Garcke, Harald and Lam, Kei Fong and Sitka, Emanuel and Styles, Vanessa (2016) A Cahn-Hilliard-Darcy model for tumour growth with chemotaxis and active transport. MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 26 (6). pp. 1095-1148. ISSN 0218-2025, 1793-6314
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Using basic thermodynamic principles we derive a Cahn-Hilliard-Darcy model for tumour growth including nutrient diffusion, chemotaxis, active transport, adhesion, apoptosis and proliferation. In contrast to earlier works, the model is based on a volume-averaged velocity and in particular includes active transport mechanisms which ensure thermodynamic consistency. We perform a formally matched asymptotic expansion and develop several sharp interface models. Some of them are classical and some are new which for example include a jump in the nutrient density at the interface. A linear stability analysis for a growing nucleus is performed and in particular the role of the new active transport term is analysed. Numerical computations are performed to study the influence of the active transport term for specific growth scenarios.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | DIFFUSE INTERFACE MODEL; FINITE-ELEMENT APPROXIMATION; PHASE FIELD MODEL; MIXTURE MODEL; SIMULATION; SYSTEM; CANCER; FLOW; CALIBRATION; EXPRESSION; Tumour growth; diffuse interface model; Cahn-Hilliard equation; chemotaxis; Darcy's flow; matched asymptotic expansions; stability analysis; finite element computations |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics Mathematics > Prof. Dr. Harald Garcke |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 15 Mar 2019 08:48 |
| Last Modified: | 15 Mar 2019 08:48 |
| URI: | https://pred.uni-regensburg.de/id/eprint/2768 |
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