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

Vasiliki Bitsouni, Mark Andrew Joseph Chaplain, Raluca Eftimie

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)

Abstract

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.
Original languageEnglish
Article number1929
JournalMathematical Models and Methods in Applied Sciences
Volume27
Issue number10
Early online date6 Jul 2017
DOIs
Publication statusPublished - Sept 2017

Keywords

  • Non-local model of cancer progression
  • Existence
  • Boundedness of solutions
  • Cell heterogeneity
  • TGF-beta
  • Cell-cell and cell-matrix adhesion

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