A stochastic model of cell aggregation under planar flow in the dilute regime

Models of the adhesion of a population of cells in a plane flow are developed, considering the dilute regime. Cells considered as rigid punctual entities are virtually injected at regular times within a plane channel limited by two fixed planes. The pressure profile is supposed to be triangular (constant gradient), in accordance with the assumptions of a Poiseuille flow. The cell adherence to the channel wall is governed by the balance of forces, accounting for gravity, non-specific physical interactions, such as electrostatic effects (repulsive) and Van der Waals forces (attractive), specific adhesive forces representing the ligand–receptor interactions, and friction between cells and the fluid in the vicinity of the endothelium wall. The spatial distribution of the adhesion molecules along the wall is supposed to be a random event, accounted for by a stochastic spatial variability of the dipolar moments of those molecules, according to a Gaussian process. Experimental trends reported for the rate of aggregation of L-selectin mediated leukocytes under shear flow are in qualitative accordance with the evolution versus time of adhering cells obtained by the present simulations. The effect of the maximal injection pressure on those kinetics is assessed.