Analysis of Red Blood Cells relaxation time flowing out of microfluidic constrictions reveals the impact of buffer viscosity and flow speed.

International audienceFor the first time, we report that the relaxation time t of healthy human Red Blood Cells (RBCs) decreases upon increase of both the buffer viscosity and its speed, and can reach values as low as 20 ms. Such result is a decade smaller than measurements usually reported in the literature using micropipette aspiration[1], optical tweezers[2], ecktacytometry[3] or microfluidics[4]. These published values (t = 100 to 300 ms) are in good agreement with Hochmuth-Evans[1] analytical calculation of t using the Kelvin-Voigt model describing the RBC as a viscoelastic material. They predict that t only depends on intrinsic cell membrane mechanical properties such as its viscosity and shear modulus. Our finding was obtained from the analysis of video-microscopic recordings of healthy RBCs flowing in a PDMS microfluidic channel, with oscillating width (5-25 µm) as illustrated in Figure1a. More precisely, we focused on the cell behavior at the exit of the last geometrical restriction through the study of its shape relaxation. A large range of fluidic stresses was investigated by varying both the buffer viscosity (h out = 1-30 mPa.s) through the addition of Dextran and the flow velocity (100-2000 µm/s) through the modification of the applied pressure. The observations revealed two different modes of shape relaxation, according to the external flow parameters. The first mode is the stretching behavior illustrated in Figure 1b, as RBCs exit the last narrowing they undergo a large deformation normal to the flow direction before relaxing to their equilibrium parachute-like shape. The second mode is the unfolding behavior, where the RBCs relax directly from their passage in the last restriction and recover their equilibrium shape (Figure 1c). We report in the diagram Figure 2, that the unfolding behavior is mainly observed for the lowest viscosities where the hydrodynamic constraint at the exit is below the stretching modulus of RBCs, whereas the stretching behavior occurs at higher viscosity and RBCs speed, corresponding to higher constraint. For a buffer viscosity of 2 mPa.s, we observed a transition between the two modes according to the cell speed. Indeed, for intermediate velocities a mixed behavior, where both modes are represented among the cell population, is observed. As shown in Figure 3, at fixed buffer viscosity, 1/τ increases linearly with the cell velocity. Similarly, for a given RBC speed, 1/τ rises with the buffer viscosity. Upon very low buffer viscosity and low flow speed, we retrieve relaxation times similar to those reported in literature. We attribute the diminution of the cell relaxation time upon both buffer viscosity and flow velocity to a coupling between the RBC and the external medium. Indeed, the cell dissipates some of the energy accumulated during its deformation, in the suspending media when the buffer viscosity can no longer be neglected compared to the internal cell viscosity. Moreover, we showed that the velocity difference between the cell and the surrounding fluid increases with the flow speed as expected[5], leading to a larger dissipation in the buffer. Both our results and the already published data agree with this interpretation