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 i.e. the optimal dosing regimen to minimise the average size of the cancer cell population during the course of treatment.
Accepté le :
DOI : 10.1051/m2an/2019010
Mots-clés : cancer modelling, therapy optimisation, nonlocal parabolic equations, exact solutions, numerical optimal control
@article{M2AN_2019__53_4_1157_0,
author = {Almeida, Lu{\'\i}s and Bagnerini, Patrizia and Fabrini, Giulia and Hughes, Barry D. and Lorenzi, Tommaso},
title = {Evolution of cancer cell populations under cytotoxic therapy and treatment optimisation: insight from a phenotype-structured model},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {1157--1190},
publisher = {EDP-Sciences},
volume = {53},
number = {4},
year = {2019},
doi = {10.1051/m2an/2019010},
zbl = {1442.35193},
mrnumber = {3977080},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an/2019010/}
}
TY - JOUR AU - Almeida, Luís AU - Bagnerini, Patrizia AU - Fabrini, Giulia AU - Hughes, Barry D. AU - Lorenzi, Tommaso TI - Evolution of cancer cell populations under cytotoxic therapy and treatment optimisation: insight from a phenotype-structured model JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2019 SP - 1157 EP - 1190 VL - 53 IS - 4 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2019010/ DO - 10.1051/m2an/2019010 LA - en ID - M2AN_2019__53_4_1157_0 ER -
%0 Journal Article %A Almeida, Luís %A Bagnerini, Patrizia %A Fabrini, Giulia %A Hughes, Barry D. %A Lorenzi, Tommaso %T Evolution of cancer cell populations under cytotoxic therapy and treatment optimisation: insight from a phenotype-structured model %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2019 %P 1157-1190 %V 53 %N 4 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2019010/ %R 10.1051/m2an/2019010 %G en %F M2AN_2019__53_4_1157_0
Almeida, Luís; Bagnerini, Patrizia; Fabrini, Giulia; Hughes, Barry D.; Lorenzi, Tommaso. Evolution of cancer cell populations under cytotoxic therapy and treatment optimisation: insight from a phenotype-structured model. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 53 (2019) no. 4, pp. 1157-1190. doi : 10.1051/m2an/2019010. http://www.numdam.org/articles/10.1051/m2an/2019010/
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