We numerically investigated margination of leukocytes at arteriole shear rate in straight circular channels with diameters ranging from 10 to 22 μm. Our results demonstrated that passing motion of RBCs effectively induces leukocyte margination not only in small channels but also in large channels. A longer time is needed for margination to occur in a larger channel, but once a leukocyte has marginated, passing motion of RBCs occurs continuously independent of the channel diameter, and leukocyte margination is sustained for a long duration. We also show that leukocytes rarely approach the wall surface to within a microvillus length at arteriole shear rate.

A numerical analysis is presented of cell adhesion in capillaries whose diameter is comparable to or smaller than that of the cell. In contrast to a large number of previous efforts on leukocyte and tumor cell rolling, much is still unknown about cell motion in capillaries. The solid and fluid mechanics of a cell in flow was coupled with a slip bond model of ligand-receptor interactions. When the size of a capillary was reduced, the cell always transitioned to "bullet-like" motion, with a consequent decrease in the velocity of the cell. A state diagram was obtained for various values of capillary diameter and receptor density. We found that bullet motion enables firm adhesion of a cell to the capillary wall even for a weak ligand-receptor binding. We also quantified effects of various parameters, including the dissociation rate constant, the spring constant, and the reactive compliance on the characteristics of cell motion. Our results suggest that even under the interaction between P-selectin glycoprotein ligand-1 (PSGL-1) and P-selectin, which is mainly responsible for leukocyte rolling, a cell is able to show firm adhesion in a small capillary. These findings may help in understanding such phenomena as leukocyte plugging and cancer metastasis.

We present a numerical analysis of the rheology of a suspension of red blood cells (RBCs) in a wall-bounded shear flow. The flow is assumed as almost inertialess. The suspension of RBCs, modeled as biconcave capsules whose membrane follows the Skalak constitutive law, is simulated for a wide range of viscosity ratios between the cytoplasm and plasma: λ = 0.1-10, for volume fractions up to φ = 0.41 and for different capillary numbers (Ca). Our numerical results show that an RBC at low Ca tends to orient to the shear plane and exhibits the so-called rolling motion, a stable mode with higher intrinsic viscosity than the so-called tumbling motion. As Ca increases, the mode shifts from the rolling to the swinging motion. Hydrodynamic interactions (higher volume fraction) also allows RBCs to exhibit both tumbling or swinging motions resulting in a drop of the intrinsic viscosity for dilute and semi-dilute suspensions. Because of this mode change, conventional ways of modeling the relative viscosity as a polynomial function of φ cannot be simply applied in suspensions of RBCs at low volume fractions. The relative viscosity for high volume fractions, however, can be well described as a function of an effective volume fraction, defined by the volume of spheres of radius equal to the semi-middle axis of the deformed RBC. We find that the relative viscosity successfully collapses on a single non-linear curve independently of λ except for the case with Ca 0.4, where the fit works only in the case of low/moderate volume fraction, and fails in the case of a fully dense suspension.

Previous studies have concluded that microparticles (MPs) can more effectively approach the microvessel wall than nanoparticles because of margination. In this study, however, we show that MPs are not marginated in capillaries where the vessel diameter is comparable to that of red blood cells (RBCs). We numerically investigated the behavior of MPs with a diameter of 1 μm in various microvessel sizes, including capillaries. In capillaries, the flow mode of RBCs shifted from multi-file flow to bolus (single-file) flow, and MPs were captured by the bolus flow of the RBCs instead of being marginated. Once MPs were captured, they rarely escaped from the vortex-like flow structures between RBCs. These capture events were enhanced when the hematocrit was decreased, and reduced when the shear rate was increased. Our results suggest that microparticles may be rather inefficient drug carriers when targeting capillaries because of capture events, but nanoparticles, which are more randomly distributed in capillaries, may be more effective carriers.The flow behavior of microparticles (MPs) is of paramount importance in drug delivery systems targeting capillary districts 1-3 . The behavior of MPs in the microcirculation, therefore, has been widely studied over decades 3,4 . MPs in blood are subject to hydrodynamic interaction with red blood cells (RBCs), which exhibit axial migration, resulting in MPs appearing primarily in the peripheral layer. This is termed margination, which is the first step in the adhesion of circulating particles to the endothelium. The behavior of platelets has been investigated in in vivo experiments using rabbit mesentery, looking at arterioles 5 and venules 6 with vessel diameters ranging from 15 to 35 μm. The effects of physical conditions (e.g., shear rate) on margination have been systematically investigated using glass tubes 7 and PDMS channels 8 . These studies provided insight not only into microcirculatory blood flow but also into therapeutic drug carriers. In vitro experiments were performed to determine the optimal size/shape of drug carriers to effectively adhere to the vascular wall 9, 10 . For example, Charoenphol et al. showed that microspheres (1-10 μm in diameter) more efficiently adhered to the endothelium in microchannels than nanoparticles (≤500 nm in diameter) in blood flow 9 .Numerical simulations have been also performed to investigate the margination of MPs 11-18 . Müller et al. 12 investigated the effect of the particle size/shape, shear rate, channel width, and volume fraction of RBCs (hematocrit, Hct) on margination. Their two-dimensional model showed that large particles (1.83 μm or 0.91 μm in diameter) more efficiently marginated than small particles (0.25 μm in diameter) for various shear rates 12 . Some of the experimental results of MP margination were discussed with numerical results 19,20 . Lee et al. 20 , for example, demonstrated that nanoparticles (200 nm in diameter) randomly distributed in postcapillary venules with a diameter ranging from 15-30 μm, while micro...

Quantifying the behavior of circulating tumor cells (CTCs) in the blood stream is of fundamental importance for understanding metastasis. Here, we investigate the flow mode and velocity of CTCs interacting with red blood cells (RBCs) in various sized microvessels. The flow of leukocytes in microvessels has been described previously; a leukocyte forms a train with RBCs in small microvessels and exhibits margination in large microvessels. Important differences in the physical properties of leukocytes and CTCs result from size. The dimensions of leukocytes are similar to those of RBCs, but CTCs are significantly larger. We investigate numerically the size effects on the flow mode and the cell velocity, and we identify similarities and differences between leukocytes and CTCs. We find that a transition from train formation to margination occurs when (R-a)/t(R)≈1, where R is the vessel radius, a is the cell radius, and t(R) is the thickness of RBCs, but that the motion of RBCs differs from the case of leukocytes. Our results also show that the velocities of CTCs and leukocytes are larger than the average blood velocity, but only CTCs move faster than RBCs for microvessels of R/a≈1.5-2.0. These findings are expected to be useful not only for understanding metastasis, but also for developing microfluidic devices.