A mathematical model for progression and heterogeneity in colorectal cancer dynamics.

This paper deals with the development of a mathematical model that describes cancer dynamics at the cellular scale. The selected case study concerns colon and rectum cancer, which originates in colorectal crypts. Cells inside the crypts are assumed to be organized according to a compartmental-like arrangement and to be homogeneously mixing. A mathematical model for cancer 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 cancer 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 carcinogenesis rather than an increase in the mutation rate. The mutation rate instead seems to affect progression dynamics and intra-tumor heterogeneity. The role played by cells, at different differentiation stages, in the onset and progression of colorectal cancer is highlighted. The results support the fact that stem cells play a key role in cancer development and the idea that transit-amplifying cells could also take on an active role in carcinogenesis.