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Some mathematical aspects of tumor growth and therapy

Benoît Perthame 1, 2, *
* Corresponding author
2 MAMBA - Modelling and Analysis for Medical and Biological Applications
LJLL - Laboratoire Jacques-Louis Lions, Inria Paris-Rocquencourt
Abstract : Mathematical models of tumor growth, written as partial differential equations or free boundary problems, are now in the toolbox for predicting the evolution of some cancers, using model based image analysis for example. These models serve not only to predict the evolution of cancers in medical treatments but also to understand the biological and mechanical effects that are involved in the tissue growth, the optimal therapy and, in some cases, in their implication in therapeutic failures. The models under consideration contain several levels of complexity, both in terms of the biological and mechanical effects, and therefore in their mathematical description. The number of scales, from the molecules, to the cell, to the organ and the entire body, explains partly the complexity of the problem. This paper focusses on two aspects of the problem which can be described with mathematical models keeping some simplicity. They have been chosen so as to cover mathematical questions which stem from both mechanical laws and biological considerations. I shall first present an asymptotic problem describing some mechanical properties of tumor growth and secondly, models of resistance to therapy and cell adaptation again using asymptotic analysis.
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Submitted on : Monday, September 1, 2014 - 5:53:53 PM
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  • HAL Id : hal-01059766, version 1

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Benoît Perthame. Some mathematical aspects of tumor growth and therapy. ICM 2014 - International Congress of Mathematicians, Aug 2014, Seoul, South Korea. ⟨hal-01059766⟩

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