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

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posted on 2023-06-09, 01:17 authored by Harald Garcke, Kei Fong Lam, Emanuel Sitka, Vanessa StylesVanessa Styles
Using basic thermodynamical principles we derive a Cahn--Hilliard--Darcy model for tumour growth including nutrient diffusion, chemotaxis, active transport, adhesion, apoptosis and proliferation. The model generalise earlier models and in particular include active transport mechanisms which ensures thermodynamical consistency. We perform a formally matched asymptotic expansion and develop several sharp interface models. Some of them are classical and some new ones 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.

History

Publication status

  • Published

File Version

  • Accepted version

Journal

Mathematical Models and Methods in Applied Sciences

ISSN

0218-2025

Publisher

World Scientific Publishing

Issue

06

Volume

26

Page range

1095-1148

Department affiliated with

  • Mathematics Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2016-05-17

First Open Access (FOA) Date

2017-04-04

First Compliant Deposit (FCD) Date

2016-05-17

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