Influence of storage and buffer composition on the mechanical behavior of flowing red blood cells.

On-chip study of blood flow has emerged as a powerful tool to assess the contribution of each component of blood to its overall function. Blood has indeed many functions, from gas and nutrient transport to immune response and thermal regulation. Red blood cells play a central role therein, in particular through their specific mechanical properties, which directly influence pressure regulation, oxygen perfusion, or platelet and white cell segregation toward endothelial walls. As the bloom of in-vitro studies has led to the apparition of various storage and sample preparation protocols, we address the question of the robustness of the results involving cell mechanical behavior against this diversity. The effects of three conservation media (EDTA, citrate, and glucose-albumin-sodium-phosphate) and storage time on the red blood cell mechanical behavior are assessed under different flow conditions: cell deformability by ektacytometry, shape recovery of cells flowing out of a microfluidic constriction, and cell-flipping dynamics under shear flow. The impact of buffer solutions (phosphate-buffered saline and density-matched suspension using iodixanol/Optiprep) are also studied by investigating individual cell-flipping dynamics, relative viscosity of cell suspensions, and cell structuration under Poiseuille flow. Our results reveal that storing blood samples up to 7 days after withdrawal and suspending them in adequate density-matched buffer solutions has, in most experiments, a moderate effect on the overall mechanical response, with a possible rapid evolution in the first 3 days after sample collection.

Molecular rotors as intracellular probes of red blood cell stiffness.

The deformability of red blood cells is an essential parameter that controls the rheology of blood as well as its circulation in the body. Characterizing the rigidity of the cells and their heterogeneity in a blood sample is thus a key point in the understanding of occlusive phenomena, particularly in the case of erythrocytic diseases in which healthy cells coexist with pathological cells. However, measuring intracellular rheology in small biological compartments requires the development of specific techniques. We propose a technique based on molecular rotors - viscosity-sensitive fluorescent probes - to evaluate the above key point. DASPI molecular rotor has been identified with spectral fluorescence properties decoupled from those of hemoglobin, the main component of the cytosol. After validation of the rotor as a viscosity probe in model fluids, we showed by confocal microscopy that, in addition to binding to the membrane, the rotor penetrates spontaneously and uniformly into red blood cells. Experiments on red blood cells whose rigidity is varied with temperature, show that molecular rotors can detect variations in their overall rigidity. A simple model allowed us to separate the contribution of the cytosol from that of the membrane, allowing a qualitative determination of the variation of cytosol viscosity with temperature, consistent with independent measurements of the viscosity of hemoglobin solutions. Our experiments show that the rotor can be used to study the intracellular rheology of red blood cells at the cellular level, as well as the heterogeneity of this stiffness in a blood sample. This opens up new possibilities for biomedical applications, diagnosis and disease monitoring.

Vortical flow structures induced by red blood cells in capillaries.

OBJECTIVE: Knowledge about the flow field of the plasma around the red blood cells in capillary flow is important for a physical understanding of blood flow and the transport of micro- and nanoparticles and molecules in the flowing plasma. We conducted an experimental study on the flow field around red blood cells in capillary flow that is complemented by simulations of vortical flow between red blood cells. METHODS: Red blood cells were injected in a 10 × 12 µm rectangular microchannel at a low hematocrit, and the flow field around one or two cells was captured by a high-speed camera that tracked 250 nm nanoparticles in the flow field, acting as tracers. RESULTS: While the flow field around a steady "croissant" shape is found to be similar to that of a rigid sphere, the flow field around a "slipper" shape exhibits a small vortex at the rear of the red blood cell. Even more pronounced are vortex-like structures observed in the central region between two neighboring croissants. CONCLUSIONS: The rotation frequency of the vortices is to a good approximation, inversely proportional to the distance between the cells. Our experimental data are complemented by numerical simulations.

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.

Effect of spectrin network elasticity on the shapes of erythrocyte doublets.

Red blood cell (RBC) aggregates play an important role in determining blood rheology. RBCs in plasma or polymer solution interact attractively to form various shapes of RBC doublets, where the attractive interactions can be varied by changing the solution conditions. A systematic numerical study on RBC doublet formation is performed, which takes into account the shear elasticity of the RBC membrane due to the spectrin cytoskeleton, in addition to the membrane bending rigidity. RBC membranes are modeled by two-dimensional triangular networks of linked vertices, which represent three-dimensional cell shapes. The phase space of RBC doublet shapes in a wide range of adhesion strengths, reduced volumes, and shear elasticities is obtained. The shear elasticity of the RBC membrane changes the doublet phases significantly. Experimental images of RBC doublets in different solutions show similar configurations. Furthermore, we show that rouleau formation is affected by the doublet structure.

The buckling instability of aggregating red blood cells.

Plasma proteins such as fibrinogen induce the aggregation of red blood cells (RBC) into rouleaux, which are responsible for the pronounced shear thinning behavior of blood, control the erythrocyte sedimentation rate (ESR) - a common hematological test - and are involved in many situations of physiological relevance such as structuration of blood in the microcirculation or clot formation in pathological situations. Confocal microscopy is used to characterize the shape of RBCs within rouleaux at equilibrium as a function of macromolecular concentration, revealing the diversity of contact zone morphology. Three different configurations that have only been partly predicted before are identified, namely parachute, male-female and sigmoid shapes, and quantitatively recovered by numerical simulations. A detailed experimental and theoretical analysis of clusters of two cells shows that the deformation increases nonlinearly with the interaction energy. Models indicate a forward bifurcation in which the contacting membrane undergoes a buckling instability from a flat to a deformed contact zone at a critical value of the interaction energy. These results are not only relevant for the understanding of the morphology and stability of RBC aggregates, but also for a whole class of interacting soft deformable objects such as vesicles, capsules or cells in tissues.

Inversion of hematocrit partition at microfluidic bifurcations.

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

Fully automated digital holographic processing for monitoring the dynamics of a vesicle suspension under shear flow.

We investigate the dynamics of a vesicle suspension under shear flow between plates using DHM with a spatially reduced coherent source. Holograms are grabbed at a frequency of 24 frames/sec. The distribution of the vesicle suspension is obtained after numerical processing of the digital holograms sequence resulting in a 4D distribution. Obtaining this distribution is not straightforward and requires special processing to automate the analysis. We present an original method that fully automates the analysis and provides distributions that are further analyzed to extract physical properties of the fluid. Details of the numerical implementation, as well as sample experimental results are presented.

Lift and down-gradient shear-induced diffusion in red blood cell suspensions.

The distribution of red blood cells (RBCs) in a confined channel flow is inhomogeneous and shows a marked depletion near the walls due to a competition between migration away from the walls and shear-induced diffusion resulting from interactions between particles. We investigated the lift of RBCs in a shear flow near a wall and measured a significant lift velocity despite the tumbling motion of cells. We also provide values for the collective and anisotropic shear-induced diffusion of a cloud of RBCs, both in the direction of shear and in the direction of vorticity. A generic down-gradient subdiffusion characterized by an exponent 1/3 is highlighted.

Shape diagram of vesicles in Poiseuille flow.

Soft bodies flowing in a channel often exhibit parachutelike shapes usually attributed to an increase of hydrodynamic constraint (viscous stress and/or confinement). We show that the presence of a fluid membrane leads to the reverse phenomenon and build a phase diagram of shapes-which are classified as bullet, croissant, and parachute-in channels of varying aspect ratio. Unexpectedly, shapes are relatively wider in the narrowest direction of the channel. We highlight the role of flow patterns on the membrane in this response to the asymmetry of stress distribution.

Fast measurements of concentration profiles inside deformable objects in microflows with reduced spatial coherence digital holography.

We investigate the use of a digital holographic microscope working with partially coherent spatial illumination to study concentration profiles inside confined deformable bodies flowing in microchannels. The studied phenomenon is rapidly changing in time and requires the recording of the complete holographic information for every frame. For this purpose, we implemented one of the classical methods of off-axis digital holography: the Fourier method. Digital holography allows one to numerically investigate a volume by refocusing the different planes of depth, allowing one to locate the objects under investigation in three dimensions. Furthermore, the phase is directly related to the refractive index, thus to the concentration inside the body. Based on simple symmetry assumptions, we present an original method for determining the concentration profiles inside deformable objects in microconfined flows. Details of the optical and numerical implementation, as well as exemplative experimental results are presented.

Micro-macro link in rheology of erythrocyte and vesicle suspensions.

We report on the rheology of dilute suspensions of red blood cells (RBC) and vesicles. The viscosity of RBC suspensions reveals a previously unknown signature: it exhibits a pronounced minimum when the viscosity of the ambient medium is close to the value at which the transition from tank-treading to tumbling occurs. This bifurcation is triggered by varying the viscosity of the ambient fluid. It is found that the intrinsic viscosity of the suspension varies by about a factor of 4 in the explored parameter range. Surprisingly, this significant change of the intrinsic viscosity is revealed even at low hematocrit (5%). We suggest that this finding may be used to detect blood flow disorders linked to pathologies that affect RBC shape and mechanical properties. This opens future perspectives on setting up new diagnostic tools, with great efficiency even at very low hematocrit. Investigations are also performed on giant vesicle suspensions, and compared to RBCs.

Dynamics and rheology of a dilute suspension of vesicles: higher-order theory.

Vesicles under shear flow exhibit various dynamics: tank treading (TT), tumbling (TB), and vacillating breathing (VB). The VB mode consists in a motion where the long axis of the vesicle oscillates about the flow direction, while the shape undergoes a breathing dynamics. We extend here the original small deformation theory [C. Misbah, Phys. Rev. Lett. 96, 028104 (2006)] to the next order in a consistent manner. The consistent higher order theory reveals a direct bifurcation from TT to TB if Ca identical with taugamma is small enough-typically below 0.5, but this value is sensitive to the available excess area from a sphere (tau=vesicle relaxation time towards equilibrium shape, gamma=shear rate). At larger Ca the TB is preceded by the VB mode. For Ca1 we recover the leading order original calculation, where the VB mode coexists with TB. The consistent calculation reveals several quantitative discrepancies with recent works, and points to new features. We briefly analyze rheology and find that the effective viscosity exhibits a minimum in the vicinity of the TT-TB and TT-VB bifurcation points. At small Ca the minimum corresponds to a cusp singularity and is at the TT-TB threshold, while at high enough Ca the cusp is smeared out, and is located in the vicinity of the VB mode but in the TT regime.

Fingering instabilities of a reactive micellar interface.

We present an experimental study of the fingering patterns in a Hele-Shaw cell occurring when a gel-like material forms at the interface between aqueous solutions of a cationic surfactant (cetyltrimethylammonium bromide) and an organic salt (salicylic acid), two solutions known to form a highly elastic wormlike micellar fluid when mixed homogeneously. A variety of fingering instabilities are observed, depending on the velocity of the front (the injection rate), and on which fluid is injected into which. We have found a regime of nonconfined stationary or wavy fingers for which width selection seems to occur without the presence of bounding walls, unlike the Saffman-Taylor experiment. Qualitatively, some of our observations share common mechanisms with instabilities of cooling lava flows or growing biofilms.