Differentiated cell behavior: a multiscale approach using measure theory
arXiv:1108.1212 · doi:10.1007/s00285-014-0846-z
Abstract
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.
25 pages, 6 figures
References in corpus (5)
- Multiscale modeling of granular flows with application to crowd dynamics
- Generalized Wasserstein distance and its application to transport equations with source
- Pedestrian flows in bounded domains with obstacles
- A hybrid mathematical model for self-organizing cell migration in the zebrafish lateral line
- Existence and approximation of probability measure solutions to models of collective behaviors