We use mesoscale numerical simulations to investigate the unsteady dynamics of a single red blood cell (RBC) subjected to an external mechanical load. We carry out a detailed comparison between the {\it loading} (L) dynamics, following the imposition of the mechanical load on the RBC at rest, and the {\it relaxation} (R) dynamics, allowing the RBC to relax to its original shape after the sudden arrest of the mechanical load. Such a comparison is carried out by analyzing the characteristic times of the two corresponding dynamics, i.e., $t_L$ and $t_R$. When the intensity of the mechanical load is small enough, the two kinds of dynamics are {\it symmetrical} ($t_L \approx t_R$) and independent of the typology of mechanical load (intrinsic dynamics); otherwise, in marked contrast, an {\it asymmetry} is found, wherein the loading dynamics is typically faster than the relaxation one. This asymmetry manifests itself with non-universal characteristics, e.g., dependency on the applied load and/or on the viscoelastic properties of the RBC membrane. To deepen such a non-universal behaviour, we consider the viscosity of the erythrocyte membrane as a variable parameter and focus on three different typologies of mechanical load (mechanical stretching, shear flow, elongational flow): this allows to clarify how non-universality builds up in terms of the deformation and rotational contributions induced by the mechanical load on the membrane. Finally, we also investigate the effect of the elastic shear modulus on the characteristic times $t_L$ and $t_R$. Our results provide crucial and quantitative information on the unsteady dynamics of RBC and its membrane response to the imposition/cessation of external mechanical loads.
We use numerical simulations to study the dynamics of red blood cells (RBCs) in unconfined and confined Poiseuille flow. Previous numerical studies with 3D vesicles have indicated that the slipper shape observed in experiments at high capillary number can be attributed to the bistability due to the interplay of wall push and outward migration tendency at higher viscosity contrasts. In this paper, we study this outward migration and bistability using numerical simulations for 3D capsules and provide phase diagrams of RBC dynamics with and without viscosity contrast. We observe a bistability of …
Blood exhibits a heterogeneous nature of hematocrit, velocity, and effective viscosity in microcapillaries. Microvascular bifurcations have a significant influence on the distribution of the blood cells and blood flow behavior. This paper presents a simulation study performed on the two-dimensionalmotions and deformation of multiple red blood cells in microvessels with diverging and converging bifurcations. Fluid dynamics and membrane mechanics were incorporated. Effects of cell shape, hematocrit, and deformability of the cell membrane on rheological behavior of the red blood cells and the hem…
The supply of oxygen and nutrients and the disposal of metabolic waste in the organs depend strongly on how blood, especially red blood cells, flow through the microvascular network. Macromolecular plasma proteins such as fibrinogen cause red blood cells to form large aggregates, called rouleaux, which are usually assumed to be disaggregated in the circulation due to the shear forces present in bulk flow. This leads to the assumption that rouleaux formation is only relevant in the venule network and in arterioles at low shear rates or stasis. Thanks to an excellent agreement between combined e…
Red blood cells (RBCs) are an essential component of blood. A method to include the particulate nature of blood is introduced here with the goal of studying circulation in large-scale realistic vessels. The method uses a combination of the Lattice Boltzmann method (LBM) to account for the plasma motion, and a modified Molecular Dynamics scheme for the cellular motion. Numerical results illustrate the quality of the model in reproducing known rheological properties of blood as much as revealing the effect of RBC structuring on the wall shear stress, with consequences on the development of cardi…
The unique ability of a red blood cell to flow through extremely small microcapillaries depends on the viscoelastic properties of its membrane. Here, we study in vitro the response time upon flow startup exhibited by red blood cells confined into microchannels. We show that the characteristic transient time depends on the imposed flow strength, and that such a dependence gives access to both the effective viscosity and the elastic modulus controlling the temporal response of red cells. A simple theoretical analysis of our experimental data, validated by numerical simulations, further allows us…
The distribution of Red Blood Cells 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 subdiffusi…
We consider the motion of red blood cells and other non-spherical microcapsules dilutely suspended in a simple shear flow. Our analysis indicates that depending on the viscosity, membrane elasticity, geometry and shear rate, the particle exhibits either tumbling, tank-treading of the membrane about the viscous interior with periodic oscillations of the orientation angle, or intermittent behavior in which the two modes occur alternately. For red blood cells, we compute the complete phase diagram and identify a novel tank-treading-to-tumbling transition at low shear rates. Observations of such m…
Constrictions in blood vessels and microfluidic devices can dramatically change the spatial distribution of passing cells or particles and are commonly used in biomedical cell sorting applications. However, the three-dimensional nature of cell focusing in the channel cross-section remains poorly investigated. Here, we explore the cross-sectional distribution of living and rigid red blood cells passing a constricted microfluidic channel by tracking individual cells in multiple layers across the channel depth and across the channel width. While cells are homogeneously distributed in the channel …
An exhaustive description of the dynamics under shear flow of a large number of red blood cells in dilute regime is proposed, which highlights and takes into account the dispersion in cell properties within a given blood sample. Physiological suspending fluid viscosity is considered, a configuration surprisingly seldom considered in experimental studies, as well as a more viscous fluid that is a reference in the literature. Stable and unstable flipping motions well described by Jeffery orbits or modified Jeffery orbits are identified, as well as transitions to and from tank-treading motion in …
Despite its significance in microfluidics, the effect of confinement on the transition from the tank-treading (steady motion) to the tumbling (unsteady motion) dynamical state of deformable micro-particles has not been studied in detail. In this paper, we investigate the dynamics of a single viscous vesicle under confining shear as a general model system for red blood cells, capsules, or viscous droplets. The transition from tank-treading to tumbling motion can be triggered by the ratio between internal and external fluid viscosities. Here, we show that the transition can be induced solely by …
We measure the dynamical mechanical properties of human red blood cells. Single cell response is measured with optical tweezers. We investigate both the stress relaxation following a fast deformation, and the effect of varying the strain rate. We find a power law decay of the stress as a function of time, down to a plateau stress, and a power law increase of the cell's elasticity as a function of the strain rate. Interestingly, the exponents of these quantities violate the linear superposition principle, indicating a nonlinear response. We propose that this is due to breaking of a fraction of …
We study a Gaussian model of the membrane of red blood cells: a "phantom" triangular network of springs attached at its vertices to a fluid bilayer with curvature elasticity and tension. We calculate its fluctuation spectrum and we discuss the different regimes and non-monotonic features, including the precise crossover at the mesh size between the already known limits with two different tensions and the renormalisation of the bending rigidity at low wavevectors. We also show that the non-diagonal correlations reveal, in "dark field", the cytoskeletal defects. As a first step toward a non-inva…
Despite the fact that red blood cells carry negative charges, under certain conditions they form cylindrical stacks, or ``rouleaux''. It is shown here that a form of the Casimir effect, generalizing the more well-known van der Waals forces, can provide the necessary attractive force to balance the electrostatic repulsion. Erythrocytes in plasma are modelled as negatively charged dielectric disks in an ionic solution, allowing predictions to be made about the conditions under which rouleaux will form. The results show qualitative and quantitative agreement with observations, and suggest new exp…
The dynamics of single red blood cells (RBCs) determine microvascular blood flow by adapting their shape to the flow conditions in the narrow vessels. In this study, we explore the dynamics and shape transitions of RBCs on the cellular scale under confined and unsteady flow conditions using a combination of microfluidic experiments and numerical simulations. Tracking RBCs in a comoving frame in time-dependent flows reveals that the mean transition time from the symmetric croissant to the off-centered, non-symmetric slipper shape is significantly faster than the opposite shape transition, which…
We investigate the shear thinning of red blood cell - dextran suspensions. Microscopic images show that at low polymer concentration, aggregation increases with increasing concentration until it reaches a maximum and then decreases again to non-aggregation. This bell shape dependency is also deduced from the rheological measurements, if the data are correctly normalized by the viscosity of the suspending phase since a significant amount of polymers adsorb to the cell surfaces. We find that the position of the maximum of this shear rate dependent bell shape increases with increasing viscosity o…
We theoretically investigate the membrane fluctuations of red blood cells with focus laid on the role of the cytoskeleton, viewing the system as a membrane coupled to sparse spring network. This model is exactly solvable and enables us to examine the coupling strength dependence of the membrane undulation. We find that the coupling modifies the fluctuation spectrum at wavelengths longer than the mesh size of the network, while leaving the fluid-like behavior of the membrane intact at shorter wavelengths. The fluctuation spectra can be markedly different, depending on not only the relative ampl…
The plasma membrane of human red blood cells consists of a lipid bilayer attached to a regular network of underlying cytoskeletal polymers. We model this system at a dynamic coarse-grained level, treating the bilayer as an elastic sheet and the cytoskeletal network as a series of phantom entropic springs. In contrast to prior simulation efforts, we explicitly account for dynamics of the cytoskeletal network, both via motion of the protein anchors that attach the cytoskeleton to the bilayer and through breaking and reconnection of individual cytoskeletal filaments. Simulation results are explai…
The dynamics of red blood cells (RBCs) in simple shear flow was studied using a theoretical approach based on three variables: a shape parameter, the inclination angle $θ$, and phase angle $ϕ$ of the membrane rotation. At high shear rate and low viscosity contrast of internal fluid, RBCs exhibit tank-treading motion, where $ϕ$ rotates with swinging oscillation of shape and $θ$. At low shear rate, tumbling motion occurs and $θ$ rotates. In the middle region between these two phases, it is found that synchronized rotation of $ϕ$ and $θ$ with integer ratios of the frequencies occurs in addition t…
We show, via three-dimensional immersed-boundary-finite-element-lattice-Boltzmann simulations, that deformability-based red blood cell (RBC) separation in deterministic lateral displacement (DLD) devices is possible. This is due to the deformability-dependent lateral extension of RBCs and enables us to predict a priori which RBCs will be displaced in a given DLD geometry. Several diseases affect the deformability of human cells. Malaria-infected RBCs or sickle cells, for example, tend to become stiffer than their healthy counterparts. It is therefore desirable to design microfluidic devices wh…
We analyze both the static and dynamic fluctuation spectrum of the red-blood cell in a unified manner, using a simple model of the composite membrane. In this model, the two-dimensional spectrin network that forms the cytoskeleton is treated as a rigid shell which is located at some constant average separation from the lipid bilayer. The cytoskeleton thereby confines both the static and dynamic fluctuations of the lipid bilayer. The predictions of the model account for the wavevector and frequency dependence of the experimental data. The observed amplitude of the thermal fluctuations is relate…
In this work, we review previously developed coarse-grained (CG) particle models for biological membrane and red blood cells (RBCs) and discuss the advantages of the CG particle method over the continuum and atomic simulations on modeling biological phenomena. CG particle models can largely increase the length scale and time scale of atomic simulations by eliminating fast degrees of freedom while preserving the mesoscopic structures and properties of the simulated system. One the other hand, CG particle models can be used to capture microstructural alternations in diseased RBCs and simulate to…
Red blood cells are known to form aggregates in the form of rouleaux. This aggregation process is believed to be reversible, but there is still no full understanding on the binding mechanism. There are at least two competing models, based either on bridging or on depletion. We review recent experimental results on the single cell level and theoretical analyses of the depletion model and of the influence of the cell shape on the binding strength. Another important aggregation mechanism is caused by activation of platelets. This leads to clot formation which is life saving in the case of wound h…
Via computer simulations, we provide evidence that the shear rate induced red blood cell tumbling-to-tank-treading transition also occurs at quite high volume fractions, where collective effects are important. The transition takes place as the ratio of suspension stress to the characteristic cell membrane stress exceeds a certain value, independent of volume fraction and cell deformability. This value coincides with that for a transition from an orientationally less ordered to a highly ordered phase. The average cell deformation does not show any signature of the transition, but rather follows…
The nature of blood as a suspension of red blood cells makes computational hemodynamics a demanding task. Our coarse-grained blood model, which builds on a lattice Boltzmann method for soft particle suspensions, enables the study of the collective behavior of the order of 10^6 cells in suspension. After demonstrating the viscosity measurement in Kolmogorov flow, we focus on the statistical analysis of the cell orientation and rotation in Couette flow. We quantify the average inclination with respect to the flow and the nematic order as a function of shear rate and hematocrit. We further record…
The ability of cells to undergo reversible shape changes is often crucial to their survival. For Red Blood Cells (RBCs), irreversible alteration of the cell shape and flexibility often causes anemia. Here we show theoretically that RBCs may react irreversibly to mechanical perturbations because of tensile stress in their cytoskeleton. The transient polymerization of protein fibers inside the cell seen in sickle cell anemia or a transient external force can trigger the formation of a cytoskeleton-free membrane protrusion of micrometer dimensions. The complex relaxation kinetics of the cell shap…
We present a rigorous procedure to derive coarse-grained red blood cell (RBC) models, which lead to accurate mechanical properties of realistic RBCs. Based on a semi-analytic theory linear and non-linear elastic properties of the RBC membrane can be matched with those obtained in optical tweezers stretching experiments. In addition, we develop a nearly stress-free model which avoids a number of pitfalls of existing RBC models, such as non-biconcave equilibrium shape and dependence of RBC mechanical properties on the triangulation quality. The proposed RBC model is suitable for use in many exis…
Biologically driven non-equilibrium fluctuations are often characterized by their non-Gaussianity or by an "effective temperature", which is frequency dependent and higher than the ambient temperature. We address these two measures theoretically by examining a randomly kicked "particle", with a variable number of kicking "motors", and show how these two indicators of non-equilibrium behavior can contradict. Our results are compared with new experiments on shape fluctuations of red-blood cell membranes, and demonstrate how the physical nature of the motors in this system can be revealed using t…
We present rheology experiments on dilute solutions of vesicles and red blood cells (RBC). Varying the viscosity ratio $λ$ between internal and external fluids, the microscopic dynamics of suspended objects can be qualitatively changed from tank-treading ($tt$) to tumbling ($tb$). We find that in the tt regime the viscosity $η$, decreases when $λ$ increases, in contrast with droplet emulsions and elastic capsule theories which are sometimes invoked to model RBC dynamics. At a critical $λ$ (close to the tt-tb transition) $η$ exhibits a minimum before it increases in the tb regime. This is consi…
We present a new method for the geometric reconstruction of elastic surfaces simulated by the immersed boundary method with the goal of simulating the motion and interactions of cells in whole blood. Our method uses parameter-free radial basis functions for high-order meshless parametric reconstruction of point clouds and the elastic force computations required by the immersed boundary method. This numerical framework allows us to consider the effect of endothelial geometry and red blood cell motion on the motion of platelets. We find red blood cells to be crucial for understanding the motion …
Blood viscosity decreases with shear stress, a property essential for an efficient perfusion of the vascular tree. Shear-thinning is intimately related to the dynamics and mutual interactions of red blood cells (RBCs), the major constituents of blood. Our work explores RBCs dynamics under physiologically relevant conditions of flow strength, outer fluid viscosity and volume fraction. Our results contradict the current paradigm stating that RBCs should align and elongate in the flow direction thanks to their membrane circulation around their center of mass, reducing flow-lines disturbances. On …
We investigate the physics of an optically-driven micromotor of biological origin. A single, live red blood cell, when placed in an optical trap folds into a rod-like shape. If the trapping laser beam is circularly polarized, the folded RBC rotates. A model based on the concept of buckling instabilities captures the folding phenomenon; the rotation of the cell is simply understood using the Poincarè sphere. Our model predicts that (i) at a critical intensity of the trapping beam the RBC shape undergoes large fluctuations and (ii) the torque is proportional to the intensity of the laser beam. T…
Flux of rigid or soft particles (such as drops, vesicles, red blood cells, etc.) in a channel is a complex function of particle concentration, which depends on the details of induced dissipation and suspension structure due to hydrodynamic interactions with walls or between neighboring particles. Through two-dimensional and three-dimensional simulations and a simple model that reveals the contribution of the main characteristics of the flowing suspension, we discuss the existence of an optimal volume fraction for cell transport and its dependence on the cell mechanical properties. The example …
We present experiments on RBCs that flow through microcapillaries under physiological conditions. We show that the RBC clusters form as a subtle imbrication between hydrodynamics interaction and adhesion forces because of plasma proteins. Clusters form along the capillaries and macromolecule-induced adhesion contribute to their stability. However, at high yet physiological flow velocities, shear stresses overcome part of the adhesion forces, and cluster stabilization due to hydrodynamics becomes stronger. For the case of pure hydrodynamic interaction, cell-to-cell distances have a pronounced b…
Blood flow in sickle cell disease (SCD) can substantially differ from normal blood flow due to significant alterations in the physical properties of the red blood cells (RBCs). Chronic complications, such as inflammation of the endothelial cells lining blood vessel walls, are associated with SCD, for reasons that are unclear. Here, detailed boundary integral simulations are performed to investigate an idealized model flow flow in SCD, a binary suspension of flexible biconcave discoidal fluid-filled capsules and stiff curved prolate capsules that represent healthy and sickle RBCs, respectively,…
The non-linear behavior of human erythrocytes subjected to shear stress was analyzed using data series from the Erythrocyte Rheometer and a theoretical model was developed. Linear behavior was eliminated by means of a slot filter and a sixth order Savisky-Golay filter was applied to the resulting time series that allows the elimination of any possible white noise in the data. A fast Fourier transform was performed on the processed data, which resulted in a series of frequency dominant peaks. Results suggest the presence of a non-linear quadratic term in the Kelvin-Voigt phenomenological model.…
Nanoparticles delivering drugs, disseminating cancer cells, and red blood cells (RBCs) during splenic filtration must deform and pass through the sub-micrometer and high aspect ratio interstices between the endothelial cells lining blood vessels. The dynamics of passage of particles/cells through these slit-like interstices remain poorly understood because the in vitro reproduction of slits with physiological dimensions in devices compatible with optical microscopy observations requires expensive technologies. Here, novel microfluidic PDMS devices containing high aspect ratio slits with sub-mi…
