Tank treading and unbinding of deformable vesicles in shear flow: determination of the lift force

Lift at low Reynolds number

Lift forces are widespread in hydrodynamics. These are typically observed for big and fast objects and are often associated with a combination of fluid inertia (i.e. large Reynolds numbers) and specific symmetry-breaking mechanisms. In contrast, the properties of viscosity-dominated (i.e. low Reynolds numbers) flows make it more difficult for such lift forces to emerge. However, the inclusion of boundary effects qualitatively changes this picture. Indeed, in the context of soft and biological matter, recent studies have revealed the emergence of novel lift forces generated by boundary softness, flow gradients and/or surface charges. The aim of the present review is to gather and analyse this corpus of literature, in order to identify and unify the questioning within the associated communities, and pave the way towards future research.

Effect of fluid viscoelasticity, shear stress, and interface tension on the lift force in lubricated contacts

We consider a cylinder immersed in viscous fluid moving near a flat substrate covered by an incompressible viscoelastic fluid layer, and study the effect of the fluid viscoelasticity on the lift force exerted on the cylinder. The lift force is zero when the viscoelastic layer is not deformed, but becomes non-zero when it is deformed. We calculate the lift force by considering both the tangential stress and the normal stress applied at the surface of the viscoelastic layer. Our analysis indicates that as the layer changes from the elastic limit to the viscous limit, the lift force decreases with the decrease of the Deborah number (De). For small De, the effect of the layer elasticity is taken over by the surface tension and the lift force can become negative. We also show that the tangential stress and the interface slip velocity (the surface velocity relative to the substrate), which have been ignored in the previous analysis, give important contributions to the lift force. Especially for thin elastic layers, they give dominant contributions to the lift force.

Long-term adherent cell dynamics emerging from energetic and frictional interactions at the interface

Cell adhesion plays an important role in a wide range of biological situations, including embryonic development, cancer invasion, and wound healing. Although several computational models describing adhesion dynamics have been proposed, models applicable to long-term, large-length-scale cell dynamics are lacking. In this study we investigated possible states of long-term adherent cell dynamics in three-dimensional space by constructing a continuum model of interfacial interactions between adhesive surfaces. In this model a pseudointerface is supposed between each pair of triangular elements that discretize cell surfaces. By introducing a distance between each pair of elements, the physical properties of the interface are given by interfacial energy and friction. The proposed model was implemented into the model of a nonconservative fluid cell membrane where the cell membrane dynamically flows with turnover. Using the implemented model, numerical simulations of adherent cell dynamics on a substrate under flow were performed. The simulations not only reproduced the previously reported dynamics of adherent cells, such as detachment, rolling, and fixation on the substrate, but also discovered other dynamic states, including cell slipping and membrane flow patterns, corresponding to behaviors that occur on much longer timescales than the dissociation of adhesion molecules. These results illustrate the variety of long-term adherent cell dynamics, which are more diverse than the short-term ones. The proposed model can be extended to arbitrarily shaped membranes, thus being useful for the mechanical analysis of a wide range of long-term cell dynamics where adhesion is essential.

Three-dimensional numerical study on wrinkling of vesicles in elongation flow based on the immersed boundary method

We study the wrinkling dynamics of three-dimensional vesicles in a time-dependent elongation flow by utilizing an immersed boundary method. For a quasispherical vesicle, our numerical results well match the predictions of perturbation analysis, where similar exponential relationships between wrinkles' characteristic wavelength and the flow strength are observed. Using the same parameters as in the experiments by Kantsler et al. [V. Kantsler et al., Phys. Rev. Lett. 99, 178102 (2007)0031-900710.1103/PhysRevLett.99.178102], our simulations of an elongated vesicle are in good agreement with their results. In addition, we get rich three-dimensional morphological details, which are favorable to comprehend the two-dimensional snapshots. This morphological information helps identify wrinkle patterns. We analyze the morphological evolution of wrinkles using spherical harmonics. We find discrepancies in elongated vesicle dynamics between simulations and perturbation analysis, highlighting the importance of the nonlinear effects. Finally, we investigate the unevenly distributed local surface tension, which largely determines the position of wrinkles excited on the vesicle membrane.

Migration and Spreading of Droplets across a Fluid-Fluid Interface in Microfluidic Coflow

Interfacial migration of droplets in microfluidic confinements has significant relevance in cell biology and biochemical assays. So far, studies on passive interfacial migration of droplets are limited to co-flow interfaces having small interfacial tension (IFT ∼ 1 mN/m). Here, we elucidate the migration and spreading of droplets (SiO-1000, SiO-100, FC40, and castor oil as phase 3, P3) across the interface between a pair of coflowing streams (PEG as P1, SiO-100, SiO-20, FC40, and olive oil as P2) having large IFT (∼10 mN/m), with the three different phases immiscible. Interfacial migration involving interfaces of large IFT is facilitated by confining droplets between the channel wall and coflow interface. We find that contact between droplets and the coflow interface is governed by the confinement ratio (i.e., the ratio of drop size to stream width) and the ratio of the capillary numbers of the coflowing streams. Depending on the sign of the spreading parameter (S) of the co-flowing phases, droplet migration or spreading at the interface is observed. While interfacial migration is observed for S₁ < 0 and S₂ > 0, droplet spreading is observed for S₁ < 0 and S₂ < 0, where S₁ and S₂ are P1 and P2 side spreading parameters, respectively. We investigate the droplet migration dynamics and time evolution of the contact line and the interface. Our results show that the speed of interfacial migration increases with increasing spreading parameter contrast between the coflowing phases. In the droplet spreading case, we experimentally study the variation in the spreading length with time, revealing three distinct regimes in good agreement with predictions from analytical scaling. Our study explores the interfacial transport of droplets involving high IFT interfaces, advancing the fundamental understanding of the topic that may find relevance in droplet microfluidics.

The effect of stiffened diabetic red blood cells on wall shear stress in a reconstructed 3D microaneurysm

Blood flow within the vasculature of the retina has been found to influence the progression of diabetic retinopathy. In this research cell resolved blood flow simulations are used to study the pulsatile flow of whole blood through a segmented retinal microaneurysm. Images were collected using adaptive optics optical coherence tomography of the retina of a patient with diabetic retinopathy, and a sidewall (sacciform) microaneurysm was segmented from the volumetric data. The original microaneurysm neck width was varied to produce two additional aneurysm geometries in order to probe the influence of neck width on the transport of red blood cells and platelets into the aneurysm. Red blood cell membrane stiffness was also increased to resolve the impact of rigid red blood cells, as a result of diabetes, in blood flow. Wall shear stress and wall shear stress gradients were calculated throughout the aneurysm domains, and the quantification of the influence of the red blood cells is presented. Average wall shear stress and wall shear stress gradients increased due to the increase of red blood cell membrane stiffness. Stiffened red blood cells were also found to induce higher local wall shear stress and wall shear stress gradients as they passed through the leading and draining parental vessels. Stiffened red blood cells were found to penetrate the aneurysm sac more than healthy red blood cells, as well as decreasing the margination of platelets to the vessel walls of the parental vessel, which caused a decrease in platelet penetration into the aneurysm sac.

Flow driven vesicle unbinding under mechanosensitive adhesion

Ligand receptor based adhesion is the primary mode of interaction of cellular blood constituents with the endothelium. These adhered entities also experience shear flow imposed by the blood which may lead to their detachment due to the viscous lift forces. Here, we have studied the role of the ligand-receptor bond kinetics in the detachment of an adhered vesicle (a simplified cell model) under shear flow. Using boundary integral formulation we performed numerical simulation of a two dimensional vesicle under shear flow for different values of applied shear rates and time scale of bond kinetics. We observe that the vesicle demonstrates three steady state configurations - adhered, pinned and detached for fast enough ligand-receptor kinetics (akin to Lennard-Jones adhesion). However, for slow bond kinetics the pinned state is not observed. We present scaling laws for the critical shear rates corresponding to the transitions among these three states. These results can help with identifying the processes of cell adhesion/detachment in the blood stream, prevalent features during the immune response and cancer metastasis.

Shear-induced migration of confined flexible fibers

We report an experimental study of the shear-induced migration of flexible fibers in suspensions confined between two parallel plates. Non-Brownian fiber suspensions are imaged in a rheo-microscopy setup, where the top and the bottom plates counter-rotate and create a Couette flow. Initially, the fibers are near the bottom plate due to sedimentation. Under shear, the fibers move with the flow and migrate towards the center plane between the two walls. Statistical properties of the fibers, such as the mean values of the positions, orientations, and end-to-end lengths of the fibers, are used to characterize the behaviors of the fibers. A dimensionless parameter Λ_eff, which compares the hydrodynamic shear stress and the fiber stiffness, is used to analyze the effective flexibility of the fibers. The observations show that the fibers that are more likely to bend exhibit faster migration. As Λ_eff increases (softer fibers and stronger shear stresses), the fibers tend to align in the flow direction and the motions of the fibers transition from tumbling and rolling to bending. The bending fibers drift away from the walls to the center plane. Further increasing Λ_eff leads to more coiled fiber shapes, and the bending is more frequent and with larger magnitudes, which leads to more rapid migration towards the center. Different behaviors of the fibers are quantified with Λ_eff, and the structures and the dynamics of the fibers are correlated with the migration.

Continuum microhaemodynamics modelling using inverse rheology

Modelling blood flow in microvascular networks is challenging due to the complex nature of haemorheology. Zero- and one-dimensional approaches cannot reproduce local haemodynamics, and models that consider individual red blood cells (RBCs) are prohibitively computationally expensive. Continuum approaches could provide an efficient solution, but dependence on a large parameter space and scarcity of experimental data for validation has limited their application. We describe a method to assimilate experimental RBC velocity and concentration data into a continuum numerical modelling framework. Imaging data of RBCs were acquired in a sequentially bifurcating microchannel for various flow conditions. RBC concentration distributions were evaluated and mapped into computational fluid dynamics simulations with rheology prescribed by the Quemada model. Predicted velocities were compared to particle image velocimetry data. A subset of cases was used for parameter optimisation, and the resulting model was applied to a wider data set to evaluate model efficacy. The pre-optimised model reduced errors in predicted velocity by 60% compared to assuming a Newtonian fluid, and optimisation further reduced errors by 40%. Asymmetry of RBC velocity and concentration profiles was demonstrated to play a critical role. Excluding asymmetry in the RBC concentration doubled the error, but excluding spatial distributions of shear rate had little effect. This study demonstrates that a continuum model with optimised rheological parameters can reproduce measured velocity if RBC concentration distributions are known a priori. Developing this approach for RBC transport with more network configurations has the potential to provide an efficient approach for modelling network-scale haemodynamics.

A continuum mechanics model for the Fåhræus-Lindqvist effect

The decrease in apparent relative viscosity that occurs when blood is made to flow through a tube whose diameter is less than about 0.3 mm is a well-known and documented phenomenon in physiology, known as the Fåhræus-Lindqvist effect. However, since the historical work of Fåhræus and Lindqvist (Amer. J. Physiol. 96(3): pp. 562–568, 1931), the underlying physical mechanism has remained enigmatic. A widely accepted qualitative explanation was provided by Haynes (Amer. J. Physiol. 198, pp. 1193–1200, 1960) according to which blood flows in microvessels with a core-annulus structure, where the erythrocytes concentrate within a central core surrounded by a plasma layer. Although sustained by observations, this conjecture lacks a rigorous deduction from the basic principles of continuum dynamics. Moreover, relations aimed to reproduce the blood apparent relative viscosity, extensively used in micro-circulation, are all empirical and not derived from the analysis of the fluid mechanical phenomena involved. In this paper, we apply the recent results illustrated in Guadagni and Farina (Int. J. Nonlinear Mech. 126, p. 103587, 2020), with the purpose of showing that Haynes’ conjecture, slightly corrected to make it more realistic, can be proved and can be used to reach a sound explanation of the Fåhræus-Lindqvist effect based on continuum mechanics. We propose a theoretical model for the blood apparent relative viscosity which is validated by matching not only the original experimental data reported by Fåhræus and Lindqvist (Amer. J. Physiol. 96(3), pp. 562–568, 1931), but also those provided by several subsequent authors.

Computational models of cancer cell transport through the microcirculation

The transport of cancerous cells through the microcirculation during metastatic spread encompasses several interdependent steps that are not fully understood. Computational models which resolve the cellular-scale dynamics of complex microcirculatory flows offer considerable potential to yield needed insights into the spread of cancer as a result of the level of detail that can be captured. In recent years, in silico methods have been developed that can accurately and efficiently model the circulatory flows of cancer and other biological cells. These computational methods are capable of resolving detailed fluid flow fields which transport cells through tortuous physiological geometries, as well as the deformation and interactions between cells, cell-to-endothelium interactions, and tumor cell aggregates, all of which play important roles in metastatic spread. Such models can provide a powerful complement to experimental works, and a promising approach to recapitulating the endogenous setting while maintaining control over parameters such as shear rate, cell deformability, and the strength of adhesive binding to better understand tumor cell transport. In this review, we present an overview of computational models that have been developed for modeling cancer cells in the microcirculation, including insights they have provided into cell transport phenomena.

Advanced Constitutive Modeling of the Thixotropic Elasto-Visco-Plastic Behavior of Blood: Steady-State Blood Flow in Microtubes

The present work focuses on the in-silico investigation of the steady-state blood flow in straight microtubes, incorporating advanced constitutive modeling for human blood and blood plasma. The blood constitutive model accounts for the interplay between thixotropy and elasto-visco-plasticity via a scalar variable that describes the level of the local blood structure at any instance. The constitutive model is enhanced by the non-Newtonian modeling of the plasma phase, which features bulk viscoelasticity. Incorporating microcirculation phenomena such as the cell-free layer (CFL) formation or the Fåhraeus and the Fåhraeus-Lindqvist effects is an indispensable part of the blood flow investigation. The coupling between them and the momentum balance is achieved through correlations based on experimental observations. Notably, we propose a new simplified form for the dependence of the apparent viscosity on the hematocrit that predicts the CFL thickness correctly. Our investigation focuses on the impact of the microtube diameter and the pressure-gradient on velocity profiles, normal and shear viscoelastic stresses, and thixotropic properties. We demonstrate the microstructural configuration of blood in steady-state conditions, revealing that blood is highly aggregated in narrow tubes, promoting a flat velocity profile. Additionally, the proper accounting of the CFL thickness shows that for narrow microtubes, the reduction of discharged hematocrit is significant, which in some cases is up to 70%. At high pressure-gradients, the plasmatic proteins in both regions are extended in the flow direction, developing large axial normal stresses, which are more significant in the core region. We also provide normal stress predictions at both the blood/plasma interface (INS) and the tube wall (WNS), which are difficult to measure experimentally. Both decrease with the tube radius; however, they exhibit significant differences in magnitude and type of variation. INS varies linearly from 4.5 to 2 Pa, while WNS exhibits an exponential decrease taking values from 50 mPa to zero.

Effect of cytosol viscosity on the flow behavior of red blood cell suspensions in microvessels

OBJECTIVE

The flow behavior of blood is strongly affected by red blood cell (RBC) properties, such as the viscosity ratio C between cytosol and suspending medium, which can significantly be altered in several pathologies (e.g. sickle-cell disease, malaria). The main objective of this study is to understand the effect of C on macroscopic blood flow properties such as flow resistance in microvessels, and to link it to the deformation and dynamics of single RBCs.

METHODS

We employ mesoscopic hydrodynamic simulations to investigate flow properties of RBC suspensions with different cytosol viscosities for various flow conditions in cylindrical microchannels.

RESULTS

Starting from a dispersed cell configuration which approximates RBC dispersion at vessel bifurcations in the microvasculature, we find that the flow convergence and development of RBC-free layer (RBC-FL) depend only weakly on C, and require a convergence length in the range of 25D-50D, where D is channel diameter. In vessels with D ≤ 20 μ m , the final resistance of developed flow is nearly the same for C = 5 and C = 1, while for D = 40 μ m , the flow resistance for C = 5 is about 10% larger than for C = 1. The similarities and differences in flow resistance can be explained by viscosity-dependent RBC-FL thicknesses, which are associated with the viscosity-dependent dynamics of single RBCs.

CONCLUSIONS

The weak effect on the flow resistance and RBC-FL explains why RBCs can contain a high concentration of hemoglobin for efficient oxygen delivery, without a pronounced increase in the flow resistance. Furthermore, our results suggest that significant alterations in microvascular flow in various pathologies are likely not due to mere changes in cytosolic viscosity.

Membrane permeability to water measured by microfluidic trapping of giant vesicles

We use a microfluidic method to estimate the water permeability coefficient (p) of membranes. As model lipid membranes we employ giant unilamellar vesicles (GUVs) composed of palmitoyloleoyl phosphatidylcholine and cholesterol (10 mol%). We have developed a microfluidic device with multiple chambers to trap GUVs and allow controlled osmotic exchange. Each chamber has a ring-shaped pressure-controlled valve which upon closure allows isolation of the GUVs in a defined volume. Opening the valves leads to a rapid fluid exchange between the trapping region and the microchannel network outside, thus allowing precise control over solution concentration around the GUVs contrary to other experimental approaches for permeability measurements reported in the literature. The area and volume changes of individual vesicles are monitored with confocal microscopy. The solute concentration in the immediate vicinity of the GUVs, and thus the concentration gradient across the membrane, is independently assessed. The data are well fitted by a simple model for water permeability which assumes that the rate of change in volume of a GUV per unit area is linearly proportional to concentration difference with permeability as the proportionality constant. Experiments of GUV osmotic deflation with hypertonic solutions yield the permeability of POPC/cholesterol 9/1 membranes to be p = 15.7 ± 5.5 μm s-1. For comparison, we also show results using two other approaches, which either do not take into account local concentration changes and/or do not resolve the precise vesicle shape. We point out the errors associated with these limitations. Finally, we also demonstrate the applicability of the microfluidic device for studying the dynamics of vesicles under flow.

Heterogeneous partition of cellular blood-borne nanoparticles through microvascular bifurcations

Blood flowing through microvascular bifurcations has been an active research topic for many decades, while the partitioning pattern of nanoscale solutes in the blood remains relatively unexplored. Here we demonstrate a multiscale computational framework for direct numerical simulation of the nanoparticle (NP) partitioning through physiologically relevant vascular bifurcations in the presence of red blood cells (RBCs). The computational framework is established by embedding a particulate suspension inflow-outflow boundary condition into a multiscale blood flow solver. The computational framework is verified by recovering a tubular blood flow without a bifurcation and validated against the experimental measurement of an intravital bifurcation flow. The classic Zweifach-Fung (ZF) effect is shown to be well captured by the method. Moreover, we observe that NPs exhibit a ZF-like heterogeneous partition in response to the heterogeneous partition of the RBC phase. The NP partitioning prioritizes the high-flow-rate daughter branch except for extreme (large or small) suspension flow partition ratios under which the complete phase separation tends to occur. By analyzing the flow field and the particle trajectories, we show that the ZF-like heterogeneity in the NP partition can be explained by the RBC-entrainment effect caused by the deviation of the flow separatrix preceded by the tank treading of RBCs near the bifurcation junction. The recovery of homogeneity in the NP partition under extreme flow partition ratios is due to the plasma skimming of NPs in the cell-free layer. These findings, based on the multiscale computational framework, provide biophysical insights to the heterogeneous distribution of NPs in microvascular beds that are observed pathophysiologically.

Microstreaming inside Model Cells Induced by Ultrasound and Microbubbles

Studies on the bioeffects produced by ultrasound and microbubbles have focused primarily on transport in bulk tissue, drug uptake by individual cells, and disruption of biological membranes. Relatively little is known about the physical perturbations and fluid dynamics of the intracellular environment during ultrasound exposure. To investigate this, a custom acoustofluidic chamber was designed to expose model cells, in the form of giant unilamellar vesicles, to ultrasound and microbubbles. The motion of fluorescent tracer beads within the lumen of the vesicles was tracked during exposure to laminar flow (∼1 mm s^-1), ultrasound (1 MHz, ∼150 kPa, 60 s), and phospholipid-coated microbubbles, alone and in combination. To decouple the effects of fluid flow and ultrasound exposure, the system was also modeled numerically by using boundary-driven streaming field equations. Both the experimental and numerical results indicate that all conditions produced internal streaming within the vesicles. Ultrasound alone produced an average bead velocity of 6.5 ± 1.3 μm/s, which increased to 8.5 ± 3.8 μm/s in the presence of microbubbles compared to 12 ± 0.12 μm/s under laminar flow. Further research on intracellular forces in mammalian cells and the associated biological effects in vitro and in vivo are required to fully determine the implications for safety and/or therapy.

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.

Rotation of a submerged finite cylinder moving down a soft incline

A submerged finite cylinder moving under its own weight along a soft incline lifts off and slides at a steady velocity while also spinning. Here, we experimentally quantify the steady spinning of the cylinder and show theoretically that it is due to a combination of an elastohydrodynamic torque generated by flow in the variable gap, and the viscous friction on the edges of the finite-length cylinder. The relative influence of the latter depends on the aspect ratio of the cylinder, the angle of the incline, and the deformability of the substrate, which we express in terms of a single scaled compliance parameter. By independently varying these quantities, we show that our experimental results are consistent with a transition from an edge-effect dominated regime for short cylinders to a gap-dominated elastohydrodynamic regime when the cylinder is very long.

Direct Measurement of the Elastohydrodynamic Lift Force at the Nanoscale

We present the first direct measurement of the elastohydrodynamic lift force acting on a sphere moving within a viscous liquid, near and along a soft substrate under nanometric confinement. Using atomic force microscopy, the lift force is probed as a function of the gap size, for various driving velocities, viscosities, and stiffnesses. The force increases as the gap is reduced and shows a saturation at small gap. The results are in excellent agreement with scaling arguments and a quantitative model developed from the soft lubrication theory, in linear elasticity, and for small compliances. For larger compliances, or equivalently for smaller confinement length scales, an empirical scaling law for the observed saturation of the lift force is given and discussed.

Oblate to prolate transition of a vesicle in shear flow

Vesicles are micrometric soft particles whose membrane is a two-dimensional incompressible fluid governed by bending resistance leading to a zoology of shapes. The dynamics of deflated vesicles in shear flow with a bottom wall, a first minimal configuration to consider confined vesicles, is investigated using numerical simulations. Coexistence under flow of oblate (metastable) and prolate (stable) shapes is studied in details. In particular, we discuss the boundaries of the region of coexistence in the (v, Ca -plane where v is the reduced volume of the vesicle and Ca the Capillary number. We characterize the transition from oblate to prolate and analyse the divergence of the transition time near the critical capillary number. We then analyse the lift dynamics of an oblate vesicle in the weak flow regime.

Focusing and splitting streams of soft particles in microflows via viscosity gradients

Microflows are intensively used for investigating and controlling the dynamics of particles, including soft particles such as biological cells and capsules. A classic result is the tank-treading motion of elliptically deformed soft particles in linear shear flows, which do not migrate across straight streamlines in the bulk. However, soft particles migrate across straight streamlines in Poiseuille flows. In this work we describe a new mechanism of cross-streamline migration by using soft capsules with a spherical equilibrium shape. If the viscosity varies perpendicular to the streamlines then the soft particles migrate across streamlines towards regions of a lower viscosity, even in linear shear flows. An interplay with the repulsive particle-boundary interaction causes then focusing of particles in linear shear flows with the attractor streamline closer to the wall in the low viscosity region. Viscosity variations perpendicular to the streamlines in Poiseuille flows leads either to a shift of the particle attractor or even to a splitting of particle attractors, which may give rise to interesting applications for particle separation. The location of attracting streamlines depend on the particle properties, like their size and elasticity. The cross-stream migration induced by viscosity variations is explained by analytical considerations, Stokesian dynamics simulations with a generalized Oseen tensor and lattice-Boltzmann simulations.

Hemodynamic Effects on Particle Targeting in the Arterial Bifurcation for Different Magnet Positions

The present study investigated the possibilities and feasibility of drug targeting for an arterial bifurcation lesion to influence the host healing response. A micrometer sized iron particle was used only to model the magnetic carrier in the experimental investigation (not intended for clinical use), to demonstrate the feasibility of the particle targeting at the lesion site and facilitate the new experimental investigations using coated superparamagnetic iron oxide nanoparticles. Magnetic fields were generated by a single permanent external magnet (ferrite magnet). Artery bifurcation exerts severe impacts on drug distribution, both in the main vessel and the branches, practically inducing an uneven drug concentration distribution in the bifurcation lesion area. There are permanently positioned magnets in the vicinity of the bifurcation near the diseased area. The generated magnetic field induced deviation of the injected ferromagnetic particles and were captured onto the vessel wall of the test section. To increase the particle accumulation in the targeted region and consequently avoid the polypharmacology (interaction of the injected drug particles with multiple target sites), it is critical to understand flow hemodynamics and the correlation between flow structure, magnetic field gradient, and spatial position.

Deformation and dynamics of erythrocytes govern their traversal through microfluidic devices with a deterministic lateral displacement architecture

Deterministic lateral displacement (DLD) microfluidic devices promise versatile and precise processing of biological samples. However, this prospect has been realized so far only for rigid spherical particles and remains limited for biological cells due to the complexity of cell dynamics and deformation in microfluidic flow. We employ mesoscopic hydrodynamics simulations of red blood cells (RBCs) in DLD devices with circular posts to better understand the interplay between cell behavior in complex microfluidic flow and sorting capabilities of such devices. We construct a mode diagram of RBC behavior (e.g., displacement, zig-zagging, and intermediate modes) and identify several regimes of RBC dynamics (e.g., tumbling, tank-treading, and trilobe motion). Furthermore, we link the complex interaction dynamics of RBCs with the post to their effective cell size and discuss relevant physical mechanisms governing the dynamic cell states. In conclusion, sorting of RBCs in DLD devices based on their shear elasticity is, in general, possible but requires fine-tuning of flow conditions to targeted mechanical properties of the RBCs.

Droplet encapsulation of particles in different regimes and sorting of particle-encapsulating-droplets from empty droplets

Encapsulation of microparticles in droplets has profound applications in biochemical assays. We investigate encapsulation of rigid particles (polystyrene beads) and deformable particles (biological cells) inside aqueous droplets in various droplet generation regimes, namely, squeezing, dripping, and jetting. Our study reveals that the size of the positive (particle-encapsulating) droplets is larger or smaller compared to that of the negative (empty) droplets in the dripping and jetting regimes but no size contrast is observed in the squeezing regime. The size contrast of the positive and negative droplets in the different regimes is characterized in terms of capillary number C a and stream width ratio ω (i.e., ratio of stream width at the throat to particle diameter ω = w / d p ). While for deformable particles, the positive droplets are always larger compared to the negative droplets, for rigid particles, the positive droplets are larger in the dripping and jetting regimes for 0.50 ≤ ω ≤ 0.80 but smaller in the jetting regime for ω < 0.50 . We exploit the size contrast of positive and negative droplets for sorting across the fluid-fluid interface based on noninertial lift force (at R e ≪ 1 ), which is a strong function of droplet size. We demonstrate sorting of the positive droplets encapsulating polystyrene beads and biological cells from the negative droplets with an efficiency of ∼95% and purity of ∼65%. The proposed study will find relevance in single-cell studies, where positive droplets need to be isolated from the empty droplets prior to downstream processing.

Emerging Attractor in Wavy Poiseuille Flows Triggers Sorting of Biological Cells

Microflows constitute an important instrument to control particle dynamics. A prominent example is the sorting of biological cells, which relies on the ability of deformable cells to move transversely to flow lines. A classic result is that soft microparticles migrate in flows through straight microchannels to an attractor at their center. Here, we show that flows through wavy channels fundamentally change the overall picture. They lead to the emergence of a second, coexisting attractor for soft particles. Its emergence and off-center location depends on the boundary modulation and the particle properties. The related cross-stream migration of soft particles is explained by analytical considerations, Stokesian dynamics simulations in unbounded flows, and Lattice-Boltzmann simulations in bounded flows. The novel off-center attractor can be used, for instance, in diagnostics, for separating cells of different size and elasticity, which is often an indicator of their health status.

Migration velocity of red blood cells in microchannels

The lateral migration of red blood cells (RBCs) in confined channel flows is an important ingredient of microcirculatory hydrodynamics and is involved in the development of a cell free layer near vessel walls and influences the distribution of RBCs in networks. It is also relevant to a number of lab-on-chip applications. This migration is a consequence of their deformability and is due to the combined effects of hydrodynamic wall repulsion and the curvature of the fluid velocity profile. We performed microfluidic experiments with dilute suspensions of RBCs in which the trajectories and migration away from the channel wall are analyzed to extract the mean behavior, from which we propose a generic scaling law for the transverse migration velocity valid in a whole range of parameters relevant to microcirculatory and practical situations. Experiments with RBCs of different mechanical properties (separated by density gradient sedimentation or fixed with glutaraldehyde) show the influence of this parameter which can induce significant dispersion of the trajectories.

Non-inertial lift induced migration for label-free sorting of cells in a co-flowing aqueous two-phase system

We present a novel label-free passive microfluidic technique for isolation of cancer cells (EpCAM+ and CD45−) from peripheral blood mononuclear cells (PBMCs) (CD45+ and EpCAM−) in aqueous two-phase system (ATPS).

Splitting and separation of colloidal streams in sinusoidal microchannels

The control of the distribution of colloidal particles in microfluidic flows plays an important role in biomedical and industrial applications. A particular challenge is to induce cross-streamline migration in laminar flows, enabling the separation of colloidal particles according to their size, shape or elasticity. Here we show that viscoelastic fluids can mediate cross-streamline migration of deformable spherical and cylindrical colloidal particles in sinusoidal microchannels at low Reynolds numbers. For colloidal streams focused into the center of the channel entrance this leads to a symmetric stream-splitting and separation into four substreams. The degree of stream splitting and separation can be controlled via the flow rates, viscoelasticity of the focusing fluid, and the spatial microchannel modulation with an upper limit when reaching the microchannel walls. We demonstrate that this effect can be used to separate flexible particles of different size and shape. This methodology of cross-stream migration has thus great potential for the passive separation of colloids and cells in microfluidic channels.

Shear rate dependent margination of sphere-like, oblate-like and prolate-like micro-particles within blood flow

This study investigates the shear rate dependent margination of micro-particles (MPs) with different shapes in blood flow through numerical simulations. We develop a multiscale computational model to handle the fluid-structure interactions involved in the blood flow simulations. The lattice Boltzmann method (LBM) is used to solve the plasma dynamics and a coarse-grained model is employed to capture the dynamics of red blood cells (RBCs) and MPs. These two solvers are coupled together by the immersed boundary method (IBM). The shear rate dependent margination of sphere MPs is firstly investigated. We find that margination of sphere MPs dramatically increases with the increment of wall shear rate [small gamma, Greek, dot above]ω under 800 s-1, induced by the breaking of rouleaux in blood flow. However, the margination probability only slowly grows when [small gamma, Greek, dot above]ω > 800 s-1. Furthermore, the shape effect of MPs is examined by comparing the margination behaviors of sphere-like, oblate-like and prolate-like MPs under different wall shear rates. We find that the margination of MPs is governed by the interplay of two factors: hydrodynamic collisions with RBCs including the collision frequency and collision displacement of MPs, and near wall dynamics. MPs that demonstrate poor performance in one process such as collision frequency may stand out in the other process like near wall dynamics. Specifically, the ellipsoidal MPs (oblate and prolate) with small aspect ratio (AR) outperform those with large AR regardless of the wall shear rate, due to their better performance in both the collision with RBCs and near wall dynamics. Additionally, we find there exists a transition shear rate region 700 s-1 < [small gamma, Greek, dot above]ω < 900 s-1 for all of these MPs: the margination probability dramatically increases with the shear rate below this region and slowly grows above this region, similar to sphere MPs. We further use the surface area to volume ratio (SVR) to distinguish different shaped MPs and illustrate their shear rate dependent margination in a contour in the shear rate-SVR plane. It is of significance that we can approximately predict the margination of MPs with a specific SVR. All these simulation results can be potentially applied to guide the design of micro-drug carriers for biomedical applications.

Influence of particle size and shape on their margination and wall-adhesion: implications in drug delivery vehicle design across nano-to-micro scale

Intravascular drug delivery technologies majorly utilize spherical nanoparticles as carrier vehicles. Their targets are often at the blood vessel wall or in the tissue beyond the wall, such that vehicle localization towards the wall (margination) becomes a pre-requisite for their function. To this end, some studies have indicated that under flow environment, micro-particles have a higher propensity than nano-particles to marginate to the wall. Also, non-spherical particles theoretically have a higher area of surface-adhesive interactions than spherical particles. However, detailed systematic studies that integrate various particle size and shape parameters across nano-to-micro scale to explore their wall-localization behavior in RBC-rich blood flow, have not been reported. We address this gap by carrying out computational and experimental studies utilizing particles of four distinct shapes (spherical, oblate, prolate, rod) spanning nano- to-micro scale sizes. Computational studies were performed using the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) package, with Dissipative Particle Dynamics (DPD). For experimental studies, model particles were made from neutrally buoyant fluorescent polystyrene spheres, that were thermo-stretched into non-spherical shapes and all particles were surface-coated with biotin. Using microfluidic setup, the biotin-coated particles were flowed over avidin-coated surfaces in absence versus presence of RBCs, and particle adhesion and retention at the surface was assessed by inverted fluorescence microscopy. Our computational and experimental studies provide a simultaneous analysis of different particle sizes and shapes for their retention in blood flow and indicate that in presence of RBCs, micro-scale non-spherical particles undergo enhanced 'margination + adhesion' compared to nano-scale spherical particles, resulting in their higher binding. These results provide important insight regarding improved design of vascularly targeted drug delivery systems.

Heterogeneous blood flow in microvessels with applications to nanodrug transport and mass transfer into tumor tissue

Nanodrug transport in tumor microvasculature and deposition/extravasation into tumor tissue are an important link in the nanodrug delivery process. Considering heterogeneous blood flow, such a dual process is numerically studied. The hematocrit distribution is solved by directly considering the forces experienced by the red blood cells (RBCs), i.e., the wall lift force and the random cell collision force. Using a straight microvessel as a test bed, validated computer simulations are performed to determine blood flow characteristics as well as the resulting nanodrug distribution and extravasation. The results confirm that RBCs migrate away from the vessel wall, leaving a cell-free layer (CFL). Nanodrug particles tend to preferentially accumulate in the CFL, leading to increased concentration near the endothelial surface layer. However, shear-induced NP diffusion is diminished within the CFL, causing to a much slower lateral transport rate into tumor tissue. These competing effects determine the NP deposition/extravasation rates. The present modeling framework and NP flux results provide new physical insight. The analysis can be readily extended to simulations of NP transport in blood microvessels of actual tumors.

Elastohydrodynamic Lift at a Soft Wall

We study experimentally the motion of nondeformable microbeads in a linear shear flow close to a wall bearing a thin and soft polymer layer. Combining microfluidics and 3D optical tracking, we demonstrate that the steady-state bead-to-surface distance increases with the flow strength. Moreover, such lift is shown to result from flow-induced deformations of the layer, in quantitative agreement with theoretical predictions from elastohydrodynamics. This study thus provides the first experimental evidence of "soft lubrication" at play at small scale, in a system relevant, for example, to the physics of blood microcirculation.

Elastic particle deformation in rectangular channel flow as a measure of particle stiffness

In this study, we experimentally observed and characterized soft elastic particle deformation in confined flow in a microchannel with a rectangular cross-section. Hydrogel microparticles of pNIPAM were produced using two different concentrations of crosslinker. This resulted in particles with two different shear moduli of 13.3 ± 5.5 Pa and 32.5 ± 15.7 Pa and compressive moduli of 66 ± 10 Pa and 79 ± 15 Pa, respectively, as measured by capillary micromechanics. Under flow, the particle shapes transitioned from circular to egg, triangular, arrowhead, and ultimately parachute shaped with increasing shear rate. The shape changes were reversible, and deformed particles relaxed back to circular/spherical in the absence of flow. The thresholds for each shape transition were quantified using a non-dimensional radius of curvature at the tip, particle deformation, circularity, and the depth of the concave dimple at the trailing edge. Several of the observed shapes were distinct from those previously reported in the literature for vesicles and capsules; the elastic particles had a narrower leading tip and a lower circularity. Due to variations in the shear moduli between particles within a batch of particles, each flow rate corresponded to a small but finite range of capillary number (Ca) and resulted in a series of shapes. By arranging the images on a plot of Ca versus circularity, a direct correlation was developed between shape and Ca and thus between particle deformation and shear modulus. As the shape was very sensitive to differences in shear modulus, particle deformation in confined flow may allow for better differentiation of microparticle shear modulus than other methods.

Margination of Stiffened Red Blood Cells Regulated By Vessel Geometry

Margination of stiffened red blood cells has been implicated in many vascular diseases. Here, we report the margination of stiffened RBCs in vivo, and reveal the crucial role of the vessel geometry in the margination by calculations when the blood is seen as viscoelastic fluid. The vessel-geometry-regulated margination is then confirmed by in vitro experiments in microfluidic devices, and it establishes new insights to cell sorting technology and artificial blood vessel fabrication.

Margination and stretching of von Willebrand factor in the blood stream enable adhesion

The protein von Willebrand factor (VWF) is essential in primary hemostasis, as it mediates platelet adhesion to vessel walls. VWF retains its compact (globule-like) shape in equilibrium due to internal molecular associations, but is able to stretch when a high enough shear stress is applied. Even though the shear-flow sensitivity of VWF conformation is well accepted, the behavior of VWF under realistic blood flow conditions remains poorly understood. We perform mesoscopic numerical simulations together with microfluidic experiments in order to characterize VWF behavior in blood flow for a wide range of flow-rate and hematocrit conditions. In particular, our results demonstrate that the compact shape of VWF is important for its migration (or margination) toward vessel walls and that VWF stretches primarily in a near-wall region in blood flow making its adhesion possible. Our results show that VWF is a highly optimized protein in terms of its size and internal associations which are necessary to achieve its vital function. A better understanding of the relevant mechanisms for VWF behavior in microcirculation provides a further step toward the elucidation of the role of mutations in various VWF-related diseases.

Effects of membrane deformability and bond formation/dissociation rates on adhesion dynamics of a spherical capsule in shear flow

Cellular adhesion plays a critical role in biological systems and biomedical applications. Cell deformation and biophysical properties of adhesion molecules are of significance for the adhesion behavior. In the present work, dynamic adhesion of a deformable capsule to a planar substrate, in a linear shear flow, is numerically simulated to investigate the combined influence of membrane deformability (quantified by the capillary number) and bond formation/dissociation rates on the adhesion behavior. The computational model is based on the immersed boundary-lattice Boltzmann method for the capsule-fluid interaction and a probabilistic adhesion model for the capsule-substrate interaction. Three distinct adhesion states, detachment, rolling adhesion and firm adhesion, are identified and presented in a state diagram as a function of capillary number and bond dissociation rate. The impact of bond formation rate on the state diagram is further investigated. Results show that the critical bond dissociation rate for the transition of rolling or firm adhesion to detachment is strongly related to the capsule deformability. At the rolling-adhesion state, smaller off rates are needed for larger capillary number to increase the rolling velocity and detach the capsule. In contrast, the critical off rate for firm-to-detach transition slightly increases with the capillary number. With smaller on rate, the effect of capsule deformability on the critical off rates is more pronounced and capsules with moderate deformability are prone to detach by the shear flow. Further increasing of on rate leads to large expansion of both rolling-adhesion and firm-adhesion regions. Even capsules with relatively large deformability can maintain stable rolling adhesion at certain off rate.

Direct Tracking of Particles and Quantification of Margination in Blood Flow

Margination refers to the migration of particles toward blood vessel walls during blood flow. Understanding the mechanisms that lead to margination will aid in tailoring the attributes of drug-carrying particles for effective drug delivery. Most previous studies evaluated the margination propensity of these particles via an adhesion mechanism, i.e., by measuring the number of particles that adhered to the channel wall. Although particle adhesion and margination are related, adhesion also depends on other factors. In this study, we quantified the margination propensity of particles of varying diameters (0.53, 0.84, and 2.11 μm) and apparent wall shear rates (30, 61, and 121 s^-1) by directly tracking fluorescent particles flowing through a microfluidic channel. The margination parameter, M, is defined as the total number of particles found within the cell-free layers normalized by the total number of particles that passed through the channel. In this study, an M-value of 0.2 indicated no margination, which was observed for all particle sizes in water. In the case of blood, larger particles were found to have higher M-values and thus marginated more effectively than smaller particles. The corresponding M-values at the device outlet were 0.203, 0.223, and 0.285 for 0.53-, 0.84-, and 2.11-μm particles, respectively. At the inlet, the M-values for all particle sizes in blood were <0.2, suggesting that non-fully-developed flow and constriction may lead to demargination. For particle velocities transverse to the flow direction (v_y), all particle sizes showed a larger standard deviation of v_y as well as a higher effective diffusivity when the particles were suspended in blood relative to water. These higher values are attributed to collisions between the blood cells and particles, further supporting recent simulation results. In terms of flow rates, for a given particle size, the higher the flow rate, the higher the M-value.

Dynamics of rigid microparticles at the interface of co-flowing immiscible liquids in a microchannel

We report the dynamical migration behavior of rigid polystyrene microparticles at an interface of co-flowing streams of primary CP₁ (aqueous) and secondary CP₂ (oils) immiscible phases at low Reynolds numbers (Re) in a microchannel. The microparticles initially suspended in the CP₁ either continue to flow in the bulk CP₁ or migrate across the interface into CP₂, when the stream width of the CP₁ approaches the diameter of the microparticles. Experiments were performed with different secondary phases and it is found that the migration criterion depends on the sign of the spreading parameter S and the presence of surfactant at the interface. To substantiate the migration criterion, experiments were also carried out by suspending the microparticles in CP₂ (oil phase). Our study reveals that in case of aqueous-silicone oil combination, the microparticles get attached to the interface since S<0 and the three phase contact angle, θ>90°. For complete detachment of microparticles from the interface into the secondary phase, additional energy ΔG is needed. We discuss the role of interfacial perturbation, which causes detachment of microparticles from the interface. In case of mineral and olive oils, the surfactants present at the interface prevents attachment of the microparticles to the interface due to the repulsive disjoining pressure. Finally, using a aqueous-silicone oil system, we demonstrate size based sorting of microparticles of size 25μm and 15μm respectively from that of 15μm and 10μm and study the variation of separation efficiency η with the ratio of the width of the aqueous stream to the diameter of the microparticles ρ.

Sorting cells by their dynamical properties

Recent advances in cell sorting aim at the development of novel methods that are sensitive to various mechanical properties of cells. Microfluidic technologies have a great potential for cell sorting; however, the design of many micro-devices is based on theories developed for rigid spherical particles with size as a separation parameter. Clearly, most bioparticles are non-spherical and deformable and therefore exhibit a much more intricate behavior in fluid flow than rigid spheres. Here, we demonstrate the use of cells’ mechanical and dynamical properties as biomarkers for separation by employing a combination of mesoscale hydrodynamic simulations and microfluidic experiments. The dynamic behavior of red blood cells (RBCs) within deterministic lateral displacement (DLD) devices is investigated for different device geometries and viscosity contrasts between the intra-cellular fluid and suspending medium. We find that the viscosity contrast and associated cell dynamics clearly determine the RBC trajectory through a DLD device. Simulation results compare well to experiments and provide new insights into the physical mechanisms which govern the sorting of non-spherical and deformable cells in DLD devices. Finally, we discuss the implications of cell dynamics for sorting schemes based on properties other than cell size, such as mechanics and morphology.

Behavior of rigid and deformable particles in deterministic lateral displacement devices with different post shapes

Deterministic lateral displacement (DLD) devices have great potential for the separation and sorting of various suspended particles based on their size, shape, deformability, and other intrinsic properties. Currently, the basic idea for the separation mechanism is that the structure and geometry of DLDs uniquely determine the flow field, which in turn defines a critical particle size and the particle lateral displacement within a device. We employ numerical simulations using coarse-grained mesoscopic methods and two-dimensional models to elucidate the dynamics of both rigid spherical particles and deformable red blood cells (RBCs) in different DLD geometries. Several shapes of pillars, including circular, diamond, square, and triangular structures, and a few particle sizes are considered. The simulation results show that a critical particle size can be well defined for rigid spherical particles and depends on the details of the DLD structure and the corresponding flow field within the device. However, non-isotropic and deformable particles such as RBCs exhibit much more complex dynamics within a DLD device, which cannot properly be described by a single parameter such as the critical size. The dynamics and deformation of soft particles within a DLD device become also important, indicating that not only size sorting, but additional sorting targets (e.g., shape, deformability, internal viscosity) are possible.

Controlled deformation of vesicles by flexible structured media

Liquid crystalline (LC) materials, such as actin or tubulin networks, are known to be capable of deforming the shape of cells. Here, elements of that behavior are reproduced in a synthetic system, namely, a giant vesicle suspended in a LC, which we view as a first step toward the preparation of active, anisotropic hybrid systems that mimic some of the functionality encountered in biological systems. To that end, we rely on a coupled particle-continuum representation of deformable networks in a nematic LC represented at the level of a Landau-de Gennes free energy functional. Our results indicate that, depending on its elastic properties, the LC is indeed able to deform the vesicle until it reaches an equilibrium, anisotropic shape. The magnitude of the deformation is determined by a balance of elastic and surface forces. For perpendicular anchoring at the vesicle, a Saturn ring defect forms along the equatorial plane, and the vesicle adopts a pancake-like, oblate shape. For degenerate planar anchoring at the vesicle, two boojum defects are formed at the poles of the vesicle, which adopts an elongated, spheroidal shape. During the deformation, the volume of the topological defects in the LC shrinks considerably as the curvature of the vesicle increases. These predictions are confirmed by our experimental observations of spindle-like shapes in experiments with giant unilamellar vesicles with planar anchoring. We find that the tension of the vesicle suppresses vesicle deformation, whereas anchoring strength and large elastic constants promote shape anisotropy.

Dynamics of Aqueous Droplets at the Interface of Coflowing Immiscible Oils in a Microchannel

We report the dynamics of aqueous droplets of different size and viscosity at the interface of a coflowing stream of immiscible oils (i.e., primary and secondary continuous phases) in a microchannel, at low Re. The lateral migration of droplets introduced into the primary continuous phase toward the interface and subsequent selective migration of droplets across the interface into the secondary continuous phase is investigated. The interplay between the competing noninertial lift and interfacial tension forces, which govern the interfacial migration of the droplets, is presented and discussed. The velocity and strain rate profiles, and interface location, which are critical for calculating the lift force and migration behavior of droplets, are presented. The trajectories of droplets of different size and viscosity in the primary continuous phase are obtained for different interface locations. During interfacial migration, the deformation behavior of droplets of different viscosities is studied. Finally, sorting of droplets based on size contrast is demonstrated and sorting efficiency is found. A new paradigm of migration and sorting of droplets is reported, which could find importance in chemical and biological applications.

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.

Understanding particle margination in blood flow - A step toward optimized drug delivery systems

Targeted delivery of drugs and imaging agents is very promising to develop new strategies for the treatment of various diseases such as cancer. For an efficient targeted adhesion, the particles have to migrate toward the walls in blood flow - a process referred to as margination. Due to a huge diversity of available carriers, a good understanding of their margination properties in blood flow depending on various flow conditions and particle properties is required. We employ a particle-based mesoscopic hydrodynamic simulation approach to investigate the margination of different carriers for a wide range of hematocrits (volume fraction of red blood cells) and flow rates. Our results show that margination strongly depends on the thickness of the available free space close to the wall, the so-called red blood cell-free layer (RBC-FL), in comparison to the carrier size. The carriers with a few micrometers in size are comparable with the RBC-FL thickness and marginate better than their sub-micrometer counterparts. Deformable carriers, in general, show worse margination properties than rigid particles. Particle margination is also found to be most pronounced in small channels with a characteristic size comparable to blood capillaries. Finally, different margination mechanisms are discussed.

Microfluidic Strategies for Understanding the Mechanics of Cells and Cell-Mimetic Systems

Microfluidic systems are attracting increasing interest for the high-throughput measurement of cellular biophysical properties and for the creation of engineered cellular microenvironments. Here we review recent applications of microfluidic technologies to the mechanics of living cells and synthetic cell-mimetic systems. We begin by discussing the use of microfluidic devices to dissect the mechanics of cellular mimics, such as capsules and vesicles. We then explore applications to circulating cells, including erythrocytes and other normal blood cells, and rare populations with potential disease diagnostic value, such as circulating tumor cells. We conclude by discussing how microfluidic devices have been used to investigate the mechanics, chemotaxis, and invasive migration of adherent cells. In these ways, microfluidic technologies represent an increasingly important toolbox for investigating cellular mechanics and motility at high throughput and in a format that lends itself to clinical translation.

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.

Label-free microfluidic enrichment of ring-stage Plasmodium falciparum-infected red blood cells using non-inertial hydrodynamic lift

BACKGROUND

Understanding of malaria pathogenesis caused by Plasmodium falciparum has been greatly deepened since the introduction of in vitro culture system, but the lack of a method to enrich ring-stage parasites remains a technical challenge. Here, a novel way to enrich red blood cells containing parasites in the early ring stage is described and demonstrated.

METHODS

A simple, straight polydimethylsiloxane microchannel connected to two syringe pumps for sample injection and two height reservoirs for sample collection is used to enrich red blood cells containing parasites in the early ring stage (8-10 h p.i.). The separation is based on the non-inertial hydrodynamic lift effect, a repulsive cell-wall interaction that enables continuous and label-free separation with deformability as intrinsic marker.

RESULTS

The possibility to enrich red blood cells containing P. falciparum parasites at ring stage with a throughput of ~12,000 cells per hour and an average enrichment factor of 4.3 ± 0.5 is demonstrated.

CONCLUSION

The method allows for the enrichment of red blood cells early after the invasion by P. falciparum parasites continuously and without any need to label the cells. The approach promises new possibilities to increase the sensitivity of downstream analyses like genomic- or diagnostic tests. The device can be produced as a cheap, disposable chip with mass production technologies and works without expensive peripheral equipment. This makes the approach interesting for the development of new devices for field use in resource poor settings and environments, e.g. with the aim to increase the sensitivity of microscope malaria diagnosis.