Front-tracking methods for capsules, vesicles and blood cells

High-accuracy computational modeling and simulation of microhemodynamics is a major challenge, primarily because blood in small vessels must be described as a dense suspension of deformable cells. Flow-induced deformation of erythrocytes combined with inter-cellular and cell–wall interactions give rise to a variety of phenomena including the formation of cell-depleted layers, the Fåhraeus effect, and the Fåhraeus–Lindqvist effect. Cell–wall hydrodynamic interactions play a critical role in leukocyte adhesion, a key process in inflammatory response. In this chapter, a front-tracking method for simulating cell motion is presented, accounting for the flow-induced deformation. The salient features of the algorithm are described and the hydrodynamics of isolated capsules, vesicles, and erythrocytes in a dilute suspension are discussed. Simulations illustrate the hydrodynamic interception of a pair of cells and the lateral migration of isolated capsules in wall-bounded Poiseuille flow. In the most comprehensive simulations, the channel flow of 1096 capsules in a dense suspension is described. Combining the basic algorithm with a coarse-grain Monte-Carlo method for describing intermolecular forces allows us to study the molecular interaction between a cell and a vessel wall. The integrated algorithm is applied to illustrate leukocyte rolling under the influence of a shear flow.