We reveal that under moderate shear stress (ηγ ≈ 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 ηγ, a ηγ-triggered transition towards a narrow ηγ-range intermittent regime of successive swinging and tumbling, and a pure tumbling motion at lower ηγ-values. A human red blood cell (RBC) is a biconcave flattened disk, essentially made of a Newtonian hemoglobin solution encapsulated by a fluid and incompressible lipid bilayer, underlined by a thin elastic cytoskeleton (spectrin network) [1]. The complex structure of RBCs and their response to a viscous shear flow have a great influence on flow and mass transport in the microcirculation in both health and disease [2]. The full understanding of this response requires a direct comprehensive observation of cell motion and deformation, and a model for deducing the cell intrinsic properties from its behavior in shear flow. It is generally admitted that the two possible RBC movements are the unsteady tumbling solid-like motion [3], and the drop-like 'tanktreading' motion for higher shear stresses, where the cell maintains a steady orientation, while the membrane rotates about the internal fluid, as reported respectively for RBCs suspended in plasma or in high-viscosity media and submitted to high shear stresses [3,4,5,6]. However, the RBC movement at smaller shear rate and close to the tumbling-tanktreading transition, has not been fully explored. Moreover, the actual state of deformation of the elastic skeleton either in the flowing or in the resting RBC is still conjectural ("shape memory" problem) [7]. Most models [6,8] derive from the analytical framework of Keller and Skalak (KS) [9], which treats the RBC as a fluid ellipsoidal membrane enclosing a viscous liquid. Although this model qualitatively retrieves the two modes of motion, it does not capture the observed shear-rate dependency of the tumblingtanktreading transition. In particular, the model does not account for the possible elastic energy storage induced by the local deformations of the cytoskeleton during tanktreading. Approaches including membrane elasticity are either restricted to spherical resting shapes because of analytical complexities [10], or propose encouraging but still limited numerical analysis on tanktreading elastic biconcave capsules [11].Here, we reveal a new regime of motion for RBCs under small shear flow, characterized by an elastic capsule-like oscillation of the cell inclination superimposed to tanktreading that we name swinging. We develop a model, which predicts both swinging and the shear-stress dependency of the tumbling-tanktreading transition. It demonstrates the existence of the elastic shape memory in the membrane.Direct measurements of cell ori...
At the cellular scale, blood fluidity and mass transport depend on the dynamics of red blood cells in blood flow, specifically on their deformation and orientation. These dynamics are governed by cellular rheological properties, such as internal viscosity and cytoskeleton elasticity. In diseases in which cell rheology is altered genetically or by parasitic invasion or by changes in the microenvironment, blood flow may be severely impaired. The nonlinear interplay between cell rheology and flow may generate complex dynamics, which remain largely unexplored experimentally. Under simple shear flow, only two motions, "tumbling" and "tank-treading," have been described experimentally and relate to cell mechanics. Here, we elucidate the full dynamics of red blood cells in shear flow by coupling two videomicroscopy approaches providing multidirectional pictures of cells, and we analyze the mechanical origin of the observed dynamics. We show that contrary to common belief, when red blood cells flip into the flow, their orientation is determined by the shear rate. We discuss the "rolling" motion, similar to a rolling wheel. This motion, which permits the cells to avoid energetically costly deformations, is a true signature of the cytoskeleton elasticity. We highlight a hysteresis cycle and two transient dynamics driven by the shear rate: an intermittent regime during the "tank-treading-to-flipping" transition and a Frisbee-like "spinning" regime during the "rolling-to-tank-treading" transition. Finally, we reveal that the biconcave red cell shape is highly stable under moderate shear stresses, and we interpret this result in terms of stress-free shape and elastic buckling. . Its fluidity strongly depends on its behavior in flow, which is a key factor of proper tissue perfusion. At the cellular scale, blood flow behavior is affected primarily by the RBC response to the hydrodynamic stress in terms of cell orientation relative to the flow direction and of cell deformation. For example, on one hand, at low shear rates, similar cell orientations may favor the formation of stacks (rouleaux) (1) of RBCs, like rolls of coins, which increases blood viscosity. On the other hand, at high shear rates, the individualization of RBCs, their alignment, and their stretching in the flow (2) decrease blood viscosity (3). The orientation and the deformation in flow of RBCs are governed by their rheological properties. They result from the viscoelastic contributions of all components of the cell composite structure. Moreover, RBC rheological properties also depend on the microenvironment and on metabolic functionality (4). Both local and systemic disturbances of homeostasis (in diabetes mellitus, hypertension) have the potential to induce RBC rheological alterations and consequently to impair blood circulation. It therefore is crucial to understand the relationships between the rheological properties of RBCs and their orientation and deformation in flow. This question is far from trivial because even in a simple shear flow, RBCs present a v...
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