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.     

Particle Margination and Its Implications on Intravenous Anticancer Drug Delivery

“Margination” refers to the movement of particles in flow toward the walls of a channel. The term was first coined in physiology for describing the behavior of white blood cells (WBCs) and platelets in blood flow. The margination of particles is desirable for anticancer drug delivery because it results in the close proximity of drug-carrying particles to the endothelium, where they can easily diffuse into cancerous tumors through the leaky vasculature. Understanding the fundamentals of margination may further lead to the rational design of particles and allow for more specific delivery of anticancer drugs into tumors, thereby increasing patient comfort during cancer treatment. This paper reviews existing theoretical and experimental studies that focus on understanding margination. Margination is a complex phenomenon that depends on the interplay between inertial, hydrodynamic, electrostatic, lift, van der Waals, and Brownian forces. Parameters that have been explored thus far include the particle size, shape, density, stiffness, shear rate, and the concentration and aggregation state of red blood cells (RBCs). Many studies suggested that there exists an optimal particle size for margination to occur, and that nonspherical particles tend to marginate better than spherical particles. There are, however, conflicting views on the effects of particle density, stiffness, shear rate, and RBCs. The limitations of using the adhesion of particles to the channel walls in order to quantify margination propensity are explained, and some outstanding questions for future research are highlighted.     

The Margination of Particles in Areas of Constricted Blood Flow

Stroke is a leading cause of death globally and is caused by stenoses, abnormal narrowings of blood vessels. Recently, there has been an increased interest in shear-activated particle clusters for the treatment of stenosis, but there is a lack of literature investigating the impact of different stenosis geometries on particle margination. Margination refers to the movement of particles toward the blood vessel wall and is desirable for drug delivery. The current study investigated ten different geometries and their effects on margination. Microfluidic devices with a constricted area were fabricated to mimic a stenosed blood vessel with different extent of occlusion, constricted length, and eccentricity (gradualness of the constriction and expansion). Spherical fluorescent particles with a diameter of 2.11 μm were suspended in blood and tracked as they moved into, through, and out of the constricted area. A margination parameter, M, was used to quantify margination based on the particle distribution after velocity normalization. Experimental results suggested that a constriction leads to an enhanced margination, whereas an expansion is responsible for a decrease in margination. Further, margination was found to increase with increasing percent occlusion and constriction length, likely a result of higher shear rate and longer residence time, respectively. Margination decreases as the stenosis geometry becomes more gradual (eccentricity increases) with the exception of a sudden constriction/expansion geometry. The findings demonstrate the importance of geometric effects on margination and call for detailed numerical modeling and geometric characterization of the stenosed areas to fully understand the underlying physics.     

Rapid determination of particle velocity from space-time images using the Radon transform

Laser-scanning methods are a means to observe streaming particles, such as the flow of red blood cells in a blood vessel. Typically, particle velocity is extracted from images formed from cyclically repeated line-scan data that is obtained along the center-line of the vessel; motion leads to streaks whose angle is a function of the velocity. Past methods made use of shearing or rotation of the images and a Singular Value Decomposition (SVD) to automatically estimate the average velocity in a temporal window of data. Here we present an alternative method that makes use of the Radon transform to calculate the velocity of streaming particles. We show that this method is over an order of magnitude faster than the SVD-based algorithm and is more robust to noise.     

Investigation of platelet margination phenomena at elevated shear stress

Thrombosis is a common complication following the surgical implantation of blood contacting artificial organs. Platelet transport, which is an important process of thrombosis and strongly modulated by flow dynamics, has not been investigated under the shear stress level associated with these devices, which may range from tens to several hundred Pascal.The current research investigated platelet transport within blood under supra-physiological shear stress conditions through a micro flow visualization approach. Images of platelet-sized fluorescent particles in the blood flow were recorded within microchannels (2 cm x 100 microm x 100 microm). The results successfully demonstrated the occurrence of platelet-sized particle margination under shear stresses up to 193 Pa, revealing a platelet near-wall excess up to 8.7 near the wall (within 15 microm) at the highest shear stress. The concentration of red blood cells was found to influence the stream-wise development of platelet margination which was clearly observed in the 20% Ht sample but not the 40% Ht sample. Shear stress had a less dramatic effect on the margination phenomenon than did hematocrit. The results imply that cell-cell collision is an important factor for platelet transport under supra-physiologic shear stress conditions. It is anticipated that these results will contribute to the future design and optimization of artificial organs.     

Margination of red blood cells infected by Plasmodium falciparum in a microvessel

We investigated numerically the mechanism of margination of Plasmodium falciparum malaria-infected red blood cells (Pf-IRBCs) in micro-scale blood flow. Our model illustrates that continuous hydrodynamic interaction between a Pf-IRBC in the trophozoite stage (Pf-T-IRBC) and healthy red blood cells (HRBCs) results in the margination of the Pf-T-IRBC and, thus, a longer duration of contact with endothelial cells. The Pf-T-IRBC and HRBCs first form a "train". The volume fraction of RBCs is then locally increased, to approximately 40%, and this value is maintained for a long period of time due to the formation of a long train in high-hematocrit conditions. Even in low-hematocrit conditions, the local volume fraction is instantaneously elevated to 40% and the Pf-T-IRBC can migrate to the wall. However, the short train formed in low-hematocrit conditions does not provide continuous interaction, and the Pf-T-IRBC moves back to the center of the channel.     

Forces on a Wall-Bound Leukocyte in a Small Vessel Due to Red Cells in the Blood Stream

As part of the inflammation response, white blood cells (leukocytes) are well known to bind nearly statically to the vessel walls, where they must resist the force exerted by the flowing blood. This force is particularly difficult to estimate due to the particulate character of blood, especially in small vessels where the red blood cells must substantially deform to pass an adhered leukocyte. An efficient simulation tool with realistically flexible red blood cells is used to estimate these forces. At these length scales, it is found that the red cells significantly augment the streamwise forces that must be resisted by the binding. However, interactions with the red cells are also found to cause an average wall-directed force, which can be anticipated to enhance binding. These forces increase significantly as hematocrit values approach 25% and decrease significantly as the leukocyte is made flatter on the wall. For a tube hematocrit of 25% and a spherical protrusion with a diameter three-quarters that of the vessel, the average forces are increased by ∼40% and the local forces are more than double those estimated with an effective-viscosity-homogenized blood. Both the enhanced streamwise and wall-ward forces and their unsteady character are potentially important in regard to binding mechanisms.     

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.     

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.     

Finite platelet size could be responsible for platelet margination effect

Blood flows through vessels as a segregated suspension. Erythrocytes distribute closer to the vessel axis, whereas platelets accumulate near vessel walls. Directed platelet migration to the vessel walls promotes their hemostatic function. The mechanisms underlying this migration remain poorly understood, although various hypotheses have been proposed to explain this phenomenon (e.g., the available volume model and the drift-flux model). To study this issue, we constructed a mathematical model that predicts the platelet distribution profile across the flow in the presence of erythrocytes. This model considers platelet and erythrocyte dimensions and assumes an even platelet distribution between erythrocytes. The model predictions agree with available experimental data for near-wall layer margination using platelets and platelet-modeling particles and the lateral migration rate for these particles. Our analysis shows that the strong expulsion of the platelets from the core to the periphery of the blood vessel may mainly arise from the finite size of the platelets, which impedes their positioning in between the densely packed erythrocytes in the core. This result provides what we believe is a new insight into the rheological control of platelet hemostasis by erythrocytes.     

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.     

Magnetic separation techniques: their application to medicine

Summary Whilst separation techniques relying on gravitational forces have become relatively sophisticated in their application to biology the same is not true for magnetic separation procedures. The use of the latter has been limited to the few cells which contain paramagnetic iron. However with the development of several different types of magnetic particles and selective delivery system (e.g. monoclonal antibodies) the use of magnetic separation techniques is growing rapidly. This review describes the different types of particles currently available, the magnetic separation technique applied to the different magnetic compounds and illustrates major uses to which magnetic separation procedures are currently applied in the area of biology and medicine.Abbreviations WBC White blood cells - RBC Red blood cells - Met-Hb Methemoglobin - SRBC Sheep red blood cells - Ig Immunoglobulin - FACS Fluorescent activated cell sorter     

Design of bio-mimetic particles with enhanced vascular interaction

The majority of particle-based delivery systems for the ‘smart’ administration of therapeutic and imaging agents have a spherical shape, are made by polymeric or lipid materials, have a size in the order of few hundreds of nanometers and a negligibly small relative density to aqueous solutions. In the microcirculation and deep airways of the lungs, where the creeping flow assumption holds, such small spheres move by following the flow stream lines and are not affected by external volume force fields. A delivery system should be designed to drift across the stream lines and interact repeatedly with the vessel walls, so that vascular interaction could be enhanced. The numerical approach presented in [Gavze, E., Shapiro, M., 1997. Particles in a shear flow near a solid wall: effect of nonsphericity on forces and velocities. International Journal of Multiphase Flow 23, 155–182.] is, here, proposed as a tool to analyze the dynamics of arbitrarily shaped particles in a creeping flow, and has been extended to include the contribution of external force fields. As an example, ellipsoidal particles with aspect ratio 0.5 are considered. In the absence of external volume forces, a net lateral drift (margination) of the particles has been observed for Stokes number larger than unity (St>1); whereas, for smaller St, the particles oscillate with no net lateral motion. Under these conditions, margination is governed solely by particle inertia (geometry and particle-to-fluid density ratio). In the presence of volume forces, even for fairly small St, margination is observed but in a direction dictated by the external force field. It is concluded that a fine balance between size, shape and density can lead to EVI particles (particles with enhanced vascular interaction) that are able to sense endothelial cells for biological and biophysical abnormalities, mimicking circulating platelets and leukocytes.     

The effect of shape on the margination dynamics of non-neutrally buoyant particles in two-dimensional shear flows

The margination dynamics of microparticles with different shapes has been analyzed within a laminar flow mimicking the hydrodynamic conditions in the microcirculation. Silica spherical particles, quasi-hemispherical and discoidal silicon particles have been perfused in a parallel plate flow chamber. The effect of the shape and density on their margination propensity has been investigated at different physiologically relevant shear rates S. Simple scaling laws have been derived showing that the number n of marginating particles scales as S(-0.63) for the spheres; S(-0.85) for discoidal and S(-1) for quasi-hemispherical particles, regardless of their density and size. Within the range considered for the shear rate, discoidal particles marginate in a larger number compared to quasi-hemispherical and spherical particles. These results may be of interest in drug delivery and bio-imaging applications, where particles are expected to drift towards and interact with the walls of the blood vessels.     

Characterization of the growth plate-bone interphase region using cryo-FIB SEM 3D volume imaging

The interphase region at the base of the growth plate includes blood vessels, cells and mineralized tissues. In this region, cartilage is mineralized and replaced with bone. Blood vessel extremities permeate this space providing nutrients, oxygen and signaling factors. All these different components form a complex intertwined 3D structure. Here we use cryo-FIB SEM to elaborate this 3D structure without removing the water. As it is challenging to image mineralized and unmineralized tissues in a hydrated state, we provide technical details of the parameters used. We obtained two FIB SEM image stacks that show that the blood vessels are in intimate contact not only with cells, but in some locations also with mineralized tissues. There are abundant red blood cells at the extremities of the vessels. We also documented large multinucleated cells in contact with mineralized cartilage and possibly also with bone. We observed membrane bound mineralized particles in these cells, as well as in blood serum, but not in the hypertrophic chondrocytes. We confirm that there is an open pathway from the blood vessel extremities to the mineralizing cartilage. Based on the sparsity of the mineralized particles, we conclude that mainly ions in solution are used for mineralizing cartilage and bone, but these are augmented by the supply of mineralized particles.     

Rheological properties of the blood influencing selectin-mediated adhesion of flowing leukocytes

We studied how the rheological properties of blood influenced capture and rolling adhesion of leukocytes as well as their margination in the bloodstream. When citrated, fluorescently labeled blood was perfused through glass capillaries coated with P-selectin, leukocytes formed numerous rolling attachments. The number of attached leukocytes increased as the hematocrit was increased between 10% and 30% and was essentially constant from 30% to 50%. In EDTA-treated blood, adhesion was absent, and the flux of marginated cells varied little with increasing hematocrit. However, the velocity of marginated leukocytes increased monotonically, whereas the volumetric flow rate was constant, implying that the flow velocity profile became blunted and wall shear rate increased. Thus increasing hematocrit promoted attachment for a given total flow rate, without increasing margination, even though wall shear rate and blood viscosity increased. Blood was diluted to 20% hematocrit with plasma, 40-kDa dextran (to reduce red blood cell aggregation), or 500-kDa dextran (to enhance aggregation). Increasing aggregation correlated with increasing leukocyte adhesion and with more slow-flowing leukocytes near the wall. Thus flowing erythrocytes promote leukocyte adhesion, either by causing margination of leukocytes or by initiating and stabilizing attachments that follow.     

Determinants of Leukocyte Margination in Rectangular Microchannels

Microfabrication of polydimethylsiloxane (PDMS) devices has provided a new set of tools for studying fluid dynamics of blood at the scale of real microvessels. However, we are only starting to understand the power and limitations of this technology. To determine the applicability of PDMS microchannels for blood flow analysis, we studied white blood cell (WBC) margination in channels of various geometries and blood compositions. We found that WBCs prefer to marginate downstream of sudden expansions, and that red blood cell (RBC) aggregation facilitates the process. In contrast to tubes, WBC margination was restricted to the sidewalls in our low aspect ratio, pseudo-2D rectangular channels and consequently, margination efficiencies of more than 95% were achieved in a variety of channel geometries. In these pseudo-2D channels blood rheology and cell integrity were preserved over a range of flow rates, with the upper range limited by the shear in the vertical direction. We conclude that, with certain limitations, rectangular PDMS microfluidic channels are useful tools for quantitative studies of blood rheology.     

Dynamical clustering of red blood cells in capillary vessels

We have modeled the dynamics of a 3-D system consisting of red blood cells (RBCs), plasma and capillary walls using a discrete-particle approach. The blood cells and capillary walls are composed of a mesh of particles interacting with harmonic forces between nearest neighbors. We employ classical mechanics to mimic the elastic properties of RBCs with a biconcave disk composed of a mesh of spring-like particles. The fluid particle method allows for modeling the plasma as a particle ensemble, where each particle represents a collective unit of fluid, which is defined by its mass, moment of inertia, translational and angular momenta. Realistic behavior of blood cells is modeled by considering RBCs and plasma flowing through capillaries of various shapes. Three types of vessels are employed: a pipe with a choking point, a curved vessel and bifurcating capillaries. There is a strong tendency to produce RBC clusters in capillaries. The choking points and other irregularities in geometry influence both the flow and RBC shapes, considerably increasing the clotting effect. We also discuss other clotting factors coming from the physical properties of blood, such as the viscosity of the plasma and the elasticity of the RBCs. Modeling has been carried out with adequate resolution by using 1 to 10 million particles. Discrete particle simulations open a new pathway for modeling the dynamics of complex, viscoelastic fluids at the microscale, where both liquid and solid phases are treated with discrete particles. Figure A snapshot from fluid particle simulation of RBCs flowing along a curved capillary. The red color corresponds to the highest velocity. We can observe aggregation of RBCs at places with the most stagnant plasma flow.     

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.