This paper deals with the derivation of a collective model of cell
populations out of an individual-based description of the underlying physical
particle system. By looking at the spatial distribution of cells in terms of
time-evolving measures, rather than at individual cell paths, we obtain an
ensemble representation stemming from the phenomenological behavior of the
single component cells. In particular, as a key advantage of our approach, the
scale of representation of the system, i.e., microscopic/discrete vs.
macroscopic/continuous, can be chosen a posteriori according only to the
spatial structure given to the aforesaid measures. The paper focuses in
particular on the use of different scales based on the specific functions
performed by cells. A two-population hybrid system is considered, where cells
with a specialized/differentiated phenotype are treated as a discrete
population of point masses while unspecialized/undifferentiated cell aggregates
are represented with a continuous approximation. Numerical simulations and
analytical investigations emphasize the role of some biologically relevant
parameters in determining the specific evolution of such a hybrid cell system.Comment: 25 pages, 6 figure
