Two-dimensional lattice Boltzmann study of red blood cell motion through microvascular bifurcation: cell deformability and suspending viscosity effects

Partitioning of dense RBC suspensions in single microfluidic bifurcations: role of cell deformability and bifurcation angle

Red blood cells (RBCs) are a key determinant of human physiology and their behaviour becomes extremely heterogeneous as they navigate in narrow, bifurcating vessels in the microvasculature, affecting local haemodynamics. This is due to partitioning in bifurcations which is dependent on the biomechanical properties of RBCs, especially deformability. We examine the effect of deformability on the haematocrit distributions of dense RBC suspensions flowing in a single, asymmetric Y-shaped bifurcation, experimentally. Human RBC suspensions (healthy and artificially hardened) at 20% haematocrit (Ht) were perfused through the microchannels at different flow ratios between the outlet branches, and negligible inertia, and imaged to infer cell distributions. Notable differences in the shape of the haematocrit distributions were observed between healthy and hardened RBCs near the bifurcation apex. These lead to more asymmetric distributions for healthy RBCs in the daughter and outlet branches with cells accumulating near the inner channel walls, exhibiting distinct hematocrit peaks which are sharper for healthy RBCs. Although the hematocrit distributions differed locally, similar partitioning characteristics were observed for both suspensions. Comparisons with RBC distributions measured in a T-shaped bifurcation showed that the bifurcation angle affects the haematocrit characteristics of the healthy RBCs and not the hardened ones. The extent of RBC partitioning was found similar in both geometries and suspensions. The study highlights the differences between local and global characteristics which impact RBC distribution in more complex, multi-bifurcation networks.

Red blood cell lingering modulates hematocrit distribution in the microcirculation

The distribution of red blood cells (RBCs) in the microcirculation determines the oxygen delivery and solute transport to tissues. This process relies on the partitioning of RBCs at successive bifurcations throughout the microvascular network, and it has been known since the last century that RBCs partition disproportionately to the fractional blood flow rate, therefore leading to heterogeneity of the hematocrit (i.e., volume fraction of RBCs in blood) in microvessels. Usually, downstream of a microvascular bifurcation, the vessel branch with a higher fraction of blood flow receives an even higher fraction of RBC flux. However, both temporal and time-average deviations from this phase-separation law have been observed in recent studies. Here, we quantify how the microscopic behavior of RBC lingering (i.e., RBCs temporarily residing near the bifurcation apex with diminished velocity) influences their partitioning, through combined in vivo experiments and in silico simulations. We developed an approach to quantify the cell lingering at highly confined capillary-level bifurcations and demonstrate that it correlates with deviations of the phase-separation process from established empirical predictions by Pries et al. Furthermore, we shed light on how the bifurcation geometry and cell membrane rigidity can affect the lingering behavior of RBCs; e.g., rigid cells tend to linger less than softer ones. Taken together, RBC lingering is an important mechanism that should be considered when studying how abnormal RBC rigidity in diseases such as malaria and sickle-cell disease could hinder the microcirculatory blood flow or how the vascular networks are altered under pathological conditions (e.g., thrombosis, tumors, aneurysm).

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.

Investigating the Interaction Between Circulating Tumor Cells and Local Hydrodynamics via Experiment and Simulations

Introduction

The biological and mechanical properties of circulating tumor cells (CTCs) in combination with the hemodynamics affect the preference of metastatic sites in the vasculature. Despite the extensive literature on the effects of biological properties on cell adhesion, the effects of hydrodynamic forces on primary attachment remains an active area of research. Using simulations in conjunction with experimentation, we provide new insight into the interplay of CTCs dynamics and local hydrodynamics.

Methods

A flow experiment of CTC attachment was performed within a bioprinted, double branching endothelialized vessel. Simulations of fluid flow and CTC transport in the reconstructed and idealized bifurcated vessel were respectively performed by HARVEY, our in-house massively parallel computational fluid dynamics solver. HARVEY is based on the lattice Boltzmann and finite element methods to model the fluid and cells dynamics. The immersed boundary method is employed for resolving the fluid-structure interaction.

Results

CTC attachment was quantified experimentally at all regions of the complex vessel. The results demonstrate a clear preference for CTCs to attach at the branch points. To elucidate the effect of the vessel topology on the location of attachment, a fluid-only simulation was performed assessing the differences in the hydrodynamics along the vessel. CTC transport in idealized bifurcated vessels was subsequently studied to examine the effects of cell deformability on the local hydrodynamics patterns and, thus, the preference of attachment sites.

Conclusions

The current work provides evidence on the correlation of the hydrodynamics forces arising from the vessel topology and CTC properties on the attachment regions.

A 3D computational model of perfusion seeding for investigating cell transport and adhesion within a porous scaffold

The process of cell seeding within a porous scaffold is an essential first step in the development of tissue-engineered bone grafts. Understanding the underlying mechanisms of cell distribution and adhesion is fundamental for the design and optimization of the seeding process. To that end, we present a numerical model to investigate the perfusion cell seeding process that incorporates cell mechanics, cell-fluid interaction, and cell-scaffold adhesion. The individual cells are modeled as deformable spherical capsules capable of adhering to the scaffold surface as well as to other cells with probabilistic bond formation and rupture. The mechanical deformation of the cell is calibrated with the stretching of mice mesenchymal stem cells induced by optical tweezers, while the predicted adhesive forces are consistent with the experimental data reported in the literature. A sub-domain is numerically reconstructed as the region of interest (ROI) which is representative of an actual scaffold. Through the simulations, the perfusion seeding kinetics within the ROI involving detailed transport and adhesion of cells over time is analyzed. The effects of the perfusion pressure and initial cell concentration on the seeding kinetics are studied in terms of adhesion rates, cell cluster formation, seeding uniformity, and efficiency, as well as scaffold permeability. The results highlight the importance of cell-fluid interaction and adhesion dynamics in modeling the dynamic seeding process. This bottom-up model provides a way to bridge detailed behaviors of individual cells to the seeding outcomes at the macroscopic scale, allowing for finding the best configuration to enhance cell seeding.

Dissipative particle dynamics for modeling micro-objects in microfluidics: application to dielectrophoresis

The dissipative particle dynamics (DPD) technique is employed to model the trajectories of micro-objects in a practical microfluidic device. The simulation approach is first developed using an in-house Fortran code to model Stokes flow at Reynolds number of 0.01. The extremely low Reynolds number is achieved by adjusting the DPD parameters, such as force coefficients, thermal energies of the particles, and time steps. After matching the numerical flow profile with the analytical results, the technique is developed further to simulate the deflection of micro-objects under the effect of a deflecting external force in a rectangular microchannel. A mapping algorithm is introduced to establish the scaling relationship for the deflecting force between the physical device and the DPD domain. Dielectrophoresis is studied as a case study for the deflecting force, and the trajectory of a single red blood cell under the influence of the dielectrophoretic force is simulated. The device is fabricated using standard microfabrication techniques, and the experiments involving a dilute sample of red blood cells are performed at two different cases of the actuation voltage. Good agreement between the numerical and experimental results is achieved.

Cell trapping in Y-junction microchannels: A numerical study of the bifurcation angle effect in inertial microfluidics

The majority of microfluidic technologies for cell sorting and isolation involve bifurcating (e.g., Y- or T-shaped junction) microchannels to trap the cells of a specific type. However, the microfluidic trapping efficiency remains low, independently of whether the cells are separated by a passive or an active sorting method. Using a custom computational algorithm, we studied the migration of separated deformable cells in a Y-junction microchannel, with a bifurcation angle ranging from 30° to 180°. Single or two cells of initially spherical shape were considered under flow conditions corresponding to inertial microfluidics. Through the numerical simulation, we identified the effects of cell size, cytoplasmic viscoelasticity, cortical tension, flow rate, and bifurcation angle on the critical separation distance for cell trapping. The results of this study show that the trapping and isolation of blood cells, and circulating tumor cells in a Y-junction microchannel was most efficient and least dependent on the flow rate at the bifurcation angle of 120°. At this angle, the trapping efficiency for white blood cells and circulating tumor cells increased, respectively, by 46% and 43%, in comparison with the trapping efficiency at 60°. The efficiency to isolate invasive tumor cells from noninvasive ones increased by 32%. This numerical study provides important design criteria to optimize microfluidic technology for deformability-based cell sorting and isolation.

Red blood cell distribution in a microvascular network with successive bifurcations

Nonproportional RBC distribution is an important characteristic in microvascular networks, which can result in heterogeneity of oxygen supply that may cause ischemic death in severe cases. In this paper, we perform three-dimensional numerical simulations of a large number of RBCs in a microvascular network, by using a hybrid method of smoothed dissipative particle dynamic and immersed boundary method. The distribution of multiple RBCs in a T-bifurcation is first simulated as a validation study, and a reasonable agreement is observed both qualitatively and quantitatively on the RBC flux between our results and the previously published numerical and empirical results. Next, the distribution of a large number of RBCs in a microvascular network is investigated, including the effects of cell deformability, aggregation and tube hematocrit. The simulation results indicate that decreased deformability and increased aggregation strength have a similar effect on the RBC distribution: the large RBC flux becomes larger, but the small becomes smaller. A high hematocrit also causes a similar phenomenon that the RBCs are more apt to flow into a high RBC-flux branch, because they are arranged compactly into a rouleaux and difficultly broken up at a high hematocrit. These results imply that lower cell deformability, stronger aggregation or higher tube hematocrit would be conducive to the phase separation of hematocrit and plasma skimming processes in microcirculation.

Numerical Simulations of the Motion and Deformation of Three RBCs during Poiseuille Flow through a Constricted Vessel Using IB-LBM

The immersed boundary-lattice Boltzmann method (IB-LBM) was used to examine the motion and deformation of three elastic red blood cells (RBCs) during Poiseuille flow through constricted microchannels. The objective was to determine the effects of the degree of constriction and the Reynolds (Re) number of the flow on the physical characteristics of the RBCs. It was found that, with decreasing constriction ratio, the RBCs experienced greater forced deformation as they squeezed through the constriction area compared to at other parts of the microchannel. It was also observed that a longer time was required for the RBCs to squeeze through a narrower constriction. The RBCs subsequently regained a stable shape and gradually migrated toward the centerline of the flow beyond the constriction area. However, a sick RBC was observed to be incapable of passing through a constricted vessel with a constriction ratio ≤1/3 for Re numbers below 0.40.

Computational fluid dynamics in the microcirculation and microfluidics: what role can the lattice Boltzmann method play?

Patient-specific simulations, efficient parametric analyses, and the study of complex processes that are otherwise experimentally intractable are facilitated through the use of Computational Fluid Dynamics (CFD) to study biological flows. This review discusses various CFD methodologies that have been applied across different biological scales, from cell to organ level. Through this discussion the lattice Boltzmann method (LBM) is highlighted as an emerging technique capable of efficiently simulating fluid problems across the midrange of scales; providing a practical analytical tool compared to methods more attuned to the extremities of scale. Furthermore, the merits of the LBM are highlighted through examples of previous applications and suggestions for future research are made. The review focusses on applications in the midrange bracket, such as cell-cell interactions, the microcirculation, and microfluidic devices; wherein the inherent mesoscale nature of the LBM renders it well suited to the incorporation of fluid-structure interaction effects, molecular/particle interactions and interfacial dynamics. The review demonstrates that the LBM has the potential to become a valuable tool across a range of emerging areas in bio-CFD, such as understanding and predicting disease, designing lab-on-a-chip devices, and elucidating complex biological processes.

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.

A micro-scale simulation of red blood cell passage through symmetric and asymmetric bifurcated vessels

Blood exhibits a heterogeneous nature of hematocrit, velocity, and effective viscosity in microcapillaries. Microvascular bifurcations have a significant influence on the distribution of the blood cells and blood flow behavior. This paper presents a simulation study performed on the two-dimensional motions and deformation of multiple red blood cells in microvessels with diverging and converging bifurcations. Fluid dynamics and membrane mechanics were incorporated. Effects of cell shape, hematocrit, and deformability of the cell membrane on rheological behavior of the red blood cells and the hemodynamics have been investigated. It was shown that the blood entering the daughter branch with a higher flow rate tended to receive disproportionally more cells. The results also demonstrate that red blood cells in microvessels experienced lateral migration in the parent channel and blunted velocity profiles in both straight section and daughter branches, and this effect was influenced by the shape and the initial position of the cells, the hematocrit, and the membrane deformability. In addition, a cell free region around the tip of the confluence was observed. The simulation results are qualitatively consistent with existing experimental findings. This study may provide fundamental knowledge for a better understanding of hemodynamic behavior of micro-scale blood flow.

Inversion of hematocrit partition at microfluidic bifurcations

Partitioning of red blood cells (RBCs) at the level of bifurcations in the microcirculatory system affects many physiological functions yet it remains poorly understood. We address this problem by using T-shaped microfluidic bifurcations as a model. Our computer simulations and in vitro experiments reveal that the hematocrit (ϕ0) partition depends strongly on RBC deformability, as long as ϕ0<20% (within the normal range in microcirculation), and can even lead to complete deprivation of RBCs in a child branch. Furthermore, we discover a deviation from the Zweifach-Fung effect which states that the child branch with lower flow rate recruits less RBCs than the higher flow rate child branch. At small enough ϕ0, we get the inverse scenario, and the hematocrit in the lower flow rate child branch is even higher than in the parent vessel. We explain this result by an intricate up-stream RBC organization and we highlight the extreme dependence of RBC transport on geometrical and cell mechanical properties. These parameters can lead to unexpected behaviors with consequences on the microcirculatory function and oxygen delivery in healthy and pathological conditions.

Microfluidic analysis of pressure drop and flow behavior in hypertensive micro vessels

The retinal arterial network is the only source of the highly nutrient-consumptive retina, thus any insult on the arteries can impair the retinal oxygen and nutrient supply and affect its normal function. The aim of this work is to study the influences of vascular structure variation on the flow and pressure characteristics via microfluidic devices. Two sets of micro-channel were designed to mimic the stenosed microvessels and dichotomous branching structure in the retinal arteries. Three working fluids including red blood cell (RBC) suspension were employed to investigate the pressure drop in the stenosed channel. The flow behaviors of RBC suspensions inside the micro channels were observed using high speed camera system. Pressure drop of different working fluids and RBC velocity profiles in the stenosed channel were obtained. Moreover, hematocrit levels of RBC suspensions inside the bifurcated channels were analyzed from the sequential images of RBC flow. The results of the flow in the stenosed channel show that RBCs drift from the center of the channels, and RBC velocity is influenced not only by the inlet flow rate but also the interaction between RBCs. The measured pressure drops in the stenosed channel increase notably with the increase of fluid viscosity. Furthermore, the dimensionless pressure drop due to the stenosis decreases with Reynolds number. On the other hand, the results of flow through the bifurcated channels show that as the ratio of the daughter-branch width to the mother-channel width increases, the ratio of hematocrit in two connected branches (Ht/Hd) decreases, which is in favorable agreement with the available analysis results.

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.

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.

Numerical simulation of red blood cell distributions in three-dimensional microvascular bifurcations

We constructed three-dimensional microvascular bifurcation models using a parent vessel of diameter 10μm and investigated the flow behavior of the red blood cells (RBCs) through bifurcations. We considered symmetric and asymmetric model types. Two cases of equal daughter vessel diameter were employed for the asymmetric models, where the first was 10μm, which is the same as the parent vessel and the second was 7.94μm, which satisfies Murray's law. Simulated blood flow was computed using the lattice Boltzmann method in conjunction with the immersed boundary method for incorporating fluid-membrane interactions between the flow field and deformable RBCs. First, we investigated the flow behavior of a single RBC through microvascular bifurcations. In the case of the symmetric bifurcation, the turning point of the fractional plasma flow wherein the RBC flow changed from one daughter vessel to the other was 0.50. This turning point was however different for asymmetric bifurcations. Additionally, we varied the initial offset of RBCs from the centerline of the parent vessel. The simulation results indicated that the RBCs preferentially flow through the branch of a larger flow ratio. Next, we investigated the distribution characteristics of multiple RBCs. Simulations indicated that the results of the symmetric model were similar to those predicted by a previously published empirical model. On the other hand, results of asymmetric models deviated from those of the symmetric and empirical models. These results suggest that the distribution of RBCs varies according to the bifurcation angle and daughter vessel diameter in a microvascular bifurcation of the size considered.

The influence of size, shape and vessel geometry on nanoparticle distribution

Nanoparticles (NPs) are emerging as promising carrier platforms for targeted drug delivery and imaging probes. To evaluate the delivery efficiency, it is important to predict the distribution of NPs within blood vessels. NP size, shape and vessel geometry are believed to influence its biodistribution in circulation. Whereas, the effect of size on nanoparticle distribution has been extensively studied, little is known about the shape and vessel geometry effect. This paper describes a computational model for NP transport and distribution in a mimetic branched blood vessel using combined NP Brownian dynamics and continuum fluid mechanics approaches. The simulation results indicate that NPs with smaller size and rod shape have higher binding capabilities as a result of smaller drag force and larger contact area. The binding dynamics of rod-shaped NPs is found to be dependent on their initial contact points and orientations to the wall. Higher concentration of NPs is observed in the bifurcation area compared to the straight section of the branched vessel. Moreover, it is found that Péclet number plays an important role in determining the fraction of NPs deposited in the branched region and the straight section. Simulation results also indicate that NP binding decreases with increased shear rate. Dynamic NP re-distribution from low to high shear rates is observed due to the non-uniform shear stress distribution over the branched channel. This study would provide valuable information for NP distribution in a complex vascular network.

Blood-plasma separation in Y-shaped bifurcating microfluidic channels: a dissipative particle dynamics simulation study

The motion of a suspension of red blood cells (RBCs) flowing in a Y-shaped bifurcating microfluidic channel is investigated using a validated low-dimensional RBC model based on dissipative particle dynamics. Specifically, the RBC is represented as a closed torus-like ring of ten colloidal particles, which leads to efficient simulations of blood flow in microcirculation over a wide range of hematocrits. Adaptive no-slip wall boundary conditions were implemented to model hydrodynamic flow within a specific wall structure of diverging three-dimensional microfluidic channels, paying attention to controlling density fluctuations. Plasma skimming and the all-or-nothing phenomenon of RBCs in a bifurcating microfluidic channel have been investigated in our simulations for healthy and diseased blood, including the size of a cell-free layer on the daughter branches. The feed hematocrit level in the parent channel has considerable influence on blood-plasma separation. Compared to the blood-plasma separation efficiencies of healthy RBCs, malaria-infected stiff RBCs (iRBCs) have a tendency to travel into the low flow-rate daughter branch because of their different initial distribution in the parent channel. Our simulation results are consistent with previously published experimental results and theoretical predictions.