Spatio-temporal variations in cell-free layer formation near bifurcations of small arterioles

Emergent cell-free layer asymmetry and biased haematocrit partition in a biomimetic vascular network of successive bifurcations

Blood is a vital soft matter, and its normal circulation in the human body relies on the distribution of red blood cells (RBCs) at successive bifurcations. Understanding how RBCs are partitioned at bifurcations is key for the optimisation of microfluidic devices as well as for devising novel strategies for diagnosis and treatment of blood-related diseases. We report the dynamics of RBC suspensions flowing through a biomimetic vascular network incorporating three generations of microchannels and two classical types of bifurcations at the arteriole level. Our microfluidic experiments with dilute and semidilute RBC suspensions demonstrate the emergence of excessive heterogeneity of RBC concentration in downstream generations upon altering the network's outflow rates. Through parallel simulations using the immersed-boundary-lattice-Boltzmann method, we reveal that the heterogeneity is attributed to upstream perturbations in the cell-free layer (CFL) and lack of its recovery between consecutive bifurcations owing to suppressed hydrodynamic lift under reduced flow conditions. In the dilute/semidilute regime, this perturbation dominates over the effect of local fractional flow at the bifurcation and can lead to inherently unfavourable child branches that are deprived of RBCs even for equal flow split. Our work highlights the importance of CFL asymmetry cascading down a vascular network, which leads to biased phase separation that deviates from established empirical predictions.

Spatiotemporal Dynamics of Dilute Red Blood Cell Suspensions in Low-Inertia Microchannel Flow

Microfluidic technologies are commonly used for the manipulation of red blood cell (RBC) suspensions and analyses of flow-mediated biomechanics. To enhance the performance of microfluidic devices, understanding the dynamics of the suspensions processed within is crucial. We report novel, to our knowledge, aspects of the spatiotemporal dynamics of RBC suspensions flowing through a typical microchannel at low Reynolds number. Through experiments with dilute RBC suspensions, we find an off-center two-peak (OCTP) profile of cells contrary to the centralized distribution commonly reported for low-inertia flows. This is reminiscent of the well-known "tubular pinch effect," which arises from inertial effects. However, given the conditions of negligible inertia in our experiments, an alternative explanation is needed for this OCTP profile. Our massively parallel simulations of RBC flow in real-size microfluidic dimensions using the immersed-boundary-lattice-Boltzmann method confirm the experimental findings and elucidate the underlying mechanism for the counterintuitive RBC pattern. By analyzing the RBC migration and cell-free layer development within a high-aspect-ratio channel, we show that such a distribution is co-determined by the spatial decay of hydrodynamic lift and the global deficiency of cell dispersion in dilute suspensions. We find a cell-free layer development length greater than 46 and 28 hydraulic diameters in the experiment and simulation, respectively, exceeding typical lengths of microfluidic designs. Our work highlights the key role of transient cell distribution in dilute suspensions, which may negatively affect the reliability of experimental results if not taken into account.

Near-Wall Migration Dynamics of Erythrocytes in Vivo: Effects of Cell Deformability and Arteriolar Bifurcation

Red blood cell (RBC) deformability has a significant impact on microcirculation by affecting cell dynamics. Despite previous studies that have demonstrated the margination of rigid cells and particles in vitro, little information is available on the in vivo margination of deformability-impaired RBCs under physiological flow and hematocrit conditions. Thus, in this study, we examined how the deformability-dependent, RBC migration alters the cell distribution under physiological conditions, particularly in arteriolar network flows. The hardened RBCs (hRBCs) were found to preferentially flow near the vessel walls of small arterioles (diameter = 47.1-93.3 μm). The majority of the hRBCs (63%) were marginated within the range of 0.7R-0.9R (R: radial position normalized by vessel radius), indicating that the hRBCs preferentially accumulated near the vessel walls. The laterally marginated hRBCs maintained their lateral positions near the walls while traversing downstream with attenuated radial dispersion. In addition, the immediate displacement of RBCs while traversing a bifurcation also contributes to the near-wall accumulation of hRBCs. The notable difference in the inward migration between the marginated nRBCs and hRBCs after bifurcations further supports the potential role of bifurcations in the accumulation of hRBCs near the walls.

Numerical investigation on red blood cell dynamics in microflow: Effect of cell deformability

The radial dispersion of red blood cells (RBCs) near the vessel wall can significantly affect the transport dynamics in small vessels. The radial dispersion of RBCs is mainly caused by collisions between RBCs and this can be enhanced by aggregation. The objective of this study is to numerically investigate on the effect of RBC deformability on the radial motion of individual RBCs in a range of flow rates. Immersed Boundary - Lattice Boltzmann Method was utilized to study the radial motion of RBCs in a two-dimensional flow domain. The RBC flow simulations were performed at 40% hematocrit in a microvessel with diameter of 25μm and length of 100μm. The dispersion of less deformable RBCs was notably greater than that of normal RBCs at all flow rates and this effect seemed to be more pronounced when the flow rate was increased. The cell dispersion was higher near the vessel wall than the flow center regardless of flow rate and RBCs deformability. Thus, the dispersion of RBCs could be enhanced with flow rate and RBC rigidity. Our findings would be especially useful in investigating blood flows in arterioles and venules.

Biomimetic Precapillary Flow Patterns for Enhancing Blood Plasma Separation: A Preliminary Study

In this study, a biomimetic microfluidic plasma separation device is discussed. The design of the device drew inspiration from in vivo observations of enhanced cell-free layer (CFL) formation downstream of vascular bifurcations. The working principle for the plasma separation was based on the plasma skimming effect in an arteriolar bifurcation, which is modulated by CFL formation. The enhancement of the CFL width was achieved by a local hematocrit reduction near the collection channel by creating an uneven hematocrit distribution at the bifurcation of the channel. The device demonstrated a high purity of separation (~99.9%) at physiological levels of hematocrit (~40%).

Symmetry recovery of cell-free layer after bifurcations of small arterioles in reduced flow conditions: effect of RBC aggregation

Heterogeneous distribution of red blood cells (RBCs) in downstream vessels of arteriolar bifurcations can be promoted by an asymmetric formation of cell-free layer (CFL) in upstream vessels. Consequently, the CFL widths in subsequent downstream vessels become an important determinant for tissue oxygenation (O2) and vascular tone change by varying nitric oxide (NO) availability. To extend our previous understanding on the formation of CFL in arteriolar bifurcations, this study investigated the formation of CFL widths from 2 to 6 vessel-diameter (2D-6D) downstream of arteriolar bifurcations in the rat cremaster muscle (D = 51.5 ± 1.3 μm). As the CFL widths are highly influenced by RBC aggregation, the degree of aggregation was adjusted to simulate levels seen during physiological and pathological states. Our in vivo experimental results showed that the asymmetry of CFL widths persists along downstream vessels up to 6D from the bifurcating point. Moreover, elevated levels of RBC aggregation appeared to retard the recovery of CFL width symmetry. The required length of complete symmetry recovery was estimated to be greater than 11D under reduced flow conditions, which is relatively longer than interbifurcation distances of arterioles for vessel diameter of ∼50 μm. In addition, our numerical prediction showed that the persistent asymmetry of CFL widths could potentially result in a heterogeneous vasoactivity over the entire arteriolar network in such abnormal flow conditions.

Recovery of cell-free layer and wall shear stress profile symmetry downstream of an arteriolar bifurcation

Unequal RBC partitioning at arteriolar bifurcations contributes to dissimilar flow developments between daughter vessels in a bifurcation. Due to the importance of the cell-free layer (CFL) and the wall shear stress (WSS) to physiological processes such as vasoregulation and gas diffusion, we investigated the effects of a bifurcation disturbance on the development of the CFL width and WSS in bifurcation daughter branches. The analysis was performed on a two-dimensional (2-D) computational model of a transverse arteriole at three different flow rates corresponding to parent branch (PB) pseudoshear rates of 60, 170 and 470s(-1), while maintaining a 2-D hematocrit of about 55% in the PB. Flow symmetry was defined using the statistical similarity of the CFL and WSS distributions between the two walls of the vessel branch. In terms of the flow symmetry recovery, higher flow rates caused larger reductions in the flow symmetry indices in the MB and subsequently required longer vessel lengths for complete recovery. Lower tube hematocrits in the SB led to complete symmetry recovery for all flow rates despite the higher initial asymmetry in the SB than in the MB. Arteriolar bifurcations produce unavoidable local CFL asymmetry and the persistence of the asymmetry downstream may increase effective blood viscosity which is especially significant at higher physiological flow rates.

Modeling microcirculatory blood flow: current state and future perspectives

Microvascular blood flow determines a number of important physiological processes of an organism in health and disease. Therefore, a detailed understanding of microvascular blood flow would significantly advance biophysical and biomedical research and its applications. Current developments in modeling of microcirculatory blood flow already allow to go beyond available experimental measurements and have a large potential to elucidate blood flow behavior in normal and diseased microvascular networks. There exist detailed models of blood flow on a single cell level as well as simplified models of the flow through microcirculatory networks, which are reviewed and discussed here. The combination of these models provides promising prospects for better understanding of blood flow behavior and transport properties locally as well as globally within large microvascular networks.

Erythrocyte aggregation may promote uneven spatial distribution of NO/O2 in the downstream vessel of arteriolar bifurcations

This study examined the effect of red blood cell (RBC) aggregation on nitric oxide (NO) and oxygen (O2) distributions in the downstream vessels of arteriolar bifurcations. Particular attention was paid to the inherent formation of asymmetric cell-free layer (CFL) widths in the downstream vessels and its consequential impact on the NO/O2 bioavailability after the bifurcations. A microscopic image-based two-dimensional transient model was used to predict the NO/O2 distribution by utilizing the in vivo CFL width data obtained under non-, normal- and hyper-aggregating conditions at the pseudoshear rate of 15.6±2.0s(-1). In vivo experimental result showed that the asymmetry of CFL widths was enhanced by the elevation in RBC aggregation level. The model demonstrated that NO bioavailability was regulated by the dynamic fluctuation of the local CFL widths, which is corollary to its modulation of wall shear stress. Accordingly, the uneven distribution of NO/O2 was prominent at opposite sides of the arterioles up to six vessel-diameter (6D) away from the bifurcating point, and this was further enhanced by increasing the levels of RBC aggregation. Our findings suggested that RBC aggregation potentially augments both the formation of asymmetric CFL widths and its influence on the uneven distribution of NO/O2 in the downstream flow of an arteriolar bifurcation. The extended heterogeneity of NO/O2 downstream (2D-6D) also implied its potential propagation throughout the entire arteriolar microvasculature.

Temporal and spatial variations of wall shear stress in the entrance region of microvessels

Using a simplified two-dimensional divider-channel setup, we simulate the development process of red blood cell (RBC) flows in the entrance region of microvessels to study the wall shear stress (WSS) behaviors. Significant temporal and spatial variation in WSS is noticed. The maximum WSS magnitude and the strongest variation are observed at the channel inlet due to the close cell-wall contact. From the channel inlet, both the mean WSS and variation magnitude decrease, with a abrupt drop in the close vicinity near the inlet and then a slow relaxation over a relatively long distance; and a relative stable state with approximately constant mean and variation is established when the flow is well developed. The correlations between the WSS variation features and the cell free layer (CFL) structure are explored, and the effects of several hemodynamic parameters on the WSS variation are examined. In spite of the model limitations, the qualitative information revealed in this study could be useful for better understanding relevant processes and phenomena in the microcirculation.

Microvascular blood flow resistance: Role of red blood cell migration and dispersion

Microvascular blood flow resistance has a strong impact on cardiovascular function and tissue perfusion. The flow resistance in microcirculation is governed by flow behavior of blood through a complex network of vessels, where the distribution of red blood cells across vessel cross-sections may be significantly distorted at vessel bifurcations and junctions. In this paper, the development of blood flow and its resistance starting from a dispersed configuration of red blood cells is investigated in simulations for different hematocrit levels, flow rates, vessel diameters, and aggregation interactions between red blood cells. Initially dispersed red blood cells migrate toward the vessel center leading to the formation of a cell-free layer near the wall and to a decrease of the flow resistance. The development of cell-free layer appears to be nearly universal when scaled with a characteristic shear rate of the flow. The universality allows an estimation of the length of a vessel required for full flow development, lc ≲ 25D, for vessel diameters in the range 10 μm < D < 100 μm. Thus, the potential effect of red blood cell dispersion at vessel bifurcations and junctions on the flow resistance may be significant in vessels which are shorter or comparable to the length lc. Aggregation interactions between red blood cells generally lead to a reduction of blood flow resistance. The simulations are performed using the same viscosity for both external and internal fluids and the RBC membrane viscosity is not considered; however, we discuss how the viscosity contrast may affect the results. Finally, we develop a simple theoretical model which is able to describe the converged cell-free-layer thickness at steady-state flow with respect to flow rate. The model is based on the balance between a lift force on red blood cells due to cell-wall hydrodynamic interactions and shear-induced effective pressure due to cell-cell interactions in flow. We expect that these results can also be used to better understand the flow behavior of other suspensions of deformable particles such as vesicles, capsules, and cells.

Cell-free layer development process in the entrance region of microvessels

We simulated red blood cell flows through a finite length channel with a two-dimensional immersed boundary lattice Boltzmann model. The local instantaneous variation in wall-cell distance has been examined in details, and a nominal cell-free layer (CFL) thickness has been proposed. The CFL development process along the channel has been then analyzed, showing that the CFL thickness profile can be basically split into two regimes: the initial rapid increase due to cell migration and the later gradual growth due to cell reorganization. Effects of various hemorheological factors, such as rigidity, aggregation, hematocrit, and channel width, have also been investigated. The development length of the CFL to 90% of its final width ranges from 150 to 300 μm, and the development length is sensitive to changes in hemorheological conditions. The correlation between the CFL features and hemorheological parameters has also been explored. The simulation results have been compared to available experimental studies, and qualitative agreement has been noticed. In spite of the model limitations, this study reveals the complexity of CFL development process, and it could be useful for better understanding relevant processes and phenomena in the microcirculation.

Hemorheology in experimental research: is it necessary to consider blood fluidity differences in the laboratory rat?

This study was designed to identify whether blood fluidity differs between commercially available laboratory rat strains. The hemorheological profiles of seven clinically healthy wild-type rat strains were analyzed to determine whether any diversity in blood fluidity might affect the outcome of cardiovascular studies. Study 1: 65 healthy adult rats (Lewis, Long-Evans, Hairless, Wistar and Fisher; mixed gender and comparable ages) were compared. In order to determine the greatest possible difference, the two strains with the greatest hematocrit (HCT) differences were selected for more detailed evaluation. Red blood cell (RBC) deformability (maximum elongation index, shear stress for half-maximal deformation of RBC; both P < 0.0001), and the effect of plasma protein concentration upon plasma viscosity (P < 0.0001) were different between Lewis and Long-Evans strains. Whole blood viscosity - although different at native HCT (P < 0.004) - was unaltered following HCT standardization of samples. Differences in RBC aggregation were statistically significant but these were small and may not be clinically relevant. Study 2: these 65 animals were compared with 21 animals (10-16 weeks old; both sexes) from mutant strains (Dahl SS/JrHsdMcwiCrl, n = 10; ZDF-Lepr(fa)/Crl, n = 11). In both mutant strains, plasma and whole blood viscosity were increased compared with commonly used strains at native and standardized HCT (P < 0.001). Unusually high RBC aggregation values were seen in the ZDF rat strain (P < 0.001). It was concluded that the variability in blood fluidity among clinically healthy adult laboratory rat strains was both statistically and clinically significant. A hemorheological profile should be added to a routine phenotyping process, since both variables can significantly influence study outcomes.

Effect of erythrocyte aggregation on spatiotemporal variations in cell-free layer formation near on arteriolar bifurcation

OBJECTIVE

To investigate how red blood cell aggregation could modulate the spatial variations in cell-free layer formation in the vicinity of an arteriolar bifurcation.

METHODS

Visualization of blood flow was performed in upstream and downstream vessels of arteriolar bifurcations in the rat cremaster muscles under reduced flow conditions before and after induction of red blood cell aggregation to both physiological normal- and pathological hyperlevels seen in humans.

RESULTS

Large asymmetries of layer widths on opposite sides of the downstream vessel were attenuated along the vessel and this effect could be prominently enhanced by the hyperaggregation due to a higher formation rate of the layer which was greater on one side than the other of the vessel. The proportion of downstream layer formation constituted by the smaller downstream vessel generally increased with a thicker layer width at the wall of the upstream vessel adjacent it. A greater tendency of the layer formation in the smaller downstream vessel was found under the hyperaggregating condition than normal-aggregating and nonaggregating conditions.

CONCLUSION

Red blood cell aggregation could attenuate the asymmetry in cell-free layer formation on opposite sides of the downstream vessel, but enhances the heterogeneity of the layer formation between downstream vessels.

Effect of uneven red cell influx on formation of cell-free layer in small venules

This study examined how the uneven influx of red blood cells (RBCs) from feeding vessels influences formation of cell-free layer (CFL) in the downstream vessel of a venular bifurcation. Spatio-temporal variations of the CFL width along the downstream vessel (19-41-μm inner diameter, D) were determined at 0.5D intervals from 0.5D to 3.0D away from the bifurcation. Upstream flow conditions were quantified by the ratio of volume flow rates (Q*=Q(High)/Q(Low)) between high flow (Q(High)) and low flow feeding (Q(Low)) vessels. The RBC aggregation level in the rats was adjusted to be at healthy human levels by infusing Dextran 500. Our results suggested that the CFL formation process could be seen only from 2.0D away from the bifurcating point. The mean CFL width at the wall adjacent to the feeding vessel with a higher flow rate was consistently greater than that at the opposite wall, leading to an asymmetric CFL formation in the vessel. A positive relation (P<0.05) between the asymmetry of the CFL width and the volume flow rate ratio (Q*) was found. Our numerical prediction showed that flow resistance in the venular network could be significantly increased by the asymmetric formation of CFL downstream and this effect might become more pronounced under pathological flow conditions such as hyper-aggregating and/or low shear conditions.

New insights into the microvascular mechanisms of drag reducing polymers: effect on the cell-free layer

Drag-reducing polymers (DRPs) significantly increase blood flow, tissue perfusion, and tissue oxygenation in various animal models. In rectangular channel microfluidic systems, DRPs were found to significantly reduce the near-wall cell-free layer (CFL) as well as modify traffic of red blood cells (RBC) into microchannel branches. In the current study we further investigated the mechanism by which DRP enhances microvascular perfusion. We studied the effect of various concentrations of DRP on RBC distribution in more relevant round microchannels and the effect of DRP on CFL in the rat cremaster muscle in vivo. In round microchannels hematocrit was measured in parent and daughter branch at baseline and after addition of DRP. At DRP concentrations of 5 and 10 ppm, the plasma skimming effect in the daughter branch was eliminated, as parent and daughter branch hematocrit were equivalent, compared to a significantly lowered hematocrit in the daughter branch without DRPs. In anesthetized rats (N=11) CFL was measured in the cremaster muscle tissue in arterioles with a diameter of 32.6 ± 1.7 µm. In the control group (saline, N=6) there was a significant increase in CFL in time compared to corresponding baseline. Addition of DRP at 1 ppm (N=5) reduced CFL significantly compared to corresponding baseline and the control group. After DRP administration the CFL reduced to about 85% of baseline at 5, 15, 25 and 35 minutes after DRP infusion was complete. These in vivo and in vitro findings demonstrate that DRPs induce a reduction in CFL width and plasma skimming in the microvasculature. This may lead to an increase of RBC flux into the capillary bed, and thus explain previous observations of a DRP mediated enhancement of capillary perfusion.

Velocimetry of red blood cells in microvessels by the dual-slit method: effect of velocity gradients

The dual-slit is a photometric technique used for the measurement of red blood cell (RBC) velocity in microvessels. Two photometric windows (slits) are positioned along the vessel. Because the light is modulated by the RBCs flowing through the microvessel, a time dependent signal is captured for each window. A time delay between the two signals is obtained by temporal cross correlation, and is used to deduce a velocity, knowing the distance between the two slits. Despite its wide use in the field of microvascular research, the velocity actually measured by this technique has not yet been unambiguously related to a relevant velocity scale of the flow (e.g. mean or maximal velocity) or to the blood flow rate. This is due to a lack of fundamental understanding of the measurement and also because such a relationship is crucially dependent on the non-uniform velocity distribution of RBCs in the direction parallel to the light beam, which is generally unknown. The aim of the present work is to clarify the physical significance of the velocity measured by the dual-slit technique. For that purpose, dual-slit measurements were performed on computer-generated image sequences of RBCs flowing in microvessels, which allowed all the parameters related to this technique to be precisely controlled. A parametric study determined the range of optimal parameters for the implementation of the dual-slit technique. In this range, it was shown that, whatever the parameters governing the flow, the measured velocity was the maximal RBC velocity found in the direction parallel to the light beam. This finding was then verified by working with image sequences of flowing RBCs acquired in PDMS micro-systems in vitro. Besides confirming the results and physical understanding gained from the study with computer generated images, this in vitro study showed that the profile of RBC maximal velocity across the channel was blunter than a parabolic profile, and exhibited a non-zero sliding velocity at the channel walls. Overall, the present work demonstrates the robustness and high accuracy of the optimized dual-slit technique in various flow conditions, especially at high hematocrit, and discusses its potential for applications in vivo.