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.     

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.     

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.     

Platelet near-wall excess in porcine whole blood in artery-sized tubes under steady and pulsatile flow conditions

Platelet margination (enhanced platelet concentration in the near wall region of a blood vessel) has been well documented in small vessels. In artery-sized vessels margination has only been demonstrated in one study, using ghost cell suspensions and under relatively non-physiologic conditions of steady flow and 50 cm development length. Local sampling experiments were performed to confirm platelet margination in artery-sized stainless steel tubes, for a typical anatomical length and under pulsatile flow, using fresh EDTA-anticoagulated porcine whole blood (N=21). Experiments were designed using three-dimensional Computational Fluid Dynamics (CFD) to model the sample region with greater fidelity. Steady flow experiments in 50 cm long tubes verify published laser Doppler measurements of platelet margination in 3 mm ID tubes at normal arterial shear rate (500 s(-1). Margination persists under pulsatile flow conditions (63.8 pulses/min), but in steady flow at length of 10 cm, margination is reduced. Platelet margination ratio (the ratio of the platelet concentration near the wall to bulk average platelet count) ranges from 1.21 to 2.48. No significant effects of calculated sampling thickness (20 microm and 50 microm) or pulsatility were detected. Hematocrit margination ratio is 0.68 to 0.90. Two model platelet concentration profiles are fit to the experimental results.     

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.     

Strongly Accelerated Margination of Active Particles in Blood Flow

Synthetic nanoparticles and other stiff objects injected into a blood vessel filled with red blood cells are known to marginate toward the vessel walls. By means of hydrodynamic lattice-Boltzmann simulations, we show that active particles can strongly accelerate their margination by moving against the flow direction: particles located initially in the channel center migrate much faster to their final position near the wall than in the nonactive case. We explain our findings by an enhanced rate of collisions between the stiff particles and the deformable red blood cells. Our results imply that a significantly faster margination can be achieved either technically by the application of an external magnetic field (if the particles are magnetic) or biologically by self-propulsion (if the particles are, e.g., swimming bacteria).     

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.     

Three-dimensional focusing of red blood cells in microchannel flows for bio-sensing applications

Three-dimensional (3D) focusing of particles in microchannels has been a long-standing issue in the design of biochemical/biomedical microdevices. Current microdevices for 3D cell or bioparticle focusing involve complex channel geometries in view of their fabrication because they require multiple layers and/or sheath flows. This paper proposes a simple method for 3D focusing of red blood cells (RBCs) in a single circular microcapillary, without any sheath flows, which is inspired from the fluid dynamics phenomenon in that a spherical particle lagging behind a Poiseuille flow migrates toward and along the channel axis. More explicitly, electrophoresis of RBCs superimposed on the pressure-driven flow is utilized to generate an RBC migration mode analogous to this phenomenon. A particle-tracking scheme with a sub-pixel resolution is implemented to spatially position red blood cells flowing through the channel, so that a probability density function (PDF) is constructed to evaluate the tightness of the cell focusing. Above a specific strength of the electric field, approximately 90% of the sheep RBCs laden in the flow are tightly focused within a beam diameter that is three times the cell dimension. Particle shape effect on the focusing is discussed by making comparisons between the RBCs and the spherical particles. The lateral migration velocity, predicted by an existing theoretical model, is in good agreement with the present experimental data. It is noteworthy that 3D focusing of non-spherical particles, such as RBCs, has been achieved in a circular microchannel, which is a significant improvement over previous focusing methodologies.     

Conductometric study of shear-dependent processes in red cell suspensions. II. Transient cross-stream hematocrit distribution

A novel experimental approach based on electrical properties of red blood cell (RBC) suspensions was applied to study the effects of the size and morphology of RBC aggregates on the transient cross-stream hematocrit distribution in suspensions flowing through a square cross-section flow channel. The information about the effective size of RBC aggregates and their morphology is extracted from the capacitance (C) and conductance (G) recorded during RBC aggregation, whereas a slower process of particle migration is manifested by delayed long-term changes in the conductance. Migration-induced changes in the conductance measured at low shear rates (< or =3.1 s(-1)) for suspensions of RBCs in a strongly aggregating medium reveal an increase to a maximum followed by a decrease to the stationary level. The ascending branch of G(t) curves reflects the aggregate migration in the direction of decreasing shear rate. A further RBC aggregation in the region of lower shear stresses leads to the formation of RBC networks and results in the transformation of the rheological behavior of suspensions from the thinning to the thickening. It is suggested that the descending branches of the G(t) curves recorded at low shear rates reflect an adjustment of the Hct distribution to a new state caused by a partial dispersion of RBC networks. For suspensions of non-aggregating RBCs it is found that depending on whether the shear rate is higher or lower compared with the prior value, individual RBCs migrate either toward the centerline of the flow or in the opposite direction.     

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.     

Microscopic photometric quantification of stiffness and relaxation time of red blood cells in a flow chamber

The Microscopic Photometric Monolayer Technique provides a tool to measure red blood cell (RBC) stiffness (resistance to elongation) and relaxation time. It combines many of the advantages of flow channel studies of point-attached RBCs with the simplicity, sensitivity and accuracy of photometric light transmission measurement This technique allows the study of the effects of physicochemical factors on the elongation and relaxation time of the same cells within an average of four to five thousand cells adhered as a monolayer to glass. Further, the time course of physicochemical effects on cell membrane and wash-in/wash-out kinetics of interactions can be followed. An automated version of this technique was developed. A dense monolayer of point-attached RBCs was prepared at the bottom of a flow-chamber. A steady-state flow, with stepwise increases of flow rate, induced the RBC elongation. The light transmission perpendicular through the monolayer plane was measured photometrically. Photomicrographs compared with photometric results showed that the flow-induced bending and curvature change of RBC membrane was associated with the increase of light transmission. There was a linear correlation between the photometric index of elongation and the elongation taken from photomicrographs for shear stresses up to 0.75 Pa. A stiffness parameter, S (in Pa), was defined as the ratio of shear stress and elongation at a shear stress of 0.25 Pa. Following a sudden flow stoppage, the RBCs returned to their resting shape and the RBC relaxation time was measured. The stiffness-relaxation time product, V (in mPas), was calculated to provide an estimate of viscosity. Diamide treatment, known to stiffen RBCs, did result in dose-dependent decreases of elongation and relaxation time. With increasing temperature, the relaxation time decreased at a rate of −2.96 ms/K; the stiffness increased significantly at a rate of 0.0038 Pa/K, and the stiffness-relaxation time product decreased with −2.95 mPas/K, reflecting an inverse relationship between RBC viscosity and temperature. Using the automated version of this technique (Elias-c-) to test RBCs of 36 healthy subjects, we found the inter-individual coefficients of variation to be 8.6% for stiffness, 7.9% for relaxation time and 12.4% for stiffness-relaxation time product.     

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.     

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.     

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.     

The margination propensity of spherical particles for vascular targeting in the microcirculation

The propensity of circulating particles to drift laterally towards the vessel walls (margination) in the microcirculation has been experimentally studied using a parallel plate flow chamber. Fluorescent polystyrene particles, with a relative density to water of just 50 g/cm ³comparable with that of liposomal or polymeric nanoparticles used in drug delivery and bio-imaging, have been used with a diameter spanning over three order of magnitudes from 50 nm up to 10 μm. The number of particles marginating per unit surface have been measured through confocal fluorescent microscopy for a horizontal chamber, and the corresponding total volume of particles has been calculated. Scaling laws have been derived as a function of the particle diameter d. In horizontal capillaries, margination is mainly due to the gravitational force for particles with d > 200 nm and increases with d ⁴; whereas for smaller particles increases with d ³. In vertical capillaries, since the particles are heavier than the fluid they would tend to marginate towards the walls in downward flows and towards the center in upward flows, with increasing with d ^9/2. However, the margination in vertical capillaries is predicted to be much smaller than in horizontal capillaries. These results suggest that, for particles circulating in an external field of volume forces (gravitation or magnetic), the strategy of using larger particles designed to marginate and adhere firmly to the vascular walls under flow could be more effective than that of using particles sufficiently small (d < 200 nm) to hopefully cross a discontinuous endothelium.     

How malaria parasites reduce the deformability of infected red blood cells

The pathogenesis of malaria is largely due to stiffening of the infected red blood cells (RBCs). Contemporary understanding ascribes the loss of RBC deformability to a 10-fold increase in membrane stiffness caused by extra cross-linking in the spectrin network. Local measurements by micropipette aspiration, however, have reported only an increase of ～3-fold in the shear modulus. We believe the discrepancy stems from the rigid parasite particles inside infected cells, and have carried out numerical simulations to demonstrate this mechanism. The cell membrane is represented by a set of discrete particles connected by linearly elastic springs. The cytosol is modeled as a homogeneous Newtonian fluid, and discretized by particles as in standard smoothed particle hydrodynamics. The malaria parasite is modeled as an aggregate of particles constrained to rigid-body motion. We simulate RBC stretching tests by optical tweezers in three dimensions. The results demonstrate that the presence of a sizeable parasite greatly reduces the ability of RBCs to deform under stretching. With the solid inclusion, the observed loss of deformability can be predicted quantitatively using the local membrane elasticity measured by micropipettes.     

Mixed Exciton-Charge-Transfer States in Photosystem II: Stark Spectroscopy on Site-Directed Mutants

Sickle erythrocytes exhibit abnormal morphology and membrane mechanics under deoxygenated conditions due to the polymerization of hemoglobin S. We employed dissipative particle dynamics to extend a validated multiscale model of red blood cells (RBCs) to represent different sickle cell morphologies based on a simulated annealing procedure and experimental observations. We quantified cell distortion using asphericity and elliptical shape factors, and the results were consistent with a medical image analysis. We then studied the rheology and dynamics of sickle RBC suspensions under constant shear and in a tube. In shear flow, the transition from shear-thinning to shear-independent flow revealed a profound effect of cell membrane stiffening during deoxygenation, with granular RBC shapes leading to the greatest viscosity. In tube flow, the increase of flow resistance by granular RBCs was also greater than the resistance of blood flow with sickle-shape RBCs. However, no occlusion was observed in a straight tube under any conditions unless an adhesive dynamics model was explicitly incorporated into simulations that partially trapped sickle RBCs, which led to full occlusion in some cases.     

Red blood cells under flow show maximal ATP release for specific hematocrit

ATP release by red blood cells (RBCs) under shear stress (SS) plays a pivotal role in endothelial biochemical signaling cascades. The aim of this study is to investigate through numerical simulation how RBC spatiotemporal organization depends on flow and geometrical conditions to generate ATP patterns. Numerical simulations were conducted in a straight channel by considering both plasma and explicit presence of RBCs, their shape deformation and cell-cell interaction, and ATP release by RBCs. Two ATP release pathways through cell membrane are taken into account: pannexin 1 channel, sensitive to SS, and cystic fibrosis transmembrane conductance regulator, which responds to cell deformation. Several flow and hematocrit conditions are explored. The problem is solved by the lattice Boltzmann method. Application of SS to the RBC suspension triggers a nontrivial spatial RBC organization and ATP patterns. ATP localizes preferentially in the vicinity of the cell-free layer close to channel wall. Conditions for maximal ATP release per cell are identified, which depend on vessel size and hematocrit Ht. Increasing further Ht beyond optimum enhances the total ATP release but should degrade oxygen transport capacity, a compromise between an efficient ATP release and minimal blood dissipation. Moreover, ATP is boosted in capillaries, suggesting a vasomotor activity coordination throughout the resistance network.