Stenosis Shape Research Articles

Non-Newtonian blood flow across stenosed elliptical artery: Case study of nanoparticles for brain disabilities with fuzzy logic

This analysis aimed to explore the blood-based non-Newtonian hybrid nanofluid flow in elliptical stenosed artery with single- and multi-walled carbon nanotubes as nanoparticles. The Carreau fluid model is incorporated to assess the non-Newtonian rheology of blood-based nanofluid for mild stenosis. In particular, the carotid artery is responsible for delivering blood to the brain. If normal blood circulation is disrupted or in the case of severe stenosis, blockage of the carotid artery can lead to the development of brain disability or stroke, which in turn can lead to death. The idealized mathematical equation is transformed into a nondimensional form and solved analytically via the perturbation method through a novel polynomial technique. These analytical solutions are explored and explained graphically. The system’s disorder and variability are assessed by completing an entropy production analysis. The disruption in blood flow due to the presence of nanoparticles causes uncertainty in the flow nature. This uncertainty is dealt with by fuzzy analysis of temperature distribution by accounting for the nanoparticle volume fractions as triangular fuzzy numbers. It is noticed that stenosis shapes and height greatly impact the flow characteristics. The nanoparticles’ percentage in fluid affected the temperature profile. The non-Newtonian characteristics of blood are found to be more dominant along the minor axis, and an effectively higher disorder is produced in this direction. It is observed that the temperature of nanofluid emerged as a triangular fuzzy number of symmetric shape.

Entropy-based analysis of hemodynamics in elliptical arterial flows with non-Newtonian Rabinowitsch fluid

This research concerns examining the non-Newtonian blood flow behavior through an artery of elliptic cross-section, affected by several stenoses. The Rabinowitsch fluid model is used to investigate the non-Newtonian behavior of the blood for uniform and nonuniform shapes of stenosis. The mathematical equations have been converted into a dimensionless form, and their nonlinearity is reduced by applying the assumptions of mild stenosis. The resulting differential equations are solved by using analytical techniques. A new polynomial of degree eight is introduced to complete the solutions of mathematical equations. The entropy generation is studied mathematically to analyze the irreversibility effects. The detailed graphical examination delineates the physical aspects of mathematical results. The flow velocity is higher for uniform shape than for nonuniform stenosis. The rising percentage of stenosis significantly enhances the flow velocity of the stenotic region. The entropy is enormous near the stenotic wall and has small values near the centerline, which assures the smooth flow in this region. Further, the streamlines are plotted to find the position of stenosis and assess the flow nature for the growing height of stenosis and rising flow rate.

Computational fluid dynamics analysis on endoscopy of main left coronary artery: An application of applied mathematics

The endoscopy of a coronary arterial segment having a symmetric emergence of plaque at its innermost region is numerically modeled via computational fluid dynamics toolbox Open-FOAM. The considered left coronary artery for this model has a radius of 2 mm and span of 10 mm. The formation of plaque inside the artery that is a stenosis has length 2 mm and height 0.82 mm. The catheter used for this analysis has a diameter of 1 mm with a balloon over it with a height of 0.53 mm. The blood flow rate considered for this analysis has a range 2.00 ml/s to 2.50 ml/s. The fluid under consideration for this endoscopy review is the non-Newtonian Casson model. The mesh illustrations are arranged for the proposed model with numerical simulations of velocity, pressure profile and streamlines. The narrow channel formed due to assembly of stenosis and balloon over catheter inside this arterial segment has developed some swirling flow profile with turbulence effects just after the flow leaves the stenosis plus balloon region. Although this disturbance caused due to narrowing of channel has made the flow slightly turbulent, the flow eventually leaves the arterial segment again as a laminar flow. To cure coronary artery disease, catheterization, and balloon dilation of stenosed arteries is performed to locate the position and shape of stenosis. A catheter is inserted inside the body through a minor cut and then it is moved inside arteries to place it exactly at the stenosis location. A balloon is placed at front of that catheter and the stenosed region can be opened wide by using balloon dilation.

Prediction of Hemodynamic-Related Hemolysis in Carotid Stenosis and Aiding in Treatment Planning and Risk Stratification Using Computational Fluid Dynamics.

Atherosclerosis affects human health in many ways, leading to disability or premature death due to ischemic heart disease, stroke, or limb ischemia. Poststenotic blood flow disruption may also play an essential role in artery wall impairment linked with hemolysis related to shear stress. The maximum shear stress in the atherosclerotic plaque area is the main parameter determining hemolysis risk. In our work, a 3D internal carotid artery model was built from CT scans performed on patients qualified for percutaneous angioplasty due to its symptomatic stenosis. The obtained stenosis geometries were used to conduct a series of computer simulations to identify critical parameters corresponding to the increase in shear stress in the arteries. Stenosis shape parameters responsible for the increase in shear stress were determined. The effect of changes in the carotid artery size, length, and degree of narrowing on the change in maximum shear stress was demonstrated. Then, a correlation for the quick initial diagnosis of atherosclerotic stenoses regarding the risk of hemolysis was developed. The developed relationship for rapid hemolysis risk assessment uses information from typical non-invasive tests for treated patients. Practical guidelines have been developed regarding which stenosis shape parameters pose a risk of hemolysis, which may be adapted in medical practice.

Entropy-based investigation of blood flow in elliptical multi-stenotic artery with hybrid nanofluid in a fuzzy environment: Applications as drug carriers for brain diseases

The growing stenosis alters the blood flow characteristics and causes different diseases of arteries such as Carotid artery, Peripheral artery, and Coronary artery diseases. The proposed study aims to investigate the blood-based hybrid nanofluid flow via a multi-stenotic elliptical artery. The nanoparticles are vital as drug carriers in curing arterial diseases with consequences like Carotid artery disease (causes brain diseases), Peripheral artery disease, etc., and other medical applications. The single-wall and multi-wall carbon nanotubes are accounted as nanoparticles in blood. The mathematical equations have been transformed into dimensionless form and reduced non-linearity using mild case assumptions to get the exact solution. The local sensitivity analysis of temperature solution clarifies that the volume fraction of both types of nanoparticles is the most and equally influential parameter. The sensitivity of these parameters causes uncertainty in the temperature profile, and therefore, they are also analyzed in the fuzzy environment by considering them as triangular fuzzy numbers. The exact classical and fuzzy solutions are examined graphically in a comprehensive way. It is found that the non-symmetric stenosis shape and developing stenosis height cause to decline and grow the fluid’s velocity, respectively, but the flow nature reverses near the wall of the stenotic elliptic artery. The temperature profile appeared more accurate in parabolic shape along the major axis, while a quick decrease occurred near the stenosed wall along the minor axis. Further, the temperature profile revealed as triangular fuzzy number of non-uniform shapes at various points inside the elliptic artery.

Solute Dispersion in an Unsteady Herschel-Bulkley Flow through an Inclined Stenosed Arter

Motivated by the concept of blood flow in a stenosed artery, this present research investigates the influence of stenosis shape in terms of height and arterial inclination on the blood flow and solute dispersion behaviour through an inclined stenosed artery. The blood rheology is depicted using the Herschel-Bulkley model in a laminar, axisymmetric and incompressible unsteady flow through the stenosed artery. The effect of stenosis is focused on the stenosis height for both sine and cosine stenosis. Parameters of arterial inclination are also investigated to observe the effect of inclination on the blood velocity and dispersion function. Perturbation method is adopted in solving for the blood flow velocity under the effect of stenosis height and arterial inclination. The dispersion function of solute dispersion is solved using the obtained blood velocity by adopting the Generalized Dispersion Model (GDM) in obtaining steady dispersion functions. This present study shows that the increase in stenosis height decreases both blood velocity and dispersion function. Meanwhile, the increase in arterial inclination increases the blood velocity and dispersion function. The effect of stenosis height also affects blood velocity and dispersion function for the sine stenosis more than the cosine stenosis.

Numerical analysis of hemodynamic parameters in stenosed arteries under pulsatile flow conditions

This research studies the changes in flow patterns and hemodynamic parameters of diverse shapes and sizes of stenosis. Six different shapes and sizes of stenosis are constructed to investigate the variations in hemodynamics as the morphology changes. Changes in shape (trapezoidal and bell-shaped) and sizes of stenosis change the stresses on the walls and their flow patterns. TAWSS and OSI results specify that trapezoidal stenosis exerts greater stress than bell-shaped stenosis. Also, as the length of the trapezoidal stenosis increases, the TAWSS increases, whereas the trend is the opposite for bell-shaped stenosis. Later, this paper also studies different degrees of stenosis extracted from real images. Changes in velocity flow patterns, wall shear stress (WSS), Time-averaged wall shear stress (TAWSS) and Oscillatory shear index (OSI) have been studied for these images. Results illustrate that the peak velocity rises drastically as the stenosis percentage increases. Negative velocity is seen close to the artery's walls, indicating flow separation. This flow separation region is seen throughout the cycle except in the accelerating flow region. An increase in stenosis also increases WSS and TAWSS drastically. Negative WSS is seen downstream of stenosis, indicating flow recirculation. Such negative WSS in the blood vessels also promotes endothelial dysfunction. OSI values greater than 0.2 are seen near the stenosis region, indicating atherosclerosis growth. Regions of high OSI and low TAWSS are also identified, indicating probable regions of plaque development.

Analysis of pulsatile blood flow through elliptical multi-stenosed inclined artery influenced by body acceleration

The effect of body acceleration on the pulsatile flow of blood through the elliptical artery having stenosis at the multiple positions of its wall is investigated in the current study. The artery is inclined at angle θ with horizontal, and blood is considered as Casson fluid. The mathematical model is processed into non-dimensional form and simplified using assumptions of mild stenosis. The analytical solution of mathematical equations is obtained in the elliptic bounded domain by employing the perturbation technique with Womersley frequency as a perturbation parameter and validated through case comparison with the previous study. The impacts of external acceleration, stenosis height, shape, gravitational acceleration, yield stress, and inclination angle on the flow velocity, flow rate, wall shear stress, and flow resistance are analyzed. It is found that body acceleration, gravitational acceleration, and inclination angle increase the flow rate and diminish the frictional resistance. The more significant yield stress and stenosis height enhance the flow resistance and reduce the flow rate. Moreover, fluid has higher velocity in the case of the non-symmetric shape of stenosis compared with the symmetric form.

Analysis of unsteady non-Newtonian Jeffrey blood flow and transport of magnetic nanoparticles through an inclined porous artery with stenosis using the time fractional derivative

In the present study, a Caputo–Fabrizio (C–F) time-fractional derivative is introduced to the governing equations to present the flow of blood and the transport of magnetic nanoparticles (MNPs) through an inclined porous artery with mild stenosis. The rheology of blood is defined by the non-Newtonian visco-elastic Jeffrey fluid. The transport of MNPs is used as a drug delivery application for cardiovascular disorder therapy. The momentum and transport equations are solved analytically by using the Laplace transform and the finite Hankel transform along with their inverses, and the solutions are presented in the form of Laplace convolutions. To display the solutions graphically, the Laplace convolutions are solved using the numerical integration technique. The study presents the impacts of different governing parameters on blood and MNP velocities, volumetric flow rate, flow resistance, and skin friction. The study demonstrates that blood and MNP velocities boost with an increase in the fractional order parameter, Darcy number, and Jeffrey fluid parameter. The volumetric flow rate decreases and flow resistance increases with enhancement in stenosis height. The non-symmetric shape of stenosis and the rheology of blood decrease skin friction, whereas enhancement in MNP concentration increases skin friction. A comparison of the present result with the previous work shows excellent agreement. The present study will be beneficial for the field of medical science to further study atherosclerosis therapy and other similar disorders.

Study of red blood cells and particles in stenosed microvessels using coupled discrete and continuous forcing immersed boundary methods

A computational study of the blood flow in a stenosed microvessel is presented using coupled discrete ghost-cell and continuous-forcing immersed boundary methods. This study focuses on studying platelet behaviors near the stenosis with deformable red blood cells (RBCs). The influence of varying hematocrit, area blockage, stenosis shape, and driving force on flow characteristics, RBCs, and particle behaviors is considered. Distinct flow characteristics are observed in stenosed microvessels in the presence of RBCs. The motion of RBCs is the major cause of time-dependent oscillations in flow rates, while the contribution of particles to the fluctuations is negligible. However, this effect decreases when the stenosis is elongated in the axial direction. Interestingly, as the hematocrit level increases, downstream particles move closer to the vessel wall due to the enhanced shear-induced lift force resulting from the interaction among RBCs and particles. Furthermore, it is observed that geometrical changes in the stenosis have a more significant impact on the axial profile of particle concentration compared to changes in hematocrit or driving force. An asymmetric stenosis leads to asymmetric profiles in the flow velocity and the distribution of cells and particles due to the geometric focusing effect of the stenosis. There is no significant change in flow rates until a blockage of 0%–50%, but a sudden increase in the root mean square of flow rates occurs at an 80% blockage. This study contributes to our understanding of the rheological behaviors of RBCs and rigid particles in a stenosed microvessel under various hemodynamic conditions.

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.

Assessing the impact of hyperviscosity on stenosis shape in COVID patients

Recent studies have proven that the shape of the stenosis greatly affects the flow characteristics. The 2D rigid wall model examined in this research is analyzed mathematically using various principles and results of functional analysis for the existence and uniqueness of the solution. The model taken into consideration for the current study has also been used to examine the consequences of hyperviscosity in COVID-19 cases. The results of the investigation surmise that the maximum peak velocity of 3.155m/s and the minimum trough pressure of 7041.538Pa were manifested in the high slope geometry. Also, the number of spots over the upper wall of high slope geometry bearing the least wall shear stress was considerably high when compared to the other geometries. The study deduced that the arterial segment bearing dual high slope stenosis was more susceptible to new plaques, plaque ruptures, and hyper viscous syndrome.

Analysis of biological mechanism of blood flow containing nanoparticles through an arterial stenosis

ABSTRACT This article aims to discuss the flow of nanoparticles in the blood through a stenosed artery in the presence of a magnetic field and periodic body acceleration. The overlapping shape of stenosis is chosen to show the impact of blood flow. The Bingham plastic fluid model is utilized to capture the non-Newtonian behavior of blood in the stenosed artery under diseased conditions. The resultant equations are solved analytically using the regular perturbation method. The impact of various emerging parameters on velocity, flow rate, effective viscosity, and wall shear stress are presented through graphs and discussed in detail. It is noticed that liquid velocity and flow rate increase whereas effective viscosity decreases with an increase in slip velocity and Womersley’s frequency parameter. It is also noted that liquid velocity and flow rate are decreased by enhancing the Lorentz force. The increase in body acceleration enhances fluid velocity.

Impact of Stenosis Geometry on Blood Flow Behavior in Human Artery

Atherosclerosis in human arteries affects the blood flow behaviour in different ways and sometimes leads to fatal diseases. This study is focused on the impact of the elasticity of human arteries and the geometry of stenosis on non-Newtonian blood flow across the constricted arteries. The mathematical analysis is carried out using MatLab software. The elastic nature of human arteries and the non-Newtonian nature of blood are described under the power-law, Herschel-Bulkley and Casson model. The numerical derivations for blood flow velocity, volume flow rate and wall shear stress are derived for all three types of the model under consideration and results are also depicted graphically. The influence of elasticity, flow index, yield stress and geometry of stenosis on the blood flow is examined. Power-law model gives higher velocity as compared to Herschel-Bulkley model for the fixed magnitude of flow index 𝑛. It is observed that in the constricted region, the volume flow rate amplifies with the increasing value of stenosis shape parameter 𝑚 for the fixed magnitude of flow index 𝑛. The height of stenosis has a diminishing effect on the flow rate. A comparative analysis of the outcomes of the present study and that of the other published work is carried out for authentication.

The Comparative Method Based on Coronary Computed Tomography Angiography for Assessing the Hemodynamic Significance of Coronary Artery Stenosis

PurposeAn important aspect in the prevention and treatment of coronary artery disease is the functional evaluation of narrowed blood vessels. Medical image-based Computational Fluid Dynamic methods are currently increasingly being used in the clinical setting for flow studies of cardio vascular system. The aim of our study was to confirm the feasibility and functionality of a non-invasive computational method providing information about hemodynamic significance of coronary stenosis.MethodsA comparative method was used to simulate the flow energy losses in real (stenotic) and reconstructed models without (reference) stenosis of the coronary arteries under stress test conditions, i.e. for maximum blood flow and minimal, constant vascular resistance.In addition to the absolute pressure drop in the stenotic arteries (FFRsten) and in the reconstructed arteries (FFRrec), a new energy flow reference index (EFR) was also defined, which expresses the total pressure changes caused by stenosis in relation to the pressure changes in normal coronary arteries, which also allows a separate assessment of the haemodynamic significance of the atherosclerotic lesion itself. The article presents the results obtained from flow simulations in coronary arteries, reconstructed on the basis of 3D segmentation of cardiac CT images of 25 patients from retrospective data collection, with different degrees of stenoses and different areas of their occurrence.ResultsThe greater the degree of narrowing of the vessel, the greater drop of flow energy. Each parameter introduces an additional diagnostic value. In contrast to FFRsten, the EFR indices that are calculated on the basis of a comparison of stenosed and reconstructed models, are associated directly with localization, shape and geometry of stenosis only. Both FFRsten and EFR showed very significant positive correlation (P < 0.0001) with coronary CT angiography–derived FFR, with a correlation coefficient of 0.8805 and 0.9011 respectively.ConclusionThe study presented promising results of non-invasive, comparative test to support of prevention of coronary disease and functional evaluation of stenosed vessels.

Herschel-Bulkley Model of Blood Flow through an Asymmetric Stenosed Artery on Unsteady Reactive Solute Dispersion

This study examined the effects of chemical reaction, stenosis shape parameter and non-Newtonian behaviour on solute dispersion in blood flow via an asymmetric stenosed artery using the generalised dispersion model (GDM). The Herschel–Bulkley (H-B) fluid model, which consists of a yield stress and power-law index, is used to represent the non-Newtonian characteristics of blood in a narrow artery at a low shear rate. The impact of stenosis shape parameter, chemical reaction, power-law index and plug flow radius on the dispersion coefficient and effective axial diffusion of solute is shown. The findings showed that the aforementioned parameters significantly impact the overall process of the chemically reactive solute in a bulk flow. The dispersion coefficient and effective axial diffusion decreases with an increase in the chemical reaction rate, stenosis shape parameter and power-law index. As time passes, the dispersion process slows and becomes almost constant implying a steady state of diffusion. In short, this study provides further insights into the physiological processes involved in the dispersion of drugs and nutrients in the circulatory system.

Entropy and stability analysis on blood flow with nanoparticles through a stenosed artery having permeable walls.

In this research, the electro-osmotic effects are highlighted for a blood-based hybrid nanofluid flow across an artery infected with multiple stenosis. The artery has permeable walls together with slip boundary effects. The slip and permeable boundary conditions model the more realistic blood flow problems. The governing equations of the problem are converted into non-dimensional form by introducing adequate dimensionless variables and acquired the exact solutions. The detailed study of heat transfer is given by Joule heating and viscous dissipation effects. The disorder of fluid flow is investigated by the mathematical study of entropy generation. Analytically attained solutions are examined graphically for both symmetric and non-symmetric shapes of stenosis. Streamlines are analyzed for varying values of flow rate Q and electro-osmotic parameter m. The flow velocity has smallest values on the axis of channel and gets higher value near the boundary walls. The temperature profile delineates opposite behavior to the velocity, and it is parabolic in nature. The velocity reduces towards the non-uniform stenosis except for electroosmotic parameter m. The temperature has larger magnitude in the case of anti-symmetric stenosis. Moreover, the stability of velocity solution is also analyzed.

Hemodynamics and Wall Shear Stress of Blood Vessels in Aortic Coarctation with Computational Fluid Dynamics Simulation

The purpose of this study was to identify the characteristics of blood flow in aortic coarctation based on stenotic shape structure, stenosis rate, and the distribution of the wall load delivered into the blood vessels and to predict the impact on aneurysm formation and rupture of blood vessels by using a computational fluid dynamics modeling method. It was applied on the blood flow in abdominal aortic blood vessels in which stenosis occurred by using the commercial finite element software ADINA on fluid-solid interactions. The results of modeling, with an increasing stenosis rate and Reynolds number, showed the pressure drop was increased and the velocity was greatly changed. When the stenosis rate was the same, the pressure drop and the velocity change were larger in the stenosis with a symmetric structure than in the stenosis with an asymmetric one. Maximal changes in wall shear stress were observed in the area before stenosis and minimal changes were shown in stenosis areas. The minimal shear stress occurred at different locations depending on the stenosis shape models. With an increasing stenosis rate and Reynolds number, the maximal wall shear stress was increased and the minimal wall shear stress was decreased. Through such studies, it is thought that the characteristics of blood flow in the abdominal aorta where a stenosis is formed will be helpful in understanding the mechanism of growth of atherosclerosis and the occurrence and rupture of the abdominal aortic flow.

Non-Newtonian blood flow model with the effect of different geometry of stenosis

The objective of this paper is to present a non-Newtonian blood flow model with the effect of different geometry of stenosis on various flow quantities. The Power-law model is considered to explore the non-Newtonian property of blood. Two-point Gauss quadrature formula is applied to obtain the numerical expressions of dimensionless flow resistance, skin-friction and flow rate. The variation of dimensionless flow resistance, skin-friction and flow rate with degree of stenosis, axial distance and power-law index is shown graphically. Moreover, the power-law index is adjusted to explore the non-Newtonian characteristics of blood. The importance of the present work has been carried out by comparing the results with other theories both numerically and graphically. It has been found that resistance to flow becomes maximum with total blockage of artery for different shape of stenosis.

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.