A multiphase Cahn-Hilliard-Darcy model for tumour growth with necrosis

作者：Garcke, Harald; Lam, Kei Fong^*; Nuernberg, Robert; Sitka, Emanuel

来源：Mathematical Models and Methods in Applied Sciences, 2018, 28(3): 525-577.

DOI：10.1142/S0218202518500148

• Multiphase tumour growth
• phase-field model
• Darcy flow
• necrosis
• cellular adhesion
• matched asymptotic expansions
• finite element computations

We derive a Cahn-Hilliard-Darcy model to describe multiphase tumour growth taking interactions with multiple chemical species into account as well as the simultaneous occurrence of proliferating, quiescent and necrotic regions. A multitude of phenomena such as nutrient diffusion and consumption, angiogenesis, hypoxia, blood vessel growth, and inhibition by toxic agents, which are released for example by the necrotic cells, are included. A new feature of the modelling approach is that a volume-averaged velocity is used, which dramatically simplifies the resulting equations. With the help of formally matched asymptotic analysis we develop new sharp interface models. Finite element numerical computations are performed and in particular the effects of necrosis on tumour growth are investigated numerically. In particular, for certain modelling choices, we obtain some form of focal and patchy necrotic growth that have been observed in experiments.

• 出版日期2018-3