Population Scale Spatio-Structural Modelling of Directed Cancer Invasion

As treatments for cancer continue to elude the biomedical community, and although it is well documented that cancer cells exert significant forces to dynamically rearrange the extra-cellular matrix (ECM), there remains a need for tumour, or population, scale mathematical models fit for spatial comparison to in vivo data. Employing a spatio-structural partial differential equation (PDE) framework, we are able to model the tissue scale dynamics resulting from tensile forces exerted by the cell population upon the ECM and the subsequent invasion of cells into their local environments. We also develop qualitative methods to theoretically explore the effects of alignment between cell polarisation and ECM fibre orientation on the invasive displacement of cancer sub-clusters. Numerical results show the multi-dimensional capacity of cells to reorient the fibrous ECM environment and invade the local tissue, where initial conflict between the cellular polarisation and fibre alignment impedes this process. The model also demonstrates the emergent phenomenon of structural heterogeneity from near-homogeneous initial conditions. This modelling framework provides a novel opportunity for the quantitative exploration of the biochemical and spatial processes of cancer invasion, whilst the resulting images provide an interesting candidate for comparison with robust experimental results.