Re-polarisation of macrophages within a multi-scale moving boundary tumour invasion model

Cancer invasion of the surrounding tissue is a multiscale process that involves not only tumour cells but also other immune cells in the environment, such as the tumour-associated macrophages (TAMs). The heterogeneity of these immune cells, with the two extremes being the pro-inflammatory and anti-tumour M1 cells, and the anti-inflammatory and pro-tumour M2 cells, has a significant impact on cancer invasion as these cell interact in different ways with the tumour cells and with the ExtraCellular Matrix (ECM). Experimental studies have shown that cancer cells co-migrate with TAMs, but the impact of these different TAM sub-populations (which can change their phenotype and re-polarise depending on the microenvironment) on this co-migration is not fully understood. In this study, we extend a previous multi-scale moving boundary mathematical model, by introducing the M1-like macrophages alongside with their exerted multi-scale effects on the tumour invasion process. With the help of this model we investigate numerically the impact of re-polarising the M2 TAMs into the anti-tumoral M1 phenotype and how such a strategy affects the overall tumour progression. In particular, we investigate numerically whether the M2-->M1 re-polarisation could depend on time and/or space, and what would be the macroscopic effects of this spatial- and temporal-dependent re-polarisation on tumour invasion.