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

Abstract

Inspired by the recent experiment on erythrocytes (red blood cells, RBCs) in weak shear flows by Dupire et al. 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.

Mechanical response of red blood cells entering a constriction

“…A key consistency check is to determine whether the motions are qualitatively consistent with the applied shear stresses. Although the motion of RBCs has been the subject of extensive simulation and computational efforts, [42][43][44][45][46] little work has examined the motion of RBCs entering a constriction as tested here. In the absence of detailed predictions, we instead examine the limiting case of perfectly rigid ellipsoids.…”

Dynamics of biconcave vesicles in a confined shear flow

“…It is similar to the methods developed by Bagchi et al (Cordasco, Yazdani & Bagchi, 2014;Yazdani, Kalluri & Bagchi, 2011). It should be noted that some other methods are also developed to model RBCs under flow such as the particle-based model (Fedosov et al, 2011a;Fedosov et al, 2011b) and the three-level multiscale structural model (Peng, Mashayekh & Zhu, 2014;Peng & Zhu, 2013). In the front tracking method, the cell membrane is discretized into a set of triangular planar elements ( Fig.…”

Hemodynamics in the Microcirculation and in Microfluidics

“…In most computational studies, the reference shape is assumed to be a biconcave disk, 47,108,129,138 and several important RBC dynamics, such as tank-treading, tumbling, and swinging motions in simple shear flow, can be simulated using this assumption. Peng et al 113 also numerically investigated RBC dynamics in shear flow using a multi-scale membrane model. The authors assumed a spheroidal stress-free shape in the cytoskeleton, instead of a biconcave shape, and reported that the cell maintained its biconcave shape during the tank-treading motion at a low shear rate.…”

“…A BEM is now widely used for cellular flow. 47,108,113,129 This method can explicitly treat viscous stress jump across the membrane, and is one of the most accurate computational schemes for tracking the interface. However, BEM is limited to a Stokes flow regime, and it is difficult to discuss an inertia effect.…”