We reveal that under moderate shear stress (of the order of 0.1 Pa) red blood cells present an oscillation of their inclination (swinging) superimposed to the long-observed steady tanktreading (TT) motion. A model based on a fluid ellipsoid surrounded by a visco-elastic membrane initially unstrained (shape memory) predicts all observed features of the motion: an increase of both swinging amplitude and period (1/2 the TT period) upon decreasing the shear stress, a shear stress-triggered transition towards a narrow shear stress-range intermittent regime of successive swinging and tumbling, and a pure tumbling motion at lower shear stress-values.
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 …
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…
The dynamics of red blood cells (RBCs) in oscillatory shear flow was studied using differential equations of three variables: a shape parameter, the inclination angle $θ$, and phase angle $ϕ$ of the membrane rotation. In steady shear flow, three types of dynamics occur depending on the shear rate and viscosity ratio. i) tank-treading (TT): $ϕ$ rotates while the shape and $θ$ oscillate. ii) tumbling (TB): $θ$ rotates while the shape and $ϕ$ oscillate. iii) intermediate motion: both $ϕ$ and $θ$ rotate synchronously or intermittently. In oscillatory shear flow, RBCs show various dynamics based on…
We argue that the paradoxal softness of the red blood cells (RBC) in fluctuation spectra experiments is apparent. We show that the effective surface shear modulus $μ_s$ of the RBC obtained from fluctuation data and that measured in static deformation experiments have the same order of magnitude. A simple micromechanical model of the RBC developped for this purpose accounts for the influence of a finite-thickness cytoskeleton on the fluctuations of the composite membrane-cytoskeleton system. The spectrin network cytoskeleton with the bulk shear modulus estimated as $μ\approx105÷165$ Pa contribu…
The fluid dynamics video that is presented here outlines recent advances in the simulation of multiphase cellular blood flow through the direct numerical simulations of deformable red blood cells (RBCs) demonstrated through several numerical experiments. Videos show particle deformation, shear stress on the particle surface, and the formation of particle clusters in both Hagen-Poiseuille and shear flow.
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 …
The traditional view is that low shear stress of blood flow accelerates atherosclerosis. How does a low shear stress damage the vessel or aggravate atherosclerosis? It is a puzzling question. Furthermore, shear stress of veins is similar to that of Relatively Vulnerable Zones (RVZ) of arteries, while intimal thickening of veins is not obvious as the arteries. There are many places in arterioles with lower shear stress as the decrease of blood velocity, while the thickening of arterioles is not as obvious as that of the medium-sized arteries. These issues make it unconvincing for us to explain …
Using a multiscale blood flow solver, the complete diffusion tensor of nanoparticle (NP) in sheared cellular blood flow is calculated over a wide range of shear rate and haematocrit. In the short-time regime, NPs exhibit anomalous dispersive behaviors under high shear and high haematocrit due to the transient elongation and alignment of the red blood cells (RBCs). In the long-time regime, the NP diffusion tensor features high anisotropy. Particularly, there exists a critical shear rate ($\sim$100 $s^{-1}$) around which the shear-rate dependence of the diffusivity tensor changes from linear to …
Proteolysis of the multimeric blood coagulation protein von Willebrand Factor (VWF) by ADAMTS13 is crucial for prevention of microvascular thrombosis. ADAMTS13 cleaves VWF within the mechanosensitive A2 domain, which is believed to open under shear flow. Here, we combine Fluorescence Correlation Spectroscopy (FCS) and a microfluidic shear cell to monitor real-time kinetics of full-length VWF proteolysis as a function of shear stress. For comparison, we also measure the Michaelis-Menten kinetics of ADAMTS13 cleavage of wild-type VWF in the absence of shear but partially denaturing conditions. U…
Shear stress plays an important role in the creation and evolution of atherosclerosis. An key element for in-vivo measurements and extrapolations is the dependence of shear stress on body mass. In the case of a Poiseuille modeling of the blood flow, P. Weinberg and C. Ethier have shown that shear stress on the aortic endothelium varies like body mass to the power $-\frac{3}{8}$, and is therefore 20-fold higher in mice than in men. However, by considering a more physiological oscillating Poiseuille + Womersley combinated flow in the aorta, we show that results differ notably: at larger masses (…
Haematocrit and Shear Rate Modulate Local Cell-free Layer Thickness and Platelet Margination in Blood Flow Along a Sinusoidal Wall
Università degli Studi di Napoli “Federico II”（那不勒斯费德里科二世大学）；CEINGE Biotecnologie Avanzate “Franco Salvatore”（CEINGE先进生物技术“弗朗哥·萨勒瓦托雷”中心）；University of Edinburgh（爱丁堡大学）
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…
Thrombosis under high-shear conditions is mediated by the mechanosensitive blood glycoprotein von Willebrand Factor (vWF). vWF unfolds in response to strong flow gradients and facilitates rapid recruitment of platelets in flowing blood. While the thrombogenic effect of vWF is well recognized, its conformational response in complex flows has largely been omitted from numerical models of thrombosis. We recently presented a continuum model for the unfolding of vWF, where we represented vWF transport and its flow-induced conformational change using convection-diffusion-reaction equations. Here, we…
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,…
We investigate the rheological characteristics of human blood plasma in shear and elongational flows. While we can confirm a Newtonian behavior in shear flow within experimental resolution, we find a viscoelastic behavior of blood plasma in the pure extensional flow of a capillary break-up rheometer. The influence of the viscoelasticity of blood plasma on capillary blood flow is tested in a microfluidic device with a contraction-expansion geometry. Differential pressure measurements revealed that the plasma has a pronounced flow resistance compared to that of pure water. Supplementary measurem…
Red blood cells (RBCs) -- erythrocytes -- suspended in plasma tend to aggregate and form rouleaux. During aggregation the first stage consists in the formation of RBC doublets [Blood cells, molecules, and diseases 25, 339 (1999)]. While aggregates are normally dissociated by moderate flow stresses, under some pathological conditions the aggregation becomes irreversible, which leads to high blood viscosity and vessel occlusion. We perform here two-dimensional simulations to study the doublet dynamics under shear flow in different conditions and its impact on rheology. We sum up our results on t…
The fluid shear stress is an important regulator of the cardiovascular system via the endothelium-derived relaxing factor (EDRF) that is Nitric Oxide. This mechanism involves biochemical reactions in an arterial wall. The autoregulation process is managed by the vascular tonus and gives the negative feedback for the shear stress changing. A new mathematical model for the autoregulation of a blood flow through arteria under the constant transmural pressure is presented. Endothelium-derived relaxing factor Nitric Oxide, the multi-layer structure of an arterial wall, and kinetic-diffusion process…
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…
Reduced blood flow, as occurring in ischemia or resulting from exposure to microgravity such as encountered in space flights, induces a decrease in the level of shear stress sensed by the endothelial cells forming the inner part of blood vessels. In the present study, we use a microvasculature-on-a-chip device in order to investigate in vitro the effect of such a reduction in shear stress on shear-adapted endothelial cells. We find that, within one hour of exposition to reduced wall shear stress, human umbilical vein endothelial cells undergo a reorganization of their actin skeleton, with a de…
The paper is devoted to a study of the peristaltic motion of blood in the micro-circulatory system. The vessel is considered to be of varying cross-section. The progressive peristaltic waves are taken to be of sinusoidal nature. Blood is considered to be a Herschel-Bulkley fluid. Of particular concern here is to investigate the effects of amplitude ratio, mean pressure gradient, yield stress and the power law index on the velocity distribution, streamline pattern and wall shear stress. On the basis of the derived analytical expression, extensive numerical calculations have been made. The study…
A discrete boundary-sensitive Hodge decomposition is proposed as a central tool for the analysis of wall shear stress (WSS) vector fields in aortic blood flows. The method is based on novel results for the smooth and discrete Hodge-Morrey-Friedrichs decomposition on manifolds with boundary and subdivides the WSS vector field into five components: gradient (curl-free), co-gradient (divergence-free), and three harmonic fields induced from the boundary, which are called the center, Neumann and Dirichlet fields. First, an analysis of WSS in several simulated simplified phantom geometries (duct and…
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 erythro- cyte 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 morp…
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 numerically investigate the influence of flow development on secondary flow patterns and subsequent wall shear stress distributions in a curved artery model, and we compute vascular metrics commonly used to assess variations in blood flow characteristics as it applies to arterial disease. We model a human artery with a simple, rigid 180-degree curved tube with circular cross-section and constant curvature, neglecting effects of taper, torsion and elasticity. High-fidelity numerical results are computed from an in-house discontinuous spectral element flow solver. The flow rate used in this s…
Vesicles under a shear flow exhibit a tank-treading motion of their membrane, while their long axis points with an angle < 45 degrees with respect to the shear stress if the viscosity contrast between the interior and the exterior is not large enough. Above a certain viscosity contrast, the vesicle undergoes a tumbling bifurcation, a bifurcation which is known for red blood cells. We have recently presented the full numerical analysis of this transition. In this paper, we introduce an analytical model that has the advantage of being both simple enough and capturing the essential features found…
Thromboembolic complications remain a central issue in management of patients on mechanical circulatory support. Despite the best practices employed in design and manufacturing of modern ventricular assist devices, complexity and modular nature of these systems often introduces internal steps and crevices in the flow path which can serve as nidus for thrombus formation. Thrombotic potential is influenced by multiple factors including the characteristics of the flow and surface chemistry of the biomaterial. This study explored these elements in the setting of blood flow over a micro-crevice usi…
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 significant rates of post-operative arterial thrombus formation following the sutured anastomosis (surgical connection) of vessels in microvascular reconstruction has kindled the development of engineered solutions such as the UNILINK coupler. These devices reduce thrombosis rates, which recent numerical studies suggest to be due to decreases in shear strain rate across the anastomosis site when compared to sutured vessels. In this work we develop and analytically solve the first mathematical model for the problem of microvascular anastomosis, leading to the discovery that the rates of thr…
Experimental characterization of blood flow in living organisms is crucial for understanding the development and function of cardiovascular systems, but there have been no techniques reported for snapshot imaging of thick samples in large volumes with high precision. We have combined computational microscopy and the diffraction-free, self-bending property of Airy beams to track fluorescent beads with sub-micron precision through an extended axial range (up to 600 $μ$m) within the flowing blood of 3 days post-fertilization (dpf) zebrafish embryos. The spatial trajectories of the tracer beads wi…
Of concern in the paper is a generalized theoretical study of the non-Newtonian characteristics of peristaltic flow of blood through micro-vessels, e.g. arterioles. The vessel is considered to be of variable cross-section and blood to be a Herschel-Bulkley type of fluid. The progressive wave front of the peristaltic flow is supposed sinusoidal/straight section dominated (SSD) (expansion/contraction type); Reynolds number is considered to be small with reference to blood flow in the micro-circulatory system. The equations that govern the non-Newtonian peristaltic flow of blood are considered to…
Flowing blood displays a phenomenon called margination, in which leukocytes and platelets are preferentially found near blood vessel walls, while erythrocytes are depleted from these regions. Here margination is investigated using direct hydrodynamic simulations of a binary suspension of stiff (s) and floppy (f) capsules, as well as a stochastic model that incorporates the key particle transport mechanisms in suspensions -- wall-induced hydrodynamic migration and shear-induced pair collisions. The stochastic model allows the relative importance of these two mechanisms to be directly evaluated …
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…
We developed a new mechanical model for determining the compression and shear mechanical behavior of four different hemoglobin structures. Previous studies on hemoglobin structures have focused primarily on overall mechanical behavior; however, this study investigates the mechanical behavior of hemoglobin, a major constituent of red blood cells (RBCs), using steered molecular dynamics (SMD) simulations to obtain anisotropic mechanical behavior under compression and shear loading conditions. Four different configurations of hemoglobin molecules were considered: deoxyhemoglobin (deoxyHb), oxyhem…
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 fast blood stream of animals is associated with large shear stresses. Consequently, blood cells have evolved a special morphology and a specific internal architecture allowing them to maintain their integrity over several weeks. For instance, non-mammalian red blood cells, mammalian erythroblasts and platelets have a peripheral ring of microtubules, called the marginal band, that flattens the overall cell morphology by pushing on the cell cortex. In this article, we model how the shape of these cells stems from the balance between marginal band elasticity and cortical tension. We predict t…
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.…
In this work the computer modeling has been used to show that longer ligands allow biological cells (e.g., blood platelets) to withstand stronger flows after their adhesion to solid walls. Mechanistic model of polymer-mediated ligand-receptor adhesion between a microparticle (cell) and a flat wall has been developed. Theoretical threshold between adherent and non-adherent regimes has been derived analytically and confirmed by simulations. These results lead to a deeper understanding of numerous biophysical processes, e.g., arterial thrombosis, and to the design of new biomimetic colloid-polyme…
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 …
Various biological processes such as transport of oxygen and nutrients, thrombus formation, vascular angiogenesis and remodeling are related to cellular/subcellular level biological processes, where mesoscopic simulations resolving detailed cell dynamics provide a key to understanding and identifying the cellular basis of disease. To break this bottleneck and achieve a biologically meaningful timescale, we propose a multiscale parareal algorithm in which a continuum-based solver supervises a mesoscopic simulation in the time-domain. Using an iterative prediction-correction strategy, the parall…
The manual evaluation, classification and counting of biological objects demands for an enormous expenditure of time and subjective human input may be a source of error. Investigating the shape of red blood cells (RBCs) in microcapillary Poiseuille flow, we overcome this drawback by introducing a convolutional neural regression network for an automatic, outlier tolerant shape classification. From our experiments we expect two stable geometries: the so-called `slipper' and `croissant' shapes depending on the prevailing flow conditions and the cell-intrinsic parameters. Whereas croissants mostly…
Transport of solid particles in blood flow exhibits qualitative differences in the transport mechanism when the particle varies from nanoscale to microscale size comparable to the red blood cell (RBC). The effect of microscale particle margination has been investigated by several groups. Also, the transport of nanoscale particles (NPs) in blood has received considerable attention in the past. This study attempts to bridge the gap by quantitatively showing how the transport mechanism varies with particle size from nano- to microscale. Using a three-dimensional (3D) multiscale method, the disper…
As the original velocity field obtained from four-dimensional (4D) flow magnetic resonance imaging (MRI) contains considerable amount of noises and errors, the available Divergence-free smoothing (DFS) method can be used to process the 4D flow MRI data for reducing noises, eliminating errors, fixing missing data and eventually providing the smoothed flow field. However, the traditional DFS does not have the ability to deal with the flow in the near wall region of vessel, especially for satisfying the no-slip boundary condition. In this study, therefore, an improved DFS method with specific nea…
Swimming microbes, such as bacteria and algae, live in diverse habitats including soil, ocean and human body which are characterized by structural boundaries and heterogeneous fluid flows. Although much progress has been made in understanding the Brownian ratchet motions of microbes and their hydrodynamic interactions with the wall over the last decades, the complex interplay between the structural and fluidic environment and the self-propelling microbial motions still remains elusive. Here, we developed a Langevin model to simulate and investigate the transport and dispersion of microbes in p…
Shear stress is an important physical factor that regulates proliferation, migration and morphogenesis. In particular, the homeostasis of blood vessels is dependent on shear stress. To mimic this process ex vivo, efforts have been made to seed scaffolds with vascular and other cell types in the presence of growth factors and under pulsatile flow conditions. However, the resulting bioreactors lack information on shear stress and flow distributions within the scaffold. Consequently, it is difficult to interpret the effects of shear stress on cell function. Such knowledge would enable researchers…
Quantifying the Biophysical Properties of Red Blood Cells in Gaucher Disease
Brown University（布朗大学）；Université Paris Saclay（巴黎萨克雷大学）；CNRS UMR 8000（法国国家科学研究中心第8000联合研究单位）；Institut de Chimie Physique（物理化学研究所）；Université Paris Cité（巴黎西岱大学）；INSERM（法国国家健康与医学研究院）；EFS（法国血液服务机构）；BIGR U1134（BIGR第1134联合研究单位）；Team BioTiGR（BioTiGR团队）；Initiatives IdEx Globule Rouge d’Excellence (InIdex GR-Ex)（卓越红细胞倡议（InIdex GR-Ex））；Team PAMS（PAMS团队）
