Journal Article

Cell-cycle times and the tumour control probability

Adrian Maler and Frithjof Lutscher

in Mathematical Medicine and Biology: A Journal of the IMA

Published on behalf of Institute of Mathematics and its Applications

Volume 27, issue 4, pages 313-342
Published in print December 2010 | ISSN: 1477-8599
Published online December 2009 | e-ISSN: 1477-8602 | DOI:
Cell-cycle times and the tumour control probability

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  • Applied Mathematics
  • Biomathematics and Statistics


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Mechanistic dynamic cell population models for the tumour control probability (TCP) to date have used a simplistic representation of the cell cycle: either an exponential cell-cycle time distribution (Zaider & Minerbo, 2000, Tumour control probability: a formulation applicable to any temporal protocol of dose delivery. Phys. Med. Biol., 45, 279–293) or a two-compartment model (Dawson & Hillen, 2006, Derivation of the tumour control probability (TCP) from a cell cycle model. Comput. Math. Methods Med., 7, 121–142; Hillen, de Vries, Gong & Yurtseven, 2009, From cell population models to tumour control probability: including cell cycle effects. Acta Oncol. (submitted)). Neither of these simplifications captures realistic cell-cycle time distributions, which are rather narrowly peaked around the mean. We investigate how including such distributions affects predictions of the TCP. At first, we revisit the so-called ‘active–quiescent’ model that splits the cell cycle into two compartments and explore how an assumption of compartmental independence influences the predicted TCP. Then, we formulate a deterministic age-structured model and a corresponding branching process. We find that under realistic cell-cycle time distributions, lower treatment intensities are sufficient to obtain the same TCP as in the aforementioned models with simplified cell cycles, as long as the treatment is constant in time. For fractionated treatment, the situation reverses such that under realistic cell-cycle time distributions, the model requires more intense treatment to obtain the same TCP.

Keywords: tumour control probability; cell cycle; age-structured model; Bellman–Harris process

Journal Article.  0 words. 

Subjects: Applied Mathematics ; Biomathematics and Statistics

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