Deformable cell–cell and cell–substrate interactions in semi-infinite domain

Leukocyte trafficking in the microvasculature during inflammatory response is known to involve multiple adhesion molecules and is referred to as the leukocyte adhesion cascade (LAC). Surface-bound selectins and their respective ligands are primarily responsible for tethering and rolling of leukocytes over inflamed endothelium. Numerical modeling of this response is challenging due to the nature of cell–cell interactions in Stokes flow (i.e., large domain of influence for each cell over its neighbors). Here, we discuss a novel simulation capable of modeling several steps of the LAC. The new model includes relevant contact and lubrication forces and extends a physics-based model for single particle rolling interactions developed by Hammer and Apte (1992), for multiparticle interactions by King and Hammer (2001a), and for deformable particles by Gee and King (2006). We initially demonstrate the model for cell–cell collisions occurring near a planar substrate, and for cell–substrate adhesive interactions. The adhesion studies provide a new perspective of the contribution of Hertzian contact mechanics toward variations in contact area at the cell–substrate interface. The results confirm that interfacial contact area will increase as a result of the contact formulation and that this mechanism may enhance cell rolling interactions for cells driven toward endothelium by cell–cell collisions. As a result of cell compliance, rolling velocity may decrease significantly, compared to non-compliant cells.