NURBS-based numerical proxies for red blood cells and circulating tumor cells in microscale blood flow

We explore the use of NURBS-based immersed fluid-structure interaction algorithms to model the dynamics and rheology of red blood cells (RBCs) and nucleated cells. Prime examples of cells with nucleus that are relevant to this study are white blood cells (WBCs) and circulating tumor cells (CTCs). In this work, RBCs are modeled as thin solid membranes called capsules. To model cells with nucleus we introduce the concept of compound capsule which explicitly takes into account the nucleus as a bulky deformable solid. Our results indicate that to reproduce the behavior of RBCs in shear and parabolic flows, it is crucial to accurately solve the mass conservation equation near the fluid-solid interface. We show results of hyperelastic capsules and compound capsules in two- and three-dimensional settings. Finally, taking advantage of the geometric flexibility of our method, we simulate how a CTC passes through a narrowing. This is a feature of CTCs that has recently triggered excitement in the experimental community.