|
Krzysztof Psiuk-Maksymowicz, "Modelling of tumour growth in situ." Short abstract: In spite of the fact that tumour in situ is non-invasive, it generates a potential risk for the host of having cancer. Basement membrane (BM) surrounding the tissue may constitute physical barrier for a tumour expansion. Growth of the tumour mass within a closed domain results in elevation of residual stress, which in turn may change functionality of blood and lymphatic vessels, and eventually may lead to phenomena of a high interstitial fluid pressure, hypoxia, necrosis, and angiogenesis. Proposed mathematical model describes dynamics of growth of the tumour within the healthy tissue surrounded by the BM. Thus, changes in location of the BM constitutes moving interface problem. In addition to continuous variables of the model for cell populations and oxygen concentration, model possesses discrete variables for distribution of blood and lymphatic vessels. By means of numerical simulations we examine different scenarios of tumour growth with accompanying blood and lymphatic vessels collapse, and rise of necrotic micro-regions. Prospective application of the model includes the framework for predicting perivascular distribution of drugs within interior and exterior of 'immobilised' solid tumour. |