Red blood cell simulation using a coupled shell-fluid analysis purely based on the SPH method

In this paper, a novel 3D numerical method has been developed to simulate red blood cells (RBCs) based on the interaction between a shell-like solid structure and a fluid. RBC is assumed to be a thin shell encapsulating an internal fluid (cytoplasm) which is submerged in an external fluid (blood plasma). The approach is entirely based on the smoothed particle hydrodynamics (SPH) method for both fluid and the shell structure. Both cytoplasm and plasma are taken to be incompressible Newtonian fluid. As the kinematic assumptions for the shell, Reissner-Mindlin theory has been introduced into the formulation. Adopting a total Lagrangian (TL) formulation for the shell in the realm of small strains and finite deflection, the presented computational tool is capable of handling large displacements and rotations. As an application, the deformation of a single RBC while passing a stenosed capillary has been modeled. If the rheological behavior of the RBC changes, for example, due to some infection, it is reflected in its deformability when it passes through the microvessels. It can severely affect its proper function which is providing the oxygen and nutrient to the living cells. Hence, such numerical tools are useful in understanding and predicting the mechanical behavior of RBCs. Furthermore, the numerical simulation of stretching an RBC in the optical tweezers system is presented and the results are verified. To the best of authors' knowledge, a computational tool purely based on the SPH method in the framework of shell-fluid interaction for RBCs simulation is not available in the literature.