Mathematical study and asymptotic analysis of a model for tumor drug resistance

Thierry Colin 1, 2, 3 Thomas Michel 2, 1, 3 Clair Poignard 2, 3
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 (TKI) targeted 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 equation for the nutrients and oxygen concentration. We also consider a necrotic phase composed of dead cells, which are eliminated at a rate 1/τ . We first prove that, for any non-negative τ , the model is well-posed and in a second part we study the asymptotic behavior for small τ . Such a result is of great interest for the modeling, since it provides a family of τ -dependent models which is continuous with respect to τ
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Thierry Colin, Thomas Michel, Clair Poignard. Mathematical study and asymptotic analysis of a model for tumor drug resistance. [Research Report] RR-8784, Inria Bordeaux Sud-Ouest. 2015, 32 p. ⟨hal-01211770v2⟩

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