MICROSCOPIC CONSIDERATIONS: THE MOTIONS OF INDIVIDUAL PARTICLES

An experimental study of shear-dependent human platelet adhesion and underlying protein-binding mechanisms in a cylindrical Couette system

Undesirable thrombotic reactions count among the most frequent and serious complications for patients who rely on the use of medical devices. To improve the design of medical devices, it is essential to develop a more precise understanding of platelet reactions. Clinical studies and experiments have shown a strong dependence of platelet deposition behavior on the flow. However, today the influence of hemodynamic parameters such as the shear rate on thrombotic reactions is not well understood. For the study of the shear-dependent mechanisms leading to the activation, adhesion and aggregation of platelets, a Couette flow system was used to investigate thrombocyte behavior with regard to well-defined flow conditions at shear-rate values between γ˙=400 $\dot \gamma = {\rm{400}}$ and 1400 1/s. Results were calculated for physiological temperature. It could be shown that the platelet adhesion density increased with increasing shear rates up to γ˙=800 1/s $\dot \gamma = {\rm{800 1/s}}$ and the adhesion pattern was homogeneous. At γ˙=800 1/s, $\dot \gamma = {\rm{800 1/s}},$ a sudden drop in platelet adhesion density occurred and platelets adhered in filaments. Fluorescence microscopy results of von Willebrand factor (vWF) confirm that a shear rate of γ˙=800 1/s $\dot \gamma = {\rm{800 1/s}}$ represents the threshold where a switch of the platelet-binding mechanism from fibrinogen-mediated to vWF-mediated platelet adhesion takes place.

Mechanical response of red blood cells entering a constriction

Most work on the dynamic response of red blood cells (RBCs) to hydrodynamic stress has focused on linear velocity profiles. Relatively little experimental work has examined how individual RBCs respond to pressure driven flow in more complex geometries, such as the flow at the entrance of a capillary. Here, we establish the mechanical behaviors of healthy RBCs undergoing a sudden increase in shear stress at the entrance of a narrow constriction. We pumped RBCs through a constriction in a microfluidic device and used high speed video to visualize and track the flow behavior of more than 4400 RBCs. We show that approximately 85% of RBCs undergo one of four distinct modes of motion: stretching, twisting, tumbling, or rolling. Intriguingly, a plurality of cells (∼30%) exhibited twisting (rotation around the major axis parallel to the flow direction), a mechanical behavior that is not typically observed in linear velocity profiles. We present detailed statistical analyses on the dynamics of each motion and demonstrate that the behavior is highly sensitive to the location of the RBC within the channel. We further demonstrate that the observed tumbling, twisting, and rolling rotations can be rationalized qualitatively in terms of rigid body mechanics. The detailed experimental statistics presented here should serve as a useful resource for modeling of RBC behavior under physiologically important flow conditions.

A multiscale SPH particle model of the near-wall dynamics of leukocytes in flow

A novel multiscale Lagrangian particle solver based on SPH is developed with the intended application of leukocyte transport in large arteries. In such arteries, the transport of leukocytes and red blood cells can be divided into two distinct regions: the bulk flow and the near-wall region. In the bulk flow, the transport can be modeled on a continuum basis as the transport of passive scalar concentrations. Whereas in the near-wall region, specific particle tracking of the leukocytes is required and lubrication forces need to be separately taken into account. Because of large separation of spatio-temporal scales involved in the problem, simulations of red blood cells and leukocytes are handled separately. In order to take the exchange of leukocytes between the bulk fluid and the near-wall region into account, solutions are communicated through coupling of conserved quantities at the interface between these regions. Because the particle tracking is limited to those leukocytes lying in the near-wall region only, our approach brings considerable speedup to the simulation of leukocyte circulation in a test geometry of a backward-facing step, which encompasses many flow features observed in vivo.

Passive recruitment of circulating leukocytes into capillary sprouts from existing capillaries in a microfluidic system

Recent evidence implicating leukocytes in angiogenesis raises the question of whether leukocytes and other cells circulating with the blood in microvascular networks can home to capillary sprouts intraluminally. This study describes an investigation of leukocyte trafficking in sprouting capillaries fabricated using soft lithography. The leukocytes passing with whole blood through existing capillaries were able to enter microfabricated capillary sprouts of variable length and sprouting angle due to the mechanical interaction with red blood cells (RBCs) at the sprouting bifurcation, in spite of the complete absence of blood flow through the blind-ended sprouts or any chemoattractants. The RBCs formed "comet tails" (the densely packed cellular trains forming behind leukocytes as they move through narrow capillaries) and effectively pushed leukocytes into the microfabricated sprouts while bypassing them at the sprouting bifurcation. Individual sprouts filled with several leukocytes, as wells as RBCs and platelets, were observed. The results of this study suggest that (i) blood cells are likely present in capillary sprouts throughout their development, (ii) leukocytes and other circulating cells may use this mechanism to home to capillary sprouts intraluminally for direct engraftment, and (iii) tissues may use this phenomenon as another mechanism for local recruitment of leukocytes from the blood stream.

Fluid particle diffusion through high-hematocrit blood flow within a capillary tube

Fluid particle diffusion through blood flow within a capillary tube is an important phenomenon to understand, especially for studies in mass transport in the microcirculation as well as in solving technical issues involved in mixing in biomedical microdevices. In this paper, the spreading of tracer particles through up to 20% hematocrit blood, flowing in a capillary tube, was studied using a confocal micro-PTV system. We tracked hundreds of particles in high-hematocrit blood and measured the radial dispersion coefficient. Results yielded significant enhancement of the particle diffusion, due to a micron-scale flow-field generated by red blood cell motions. By increasing the flow rate, the particle dispersion increased almost linearly under constant hematocrit levels. The particle dispersion also showed near linear dependency on hematocrit up to 20%. A scaling analysis of the results, on the assumption that the tracer trajectories were unbiased random walks, was shown to capture the main features of the results. The dispersion of tracer particles was about 0.7 times that of RBCs. These findings provide good insight into transport phenomena in the microcirculation and in biomedical microdevices.

Velocity variation assessment of red blood cell aggregation with spectral domain Doppler optical coherence tomography

We propose spectral domain Doppler optical coherence tomography (SD-D-OCT) to qualitatively measure red blood cell aggregation. Variance/standard deviation (SD) of the Doppler frequency spectrum in Doppler variance imaging of flowing blood under shearing conditions was developed as a new aggregation index. In in vitro microchannel-flow experiments, porcine blood at various hematocrits with aggregation characteristics induced by dextran 500 or at the presence of plasma fibrinogen was measured by a SD-D-OCT system with a spectrum centered at 1310 nm. The effects of shear rate, hematocrit, aggregation level on the SD values were investigated. The results demonstrate that Doppler variance imaging using the SD value was capable of differentiating the normal and the aggregated blood with hematocrits of 30-55% flowing at a shear rate of 40-60 s(-1). The SD value was found to be nonsignificant hematocrit-dependent. It is also a sensitive and repeatable aggregation index for comparison between nonaggregated and aggregated blood samples.

Radial dispersion of red blood cells in blood flowing through glass capillaries: the role of hematocrit and geometry

The flow properties of blood in the microcirculation depend strongly on the hematocrit (Hct), microvessel geometry, and cell properties. Previous in vitro studies have measured the radial displacement of red blood cells (RBCs) at concentrated suspensions using conventional microscopes. However, to measure the RBCs motion they used transparent suspensions of ghost red cells, which may have different physical properties than normal RBCs. The present study introduces a new approach (confocal micro-PTV) to measure the motion of labeled RBCs flowing in concentrated suspensions of normal RBCs. The ability of confocal systems to obtain thin in-focus planes allowed us to measure the radial position of individual RBCs accurately and to consequently measure the interaction between multiple labeled RBCs. All the measurements were performed in the center plane of both 50 and 100 microm glass capillaries at Reynolds numbers (Re) from 0.003 to 0.005 using Hcts from 2% to 35%. To quantify the motion and interaction of multiple RBCs, we used the RBC radial dispersion (D(yy)). Our results clearly demonstrate that D(yy) strongly depends on the Hct. The RBCs exhibited higher D(yy) at radial positions between 0.4 and 0.8R and lower D(yy) at locations adjacent to the wall (0.8-1R) and around the middle of the capillary (0-0.2R). The present work also demonstrates that D(yy) tends to decrease with a decrease in the diameter. The information provided by this study not only complements previous investigations on microhemorheology of both dilute and concentrated suspensions of RBCs, but also shows the influence of both Hct and geometry on the radial dispersion of RBCs. This information is important for a better understanding of blood mass transport mechanisms under both physiological and pathological conditions.

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.

Effect of aggregation and shear rate on the dispersion of red blood cells flowing in venules

Previous in vitro studies of blood flow in small glass tubes have shown that red blood cells exhibit significant erratic deviations in the radial position in the laminar flow regime. The purpose of the present study was to assess the magnitude of this variability and that of velocity in vivo and the effect of red blood cell aggregation and shear rate upon them. With the use of a gated image intensifier and fluorescently labeled red blood cells in tracer quantities, we obtained multiple measurements of red blood cell radial and longitudinal positions at time intervals as short as 5 ms within single venous microvessels (diameter range 45-75 microm) of the rat spinotrapezius muscle. For nonaggregating red blood cells in the velocity range of 0.3-14 mm/s, the mean coefficient of variation of velocity was 16.9 +/- 10.5% and the SD of the radial position was 1.98 +/- 0.98 microm. Both quantities were inversely related to shear rate, and the former was significantly lowered on induction of red blood cell aggregation by the addition of Dextran 500 to the blood. The shear-induced random movements observed in this study may increase the radial transport of particles and solutes within the bloodstream by orders of magnitude.

Sickle erythrocyte adherence to endothelium at low shear: role of shear stress in propagation of vaso-occlusion

Under venular flow conditions, sickle cell adherence to endothelium is mediated by cell adhesion molecules and adhesive proteins associated with inflammation, coagulation, and endothelial perturbation. Periodic and reduced blood flow are observed in sickle microcirculation during hematologic steady state, suggesting that blood flow is compromised in sickle microcirculation. We tested the hypothesis that low blood flow enhances adherence by quantifying sickle cell adhesion to endothelium under venular flow (1.0 dyne/cm(2) shear stress) and low flow (0.1 dyne/cm(2) shear stress), with and without addition of adhesion promoting agonists. Under low flow, sickle cell adherence to endothelium increases with contact time in the absence of endothelial activation or adhesive protein addition. In contrast, at venular shear stress, sickle cell adherence only occurs following endothelial activation with TNF-alpha or addition of thrombospondin. Analysis of these data with a mathematical model reveals that at low flow adherence is "transport-controlled," meaning that contact time between sickle cells and endothelium is a more important determinant of adherence than high-affinity receptor-ligand interactions. Low-affinity interactions are sufficient for adhesion at low flow. In contrast, at venular flow (1 dyne/cm(2) shear stress) adherence is "affinity-controlled," meaning that adherence requires induction of specific high-affinity receptor-ligand interactions. These findings demonstrate that in addition to activating factors and adherence proteins, microvascular shear stress is an important determinant of sickle cell adhesion to endothelium. This suggests that in vivo, erythrostasis is an important determinant of adhesion that can act either independently or concurrently with ongoing acute events to induce adhesive interactions and vaso-occlusion.

Transport of platelets in flowing blood

Distribution and transport of platelets in flowing blood were studied experimentally using suspensions of washed red cells and fluorescent latex beads as platelet analogues. Distributions of the platelet analogues were obtained from stroboscopic epifluorescence photomicrographs of flow in 50-micron channels and from images of the cut cross sections of cryogenically frozen thin-walled 200-micron tubes. Concentration profiles of platelet analogues had a substantial near-wall excess for situations with a substantial hematocrit (greater than 10%) and a substantial wall shear rate (greater than 400 s-1). The viscosity of the suspending fluid was found to affect the size of the near-wall excess and its shear-dependent onset. Additionally, the shear-rate dependence of the near-wall excess did not occur with suspensions of hardened red cells. The excess extended a substantial distance from the wall in the 200-micron tubes and a portion of the profile could be fitted to an exponential curve. The random walk model that is used to describe enhanced platelet diffusion is envisioned as a walk (lateral platelet motion) caused by shear-induced collisions with red cells. A more comprehensive random walk model that includes biased collisions produces an effective lateral motion of convective nature in addition to a diffusional motion; it is used to explain the observed nonuniform distributions of platelet analogues.

Margination of leukocytes in blood flow through small tubes

Leukocyte margination in the vessels of the microcirculation has been attributed to a flow-dependent interaction with red cells. To determine the extent of this effect, experiments with human blood were done in 100- to 180-micron tubes to detect changes in cell distribution as a function of hematocrit and flow rate. Using a flow visualization technique, the leukocyte concentration distribution was determined in 45% ghost cell suspensions. Migration of cells toward the wall was observed at centerline velocities greater than 1 mm sec-1 and increased with increasing flow rate. The effect was probably due to a more rapid inward migration of ghosts than leukocytes because of fluid inertia and cell density differences. Experiments were therefore carried out in whole blood at hematocrits from 20 to 60%, measuring the number concentration of leukocytes and erythrocytes within the tube, nt, and comparing it to that in the infusing reservoir, no, (Fahraeus effect). At mean tube shear rates G less than 100 sec-1, nt/no less than 1 for both leukocytes and erythrocytes showing net migration of cells away from the wall, although at nearly all hematocrits there was an enrichment of leukocytes relative to erythrocytes in the tubes. At G less than 50 sec-1, nt/no remained less than 1 for erythrocytes but increased to greater than 1 for leukocytes showing migration toward the wall, the increase being greatest at 20% hematocrit in the 100-micron tubes. The nature of the effect was revealed by cine films which showed that, as the flow rate decreased, erythrocytes formed rouleaux which migrated inward creating a core and displacing leukocytes to the periphery. In control experiments using washed blood cells in phosphate buffer-albumin, nt/no less than 1 for both leukocytes and erythrocytes at all G and hematocrits, and leukocytes were now distributed. Cine films of washed blood confirmed that, in the absence of rouleaux, no significant inward migration of erythrocytes occurred.

Red blood cells: their dual role in thrombus formation

Red blood cells may have a physical and chemical effect on the interaction between platelets and blood vessel surfaces. Under flow conditions in which primarily physical effects prevail, platelet adhesion increases fivefold as hematocrit values increase from 10 to 40 percent but undergoes no further increase from 40 to 70 percent, implying a saturation of the transport-enhancing capabilities of red cells. For flow conditions in which platelet-surface reactivity is more dominant, platelet adhesion and thrombus formation increase monotonically as hematocrit values increase from 10 to 70 percent. Thus red cells may have a significant influence on hemostasis and thrombosis; the nature of the effect is apparently related to the flow conditions.

Significance of luminal plasma layer resistance in arterial wall oxygen supply

Previous analyses of the arterial wall oxygen supply system have assumed that a cell-free layer of plasma next to the endothelium is the major transport barrier in the lumen. Using a computer simulation, we have quantitatively tested this assumption. Our results show that oxygen diffusion gradients extend significantly into the flowing blood well beyond any plasma layer and that the major luminal transport resistance lies in the flowing blood and not in the plasma layer. The simulation was also employed to compute the effect of a reported 50% drop in plasma oxygen diffusivity. This rather large reduction did significantly lower oxygen levels within the arterial wall tissue. Whether such large reductions in diffusivity ever actually occur in human plasma is a subject of current controversy.