Non-Local Effects and Surface-Bound Reactions in Cancer Invasion Model Development, Analysis and Numerical Simulation

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The ability to invade tissue and form metastases (secondary tumours) is what makes cancer so dangerous. Key biological processes occurring during invasion are the secretion of matrix degrading enzymes, cell proliferation, the loss of cell-cell adhesion on one hand and enhanced cell-matrix adhesion on the other hand as well as active migration. A better understanding of the effect that biochemical (intracellular) and cellular processes have on tissue scale rearrangement of cells and matrix may help to develop treatment strategies. Hence, the modelling and numerical simulation of cancer cell invasion is of great interest and is the subject of ongoing research.In this project, we focus on two key aspects in the modelling of cancer invasion: cell-cell and cell-matrix adhesion (tissue-level modelling) and surface-bound reactions involved in cancer invasion.The modelling will be done on the tissue scale, which allows for an efficient simulation. The model will be analyzed regarding positivity, Turing-type instabilities and the influence of parameters, which are not well-characterized by experiments, on the model output. We will develop a simulation framework to test these models against the original model. Finally, these results will be transferred to a model of lymphangiogenesis in tumors.