A Cahn–Hilliard–Darcy model for tumour growth with chemotaxis and active transport

Author:

Garcke Harald1,Lam Kei Fong1,Sitka Emanuel2,Styles Vanessa3

Affiliation:

1. Fakultät für Mathematik, Universität Regensburg, 93040 Regensburg, Germany

2. Fakultät für Medizin, Universität Regensburg, 93040 Regensburg, Germany

3. University of Sussex, Sussex House, Falmer, Brighton BN1 9RH, UK

Abstract

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.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modelling and Simulation

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