Multiscale mathematical treatise of the invasion-metastasis cascade: from the solitary cancer cell migration to the holistic representation of the org

Cancer is one of the primer causes of death globally and one of the biggest health problems humanity faces. It is also one of the most complex questions that modern science addresses with the contribution of a multitude of scientific disciplines. Mathematics, in particular contributes, with its predictive competences and the precision of its results, in gaining a deeper understanding of cancer. Moreover, Mathematics enables the development and optimisation of new treatments and early detection strategies becoming thusly an integral part of the eventual cure of cancer.
The current PhD project is a part of this overall effort by employing an amalgamation of single- and multiscale mathematical methods with the aim to combine under a unified mathematical umbrella, several of the biomedical processes of the invasion-metastasis cascade.
In more detail, we will model and simulate morphological and migratory changes that the cancer cells undergo during the Epithelial-to-Mesenchymal Transition (EMT); a cellular differentiation procedure after which the cells obtain mesenchymal character, break their cell-cell adhesions, and enhance their motility properties. We also study short- and long-range cell-cell interactions and investigate the collective migration of cancer cells and the formation of new cancer cell-clusters. At higher scale, at the level of the tissue, we will address the epithelial movement of a contiguous cluster of cancer cells while allowing for the EMT to take place and give rise to solitary mesenchymal-like cancer cells. When these cancer cells invade the local tissue and reach a nearby blood vessel, they intravasate and enter the blood stream. Of particular importance in the current PhD project will be the modelling of the circulation of cancer cells (termed Circulatory Tumour Cells) in the blood stream and of the subsequent extravasation to new locations in the organism. These cancer cells undergo the opposite Mesenchymal-to-Epithelial Transition (MET) and conditionally engender new tumours; at this stage the metastasis has occurred. The final scale in the development of this PhD project will be the comprehensive combination of the circulatory network and various body organs in a holistic mathematical and computational representation of the organism.