Populational adaptive evolution, chemotherapeutic resistance and multiple anti-cancer therapies

Alexander Lorz; Tommaso Lorenzi; Michael E. Hochberg; Jean Clairambault; Benoît Perthame

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2013)

  • Volume: 47, Issue: 2, page 377-399
  • ISSN: 0764-583X

Abstract

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Resistance to chemotherapies, particularly to anticancer treatments, is an increasing medical concern. Among the many mechanisms at work in cancers, one of the most important is the selection of tumor cells expressing resistance genes or phenotypes. Motivated by the theory of mutation-selection in adaptive evolution, we propose a model based on a continuous variable that represents the expression level of a resistance gene (or genes, yielding a phenotype) influencing in healthy and tumor cells birth/death rates, effects of chemotherapies (both cytotoxic and cytostatic) and mutations. We extend previous work by demonstrating how qualitatively different actions of chemotherapeutic and cytostatic treatments may induce different levels of resistance. The mathematical interest of our study is in the formalism of constrained Hamilton–Jacobi equations in the framework of viscosity solutions. We derive the long-term temporal dynamics of the fittest traits in the regime of small mutations. In the context of adaptive cancer management, we also analyse whether an optimal drug level is better than the maximal tolerated dose.

How to cite

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Lorz, Alexander, et al. "Populational adaptive evolution, chemotherapeutic resistance and multiple anti-cancer therapies." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 47.2 (2013): 377-399. <http://eudml.org/doc/273323>.

@article{Lorz2013,
abstract = {Resistance to chemotherapies, particularly to anticancer treatments, is an increasing medical concern. Among the many mechanisms at work in cancers, one of the most important is the selection of tumor cells expressing resistance genes or phenotypes. Motivated by the theory of mutation-selection in adaptive evolution, we propose a model based on a continuous variable that represents the expression level of a resistance gene (or genes, yielding a phenotype) influencing in healthy and tumor cells birth/death rates, effects of chemotherapies (both cytotoxic and cytostatic) and mutations. We extend previous work by demonstrating how qualitatively different actions of chemotherapeutic and cytostatic treatments may induce different levels of resistance. The mathematical interest of our study is in the formalism of constrained Hamilton–Jacobi equations in the framework of viscosity solutions. We derive the long-term temporal dynamics of the fittest traits in the regime of small mutations. In the context of adaptive cancer management, we also analyse whether an optimal drug level is better than the maximal tolerated dose.},
author = {Lorz, Alexander, Lorenzi, Tommaso, Hochberg, Michael E., Clairambault, Jean, Perthame, Benoît},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {mathematical oncology; adaptive evolution; Hamilton–Jacobi equations; integro-differential equations; cancer; drug resistance; Hamilton-Jacobi equations},
language = {eng},
number = {2},
pages = {377-399},
publisher = {EDP-Sciences},
title = {Populational adaptive evolution, chemotherapeutic resistance and multiple anti-cancer therapies},
url = {http://eudml.org/doc/273323},
volume = {47},
year = {2013},
}

TY - JOUR
AU - Lorz, Alexander
AU - Lorenzi, Tommaso
AU - Hochberg, Michael E.
AU - Clairambault, Jean
AU - Perthame, Benoît
TI - Populational adaptive evolution, chemotherapeutic resistance and multiple anti-cancer therapies
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2013
PB - EDP-Sciences
VL - 47
IS - 2
SP - 377
EP - 399
AB - Resistance to chemotherapies, particularly to anticancer treatments, is an increasing medical concern. Among the many mechanisms at work in cancers, one of the most important is the selection of tumor cells expressing resistance genes or phenotypes. Motivated by the theory of mutation-selection in adaptive evolution, we propose a model based on a continuous variable that represents the expression level of a resistance gene (or genes, yielding a phenotype) influencing in healthy and tumor cells birth/death rates, effects of chemotherapies (both cytotoxic and cytostatic) and mutations. We extend previous work by demonstrating how qualitatively different actions of chemotherapeutic and cytostatic treatments may induce different levels of resistance. The mathematical interest of our study is in the formalism of constrained Hamilton–Jacobi equations in the framework of viscosity solutions. We derive the long-term temporal dynamics of the fittest traits in the regime of small mutations. In the context of adaptive cancer management, we also analyse whether an optimal drug level is better than the maximal tolerated dose.
LA - eng
KW - mathematical oncology; adaptive evolution; Hamilton–Jacobi equations; integro-differential equations; cancer; drug resistance; Hamilton-Jacobi equations
UR - http://eudml.org/doc/273323
ER -

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