Nonlinear Nonlocal Parabolic-Hyperbolic Coupled Systems for Cancer Cell Movement and Aggregation

  • Vasiliki Bitsouni

Student thesis: Doctoral ThesisDoctor of Philosophy


Cells adhere to each other and to the extracellular matrix (ECM) through protein molecules on the surface of the cells. The breaking and forming of adhesive bonds, a process critical in cancer invasion and metastasis, can be influenced by the mutation of cancer cells. Several molecules have been reported to play a crucial role in cellular adhesion and proliferation, and eventually in cancer progression, with TGF-β being one of the most important.

In this thesis, we propose a general framework to model cancer cells movement and aggregation, in response to nonlocal social interactions (that is, attraction towards neighbours that are far away, repulsion from those that are near by, and alignment with neighbours at intermediate distances), as well as other molecules' effect, e.g., TGF-β. We develop nonlocal mathematical models describing cancer invasion and metastasis as a result of integrin-controlled cell-cell adhesion and cell-matrix adhesion, for two cancer cell populations with different levels of mutation. The models consist of nonlinear partial differential equations, describing the dynamics of cancer cells and TGF-β dynamics, coupled with nonlinear ordinary differential equations describing the ECM and integrins dynamics. We study our models analytically and numerically, and we demostrate a wide range of spatiotemporal patterns. We investigate the effect of mutation and TGF-β concentration on the speed on cancer spread, as well as the effect of nonlocal interactions on cancer cells' speed and turning behaviour.
Date of Award2017
Original languageEnglish
SponsorsEngineering and Physical Sciences Research Council, Society for Mathematical Biology & British Applied Mathematics Colloquium Organising Committee
SupervisorRaluca Eftimie (Supervisor) & Mark Chaplain (Supervisor)


  • Non-local models of cancer invasion
  • Cell-cell and cell-matrix adhesion
  • Aggregation patterns
  • Cell heterogeneity
  • TGF-β
  • Existence and boundedness of solution

Cite this