Modeling cell interactions under flow

In this review, we summarize the current state of understanding of the processes by which leukocytes, and other cells, such as tumor cells interact with the endothelium under various blood flow conditions. It is shown that the interactions are influenced by cell-cell adhesion properties, shear stresses due to the flow field and can also be modified by the cells microrheological properties. Different adhesion proteins are known to be involved leading to particular mechanisms by which interactions take place during inflammation or metastasis. Cell rolling, spreading, migration are discussed, as well as the effect of flow conditions on these mechanisms, including microfluidic effects. Several mathematical models proposed in recent years capturing the essential features of such interaction mechanisms are reviewed. Finally, we present a recent model in which the adhesion is given by a kinetics theory based model and the cell itself is modeled as a viscoelastic drop. Qualitative agreement is found between the predictions of this model and in vitro experiments.