Differentiated cell behavior: a multiscale approach using measure theory

This paper deals with the derivation of Eulerian models of cell populations out of a microscopic Lagrangian description of the underlying physical particle system. By looking at the spatial distribution of cells in terms of time-evolving probability measures, rather than at individual cell paths, an ensemble representation of the cell colony is obtained, which can be either discrete or continuous according to the spatial structure of the probability. Remarkably, such an approach does not call for any assumption of continuity of the matter, thus providing consistency to the same modeling framework across all levels of representation. In addition, it is suitable to cope with the often ambiguous translation of microscopic arguments into continuous descriptions. Finally, by grounding cell dynamics on cell-cell interactions, it enables the concept of multiscale dynamics to be introduced and linked to the sensing ability of the cells.