Modelling targets for anticancer drug control optimization in physiologically structured cell population models

Frédérique Billy; Jean Clairambault; Olivier Fercoq; Tommaso Lorenzi; Alexander Lorz; Benoit Perthame

doi:10.1063/1.4756399

Modelling targets for anticancer drug control optimization in physiologically structured cell population models

Frédérique Billy
, Jean Clairambault
, Olivier Fercoq
, Tommaso Lorenzi
, Alexander Lorz
, Benoit Perthame

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

The main two pitfalls of therapeutics in clinical oncology, that limit increasing drug doses, are unwanted toxic side effects on healthy cell populations and occurrence of resistance to drugs in cancer cell populations. Depending on the constraint considered in the control problem at stake, toxicity or drug resistance, we present two different ways to model the evolution of proliferating cell populations, healthy and cancer, under the control of anti-cancer drugs. In the first case, we use a McKendrick age-structured model of the cell cycle, whereas in the second case, we use a model of evolutionary dynamics, physiologically structured according to a continuous phenotype standing for drug resistance. In both cases, we mention how drug targets may be chosen so as to accurately represent the effects of cytotoxic and of cytostatic drugs, separately, and how one may consider the problem of optimisation of combined therapies.

Original language	English
Title of host publication	Numerical Analysis and Applied Mathematics, ICNAAM 2012 - International Conference of Numerical Analysis and Applied Mathematics
Pages	1323-1326
Number of pages	4
Edition	1
DOIs	https://doi.org/10.1063/1.4756399
Publication status	Published - 1 Dec 2012
Event	International Conference of Numerical Analysis and Applied Mathematics, ICNAAM 2012 - Kos, Greece Duration: 19 Sept 2012 → 25 Sept 2012

Publication series

Name	AIP Conference Proceedings
Number	1
Volume	1479
ISSN (Print)	0094-243X
ISSN (Electronic)	1551-7616

Conference

Conference	International Conference of Numerical Analysis and Applied Mathematics, ICNAAM 2012
Country/Territory	Greece
City	Kos
Period	19/09/12 → 25/09/12

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

SDG 3 Good Health and Well-being

Keywords

Adaptive dynamics
Cancer
Cell division cycle
Cell population dynamics
Drug control
Partial Differential Equations
Physiologically structured Models

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10.1063/1.4756399

Cite this

Billy, F., Clairambault, J., Fercoq, O., Lorenzi, T., Lorz, A., & Perthame, B. (2012). Modelling targets for anticancer drug control optimization in physiologically structured cell population models. In Numerical Analysis and Applied Mathematics, ICNAAM 2012 - International Conference of Numerical Analysis and Applied Mathematics (1 ed., pp. 1323-1326). (AIP Conference Proceedings; Vol. 1479, No. 1). https://doi.org/10.1063/1.4756399

Billy, Frédérique ; Clairambault, Jean ; Fercoq, Olivier et al. / Modelling targets for anticancer drug control optimization in physiologically structured cell population models. Numerical Analysis and Applied Mathematics, ICNAAM 2012 - International Conference of Numerical Analysis and Applied Mathematics. 1. ed. 2012. pp. 1323-1326 (AIP Conference Proceedings; 1).

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title = "Modelling targets for anticancer drug control optimization in physiologically structured cell population models",

abstract = "The main two pitfalls of therapeutics in clinical oncology, that limit increasing drug doses, are unwanted toxic side effects on healthy cell populations and occurrence of resistance to drugs in cancer cell populations. Depending on the constraint considered in the control problem at stake, toxicity or drug resistance, we present two different ways to model the evolution of proliferating cell populations, healthy and cancer, under the control of anti-cancer drugs. In the first case, we use a McKendrick age-structured model of the cell cycle, whereas in the second case, we use a model of evolutionary dynamics, physiologically structured according to a continuous phenotype standing for drug resistance. In both cases, we mention how drug targets may be chosen so as to accurately represent the effects of cytotoxic and of cytostatic drugs, separately, and how one may consider the problem of optimisation of combined therapies.",

keywords = "Adaptive dynamics, Cancer, Cell division cycle, Cell population dynamics, Drug control, Partial Differential Equations, Physiologically structured Models",

author = "Fr{\'e}d{\'e}rique Billy and Jean Clairambault and Olivier Fercoq and Tommaso Lorenzi and Alexander Lorz and Benoit Perthame",

year = "2012",

month = dec,

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language = "English",

isbn = "9780735410916",

series = "AIP Conference Proceedings",

number = "1",

pages = "1323--1326",

booktitle = "Numerical Analysis and Applied Mathematics, ICNAAM 2012 - International Conference of Numerical Analysis and Applied Mathematics",

edition = "1",

note = "International Conference of Numerical Analysis and Applied Mathematics, ICNAAM 2012 ; Conference date: 19-09-2012 Through 25-09-2012",

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Billy, F, Clairambault, J, Fercoq, O, Lorenzi, T, Lorz, A & Perthame, B 2012, Modelling targets for anticancer drug control optimization in physiologically structured cell population models. in Numerical Analysis and Applied Mathematics, ICNAAM 2012 - International Conference of Numerical Analysis and Applied Mathematics. 1 edn, AIP Conference Proceedings, no. 1, vol. 1479, pp. 1323-1326, International Conference of Numerical Analysis and Applied Mathematics, ICNAAM 2012, Kos, Greece, 19/09/12. https://doi.org/10.1063/1.4756399

Modelling targets for anticancer drug control optimization in physiologically structured cell population models. / Billy, Frédérique; Clairambault, Jean; Fercoq, Olivier et al.
Numerical Analysis and Applied Mathematics, ICNAAM 2012 - International Conference of Numerical Analysis and Applied Mathematics. 1. ed. 2012. p. 1323-1326 (AIP Conference Proceedings; Vol. 1479, No. 1).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Modelling targets for anticancer drug control optimization in physiologically structured cell population models

AU - Billy, Frédérique

AU - Clairambault, Jean

AU - Fercoq, Olivier

AU - Lorenzi, Tommaso

AU - Lorz, Alexander

AU - Perthame, Benoit

PY - 2012/12/1

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N2 - The main two pitfalls of therapeutics in clinical oncology, that limit increasing drug doses, are unwanted toxic side effects on healthy cell populations and occurrence of resistance to drugs in cancer cell populations. Depending on the constraint considered in the control problem at stake, toxicity or drug resistance, we present two different ways to model the evolution of proliferating cell populations, healthy and cancer, under the control of anti-cancer drugs. In the first case, we use a McKendrick age-structured model of the cell cycle, whereas in the second case, we use a model of evolutionary dynamics, physiologically structured according to a continuous phenotype standing for drug resistance. In both cases, we mention how drug targets may be chosen so as to accurately represent the effects of cytotoxic and of cytostatic drugs, separately, and how one may consider the problem of optimisation of combined therapies.

AB - The main two pitfalls of therapeutics in clinical oncology, that limit increasing drug doses, are unwanted toxic side effects on healthy cell populations and occurrence of resistance to drugs in cancer cell populations. Depending on the constraint considered in the control problem at stake, toxicity or drug resistance, we present two different ways to model the evolution of proliferating cell populations, healthy and cancer, under the control of anti-cancer drugs. In the first case, we use a McKendrick age-structured model of the cell cycle, whereas in the second case, we use a model of evolutionary dynamics, physiologically structured according to a continuous phenotype standing for drug resistance. In both cases, we mention how drug targets may be chosen so as to accurately represent the effects of cytotoxic and of cytostatic drugs, separately, and how one may consider the problem of optimisation of combined therapies.

KW - Adaptive dynamics

KW - Cancer

KW - Cell division cycle

KW - Cell population dynamics

KW - Drug control

KW - Partial Differential Equations

KW - Physiologically structured Models

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SN - 9780735410916

T3 - AIP Conference Proceedings

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BT - Numerical Analysis and Applied Mathematics, ICNAAM 2012 - International Conference of Numerical Analysis and Applied Mathematics

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Billy F, Clairambault J, Fercoq O, Lorenzi T, Lorz A, Perthame B. Modelling targets for anticancer drug control optimization in physiologically structured cell population models. In Numerical Analysis and Applied Mathematics, ICNAAM 2012 - International Conference of Numerical Analysis and Applied Mathematics. 1 ed. 2012. p. 1323-1326. (AIP Conference Proceedings; 1). doi: 10.1063/1.4756399

Modelling targets for anticancer drug control optimization in physiologically structured cell population models

Abstract

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UN SDGs

Keywords

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