Mathematical models of the interaction of cells and cell aggregates with the extracellular matrix

It is nowadays understood that the interactions cells have with the fibrous environment they live in determine their behaviour. In fact, for instance, they play a fundamental role in cell motion, in tumour spread, in stem cell differentiation, and in tissue development. In this chapter we will describe several models that deal with different aspects characterizing these interactions. In particular, from the tutorial point of view, the topic will be used as a playground to briefly present several modelling frameworks, e.g., age-structured models, individual cell-based models, continuum mechanics, and mixture theory. The models presented will be usually characterised by multiscale aspects because, for instance, the physical parameters determining cell motion and duplication are affected by the expression of proteins inside the cell and of receptors at its membrane. In turn, the behaviour of cellular aggregates and of tissues depends on the behaviour of single cells. For this reason, some upscaling tool will also be described