the post-stenotic region are compared with previous experimental and theoretical results. It is found that increasing the Reynolds number does not change the location of the maximum root mean square wall pressure, but causes a general increase in the spectrum level, although the change in the shape of the spectrum is not significant. On the contrary, compared to the concentric model at the same Reynolds number, eccentricity leads to an increase both at the distance of the location of the maximum root mean square wall pressure from the stenosis exit and the spectrum level. This effect becomes more distinct when radial eccentricity of the stenosis increases. Both the flow rate and the eccentricity of the stenosis shape are evaluated to be clinically important parameters in diagnosing stenosis.

Geometrical effects in the hemodynamics of stenotic and non-stenotic left coronary arteries-numerical and in vitro approaches.

Atherosclerosis is a common cardiovascular disease found in the left coronary artery (LCA), closely linked to local hemodynamic, which, in turn, is highly influenced by the artery geometry. The hemodynamics in the LCA was studied in a patient-specific geometry without any sign of disease using both numerical and in vitro approaches. The influence of non-planarity was evaluated through two models of the patient-specific LCA that deviate from its original geometry in their planarity. Afterwards, in all models, irregular stenoses were created by a procedure in which the stenosis emerges by diffusion from low wall shear stress (WSS) areas. The WSS distribution and flow patterns were evaluated in all the models. The experimental results validate the numerical code developed to study the blood flow assuming a steady state Newtonian behavior. Comparison between the planar and non-planar idealized LCA revealed no significant differences in low WSS regions forming stenotic regions with identical shape. In the patient-specific LCA, the low WSS regions are not consistent with the idealized models leading to a different stenosis shape. The results revealed that the non-planarity has an unquestionable effect in helicity. It was also demonstrated that eccentricity of the vessels cross section and the position of the apex in relation to the axis of the parent branch contribute to the flow patterns observed. Numerical results of pulsatile blood flow assuming a non-Newtonian behavior, in the patient-specific LCA, reinforce the non-planarity effect in local hemodynamics.

Hemodynamic Characteristics of Gold Nanoparticle Blood Flow Through a Tapered Stenosed Vessel with Variable Nanofluid Viscosity

This paper presents a theoretical study of gold nanoparticle blood flow through a tapered blood vessel with an overlapping stenosis. The variable nanofluid viscosity depending on temperature is taken into account. The governing equations for steady incompressible fluid subject to the boundary conditions are solved analytically under mild stenosis assumptions. The results are presented graphically for pertinent flow and stenosis shape parameters. The results show that as the concentration of gold nanoparticles increases, velocity increases while resistance impedance decreases. The obtained results for Au blood flow model are compared with both Cu blood and TiO2 blood flow models. The results showed that the velocity values are higher in case of Au blood flow model than the other models. This indicates that gold nanoparticles can improve blood flow and enhance the hemodynamic performance in the stenosed blood vessel.

Nanofluid flow in a catheterized tapered artery

This study was conducted with the aim of investigating the Newtonian nanofluid flow in a catheterized tapered artery through using a completely consistent couple stress theory. In the process of carrying out this study, the slip condition at the arterial wall and the catheter, as well as, the permeability was taken into account. Further, the velocity, temperature, and concentration profiles were analytically modeled and the effect of the length scale on these profiles was well presented through the way it influences small-scale flows. The effect of the slip condition at the artery and catheter walls on the velocity was also investigated and revealed that any increase in the velocity leads to an increase in the slip velocity. Furthermore, the effect of other parameters such as the catheter diameter, shape, and height of the stenosis on these profiles was explored for all three artery geometries, i.e., diverging tapered artery, converging tapered artery, and non-tapered artery, respectively. The findings suggested that any increase in the catheter diameter and stenosis height can decrease the velocity and nanoparticle concentration profiles, while the temperature profile increases. It was also found that by increasing the stenosis shape parameter the velocity and concentration profiles increase and temperature decreases.

Blood Flow in a Radially Non Symmetric Stenosed Artery Under Slip Effect Through Porous Medium

A mathematical model is developed to analyze the non-Newtonian flow of blood in an axially symmetric but radially non symmetric stenosed artery through porous medium in the presence of slip velocity. Blood is modeled as Casson fluid to characterize the non-Newtonian behaviour. Flow characteristics like axial velocity, flow rate and impedance are expressed analytically. These expressions show remarkable variations in flow of blood through constricted artery. The effects of porosity, slip velocity and stenosis shape on the various flow characteristics have been examined and shown graphically. These results are in good agreement with the experimental findings existing in the literature and can aid medical practitioner to treat cardiovascular diseases.

A numerical study on the effect of trapezium stenosis shape on the axisymmetric flow field around stenosis

Numerical simulations on the pulsatile flow in stenosed tubes were conducted to investigate the effect of trapezium shape of stenosis on the flow field around stenoses. Four trapezium shapes of stenoses were considered by varying contraction, plateau, and expansion parts of stenoses for different stenosis area reduction ratios. The Galerkin finite element method based on the P2P1 mixed element was employed to solve the axisymmetric incompressible Navier-Stokes equations and the continuity equation. The proposed numerical method was validated by solving a benchmark problem of stenotic flow. It was found that the average pressure profile along the centerline was more affected by the contraction shape than the expansion shape. It was also revealed that the average wall shear stress of mild contraction was greater than that of sudden contraction around the stenotic region. Furthermore, the pressure drop across the stenosis was found to be associated with the form drag experienced by the stenosis.

Effect of magnetic field and rotation on the micropolar fluid model of blood flow through stenotic arteries

The problem of blood flow through a horizontal non-symmetric artery with a mild stenosis has been investigated. Blood is modelled as a homogeneous and incompressible micropolar fluid. The effect of both rotation and magnetic field are studied analytically and computed numerically. To evaluate the influence of the stenosis shape, an appropriate geometry has been considered such that the shape of the stenosis can be changed simply just by varying a parameter (referred to as the shape parameter). The expressions for the flow characteristics such as velocity, the impedance (resistance to flow), the wall shear stress distribution and its magnitude at the stenosis throat have been derived and analysed for different values of shape parameter n, rotation parameter ω, the magnetic field parameter M, the coupling number N and the micropolar fluid parameter m.

A study on the effect of inclined magnetic field and Hall current on the micropolar fluid model of blood flow through stenotic arteries in a porous medium

The problem of blood flow through a horizontal non-symmetric artery with a mild stenosis in a porous medium has been investigated. The natures of blood in small arteries are analysed mathematically by considering it as a homogeneous and incompressible micropolar fluid. The effect of both rotation and inclined magnetic field are studied analytically and computed numerically. To evaluate the influence of the stenosis shape, an appropriate geometry has been considered such that the shape of the stenosis can be changed simply just by varying a parameter (referred to as the shape parameter). The expressions for the flow characteristics such as velocity, the impedance (resistance to flow), the wall shear stress distribution and its magnitude at the stenosis throat have been derived and analysed for different values of shape parameter n, rotation parameter Ω, the magnetic field parameter M, inclination angle of the magnetic field parameter (θ), permeability parameter (K1), the coupling number N and the micropolar fluid parameter m.

The Influence of Geometrical Shapes of Stenosis on the Blood Flow in Stenosed Artery

The present work was carried out to investigate the blood flow behavior and the severity of blockage caused in the arterial passage due to the different geometries such as elliptical, trapezium and triangular shapes of stenosis. The study was conducted with respect to various sizes of stenosis in terms of 70%, 80% and 90% area blockage of the arterial blood flow. The study was carried out numerically with the help of advance computational fluid dynamic software. It was found that the shape of the stenosis plays an important role in overall pressure drop across the blockage region of artery. The highest level of pressure drop was observed for trapezoidal shape of stenosis followed by elliptical and then by triangular shaped stenosis. The wall shear stress across the stenosis is great for trapezoidal shape followed by triangular and elliptical stenosis for same blockage area in the artery.