Blood Flow In Stenosed Artery Research Articles

Thermal analysis in unsteady oscillatory Darcy blood flow through stenosed artery

This study aims to provide an extensive overview of the consequences of heat source and thermal radiation on blood flow in stenosed arteries through Casson fluid. We examine the behaviour of an unsteady non-Newtonian fluid under oscillatory Darcy flow. This analysis explores the impact of blood flow in the stenosed arteries on the momentum and energy profiles of the Casson fluid. In addition, this study examines a parametric analysis to illustrate the impact of the Nusselt number and Casson parameter. Higher values of the thermal radiation and Casson-Viscous parameters result in enhanced velocity fields. The Brinkman model accurately represents the resistance to flow caused by the porous material, known as Darcy resistance. The inner space of the coronary artery generates cholesterol-rich fatty plaques and blood clots that block the artery, simulating the diseased condition of blood circulation in this study. We employ a set of non-dimensional variables to convert the governing equations of the current flow into dimensionless partial differential equations. Analytical methods have derived a solution for the studied problem. The discovery is pertinent to the natural circulation of blood through coronary arteries, which are highly porous. A particular artery pathology creates a permeable structure within the arterial lumen. The current study demonstrates that blood flow may be manipulated by adjusting the intensity of the external magnetic field, while the temperature of the blood can be managed by either increasing or decreasing its thermal conductivity. The graphical representation demonstrates the impact of different physical parameters on velocity, temperature, and concentration profiles. The significant results of the current studies are that, the fluid velocity diminishes with rising magnetic and Biot numbers but exhibits an increase when considering the Darcy number and Hall parameter. There is a gentle increase in the wall shear stress as the Casson parameter (β) increases from 0.1 to 0.3. For β= 0.3, the percentage change along the axial direction (x) is more pronounced. This is because the wall shear stress is proportional to the number of Casson parameters.

Impact of hematocrit on pulsatile blood flow in stenosed arteries: a computational study in healthy, diabetic, and anemic models

In this study, researchers aim to enhance the realism of circulatory system simulations, focusing on factors affecting flow variations, particularly in stenotic arteries of individuals with altered hematocrit levels. Through extensive data collection and varied conditions, the goal is to attain more precise and valid results. The study conducts approximate simulations to comprehensively describe the dynamic motion of pulsatile flow. Different values of inlet velocity (UDF) are introduced, considering potential arterial distortion or occlusion due to plaque deposition, along with variations in hematocrit (Hct) levels commonly observed in patients. Three distinct types of pulsatile blood flow, corresponding to diabetes (Hct 65%), healthy (Hct 45%), and anemia (Hct 25%), are studied and compared. The research illuminates that stenosis in arteries with varying hematocrit levels significantly impacts hydrodynamic features, potentially predisposing individuals to cardiovascular diseases. Through meticulous analysis, several conclusions about hemodynamic characteristics are drawn. It is observed that both velocity and wall shear stress exhibit variation along the affected artery, influenced by stenosis and changes in hematocrit levels. Notably, the highest influence on velocity and wall shear stress is observed with Hct 65%, compared to Hct 45% and Hct 25% at the moment of stenosis. These findings hold substantial practical implications for the field of cardiovascular health, providing valuable insights into blood flow behavior in stenotic arteries with diverse hematocrit levels. Ultimately, this research contributes to more effective clinical interventions.

The significance of ternary hybrid cross bio-nanofluid model in expanding/contracting cylinder with inclined magnetic field

Significance: Bio-nanofluids have achieved rapid attention due to their potential and vital role in various fields like biotechnology and energy, as well as in medicine such as in drug delivery, imaging, providing scaffolds for tissue engineering, and providing suitable environments for cell growth, as well as being used as coolants in various energy systems, wastewater treatment, and delivery of nutrients to plants.Objective: The present study proposes a novel mathematical model for the ternary hybrid cross bio-nanofluid model to analyse the behaviour of blood that passes through a stenosed artery under the influence of an inclined magnetic field. The model considers the effect of expanding/contracting cylinder, infinite shear rate viscosity, and bio-nanofluids.Methodology: The considered model of the problem is bounded in the form of governing equations such as PDEs. These PDEs are transformed into ODEs with the help of similarity transformations and then solved numerically with the help of the bvp4c method.Findings: The results show that the flow rate and velocity decrease as the inclination angle of the magnetic field increases. Additionally, research has found that the presence of nanoparticles in the bio-nanofluid has a significant impact on the velocity and flow rate. Therefore, the flow rate decreases, in general, as the stenosis becomes more severe.Advantages of the study: The results obtained from this study may provide insights into the behaviour of blood flow in stenosed arteries and may be useful in the design of medical devices and therapies for the treatment of cardiovascular diseases.

Unsteady blood flow of Carreau fluid in a porous saturated medium with stenosis under the influence of acceleration and magnetic fields: A comprehensive analysis

Blood flow in stenosed arteries is a common cause of cardiovascular diseases, leading to serious health problems. The present study aims to investigate the unsteady Womersley blood flow in a stenosed, porous saturated artery under the influence of acceleration and magnetic fields. The study utilizes a Carreau constitutive equation to model blood rheology and employs the finite difference technique to compute the governing equations under the assumption of unsteady, unidirectional, and laminar flow. The importance of this study lies in its potential to provide a better understanding of the complex behavior of hemodynamic flow in the presence of external fields and porous media, which has significant implications for the control and management of cardiovascular diseases. In particular, the study analyses the impacts of non-dimensional parameters, such as magnetic field, channel permeability, acceleration field, Weissenberg number, and stenosis amplitude, on critical flow variables, such as velocity, resistivity, wall shear stress, and flow rate. Our calculations suggest that a magnetic field is an effective instrument for regulating hemodynamic flow because it increases resistance by up to 8.31% while decreasing flow by up to 8.44%. Channel permeability, on the other hand, improves blood velocity by up to 33.35% while eliminating resistance by up to 23.43%. Furthermore, greater acceleration fields decrease resistivity while increasing velocity, flow rate, and wall shear stress. Additionally, the severity of the stenosis and the Weissenberg number substantially affect flow factors. By raising the stenosis amplitude, resistivity rises, and other flow characteristics diminish, whereas modifying the Weissenberg number causes the reverse effect.

Study of fractional-order model on Casson blood flow in stenosed artery with magnetic field effect

In this research work, the impacts of magnetic fields on Casson blood flow with stenosed artery are studied. The flow under investigation is affected by a magnetic field and an oscillating pressure gradient. The Caputo–Fabrizio fractional-order derivative was used to express the governing system of partial differential equations with imposed boundary and initial conditions. The governing problem is solved using Laplace and Finite Hankel transformations. The exact solution for blood velocity, magnetic particle velocity, and temperature profiles are defined. For better understanding of the various physical parameter, numerical results are obtained for blood velocity, magnetic particle velocity and temperature profiles and presented through the graphs. It is seen that the magnetic fields tend to reduce the blood viscosity which can be used for controlling the blood flow rate. It is also seen that Casson fluid parameter tends to improve the blood flow rate. From the results, it is illustrated that the heat transfer process improves with thermal radiation and heat generation parameter.

Fast prediction of blood flow in stenosed arteries using machine learning and immersed boundary-lattice Boltzmann method.

A fast prediction of blood flow in stenosed arteries with a hybrid framework of machine learning and immersed boundary-lattice Boltzmann method (IB–LBM) is presented. The integrated framework incorporates the immersed boundary method for its excellent capability in handling complex boundaries, the multi-relaxation-time LBM for its efficient modelling for unsteady flows and the deep neural network (DNN) for its high efficiency in artificial learning. Specifically, the stenosed artery is modelled by a channel for two-dimensional (2D) cases or a tube for three-dimensional (3D) cases with a stenosis approximated by a fifth-order polynomial. An IB–LBM is adopted to obtain the training data for the DNN which is constructed to generate an approximate model for the fast flow prediction. In the DNN, the inputs are the characteristic parameters of the stenosis and fluid node coordinates, and the outputs are the mean velocity and pressure at each node. To characterise complex stenosis, a convolutional neural network (CNN) is built to extract the stenosis properties by using the data generated by the aforementioned polynomial. Both 2D and 3D cases (including 3D asymmetrical case) are constructed and examined to demonstrate the effectiveness of the proposed method. Once the DNN model is trained, the prediction efficiency of blood flow in stenosed arteries is much higher compared with the direct computational fluid dynamics simulations. The proposed method has a potential for applications in clinical diagnosis and treatment where the real-time modelling results are desired.

Numerical Study of Unsteady Boundary Layer Flow of a Biomagnetic Fluid over a Horizontal Stretching Sheet with Magnetic Dipole

This paper focuses on the theoretical and numerical investigation of the unsteady, viscous, incompressible, two-dimensional laminar boundary layer flow of a Newtonian biomagnetic fluid over a stretching sheet under the influence of an applied magnetic field in the presence of heat transfer. The magnetic field is induced by a magnetic dipole placed below the stretching sheet. The magnetic field intensity represents the magneto-thermo-mechanical coupling. This allows exclusion of the biofluid that is distant from the sheet at Curie temperature to avoid further magnetization. The unsteadiness of the flow is discernible in the fluid flow properties. The mathematical model of the problem conforms to the principles of Magnetohydrodynamics (MHD) and Ferrohydrodynamics (FHD). In this work, the study is performed on a specific biofluid, human blood. The modified Stokes principle is used to implement the model under the assumption that along with the three thermodynamic variables P, ρ, and T, the Biomagnetic Fluid Dynamics (BFD) fluid behavior can be characterized as a function of magnetization M. To describe the physical problem, a coupled non-linear system of ordinary differential equations subject to appropriate boundary conditions is derived from Navier-Stokes and thermal energy equations by performing non-dimensionalization of the considered variables. To solve these equations, the dsolve routine in the MAPLE software is used. Numerical results for flow profiles and the local skin friction coefficient (Cfx) and the local Nusselt number (Nux) are discussed for different values of unsteadiness parameter (A), biomagnetic interaction parameter (B) and a rational quantity (ϵ). The achieved results are compared with previously published work for steady state flow, and they seem to be in good agreement. It is found that MHD and FHD interaction parameters affect significantly on the velocity, temperature and pressure field. A successful completion will bring interesting results for better understanding of the biomagnetic fluid flow characteristics and can be beneficial to medical and bioengineering applications; particularly for estimating the characteristics of blood flow in stenosed arteries.

Bibliometric analysis of effect of applied magnetic field on blood flow in stenosed artery

Around 50% of the deaths in the world are because of heart diseases. One of the heart diseases is Atherosclerosis which occurs due to stenosis in arteries. Researchers and medical practioners are working on how to reduce the reduction/fluctuations in blood flow in stenosed arteries. One of the methods under consideration is the application of magnetic field on blood flow in stenosed arteries. With limited healthcare resources, Bibliometric studies help scholars and funding agencies to focus on the research area in which more attention is needed. The main purpose of this bibliometric analysis is to find the development in blood flow in stenosed arteries and to identify potential areas for further research. This paper provides an overall picture of research carried in blood flow in stenosed arteries in the presence of applied magnetic field and, in the current century. This analysis is done using mainly Scopus database along with Google scholar, data taken from Mendeley and using some graphical tools. This survey revealed that the maximum publications are from journals and conferences and India lead the publications in this area. Blood flow and stenosis are frequently used key words and major contributions in this area are from computer science journals followed by mechanical journals. Medical and Engineering are two main fields in which the publications in this topic are more. The high number of citations of the journals in which the related articles are published shows the importance and thrust in this area. This paper puts a light on contribution of researchers in the area which will help medical practioners to take up the idea to next level.

Bibliometric analysis of effect of applied magnetic field on blood flow in stenosed artery

Around 50% of the deaths in the world are because of heart diseases. One of the heart diseases is Atherosclerosis which occurs due to stenosis in arteries. Researchers and medical practioners are working on how to reduce the reduction/fluctuations in blood flow in stenosed arteries. One of the methods under consideration is the application of magnetic field on blood flow in stenosed arteries. With limited healthcare resources, Bibliometric studies help scholars and funding agencies to focus on the research area in which more attention is needed. The main purpose of this bibliometric analysis is to find the development in blood flow in stenosed arteries and to identify potential areas for further research. This paper provides an overall picture of research carried in blood flow in stenosed arteries in the presence of applied magnetic field and, in the current century. This analysis is done using mainly Scopus database along with Google scholar, data taken from Mendeley and using some graphical tools. This survey revealed that the maximum publications are from journals and conferences and India lead the publications in this area. Blood flow and stenosis are frequently used key words and major contributions in this area are from computer science journals followed by mechanical journals. Medical and Engineering are two main fields in which the publications in this topic are more. The high number of citations of the journals in which the related articles are published shows the importance and thrust in this area. This paper puts a light on contribution of researchers in the area which will help medical practioners to take up the idea to next level.

Performance of k-ω and k-ε Model for Blood Flow Simulation in Stenosed Artery

Blood flow through arterial stenosis can play a crucial role at the post stenotic flow regions. This produces a disturbance in the normal flow path. The intensity of the flow disturbance (i.e. laminar, transitional and turbulent flow characteristics) depends not only on the severity of the stenosis but also on the pattern of the geometrical model. In that case, the turbulence model plays vital role to measure these flow disturbances. However, it is very important to choose a proper flow simulation model that can predict the flow behavior of fluid accurately and efficiently with less computational cost and time. Thus, this study aims to analyze the results of two turbulence models i.e. k-ω and k-ε for blood flow simulation to compare their performance for the prediction of the flow behavior. Simulations have been performed with 75% area reductions in the arteries. The results of simulation show that, the flow parameters obtained from the k-ε model exhibits lack of fits with the experimental data. On the other hand, k-ω model can capture large scale gradient in the different parameters of blood flow and has a good agreement with the experimental data. This study suggests that, k-ω model has the better performance comparing to k-ε model to predict the behavior of blood flow in stenosed artery. GANIT J. Bangladesh Math. Soc. 40.2 (2020) 111-125

Distinct dietary alpha-linolenic acid-dependent shifts in the fecal microbiome composition suppresses aging-associated inflammatory responses and thrombus formation

Abstract Background Aging is associated with alterations in the fecal microbiome composition. The microbiota-derived trimethylamine-N-oxide (TMAO) correlates with arterial thrombotic events, e.g. myocardial infarction and stroke, the leading causes of mortality worldwide. The omega-3 fatty acid (n-3 FA) α-linolenic acid (ALA) has been shown to be protective against thrombosis and associated pathologies. Therefore, we hypothesized that long-term dietary ALA supplementation protects against the aging-associated microbiome dysbiosis, and reduces inflammatory and thrombotic responses. Methods 24 week-old male C57BL/6 mice were fed either a high ALA (7.3g%) or low ALA (0.03g%) diet for 12 months. We examined the compositional changes of fecal microbiota of the animals treated with high vs. low ALA via 16S rRNA gene sequencing. The plasma levels of TMAO and its precursors choline and betaine, and LPS were measured by ELISA. Additionally, the platelet aggregation in response to thrombin, and thrombus formation on collagen under high-shear flow conditions of 3000/sec (to mimic blood flow in stenosed arteries) were investigated. Results Genomic analyses showed that the abundance of Phylum Proteobacteria and the family of desulfovibrio were reduced 71.72% and 51.73% in the aged high ALA-treated mice (p<0.01 and p<0.001, resp.) that may result in decrease in TAMO production and the subsequent inflammatory responses. However, microbial diversity of Bacteroidetes or Fermicutes and Bacteroidetes/Fermicutes ratio did not demonstrate a significant change between high vs. low ALA groups. Interestingly, the dietary intake of high ALA increased the abundance of Lachnospiraceae (p<0.01) that may exert anti-inflammatory effects. Importantly, high ALA significantly decreased the plasma levels of TMAO (p<0.01) and its precursor choline (P<0.05), but not betaine. The pro-inflammatory cytokine TNF-α showed a significant reduction (p<0.05), whereas plasma IL-1β did not change significantly following high ALA supplementation. An increased thrombus formation on collagen under high-shear flow (36.34%, p<0.01) and thrombin-induced platelet aggregation (31.31%, p<0.05) were found in the aged mice. Conclusion These studies demonstrate that an ALA-rich diet induces beneficial bacterial shifts in the aging-associated fecal microbiome that may lead to the suppression of inflammatory and thrombotic responses. Hence, long-term dietary ALA supplementation may be exploited as a nutritional antithrombotic strategy in the aging. Microbiome-Thrombosis-Aging Funding Acknowledgement Type of funding source: Foundation. Main funding source(s): Swiss National Science Foundation (SNSF)

A Metamodeling Approach for Instant Severity Assessment and Uncertainty Quantification of Iliac Artery Stenoses.

Two-dimensional (2D) or three-dimensional (3D) models of blood flow in stenosed arteries can be used to patient-specifically predict outcome metrics, thereby supporting the physicians in decision making processes. However, these models are time consuming which limits the feasibility of output uncertainty quantification (UQ). Accurate surrogates (metamodels) might be the solution. In this study, we aim to demonstrate the feasibility of a generalized polynomial chaos expansion-based metamodel to predict a clinically relevant output metric and to quantify the output uncertainty. As an example, a metamodel was constructed from a recently developed 2D model that was shown to be able to estimate translesional pressure drops in iliac artery stenoses (-0.9 ± 12.7 mmHg, R2 = 0.81). The metamodel was constructed from a virtual database using the adaptive generalized polynomial chaos expansion (agPCE) method. The constructed metamodel was then applied to 25 stenosed iliac arteries to predict the patient-specific pressure drop and to perform UQ. Comparing predicted pressure drops of the metamodel and in vivo measured pressure drops, the mean bias (-0.2 ± 13.7 mmHg) and the coefficient of determination (R2 = 0.80) were as good as of the original 2D computational fluid dynamics (CFD) model. UQ results of the 2D and metamodel were comparable. Estimation of the uncertainty interval using the original 2D model took 14 days, whereas the result of the metamodel was instantly available. In conclusion, it is feasible to quantify the uncertainty of the output metric and perform sensitivity analysis (SA) instantly using a metamodel. Future studies should investigate the possibility to construct a metamodel of more complex problems.

Glycoprotein Ib clustering in platelets can be inhibited by α-linolenic acid as revealed by cryo-electron tomography.

Platelet adhesion to the sub-endothelial matrix and damaged endothelium occurs through a multi-step process mediated in the initial phase by glycoprotein Ib binding to von Willebrand factor (vWF), which leads to the subsequent formation of a platelet plug. The plant-derived ω-3 fatty acid α-linolenic acid is an abundant alternative to fish-derived n-3 fatty acids and has anti-inflammatory and antithrombotic properties. In this study, we investigated the impact of α-linolenic acid on human platelet binding to vWF under high-shear flow conditions (mimicking blood flow in stenosed arteries). Pre-incubation of fresh human blood from healthy donors with α-linolenic acid at dietary relevant concentrations reduced platelet binding and rolling on vWF-coated microchannels at a shear rate of 100 dyn/cm2. Depletion of membrane cholesterol by incubation of platelet-rich plasma with methyl-β cyclodextrin abrogated platelet rolling on vWF. Analysis of glycoprotein Ib by applying cryo-electron tomography to intact platelets revealed local clusters of glycoprotein Ib complexes upon exposure to shear force: the formation of these complexes could be prevented by treatment with α-linolenic acid. This study provides novel findings on the rapid local rearrangement of glycoprotein Ib complexes in response to high-shear flow and highlights the mechanism of in vitro inhibition of platelet binding to and rolling on vWF by α-linolenic acid.

Biomathematical study of Sutterby fluid model for blood flow in stenosed arteries

In this paper, we have discussed the biomathematical analysis of Sutterby fluid model for blood flow in stenosed tapered arteries. The equations for the Sutterby fluid model are modeled in cylindrical geometry. The equations have been developed for the case of mild stenosis. Perturbation solutions are attained in terms of small Sutterby fluid parameter β for the velocity, impedance resistance and wall shear stress. Three types of arteries i.e. converging, diverging and non-tapered have been considered for the analysis and discussion. Graphical results have been presented for different parameters of interest. Streamlines have been plotted at the end of the paper.

A computational study on spiral blood flow in stenosed arteries with and without an upstream curved section

Spiral and non-spiral blood flows through three-dimensional models of 75% axisymmetric arterial stenosis are investigated by using two-equation standard k-ω transitional model and Large Eddy Simulation (LES). The arterial stenosis models chosen are straight stenosed tubes without and with upstream curved segments of various angles of curvature. The Reynolds numbers investigated are 500, 1000, 1500 and 2000. Spiral effect is introduced by taking one-sixth of the bulk velocity as a tangential velocity at the inlet, and the inlet turbulence intensity was introduced for matching experimental results. LES results with a right amount of inlet turbulence intensity matches experimental results better than the k-ω results. The results show that the spiral flow affects the turbulence kinetic energy in the post stenosis region. Other important results such as the wall pressure and shear stress remain almost unchanged by the spiral velocity. But the presence of the upstream curved segment in artery moderately affects the results of the maximum pressure drop and wall shear stress.

Biomechanical Analysis of Eyring Prandtl Fluid Model for Blood Flow in Stenosed Arteries

Abstract In this article, we have examined biomechanical analysis of Eyring Prandtl fluid model for blood flow in stenosed arteries. Blood flow in arteries is an important phenomenon from biological and medical point of view. No one can survive without blood flow in tapered arteries. Blood flow is the continuous running of blood in the cardiovascular system. The human body is made up of several processes all carrying out various functions. We have the gastrointestinal system which aids the digestion and the absorption of food. We also have the respiratory system which is responsible for the absorption of O2 and elimination of CO2. The urinary system removes waste from the body. The cardiovascular system helps to distribute food, O2 and other products of metabolism. The reproductive system is responsible for perpetuating the species. The nervous and endocrine system is responsible for coordinating the integration and functions of other system. The equations govern the flow for considered model are presented in cylindrical coordinates. Perturbation solutions are developed in terms of small Eyring Prandtl fluid parameter β for the velocity, impedance resistance, wall shear stress and shearing stress at the stenosis throat. Three types of arteries i.e converging, diverging and non-tapered arteries have been considered for the analysis and discussion. Graphical results have been presented for different physical parameters of the flow problem. Streamlines have been plotted at the end of the article. We observed that due to increase in Eyring Prandtl fluid parameter α, β the stenosis shape n and maximum height of the stenosis δ the velocity profile increases.

Blood flow in stenosed arteries with radially variable viscosity, peripheral plasma layer thickness and magnetic field

A novel approach of combined mathematical and computational models has been developed to investigate the oscillatory two-layered flow of blood through arterial stenosis in the presence of a transverse uniform magnetic field applied. Blood in the core region and plasma fluid in the peripheral layer region are assumed to obey the law of Newtonian fluid. An analytical solution is obtained for velocity profile and volumetric flow rate in the peripheral plasma region and also wall shear stress. Finite difference method is employed to solve the momentum equation for the core region. The numerical solutions for velocity, flow rate and flow resistance are computed. The effects of various parameters associated with the present flow problem such as radially variable viscosity, hematocrit, plasma layer thickness, magnetic field and pulsatile Reynolds number on the physiologically important flow characteristics namely velocity distribution, flow rate, wall shear stress and resistance to flow have been investigated. It is observed that the velocity increases with the increase of plasma layer thickness. An increase or a decrease in the velocity and wall shear stress against the increase in the value of magnetic parameter (Hartmann number) and hematocrit is dependent on the value of t. An increase in magnetic field leads to an increase in the flow resistance and it decreases with the increase in the plasma layer thickness and pulsatile Reynolds number. The information concerning the phase lag between the flow characteristics and how it is affected by the hematocrit, plasma layer thickness and Hartmann number has, for the first time, been added to the literature.

A coupled flow-acoustic computational study of bruits from a modeled stenosed artery

The sound generated by blood flow in stenosed arteries is investigated for a model that consists of a channel with a one-sided constriction. The blood flow-induced arterial "bruits" are computed directly using a hybrid approach wherein the hemodynamic flow field is solved by an immersed boundary, incompressible flow solver, and the sound generation is modeled by a first-principles approach that employs the linearized compressible perturbation equations. The transmission and propagation of the sound through the surrounding biological tissues is also modeled with a simplified, linear structural wave equation. The flow field inside the artery and the bruit sound signal at the epidermal surface are examined to delineate the precise source of the arterial bruit and the correlation between the bruit and the arterial wall pressure fluctuations. It is found that the bruits are related primarily to the time-derivative of the integrated pressure force on the post-stenotic segment of arterial wall. The current study provides a clear perspective on the generation of bruits from stenosed arteries and enables an assessment of the conjectures of previous researchers regarding the source of arterial bruits.

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.

FDM analysis for MHD flow of a non-Newtonian fluid for blood flow in stenosed arteries

A computational model is developed to analyze the effects of magnetic field in a pulsatile flow of blood through narrow arteries with mild stenosis, treating blood as Casson fluid model. Finite difference method is employed to solve the simplified nonlinear partial differential equation and an explicit finite difference scheme is obtained for velocity and subsequently the finite difference formula for the flow rate, skin friction and longitudinal impedance are also derived. The effects of various parameters associated with this flow problem such as stenosis height, yield stress, magnetic field and amplitude of the pressure gradient on the physiologically important flow quantities namely velocity distribution, flow rate, skin friction and longitudinal impedance to flow are analyzed by plotting the graphs for the variation of these flow quantities for different values of the aforesaid parameters. It is found that the velocity and flow rate decrease with the increase of the Hartmann number and the reverse behavior is noticed for the wall shear stress and longitudinal impedance of the flow. It is noted that flow rate increases and skin friction decreases with the increase of the pressure gradient. It is also observed that the skin friction and longitudinal impedance increase with the increase of the amplitude parameter of the artery radius. It is also found that the skin friction and longitudinal impedance increases with the increase of the stenosis depth. It is recorded that the estimates of the increase in the skin friction and longitudinal impedance to flow increase considerably with the increase of the Hartmann number.