Deterministic Mathematical Modelling for Cancer Chronotherapeutics: Cell Population Dynamics and Treatment Optimization

  • Jean ClairambaultEmail author
Part of the Modeling and Simulation in Science, Engineering and Technology book series (MSSET)


In this short review paper, I will present the mathematical models that have been designed in the frame of continuous deterministic cell population dynamics that aim at optimization of cancer treatments using chronotherapeutics. Many authors have dealt with chronobiology of cancer, less with continuous mathematical models and even less with the declared aim to optimize chronotherapeutics. The biological and theoretical bases for these models are sketched, started from a historical viewpoint, and the main theoretical results are presented, with biological suggestions to account for them. Chronotherapeutics that leads to therapeutic optimization with the constraint of limiting unwanted toxicity of anticancer drugs towards healthy cell populations is put in a medical perspective together with the other main pitfall of cancer therapeutics, for which optimization procedures should have little to do with circadian biology, i.e., emergence of drug resistance in cancer cell populations, which is amenable to the use of other sorts of models, that are briefly mentioned.


Deterministic differential equations Cell population dynamics Control Optimization Cell and tissue biology Cancer Therapeutics 



The author is gratefully indebted to his young colleagues Frédérique Billy and Olivier Fercoq for the work achieved together in modelling, model identification and theoretical therapeutic optimization, and to Francis Lévi for his long-lasting collaboration and frequent and fruitful discussions. This work has been supported by a grant from the European Research Area in Systems Biology (ERASysBio+) to the French National Research Agency (ANR) #ANR-09-SYSB-002 for the research network Circadian and Cell Cycle Clock Systems in Cancer (C5Sys) coordinated by Francis Lévi (INSERM U776, Villejuif, France).


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© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.MAMBA (ex-BANG) project-teamINRIA Paris-RocquencourtRocquencourtFrance
  2. 2.Lab. Jacques-Louis Lions, BC 187, UPMCParis cedex 05France

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