Mathematical Modelling of Cancer Invasion: The Multiple Roles of TGF-β Pathway on Tumour Proliferation and Cell Adhesion

Vasiliki Bitsouni (Lead / Corresponding author), Mark Chaplain, Raluca Eftimie

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)
189 Downloads (Pure)

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
Pages (from-to)1929-1962
Number of pages34
JournalMathematical Models and Methods in Applied Sciences
Volume27
Issue number10
DOIs
Publication statusPublished - 6 Jul 2017

Keywords

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

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