A degenerate haptotaxis system arising in the modelling of cancer invasion

30/11/2018, 14:00 - 15:00 in MAP/0G/017

Zhigun, Anna (Queen’s University Belfast)


Cancer cell migration is an essential stage in the development and expansion of tumours and their metastases. Once a tumour develops in some part of the body, it can grow and make its way through the surrounding tissue in order to reach the blood vessels. After transportation across the blood system and subsequent extravasation, further tumours thus emerge. This process is known as metastasis. Migrating through the extracellular matrix (ECM), the cells need to adhere to it for support and information exchange with their surroundings. Mathematical models of cancer invasion and their subsequent analysis and simulation can contribute to better understanding the involved biological phenomena and enable predictions about the development and the extent of a tumour. Therefore, they can suggest approaches to therapy improvements.
This talk is devoted to a class of strongly coupled PDE-ODE systems with tissue-dependent degenerate diffusion and haptotaxis that can serve as a model prototype for cancer cell invasion through the ECM. The talk covers both the modellings aspects and a discussion of the analytical challenges for this kind of non-standard degenerate systems for which the global existence of weak solutions was established. Moreover, some numerical simulations will be presented which illustrate a possible model behaviour in a two-dimensional setting. The numerical results recover qualitatively the infiltrative patterns observed histologically. They further allow to establish a qualitative relationship between the structure of the tissue and the expansion of the tumour, thus paying heed to its heterogeneity.