Erythrocyte responses in low-shear-rate flows: effects of non-biconcave stress-free state in the cytoskeleton

Inspired by the recent experiment on erythrocytes (red blood cells, RBCs) in weak shear flows by Dupire et al. (Proc. Nail Acad. Sci. USA, vol. 109, 2012, pp. 20808-20813), we conduct a numerical investigation to study the dynamics of RBCs in low-shear-rate flows by applying a multiscale fluid structure interaction model. By employing a spheroidal stress-free state in the cytoskeleton, we are able to numerically predict an important feature, namely that the cell maintains its biconcave shape during tank-treading motions. Furthermore, we numerically confirm the hypothesis that, as the stress-free state approaches a sphere, the threshold shear rates corresponding to the establishment of tank treading decrease. By comparing with the experimental measurements, our study suggests that the stress-free state of RBCs is a spheroid that is close to a sphere, rather than the biconcave shape applied in existing models (the implication is that the RBC skeleton is pre-stressed in its natural biconcave state). It also suggests that the response of RBCs in low-shear-rate flows may provide a measure to quantitatively determine the distribution of shear stress in the RBC cytoskeleton in the natural state.