Mathematical modeling of gastro-intestinal metastasis resistance to tyrosine kinase inhibitors. (English) Zbl 1497.92110
Suzuki, Takashi (ed.) et al., Methods of mathematical oncology. Fusion of mathematics and biology. Selected papers based on the presentations at the symposium, Osaka, Japan, October 26–28, 2020. Singapore: Springer. Springer Proc. Math. Stat. 370, 15-49 (2021).
Summary: In this paper, we study a continuum mechanics model of gastrointestinal stroma tumor (GIST) evolution under the action of two specific treatments. The first-line treatment is a specific tyrosine kinase inhibitor (TKI), with a cytotoxic effect, that induces direct cell death. The second-line treatment is a multi-targeted TKI, with both cytotoxic and anti-angiogenic effect. The model is a coupled hyperbolic/elliptic system based on mass balance equations on cell densities coupled with a diffusion equation on the nutrients and oxygen concentrations. The tumor model involves 3 proliferating cell densities and a necrotic phase. Each proliferating cell density responds differently to the treatments: \(P_1\)-cells are killed by both treatments, \(P_2\)-cells are affected by the second-line treatment only, and \(P_3\) cells are resistant to both therapies. The necrotic cells are eliminated at a rate \(1/\tau\). We first prove the well-posedness of the model for any non-negative \(\tau\). Then we study the asymptotic behavior of the solution as \(\tau\) goes to zero. In particular, we proved that the limit problem correspond to a tumor growth model without necrosis. This is of great interest regarding the modeling, since it proves the continuity with respect to \(\tau\) of the family of \(\tau\)-dependent, ensuring the consistency of the modeling.
For the entire collection see [Zbl 1480.92010].
For the entire collection see [Zbl 1480.92010].
MSC:
| 92C50 | Medical applications (general) |
| 35B40 | Asymptotic behavior of solutions to PDEs |
| 35Q92 | PDEs in connection with biology, chemistry and other natural sciences |
| 92C10 | Biomechanics |
| 92-10 | Mathematical modeling or simulation for problems pertaining to biology |
Keywords:
tumor growth modeling; drug resistance; partial differential equations; well-posedness; asymptotic analysisReferences:
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