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

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.