The importance of volume exclusion in modelling cellular migration.

The modelling of collective migration has traditionally been undertaken in a continuous framework, with little reference to the individual-level mechanisms that give rise to such a concerted movement. One factor whose importance is now coming to light is that the individuals themselves occupy space in the domain, thus obstructing others from moving past them (volume exclusion). In this work, we systematically derive continuous descriptions of cellular migration with volume exclusion for a wide range of individual-based mechanisms and in one, two and three dimensions. We also consider subpopulations of migrating individuals, which may have different characteristics, such as differing sizes and speeds of migration. We demonstrate that volume exclusion is of particular importance when biased movement is included, and thus conclude that volume exclusion may have its greatest effect when considering directed migratory mechanisms such as chemotaxis.