Fahraeus-Lindqvist Effect Research Articles

A Mathematical Analysis and Simulation of the F-L Effect in Two-Layered Blood Flow through the Capillaries Remote from the Heart and Proximate to Human Tissue

In this paper, we have provided a mathematical analysis of an empirical result, namely, the Fahraeus–Lindqvist effect, a phenomenon that occurs in capillary tubes with a diameter lower than 0.3 mm. According to this effect, in capillary tubes under 0.3 mm in diameter, the apparent viscosity of blood decreases as the diameter of the tube decreases, making flow possible in these vessels. A two-phase blood flow mathematical model for human capillaries has been presented here. According to Haynes’ theory, blood is separated into two layers when it flows from the capillary. It is assumed that the first layer is plasma, and the second layer is the core layer. The plasma layer flows near the wall of the capillary, and the core layer flows along the axis of the capillary. Further, the core layer is assumed to be a mixture of two phases: one is the plasma, and the other is that of RBCs. For mathematical modeling purposes, a curvilinear coordinate system has been adopted, with physical quantities used in tensorial form. Derived equations are solved to find the effective viscosity, which depends upon the radius of the capillary; that is, it reduces viscosity to make blood flow possible. A comparative study was conducted with the experimental result of this effect, and it was observed that the proposed two-phase blood flow model is much closer to the experimental data than the single-phase blood flow model, and both have the same trends. After validation of the model with the experimental result, this model was applied to human capillaries (diameter lower than 10 μm) to show the F-L effect, and the impact of various physiological quantities that are relevant to the flow of blood into human capillaries are also discussed here. The impact of hematocrit on various parameters has been demonstrated explicitly.

Numerical investigation on red blood cell flow based on unstructured grid.

Prediction of blood cell flow is known as the difficult research by reason of the complexity of blood vessel. In this study, considering the complex structure of blood vessels, a mechanical model for red blood cell (RBC) based on unstructured grid has been established to study the flow characteristics of RBCs in complex blood vessels. In the model, the strain-energy function by Skalak is employed to model the shear elasticity and surface-area conservation of the membrane, and the hinge spring is used to describe the forces originating from local bending of the membrane. The immersed boundary method is utilized to couple the interphase force. Using the model, the stretching test of RBC is compared with the experiment data, and the good agreement verified the validation of the present model. The morphology of red blood cell and the blood viscosity in micro-vessel are studied. RBCs move with a symmetric shape (parachute shape) in small blood vessels, and the buckling instability is observed when the RBC flow slowly through a micro-vessel or a converging-diverging capillary. When the vessel diameter is around 10μm, the reverse Fahraeus-Lindqvist effect is presented. The blood apparent viscosity shows linear increase with the blood hematocrit. In addition, Malaria infection can make the RBC deformability decreased and the blood apparent viscosity increased.

Genesis of Antibiotic Resistance LXXIII: Turbulence Modeling of Simplified Severe Sepsis Protocol‐2 (SSSP‐2), NCT01663701: Mechanism(s) of Fluid Overload, Concurrent Endotoxemia Exacerbate Leucocyte(S)‐Platelet(S)‐Erythrocyte(S) Aggregates’ (LPE) Consummate Vasoplegia Lead Torque Rifled Viscoelasticity: Connotation of Kolmogorov's scaling theory

NCT01663701 SSSP-2 (PMID: 28973227) noted that within 6 hours of ERP, among sepsis protocol cohort 11 patients sustained GCS score 3-8 with in-hospital mortality 10 patients, with a median jugular vein pressure (JVP) of ~ 2 cm H20 below the clavicle or -2cm H20 implicit of hypovolemia, (ref table 3, p1239, ibid). Here, we present a plausible physiological sequel of the patient(s) from the time of presentation to the emergency dept. and 6 hours after ERP, and the onset of comatose followed with mortality. The geometry for this analysis are following: PMN 8-15μm, eosinophils ~15 μm, basophils ~12-15 μm, monocytes ~14-25 μm, lymphocytes (T, B & NK cells) ~8-15 μm, platelets ~2-3 μm, erythrocytes ~ 7.7 ± 0.7 μm; capillaries (med. size) internal diameter 6 μm, wall thickness, 1 μm, length ~0.1cm, ~blood viscosity 0.03 cm/s (human) (p48, 63: ISBN 9780128024089). Elements: Fahraeus Effect, the hematocrit in true capillaries (Hctv) is lower compare to that of blood entering (due to cell-free layer formation (p95-96, Fig3.8. ibid) vs discharge hematocrit (HctD) and Fahraeus-Lindqvist effect where the apparent viscosity of (μapp) blood is the function of capillary diameter for a range of 10μm ≤ D ≤ 300μm. For the thoroughfare channel, to venules, the viscosity will be reversed as it increases in viscosity (μrel) (Fig 3.10, p98 ibid). Platelet and RBC morphological deformity as shown in Fig 1, panel a; fig 6 a-c, turning, crossing, and riding of platelet and tracer particle deflections in presence of a tumbling RBC; streamlines around a tank-treading RBC Fig 9 panel a-c, platelet crossing, rolling; from PMID: 24231958; Fig 1, of PMID: 17208982; PMID: 24896133; PMID: 17851167; Fig 3 and 5 for skewed hematocrit, PMID: 31933711, would likely to be rapid in vivo., extrapolated to sepsis cohort in NCT01663701. It is suggested that the LPE either forms or part of the bluff body at the junction of precapillary sphincters & thoroughfare channel / true capillaries impede the vasomotion into the arterial end of capillary bed, which may lead terminal arteriole directly connecting metarteriole to venules (bypassing true capillaries, thoroughfare channel) causing vascular shunt with no blood flow in capillary bed en masse. As a result NFP for filtration and net reabsorption pressure is impaired. It is envisioned that LPE anchoring on the scruffy (Awol?) glycocalyx on the endothelial surface of arteries will generate torque Ref Eq-1 (PMCID: PMC5437748, PMID: 28529430 and PMID: 8304490), increase in Kolmogorov length - scale (l) ratio eq. 3.1a, Time-scale ratio (t) eq 3.1b, Velocity-scale ratio (v) eq 3.1c, p43(ISBN:9780131274983) for bluff bodies/large eddies, causing cyclical, relaxation, creep and hysteresis, impairing viscoelasticity, rupturing the capillary bed en masse, resulting in irreversible traumatic brain injury (CVA!). It is implicit that under such conditions onset of CCP in true capillaries. Such a scenario would likely be the contributing factor for the investiture of comatose in turn mortality.

Simulation of a detoxifying organ function: Focus on hemodynamics modeling and convection-reaction numerical simulation in microcirculatory networks.

When modeling a detoxifying organ function, an important component is the impact of flow on the metabolism of a compound of interest carried by the blood. We here study the effects of red blood cells (such as the Fahraeus-Lindqvist effect and plasma skimming) on blood flow in typical microcirculatory components such as tubes, bifurcations and entire networks, with particular emphasis on the liver as important representative of detoxifying organs. In one of the plasma skimming models, under certain conditions, oscillations between states are found and analyzed in a methodical study to identify their causes and influencing parameters. The flow solution obtained is then used to define the velocity at which a compound would be transported. A convection-reaction equation is studied to simulate the transport of a compound in blood and its uptake by the surrounding cells. Different types of signal sharpness have to be handled depending on the application to address different temporal compound concentration profiles. To permit executing the studied models numerically stable and accurate, we here extend existing transport schemes to handle converging bifurcations, and more generally multi-furcations. We study the accuracy of different numerical schemes as well as the effect of reactions and of the network itself on the bolus shape. Even though this study is guided by applications in liver micro-architecture, the proposed methodology is general and can readily be applied to other capillary network geometries, hence to other organs or to bioengineered network designs.

Genesis of Antibiotic Resistance (AR) LIV: “Confounder Effect”: Sepsis with Comorbidity ‐ An Indomitable Turbulence Modeling Consignment

To delineate the hemodynamic basis of exacerbated mortality rate in Early Resuscitation Protocol (ERP) for sepsis with comorbidity, here we present the results of a comparative simulation analysis of “Net Filtration Pressure” (NFP) at homeostasis (Laminar) vs Sepsis with comorbidity (Laminar‐transition‐turbulence‐collapse) in the contexture of Fahraeus – Lindqvist Effect (FLE), plasma skimming, swirling & sigma effect and its role in Critical Closing Pressure (CCP) (Transition to Turbulence consequent collapse). At homeostasis, Starling Forces: NFP= (BHP+IFOP) − (BCOP+IFHP)] at the arterial end, net pressure is outward at 10 mmHg (filtration) and at the venous end, net pressure is inward at −9 mmHg (reabsorption). [Starling equation: Jv = Kf ([Pc − Pi] − σ [πc − πi]), where Jv is the net fluid movement between compartments and [Pc − Pi] − σ [πc − πi] is the net driving force, Pc is the capillary hydrostatic pressure, Pi is the interstitial hydrostatic pressure, πc is the capillary oncotic pressure, πi is the interstitial oncotic pressure, Kf is the filtration coefficient – a proportionality constant, and σ is the reflection coefficient (Fig 3a ‐ Ind J Ana. 2019; 63(1):6). The ERP, NCT01663701 (JAMA.2017;318(13):1233) based sepsis cohort data are sepsis‐ suspected infection plus ≥2 (SIRS), MAP < 65mmHg, sepsis‐induced hypotension 89mmHg/55mmHg (~ 2 liters of bolus administered within 1 hr of enrollment, edema, hypoxemia, hypoperfusion, tachypnea, and respiratory failure due to a lack of ventilator support. For simulation of Starling forces, the impact of FLE, plasma skimming effect, sigma effect (blood flow is not continuum), loss and/or dysfunctional glycocalyx (Crit Care. 2019;23(1):259) (substituting πg = 0mmHg (null & void) instead of πi, revised starling equation: Jv = Kf ([Pc − Pi] − σ [πc − πg] (Br J Ana. 2012 Mar;108(3):384) induce sustained leakage & hemoconcentration cellular aggregates (RBC, WBC, thrombocytes) – large eddies, CCP derived based on Law of La Place, and swirling effect (variable Schmidt number) were considered. Based on the simulation analysis, the prediction of NFP at arterial and venous end would be ~ +10mmHg favoring fluid filtration into the interstitial space causing edema, intra vascular hypotension, hypoperfusion and rheological factors predicted to be PI <1.05%, SpO2≦95%, PaO2 of 55 mmHg, SaO2<90%, SvO2<90%, StO2 below normal, DO2I below normal range, FiO2 <0.21(21%), PaCO2< 38 – 42 mmHg and PaO2/FiO2 <200mmHg. If numerous thrombi are forming simultaneously (equivalent to large‐eddy: Laminar to turbulence transition, then coagulation factors and platelets can become depleted (plasma skimming) causing hemorrhage (septic embolism tend to break up but not in this instance since glycocalyx is null and void) analogous to large‐eddy cascading in to smaller eddies (Fully Turbulent flow). Absence of cascading would likely to obstruct the blood flow and induce ischemia‐induced infarcts in the capillary bed. Though the “Counter‐Inflammatory response syndrome” would likely to mitigate thrombosis, plasma skimming/sigma effect on the cellular aggregates, would lead to thrombosis (large eddies) and CCP.Support or Funding InformationSupported by professional development funds provided by SWTJC to Subburaj Kannan

Modeling cerebral network hemodynamics: Effect of conducted vasodilation on brain perfusion.

Neuronal activity signals local changes in functional hyperemia which match metabolic demands for oxygen (O2) ‐and other nutrients, referred to as Neurovascular Coupling (NVC). NVC is essential for proper functioning of the brain and is impaired in various clinical conditions including Alzheimer’s disease, stroke and aging. The emerging paradigm is that neurons and astrocytes release vasoactive mediators in the perivascular space of penetrating arterioles to increase their diameter and blood supply. Recent evidence supports the concept that NVC mediators initiate electrical vasoactive signaling on arterioles that propagate upstream to cause dilation and increase local blood flow. How electrical conduction of neuronal activity along the vasculature shapes the hyperemic response has not been elucidated. In this study, we model hemodynamic responses by conservation of flow, Fahraeus–Lindqvist effect, and the phase separation. Simulations are performed in macroscale reconstructed brain vascular networks. The model examines changes in tissue perfusion in response to neuronal activity and predicts the requirements for propagating electrical signals to evoke physiologically relevant changes in blood perfusion. The theoretical framework presented allows for testing proposed NVC mechanisms and assisting in the interpretation of macroscale functional imaging responses in health and in disease.

A Two-Zone Shear-Induced Red Blood Cell Migration Model for Blood Flow in Microvessels

The Fahraeus and Fahraeus-Lindqvist effects are both associated with the concentration of red blood cells (RBCs) in the core region of microvessels. The annular region is a cell-free layer. Blood flow dynamics and both effects are related to the hematocrit level profile. The aim is to propose a model for blood flow in microvessels that is not compute intensive like many other models such as those using finite element methods. Modeling blood flow requires solving for both the hematocrit level and velocity profiles as blood viscosity depends on the hematocrit level. The two-zone shear-induced model for blood flow is adopted while including an annular cell-free layer, as in the marginal zone theory and in consistency with experimental observations. In the core region, the hematocrit level is not considered to be uniform, and the concentration and viscous fluxes are equal in magnitude and opposite in directions in the fully developed velocity and concentration profiles case. The momentum and hematocrit balance equations are solved. Both analytical and numerical solutions for the velocity and hematocrit level profiles are determined. The numerical results are found to exactly match the analytical solutions, and to be in very good agreement with published experimental data for the cell-free layer thickness, the velocity profile, and the hematocrit ratio.

Experimental and Numerical Study of Blood Flow in μ-vessels: Influence of the Fahraeus–Lindqvist Effect

The study of hemodynamics is particularly important in medicine and biomedical engineering as it is crucial for the design of new implantable devices and for understanding the mechanism of various diseases related to blood flow. In this study, we experimentally identify the cell free layer (CFL) width, which is the result of the Fahraeus–Lindqvist effect, as well as the axial velocity distribution of blood flow in microvessels. The CFL extent was determined using microscopic photography, while the blood velocity was measured by micro-particle image velocimetry (μ-PIV). Based on the experimental results, we formulated a correlation for the prediction of the CFL width in small caliber (D < 300 μm) vessels as a function of a modified Reynolds number (Re∞) and the hematocrit (Hct). This correlation along with the lateral distribution of blood viscosity were used as input to a “two-regions” computational model. The reliability of the code was checked by comparing the experimentally obtained axial velocity profiles with those calculated by the computational fluid dynamics (CFD) simulations. We propose a methodology for calculating the friction loses during blood flow in μ-vessels, where the Fahraeus–Lindqvist effect plays a prominent role, and show that the pressure drop may be overestimated by 80% to 150% if the CFL is neglected.

Effects of red blood cell aggregation on the blood flow in a symmetrical stenosed microvessel.

In order to figure out whether red blood cell (RBC) aggregation is beneficial or deleterious for the blood flow through a stenosis, fluid mechanics of a microvascular stenosis was examined through simulating the dynamics of deformable red blood cells suspended in plasma using dissipative particle dynamics. The spatial variation in time-averaged cell-free layer (CFL) thickness and velocity profiles indicated that the blood flow exhibits asymmetry along the flow direction. The RBC accumulation occurs upstream the stenosis, leading to a thinner CFL and reduced flow velocity. Therefore, the emergence of stenosis produces an increased blood flow resistance. In addition, an enhanced Fahraeus-Lindqvist effect was observed in the presence of the stenosis. Finally, the effect of RBC aggregation combined with decreased stenosis on the blood flow was investigated. The findings showed that when the RBC clusters pass through the stenosis with a throat comparable to the RBC core in diameter, the blood flow resistance decreases with increasing intercellular interaction strength. But if the RBC core is larger and even several times than the throat, the blood flow resistance increases largely under strong RBC aggregation, which may contribute to the mechanism of the microthrombus formation.

Collective behavior of red blood cells in confined channels.

We study the flow properties of red blood cells in confined channels, when the channel width is comparable to the cell size. We focus on the case of intermediate concentrations when hydrodynamic interactions between cells play a dominant role. This regime is different to the case of low concentration in which the cells behave as hydrodynamically isolated. In this last case, the dynamic behavior is entirely controlled by the interplay between the interaction with the wall and the elastic response of the cell membrane. Our results highlight the different fluid properties when collective flow is present. The cells acquire a characteristic slipper shape, and parachute shapes are only observed at very large capillary numbers. We have characterized the spatial ordering and the layering by means of a pairwise correlation function. Focusing effects are observed at the core of the channel instead of at the lateral position typical of the single-train case. These results indicate that at these intermediate concentrations we observed at the microscale the first steps of the well-known macroscopic Fahraeus-Lindqvist effect. The rheological properties of the suspension are studied by means of the effective viscosity, with an expected shear-thinning behavior. Two main differences are obtained with respect to the single-train case. First, a large magnitude of the viscosity is obtained indicating a high resistance to flow. Secondly, the shear-thinning behavior is obtained at larger values of the capillary number respect to the single-train case. These results suggest that the phenomena of ordering in space and orientation occur at higher values of the capillary number.

A computational model for microcirculation including Fahraeus-Lindqvist effect, plasma skimming and fluid exchange with the tissue interstitium.

We present a two-phase model for microcirculation that describes the interaction of plasma with red blood cells. The model takes into account of typical effects characterizing the microcirculation, such as the Fahraeus-Lindqvist effect and plasma skimming. Besides these features, the model describes the interaction of capillaries with the surrounding tissue. More precisely, the model accounts for the interaction of capillary transmural flow with the surrounding interstitial pressure. Furthermore, the capillaries are represented as one-dimensional channels with arbitrary, possibly curved configuration. The latter two features rely on the unique ability of the model to account for variations of flow rate and pressure along the axis of the capillary, according to a local differential formulation of mass and momentum conservation. Indeed, the model stands on a solid mathematical foundation, which is also addressed in this work. In particular, we present the model derivation, the variational formulation, and its approximation using the finite element method. Finally, we conclude the work with a comparative computational study of the importance of the Fahraeus-Lindqvist, plasma skimming, and capillary leakage effects on the distribution of flow in a microvascular network.

Hemodynamic Flow in a Vertical Cylinder with Heat Transfer : Two-phase Caputo Fabrizio Fractional Model

In blood, the concentration of red blood cells varies with the arterial diameter. In the case of narrow arteries, red blood cells concentrate around the centre of the artery and there exists a cell-free plasma layer near the arterial wall due to Fahraeus-Lindqvist effect. Due to non-uniformity of the fluid in the narrow arteries, it is preferable to consider the two-phase model of the blood flow. The present article analyzes the heat transfer effects on the two-phase model of the unsteady blood flow when it flows through the stenosed artery under an external pressure gradient. The direction of the artery is assumed to be vertical and the magnetic field is applied along the radial direction of the artery. Blood is considered as a non-Newtonian Casson fluid with uniformly distributed magnetic particles. Both the blood and magnetic particles are moving with distinct velocities. This two-phase problem is modelled using the Caputo-Fabrizio derivative approach and then solved for an exact solution using joint Laplace & Hankel transforms. Effects of pertinent parameters such as Grashoff number, Prandtl number, Casson fluid parameter and fractional parameters, and magnetic field on blood velocity and particle velocity have been shown graphically for both large and small values of time. Both velocity profiles increase with the increase of Grashoff number and Casson fluid parameter and reduce with the increase of magnetic field and Prandtl number. The behaviour of temperature is studied for different values of the fractional parameter.

Effect Of Slip On Jeffrey Fluid Flow Through An Inclination Tube

In this paper, the effect of slip on a two-fluid model for Jeffrey fluid flow through an inclined tube of small diameters is studied. It is assumed that the core region consists of Jeffrey fluid and Newtonian fluid in the peripheral region. The expressions for velocity, flow flux, and effective viscosity have been obtained analytically and the effects of various relevant parameters on these flow variables have been studied. It is found that the effective viscosity increases with Jeffrey parameter, the angle of inclination, gamma parameter, Darcy number but decreases with slip and tube hematocrit. Further, it is significant to mention that, the flow exhibits the anomalous Fahraeus-Lindqvist effect.

Automatic construction of 3D models of arterial tree incorporating the Fahraeus-Lindqvist effect

Automatic construction of 3D models of arterial tree incorporating the Fahraeus-Lindqvist effect

MAGNETOHYDRODYNAMIC EFFECTS ON THE GRANULAR TEMPERATURE OF RED BLOOD CELLS IN MICROVASCULATURE

The migration of Red Blood Cells (RBCs) from the wall towards the center of a narrow vessel is the result of the Fahraeus–Lindqvist effect which contemplates the dependence of viscosity and diameter. The kinetic theory explains the formation of the near-wall cell-depleted layer introducing the granular temperature that is defined as the mean square of RBCs fluctuations. The proposed mathematical model elucidates the effect of an externally applied magnetic field on the velocity and granular temperature of RBCs in a microvasculature. The effect of the volume fraction of RBCs on the velocity and granular temperature profiles is also presented and discussed. Based on the insight of the kinetic theory, the application of a stronger static magnetic field probably leads to a restriction of the migration process of RBCs towards the center of the microvessel.

MODELING THE LOWER AND THE UPPER REGIME OF THE BLOOD UNIDIRECTIONAL FLOW IN MICRO-VESSELS

There is a formation of a cell-depleted layer adjacent to micro-vessel walls during blood flow in regime of creeping flow. This biological layer is of vital importance in the transport of oxygen-saturated red cells to the unsaturated tissues. In this work, we first discuss the physical mechanisms in this creeping flow which lead to the formation of a cell-depleted layer. The main non-dimensional physical parameter governing the layer formation are presented from a simple model of predicting the layer thickness in steady state. In particular, we study the blood flow in two different scales (i.e. lower and upper bound limit) of the in vitromicrocirculation. For this end we examine the capillary core flow solution in which the inner fluid is considered a non-Newtonian one facing a small annular gap of a Newtonian plasma. This model is a good approximation for the blood flow occurring in the length scales of venules and arterioles diameters. In addition, we also propose a model for smaller vessels, like capillaries with diameter of few micrometers. In this lower bound limit we consider a periodic configuration of lined up paraboloidal cells moving in a flow under regime of lubrication approximation. So, the boundary condition in this lower flow limit considers the cell velocity and a numerical integration is used to solve the volumetric flux as a function of the pressure drop inside the capillary. The effect of the cell volume fraction in terms of the depleted layer thickness and cell aggregations is also investigated with this model. The influence of the wall irregularities on the flow is studied by using a simple sinusoidal model for the wall. Finally, an intrinsic viscosity of the blood is predicted theoretically for both the lower and upper bound regimes as a function of the non-dimensional vessel diameter, in good agreement with previous experimental works. We compare our theoretical predictions with experimental data and obtain a qualitative good for the classic Fahraeus-Lindqvist effect. A possible application of this work could be in illness diagnosis by evaluating of changes in the intrinsic viscosity due to blood abnormalities. Keywords: blood, hydrodynamic diffusion, non-Newtonian, rheology, cell-depleted layer

Flow of Red Blood Cells in Stenosed Microvessels.

A computational study is presented on the flow of deformable red blood cells in stenosed microvessels. It is observed that the Fahraeus-Lindqvist effect is significantly enhanced due to the presence of a stenosis. The apparent viscosity of blood is observed to increase by several folds when compared to non-stenosed vessels. An asymmetric distribution of the red blood cells, caused by geometric focusing in stenosed vessels, is observed to play a major role in the enhancement. The asymmetry in cell distribution also results in an asymmetry in average velocity and wall shear stress along the length of the stenosis. The discrete motion of the cells causes large time-dependent fluctuations in flow properties. The root-mean-square of flow rate fluctuations could be an order of magnitude higher than that in non-stenosed vessels. Several folds increase in Eulerian velocity fluctuation is also observed in the vicinity of the stenosis. Surprisingly, a transient flow reversal is observed upstream a stenosis but not downstream. The asymmetry and fluctuations in flow quantities and the flow reversal would not occur in absence of the cells. It is concluded that the flow physics and its physiological consequences are significantly different in micro- versus macrovascular stenosis.

Role of response to changes in flow rate in the regulation of vessel radius and blood flow

Estimates are presented for the effect of susceptibility of the inner surface of the blood vessel wall to shear stress on changes in diameter and volume blood flow rate. The model of thin-walled vessel with radius controlled by two parameters is used. The effect of rheological factors, hematocrit, and oxygen content in blood on the value of vessel response to a change in shear stress is considered. The estimates showed that the contribution of the vessel response in question to a change in blood volume flow rate amounts tens per cent. The influence of rheological (Fahraeus and Fahraeus-Lindqvist) effects on flow rate lies within several per cent. The role of the vessel response considered increases with anaemia: at low hematocrit its contribution to increase in flow rate exceeds 10%. Variation of oxygen concentration within the normal range has almost no effect on the hemodynamic parameters. With hypoxia, on the contrary, the participation of this response on changes in flow rate weakens: in severe hypoxia decrease in blood flow rate owing to a change in oxygen concentration equals approximately 9%.

Development of a microfluidic device for cell concentration and blood cell-plasma separation.

This work presents design, fabrication and test of a microfluidic device which employs Fahraeus-Lindqvist and Zweifach-Fung effects for cell concentration and blood cell-plasma separation. The device design comprises a straight main channel with a series of branched channels placed symmetrically on both sides of the main channel. The design implements constrictions before each junction (branching point) in order to direct cells that would have migrated closer to the wall (naturally or after liquid extraction at a junction) towards the centre of the main channel. Theoretical and numerical analysis are performed for design of the microchannel network to ensure that a minimum flow rate ratio (of 2.5:1, main channel-to-side channels) is maintained at each junction and predict flow rate at the plasma outlet. The dimensions and location of the constrictions were determined using numerical simulations. The effect of presence of constrictions before the junctions was demonstrated by comparing the performances of the device with and without constrictions. To demonstrate the performance of the device, initial experiments were performed with polystyrene microbeads (10 and 15μm size) and droplets. Finally, the device was used for concentration of HL60 cells and separation of plasma and cells in diluted blood samples. The cell concentration and blood-plasma purification efficiency was quantified using Haemocytometer and Fluorescence-Activated Cell Sorter (FACS). A seven-fold cell concentration was obtained with HL60 cells and a purification efficiency of 70% and plasma recovery of 80% was observed for diluted (1:20) blood sample. FACS was used to identify cell lysis and the cell viability was checked using Trypan Blue test which showed that more than 99% cells are alive indicating the suitability of the device for practical use. The proposed device has potential to be used as a sample preparation module in lab on chip based diagnostic platforms.

Effect of slip on Herschel–Bulkley fluid flow through narrow tubes

A two-fluid model of Herschel–Bulkley fluid flow through tubes of small diameters and slip at the wall is studied. It is assumed that the core region consists of Herschel–Bulkley fluid and Newtonian fluid in the peripheral region. Following the analysis of Chaturani and Upadhya, the equations of motion have been linearized and analytical solution for velocity, flow flux, effective viscosity, core hematocrit and mean hematocrit has been obtained. The expressions for all these flow relevant quantities have been numerically computed by using Mathematica software and the effects of various relevant parameters on these flow variables have been studied. It is found that effective viscosity, core hematocrit and mean hematocrit of Newtonian fluid are less than those for Bingham fluid, power-law fluid and Herschel–Bulkley fluid. Effective viscosity increases with the yield stress, power-law index, slip and tube hematocrit but decreases with Darcy number. It is observed that the effective viscosity and mean hematocrit increase with tube radius but the core hematocrit decreases with tube radius. Further, it is noticed that the flow exhibits the anomalous Fahraeus–Lindqvist effect.