Multiscale Modeling of a Red Blood Cell and its Fluid-Structure Interaction

We develop a three-level multiscale approach of the red blood cell (RBC) membrane and couple this approach with a boundary element method (BEM) for the surrounding Stokes flow to simulate the mechanical behavior of a RBC under various in vitro and in vivo conditions.;Our multiscale approach of this membrane includes three models: in the whole cell level (Level III), a finite element method (FEM) is employed to model the lipid bilayer and the cytoskeleton as two distinct layers of shells with sliding-only interaction. The mechanical properties of the cytoskeleton are obtained from a coarsegrained molecular dynamics model (Level II) of the junctional complex. The spectrin, a major protein of the cytoskeleton, is simulated using a molecular-based constitutive model (Level I), including its domain folding/unfolding reactions. A BEM of the surrounding Stokes flow is coupled with the FEM model of the membrane through a staggered coupling algorithm.;Using this method, we first predict the resting shapes of healthy and diseased RBCs.;Secondly, we simulate three quasi-static experiments of the micropipette aspiration, the optical tweezer stretching, and the flow channel stretching. Detailed distributions of the bilayer-skeleton interaction force that may cause their dissociation and lead to phenomena such as vesiculation are predicted. Specifically, our model predicts a correlation between the occurrence of spectrin unfolding and increase in the mechanical load upon individual bilayer-skeleton pinning points in micropipette aspirations. A simulation of the necking process after bilayer-skeleton dissociation is also conducted.;Thirdly, we study RBC dynamics in capillary flow and find that the skeleton density is large near the vessel wall, and the maximum bilayer-skeleton interaction force occurs at the trailing edge.;Finally, we investigate the tumbling, tank-treading, and swinging motions of RBCs in shear flow. The dependencies of tank-treading frequency on the blood plasma viscosity and the membrane viscosity we found match well with the existing experimental and computational data. The simulation results show that during tank-treading there is almost no protein density variation of the skeleton due to the significant bilayer-skeleton friction. The distributions of shear deformation, bilayer-skeleton interaction forces are also predicted.