A mathematical model for progression and heterogeneity in XXXX dynamics.

@entity5 @entity8553 @entity14 @entity105 @entity694
This paper deals with the development of a mathematical model that describes @entity5 dynamics at the cellular scale. The selected case study concerns @entity694 , which originates in colorectal crypts. Cells inside the crypts are assumed to be organized according to @entity8553 and to be homogeneously mixing. A mathematical model for @entity5 progression is proposed here. This model describes the generation of multiple clonal sub-populations of cells at different progression stages in a single crypt. Asymptotic analysis and simulations are developed with an exploratory aim. The obtained results offer some insights into the role played by mutation, proliferation and differentiation phenomena on @entity5 dynamics. In particular, the acquisition of an additional growing power and a reduction for cellular differentiation seem more likely to be the driving force behind @entity105 rather than an increase in the mutation rate. The mutation rate instead seems to affect progression dynamics and @entity5 heterogeneity. The role played by cells, at different differentiation stages, in the onset and progression of @entity14 is highlighted. The results support the fact that stem cells play a key role in @entity5 development and the idea that transit-amplifying cells could also take on an active role in @entity105 .
