Analysis of a molecular structured population model with possible polynomial growth for the cell division cycle

We analyse both theoretically and numerically a nonlinear model of the dynamics of a cell population divided into proliferative and quiescent compartments that is described in [F. Bekkal Brikci, J. Clairambault, B. Ribba, B. Perthame, An age-and-cyclin-structured cell population model with proliferation and quiescence, INRIA Research Report No 5941, 2006]. It is a physiological age and molecule-structured population model for the cell division cycle, which aims at representing both healthy and tumoral tissues. A noticeable feature of this model is to exhibit tissue homeostasis for healthy tissue and unlimited growth for tumoral tissue. In particular, the present paper analyses model parameters for which a tumoral tissue exhibits polynomial growth and not mere exponential growth. Polynomial tumour growth has been recently advocated by several authors, on the basis either of experimental observations or of individual cell-based simulations which take space limitations into account. This model is able to take such polynomial growth behaviour into account without considerations of space, by proposing exchange functions between the proliferative and quiescent compartments.