Red blood cells augment leukocyte rolling in a virtual blood vessel

Leukocyte rolling and arrest on the vascular endothelium is a central event in normal and pathological immune responses. However, rigorous estimation of the fluid and surface forces involved in leukocyte-endothelial interactions has been difficult due to the particulate, non-Newtonian nature of blood. Here we present a Lattice-Boltzmann approach to quantify forces exerted on rolling leukocytes by red blood cells in a "virtual blood vessel." We report that the normal force imparted by erythrocytes is sufficient to increase leukocyte binding and that increases in tangential force and torque can promote rolling of previously adherent leukocytes. By simulating changes in hematocrit we show that a close "envelopment" of the leukocyte by the red blood cells is necessary to produce significant changes in the forces. This novel approach can be applied to a large number of biological and industrial problems involving the complex flow of particulate suspensions.     

Computational fluid dynamic studies of leukocyte adhesion effects on non-Newtonian blood flow through microvessels

The study of the effect of leukocyte adhesion on blood flow in small vessels is of primary interest to understand the resistance changes in venular microcirculation. Available computational fluid dynamic studies provide information on the effect of leukocyte adhesion when blood is considered as a homogeneous Newtonian fluid. In the present work we aim to understand the effect of leukocyte adhesion on the non-Newtonian Casson fluid flow of blood in small venules; the Casson model represents the effect of red blood cell aggregation. In our model the blood vessel is considered as a circular cylinder and the leukocyte is considered as a truncated spherical protrusion in the inner side of the blood vessel. The cases of single leukocyte adhesion and leukocyte pairs in positions aligned along the same side, and opposite sides of the vessel wall are considered. The Casson fluid parameters are chosen for cat blood and human blood and comparisons are made for the effects of leukocyte adhesion in both species. Numerical simulations demonstrated that for a Casson fluid with hematocrit of 0.4 and flow rate Q = 0.072 nl/s, a single leukocyte increases flow resistance by 5% in a 32 microns diameter and 100 microns long vessel. For a smaller vessel of 18 microns, the flow resistance increases by 15%.     

Effects of flowing RBCs on adhesion of a circulating tumor cell in microvessels

Adhesion of circulating tumor cells (CTCs) to the microvessel wall largely depends on the blood hydrodynamic conditions, one of which is the blood viscosity. Since blood is a non-Newtonian fluid, whose viscosity increases with hematocrit, in the microvessels at low shear rate. In this study, the effects of hematocrit, vessel size, flow rate and red blood cell (RBC) aggregation on adhesion of a CTC in the microvessels were numerically investigated using dissipative particle dynamics. The membrane of cells was represented by a spring-based network connected by elastic springs to characterize its deformation. RBC aggregation was modeled by a Morse potential function based on depletion-mediated assumption, and the adhesion of the CTC to the vessel wall was achieved by the interactions between receptors and ligands at the CTC and those at the endothelial cells forming the vessel wall. The results demonstrated that in the microvessel of \(15\,\upmu \hbox {m}\) diameter, the CTC has an increasing probability of adhesion with the hematocrit due to a growing wall-directed force, resulting in a larger number of receptor–ligand bonds formed on the cell surface. However, with the increase in microvessel size, an enhanced lift force at higher hematocrit detaches the initial adherent CTC quickly. If the microvessel is comparable to the CTC in diameter, CTC adhesion is independent of Hct. In addition, the velocity of CTC is larger than the average blood flow velocity in smaller microvessels and the relative velocity of CTC decreases with the increase in microvessel size. An increased blood flow resistance in the presence of CTC was also found. Moreover, it was found that the large deformation induced by high flow rate and the presence of aggregation promote the adhesion of CTC.     

A commercial whole blood glucose biosensor with a low sensitivity to hematocrit based on an impregnated porous carbon electrode

Erythrocytes (red blood cells) are a major source of response variation in biosensor electrodes expected to operate in whole blood. Such a blood-to-plasma difference (hematocrit effect) must be minimized for those sensors directed towards the hospital market where wide variations in hematocrit can be seen. Typically, many current glucose sensors demonstrate a decreasing response to the analyte in the presence of increasing hematocrit levels. A sensor electrode for glucose is described which displays a reduced sensitivity to changes in hematocrit. The working electrode comprises a base porous conducting carbon layer, which is impregnated with a mixture including glucose oxidase and a ferrocene redox mediator. The base carbon layer has a void volume of 50%, an average pore diameter of less than 0.1 microm and a thickness of about 20 microm. The interior void volume of the base carbon layer is filled entirely with a substantial proportion of the impregnating mixture such that very little remains on the exterior. The resulting impregnated porous electrode excludes erythrocytes and is consequently capable of operating acceptably in venous, capillary, arterial and neonatal blood over a wide hematocrit range of 20-70%.     

Magnetic resonance microscopy determined velocity and hematocrit distributions in a Couette viscometer

Magnetic resonance microscopy is used to non-invasively measure the radial velocity distribution in Couette flow of erythrocyte suspensions of varying aggregation behavior at a nominal shear rate of 2.20 s(-1) in a 1 mm gap. Suspensions of red blood cells in albumin-saline, plasma and 1.48% Dextran added plasma at average hematocrits near 0.40 are studied, providing a range of aggregation ability. The spatial distribution of the red blood cell volume fraction, hematocrit, is calculated from the velocity distribution. The hematocrit profiles provide direct measure of the thickness of the aggregation and shear rate dependent red blood cell depletion at the Couette surfaces. At the nominal shear rate studied hematocrit distributions for the red blood cells in plasma show a depletion zone near the inner Couette wall but not the outer wall. The red blood cells in plasma with Dextran show cell depletion regions of approximately 100 mum at both the inner and outer Couette surfaces, with greater depletion at the inner wall, but approach the normal blood hematocrit distribution with a doubling of shear rate due to decreased aggregation. The material response of the blood is spatially dependent with the shear rate and the hematocrit distribution non-uniform across the gap.     

Margination and adhesion dynamics of tumor cells in a real microvascular network

In tumor metastasis, the margination and adhesion of tumor cells are two critical and closely related steps, which may determine the destination where the tumor cells extravasate to. We performed a direct three-dimensional simulation on the behaviors of the tumor cells in a real microvascular network, by a hybrid method of the smoothed dissipative particle dynamics and immersed boundary method (SDPD-IBM). The tumor cells are found to adhere at the microvascular bifurcations more frequently, and there is a positive correlation between the adhesion of the tumor cells and the wall-directed force from the surrounding red blood cells (RBCs). The larger the wall-directed force is, the closer the tumor cells are marginated towards the wall, and the higher the probability of adhesion behavior happen is. A relatively low or high hematocrit can help to prevent the adhesion of tumor cells, and similarly, increasing the shear rate of blood flow can serve the same purpose. These results suggest that the tumor cells may be more likely to extravasate at the microvascular bifurcations if the blood flow is slow and the hematocrit is moderate.     

Effect of a Preparative Technique on the Viability of Concentrated Red Cells

In a study of the technique employed by the Canadian Red Cross Blood Transfusion Service in Montreal, the authors found that the packed red blood cells from 10 healthy donors had a mean hematocrit of 83 ± 1.45 with a 24-hour red cell survival after three weeks'' storage of 79.4 ± 2%. The technique used a centrifugal force of 6975 G, the practical maximum of present-day equipment. In addition to finding excellent survival of packed cells subjected to extreme plasma deprivation and extreme forces of centrifugation they also report excellent survival of stored, highly concentrated red cells infused under pressure.     

Mesoscale simulation of blood flow in small vessels

Computational modeling of blood flow in microvessels with internal diameter 20-500 microm is a major challenge. It is because blood in such vessels behaves as a multiphase suspension of deformable particles. A continuum model of blood is not adequate if the motion of individual red blood cells in the suspension is of interest. At the same time, multiple cells, often a few thousands in number, must also be considered to account for cell-cell hydrodynamic interaction. Moreover, the red blood cells (RBCs) are highly deformable. Deformation of the cells must also be considered in the model, as it is a major determinant of many physiologically significant phenomena, such as formation of a cell-free layer, and the Fahraeus-Lindqvist effect. In this article, we present two-dimensional computational simulation of blood flow in vessels of size 20-300 microm at discharge hematocrit of 10-60%, taking into consideration the particulate nature of blood and cell deformation. The numerical model is based on the immersed boundary method, and the red blood cells are modeled as liquid capsules. A large RBC population comprising of as many as 2500 cells are simulated. Migration of the cells normal to the wall of the vessel and the formation of the cell-free layer are studied. Results on the trajectory and velocity traces of the RBCs, and their fluctuations are presented. Also presented are the results on the plug-flow velocity profile of blood, the apparent viscosity, and the Fahraeus-Lindqvist effect. The numerical results also allow us to investigate the variation of apparent blood viscosity along the cross-section of a vessel. The computational results are compared with the experimental results. To the best of our knowledge, this article presents the first simulation to simultaneously consider a large ensemble of red blood cells and the cell deformation.     

Red blood cells initiate leukocyte rolling in postcapillary expansions: a lattice Boltzmann analysis

Leukocyte rolling on the vascular endothelium requires initial contact between leukocytes circulating in the blood and the vessel wall. Although specific adhesion mechanisms are involved in leukocyte-endothelium interactions, adhesion patterns in vivo suggest other rheological mechanisms also play a role. Previous studies have proposed that the abundance of leukocyte rolling in postcapillary venules is due to interactions between red blood cells (RBCs) and leukocytes as they enter postcapillary expansions, but the details of the fluid dynamics have not been elucidated. We have analyzed the interactions of red and white blood cells as they flow from a capillary into a postcapillary venule using a lattice Boltzmann approach. This technique provides the complete solution of the flow field and quantification of the particle-particle forces in a relevant geometry. Our results show that capillary-postcapillary venule diameter ratio, RBC configuration, and RBC shape are critical determinants of the initiation of cell rolling in postcapillary venules. The model predicts that an optimal configuration of the trailing red blood cells is required to drive the white blood cell to the wall.     

Particulate nature of blood determines macroscopic rheology: a 2-D lattice Boltzmann analysis

Historically, predicting macroscopic blood flow characteristics such as viscosity has been an empirical process due to the difficulty in rigorously including the particulate nature of blood in a mathematical representation of blood rheology. Using a two-dimensional lattice Boltzmann approach, we have simulated the flow of red blood cells in a blood vessel to estimate flow resistance at various hematocrits and vessel diameters. By including white blood cells (WBCs) in the flow, we also calculate the increase in resistance due to white cell rolling and adhesion. The model considers the blood as a suspension of particles in plasma, accounting for cell-cell and cell-wall interactions to predict macroscopic blood rheology. The model is able to reproduce the Fahraeus-Lindqvist effect, i.e., the increase in relative apparent viscosity as tube size increases, and the Fahraeus effect, i.e., tube hematocrit is lower than discharge hematocrit. In addition, the model allows direct assessment of the effect of WBCs on blood flow in the microvasculature, reproducing the dramatic increases in flow resistance as WBCs enter short capillary segments. This powerful and flexible model can be used to predict blood flow properties in any vessel geometry and with any blood composition.     

Blood flow in the capillary bed

From arteries to veins, the blood has to go through the ‘capillary’ blood vessels. These blood vessels are so small that often their diameter is smaller than that of the red blood cells. Intimate interactions occur, therefore, between the blood cells and the blood vessels.

A general survey of recent works on capillary blood flow is given in this article. Some details are presented for two problems: the problem of deformation of the flexible red blood cells, their motion in the capillary blood vessels, and the pressure drop due to the red cell blood vessel interaction; and the problem of the flow of plasma ‘bolus’ between neighboring red cells.

The solution supplies many details about the microcirculation phenomenon. Taken together, a method is offered for the calculation of pressure drop in the capillary as a function of various physical parameters: the red cell volume per unit blood volume, (hematocrit), the ratio of the cell diameter to the blood vessel diameter, the ratio of the length of the blood vessel to its length, the volume of individual red cells, and a parameter relating the cell membrane elasticity, plasma viscosity and the cell velocity.     

In?Vitro Measurement of Particle Margination in the Microchannel Flow: Effect of Varying Hematocrit

It has long been known that platelets undergo margination when flowing in blood vessels, such that there is an excess concentration near the vessel wall. We conduct experiments and three-dimensional boundary integral simulations of platelet-sized spherical particles in a microchannel 30 μm in height to measure the particle-concentration distribution profile and observe its margination at 10%, 20%, and 30% red blood cell hematocrit. The experiments involved adding 2.15-μm-diameter spheres into a solution of red blood cells, plasma, and water and flowing this mixture down a microfluidic channel at a wall shear rate of 1000 s⁻¹. Fluorescence imaging was used to determine the height and velocity of particles in the channel. Experimental results indicate that margination has largely occurred before particles travel 1 cm downstream and that hematocrit plays a role in the degree of margination. With simulations, we can track the trajectories of the particles with higher resolution. These simulations also confirm that margination from an initially uniform distribution of spheres and red blood cells occurs over the length scale of O(1 cm), with higher hematocrit showing faster margination. The results presented here, from both experiments and 3D simulations, may help explain the relationship between bleeding time in vessel trauma and red blood cell hematocrit as platelets move to a vessel wall.     

Mechanics of cellular adhesion to artificial artery templates

We are using polymer templates to grow artificial artery grafts in vivo for the replacement of diseased blood vessels. We have previously shown that adhesion of macrophages to the template starts the graft formation. We present a study of the mechanics of macrophage adhesion to these templates on a single cell and single bond level with optical tweezers. For whole cells, in vitro cell adhesion densities decreased significantly from polymer templates polyethylene to silicone to Tygon (167, 135, and 65 cells/mm(2)). These cell densities were correlated with the graft formation success rate (50%, 25%, and 0%). Single-bond rupture forces at a loading rate of 450 pN/s were quantified by adhesion of trapped 2-microm spheres to macrophages. Rupture force distributions were dominated by nonspecific adhesion (forces <40 pN). On polystyrene, preadsorption of fibronectin or presence of serum proteins in the cell medium significantly enhanced adhesion strength from a mean rupture force of 20 pN to 28 pN or 33 pN, respectively. The enhancement of adhesion by fibronectin and serum is additive (mean rupture force of 43 pN). The fraction of specific binding forces in the presence of serum was similar for polystyrene and polymethyl-methacrylate, but specific binding forces were not observed for silica. Again, we found correlation to in vivo experiments, where the density of adherent cells is higher on polystyrene than on silica templates, and can be further enhanced by fibronectin adsorption. These findings show that in vitro adhesion testing can be used for template optimization and to substitute for in-vivo experiments.     

Effect of nonaxisymmetric hematocrit distribution on non-Newtonian blood flow in small tubes

Hematocrit distribution and red blood cell aggregation are the major determinants of blood flow in narrow tubes at low flow rates. It has been observed experimentally that in microcirculation the hematocrit distribution is not uniform. This nonuniformity may result from plasma skimming and cell screening effects and also from red cell sedimentation. The goal of the present study is to understand the effect of nonaxisymmetric hematocrit distribution on the flow of human and cat blood in small blood vessels of the microcirculation. Blood vessels are modeled as circular cylindrical tubes. Human blood is described by Quemada's rheological model, in which local viscosity is a function of both the local hematocrit and a structural parameter that is related to the size of red blood cell aggregates. Cat blood is described by Casson's model. Eccentric hematocrit distribution is considered such that the axis of the cylindrical core region of red cell suspension is parallel to the axis of the blood vessel but not coincident. The problem is solved numerically by using finite element method. The calculations predict nonaxisymmetric distribution of velocity and shear stress in the blood vessel and the increase of apparent viscosity with increasing eccentricity of the core.     

Plug Effect of Erythrocytes in Capillary Blood Vessels

As an idealized problem of the motion of blood in small capillary blood vessels, the low Reynolds number flow of plasma (a newtonian fluid) in a circular cylindrical tube involving a series of circular disks is studied. It is assumed in this study that the suspended disks are equally spaced along the axis of the tube, and that their centers remain on the axis of the tube and that their faces are perpendicular to the tube axis. The inertial force of the fluid due to the convective acceleration is neglected on the basis of the smallness of the Reynolds number. The solution of the problem is derived for a quasi-steady flow involving infinitesimally thin disks. The numerical calculation is carried out for a set of different combinations of the interdisk distance and the ratio of the disk radius to the tube radius. The ratio of the velocity of the disk to the average velocity of the fluid is calculated. The different rates of transport of red blood cells and of plasma in capillary blood vessels are discussed. The average pressure gradient along the axis of the tube is computed, and the dependence of the effective viscosity of the blood on the hematocrit and the diameter of the capillary vessel is discussed.     

Blood flow switching among pulmonary capillaries is decreased during high hematocrit.

Pulmonary capillary perfusion within a single alveolar wall continually switches among segments, even when large-vessel hemodynamics are constant. The mechanism is unknown. We hypothesize that the continually varying size of plasma gaps between individual red blood cells affects the likelihood of capillary segment closure and the probability of cells changing directions at the next capillary junction. We assumed that an increase in hematocrit would decrease the average distance between red blood cells, thereby decreasing the switching at each capillary junction. To test this idea, we observed 26 individual alveolar capillary networks by using videomicroscopy of excised canine lung lobes that were perfused first at normal hematocrit (31-43%) and then at increased hematocrit (51-62%). The number of switches decreased by 38% during increased hematocrit (P < 0.01). These results support the idea that a substantial part of flow switching among pulmonary capillaries is caused by the particulate nature of blood passing through a complex network of tubes with continuously varying hematocrit.     

Dynamics of blood flow: modeling of the Fåhræus–Lindqvist effect

To model the Fåhræus–Lindqvist effect, Haynes’ marginal zone theory is used, following previous works, i.e., a core layer of uniform red blood cells (RBCs) is assumed to be surrounded by an annular plasma layer in which no RBCs are present. A simplified trial-and-error solution procedure is provided to determine the size of the core region and the hematocrit level in that zone in addition to the apparent viscosity, given the (upstream) large vessel hematocrit level and the average hematocrit level in the (downstream) small vessel. To test the model, a set of experimental data is selected to provide not only apparent viscosity data but also the average hematocrit levels in small tubes of different diameters. The results are found to support Haynes’ marginal theory, with no fitting parameters used in the computations. Viscous dissipation is determined. The use of the mechanical energy balance is found to lead to results that are consistent with those based on the momentum balance, while leaving the average hematocrit level undetermined and required by either experimental data or an additional equation based on further theoretical work. The present analysis is used to model bifurcation using published empirical correlations quantifying the Fåhræus effect and phase separation. The model equations are extended to microvascular networks with repeated bifurcations.     

Red cell distribution and the recruitment of pulmonary diffusing capacity.

The distribution of red blood cells in alveolar capillaries is typically nonuniform, as shown by intravital microscopy and in alveolar tissue fixed in situ. To determine the effects of red cell distribution on pulmonary diffusive gas transport, we computed the uptake of CO across a two-dimensional geometric capillary model containing a variable number of red blood cells. Red blood cells are spaced uniformly, randomly, or clustered without overlap within the capillary. Total CO diffusing capacity (DLCO) and membrane diffusing capacity (DmCO) are calculated by a finite-element method. Results show that distribution of red blood cells at a fixed hematocrit greatly affects capillary CO uptake. At any given average capillary red cell density, the uniform distribution of red blood cells yields the highest DmCO and DLCO, whereas the clustered distribution yields the lowest values. Random nonuniform distribution of red blood cells within a single capillary segment reduces diffusive CO uptake by up to 30%. Nonuniform distribution of red blood cells among separate capillary segments can reduce diffusive CO uptake by >50%. This analysis demonstrates that pulmonary microvascular recruitment for gas exchange does not depend solely on the number of patent capillaries or the hematocrit; simple redistribution of red blood cells within capillaries can potentially account for 50% of the observed physiological recruitment of DLCO from rest to exercise.     

Role of erythrocytes in leukocyte-endothelial interactions: mathematical model and experimental validation.

The binding of circulating cells to the vascular wall is a central process in inflammation, metastasis, and therapeutic cell delivery. Previous in vitro studies have identified the adhesion molecules on various circulating cells and the endothelium that govern the process under static conditions. Other studies have attempted to simulate in vivo conditions by subjecting adherent cells to shear stress as they interact with the endothelial cells in vitro. These experiments are generally performed with the cells suspended in Newtonian solutions. However, in vivo conditions are more complex because of the non-Newtonian flow of blood, which is a suspension consisting of 20-40% erythrocytes by volume. The forces imparted by the erythrocytes in the flow can contribute to the process of cell adhesion. A number of experimental and theoretical studies have suggested that the rheology of blood can influence the binding of circulating leukocytes by increasing the normal and axial forces on leukocytes or the frequency of their collision with the vessel wall, but there have been no systematic investigations of these phenomena to date. The present study quantifies the contribution of red blood cells (RBCs) in cell capture and adhesion to endothelial monolayers using a combination of mathematical modeling and in vitro studies. Mathematical modeling of the flow experiments suggested a physical mechanism involving RBC-induced leukocyte dispersion and/or increased normal adhesive contact. Flow chamber studies performed with and without RBCs in the suspending medium showed increases in wall collision and binding frequencies, and a decrease in rolling velocity in the presence of erythrocytes. Increased fluid viscosity alone did not influence the binding frequency, and the differences could not be attributed to large near-wall excesses of the lymphocytes. The results indicate that RBCs aid in the transport and initial engagement of lymphocytes to the vascular wall, modifying the existing paradigm for immune cell surveillance of the vascular endothelium by adding the erythrocyte as an essential contributor to this process.     

GF昆明小鼠主要重量系数及血液生理指标的测定

目的测定无菌KM小鼠体重、体长、尾长、脏器系数、血常规值。方法选取8只全雄无菌KM小鼠,8只SPF级测量体重、体长、尾长;检测红细胞总数(RBC),血红蛋白(HGB),红细胞压积(HCT),平均红细胞体积(MCV),血小板总数(PLT),白细胞总数(WBC),白细胞分类(DLC),平均血红蛋白含量(MCH),平均血红蛋白浓度(MCHC)等血液生理指标;解剖采集小鼠心脏、肝脏、脾脏、肺、肾、睾丸、盲肠,称重,计算脏器系数(脏器系数=脏器湿重/体重×100)。结果体长、尾长、心脏、脾脏、肺、肾脏、脑、睾丸、及血液生理指标等项目差异无统计学意义(P>0.05),体重、肝脏、盲肠项目差异有统计学意义(P<0.05)。结论所测数值为研究者提供基础数据,建立国内无菌KM小鼠背景资料。