A Measure-Theoretic Model for Collective Cell Migration and Aggregation

The aim of this paper is to present a measure-theoretic approach able to derive an Eulerian model of the dynamics of a cell population with a finite number of cells out of a microscopic Lagrangian description of the underlying cellular particle system. By looking at the spatial distribution of cells in terms of a time-evolving probability measure, rather than at individual cell paths, an ensemble representation of the cell colony is obtained, which can then result either in discrete, continuous, or hybrid approaches according to the spatial structure of such a probability measure. Remarkably, such an approach does not call for any assumption on the number of cells taken into account, thus providing consistency of the same modeling framework across all levels of representation. In addition, it is suitable to cope with the often ambiguous translation of microscopic arguments (i.e., cell dimensions and interaction radii) into macroscopic descriptions. The proposed approach, also extended to the case of multiple coexisting cell populations, is then tested with sample simulations that provide a useful sensitivity analysis of the model parameters.