A Multiscale Framework for Simulation of Individual Red Blood Cells in Macroscale Flows with Relevance to Hemolysis

The accurate simulation of the dynamics of red blood cells (RBCs) can be a challenging computational task, especially when they are flowing in a macroscale domain that is orders of magnitude larger than the cell. However, simulation of RBCs in macroscale domains is important, as hemolysis, the rupture of RBCs, often occurs in flows of this scale, particularly in implanted medical devices. This work presents a computational framework for accurately computing the behavior of RBCs as they traverse these types of flows. The RBCs are treated as Lagrangian tracers in which the local effects of the fluid on the RBCs are resolved, but the effects of the cell on the fluid are incorporated into the flow at the macroscale (e.g., via a shear-thinning model), allowing the RBC computations to be treated essentially as a post-processing step. At each time step, the boundary integral method is used in conjunction with the local velocity gradient of the fluid to solve for the velocity of the cell. The cells are represented in terms of spherical harmonic basis functions, which ensure exponential convergence of the integrals. The solver has shown good agreement with simulations of spherical capsules in shear flow, as well as with optical tweezer experiments on RBCs.