Mathematical modelling of cancer cell invasion of tissue
: discrete and continuum approaches to studying the central role of adhesion

  • Vivi Andasari

    Student thesis: Doctoral ThesisDoctor of Philosophy


    Adhesion, which includes cell-to-cell and cell-to-extracellular-matrix adhesion, plays an important role in cancer invasion and metastasis. After undergoing morphological changes malignant and invasive tumour cells, i.e., cancer cells, break away from the primary tumour by loss of cell-cell adhesion, degrade their basement membrane and migrate through the extracellular matrix by enhancement of cell-matrix adhesion. These processes require interactions and signalling cross-talks between proteins and cellular components facilitating the cell adhesion. Although such processes are very complex, the necessity to fully understand the mechanism of cell adhesion is crucial for cancer studies, which may contribute to improving cancer treatment strategies. We consider mathematical models in an attempt to understand better the roles of cell adhesion involved in cancer invasion. Using mathematical models and computational simulations, the underlying complex biological processes can be better understood and their properties can be predicted that might not be evident in laboratory experiments. Cancer cell migration and invasion of the extracellular matrix involving adhesive interactions between cells mediated by cadherins and between cell and matrix mediated by integrins, are modelled by employing two types of mathematical models: a continuum approach and an individual-based approach. In the continuum approach, we use Partial Differential Equations in which cell adhesion is treated as non-local and formulated by integral terms. In the individual-based approach, we first develop pathways for cell-cell and cell-matrix adhesion using Ordinary Differential Equations and later incorporate the pathways in a simulation environment for multiscale computational modelling. The computational simulation results from the two different mathematical models show that we can predict invasive behaviour of cancer cells from cell adhesion properties. Invasion occurs if we reduce cell-cell adhesion and increase cell-matrix adhesion and vice versa. Changing the cell adhesion properties can affect the spatio-temporal behaviour of cancer cell invasion. These results may lead to broadening our understanding of cancer cell invasion and in the long term, contributing to methods of patient treatment.
    Date of Award2011
    Original languageEnglish
    SponsorsThe Northern Research Partnership
    SupervisorMark Chaplain (Supervisor)


    • Mathematics
    • Biology
    • Cancer
    • Cell adhesion
    • CompuCell3D
    • Bionetsolver
    • Cancer modelling
    • Multiscale
    • uPA
    • Nonlocal

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