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
Copyright the Authors 2017. This is an Open Access article published by World Scientific Publishing Company. It is distributed under the terms of the Creative Commons Attribution 4.0 (CC-BY) License. Further distribution of this work is permitted, provided the original work is properly cited.
VB 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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