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

  • Authors:

  • Fré/dé/rique Billy;Jean Clairambaultt;Olivier Fercoq;Sté/phane Gaubertt;Thomas Lepoutre;Thomas Ouillon;Shoko Saito

  • Affiliations:

  • Inria Paris-Rocquencourt, Domaine de Voluceau, Rocquencourt, B.P. 105, F-78153, Le Chesnay, France and UPMC Univ Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions, F-75005, Paris, France;Inria Paris-Rocquencourt, Domaine de Voluceau, Rocquencourt, B.P. 105, F-78153, Le Chesnay, France and UPMC Univ Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions, F-75005, Paris, France;Inria Saclay Ile-de-France, Parc Orsay Université/, 4 rue Jacques Monod, F-91893, Orsay Cedex, France and Centre de Mathé/matiques Appliqué/es, CNRS UMR 7641, í/cole Polytechnique, ...;Inria Saclay Ile-de-France, Parc Orsay Université/, 4 rue Jacques Monod, F-91893, Orsay Cedex, France and Centre de Mathé/matiques Appliqué/es, CNRS UMR 7641, í/cole Polytechnique, ...;Inria Grenoble - Rhô/ne-Alpes, Inovallé/e, 655 avenue de l'Europe, Montbonnot, F-38 334, Saint Ismier Cedex, France and Université/ de Lyon, F-69000, Lyon, France/ Université/ Lyon ...;ENSTA ParisTech, 32 Bd Victor, F-75739, Paris Cedex 15, France;Department of Genetics, Center for Biomedical Genetics, Erasmus University Medical Center, Rotterdam, The Netherlands

  • Venue:
  • Mathematics and Computers in Simulation
  • Year:
  • 2014

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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, tumour-bearing 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.