An age-and-cyclin-structured cell population model with proliferation and quiescence for healthy and tumoral tissues

Fadia Bekkal Brikci (1) , Jean Clairambault (1) , Benjamin Ribba (2) , Benoît Perthame (1, 3)

1 BANG - Nonlinear Analysis for Biology and Geophysical flows
2 NUMED - Numerical Medicine
3 DMA - Département de Mathématiques et Applications - ENS Paris

We present a nonlinear model of the dynamics of a cell population divided in a proliferative and a quiescent compartments. The proliferative phase represents the complete cell division cycle ($G_{1}-S-G_{2}-M$) of a population committed to divide at its end. The model is structured by the time spent by a cell in the proliferative phase, and by the amount of \emph{cyclin~D/(CDK4 or 6)} complexes. Cells can transit from one compartment to the other, following transition rules which differ according to the tissue state: healthy or tumoral. The asymptotic behaviour of solutions of the nonlinear model is analysed in both cases, exhibiting tissue homeostasis or tumour exponential growth. The model is simulated by numerical solutions which confirm its theoretical predictions.

Mots clés: Cancer.; Population dynamics; Cell cycle; Cancer; Cyclins; Partial Differential Equations; Tumour growth

Domaines: Equations aux dérivées partielles [math.AP]

Fadia Bekkal Brikci, Jean Clairambault, Benjamin Ribba, Benoît Perthame. An age-and-cyclin-structured cell population model with proliferation and quiescence for healthy and tumoral tissues. [Research Report] RR-5941, INRIA. 2006. ⟨inria-00081301v2⟩