Relevance of cell-ECM interactions: From a biological perspective to the mathematical modeling

Cell migration across fibre networks and micro-channel structures has been widely demonstrated to be strongly influenced by the interactions between moving individuals and the surrounding extracellular matrix as well as by the mechanical properties of cell nucleus. In this respect, our work will be devoted to describe several mathematical models, which deal either with cell adhesion mechanics or with suitable analysis of the role played in cell movement by nucleus stiffness. In particular, the presented approaches span from discrete individual-based methods to continuous models and provide useful insights into selected determinant underlying cell migration within two- and three-dimensional matrix environments.