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Coronavirus disease 2019 (COVID-19) is caused by the Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) and can affect multiple organs, among which is the circulatory system. Inflammation and mortality risk markers were previously detected in COVID-19 plasma and red blood cells (RBCs) metabolic and proteomic profiles. Additionally, biophysical properties, such as deformability, were found to be changed during the infection. Based on such data, we aim to better characterize RBC functions in COVID-19. We evaluate the flow properties of RBCs in severe COVID-19 patients admitted to the intensive care unit by usingin vitromicrofluidic techniques and automated methods, including artificial neural networks, for an unbiased RBC analysis. We find strong flow and RBC shape impairment in COVID-19 samples and demonstrate that such changes are reversible upon suspension of COVID-19 RBCs in healthy plasma. Vice versa, healthy RBCs immediately resemble COVID-19 RBCs when suspended in COVID-19 plasma. Proteomics and metabolomics analyses allow us to detect the effect of plasma exchanges on both plasma and RBCs and demonstrate a new role of RBCs in maintaining plasma equilibria at the expense of their flow properties. Our findings provide a framework for further investigations of clinical relevance for therapies against COVID-19 and possibly other infectious diseases.

Transport of deformable particles in a honeycomb network is studied numerically. It is shown that the particle deformability has a strong impact on their distribution in the network. For sufficiently soft particles, we observe a short memory behavior from one bifurcation to the next, and the overall behavior consists in a random partition of particles, exhibiting a diffusion-like transport. On the contrary, stiff enough particles undergo a biased distribution whereby they follow a deterministic partition at bifurcations, leading to a lateral drift in the network. An increase of concentration enhances particle-particle interactions which shorten the memory effect, turning the particle lateral drift into an effective diffusion. We expect the drifting/diffusive regime transition to be generic for deformable particles.

Vesicles are soft elastic bodies with distinctive mechanical properties such as bending resistance, membrane fluidity, and their strong ability to deform, mimicking some properties of biological cells. While previous three-dimensional (3D) studies have identified stationary shapes such as slipper and axisymmetric ones, we report a complete phase diagram of 3D vesicle dynamics in a bounded Poiseuille flow with two more oscillatory dynamics, 3D snaking and swirling. 3D snaking is characterized by planar oscillatory motion of the mass center and shape deformations, which is unstable and leads to swirling or slipper. Swirling emerges from supercritical pitchfork bifurcation. The mass center moves along a helix, the preserved shape rolls on itself and spins around the flow direction. Swirling can coexist with slipper., 6 pages, 6 figures

Several nonlinear and nonequilibrium driven as well as active systems (e.g. microswimmers) show bifurcations from one state to another (for example a transition from a non motile to motile state for microswimmers) when some control parameter reaches a critical value. Bifurcation analysis relies either on a regular perturbative expansion close to the critical point, or on a direct numerical simulation. While many systems exhibit a regular bifurcation such as a pitchfork one, other systems undergo a singular bifurcation not falling in the classical nomenclature, in that the bifurcation normal form is not analytic. We present a swimmer model which offers an exact solution showing a singular normal form, and serves as a guide for the general theory. We provide an adequate general regularization theory that allows us to handle properly the limit of singular bifurcations, and provide several explicit examples of normal forms of singular bifurcations. This study fills a longstanding gap in bifurcations theory., Comment: 9 pages 3 figures

International audience

Optimal hematocrit $H_o$ maximizes oxygen transport. In healthy humans, the average hematocrit $H$ is in the range of 40-45$\%$, but it can significantly change in blood pathologies such as severe anemia (low $H$) and polycythemia (high $H$). Whether the hematocrit level in humans corresponds to the optimal one is a long standing physiological question. Here, using numerical simulations with the Lattice Boltzmann method and two mechanical models of the red blood cell (RBC) we predict the optimal hematocrit, and explore how altering the mechanical properties of RBCs affects $H_o$. We develop a simplified analytical theory that accounts for results obtained from numerical simulations and provides insight into the physical mechanisms determining $H_o$. Our numerical and analytical models can easily be modified to incorporate a wide range of mechanical properties of RBCs as well as other soft particles thereby providing means for the rational design of blood substitutes. Our work lays the foundations for systematic theoretical study of the optimal hematocrit and its link with pathological RBCs associated with various diseases (e.g. sickle cell anemia, diabetes mellitus, malaria, elliptocytosis).

International audience; 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 vaso-motor 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.

The absence of gravity during space flight can alter cardio-vascular functions partially due to reduced physical activity. This affects the overall hemodynamics, and in particular the level of shear stresses to which blood vessels are submitted. Long-term exposure to space environment is thus susceptible to induce vascular remodeling through a mechanotransduction cascade that couples vessel shape and function with the mechanical cues exerted by the circulating cells on the vessel walls. Central to such processes, the glycocalyx – i.e. the micron-thick layer of biomacromolecules that lines the lumen of blood vessels and is directly exposed to blood flow – is a major actor in the regulation of biochemical and mechanical interactions. We discuss in this article several experiments performed under microgravity, such as the determination of lift force and collective motion in blood flow, and some preliminary results obtained in artificial microfluidic circuits functionalized with endothelium that offer interesting perspectives for the study of the interactions between blood and endothelium in healthy condition as well as by mimicking the degradation of glycocalyx caused by long space missions. A direct comparison between experiments and simulations is discussed., SCOPUS: sh.j, info:eu-repo/semantics/published

International audience; Microvasculatures-on-a-chip, i.e. in vitro models that mimic important features of microvessel networks, have gained increasing interest in recent years. Such devices have allowed investigating pathophysiological situations involving abnormal biophysical interactions between blood cells and vessel walls. Still, a central question remains regarding the presence, in such biomimetic systems, of the endothelial glycocalyx. The latter is a glycosaminoglycans-rich surface layer exposed to blood flow, which plays a crucial role in regulating the interactions between circulating cells and the endothelium. Here, we use confocal microscopy to characterize the layer expressed by endothelial cells cultured in microfluidic channels. We show that, under our culture conditions, endothelial cells form a confluent layer on all the walls of the circuit and display a glycocalyx that fully lines the lumen of the microchannels. Moreover, the thickness of this surface layer is found to be on the order of 600 nm, which compares well with measurements performed ex or in vivo on microcapillaries. Furthermore, we investigate how the presence of endothelial cells in the microchannels affects their hydrodynamic resistance and the near-wall motion of red blood cells. Our study thus provides an important insight into the physiological relevance of in vitro microvasculatures. Interactions between circulating blood components and vessel walls are central to the immune 1,2 and inflamma-tory 3,4 response, and to processes such as angiogenesis 5,6 or hemostasis 7. These interactions result from a complex and highly regulated interplay between specific biomolecular adhesion mechanisms at cell/wall interfaces 1,3,8 , chemoattractant expression 2,9 , mechanical properties of the cells 10,11 , and fluid stresses arising from hemody-namics 10–13. Anomalous interactions between blood cells and the endothelium, i.e. the cellular layer lining the internal lumen of blood vessels, are known to be associated with a number of blood and vascular disorders such as thrombosis, atherosclerosis, diabetes mellitus, or sickle cell anemia 3,14. In vitro studies have proven to be extremely useful in order to unravel the respective roles of mechanical, biochemical and biophysical factors that govern some vascular pathologies 15–18. These studies typically rely on microfluidic tools to create networks of channels that recapitulate the microvasculature properties. Such in vitro investigations present several important advantages for the rational studies of blood dynamics, cell trafficking and microvascular functions: (i) they solve technical and ethical issues encountered when working on animal models 19 , (ii) microchannels are made from transparent materials and facilitate the use of advanced and high-resolution microscopy techniques, and (iii) experiments are performed under tightly controlled fluid composition and flow conditions. However, these advantages often come at the cost of a partial loss of physiological relevance, in particular regarding cell/wall interactions. To overcome this limitation, several works have proposed designs of in vitro microvasculatures that mimic not only the architecture, but also the surface properties of blood microvessels: endothelial cells have been cultured in microcircuits, made of silicone elastomer or hydrogels, in order to form a confluent monolayer on their walls, thus providing perfusable channels bearing a model endothe-lium, while displaying two-or three-dimensional network architectures 20–31. Such in vitro microvasculatures have 1 Univ.

International audience; This contribution is concerned with a the numerical modeling of an isolated red blood cell (RBC), and more generally of phospholipid membranes. We propose an adaptive Eulerian finite element approximation, based on the level set method, of a shape optimization problem arising in the study of RBC's equilibrium. We simulate the equilibrium shapes that minimize the elastic bending energy under prescribed constraints of fixed volume and surface area. An anisotropic mesh adaptation technique is used in the vicinity of the cell's membrane to enhance the robustness of the method. Efficient time and spatial discretizations are considered and implemented. We address in detail the main features of the proposed method and finally we report several numerical experiments in the two-dimensional and the three-dimensional axisymmetric cases. The effectiveness of the numerical method is further demonstrated through numerical comparisons with semi-analytical solutions provided by a reduced order model.

Polymer brushes are increasingly used to tailor surface physicochemistry for various applications such as wetting, adhesion of biological objects, implantable devices, etc. We perform Dissipative Particle Dynamics simulations to study the behavior of dense polymer brushes under flow in a slit-pore channel. We discover that the system displays flow inversion at the brush interface for several disconnected ranges of the imposed flow. We associate such phenomenon to collective polymer dynamics: a wave propagating on the brush surface. The relation between the wavelength, the amplitude and the propagation speed of the flow-generated wave is consistent with the solution of the Stokes equations when an imposed traveling wave is assumed as boundary condition (the famous Taylor's swimmer)., Comment: 5 pages, 6 figures, supplemental material (5 pages, 4 figures) attached below the letter and before bibliography, videos available on request to the corresponding author, submitted to SciRep

The foundation of continuum elasticity theory is based on two general principles: (i) the force felt by a small volume element from its surrounding acts only through its surface (the Cauchy principle, justified by the fact that interactions are of short range and are therefore localized at the boundary); (ii) the stress tensor must be symmetric in order to prevent spontaneous rotation of the material points. These two requirements are presented to be necessary in classical textbooks on elasticity theory. By using only basic spatial symmetries it is shown that elastodynamics equations can be derived, for high symmetry crystals (the typical case considered in most textbooks), without evoking any of the two above physical principles., Comment: 6 pages

We study the step bunching process in three different 1D step flow models and obtain scaling relations for the step bunches formed in the long times limit. The first one was introduced by S.Stoyanov [Jap. J.Appl. Phys. 29, (1990) L659] as the simplest 'realistic' model of step bunching due to drift of the adatoms. Here we show that it could lead to (at least) two different types of step bunching, depending on the magnitude of the drift. The other two models are minimal models: the equations for step velocity are constructed ad hoc from two terms with opposite effects - destabilizing and, respectively, stabilizing the regular step train., Comment: 5 printed pages, 6 (11) figures, published in full text after reviewing process in the book of the Conference Nanoscience and Nanotechnology, Sofia, 2005

Les sciences non linéaires ont pour objet l’ensemble des phénomènes dont l’analyse résiste au principe de superposition. Elles concernent en grande partie les systèmes dits « complexes » dont l’interaction et l’interdépendance entre les parties empêchent de prédire précisément l’évolution du système. Pour expliquer ces phénomènes, deux approches complémentaires ont été proposées : la théorie des bifurcations et la théorie des catastrophes. Mais la pleine compréhension et la modélisation de la non-linéarité restent chacune un défi pour les scientifiques du XXIe siècle. C’est dans la perspective d’accompagner tous ceux qui voudront le relever que ce livre a été conçu. Son objectif est d’exposer au lecteur le langage et le formalisme nécessaires à l’étude de la non-linéarité. Partant d’exemples simples, pour ensuite atteindre un niveau d’abstraction visant l’universalité, l’auteur explore les divers scénarios possibles de bifurcations et les catastrophes élémentaires caractéristiques du changement qualitatif de comportement d’un système ; l’étude de l’évolution temporelle est abordée à travers la mise en équation de phénomènes aux solutions stationnaires ou oscillantes ; l’analyse de l’évolution spatiale des systèmes non linéaires nous introduit quant à elle au problème fascinant de la morphogenèse. Accessible dès le premier cycle universitaire aux étudiants de toutes les disciplines concernées par les phénomènes non linéaires (physique, mathématiques, chimie, géologie, économie, etc.), cet ouvrage constituera aussi une synthèse riche et utile pour les enseignants et chercheurs de ces différents domaines. Chaouqi Misbah est directeur de recherche 1re classe au sein du LIPhy – Laboratoire interdisciplinaire de physique (CNRS et université Joseph-Fourier-Grenoble-I).

Inspired by experiments on the actin driven propulsion of micrometer sized beads we develop and study a minimal mechanical model of a two-dimensional network of stiff elastic filaments grown from the surface of a cylinder. Starting out from a discrete model of the network structure and of its microscopic mechanical behavior we derive a macroscopic constitutive law by homogenization techniques. We calculate the axisymmetric equilibrium state and study its linear stability depending on the microscopic mechanical properties. We find that thin networks are linearly stable, whereas thick networks are unstable. The critical thickness for the change in stability depends on the ratio of the microscopic elastic constants. The instability is induced by the increase in the compressive load on the inner network layers as the thickness of the network increases. The here employed homogenization approach combined with more elaborate microscopic models can serve as a basis to study the evolution of polymerizing actin networks and the mechanism of actin driven motion., 19 pages, 7 figures

Motivated by the reported peculiar dynamics of a red blood cell in shear flow, we develop an analytical theory for the motion of a nearly--spherical fluid particle enclosed by a visco--elastic incompressible interface in linear flows. The analysis explains the effect of particle deformability on the transition from tumbling to swinging as the shear rate increases. Near the transition, intermittent behavior is predicted only if the particle has a fixed shape; the intermittency disappears for a deformable particle. Comparison with available phenomenological models based on the fixed shape assumption highlights their physical foundations and limitations., Under revision. Submitted to J. Fluid Mechanics on 24 April 2010

The study of vesicles under flow, a model system for red blood cells (RBCs), is an essential step in understanding various intricate dynamics exhibited by RBCs in vivo and in vitro. Quantitative 3D analyses of vesicles under flow are presented. The regions of parameters to produce tumbling (TB), tank-treating (TT), vacillating-breathing (VB) {and even Kayaking (K)} modes are determined. New qualitative features are found: (i) a significant widening of the VB mode region in parameter space upon increasing shear rate $\dot\gamma$ and (ii) a striking robustness of period of TB and VB with $\dot\gamma$. Analytical support is also provided. These findings shed new light on the dynamics of blood flow., Comment: 1 tex file and 5 figures

Starting from known kinematic picture for plasticity, we derive a set of dynamical equations describing plastic flow in a Lagrangian formulation. Our derivation is a natural and a straightforward extension of simple fluids, elastic and viscous solids theories. These equations contain the Maxwell model as a special limit. We discuss some results of plasticity which can be described by this set of equations. We exploit the model equations for the simple examples: straining of a slab and a rod. We find that necking manifests always itself (not as a result of instability), except if the very special constant-velocity stretching process is imposed., 4 pages, 1 figure

International audience; Non-planar solid-fluid-solid interfaces under stress are very common in many materials, and particularly in the rocks of the Earth's crust. Such patterns are observed in many rocks in a wide range of spatial scales, from undulate grain boundaries at the micrometer scale, to stylolite dissolution interface at the meter scale. It is proposed here that these initially flat rock-fluid interfaces become rough by a morphological instability triggered by elastic stress. A model for the formation of stylolitic patterns at all scales is thus presented. It is shown that such instability is inherently present due to the uniaxial stress that promotes them, owing to the gain in the total elastic energy: the intrinsic elastic energy plus the work of the external forces. This is shown explicitly by solving the elastic problem in a linear stability analysis, and proved more generally without having resort to the computation of the elastic field.

Colloque avec actes et comité de lecture. Internationale.; International audience; Giant vesicles are deformable lipid membranes enclosing a fluid, with diameters of several microns. They are useful models for the study of biological flows. Their behaviour under shear flow reveals a complex dynamics involving several regimes: stationary tank-treading motion, periodic fliping or tumbling motion, and periodic vacillating-breathing motion. Our experimental study reveals that the deformability of vesicles strongly influences the dynamics. One noticeable feature is a slowing down of the tumbling motion with respect to the shear rate when the latter increases. A semi-phenomonological model including the deformability of objects helps understand the connection between the slowing down of the tumbling motion and a coupling between rotation and deformation. A new vacillating-breathing motion is also predicted and a complex phase diagram can be established.

We present rheology experiments on dilute solutions of vesicles and red blood cells (RBC). Varying the viscosity ratio $\lambda$ 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 $\eta$, decreases when $\lambda$ increases, in contrast with droplet emulsions and elastic capsule theories which are sometimes invoked to model RBC dynamics. At a critical $\lambda$ (close to the tt-tb transition) $\eta$ exhibits a minimum before it increases in the tb regime. This is consistent with a recent theory for vesicles. This points to the nontrivial fact that the cytoskeleton in RBC does not alter the qualitative evolution of $\eta$ and that, as far as rheology is concerned, vesicle models might be a better description., Comment: 4 pages, 3 figures

Amplitude expansions are used to determine steady states of a semi-infinite solid subject to the Grinfeld instability in systems with a fixed (wave)length. We present two methods to obtain high-order weakly nonlinear results. Using the system size as a control parameter, we circumvent the problem that there is no instability threshold for an extended system in the absence of gravity. This way, the case without gravity becomes accessible to a weakly nonlinear treatment. The dependence of the branch structure of solution space on the level of gravity (or density difference) is exhibited. In the zero-gravity limit, we recover the solution branch obtained by Spencer and Meiron. A transition from a supercritical to a subcritical bifurcation is observed as gravity is increased or the nonhydrostatic stress is decreased at fixed gravity. At given values of the system parameters, we find a discrete, possibly infinite, set of solution branches. This is reminiscent of dendritic or eutectic growth, where similar solution sets exist, of which only a particular one is linearly stable. Despite the high order of our expansions, the approach is restricted to relatively small nondimensional amplitudes ($\lesssim 0.2$), a disadvantage we can overcome by a variational approach that will be discussed in a companion paper. At the critical point, we find that not only the first Landau coefficient is negative but all of them up to the highest amplitude order (15) we could compute so far., This article has been withdrawn by the authors. The authors determined that the results claimed were not as complete as originally thought, and the project has ended so no future work on this is planned

A phase-field approach describing the dynamics of a strained solid in contact with its melt is developed. By rigorous asymptotic analysis we show that the sharp-interface limit of this model recovers the continuum model equations for the Grinfeld instability. Moreover, we use our approach to derive hitherto unknown sharp-interface equations for a situation including a field of body forces. The numerical utility of the phase-field approach is demonstrated by comparison with a sharp-interface simulation. We then investigate the dynamics of extended systems within the phase-field model which contains an inherent lower length cutoff, thus avoiding cusp singularities. It is found that a periodic array of grooves generically evolves into a superstructure which arises from a series of imperfect period doublings. For wavenumbers close to the fastest-growing mode of the linear instability, the first period doubling can be obtained analytically. Both the dynamics of an initially periodic array and a random initial structure can be described as a coarsening process with winning grooves temporarily accelerating whereas losing ones decelerate and even reverse their direction of motion., 40 pages, 12 figures, submitted to Phys. Rev. E

From geometry and conservation we derive two nonlinear evolution equations for sand ripples. In the case of a strong wind leading to a net erosion of the sand bed, ripples obey the Benney equation. This leads either to order or disorder depending on whether dispersion is strong or weak. In the most frequent case where erosion is counterbalanced by deposition, we derive a new one-parameter nonlinear equation. It reveals ripple structures which then undergo a coarsening process at long times, a process which then slows down dramatically with the growth of the ripple wavelength., 4 pages, 1 figure

Cette thèse expérimentale s’inscrit dans le domaine des sciences séparatives et se base sur la technique de SPLITT (SPLIT-flow Thin fractionation). Son objectif consiste en l’étude des mécanismes qui sont à l’origine de la séparation, en continu et sans membrane, d’objets de taille micrométrique dans des mini-séparateurs fluidiques (Step-SPLITT). Les expériences menées, en laboratoire et lors de vols paraboliques, ont révélé le couplage complexe comme l’influence des effets hydrodynamiques et du champ gravitationnel sur la migration transverse des espèces en écoulement. Des visualisations tridimensionnelles par holographie digitale ont corroboré nos résultats et dévoilé des comportements inattendus. Les capacités séparatives des Step-SPLITT ont rendu possible l’analyse et la séparation d’objets biologiques et biomimétiques. Enfin, cette étude complétée par une modélisation tridimensionnelle de l’écoulement nous a permis de mettre au point un nouveau prototype de séparateur. This experimental thesis belongs to the field of separative sciences and is based on the SPLITT technique (SPLIT-flow Thin fractionation). The objective is to study the mechanisms that are at the origin of continuous and membraneless separation of micron-size species in mini fluidic separators (Step-SPLITT). Experiments undertaken in laboratory and during parabolic flights revealed the complex coupling of the hydrodynamic effects and the gravitational field influencing the transverse migration of the flowing species. Three-dimensional visualizations performed by digital holography confirmed our results and disclosed unexpected behaviours. The separation capacities of Step-SPLITT made the analysis and the separation of biological and biomimetic species possible. In addition this study in conjunction with a three-dimensional flow modelling enabled us to develop a new prototype of separator., Doctorat en sciences appliquées, info:eu-repo/semantics/published

Cette thèse expérimentale s’inscrit dans le domaine des sciences séparatives et se base sur la technique de SPLITT (SPLIT-flow Thin fractionation). Son objectif consiste en l’étude des mécanismes qui sont à l’origine de la séparation, en continu et sans membrane, d’objets de taille micrométrique dans des mini-séparateurs fluidiques (Step-SPLITT). Les expériences menées, en laboratoire et lors de vols paraboliques, ont révélé le couplage complexe comme l’influence des effets hydrodynamiques et du champ gravitationnel sur la migration transverse des espèces en écoulement. Des visualisations tridimensionnelles par holographie digitale ont corroboré nos résultats et dévoilé des comportements inattendus. Les capacités séparatives des Step-SPLITT ont rendu possible l’analyse et la séparation d’objets biologiques et biomimétiques. Enfin, cette étude complétée par une modélisation tridimensionnelle de l’écoulement nous a permis de mettre au point un nouveau prototype de séparateur.This experimental thesis belongs to the field of separative sciences and is based on the SPLITT technique (SPLIT-flow Thin fractionation). The objective is to study the mechanisms that are at the origin of continuous and membraneless separation of micron-size species in mini fluidic separators (Step-SPLITT). Experiments undertaken in laboratory and during parabolic flights revealed the complex coupling of the hydrodynamic effects and the gravitational field influencing the transverse migration of the flowing species. Three-dimensional visualizations performed by digital holography confirmed our results and disclosed unexpected behaviours. The separation capacities of Step-SPLITT made the analysis and the separation of biological and biomimetic species possible. In addition this study in conjunction with a three-dimensional flow modelling enabled us to develop a new prototype of separator., Doctorat en sciences appliquées, info:eu-repo/semantics/nonPublished