Mathematical Modelling of Cancer Growth and Spread: The Role of Matrix Metalloproteinases
A mass of cells that grow without normal bounds is termed a benign tumour if it does not invade locally into the tissue and malignant when it invades into its surrounding tissue. Benign tumours are often harmless unless the pressure they exhibit onto the tissue surrounding it causes trouble to the functioning of the human body as is often the case in brain tumours (gliomas) or other vital organs of the body. It is malignant tumours that are deemed to be made up of cancer cells and it is this process of invasion that defines them and will be studied in this thesis. We do this by considering two scales of interest in cancer cell invasion. In Chapters 4 and 5, we focus on tissue scale dynamics of a cancerous mass and the processes by which the cancerous mass is able to invade the surrounding tissue. Correspondingly, we focus on a continuum, deterministic approach to protease-dependent invasion where matrix degrading enzymes cleave collagen fibrils and other ECM components. Specifically, in Chapter 4 we formulate a PDE model of cancer cell invasion primarily through haptotaxis as the result of degradation of tissue from the proteolytic activity of the membrane bound MT1-MMP protein and the soluble MMP-2 protein in addition to the complexes formed, and consequences thereof, from interactions they have with one another and their endogenous inhibitor TIMP-2. In Chapter 5 we develop the PDE model of cancer cell invasion to incorporate additional dynamics of the tissue and how these may hamper cancer cell invasion and tissue degradation. Further, we investigate how the tissue may be reconditioned by MT1-MMP proteins to allow for additional cancer cell movement and tissue degradation.In Chapter 6, we consider how small protrusions from the cell termed invadopodia can affect the production of MMP-2 proteins and the focussing of ECM degradation, which has the consequence of allowing cancer cells to overcome barriers in the extracellular matrix.
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