Mathematical study and asymptotic analysis of a model for tumor drug resistanceReport as inadecuate

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1 UB - Université de Bordeaux 2 IMB - Institut de Mathématiques de Bordeaux 3 MONC - Modélisation Mathématique pour l-Oncologie IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest, Institut Bergonié - CRLCC Bordeaux

Abstract : In this paper we study a partial differential equations model for tumor drug resistance.The aim is to take two different treatments into account: a specific tyrosine kinase inhibitor TKItargeted therapy, with a cytotoxic effect, that induces direct cell death, and a multi-targeted TKI,with both cytotoxic and anti-angiogenic effect, which prevents the creation of new blood vessels.The model is based on mass balance equations on cell densities coupled with a diffusion equationfor the nutrients and oxygen concentration. We also consider a necrotic phase composed of deadcells, which are eliminated at a rate 1-τ . We first prove that, for any non-negative τ , the modelis well-posed and in a second part we study the asymptotic behavior for small τ . Such a resultis of great interest for the modeling, since it provides a family of τ -dependent models which iscontinuous with respect to τ

Keywords : Tumour growth modelling partial differential equations asymptotic analysis

Author: Thierry Colin - Thomas Michel - Clair Poignard -



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