At physiological levels of hematocrit (35–45%), red blood cells (RBCs) are continuously subjected to inter-cellular collisions in the microvascular network. Accordingly, alterations in RBC aggregation and deformability are expected to lead to a substantial modification in the distribution of RBCs over the microvascular network. In previous studies, a pathological elevation of RBC aggregation has been shown to result in the formation of a thicker cell-free layer (CFL) near the vessel wall (Ong et al., 2011), which can promote a plasma-skimming effect (Fung, 1973) resulting in a reduction in microvascular perfusion (Namgung et al., 2015).

In addition, RBC deformability is a key physical determinant in the distribution of RBCs in the microcirculation. Normal RBCs are highly deformable and thus able to travel through capillaries even narrower than their diameter. A pathological decrease in RBC deformability, however, leads to an elevation in the peripheral vascular resistance and consequently a decrease in the tissue perfusion (Simchon et al., 1987). Moreover, RBC deformability is an important factor determining the sequestration of the aged RBCs in the spleen (MacDonald et al., 1987; Mebius and Kraal, 2005) as well as affecting the shear-dependent behavior of blood viscosity (Chien, 1987). The clinical significance of RBC deformability has long been highlighted (Weed, 1970; Chien, 1987; Mokken et al., 1992) in many diseases such as sepsis (Condon et al., 2003), malaria infected blood (Dondorp et al., 2000, 2002), and in prolonged storage of blood (Haradin et al., 1969; Stuart and Nash, 1990).

Despite the clinical significance of RBC deformability, there exists limited information of its potential effects on cell migration in the microcirculation. A previous in vitro study, Hou et al. (2010) reported the outward lateral migration (margination) of less deformable malaria-infected RBCs toward the channel walls. It was further highlighted that an elevation in hematocrit promoted the cell–cell interaction between the normal and less-deformable RBCs, which leads to an enhanced displacement of the malaria-infected cells toward the walls (Hou et al., 2010). In addition, a recent in vivo study, Lee et al. (2013) showed that ~70% of rigid particles (diameter = 1 μm) infused into mice preferentially accumulated near the vessel walls (0.8R−1.0R, R: normalized radial position by vessel radius) in small vessels (diameter = 15–30 μm). It was also demonstrated that less deformable (stiff) particles were increasingly localized near the walls, whereas deformable (floppy) particles had enhanced hydrodynamic migration away from the walls resulting in their accumulation near the center of the vessel (Kumar and Graham, 2012a,b).

Such redistribution of RBCs would lead to local hematocrit changes. This could consequently influence the plasma-skimming effect and hematocrit partitioning in bifurcations (Schmid-Schonbein et al., 1980; Pries et al., 1989; Enden and Popel, 1994; Barber et al., 2008; Li et al., 2012). In a previous in vitro study (Shevkoplyas et al., 2006), RBC perfusion in a microchannel network was found to be highly sensitive to RBC deformability. It was demonstrated that the attenuated plasma skimming effect in hRBCs eventually led to blockages of capillary channels (ID = 5 μm) and also a more heterogeneous distribution of RBCs in the microchannel network. Importantly, this could in turn alter the microvascular oxygen and metabolite distributions as well as the effective viscosity of blood in the microvessels (Pries et al., 1996).

Consecutive multiple branching of the microvasculature is an essential morphological feature, which allows extensive perfusion to all peripheral tissue regions. This in vivo bifurcation have a major impact on flow patterns through the microcirculation. The impact of the arteriolar network is indicated by the finding that the travel distance required for less deformable RBCs to show a distinct margination in a straight vessel (Hou et al., 2010) has been reported to be one (or two) order of magnitude greater than an inter-bifurcation distance in the arteriolar network (Pries et al., 1989; Kiani et al., 1993; Ong et al., 2012). In this study, we examined how the diverging structure of the arteriolar networks contribute to the disparity in the migration rates of deformable and rigid RBCs toward the flow center. The radial distribution of chemically-hardened RBCs (hRBCs) was quantified in vivo after their infusion into the rat circulatory system. The contribution of bifurcations was examined using in vitro microchannel studies to further examine the suspension characteristics of the hRBCs in the presence of bifurcations.

In this study, rat RBCs were chemically hardened with glutaraldehyde (GA) solution (1.0 mM). GA is a non-specific protein cross-linker that induces cross-linking in all the components of the cell (cytosol, cytoskeleton, transmembrane) (Forsyth et al., 2010; Sosa et al., 2013), thus resulting in an overall increase in the RBC rigidity similar to a single-component solid particle. In the present study, the deformability of GA-treated RBCs (hRBCs) was consistently lower than that of the nRBCs based on the EI measured over the range of shear stresses (0.5-20 Pa). Previously, it was reported that the averaged wall shear stress in an arteriole (ID = 29.5–67.1 μm) of the rat cremaster muscle ranged from ~0.3 (MAP = 47 ± 5.5 mmHg) to 7.5 Pa (108 ± 4.7 mmHg) (Namgung et al., 2011). Another study reported that the arteriolar wall shear stress (ID = 160–220 μm) ranged from 1.0 to 4.5 Pa under physiological flow conditions (Bakker et al., 2003). Thus, under such physiological ranges of shear stresses, the difference in RBC deformability found between the hRBCs and nRBCs (5.6–35% at τ = 25–0.5 Pa in Figure 2) could lead to alterations in the suspension characteristics, which in turn result in the preferential near-wall accumulation of hRBCs. However, it is of note that the EI-based measurement of the RBC deformability only indicates the ability of the cell to elongate. RBCs are in general subjected to various types of deformations (folding, bending, and elongating) while traversing the microvasculature. Therefore, the GA-induced decrease in the RBC deformability possibly results in a different suspension behavior as compared to that of the pathologically hardened RBCs in different diseases.

It has been known that in arteriolar flows, the formation of CFL near the vessel wall is due to the shear-induced inward migration of nRBCs toward the flow center and their accumulation in the core region. Previous computational studies (Pranay et al., 2012; Hariprasad and Secomb, 2014) demonstrated that the inward migration of cells (or elastic capsules) arises from fluid mechanical interactions between the cells and the vessel walls. Particularly for RBCs, their inward migration is enhanced by the tank-treading motion of their flexible membrane. In contrast, the outward migration is elicited mainly from shear-induced dispersions due to interactions between the cells (Pranay et al., 2012; Hariprasad and Secomb, 2014). In this study, the near-wall margination (outward migration) of hRBCs shown in Figure 3B could be attributed in part to the inward migration of nRBCs, which is similar to that reported for the margination of leukocytes (Freund, 2007; Munn and Dupin, 2008). The preferential margination of leukocytes to the vessel walls at a physiological level of hematocrit is mainly due to the continuous hydrodynamic collisions with neighboring flexible nRBCs (Schmid-Schönbein et al., 1980; Goldsmith and Spain, 1984). In addition, the relatively faster inward migration of the nRBCs also partly contributed to such a margination phenomenon (Goldsmith and Spain, 1984). The rotation of the deformable nRBC membrane around its center of mass (tank-treading motion) promotes the axial migration, which subsequently displaces it away from the vessel walls (Dupire et al., 2012). In contrast, hRBCs displayed an enhanced tumbling motion (Forsyth et al., 2010) resulting in a diminished tank–treading motion. This attenuation in the tank-treading motion of the hRBCs is expected to limit their inward migration toward the flow center.

The marginated hRBCs (R₀ → 1) tended to maintain their radial positions with reduced radial dispersions (Figures 3B,C). In contrast, the significantly higher dispersion of hRBCs near the RBC core region (R₀ → 0.5) implied that the cell–cell interaction was dominant in the region where the cells were more concentrated. Similarly, a previous in vivo study Lee et al. (2013) reported that the dispersion of rigid 1-μm particles in the blood stream was greatly reduced near the walls relative to the RBC core region. Although the marginated hRBCs remained in contact with the boundary of the RBC core while flowing near the walls, they were unable to penetrate into the boundary. This suggests that the hRBCs were in an equilibrium position (Munn and Dupin, 2008). In addition, the attenuated deformability-dependent wall lift force experienced by the hRBCs potentially further contribute to the decreased radial dispersion near the wall. Accordingly, it was previously reported that deformable RBCs were affected by the lift force ranging from 31 to 155 pN at wall shear stresses between 0.2 to 1 Pa, whereas undeformed spherical leukocytes experienced zero lift force (Abkarian and Viallat, 2008).

It is important to note that the outward migration of hRBCs in a straight vessel requires a long travel distance to complete their near-wall margination induced by the hydrodynamic interaction with neighboring cells. A previous study Jain and Munn (2009) showed that the number of marginated leukocytes increased almost linearly with the length (up to 5 mm) of a rectangular microchannel with widths of 50 and 75 μm. A separate in vitro study, Hou et al. (2010) demonstrated the separation of malaria-infected RBCs (more rigid than nRBCs) based on their near-wall margination, which was achieved with an extreme channel ratio of 1: 2,000 (width: length). However, such extremely long and straight vessels are not observable in the microvasculature. The mean inter-bifurcation distance was reported to be approximately 5 to 33 vessel-diameter in arterioles (ID = 4–104 μm) of the rat cremaster muscle (Ong et al., 2012), rat mesenteric muscle (Pries et al., 1989) and hamster cremaster muscle (Kiani et al., 1993). Therefore, based on the previously proposed mechanism for the cell margination, the complete near-wall margination of hRBCs is not observed within the short inter-bifurcation distance in arteriolar network flows. A previous computational study, Müller et al. (2016) highlighted that rigid particles generally exhibit greater margination than soft particles. This could be explained by the increased lift force with correspondingly larger deformations that drives deformable particles away from the wall. Therefore, the elevation in rigidity of RBCs under pathological conditions would further increase their margination rate.

The immediate displacement of the RBCs at the inner vessel wall along the bifurcating point (Figure 4) seemed to contribute to the near-wall margination of hRBCs observed in vivo (Figure 3B). This phenomenon is likely amplified by the multiple bifurcations present in the arteriolar networks, thus resulting in the enhanced accumulation of hRBCs near the vessel walls. Due to the limited field of view of our microscopic system, it was unfeasible to perform a quantitative analysis on the radial position of hRBCs in a series of bifurcations in vivo. However, it is expected that the marginated hRBCs maintain their radial positions near the walls due to the reduced dispersion after the bifurcation (Figure 3C). This is in good agreement with a previous numerical study, Takeishi et al. (2014) which showed that the margination of leukocytes was sustained by the continuous passing motion of the RBCs in the RBC core (Takeishi et al., 2014).

The RBCs flowing at the outer channel wall exhibited a sudden inward shift by ~5% in their lateral locations (nRBC: 0.86L → 0.82L, hRBCs: 0.87L → 0.83L) immediately after the bifurcation (Figure 5B). This is likely due to a sudden local reduction in hematocrit adjacent to the outer wall which is induced by the asymmetric velocity profile developed at the bifurcation (Sherwood et al., 2014), resulting in thicker CFL formation near walls. The enhanced CFL formation at the outer wall (Ong and Kim, 2013) allows cells to migrate inward with minimal collisions with the neighboring cells. This was subsequently verified in our supplementary in vitro experiments using diluted RBC suspensions (Hct = 0.2%). The target RBCs in the diluted suspension showed a larger extent of sudden displacement away from the outer wall after the bifurcation (Supplementary Figure S2) as compared to the target RBCs in the concentrated suspension (Figure 5B). This strongly supports that the local reduction in hematocrit and the CFL formation near the outer wall at the bifurcation provide the marginal space for cells to exhibit an accelerated inward migration. Consequently, the nRBCs were able to cross the streamlines toward the flow center more effectively with a larger extent of deformation and tank-treading motions than the hRBCs. This becomes more apparent at physiological levels of hematocrit since the cell–cell interactions effectively attenuate the inward migration of hRBCs but not the nRBCs (Figure 5C).

The cumulative contribution of bifurcations to the accumulation of hRBCs near the vessel walls in vivo is depicted in Figure 6. In the blood flow, hRBCs located near the flow center are relocated to the inner wall (H → H′) after a bifurcating point (BF₁). Due to their diminished inward migration, hRBCs maintain their lateral positions near the inner wall farther downstream until the next bifurcating point (BF₂), where the inner wall in the upstream vessel becomes the outer wall in the downstream vessel (IW₁ → OW₂). As the hRBCs traverse through BF₂ (H′ → H″), they continue to remain their marginated positions along the walls. In contrast, laterally displaced nRBCs are able to migrate progressively toward the flow center (N → N′ → N″) in the downstream vessels after a series of bifurcations. This is due to the enhanced inward migration of nRBCs as well as the sudden inward shift toward the flow center at the bifurcations as observed in the present study. The disparity in the migration between nRBC and hRBC across the bifurcations consequentially leads to the selective accumulation of hRBCs near the vessel walls.

The near-wall accumulation of hRBCs could contribute to the decrease in the mean CFL width (Zhang et al., 2009). Under moderate RBC aggregation and a discharged hematocrit of ~38%, the mean normalized CFL width was predicted to decrease from 0.269 to 0.152 due to the 20-time increase in RBC rigidity. Accordingly, the increase in membrane rigidity prevented large deformation and reduced the cell–cell contact area, thus resulting in the formation of a less dense RBC core and thinner CFL. Although a direct comparison between the previous study and our findings is limited due to the stark differences in the magnitude of cell rigidity and volume concentration of hRBCs used, the decreasing trend in the CFL width due to the hardening of RBCs would still be expected. Importantly, the reduction in the CFL width could lead to a myriad of physiological influences including flow resistance (Maeda et al., 1996; Zhang et al., 2009), oxygen delivery and nutrients exchange (Tateishi et al., 2001), as well as wall shear stress-dependent nitric oxide (NO) bioavailability (Vaughn et al., 1998; Ng et al., 2015).

This study shows that a change in the overall RBC deformability significantly alters the distribution of the RBCs in arterioles. The laterally marginated hRBCs tend to maintain their lateral positions near the walls while traversing downstream with attenuated radial dispersion. Moreover, the immediate displacement of RBCs while traversing a bifurcation also contributes to the in vivo near-wall accumulation of hRBCs. The notable difference in the inward migration between the marginated nRBCs and hRBCs after the bifurcation further supports the contribution of bifurcations to the accumulation of hRBCs near the walls.

BN: Involved in study design, conducted in vivo experiments, analyzed the data and prepared the manuscript; YN: Conducted in vitro experiments, analyzed the data and revised the manuscript; HL: Verified results and revised the manuscript; JR: Verified results and revised the manuscript; SK: Designed and coordinated research, verified results and revised the manuscript.