Axial and Nonaxial Migration of Red Blood Cells in a Microtube.

Human red blood cells (RBCs) are subjected to high viscous shear stress, especially during microcirculation, resulting in stable deformed shapes such as parachute or slipper shape. Those unique deformed RBC shapes, accompanied with axial or nonaxial migration, cannot be fully described according to traditional knowledge about lateral movement of deformable spherical particles. Although several experimental and numerical studies have investigated RBC behavior in microchannels with similar diameters as RBCs, the detailed mechanical characteristics of RBC lateral movement-in particular, regarding the relationship between stable deformed shapes, equilibrium radial RBC position, and membrane load-has not yet been fully described. Thus, we numerically investigated the behavior of single RBCs with radii of 4 µm in a circular microchannel with diameters of 15 µm. Flow was assumed to be almost inertialess. The problem was characterized by the capillary number, which is the ratio between fluid viscous force and membrane elastic force. The power (or energy dissipation) associated with membrane deformations was introduced to quantify the state of membrane loads. Simulations were performed with different capillary numbers, viscosity ratios of the internal to external fluids of RBCs, and initial RBC centroid positions. Our numerical results demonstrated that axial or nonaxial migration of RBC depended on the stable deformed RBC shapes, and the equilibrium radial position of the RBC centroid correlated well with energy expenditure associated with membrane deformations.

Margination of Platelet-Sized Particles in the Red Blood Cell Suspension Flow through Square Microchannels.

In the blood flow through microvessels, platelets show high concentrations near the vessel wall. This phenomenon is called margination of platelets and is closely associated with hemostasis and thrombosis. In the present study, we conducted in vitro experiments using platelet-sized fluorescent particles as platelet substitutes to investigate the cross-sectional distribution of these particles in the red blood cell suspension flowing through microchannels with a square cross section. Fluorescence observations were performed to measure the transverse distribution of particles at various heights from the bottom face with the use of a confocal laser scanning microscope system. In downstream cross sections of the channel, particles showed focusing near the four corners rather than uniform margination along the entire circumference of the cross section. The focusing of particles near the corners was more enhanced for higher hematocrits. On the other hand, particles in circular channel flows showed nearly axisymmetric uniform accumulation adjacent to the channel wall. The present result suggests that the segregation of suspended particles in the flow of multicomponent suspensions could have such heterogeneous 2D features of particle distribution in the cross section of channels, especially for rectangular channels often used in microfluidics.

Pattern Transition on Inertial Focusing of Neutrally Buoyant Particles Suspended in Rectangular Duct Flows.

The continuous separation and filtration of particles immersed in fluid flows are important interests in various applications. Although the inertial focusing of particles suspended in a duct flow is promising in microfluidics, predicting the focusing positions depending on the parameters, such as the shape of the duct cross-section and the Reynolds number (Re) has not been achieved owing to the diversity of the inertial-focusing phenomena. In this study, we aimed to elucidate the variation of the inertial focusing depending on Re in rectangular duct flows. We performed a numerical simulation of the lift force exerted on a spherical particle flowing in a rectangular duct and determined the lift-force map within the duct cross-section over a wide range of Re. We estimated the particle trajectories based on the lift map and Stokes drag, and identified the particle-focusing points appeared in the cross-section. For an aspect ratio of the duct cross-section of 2, we found that the blockage ratio changes transition structure of particle focusing. For blockage ratios smaller than 0.3, particles focus near the centres of the long sides of the cross-section at low Re and near the centres of both the long and short sides at relatively higher Re. This transition is expressed as a subcritical pitchfork bifurcation. For blockage ratio larger than 0.3, another focusing pattern appears between these two focusing regimes, where particles are focused on the centres of the long sides and at intermediate positions near the corners. Thus, there are three regimes; the transition between adjacent regimes at lower Re is found to be expressed as a saddle-node bifurcation and the other transition as a supercritical pitchfork bifurcation.

Development of margination of platelet-sized particles in red blood cell suspensions flowing through Y-shaped bifurcating microchannels.

BACKGROUND: In the blood flow through microvessels, platelets exhibit enhanced concentrations in the layer free of red blood cells (cell-free layer) adjacent to the vessel wall. The motion of platelets in the cell-free layer plays an essential role in their interaction with the vessel wall, and hence it affects their functions of hemostasis and thrombosis. OBJECTIVE: We aimed to estimate the diffusivity of platelet-sized particles in the transverse direction (the direction of vorticity) across the channel width in the cell-free layer by in vitro experiments for the microchannel flow of red blood cell (RBC) suspensions containing platelet-sized particles. METHODS: Fluorescence microscope observations were performed to measure the transverse distribution of spherical particles immersed in RBC suspensions flowing through a Y-shaped bifurcating microchannel. We examined the development of the particle concentration profiles along the flow direction in the daughter channels, starting from asymmetric distributions with low concentrations on the inner side of the bifurcation at the inlet of the daughter channels. RESULTS: In daughter channels of 40 µm width, reconstruction of particle margination revealed that a symmetric concentration profile was attained in ∼30 mm from the bifurcation, independent of flow rate. CONCLUSIONS: We presented experimental evidence of particle margination developing in a bifurcating flow channel where the diffusivity of 2.9-µm diameter particles was estimated to be ∼40 µm2/s at a shear rate of 1000 s-1 and hematocrit of 0.2.

Cross-sectional distributions of normal and abnormal red blood cells in capillary tubes determined by a new technique.

BACKGROUND: In the microcirculation, red blood cells (RBCs) were observed to be confined to an axial stream surrounded by a marginal RBC depleted layer. This axial accumulation of RBCs is considered to arise from the RBC deformability. OBJECTIVE: To quantitatively evaluate the effect of RBC deformability on their axial accumulation at a flow condition comparable to that in arterioles by developing a new observation system for accurate measurements of radial RBC positions in the cross section of capillary tubes. METHODS: The cross-sectional distributions of normal and hardened RBCs as well as softened RBCs suspended in capillary tube flows were measured with high spatial resolution. A new observation system was developed in which enface views of the cross-section of the tube were obtained at small distances upstream of the outlet at various longitudinal positions in the tube. RESULTS: The radial positions of individual RBCs were detected within 1 µm accuracy. It was found that normal and softened RBCs rapidly migrated away from the wall towards the tube axis, whereas glutaraldehyde-hardened RBCs were dispersed widely over the tube cross-section, depending on the concentration of glutaraldehyde solution. CONCLUSIONS: The newly devised observation system revealed quantitatively the essential role of RBC deformability in their axial accumulation.

Venular valves and retrograde perfusion.

Forced retrograde perfusion through the venous system with arterial blood can provide adequate oxygen to peripheral tissues at rest through veno-capillary networks which is the basis for surgical restoration of blood flow by distal vein arterialization (DVA). To be successful such surgery requires disruption of valve leaflets in the veins, which can be accomplished easily in the larger vessels. However, the smallest veins (venules) of less than 100 µm in diameter, also possess valves, are distributed widely throughout all tissues and are too fine for any effective surgical interference. Thus venular valves cannot be disrupted or dissected with presently available technology. Nevertheless, clinical observations suggest that retrograde peripheral blood flow is rapidly established after DVA surgery. There is as yet no rational explanation for this phenomenon. In the present study, using Laplace's law, we attempt to elucidate the mechanical properties of venules and their valves. We speculate that the remarkably thin venular walls (and especially those of the smaller vessels which have the thinnest walls), are capable of considerable, rapid distension when subjected to increased hemostatic pressure. The increase in diameter of venules in response to the increased blood pressure renders their valve leaflets incompetent, so that the valves themselves cannot close the vessel lumen. In addition, the thin bicuspid leaflets may also be forced open retrogradely by the increased blood pressure.

Transition of planar Couette flow at infinite Reynolds numbers.

An outline of the state space of planar Couette flow at high Reynolds numbers (Re<10^{5}) is investigated via a variety of efficient numerical techniques. It is verified from nonlinear analysis that the lower branch of the hairpin vortex state (HVS) asymptotically approaches the primary (laminar) state with increasing Re. It is also predicted that the lower branch of the HVS at high Re belongs to the stability boundary that initiates a transition to turbulence, and that one of the unstable manifolds of the lower branch of HVS lies on the boundary. These facts suggest HVS may provide a criterion to estimate a minimum perturbation arising transition to turbulent states at the infinite Re limit.

Segregation by size difference in binary suspensions of fluid droplets in channel flow.

In channel flow of multicomponent suspensions, segregation behavior of suspended components perpendicular to the flow direction is often observed, which is considered to be caused by the differential properties of the lateral migration depending on their shape, size, flexibility, and other characteristics. In the present study, we investigate the effect of size differences between suspended components on the segregation behavior, by a two-dimensional numerical simulation for binary dispersed suspensions of fluid droplets of two different sizes subjected to a plane Poiseuille channel flow. The small and large droplets are assumed to have equal surface tensions and equal viscosity ratios of internal to external fluids. The time evolutions of the lateral positions of large and small droplets relative to the channel centerline were computed by changing the area fraction of the small droplets in a mixture with a constant total area fraction. The large droplets are found to migrate closer to the channel centerline and the small droplets are found to migrate closer to the channel wall compared to the corresponding lateral positions in mono-dispersed suspensions at the same area fractions, although the mean lateral positions of the large and small droplets in mono-dispersed suspension are comparable. This segregation behavior as well as the margination of small droplets are enhanced when the size difference between large and small droplets is increased and the area fraction of large droplets is increased. These results may arise from higher tendencies for the large droplets to approach the channel centerline compared to the small droplets, which consequently expel small droplets from the central region toward the channel walls.

Charge effects on the hindered transport of macromolecules across the endothelial surface glycocalyx layer.

A fluid mechanical and electrostatic model for the transport of solute molecules across the vascular endothelial surface glycocalyx layer (EGL) was developed to study the charge effect on the diffusive and convective transport of the solutes. The solute was assumed to be a spherical particle with a constant surface charge density, and the EGL was represented as an array of periodically arranged circular cylinders of like charge, with a constant surface charge density. By combining the fluid mechanical analyses for the flow around a solute suspended in an electrolyte solution and the electrostatic analyses for the free energy of the interaction between the solute and cylinders based on a mean field theory, we estimated the transport coefficients of the solute across the EGL. Both of diffusive and convective transports are reduced compared to those for an uncharged system, due to the stronger exclusion of the solute that results from the repulsive electrostatic interaction. The model prediction for the reflection coefficient for serum albumin agreed well with experimental observations if the charge density in the EGL is ranged from approximately -10 to -30 mEq/l.

Mechanotransduction in leukocyte activation: a review.

We review recent evidence which suggests that leukocytes in the circulation and in the tissue may readily respond to physiological levels of fluid shear stress in the range between about 1 and 10 dyn/cm 2, a range that is below the level to achieve a significant passive, viscoelastic response. The response of activated neutrophilic leukocytes to fluid shear consists of a rapid retraction of lamellipodia with membrane detachment from integrin binding sites. In contrast, a subgroup of non-activated neutrophils may project pseudopods after exposure to fluid shear stress. The evidence suggests that G-protein coupled receptor downregulation by fluid shear with concomitant downregulation of Rac-related small GTPases and depolymerization of F-actin serves to retract the lamellipodia in conjunction with proteolytic cleavage of beta 2 integrin to facilitate membrane detachment. Furthermore, there exists a mechanism to up- and down-regulate the fluid shear-response, which involves nitric oxide and the second messenger cyclic guanosine monophosphate (cGMP). Many physiological activities of circulating leukocytes are under the influence of fluid shear stress, including transendothelial migration of lymphocytes. We describe a disease model with chronic hypertension that suffers from an attenuated fluid shear-response with far reaching implications for microvascular blood flow.

The fluid shear stress distribution on the membrane of leukocytes in the microcirculation.

Recent in-vivo and in-vitro evidence indicates that fluid shear stress on the membrane of leukocytes has a powerful control over several aspects of their cell function. This evidence raises a question about the magnitude of the fluid shear stress on leukocytes in the circulation. The flow of plasma on the surface of a leukocyte at a very low Reynolds number is governed by the Stokes equation for the motion of a Newtonian fluid. We numerically estimated the distribution of fluid shear stress on a leukocyte membrane in a microvessel for the cases when the leukocyte is freely suspended, as well as rolling along or attached to a microvessel wall. The results indicate that the fluid shear stress distribution on the leukocyte membrane is nonuniform with a sharp increase when the leukocyte makes membrane attachment to the microvessel wall. In a microvessel (10 microns diameter), the fluid shear stress on the membrane of a freely suspended leukocyte (8 microns diameter) is estimated to be several times larger than the wall shear stress exerted by the undisturbed Poiseuille flow, and increases on an adherent leukocyte up to ten times. High temporal stress gradients are present in freely suspended leukocytes in shear flow due to cell rotation, which are proportional to the local shear rate. In comparison, the temporal stress gradients are reduced on the membrane of leukocytes that are rolling or firmly adhered to the endothelium. High temporal gradients of shear stress are also present on the endothelial wall. At a plasma viscosity of 1 cPoise, the peak shear stresses for suspended and adherent leukocytes are of the order of 10 dyn/cm2 and 100 dyn/cm2, respectively.