  The extracellular matrix (ECM) is a highly complex structure through which
biochemical and mechanical signals are transmitted. In processes of cell
migration, the ECM also acts as a scaffold, providing structural support to
cells as well as points of potential attachment. Although the ECM is a
well-studied structure, its role in many biological processes remains difficult
to investigate comprehensively due to its complexity and structural variation
within an organism. In tandem with experiments, mathematical models are helpful
in refining and testing hypotheses, generating predictions, and exploring
conditions outside the scope of experiments. Such models can be combined and
calibrated with in vivo and in vitro data to identify critical cell-ECM
interactions that drive developmental and homeostatic processes, or the
progression of diseases. In this review, we focus on mathematical and
computational models of the ECM in processes such as cell migration including
cancer metastasis, and in tissue structure and morphogenesis. By highlighting
the predictive power of these models, we aim to help bridge the gap between
experimental and computational approaches to studying the ECM and to provide
guidance on selecting an appropriate model framework to complement
corresponding experimental studies.
