Mathematical modelling of cancer cell invasion of tissue

Cancer cell invasion of tissue is a complex biological process during which cell migration through the extracellular matrix, facilitated by the secretion of degradative enzymes, is a central process. Cells can deform their cytoplasm to produce pseudopodia, anchor these pseudopodia to neighbouring spatial locations in the tissue and detach earlier bonds, to enable them to move and therefore migrate in a specified direction. Genetic mutations, chemoattractant gradients or a lack of nutrients in their current location can stimulate cell motility and cause them to migrate. When cancer cells migrate they degrade the surrounding extracellular matrix, thereby invading new territory. In this paper we propose a hybrid discrete-continuum two-scale model to study the early growth of solid tumours and their ability to degrade and migrate into the surrounding extracellular matrix. The cancer cells are modelled as discrete individual entities which interact with each other via a potential function, while the spatio-temporal dynamics of the other variables in the model (extracellular matrix, matrix degrading enzymes and degraded stroma) are governed by partial differential equations.