Mathematical modelling of cancer invasion: The multiple roles of TGF-beta pathway on tumour proliferation and cell adhesion

作者：Bitsouni Vasiliki^*; Chaplain Mark A J; Eftimie Raluca

来源：Mathematical Models and Methods in Applied Sciences, 2017, 27(10): 1929-1962.

DOI：10.1142/S021820251750035X

• Non-local model of cancer progression
• existence
• boundedness of solution
• cell heterogeneity
• TGF-beta
• cell-cell and cell-matrix adhesion

In this paper, we develop a non-local mathematical model describing cancer cell invasion and movement as a result of integrin-controlled cell-cell adhesion and cell-matrix adhesion, and transforming growth factor-beta (TGF-beta) effect on cell proliferation and adhesion, for two cancer cell populations with different levels of mutation. The model consists of partial integro-differential equations describing the dynamics of two cancer cell populations, coupled with ordinary differential equations describing the extracellular matrix (ECM) degradation and the production and decay of integrins, and with a parabolic PDE governing the evolution of TGF-beta concentration. We prove the globalexistence of weak solutions to the model. We then use our model to explore numerically the role of TGF-beta in cell aggregation and movement.

• 出版日期2017-9