Synchronisation and control of proliferation in cycling cell population models with age structure

Frédérique Billy 1 Jean Clairambault 1, * Olivier Fercoq 2, 3 Stéphane Gaubert 2, 3 Thomas Lepoutre 4, 5, 6 Thomas Ouillon 7 Shoko Saito 8
* Corresponding author
1 MAMBA - Modelling and Analysis for Medical and Biological Applications
LJLL - Laboratoire Jacques-Louis Lions, Inria Paris-Rocquencourt
3 MAXPLUS - Max-plus algebras and mathematics of decision
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France
4 DRACULA - Multi-scale modelling of cell dynamics : application to hematopoiesis
ICJ - Institut Camille Jordan [Villeurbanne], Inria Grenoble - Rhône-Alpes, CGPhiMC - Centre de génétique et de physiologie moléculaire et cellulaire
6 MMCS - Modélisation mathématique, calcul scientifique
ICJ - Institut Camille Jordan [Villeurbanne]
Abstract : We present and analyse in this article a mathematical question with a biological origin, the theoretical treatment of which may have far-reaching implications in the practical treatment of cancers. Starting from biological and clinical observations on cancer cells, tumourbearing laboratory rodents, and patients with cancer, we ask from a theoretical biology viewpoint questions that may be transcribed, using physiologically based modelling of cell proliferation dynamics, into mathematical questions. We then show how recent fluorescence-based image modelling techniques performed at the single cell level in proliferating cell populations allow to identify model parameters and how this may be applied to investigate healthy and cancer cell populations. Finally, we show how this modelling approach allows us to design original optimisation methods for anticancer therapeutics, in particular chronotherapeutics, by controlling eigenvalues of the differential operators underlying the cell proliferation dynamics, in tumour and in healthy cell populations. We propose a numerical algorithm to implement these principles.
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Frédérique Billy, Jean Clairambault, Olivier Fercoq, Stéphane Gaubert, Thomas Lepoutre, et al.. Synchronisation and control of proliferation in cycling cell population models with age structure. Mathematics and Computers in Simulation, Elsevier, 2014, 96, pp.66-94. ⟨10.1016/j.matcom.2012.03.005⟩. ⟨hal-00662885⟩

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