Multiple red blood cell flows through microvascular bifurcations: Cell free layer, cell trajectory, and hematocrit separation

Cell-free layer development and spatial organization of healthy and rigid red blood cells in a microfluidic bifurcation

Bifurcations and branches in the microcirculation dramatically affect blood flow as they determine the spatiotemporal organization of red blood cells (RBCs). Such changes in vessel geometries can further influence the formation of a cell-free layer (CFL) close to the vessel walls. Biophysical cell properties, such as their deformability, which is impaired in various diseases, are often thought to impact blood flow and affect the distribution of flowing RBCs. This study investigates the flow behavior of healthy and artificially hardened RBCs in a bifurcating microfluidic T-junction. We determine the RBC distribution across the channel width at multiple positions before and after the bifurcation. Thus, we reveal distinct focusing profiles in the feeding mother channel for rigid and healthy RBCs that dramatically impact the cell organization in the successive daughter channels. Moreover, we experimentally show how the characteristic asymmetric CFLs in the daughter vessels develop along their flow direction. Complimentary numerical simulations indicate that the buildup of the CFL is faster for healthy than for rigid RBCs. Our results provide fundamental knowledge to understand the partitioning of rigid RBC as a model of cells with pathologically impaired deformability in complex in vitro 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).

A mechanistic model of cross-bridge migration in RBC aggregation and disaggregation

Red blood cells (RBCs) clump together under low flow conditions in a process called RBC aggregation, which can alter RBC perfusion in a microvascular network. As elevated RBC aggregation is commonly associated with cardiovascular and inflammatory diseases, a better understanding of aggregation is essential. Unlike RBC aggregation in polymer solutions which can be well explained by polymer depletion theory, plasma-mediated RBC aggregation has features that best match explanations with cross-bridging mechanisms. Previous studies have demonstrated the dominant role of fibrinogen (Fg) in promoting aggregate formation and recent cell-force spectroscopy (CFS) experiments on interacting RBC doublets in plasma have reported an inverse relationship between disaggregation force and the adhesive contact area between RBCs. This has led investigators to revisit the hypothesis of inter-RBC cross-bridging which involves cross-bridge migration under interfacial tension during the forced disaggregation of RBC aggregates. In this study, we developed the cross-bridge migration model (CBMM) in plasma that mechanistically represents the migrating cross-bridge hypothesis. Transport of mobile Fg cross-bridges (mFg) was calculated using a convection-diffusion transport equation with our novel introduction of convective cross-bridge drift that arises due to intercellular friction. By parametrically transforming the diffusivity of mFg in the CBMM, we were able to match experimental observations of both RBC doublet formation kinematics and RBC doublet disaggregation forces under optical tweezers tension. We found that non-specific cross-bridging promotes spontaneous growth of adhesion area between RBC doublets whereas specific cross-bridging tends to prevent adhesion area growth. Our CBMM was also able to correlate Fg concentration shifts from healthy population blood plasma to SLE (lupus) condition blood plasma with the observed increase in doublet disaggregation forces for the RBC doublets in SLE plasma.

Haemodynamic analysis using multiphase flow dynamics in tubular lesions

BACKGROUND AND OBJECTIVE

The role of red blood cell dynamics is emphasised in certain cardiovascular diseases, and thus needs to be closely studied. A multiphase model of blood flow allows the resolution of locally varying density of red blood cells within a complex vessel geometrical domain, and haemodynamic consequences of such build up.

METHODS

A novel computational fluid dynamics solver for simulating multiphase flows is used for modelling blood flow using level set for a sharp interface representation. Single-phase simulations and reduced order models are used for pressure comparisons. The new solver is used for numerically studying AHA type B lesions. The impact of hematocrit and degree of stenosis on the haemodynamics of coronary arteries is investigated.

RESULTS

The comparisons with single-phase flow simulations indicate differences in pressure when considering red blood cell aggregation. Multiphase simulations provide slightly lower pressure drop for the same stenosis severity compared to the single-phase simulations. Secondary flow patterns and the interactions between the two phases leads to the red blood cell aggregation at the end of the diastole cycle, which significantly changes the red blood cell distribution, the shear stresses and velocity in tubular lesions.

CONCLUSIONS

Neither pressure drop nor mean velocity are not strongly changed in the multiphase modelling, but particle buildup significantly changes which is only revealed by the multiphase approach.

A computational study of red blood cell deformability effect on hemodynamic alteration in capillary vessel networks

Capillary blood vessels, the smallest vessels in the body, form an intricate network with constantly bifurcating, merging and winding vessels. Red blood cells (RBCs) must navigate through such complex microvascular networks in order to maintain tissue perfusion and oxygenation. Normal, healthy RBCs are extremely deformable and able to easily flow through narrow vessels. However, RBC deformability is reduced in many pathological conditions and during blood storage. The influence of reduced cell deformability on microvascular hemodynamics is not well established. Here we use a high-fidelity, 3D computational model of blood flow that retains exact geometric details of physiologically realistic microvascular networks, and deformation of every one of nearly a thousand RBCs flowing through the networks. We predict that reduced RBC deformability alters RBC trafficking with significant and heterogeneous changes in hematocrit. We quantify such changes along with RBC partitioning and lingering at vascular bifurcations, perfusion and vascular resistance, and wall shear stress. We elucidate the cellular-scale mechanisms that cause such changes. We show that such changes arise primarily due to the altered RBC dynamics at vascular bifurcations, as well as cross-stream migration. Less deformable cells tend to linger less at majority of bifurcations increasing the fraction of RBCs entering the higher flow branches. Changes in vascular resistance also seen to be heterogeneous and correlate with hematocrit changes. Furthermore, alteration in RBC dynamics is shown to cause localized changes in wall shear stress within vessels and near vascular bifurcations. Such heterogeneous and focal changes in hemodynamics may be the cause of morphological abnormalities in capillary vessel networks as observed in several diseases.

Red blood cells under flow show maximal ATP release for specific hematocrit

ATP release by red blood cells (RBCs) under shear stress (SS) plays a pivotal role in endothelial biochemical signaling cascades. The aim of this study is to investigate through numerical simulation how RBC spatiotemporal organization depends on flow and geometrical conditions to generate ATP patterns. Numerical simulations were conducted in a straight channel by considering both plasma and explicit presence of RBCs, their shape deformation and cell-cell interaction, and ATP release by RBCs. Two ATP release pathways through cell membrane are taken into account: pannexin 1 channel, sensitive to SS, and cystic fibrosis transmembrane conductance regulator, which responds to cell deformation. Several flow and hematocrit conditions are explored. The problem is solved by the lattice Boltzmann method. Application of SS to the RBC suspension triggers a nontrivial spatial RBC organization and ATP patterns. ATP localizes preferentially in the vicinity of the cell-free layer close to channel wall. Conditions for maximal ATP release per cell are identified, which depend on vessel size and hematocrit Ht. Increasing further Ht beyond optimum enhances the total ATP release but should degrade oxygen transport capacity, a compromise between an efficient ATP release and minimal blood dissipation. Moreover, ATP is boosted in capillaries, suggesting a vasomotor activity coordination throughout the resistance network.

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.

Similar but Distinct Roles of Membrane and Interior Fluid Viscosities in Capsule Dynamics in Shear Flows

PURPOSE

The dynamics of biological capsules and red blood cells in shear flows has been studied extensively with experimental, analytical, and numerical methods. In particular, the effects of various parameters, including the shear rate or shear stress, membrane elasticity, capsule shape, and interior fluid viscosity, have been investigated carefully. The role of the membrane viscosity for capsule deformation dynamics has not been examined adequately. In previous studies, the so-called energy dissipation ratio has been used to account for the membrane viscosity effect by increasing the interior viscosity; however, the applicability and accuracy of this treatment have not been evaluated carefully.

METHODS

In this study, using the recently developed finite-difference scheme for immersed boundary simulations of viscoelastic membranes, we conduct comprehensive numerical simulations of the deformation processes of an originally spherical capsule in shear flows with various combinations of membrane and interior fluid viscosities.

RESULTS

Our results show that the membrane and interior fluid viscosity have similar however different effects on the capsule deformation dynamics. While the capsule deformation decreases with both membrane and interior fluid viscosities, a typical decrease-then-increase variation is observed for the inclination angle as the membrane viscosity increases, instead of the monotonic decrease in the inclination angle with the interior fluid viscosity increase. Also, although both large membrane and interior fluid viscosity values can introduce oscillations in the capsule deformation and inclination, larger aptitudes and slow decay processes are noticed at larger membrane viscosities. The variations of other dynamic parameters of the capsule, including the circumference, average membrane velocity, and rotation frequency, are also analyzed, and an intuitive mechanism is proposed to relate the membrane velocity and rotation frequency to the capsule deformation and inclination angle. The simple mechanism is then applied to explain the spoon-like variation patterns for membrane velocity and rotation frequency observed in our results. Furthermore, we examine the validity of the energy dissipation ratio approach based on the mathematical functional dependence.

CONCLUSIONS

Our results and analysis show that the dissipation ratio is a system and process dependent variable and it cannot be treated as a constant even for the same capsule. This research is valuable for a better understanding of the complex capsule dynamics in flows and also suggests that the membrane viscosity needs to be considered explicitly for accurate and reliable results in future studies.

Vibration motor-integrated low-cost, miniaturized system for rapid quantification of red blood cell aggregation

Human red blood cells (RBCs) aggregate under low shear conditions, which significantly modulates flow resistance and tissue perfusion. A higher aggregation tendency in blood thus serves as an important clinical indicator for the screening of cardiovascular disorders. Conventional ways of measuring RBC aggregation still require large sample volumes, cumbersome manual procedures, and expensive benchtop systems. These inconvenient and high-cost measurement methods hamper their clinical applicability. Here, we propose a low-cost, miniaturized system to overcome the limitations of these methods. Our system utilizes a coin vibration motor (CVM) to generate a localized vortex for disaggregating RBCs in a disposable fluidic chip. The design of the chip was optimized with fluid dynamics simulations to ensure sufficient shear flow in the localized vortex for RBC disaggregation. The time-dependent increase in light transmittance from an LED light source through the plasma gap while the RBCs re-aggregate is captured with a CMOS camera under stasis conditions to quantify the level of RBC aggregation. Our CVM-based aggregometer was validated against a commercial benchtop system for human blood samples under physiological and pathological conditions, and showed an excellent performance with a high intraclass correlation coefficient of 0.995. In addition, we were able to achieve a rapid measurement (<4 min) with the CVM-based aggregometer, requiring only a 6 μl blood sample. These illustrate the potential of our CVM-based aggregometer for low-cost point-of-care diagnostics without compromising the measurement sensitivity.

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.

Simulation of blood flow in a sudden expansion channel and a coronary artery

In this paper, we numerically simulate the flow of blood in two benchmark problems: the flow in a sudden expansion channel and the flow through an idealized curved coronary artery with pulsatile inlet velocity. Blood is modeled as a suspension (a non-linear complex fluid) and the movement of the red blood cell (RBCs) is modeled by using a concentration flux equation. The viscosity of blood is obtained from experimental data. In the sudden expansion flow, the predicted velocity profiles for two different Reynolds numbers (based on the inlet velocity) agree well with the available experiments; furthermore, the numerical results also show that after the sudden expansion there exists a RBCs depletion region. For the second problem, the idealized curved coronary artery, it is found that the RBCs move towards and concentrate near the inner surface where the viscosity is higher and the shear stress lower; this phenomenon may be related to the atherosclerotic plaque formation which usually occurs on the inside surface of the arteries.

Streaming potential in bio-mimetic microvessels mediated by capillary glycocalyx

Implantable medical devices and biosensors are pivotal in revolutionizing the field of medical technology by opening new dimensions in the field of disease detection and cure. These devices need to harness a biocompatible and physiologically sustainable safe power source instead of relying on external stimuli, overcoming the constraints on their applicability in-vivo. Here, by appealing to the interplay of electromechanics and hydrodynamics in physiologically relevant microvessels, we bring out the role of charged endothelial glycocalyx layer (EGL) towards establishing a streaming potential across physiological fluidic conduits. We account for the complex rheology of blood-mimicking fluid by appealing to Newtonian fluid model representing the blood plasma and a viscoelastic fluid model representing the whole blood. We model the EGL as a poroelastic layer with volumetric charge distribution. Our results reveal that for physiologically relevant micro-flows, the streaming potential induced is typically of the order of 0.1 V/mm, which may turn out to be substantial towards energizing biosensors and implantable medical devices whose power requirements are typically in the range of micro to milliwatts. We also bring out the specific implications of the relevant physiological parameters towards establishment of the streaming potential, with a vision of augmenting the same within plausible functional limits. We further unveil that the dependence of streaming potential on EGL thickness might be one of the key aspects in unlocking the mystery behind the angiogenesis pattern. Our results may open up novel bio-sensing and actuating possibilities in medical diagnostics as well as may provide a possible alternative regarding the development of physiologically safe and biocompatible power sources within the human body.

Two-dimensional Simulation of Motion of Red Blood Cells with Deterministic Lateral Displacement Devices

Deterministic lateral displacement (DLD) technology has great potential for the separation, enrichment, and sorting of red blood cells (RBCs). This paper presents a numerical simulation of the motion of RBCs using DLD devices with different pillar shapes and gap configurations. We studied the effect of the pillar shape, row shift, and pillar diameter on the performance of RBC separation. The numerical results show that the RBCs enter "displacement mode" under conditions of low row-shift (∆λ < 1.4 µm) and "zigzag mode" with large row shift (∆λ > 1.5 µm). RBCs can pass the pillar array when the size of the pillar (d > 6 µm) is larger than the cell size. We show that these conclusions can be helpful for the design of a reliable DLD microfluidic device for the separation of RBCs.

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.

A finite difference method with subsampling for immersed boundary simulations of the capsule dynamics with viscoelastic membranes

The membrane or interfacial viscosity is an important property in many multiphase and biofluidic situations, such as the red blood cell dynamics and emulsion stability. The immersed boundary method (IBM), which incorporates the dynamic flow-membrane interaction via force distribution and velocity interpolation, has been extensively employed in simulations of such systems. Unfortunately, direct implementation of membrane viscosity in IBM suffers severe numerical instability, which causes an IBM calculation to break down before generating any useful results. Few attempts have been recently reported; however, several concerns exist in these attempts, such as the inconsistency to the classical definition of membrane viscosity, the inability to model the shear and dilatational viscosities separately, the unjustified mathematical formulations, and the complicated algorithms and computation. To overcome these concerns, in this paper, we propose a finite difference approach for implementing membrane viscosity in immersed boundary simulations. The viscous stress is obtained via finite difference approximations to the differential strain-stress relationship, with the help of a subsampling scheme to reduce the numerical noise in the calculated strain rates. This simple method has also avoided the complicated matrix calculations in previous attempts, and hence, a better computational efficiency is expected. Detailed mathematical description of the method and key steps for its implementation in immersed boundary programs are provided. Validation and illustration calculations are performed, and our results are compared with analytical solutions and previous publications with satisfactory agreement. The influences of membrane mesh resolution and simulation time step are also examined; and the results show no indication that our finite difference method has downgraded the general IBM accuracy. Based on these simulations and analysis, we believe that our method would be a better choice for future IBM simulations of capsule dynamics with viscoelastic membranes.

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.

Emergent behaviors in RBCs flows in micro-channels using digital particle image velocimetry

The key points in the design of microfluidic Lab-On-a-Chips for blood tests are the simplicity of the microfluidic chip geometry, the portability of the monitoring system and the ease on-chip integration of the data analysis procedure. The majority of those, recently designed, have been used for blood separation, however their introduction, also, for pathological conditions diagnosis would be important in different biomedical contexts. To overcome this lack is necessary to establish the relation between the RBCs flow and blood viscosity changes in micro-vessels. For that, the development of methods to analyze the dynamics of the RBCs flows in networks of micro-channels becomes essential in the study of RBCs flows in micro-vascular networks. A simplification in the experimental set-up and in the approach for the data collection and analysis could contribute significantly to understand the relation between the blood non-Newtonian properties and the emergent behaviors in collective RBCs flows. In this paper, we have investigated the collective behaviors of RBCs in a micro-channel in unsteady conditions, using a simplified monitoring set-up and implementing a 2D image processing procedure based on the digital particle image velocimetry. Our experimental study consisted in the analysis of RBCs motions freely in the micro-channel and driven by an external pressure. Despite the equipment minimal complexity, the advanced signal processing method implemented has allowed a significant qualitative and quantitative classification of the RBCs behaviors and the dynamical characterization of the particles velocities along both the horizontal and vertical directions. The concurrent causes for the particles displacement as the base solution-particles interaction, particle-particle interaction, and the external force due to pressure gradient were accounted in the results interpretation. The method implemented and the results obtained represent a proof of concept toward the realization of a general-purpose microfluidic LOC device for in-vitro flow analysis of RBCs collective behaviors.

Advances in microfluidics in combating infectious diseases

One of the important pursuits in science and engineering research today is to develop low-cost and user-friendly technologies to improve the health of people. Over the past decade, research efforts in microfluidics have been made to develop methods that can facilitate low-cost diagnosis of infectious diseases, especially in resource-poor settings. Here, we provide an overview of the recent advances in microfluidic devices for point-of-care (POC) diagnostics for infectious diseases and emphasis is placed on malaria, sepsis and AIDS/HIV. Other infectious diseases such as SARS, tuberculosis, and dengue are also briefly discussed. These infectious diseases are chosen as they contribute the most to disability-adjusted life-years (DALYs) lost according to the World Health Organization (WHO). The current state of research in this area is evaluated and projection toward future applications and accompanying challenges are also discussed.

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.

Design of microfluidic channels for magnetic separation of malaria-infected red blood cells

This study is motivated by the development of a blood cell filtration device for removal of malaria-infected, parasitized red blood cells (pRBCs). The blood was modeled as a multi-component fluid using the computational fluid dynamics discrete element method (CFD-DEM), wherein plasma was treated as a Newtonian fluid and the red blood cells (RBCs) were modeled as soft-sphere solid particles which move under the influence of drag, collisions with other RBCs, and a magnetic force. The CFD-DEM model was first validated by a comparison with experimental data from Han et al. 2006 (Han and Frazier 2006) involving a microfluidic magnetophoretic separator for paramagnetic deoxygenated blood cells. The computational model was then applied to a parametric study of a parallel-plate separator having hematocrit of 40% with a 10% of the RBCs as pRBCs. Specifically, we investigated the hypothesis of introducing an upstream constriction to the channel to divert the magnetic cells within the near-wall layer where the magnetic force is greatest. Simulations compared the efficacy of various geometries upon the stratification efficiency of the pRBCs. For a channel with nominal height of 100 µm, the addition of an upstream constriction of 80% improved the proportion of pRBCs retained adjacent to the magnetic wall (separation efficiency) by almost 2 fold, from 26% to 49%. Further addition of a downstream diffuser reduced remixing, hence improved separation efficiency to 72%. The constriction introduced a greater pressure drop (from 17 to 495 Pa), which should be considered when scaling-up this design for a clinical-sized system. Overall, the advantages of this design include its ability to accommodate physiological hematocrit and high throughput - which is critical for clinical implementation as a blood-filtration system.

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.

Hematocrit distribution and tissue oxygenation in large microcirculatory networks

OBJECTIVE

Oxygen tension in the brain is controlled by the microcirculatory supply of RBC, but the effect of non-Newtonian blood flow rheology on tissue oxygenation is not well characterized. This study assesses different biphasic blood flow models for predicting tissue oxygen tension as a function of microcirculatory hemodynamics.

METHODS

Two existing plasma-skimming laws are compared against measured RBC distributions in rat and hamster microcirculatory networks. A novel biphasic blood flow model is introduced. The computational models predict tissue oxygenation in the mesentery, cremaster muscle, and the human secondary cortex.

RESULTS

This investigation shows deficiencies in prior models, including inconsistent plasma-skimming trends and insufficient oxygen perfusion due to the high prevalence (33%) of RBC-free microvessels. Our novel method yields physiologically sound RBC distributions and tissue oxygen tensions within one standard deviation of experimental measurements.

CONCLUSIONS

A simple, novel biphasic blood flow model is introduced with equal or better predictive power when applied to historic raw data sets. It can overcome limitations of prior models pertaining to trifurcations, anastomoses, and loops. This new plasma-skimming law eases the computations of bulk blood flow and hematocrit fields in large microcirculatory networks and converges faster than prior procedures.

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.

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.

Two-dimensional strain-hardening membrane model for large deformation behavior of multiple red blood cells in high shear conditions

Background

Computational modeling of Red Blood Cell (RBC) flow contributes to the fundamental understanding of microhemodynamics and microcirculation. In order to construct theoretical RBC models, experimental studies on single RBC mechanics have presented a material description for RBC membranes based on their membrane shear, bending and area moduli. These properties have been directly employed in 3D continuum models of RBCs but practical flow analysis with 3D models have been limited by their computationally expensive nature. As such, various researchers have employed 2D models to efficiently and qualitatively study microvessel flows. Currently, the representation of RBC dynamics using 2D models is a limited methodology that breaks down at high shear rates due to excessive and unrealistic stretching.

Methods

We propose a localized scaling of the 2D elastic moduli such that it increases with RBC local membrane strain, thereby accounting for effects such as the Poisson effect and membrane local area incompressibility lost in the 2D simplification. Validation of our 2D Large Deformation (2D-LD) RBC model was achieved by comparing the predicted RBC deformation against the 3D model from literature for the case of a single RBC in simple shear flow under various shear rates (dimensionless shear rate G = 0.05, 0.1, 0.2, 0.5). The multi-cell flow of RBCs (38% Hematocrit) in a 20 μm width microchannel under varying shear rates (50, 150, 150 s^-1) was then simulated with our proposed model and the popularly-employed 2D neo-Hookean model in order to evaluate the efficacy of our proposed 2D-LD model.

Results

The validation set indicated similar RBC deformation for both the 2D-LD and the 3D models across the studied shear rates, highlighting the robustness of our model. The multi-cell simulation indicated that the 2D neo-Hookean model predicts noodle-like RBC shapes at high shear rates (G = 0.5) whereas our 2D-LD model maintains sensible RBC deformations.

Conclusion

The ability of the 2D-LD model to limit RBC strain even at high shear rates enables this proposed model to be employed in practical simulations of high shear rate microfluidic flows such as blood separation channels.

A bioimage informatics based reconstruction of breast tumor microvasculature with computational blood flow predictions

Induction of tumor angiogenesis is among the hallmarks of cancer and a driver of metastatic cascade initiation. Recent advances in high-resolution imaging enable highly detailed three-dimensional geometrical representation of the whole-tumor microvascular architecture. This enormous increase in complexity of image-based data necessitates the application of informatics methods for the analysis, mining and reconstruction of these spatial graph data structures. We present a novel methodology that combines ex-vivo high-resolution micro-computed tomography imaging data with a bioimage informatics algorithm to track and reconstruct the whole-tumor vasculature of a human breast cancer model. The reconstructed tumor vascular network is used as an input of a computational model that estimates blood flow in each segment of the tumor microvascular network. This formulation involves a well-established biophysical model and an optimization algorithm that ensures mass balance and detailed monitoring of all the vessels that feed and drain blood from the tumor microvascular network. Perfusion maps for the whole-tumor microvascular network are computed. Morphological and hemodynamic indices from different regions are compared to infer their role in overall tumor perfusion.