Peripheral Layer Thickness Research Articles

Magnetohydrodynamic Stenosed Blood Flow Through Microcirculation with Permeable Walls

Blood flow through the composite stenosis of a micro vessel with permeable walls in the presence of an external magnetic field was examined. Endothelial walls of blood vessels are considered to be highly permeable in nature. Thus in the study of such flows, wall permeability must be accounted for. Blood flow made up of a particle-fluid suspension in the core surrounded by a plasma layer was utilized. The effects of introducing as well as increasing wall permeability and the magnetic field were investigated by varying the Darcy number and Hartmann number respectively. Plots were presented to depict the effect of various parameters on the velocity of blood and flow impedance as well as the shear stress on both the vessel wall and at the stenosis throat. The effects of varying hematocrit and peripheral layer thickness were also discussed. These flow characteristics were found to be lower in this model than in its corresponding one layer model. Knowledge gained from this examination of blood flow can aid in understanding and diagnosing cardiovascular diseases in patients especially in cases where a magnetic field is present.

Dispersion phenomena of reactive solute in a pulsatile flow of three-layer liquids

This study aims at investigating the dispersion process in an oscillatory flow of a layered liquid. The liquid is considered as a three-layer liquid where the center region is the Casson liquid surrounded by a Newtonian liquid layer flowing through a narrow pipe under the wall reaction. The perturbation technique has been used for solving the momentum equations. In order to assist the analysis of solute transport behavior, Aris-Barton’s method of moments has been utilized, where different molecular diffusivities were assumed for different respective regions, yet to be constant. The effects of finite yield stress, viscosity ratio, density ratio, peripheral layer thickness, and irreversible absorption at the tube wall on dispersion are investigated in detail. In the cases of steady, unsteady, and combined flow situations, dispersion coefficient is found to be diminished by absorption parameter, viscosity ratio, and yield stress, respectively. In the case of a steady flow and unsteady convective diffusion of a reactive solute, dispersion coefficient is independent of density ratio. For both the unsteady and combined flows, density ratio provides a pulsatile behaviour of the dispersion process though an increase in the density ratio may faster the dispersion process. Dispersion at early times is not affected by absorption though a considerable effect is observed for large time. The presence of a peripheral layer enhances the value of the dispersion coefficient and is higher than the single layer Casson liquid flow. As strong as the non-Newtonian effect is considered, the dispersion process becomes slower. Larger values of molecular diffusivity at different layers are the reason for less dispersion coefficient. This study may be useful for understanding the dispersion process in the blood-like liquid flow analysis for microcirculation.

Unsteady solute dispersion in small blood vessels using a two-phase Casson model

This study explores the transport of a solute in an unsteady blood flow in small arteries with and without absorption at the wall. The Casson fluid model is suitable for blood flow in small vessels. Owing to the aggregation of red cells in the central region of the small vessels, a two-phase model is considered in this investigation. Using the generalized dispersion model (Sankarasubramanian & Gill 1973 Proc. R. Soc. Lond. A 333 , 115–132. (doi:10.1098/rspa.1973.0051)), the convection, dispersion and mean concentration of the solute are analysed at all times in small arteries of different radii. The effects of the yield stress, wall absorption, the amplitude of the fluctuating pressure gradient component, the peripheral layer thickness, the Womersley frequency parameter, the Schmidt number and the Peclet number on the dispersion process are discussed. A comparative study of solute dispersion among single- and two-phase fluid models is presented. For small vessels, a significant difference between these models is observed during the solute dispersion; however, this difference becomes insignificant for large vessels. The mean concentration of solute reduces with increasing radius of the vessels. The present investigation is more realistic for understanding the transportation process of drugs in blood flow in small arteries using the non-Newtonian fluid model.

Spiral Bearing Lubrication with Viscosity Variation And Thermal Effect of Two Layer Fluid

In this paper a fluid film equation for two layer fluids and generalized Reynolds equation for convergent and divergent spiral bearing is derived with thermal effect. It is applied to see the effect of pre-load factor, viscosity variation, eccentricity, peripheral layer thickness. Expressions for load, pressure and coefficient of friction are derived and are analyzed numerically. The effect of pre-load factor analyzed for convergent and divergent spiral bearings. When pre-load factor is zero then both convergent and divergent spiral bearings are becomes journal bearing. It is observed the dimensionless load capacity values form the tables. The spiral bearing bears more load capacity than journal bearing. The effects of viscosity variation and thermal effect on these parameters are also analyzed.

Effects of peripheral layer thickness on pulsatile flow of Herschel–Bulkley fluid through a stenotic artery

A study is conducted to analyze two-phase flow model of blood in a flexible stenotic artery. The Newtonian and Herschel–Bulkley constitutive relations are used to model the core and peripheral regions, respectively. The arterial wall is assumed to be elastic. By making appropriate assumptions, the flow problem is transformed into a set of nonlinear partial different equations. These equation together with suitable initial and boundary data are solved using an explicit finite difference scheme. The radial and axial velocities of the streaming blood are computed for several values of the emerging parameters. The axial distribution of flow rate, resistance impedance, and wall shear stress are also shown graphically and discussed in detail. The instantaneous streamlines patterns of the flow are also shown.

Evaluation of macular ganglion cell complex and peripheral retinal nerve fiber layer structural damage in early primary glaucomous eyes by 3D-OCT

Background In previous study, peripheral retinal nerve fiber layer (RNFL) thickness is considered to be the earliest structural changes which can be detected.3D-OCT can measure the thickness of macular ganglion cell complex (mGCC), which makes the detection of primary glaucoma possible in the early stage. Objective This study was to measure the thickness of mGCC and disc-peripheral RNFL in early stage of primary glaucomous eyes by 3D-OCT and assess the anatomic basis of glaucoma-induced optical nerve damage. Methods 3D-OCT images from 10 patients with advanced stage primary glaucoma in one lateral eye and early stage glaucoma in fellow eye from December 2010 to December 2012 were prospectively analyzed in China-Japan Friendship Hospital.The patients were diagnosed based on the recommended standard of National glaucoma group (1987 version) and received routine eye examination.3D-OCT scanning was performed using 3D-macular mode, 3D-macular Wide mode and 3D-disc mode with TOPCON 3D-OCT 2000 system, and the images at macular 6 mm×6 mm area were analyzed.The posterior pole area was divided into 5 concentric rings from fovea toward periphery and equally subdivided into 100 small checks, with the area of 0.6 mm×0.6 mm for each.The probable values in each check were calculated as the ratio of each figure and corresponding normal value.The probable values were expressed as red color (P<1%), yellow color (P<5%) and gray color (P≥5%). Then the disc-periphery RNFL thickness and disc cup were evaluated. Results No evident abnormality was found in the thicknesses of photoreceptors layer and bipolar cell layer in both advanced glaucomous eyes and the early stage of glaucomous eyes in the 10 patients.Serious damage of visual field was seen in the advanced glaucomous eyes and presented with red color in the parapapillary RNFL area, mGCC area and macular RNFL area, showing an evidently attenuation of the thicknesses of parapapillary RNFL, mGCC and RNFL.However, the visual field was close normal in the early stage glaucomous eyes, and mGCC and macular RNFL showed yellow color, while green or yellow color was exhibited in the parapapillary RNFL area, indicating mGCC and macular RNFL thickness was reduced, but parapapillar RNFL thickness was near normal. Conclusions The change of mGCC thickness is earlier than that of peripheral RNFL at optic disc in primary glaucomaous eyes, which may imply that the disappear of macular ganglion cell body is earlier than that of the axon. Key words: Glaucoma, primary; Optical coherence tomography; Biometry; Retinal nerve fiber; Retinal ganglion cells; Retinal ganglion cell complex

Meta-analysis of the relationship of peripheral retinal nerve fiber layer thickness to Alzheimer's disease and mild cognitive impairment.

BackgroundPrevious studies report that the thickness of the peripheral retinal nerve fiber layer (RNFL) in individuals with Alzheimer's disease (AD) and mild cognitive impairment (MCI) is significantly thinner than in normal controls (NC), but RNFL thickness in different quadrants of the optic nerve remains unclear.AimConduct a systematic review of studies that assess peripheral RNFL thickness in AD and MCI.MethodsBased on pre-defined criteria, studies in English or Chinese were identified from PubMed, Embase, ISI web of knowledge, Ovid/Medline, Science Direct, Cochrane Library, Chinese National Knowledge Infrastructure (CNKI), Chongqing VIP database, WANFANG DATA, and the China BioMedical Literature Service System (SinoMed). Review Manager 5.3 was used for analysis.ResultsThe 19 cross-sectional studies identified had a pooled sample of 1455 individuals. There was substantial heterogeneity between studies that compared RNFL in AD or MCI to normal controls, but this heterogeneity was primarily restricted to low-quality studies. Combining 6 high-quality studies (n=578) indicated that total RNFL thickness and the thickness of superior and inferior RNFL quadrants in AD were significantly thinner than in normal controls. Similarly, combining 5 high-quality studies (n=541) indicated significantly thinner total RNFL thickness in MCI than in controls. Six studies (n=589) found thinner RNFL in the superior and inferior quadrants in MCI than in controls;and 6 studies (n=487) found thinner RNFL in the temporal quadrant in MCI than in controls. Finally, 7 studies (n=432) indicated that total RNFL was thinner in AD than in MCI, and 6 studies (n=364) indicated thinner RNFL in the superior and inferior quadrants in AD than in MCI.ConclusionMuch of the heterogeneity in results from previous studies may be due to poor methodology. Peripheral RNFL thicknesses, particularly in the superior and inferior quadrants, becomes progressively thinner as cognitive function declines, so this could be a candidate biomarker for early identification of AD. Methodologically rigorous studies in large population-based cohort studies that follow elderly individuals over time and that simultaneously collect information on potential mediating factors (such as blood pressure, blood glucose, and lipid levels) are needed to confirm or disprove the potential predictive value of RNFL.

The Diabetes Visual Function Supplement Study (DiVFuSS)

BackgroundDiabetes is known to affect visual function before onset of retinopathy (diabetic retinopathy (DR)). Protection of visual function may signal disruption of mechanisms underlying DR.MethodsThis was a 6-month randomised, controlled...

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.

Parallel Simulation of Cellular Flow in Microvessels Using a Particle Method

We developed a numerical method for large-scale simulations of cellular flow in microvessels. We employed a particle method, where all blood components were modeled using a finite number of particles. Red blood cell deformation was modeled by a spring network of membrane particles. A domain decomposition method was used for parallel implementation on distributed memory systems. In a strong scaling test up to 64 CPU cores, we obtained a linear speedup with the number of CPU cores, and demonstrated that our model can simulate O(10 3 ) red blood cells in vessels a few tens of micrometers in diameter. For quantitative validation, we analyzed the Fahraeus effect and the formation of a cell-depleted peripheral layer. Simulations were performed for tube hematocrit ranging from 20 to 45%, and microvessel diameters from 9 to 50 μm. Our numerical results were in good agreement with previous experimental results both for the discharge hematocrit and cell-depleted peripheral layer thickness.

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 study on two-layered model (Casson–Newtonian) for blood flow through an arterial stenosis: Axially variable slip velocity at the wall

The present paper sheds some light on a mathematical model for blood flow through stenosed arteries with axially variable peripheral layer thickness and variable slip at the wall. The model consists of a core region of suspension of all the erythrocytes assumed to be a Casson fluid and a peripheral layer of plasma as a Newtonian fluid. For such models, in literature, the peripheral layer thickness and slip velocity are assumed a priori based on experimental observations. In the present analysis, new analytic expressions for the thickness of the peripheral layer, slip velocity and core viscosity have been obtained in terms of measurable quantities (flow rate ( Q), centerline velocity ( U), pressure gradient (− dp/ dz), plasma viscosity ( μ p ) and yield stress ( θ)). Using the experimental values of Q, U, (− dp/ dz), μ p and θ, the values of the peripheral layer thickness, core viscosity, and slip velocity at the wall have been computed. The theoretically obtained peripheral layer thickness has been compared with its experimental value. It is found that the agreement between the two is very good (error<1.4%). Further, a comparison between theoretical and experimental values of core viscosity is made and it is observed that the error between the two becomes 3.7465% in the case of two-layered model (Casson–Newtonian) for tube diameter 40 μm. The analysis developed here could be used to determine the more accurate values of the apparent viscosity of blood, agreeability, rigidity and deformability of red cells. This information of blood could be useful in the development of new diagnosis tools for many diseases.

Nonlinear mathematical analysis for blood flow in a constricted artery under periodic body acceleration

This study analyses the pulsatile flow of blood through mild stenosed narrow arteries, treating the blood in the core region as a Casson fluid and the plasma in the peripheral layer as a Newtonian fluid. Perturbation method is employed 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 longitudinal impedance to flow are obtained. The effects of pulsatility, 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, wall shear stress and longitudinal impedance to flow increase as the yield stress and stenosis depth increase and they decrease with the increase of the body acceleration, pressure gradient, width of the peripheral layer thickness. It is observed that the plug flow velocity and flow rate increase with the increase of the pulsatile Reynolds number, body acceleration, pressure gradient and the width of the peripheral layer thickness and the reverse behavior is found when the yield stress, stenosis depth and lead angle increase. It is also recorded that the wall shear stress and longitudinal impedance to flow are considerably lower for the two-fluid Casson model than that of the single-fluid Casson model. It is found that the presence of body acceleration and peripheral layer influences the mean flow rate and mean velocity by increasing their magnitude significantly in the arteries.

FDM Analysis for Blood Flow through Stenosed Tapered Arteries

A computational model is developed to analyze the unsteady flow of blood through stenosed tapered narrow arteries, treating blood as a two-fluid model with the suspension of all the erythrocytes in the core region as Herschel-Bulkley fluid and the plasma in the peripheral layer as Newtonian fluid. The finite difference method is employed to solve the resulting system of nonlinear partial differential equations. The effects of stenosis height, peripheral layer thickness, yield stress, viscosity ratio, angle of tapering and power law index on the velocity, wall shear stress, flow rate and the longitudinal impedance are analyzed. It is found that the velocity and flow rate increase with the increase of the peripheral layer thickness and decrease with the increase of the angle of tapering and depth of the stenosis. It is observed that the flow rate decreases nonlinearly with the increase of the viscosity ratio and yield stress. The estimates of the increase in the longitudinal impedance to flow are considerably lower for the two-fluid Herschel-Bulkley model compared with those of the single-fluid Herschel-Bulkley model. Hence, it is concluded that the presence of the peripheral layer helps in the functioning of the diseased arterial system.

Two-layered micropolar fluid flow through stenosed artery: Effect of peripheral layer thickness

An unsteady analysis of a two-layered blood flow through a flexible artery under stenotic conditions has been carried out in the present study where the flowing blood is represented by the two-fluid model, consisting of a core region of suspension of all erythrocytes assumed to be Eringen’s micropolar fluid and a plasma layer free from cells of any kind as a Newtonian fluid. The artery has been treated as an elastic (moving wall) cylindrical tube. The equations governing the unsteady flow mechanism subject to pulsatile pressure gradient, has been solved numerically using finite difference scheme by exploiting the appropriate physically realistic prescribed conditions. An extensive quantitative analysis has been performed through numerical computations in order to estimate the effect of different micropolar fluid parameters and the Reynolds number on the flow velocity, the flux, the resistive impedance and the wall shear stress together with their dependencies with time, the input pressure gradient and the severity of the stenosis. The graphical representations of these results do illustrate the flow characteristics of blood under stenotic conditions with proper scientific reasoning and hence validate the applicability of the model under consideration. Special emphasis has duly been made to compare the present theoretical results with the existing ones including experimental results and good agreement between them has been achieved both qualitatively and quantitatively.

Two -fluid nonlinear mathematical model for pulsatile blood flow through catheterized arteries

The pulsatile flow of blood through a catheterized artery is analyzed, assuming the blood as a two-fluid model with the suspension of all the erythrocytes in the core region as a Herschel-Bulkley fluid and the peripheral region of plasma as a Newtonian fluid. The resulting system of the nonlinear implicit system of partial differential equations is solved by perturbation method. The expressions for shear stress, velocity, flow rate, wall shear stress and longitudinal impedance are obtained. The variations of these flow quantities with yield stress, catheter radius ratio, amplitude, pulsatile Reynolds number ratio and peripheral layer thickness are discussed. The velocity and flow rate are observed to decrease, and the wall shear stress and resistance to flow increase when the yield stress increases. The plug flow velocity and flow rate decrease, and the longitudinal impedance increases when the catheter radius ratio increases. The velocity and flow rate increase while the wall shear stress and longitudinal impedance decrease with the increase of the peripheral layer thickness. The estimates of the increase in the longitudinal impedance are significantly lower for the present two-fluid model than those of the single-fluid model.

A two-fluid model for pulsatile flow in catheterized blood vessels

The pulsatile flow of blood through a catheterized artery is analyzed, assuming the blood as a two-fluid model with the suspension of all the erythrocytes in the core region as a Casson fluid and the peripheral region of plasma as a Newtonian fluid. The resulting non-linear implicit system of partial differential equations is solved using perturbation method. The expressions for shear stress, velocity, flow rate, wall shear stress and longitudinal impedance are obtained. The variations of these flow quantities with yield stress, catheter radius ratio, amplitude, pulsatile Reynolds number ratio and peripheral layer thickness are discussed. It is observed that the velocity distribution and flow rate decrease, while, the wall shear, width of the plug flow region and longitudinal impedance increase when the yield stress increases. It is also found that the velocity increases, but, the longitudinal impedance decreases when the thickness of the peripheral layer increases. The wall shear stress decreases non-linearly, while, the longitudinal impedance increases non-linearly when the catheter radius ratio increases. The estimates of the increase in the longitudinal impedance are considerably lower for the present two-fluid model than those of the single-fluid model.

Two-fluid Herschel-Bulkley model for blood flow in catheterized arteries

The steady flow of blood through a catheterized artery is analyzed, assuming the blood as a two-fluid model with the core region of suspension of all the erythrocytes as a Herschel-Bulkley fluid and the peripheral region of plasma as a Newtonian fluid. The expressions for velocity, flow rate, wall shear stress and frictional resistance are obtained. The variations of these flow quantities with yield stress, catheter radius ratio and peripheral layer thickness are discussed. It is observed that the velocity and flow rate decrease while the wall shear stress and resistance to flow increase when the yield stress or the catheter radius ratio increases when all the other parameters held constant. It is noticed that the velocity and flow rate increase while the wall shear stress and frictional resistance decrease with the increase of the peripheral layer thickness. The estimates of the increase in the frictional resistance are significantly much smaller for the present two-fluid model than those of the single-fluid model.

Two-fluid non-linear model for flow in catheterized blood vessels

Blood flow through a catheterized artery is analyzed, assuming the flow is steady and blood is treated as a two-fluid model with the suspension of all the erythrocytes in the core region as a Casson fluid and the plasma in the peripheral region as a Newtonian fluid. The expressions for velocity, flow rate, wall shear stress and frictional resistance are obtained. The variations of these flow quantities with yield stress, catheter radius ratio and peripheral layer thickness are discussed. It is noticed that the velocity and flow rate decrease while the wall shear stress and resistance to flow increase when the yield stress or the catheter radius ratio increases while all the other parameters were held fixed. It is found that the velocity and flow rate increase while the wall shear stress and frictional resistance decrease with the increase of the peripheral layer thickness. The estimates of the increase in the frictional resistance are significantly very small for the present two-fluid model than those of the single-fluid Casson model.

Flow of Eringen fluid (simple microfluid) through an artery with mild stenosis

This paper presents an analysis for blood flow through a stenosed artery considering the localized effects of the stenosis. The blood vessel is modelled as a rigid tube and the particulate nature of blood is accounted through an Eringen fluid (simple microfluid) model. Further a peripheral layer of Newtonian fluid has been considered in the model to account for the cell free layer. It is observed that the resistance to the flow as well as the wall shear stress increase as the height of the stenosis increases. However, the trend is reversed as the peripheral layer thickness increases.