Mathematical modelling of cancer invasion : the multiple roles of TGF-β pathway on tumour proliferation and cell adhesion
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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-β) 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-β concentration. We prove the global existence of weak solutions to the model. We then use our model to explore numerically the role of TGF-β in cell aggregation and movement.
Bitsouni , V , Chaplain , M A J & Eftimie , R 2017 , ' Mathematical modelling of cancer invasion : the multiple roles of TGF- β pathway on tumour proliferation and cell adhesion ' Mathematical Models and Methods in Applied Sciences , vol. 27 , no. 10 , 1929 . DOI: 10.1142/S021820251750035X
Mathematical Models and Methods in Applied Sciences
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DescriptionVB acknowledges support from an Engineering and Physical Sciences Research Council (UK) grant number EP/L504932/1. RE was partially supported by an Engineering and Physical Sciences Research Council (UK) grant number EP/K033689/1.
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