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| HAL : hal-00714274, version 1 |
| arXiv : 1207.0923 |
| Fiche détaillée |  Récupérer au format |
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| Populational adaptive evolution, chemotherapeutic resistance and multiple anti-cancer therapies |
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| Alexander Lorz 1, 2Tommaso Lorenzi 3 |
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| (03/07/2012) |
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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. |
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| 1 : | BANG (INRIA Rocquencourt) |
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INRIA – Laboratoire Jacques-Louis Lions |
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| 2 : | Laboratoire Jacques-Louis Lions (LJLL) |
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CNRS : UMR7598 – Université Pierre et Marie Curie [UPMC] - Paris VI |
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| 3 : | Department of Mathematics [Torino] (DIMAT) |
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Politecnico di Torino |
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| 4 : | Institut des Sciences de l'Evolution - Montpellier (ISEM) |
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CNRS : UMR5554 – Université Montpellier II - Sciences et techniques – Institut de recherche pour le développement [IRD] : UMR226 |
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| 5 : | National Center for Ecological Analysis and Synthesis (NCEAS) |
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National Center for Ecological Analysis and Synthesis |
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| 6 : | Santa Fe Institute |
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Santa Fe Institute |
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| Domaine | : | Mathématiques/Equations aux dérivées partielles Sciences du Vivant/Cancer |
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| Mathematical oncology – Adaptive evolution – Hamilton-Jacobi equations – Integro-differential equations – Cancer – Drug resistance |
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| Liste des fichiers attachés à ce document : | |||||
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| hal-00714274, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00714274 | |
| oai:hal.archives-ouvertes.fr:hal-00714274 | |
| Contributeur : Alexander Lorz | |
| Soumis le : Mardi 3 Juillet 2012, 18:07:00 | |
| Dernière modification le : Mercredi 4 Juillet 2012, 09:54:16 | |
