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Solid tumours grow through two distinct phases: the avascular and the vascular phase. During the avascular growth phase, the size of the solid tumour is restricted largely by a diffusion-limited nutrient supply and the solid tumour remains localised and grows to a maximum of a few millimetres in diameter. However, during the vascular growth stage the process of cancer invasion of peritumoral tissue can and does take place. A crucial component of tissue invasion is the over-expression by the cancer cells of proteolytic enzyme activity, such as the urokinase-type plasminogen activator (uPA) and matrix metalloproteinases (MMPs). uPA itself initiates the activation of an enzymatic cascade that primarily involves the activation of plasminogen and subsequently its matrix degrading protein plasmin. Degradation of the matrix then enables the cancer cells to migrate through the tissue and subsequently to spread to secondary sites in the body forming secondary tumours or metastases. The establishment of metastases is the most significant turning point in the disease. The metastatic spread of tumour cells is the predominant cause of cancer deaths, and with few exceptions, all cancers can metastasize. Sequential steps in the so-called “metastatic cascade” include the following:

  • metastatic cells arise within a population of neoplastic/tumourigenic cells as a result of genomic instabilities;
  • vascularization of the tumour through the angiogenesis process;
  • detachment of metastatic-competent cells that have already evolved;
  • migration of the metastatic cells;
  • local invasion of cancer cells into the surrounding tissue, requiring adhesion to and subsequent degradation of extracellular matrix (ECM) components;
  • transport of metastatic cells either travelling individually or as emboli composed of tumour cells (homotypic) or of tumour cells and host cells (heterotypic);
  • metastatic cells survive their journey in the circulation system;
  • adhesion/arrest of the metastatic cells at the secondary site, cells or emboli arrest either because of physical limitations (i.e. too large to traverse a lumen) or by binding to specific molecules in particular organs or tissues;
  • escape from the blood circulation (extravasation);
  • proliferation of the metastatic tumour cells;
  • growth of the secondary tumour in the new organ.

Members of the Dundee Mathematical Biology group have developed models of different aspects of cancer invasion, using partial differential equation models and hybrid discrete-continuum models.

Key group publications:

  • The mathematical modelling of tumour angiogenesis and invasion,
    Chaplain, M.A.J., Acta Biotheor., 43: 387-402 (1995)

  • A mathematical model of vascular tumour growth and invasion,
    Orme, M.E., Chaplain, M.A.J., Math. Comp. Model., 23(10): 43-60 (1996)

  • A mathematical model of trophoblast invasion,
    Byrne, H.M., Chaplain, M.A.J., Pettet, G.J., McElwain D.L.S., J. Theor. Med., 1: 275-286 (1999)

  • Mathematical modelling of tumour invasion and metastasis,
    Anderson, A.R.A., Chaplain, M.A.J., Newman, E.L., Steele, R.J.C., Thompson, A.M., J. Theor. Med., 2: 129-154 (2000)

  • A hybrid mathematical model of solid tumour invasion: the importance of cell adhesion,
    Anderson, A.R.A, Math. Med. Biol., 22: 163-186 (2005)

  • Mathematical modelling of cancer cell invasion of tissue: the role of the urokinase plasminogen activation system,
    Chaplain, M.A.J., Lolas, G, Math. Modell. Methods. Appl. Sci., 15: 1685-1734 (2005)

  • Mathematical modelling of cancer invasion of tissue: dynamic heterogeneity,
    Chaplain, M.A.J., Lolas, G., Net. Hetero. Med., 1: 399-439 (2006)

  • Tumor morphology and phenotypic evolution driven by selective pressure from the microenvironment,
    Anderson, A.R.A., Quaranta, V., Cell, 127: 905-915 (2006)

  • Mathematical modelling of cancer cell invasion of tissue: local and non-local models and the effect of adhesion,
    Gerisch, A., Chaplain, M.A.J., J. Theor. Biol., 250: 684-704 (2008)

  • Modelling the influence of the E-Cadherin-β-Catenin pathway in cancer cell invasion and tissue architecture: a multi-scale approach,
    Ramis-Conde, I., Drasdo, D., Chaplain, M.A.J., Anderson, A.R.A., Biophys. J., 95: 155-165 (2008)

  • Mathematical modeling of cancer cell invasion of tissue: biological insight from mathematical analysis and computational simulation,
    Andasari, V., Gerisch, A., Lolas, G., South, A.P., Chaplain, M.A.J., J. Math. Biol., 63(1): 141-171 (2011)

  • Mathematical modelling of cancer invasion: The importance of cell-cell adhesion and cell-matrix adhesion,
    Chaplain, M.A.J., Lachowicz, M., Szymanska, Z., Wrzosek, D., Math. Mod. Meth. Appl. Sci., 21: 719-743 (2011)