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

TY - JOUR

T1 - Mathematical Modelling of Cancer Invasion

T2 - The Multiple Roles of TGF-β Pathway on Tumour Proliferation and Cell Adhesion

AU - Bitsouni, Vasiliki

AU - Chaplain, Mark

AU - Eftimie, Raluca

N1 - The authors would like to thank Dr. D. Trucu for fruitful discussions. 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.

PY - 2017/7/6

Y1 - 2017/7/6

N2 - 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.

AB - 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.

KW - Non-local model of cancer progression

KW - Existence

KW - Boundedness of solution

KW - Cell heterogeneity

KW - TGF-β

KW - Cell-cell and cell-matrix adhesion

U2 - 10.1142/S021820251750035X

DO - 10.1142/S021820251750035X

M3 - Article

SN - 0218-2025

VL - 27

SP - 1929

EP - 1962

JO - Mathematical Models and Methods in Applied Sciences

JF - Mathematical Models and Methods in Applied Sciences

IS - 10

ER -