期刊
KINETIC AND RELATED MODELS
卷 10, 期 1, 页码 299-311出版社
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/krm.2017012
关键词
Cell populations; tissue growth; cancer invasion; interfaces; travelling waves; Pattern formation
资金
- French National Research Agency through the ANR blanche project Kibord [ANR-13-BS01-0004]
- Hadamard Mathematics Labex by the French National Research Agency [ANR-11-LABX-0056-LMH]
Partial differential equations describing the dynamics of cell population densities from a fluid mechanical perspective can model the growth of avascular tumours. In this framework, we consider a system of equations that describes the interaction between a population of dividing cells and a population of non-dividing cells. The two cell populations are characterised by different mobilities. We present the results of numerical simulations displaying two-dimensional spherical waves with sharp interfaces between dividing and non-dividing cells. Furthermore, we numerically observe how different ratios between the mobilities change the morphology of the interfaces, and lead to the emergence of finger-like patterns of invasion above a threshold. Motivated by these simulations, we study the existence of one-dimensional travelling wave solutions.
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