A particle-based model for the transport of erythrocytes in capillaries

This paper presents a two-dimensional particle-based model for the red blood cell, and uses it to compute cell deformation in simple shear and pressure-driven flows. The cell membrane is replaced by a set of discrete particles connected by nonlinear springs; the spring law enforces conservation of the membrane area to a high accuracy. In addition, a linear bending elasticity is implemented using the deviation of the local curvature from the innate curvature of the biconcave shape of a resting red blood cell. The cytoplasm and the external liquid are modeled as homogeneous Newtonian fluids, and discretized by particles as in standard smoothed-particle-hydrodynamics (SPH) solution of the NavierStokes equations. Thus, the discrete particles serve not only as a numerical device for solving the partial differential equations, but also as a means for incorporating microscopic physics into the model. Numerically, the fluid flow and membrane deformation are computed, via the particle motion, by a two-step explicit scheme. The model parameters are determined from experimental measurements of cell viscosity and elastic moduli for shear, areal dilatation and bending. In a simple shear flow, the cell typically deforms to an elongated shape, with the membrane and cytoplasm undergoing tank-treading motion. In a Poiseuille flow, the cell develops the characteristic parachute shape. These are consistent with experimental observations. Comparison with prior computations using continuum models shows quantitative agreement without any fitting parameters, which is taken to be a validation of the particle-based model and the numerical algorithm.