Bridging the scales for deformable red blood cells simulation: from resolved immersed boundary to unresolved CFD-DEM

Several methods exist for cell-level simulation of blood, due to the undeniable interest this topic holds in the biomedical field. Nevertheless, the amount of computational resources required for these resolved methods limits their application to large-scale problems. On the other hand, the single-phase approximation of blood as a non-Newtonian liquid, while attaining fast results, neglects its multiphase nature, hindering its application to all cases where the presence of cells cannot be overlooked. This work aims to bridge the gap between these two approaches by proposing an efficient upscaling strategy. An immersed boundary approach based on the lattice Boltzmann method (LBM), coupled with a nodal projective finite element solver (npFEM) for the dynamics of the red blood cell (RBC) membrane is adopted to construct a dataset for the properties of RBCs embedded in a flow. Different quantities such as RBC deformation and experienced drag and lift forces are then collected and utilized to derive closure models for an unresolved CFD-DEM solver, which allows the simulation of hundreds of thousands of RBCs with substantially lower computational costs. The strategy is tested against previous experimental studies and then used for real-scale applications such as the design of microfluidics devices for plasma separation and the investigation of channels with different degrees of stenosis mimicking cases of vein occlusion. The presented approach potentially allows cell-level blood flow simulations with up to O $\left({10}^6\right)$ RBCs and returns accurate results when tested in scenarios including hundreds of thousands RBCs, as proven by our prior work. The original contribution of this upscaling approach is to bridge the scale separation gap in cell-level blood flow simulations. It holds considerable potential for the simulation of practical bio-physical problems, such as thrombus formation and the investigation of RBCs as biocompatible drug carriers.