Multiscale Modelling of Tumour Invasion: Bulk Dynamics and Leading Edge Peritumoural Interactions of Cancer Cells and ECM Fibres (Keynote Speaker Talk)

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 explores the dynamic interactions that the migratory cancer cells population and the accompanying matrix degrading enzymes(MDEs) have with the extracellular matrix (ECM) components, and in particular with the ECM fibres. These complex two-scale interactions are explored via two multiscale systems that share (and contribute to) the same macro-dynamics but have independent in nature micro- dynamics. Specifically, on the bulk of the tumour, this explores the dynamics fibres degradation and realignment occurring at cell-scale (and induced by the spatial flux of invading cancer cells) as well as the immediate impact that this continuously changing field of oriented ECM fibres has over the tumour macro-dynamics. On the other hand, the cell-scale proteolytic micro-dynamics occurring at the tumour invasive edge interacts with the peritumoural ECM fibres through the molecular fluxes of MDEs. This interfacial cell-scale interaction not only results in changes of the micro-scale distribution of peritumoural ECM fibres, but also influences directly the changes of the overall tumour morphology. The new multiscale modelling framework will be accompanied by details of the computational approach and a discussion of the numerical simulation results.