Vesicles and red blood cells in shear flow

Modeling Anisotropic Electrical Conductivity of Blood: Translating Microscale Effects of Red Blood Cell Motion into a Macroscale Property of Blood

Cardiovascular diseases are a leading global cause of mortality. The current standard diagnostic methods, such as imaging and invasive procedures, are relatively expensive and partly connected with risks to the patient. Bioimpedance measurements hold the promise to offer rapid, safe, and low-cost alternative diagnostic methods. In the realm of cardiovascular diseases, bioimpedance methods rely on the changing electrical conductivity of blood, which depends on the local hemodynamics. However, the exact dependence of blood conductivity on the hemodynamic parameters is not yet fully understood, and the existing models for this dependence are limited to rather academic flow fields in straight pipes or channels. In this work, we suggest two closely connected anisotropic electrical conductivity models for blood in general three-dimensional flows, which consider the orientation and alignment of red blood cells (RBCs) in shear flows. In shear flows, RBCs adopt preferred orientations through a rotation of their membrane known as tank-treading motion. The two models are built on two different assumptions as to which hemodynamic characteristic determines the preferred orientation. The models are evaluated in two example simulations of blood flow. In a straight rigid vessel, the models coincide and are in accordance with experimental observations. In a simplified aorta geometry, the models yield different results. These differences are analyzed quantitatively, but a validation of the models with experiments is yet outstanding.

Normalization of Blood Viscosity According to the Hematocrit and the Shear Rate

The rheological properties of blood depend highly on the properties of its red blood cells: concentration, membrane elasticity, and aggregation. These properties affect the viscosity of blood as well as its shear thinning behavior. Using an experimental analysis of the interface advancement of blood in a microchannel, we determine the viscosity of different samples of blood. In this work, we present two methods that successfully normalize the viscosity of blood for a single and for different donors, first according to the concentration of erythrocytes and second according to the shear rate. The proposed methodology is able to predict the health conditions of the blood samples by introducing a non-dimensional coefficient that accounts for the response to shear rate of the different donors blood samples. By means of these normalization methods, we were able to determine the differences between the red blood cells of the samples and define a range where healthy blood samples can be described by a single behavior.

Microfluidics Approach to the Mechanical Properties of Red Blood Cell Membrane and Their Effect on Blood Rheology

In this article, we describe the general features of red blood cell membranes and their effect on blood flow and blood rheology. We first present a basic description of membranes and move forward to red blood cell membranes' characteristics and modeling. We later review the specific properties of red blood cells, presenting recent numerical and experimental microfluidics studies that elucidate the effect of the elastic properties of the red blood cell membrane on blood flow and hemorheology. Finally, we describe specific hemorheological pathologies directly related to the mechanical properties of red blood cells and their effect on microcirculation, reviewing microfluidic applications for the diagnosis and treatment of these diseases.

Quantitative Nanomechanical Analysis of Small Extracellular Vesicles for Tumor Malignancy Indication

The nanomechanical properties of tumor-derived small extracellular vesicles (sEVs) are essential to cancer progression. Here, nanoindentation is utilized on atomic force microscopy (AFM) to quantitatively investigate the nanomechanical properties of human breast cancer cell-derived sEVs at single vesicle level and explore their relationship with tumor malignancy and vesicle size. It is demonstrated that the stiffness of the sEVs results from the combined contribution of the bending modulus and osmotic pressure of the sEVs. The stiffness and osmotic pressure increase with increasing malignancy of the sEVs and decrease with increasing size of the sEVs. The bending modulus decreases with increasing malignancy of the sEVs and is lower in smaller sEVs. This study builds relationship between the nanomechanical signature of the sEV and tumor malignancy, adding information for better understanding cancer mechanobiology.

Geometry and dynamics of lipid membranes: The Scriven-Love number

The equations governing lipid membrane dynamics in planar, spherical, and cylindrical geometries are presented here. Unperturbed and first-order perturbed equations are determined and nondimensionalized. In membrane systems with a nonzero base flow, perturbed in-plane and out-of-plane quantities are found to vary over different length scales. A new dimensionless number, named the Scriven-Love number, and the well-known Föppl-von Kármán number result from a scaling analysis. The Scriven-Love number compares out-of-plane forces arising from the in-plane, intramembrane viscous stresses to the familiar elastic bending forces, while the Föppl-von Kármán number compares tension to bending forces. Both numbers are calculated in past experimental works, and span a wide range of values in various biological processes across different geometries. In situations with large Scriven-Love and Föppl-von Kármán numbers, the dynamical response of a perturbed membrane is dominated by out-of-plane viscous and surface tension forces-with bending forces playing a negligible role. Calculations of non-negligible Scriven-Love numbers in various biological processes and in vitro experiments show in-plane intramembrane viscous flows cannot generally be ignored when analyzing lipid membrane behavior.

State diagram for wall adhesion of red blood cells in shear flow: from crawling to flipping

Red blood cells in shear flow show a variety of different shapes due to the complex interplay between hydrodynamics and membrane elasticity. Malaria-infected red blood cells become generally adhesive and less deformable. Adhesion to a substrate leads to a reduction in shape variability and to a flipping motion of the non-spherical shapes during the mid-stage of infection. Here, we present a complete state diagram for wall adhesion of red blood cells in shear flow obtained by simulations, using a particle-based mesoscale hydrodynamics approach, multiparticle collision dynamics. We find that cell flipping at a substrate is replaced by crawling beyond a critical shear rate, which increases with both membrane stiffness and viscosity contrast between the cytosol and suspending medium. This change in cell dynamics resembles the transition between tumbling and tank-treading for red blood cells in free shear flow. In the context of malaria infections, the flipping-crawling transition would strongly increase the adhesive interactions with the vascular endothelium, but might be suppressed by the combined effect of increased elasticity and viscosity contrast.

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.

ATP Release by Red Blood Cells under Flow: Model and Simulations

ATP is a major player as a signaling molecule in blood microcirculation. It is released by red blood cells (RBCs) when they are subjected to shear stresses large enough to induce a sufficient shape deformation. This prominent feature of chemical response to shear stress and RBC deformation constitutes an important link between vessel geometry, flow conditions, and the mechanical properties of RBCs, which are all contributing factors affecting the chemical signals in the process of vasomotor modulation of the precapillary vessel networks. Several in vitro experiments have reported on ATP release by RBCs due to mechanical stress. These studies have considered both intact RBCs as well as cells within which suspected pathways of ATP release have been inhibited. This has provided profound insights to help elucidate the basic governing key elements, yet how the ATP release process takes place in the (intermediate) microcirculation zone is not well understood. We propose here an analytical model of ATP release. The ATP concentration is coupled in a consistent way to RBC dynamics. The release of ATP, or the lack thereof, is assumed to depend on both the local shear stress and the shape change of the membrane. The full chemo-mechanical coupling problem is written in a lattice-Boltzmann formulation and solved numerically in different geometries (straight channels and bifurcations mimicking vessel networks) and under two kinds of imposed flows (shear and Poiseuille flows). Our model remarkably reproduces existing experimental results. It also pinpoints the major contribution of ATP release when cells traverse network bifurcations. This study may aid in further identifying the interplay between mechanical properties and chemical signaling processes involved in blood microcirculation.

Spatial Cross-Correlated Diffusion of Colloids under Shear Flow

The spatial cross-correlated diffusion of colloidal particles is often used as an essential tool to study the dynamic properties of a fluid because it directly describes the hydrodynamic interaction between two particles in a fluid. However, the experimental measurement of cross-correlated diffusion can be substantially modified by even a weak shear flow. In this work, the effect of a shear flow on spatial cross-correlated diffusion is demonstrated using experimental measurements that show a clear dependence on pair angles. An analytical solution is proposed to explain the experimental observations. A numerical simulation is performed to systemically demonstrate the influence of shear flow on spatial cross-correlated diffusion. The results of the experiment, theoretical analysis, and numerical simulation agree well with each other. Therefore, this research provides a sensitive experimental method to determine the weak shear flow in any quasi-two-dimensional fluid systems.

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.

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

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

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.

Focusing and alignment of erythrocytes in a viscoelastic medium

Viscoelastic fluid flow-induced cross-streamline migration has recently received considerable attention because this process provides simple focusing and alignment over a wide range of flow rates. The lateral migration of particles depends on the channel geometry and physicochemical properties of particles. In this study, digital in-line holographic microscopy (DIHM) is employed to investigate the lateral migration of human erythrocytes induced by viscoelastic fluid flow in a rectangular microchannel. DIHM provides 3D spatial distributions of particles and information on particle orientation in the microchannel. The elastic forces generated in the pressure-driven flows of a viscoelastic fluid push suspended particles away from the walls and enforce erythrocytes to have a fixed orientation. Blood cell deformability influences the lateral focusing and fixed orientation in the microchannel. Different from rigid spheres and hardened erythrocytes, deformable normal erythrocytes disperse from the channel center plane, as the flow rate increases. Furthermore, normal erythrocytes have a higher angle of inclination than hardened erythrocytes in the region near the side-walls of the channel. These results may guide the label-free diagnosis of hematological diseases caused by abnormal erythrocyte deformability.

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.

A numerical study on the elastic modulus of volume and area dilation for a deformable cell in a microchannel

A red blood cell (RBC) in a microfluidic channel is highly interesting for scientists in various fields of research on biological systems. This system has been studied extensively by empirical, analytical, and numerical methods. Nonetheless, research of predicting the behavior of an RBC in a microchannel is still an interesting area. The complications arise from deformation of an RBC and interactions among the surrounding fluid, wall, and RBCs. In this study, a pressure-driven RBC in a microchannel was simulated with a three-dimensional lattice Boltzmann method of an immersed boundary. First, the effect of boundary thickness on the interaction between the wall and cell was analyzed by measuring the time of passage through the narrow channel. Second, the effect of volume conservation stiffness was studied. Finally, the effect of global area stiffness was analyzed.

Membranes under shear stress: visualization of non-equilibrium domain patterns and domain fusion in a microfluidic device

In this study we investigate the effect of shear force on lipid membranes induced by external fluid flow. We use giant unilamellar vesicles (GUVs) as simple cell models and chose a ternary lipid mixture that exhibits liquid-ordered and liquid-disordered domains. These domains are stained with different dyes to allow visualization of changes within the membrane after the application of flow. A microfluidic device served as a valuable platform to immobilize the vesicles and apply shear forces of a defined strength. Moreover, integration of valves allowed us to stop the flow instantaneously and visualize the relaxing domain patterns by means of high-resolution fluorescence microscopy. We observed the formation of transient, non-deterministic patterns of the formerly round domains during application of flow. When the flow is stopped, round domains are formed again on a time scale of ms to s. At longer time scales of several seconds to minutes, the domains fuse into larger domains until they reach equilibrium. These processes are accelerated with increasing temperature and vesicles with budding domains do not fuse unless the temperature is elevated. Our results show the strong effect of the flow on the lipid membrane and we believe that this phenomenon plays a crucial role in the processes of mechanotransduction in living cells.

Experimental observation of the asymmetric instability of intermediate-reduced-volume vesicles in extensional flow

Vesicles provide an attractive model system to understand the deformation of living cells in response to mechanical forces. These simple, enclosed lipid bilayer membranes are suitable for complementary theoretical, numerical, and experimental analysis. A recent study [Narsimhan, Spann, Shaqfeh, J. Fluid Mech., 2014, 750, 144] predicted that intermediate-aspect-ratio vesicles extend asymmetrically in extensional flow. Upon infinitesimal perturbation to the vesicle shape, the vesicle stretches into an asymmetric dumbbell with a cylindrical thread separating the two ends. While the symmetric stretching of high-aspect-ratio vesicles in extensional flow has been observed and characterized [Kantsler, Segre, Steinberg, Phys. Rev. Lett., 2008, 101, 048101] as well as recapitulated in numerical simulations by Narsimhan et al., experimental observation of the asymmetric stretching has not been reported. In this work, we present results from microfluidic cross-slot experiments observing this instability, along with careful characterization of the flow field, vesicle shape, and vesicle bending modulus. The onset of this shape transition depends on two non-dimensional parameters: reduced volume (a measure of vesicle asphericity) and capillary number (ratio of viscous to bending forces). We observed that every intermediate-reduced-volume vesicle that extends forms a dumbbell shape that is indeed asymmetric. For the subset of the intermediate-reduced-volume regime we could capture experimentally, we present an experimental phase diagram for asymmetric vesicle stretching that is consistent with the predictions of Narsimhan et al.

Elasto-inertial particle focusing under the viscoelastic flow of DNA solution in a square channel

Particle focusing is an essential step in a wide range of applications such as cell counting and sorting. Recently, viscoelastic particle focusing, which exploits the spatially non-uniform viscoelastic properties of a polymer solution under Poiseuille flow, has attracted much attention because the particles are focused along the channel centerline without any external force. Lateral particle migration in polymer solutions in square channels has been studied due to its practical importance in lab-on-a-chip applications. However, there are still many questions about how the rheological properties of the medium alter the equilibrium particle positions and about the flow rate ranges for particle focusing. In this study, we investigated lateral particle migration in a viscoelastic flow of DNA solution in a square microchannel. The elastic property is relevant due to the long relaxation time of a DNA molecule, even when the DNA concentration is extremely low. Further, the shear viscosity of the solution is essentially constant irrespective of shear rate. Our current results demonstrate that the particles migrate toward the channel centerline and the four corners of a square channel in the dilute DNA solution when the inertia is negligible (elasticity-dominant flow). As the flow rate increases, the multiple equilibrium particle positions are reduced to a single file along the channel centerline, due to the elasto-inertial particle focusing mechanism. The current results support that elasto-inertial particle focusing mechanism is a universal phenomenon in a viscoelastic fluid with constant shear viscosity (Boger fluid). Also, the effective flow rate ranges for three-dimensional particle focusing in the DNA solution were significantly higher and wider than those for the previous synthetic polymer solution case, which facilitates high throughput analysis of particulate systems. In addition, we demonstrated that the DNA solution can be applied to focus a wide range of particle sizes in a single channel and also align red blood cells without any significant deformation.

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.

Microfluidic assessment of mechanical cell damage by extensional stress

Mammalian cells have been widely used in bioreactors to produce biological products such as pharmaceutical materials. The productivity of such bioreactors is vastly affected by flow-induced cell damage in complicated flow environments, such as agitation-driven turbulence and oxygen bubble bursting at the interface between the culturing medium and air. However, there is no systematic approach to diagnose the cell damage caused by the hydrodynamic stress. In this work, we propose a novel microfluidic method to accurately assess the mechanical cell damage under a controlled extensional stress field, generated in a microfluidic cross-slot geometry. The cell damage in the extensional field is related to the oxygen bubble bursting process. We employed viscoelasticity-induced particle focusing to align the cells along the shear-free channel centerline, so that all the cells experience a similar extensional stress field, which also precludes the cell damage due to wall shear stress. We applied our novel microfluidic sensor to find the critical extensional stress to damage Chinese hamster ovary (CHO) cells; the critical stress is found to be ∼250 Pa. Our current results are relevant in the design of practical bioreactors, as our results clearly demonstrate that the control of the bubble bursting process is critical in minimizing cell damage in bioreactor applications. Further, our results will provide useful information on the biophysical cell properties under fluid flow environments.

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.

Microfluidic study of enhanced deposition of sickle cells at acute corners

Sickle cell anemia is a blood disorder, known to affect the microcirculation and is characterized by painful vaso-occlusive crises in deep tissues. During the last three decades, many scenarios based on the enhanced adhesive properties of the membrane of sickle red blood cells have been proposed, all related to a final decrease in vessels lumen by cells accumulation on the vascular walls. Up to now, none of these scenarios considered the possible role played by the geometry of the flow on deposition. The question of the exact locations of occlusive events at the microcirculatory scale remains open. Here, using microfluidic devices where both geometry and oxygen levels can be controlled, we show that the flow of a suspension of sickle red blood cells around an acute corner of a triangular pillar or of a bifurcation, leads to the enhanced deposition and aggregation of cells. Thanks to our devices, we follow the growth of these aggregates in time and show that their length does not depend on oxygenation levels; instead, we find that their morphology changes dramatically to filamentous structures when using autologous plasma as a suspending fluid. We finally discuss the possible role played by such aggregates in vaso-occlusive events.

Polymer-mediated interactions and their effect on the coagulation-fragmentation of nano-colloids: a self-consistent field theory approach

This feature paper reviews our recent efforts to theoretically model the effect of polymer mediated interactions on the coagulation-fragmentation of nano-colloids in different settings encountered in practical systems. The polymer-mediated interactions among nanoparticles play a key role in many biological and technological processes such as red blood cell aggregation, protein crystallization, self-healing of polymer composites, filler reinforcement of rubbers used in tire technology, etc. By developing and making use of the novel potential theory, we investigate several important cases of these interactions acting between nanoparticles in diverse nano-polymer composites. As a demonstration of its practical applicability, we use the developed theory to investigate the effect of polymer mediated interactions on the coagulation-fragmentation of fillers and their kinetic stability in the presence of non-adsorbing and adsorbing polymers. In particular, we use our findings to develop a pragmatic way of evaluating the kinetic stability of nano-filler agglomerates critical for understanding the filler reinforcement of rubbers. Finally, we perform thorough comparison of the present theoretical findings with the available experimental data and simulations.

Diffuse interface models of locally inextensible vesicles in a viscous fluid

We present a new diffuse interface model for the dynamics of inextensible vesicles in a viscous fluid with inertial forces. A new feature of this work is the implementation of the local inextensibility condition in the diffuse interface context. Local inextensibility is enforced by using a local Lagrange multiplier, which provides the necessary tension force at the interface. We introduce a new equation for the local Lagrange multiplier whose solution essentially provides a harmonic extension of the multiplier off the interface while maintaining the local inextensibility constraint near the interface. We also develop a local relaxation scheme that dynamically corrects local stretching/compression errors thereby preventing their accumulation. Asymptotic analysis is presented that shows that our new system converges to a relaxed version of the inextensible sharp interface model. This is also verified numerically. To solve the equations, we use an adaptive finite element method with implicit coupling between the Navier-Stokes and the diffuse interface inextensibility equations. Numerical simulations of a single vesicle in a shear flow at different Reynolds numbers demonstrate that errors in enforcing local inextensibility may accumulate and lead to large differences in the dynamics in the tumbling regime and smaller differences in the inclination angle of vesicles in the tank-treading regime. The local relaxation algorithm is shown to prevent the accumulation of stretching and compression errors very effectively. Simulations of two vesicles in an extensional flow show that local inextensibility plays an important role when vesicles are in close proximity by inhibiting fluid drainage in the near contact region.

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.

Vesicle dynamics in a confined Poiseuille flow: from steady state to chaos

Red blood cells (RBCs) are the major component of blood, and the flow of blood is dictated by that of RBCs. We employ vesicles, which consist of closed bilayer membranes enclosing a fluid, as a model system to study the behavior of RBCs under a confined Poiseuille flow. We extensively explore two main parameters: (i) the degree of confinement of vesicles within the channel and (ii) the flow strength. Rich and complex dynamics for vesicles are revealed, ranging from steady-state shapes (in the form of parachute and slipper shapes) to chaotic dynamics of shape. Chaos occurs through a cascade of multiple periodic oscillations of the vesicle shape. We summarize our results in a phase diagram in the parameter plane (degree of confinement and flow strength). This finding highlights the level of complexity of a flowing vesicle in the small Reynolds number where the flow is laminar in the absence of vesicles and can be rendered turbulent due to elasticity of vesicles.

Probing red blood cell mechanics, rheology and dynamics with a two-component multi-scale model

This study is partially motivated by the validation of a new two-component multi-scale cell model we developed recently that treats the lipid bilayer and the cytoskeleton as two distinct components. Here, the whole cell model is validated and compared against several available experiments that examine red blood cell (RBC) mechanics, rheology and dynamics. First, we investigated RBC deformability in a microfluidic channel with a very small cross-sectional area and quantified the mechanical properties of the RBC membrane. Second, we simulated twisting torque cytometry and compared predicted rheological properties of the RBC membrane with experimental measurements. Finally, we modelled the tank-treading (TT) motion of a RBC in a shear flow and explored the effect of channel width variation on the TT frequency. We also investigated the effects of bilayer-cytoskeletal interactions on these experiments and our simulations clearly indicated that they play key roles in the determination of cell membrane mechanical, rheological and dynamical properties. These simulations serve as validation tests and moreover reveal the capabilities and limitations of the new whole cell model.

Fluid vesicles in flow

We review the dynamical behavior of giant fluid vesicles in various types of external hydrodynamic flow. The interplay between stresses arising from membrane elasticity, hydrodynamic flows, and the ever present thermal fluctuations leads to a rich phenomenology. In linear flows with both rotational and elongational components, the properties of the tank-treading and tumbling motions are now well described by theoretical and numerical models. At the transition between these two regimes, strong shape deformations and amplification of thermal fluctuations generate a new regime called trembling. In this regime, the vesicle orientation oscillates quasi-periodically around the flow direction while asymmetric deformations occur. For strong enough flows, small-wavelength deformations like wrinkles are observed, similar to what happens in a suddenly reversed elongational flow. In steady elongational flow, vesicles with large excess areas deform into dumbbells at large flow rates and pearling occurs for even stronger flows. In capillary flows with parabolic flow profile, single vesicles migrate towards the center of the channel, where they adopt symmetric shapes, for two reasons. First, walls exert a hydrodynamic lift force which pushes them away. Second, shear stresses are minimal at the tip of the flow. However, symmetry is broken for vesicles with large excess areas, which flow off-center and deform asymmetrically. In suspensions, hydrodynamic interactions between vesicles add up to these two effects, making it challenging to deduce rheological properties from the dynamics of individual vesicles. Further investigations of vesicles and similar objects and their suspensions in steady or time-dependent flow will shed light on phenomena such as blood flow.

Hydrodynamic lift of vesicles and red blood cells in flow--from Fåhræus & Lindqvist to microfluidic cell sorting

Hydrodynamic lift forces acting on cells and particles in fluid flow receive ongoing attention from medicine, mathematics, physics and engineering. The early findings of Fåhræus & Lindqvist on the viscosity change of blood with the diameter of capillaries motivated extensive studies both experimentally and theoretically to illuminate the underlying physics. We review this historical development that led to the discovery of the inertial and non-inertial lift forces and elucidate the origins of these forces that are still not entirely clear. Exploiting microfluidic techniques induced a tremendous amount of new insights especially into the more complex interactions between the flow field and deformable objects like vesicles or red blood cells. We trace the way from the investigation of single cell dynamics to the recent developments of microfluidic techniques for particle and cell sorting using hydrodynamic forces. Such continuous and label-free on-chip cell sorting devices promise to revolutionize medical analyses for personalized point-of-care diagnosis. We present the state-of-the-art of different hydrodynamic lift-based techniques and discuss their advantages and limitations.

Inertia-dependent dynamics of three-dimensional vesicles and red blood cells in shear flow

A three-dimensional (3D) simulation study of the effect of inertia on the dynamics of vesicles and red blood cells (RBCs) has not been reported. Here, we developed a 3D model based on the front tracking method to investigate how inertia affects the dynamics of spherical/non-spherical vesicles and biconcave-shaped RBCs with the Reynolds number ranging from 0.1 to 10. The results showed that inertia induced non-spherical vesicles transitioned from tumbling to swinging, which was not observed in previous 2D models. The critical viscosity ratio of inner/outer fluids for the tumbling–swinging transition remarkably increased with an increasing Reynolds number. The deformation of vesicles was greatly enhanced by inertia, and the frequency of tumbling and tank-treading was significantly decreased by inertia. We also found that RBCs can transit from tumbling to steady tank-treading through the swinging regime when the Reynolds number increased from 0.1 to 10. These results indicate that inertia needs to be considered at moderate Reynolds number (Re ~ 1) in the study of blood flow in the human body and the flow of deformable particle suspension in inertial microfluidic devices. The developed 3D model provided new insights into the dynamics of RBCs under shear flow, thus holding great potential to better understand blood flow behaviors under normal/disease conditions.

Sorting of circulating tumor cells (MV3-melanoma) and red blood cells using non-inertial lift

We demonstrate the method of non-inertial lift induced cell sorting (NILICS), a continuous, passive, and label-free cell sorting approach in a simple single layer microfluidic device at low Reynolds number flow conditions. In the experiments, we exploit the non-inertial lift effect to sort circulating MV3-melanoma cells from red blood cell suspensions at different hematocrits as high as 9%. We analyze the separation process and the influence of hematocrit and volume flow rates. We achieve sorting efficiencies for MV3-cells up to EMV3 = 100% at Hct = 9% and demonstrate cell viability by recultivation of the sorted cells.

Sedimentation-induced tether on a settling vesicle

Destabilization of soft interfaces into thin cylindrical filaments under external stresses is ubiquitous and is generally the first step toward breakup. We show that such filaments, called tethers, emerge from a vesicle subjected to gravity. Contrary to the pendant drop experiment, we demonstrate that the bending rigidity, a specific membrane property of vesicles, ensures the tethers reach a stationary state. Moreover, unlike point-like force experiments, we show that the family of shapes is continuous.

Noisy nonlinear dynamics of vesicles in flow

We present a model for the dynamics of fluid vesicles in linear flow which consistently includes thermal fluctuations and nonlinear coupling between different modes. At the transition between tank treading and tumbling, we predict a trembling motion which is at odds with the known deterministic motions and for which thermal noise is strongly amplified. In particular, highly asymmetric shapes are observed even though the deterministic flow only allows for axisymmetric ones. Our results explain quantitatively recent experimental observations [Levant and Steinberg, Phys. Rev. Lett. 109, 268103 (2012)].

Hydrodynamic mechanisms of cell and particle trapping in microfluidics

Focusing and sorting cells and particles utilizing microfluidic phenomena have been flourishing areas of development in recent years. These processes are largely beneficial in biomedical applications and fundamental studies of cell biology as they provide cost-effective and point-of-care miniaturized diagnostic devices and rare cell enrichment techniques. Due to inherent problems of isolation methods based on the biomarkers and antigens, separation approaches exploiting physical characteristics of cells of interest, such as size, deformability, and electric and magnetic properties, have gained currency in many medical assays. Here, we present an overview of the cell/particle sorting techniques by harnessing intrinsic hydrodynamic effects in microchannels. Our emphasis is on the underlying fluid dynamical mechanisms causing cross stream migration of objects in shear and vortical flows. We also highlight the advantages and drawbacks of each method in terms of throughput, separation efficiency, and cell viability. Finally, we discuss the future research areas for extending the scope of hydrodynamic mechanisms and exploring new physical directions for microfluidic applications.

Continuum- and particle-based modeling of shapes and dynamics of red blood cells in health and disease

We review recent advances in multiscale modeling of the mechanics of healthy and diseased red blood cells (RBCs), and blood flow in the microcirculation. We cover the traditional continuum-based methods but also particle-based methods used to model both the RBCs and the blood plasma. We highlight examples of successful simulations of blood flow including malaria and sickle cell anemia.

Flow loading induces oscillatory trajectories in a bloodstream parasite

The dynamics of isolated microswimmers are studied in bounded flow using the African trypanosome, a unicellular parasite, as the model organism. With the help of a microfluidics platform, cells are subjected to flow and found to follow an oscillatory path that is well fit by a sine wave. The frequency and amplitudes of the oscillatory trajectories are dependent on the flow velocity and cell orientation. When traveling in such a manner, trypanosomes orient upstream while downstream-facing cells tumble within the same streamline. A comparison with immotile trypanosomes demonstrates that self-propulsion is essential to the trajectories of trypanosomes even at flow velocities up to ∼40 times higher than their own swimming speed. These studies reveal important swimming dynamics that may be generally pertinent to the transport of microswimmers in flow and may be relevant to microbial pathogenesis.

Effect of thermal noise on vesicles and capsules in shear flow

We add thermal noise consistently to reduced models of undeformable vesicles and capsules in shear flow and derive analytically the corresponding stochastic equations of motion. We calculate the steady-state probability distribution function and construct the corresponding phase diagrams for the different dynamical regimes. For fluid vesicles, we predict that at small shear rates thermal fluctuations induce a tumbling motion for any viscosity contrast. For elastic capsules, due to thermal mixing, an intermittent regime appears in regions where deterministic models predict only pure tank treading or tumbling.

Injectable solid peptide hydrogel as a cell carrier: effects of shear flow on hydrogels and cell payload

β-hairpin peptide-based hydrogels are a class of injectable solid hydrogels that can deliver encapsulated cells or molecular therapies to a target site via syringe or catheter injection as a carrier material. These physical hydrogels can shear-thin and consequently flow as a low-viscosity material under a sufficient shear stress but immediately recover back into a solid upon removal of the stress, allowing them to be injected as preformed gel solids. Hydrogel behavior during flow was studied in a cylindrical capillary geometry that mimicked the actual situation of injection through a syringe needle in order to quantify effects of shear-thin injection delivery on hydrogel flow behavior and encapsulated cell payloads. It was observed that all β-hairpin peptide hydrogels investigated displayed a promising flow profile for injectable cell delivery: a central wide plug flow region where gel material and cell payloads experienced little or no shear rate, and a narrow shear zone close to the capillary wall where gel and cells were subject to shear deformation. The width of the plug flow region was found to be weakly dependent on hydrogel rigidity and flow rate. Live-dead assays were performed on encapsulated MG63 cells 3 h after injection flow and revealed that shear-thin delivery through the capillary had little impact on cell viability and the spatial distribution of encapsulated cell payloads. These observations help us to fundamentally understand how the gels flow during injection through a thin catheter and how they immediately restore mechanically and morphologically relative to preflow, static gels.

Microchip-based plasma separation from whole blood via axial migration of blood cells

Highly efficient cell-free plasma separation from 200 µL of human whole blood was realized via axial migration of blood cells and cross-flow filtration in a microchip. Although various analyses of small volumes of blood have been reported, a large volume of blood is necessary for obtaining blood cells and plasma for the conventional plasma separation technique of centrifugation. A highly efficient plasma separation method using small volumes of blood without hemolysis is an important issue. We developed a plasma separation method based on a microchip with a filter, which utilizes the axial migration of blood cells observed in blood vessels. Clogging and hemolysis on the filter can be prevented by the axial migration of the blood cells. Using this method, 65% of the plasma from 200 µL of whole blood was successfully separated without hemolysis. When the plasma separation microchip interfaced with a micro-ELISA system was applied to C-reactive protein (CRP) analysis, the CRP concentration obtained by the microchip showed good correlation with that obtained by conventional centrifugation. Total analysis time, including plasma separation, was achieved in only 25 min.

Integration of geometric separation mechanisms by implementing curved constrictions in a biochip microchannel fluidic separator

This paper investigates the effectiveness of using curved constrictions in the bifurcation region of T-type fluid separators for promoting flow development in the intervals between bifurcations. A design of biofluid separator is proposed and a mathematical analysis and a numerical simulation of the blood flow in microchannels are conducted. The design is based on a modification of an existing T-shaped biochip device which consists of a main channel and a series of perpendicularly positioned side channels. By means of bifurcation effect, the blood is separated into plasma concentration flow from the side channels and blood cell concentration flow from the main channel. In this design, curved constrictions are inserted between bifurcations to replace the original straight channel section, so that the constriction and curved channel effects can be induced apart from the existing bifurcation effect. The mathematical analysis is aimed to the flow field and shear stress of the blood fluid in the microchannel geometries employed in the current design, including bifurcation, constriction and curved channel. The numerical simulation and mathematical analysis result in agreed conclusions, giving some insights into the importance of the relevant geometries in promoting biofluid separation. The main results can be summarised as follows: (i) the constrictions can largely increase the shear stress by the ratio of square of the reduction of the sections between the constriction and parent main channel. (ii) The curved channel intervals can induce centrifugal force, smoothly transit the flow field and increase the chances depleting fluid from the cell-free layer. (iii) The thickness of the boundary layer skimmed into the side channels from the main channel is decreased in this design and can be controlled, falling into the cell-free layer region by adjusting the geometry of the side channels.