In this paper, we develop a population balance model for cell aggregation and adhesion process in a nonuniform shear flow. Some Monte Carlo simulation results based on the model are presented for the heterotypic cell-cell collision and adhesion to a substrate under dynamic shear forces. In particular, we focus on leukocyte (PMN)-melanoma cell emboli formation and subsequent tethering to the vascular endothelium (EC) as a result of cell-cell aggregation. The simulation results are compared with the results of experimental measurement. Discussions are made on how we could further improve the accuracy of the population balance type modelling.

Our research focused on the polymorphonuclear neutrophils (PMNs) tethering to the vascular endothelial cells (EC) and the subsequent melanoma cell emboli formation in a shear flow, an important process of tumor cell extravasation from the circulation during metastasis. We applied population balance model based on Smoluchowski coagulation equation to study the heterotypic aggregation between PMNs and melanoma cells in the near-wall region of an in vitro parallel-plate flow chamber, which simulates in vivo cell-substrate adhesion from the vasculatures by combining mathematical modeling and numerical simulations with experimental observations. To the best of our knowledge, a multiscale near-wall aggregation model was developed, for the first time, which incorporated the effects of both cell deformation and general ratios of heterotypic cells on the cell aggregation process. Quantitative agreement was found between numerical predictions and in vitro experiments. The effects of factors, including: intrinsic binding molecule properties, near-wall heterotypic cell concentrations, and cell deformations on the coagulation process, are discussed. Several parameter identification approaches are proposed and validated which, in turn, demonstrate the importance of the reaction coefficient and the critical bond number on the aggregation process.