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

1 BANG - Nonlinear Analysis for Biology and Geophysical flows
LJLL - Laboratoire Jacques-Louis Lions, Inria Paris-Rocquencourt
2 NUMED - Numerical Medicine
UMPA-ENSL - Unité de Mathématiques Pures et Appliquées, Inria Grenoble - Rhône-Alpes
Abstract : 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.
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Reports

Cited literature [1 references]

https://hal.inria.fr/inria-00081301
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Submitted on : Thursday, June 29, 2006 - 5:28:45 PM
Last modification on : Friday, October 15, 2021 - 1:37:21 PM
Long-term archiving on: : Friday, November 25, 2016 - 11:08:18 AM

### Identifiers

• HAL Id : inria-00081301, version 2

### Citation

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⟩

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