Two-scale Moving Boundary Dynamics of Cancer Invasion:Heterotypic Cell Populations Evolution in Heterogeneous ECM

Cancer cell invasion, recognised as one of the hallmarks of cancer, is a complex process involving the secretion of matrix-degrading enzymes that have the ability to degrade the surrounding extracellular matrix (ECM). Combined with cell proliferation and migration, and changes in cell-cell and cell-matrix adhesion, the tumour is able to spread into the surrounding tissue. The multiscale character of this process is highlighted here through the double feedback link between the cell-scale molecular processes and those occurring at the tissue level. In this chapter, we build on the multiscale moving boundary framework proposed in [30] by developing the modelling of the tissue-scale dynamics to include cell-cell and cell-matrix adhesion in a heterogeneous cancer cell population. To that end, we consider here two cancer cell sub-populations, namely a primary tumour cell distribution and a second cancer cell sub-population that arises due to mutations from the primary tumour cells and exhibits higher malignancy. We explore the multiscale moving boundary dynamics of this heterogeneous tumour cell population in the presence of cell-adhesion at the tissue-scale and matrix degrading enzyme molecular processes considered at cell-scale. Using computational simulations we examine the effect of different levels of adhesion and matrix remodelling on the invasion of cancer cells