Rheology of red blood cell aggregation by computer simulation

The aggregation of red blood cells (RBC) induced by the interactions between RBCs is a dominant factor of the in vitro rheological properties of blood, and existing models of blood do not contain full cellular information. In this work, we introduce a new three-dimensional model that couples Navier–Stokes equations with cell interactions to investigate RBC aggregation and its effect on blood rheology. It consists of a depletion mediated aggregation model to describe the interactions of RBCs and an immersed continuum model to track the deformation/motion of RBCs in blood plasma. To overcome the large deformation of RBCs, the meshfree method is used to model the RBCs. Three important phenomena in blood rheology are successfully captured and studied via this approach: the shear rate dependence of blood viscosity, the influence of cell rigidity on blood viscosity, and the Fahraeus–Lindqvist effect. As a microscopic illustration of the shear-rate dependence of the blood’s viscoelasticity, the disaggregation of an RBC rouleau at shear rates varying between 0.125 and 24 s−1 is modeled. Lower RBC deformability and higher shear rates above 0.5 s−1 are found to facilitate disaggregation. The effective viscosities at different shear rates and for cells with different deformabilities are simulated. The numerical results are shown to agree with the reported experimental measurements. The Fahraeus–Lindqvist effect is, for the first time, studied through three-dimensional numerical simulations of blood flow through tubes with different diameters and is shown to be directly linked to axial-migration of deformable cells. This study shows that cell–cell interaction and cell deformability have significant effects on blood rheology in capillaries.