Evolution of cancer cell populations under cytotoxic therapy and treatment optimisation : insight from a phenotype-structured model
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We consider a phenotype-structured model of evolutionary dynamics in a population of cancer cells exposed to the action of a cytotoxic drug. The model consists of a nonlocal parabolic equation governing the evolution of the cell population density function. We develop a novel method for constructing exact solutions to the model equation, which allows for a systematic investigation of the way in which the size and the phenotypic composition of the cell population change in response to variations of the drug dose and other evolutionary parameters. Moreover, we address numerical optimal control for a calibrated version of the model based on biological data from the existing literature, in order to identify the drug delivery schedule that makes it possible to minimise either the population size at the end of the treatment or the average population size during the course of treatment. The results obtained challenge the notion that traditional high-dose therapy represents a 'one-fits-all solution' in anticancer therapy by showing that the continuous administration of a relatively low dose of the cytotoxic drug performs more closely to the optimal dosing regimen to minimise the average size of the cancer cell population during the course of treatment.
Almeida , L , Bagnerini , P , Fabrini , G , Hughes , B D & Lorenzi , T 2019 , ' Evolution of cancer cell populations under cytotoxic therapy and treatment optimisation : insight from a phenotype-structured model ' , ESAIM: Mathematical Modelling and Numerical Analysis (ESAIM: M2AN) , vol. 53 , no. 4 , pp. 1157-1190 . https://doi.org/10.1051/m2an/2019010
ESAIM: Mathematical Modelling and Numerical Analysis (ESAIM: M2AN)
Copyright © EDP Sciences, SMAI 2019. This work has been made available online in accordance with the publisher’s policies. This is the author created accepted version manuscript following peer review and as such may differ slightly from the final published version. The final published version of this work is available at https://doi.org/10.1051/m2an/2019010
DescriptionBDH acknowledges support from the Australian Research Council (DP140100339). LA and TL gratefully acknowledge support of the project PICS-CNRS no. 07688 and the French "ANR blanche" project Kibord: ANR-13-BS01-0004.
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