New Perspectives in Multiscale Modelling and Analysis of Cancer Invasion (Keynote Speaker Talk)

Recognized as one of the hallmarks of cancer, cancer cell invasion into tissue is a complex process that plays a key role in the growth and spread of cancer, culminating in metastatic spread (secondary cancers). One common aspect of all cancer progression is the secretion of matrix degrading enzymes (MDEs) by the cancer cells that modify or destroy the surrounding tissue or extracellular matrix (ECM) and support local cancer cell invasion. In conjunction with MDE activities, increased cancer cell motility due to changes in cell-adhesion properties further exacerbates the invasion. Transmembrane calcium-dependent adhesion molecules (cadherins) interact with intra-cellular proteins, such as β-catenin and give rise to adhesion junctions, resulting in cell-cell adhesion. In addition to cell-cell adhesion, the binding of various ECM ligands to cell-surface receptors (integrins) enables cell- matrix adhesion. Thus, processes occurring at a molecular (micro) scale give rise to processes occurring at the tissue (macro) scale, via processes taking place at the cellular (meso) scale. The interplay between micro-, meso- and macro-scale processes involved in cancer cell invasion are still not fully understood. Despite recent mathematical modelling advances, the understanding of the biologically multiscale process of cancer invasion remains an open question. In this work we introduce a novel multiscale moving boundary approach for cancer invasion that accounts for cell-adhesion in the context of the multiphase nature of the ECM dynamics. Distinguishing here between the fibres component and the rest of the ECM components and incorporating their multiscale dynamics within the new modelling approach, this framework connects the tissue-scale macro-dynamics with both the proteolytic cell-scale dynamics occurring at the tumour invasive edge and the micro-scale ECM fibres dynamic degradation and realignment occurring inside the tumour domain. The presentation of the new modelling framework, will be accompanied by details of the computational approach and a discussion of the numerical simulation results