Phase-Field Modeling of Individual and Collective Cell Migration

Cell motion is crucial in human health and development. Cells may migrate individually or in highly coordinated groups. Cell motion results from complex intra- and extra-cellular mechanochemical interactions. Computational models have become a powerful tool to shed light on the mechanisms that regulate cell migration. The phase-field method is an emerging modeling technique that permits a simple and direct formulation of the moving cell problem and the interaction between the cell and its environment. This paper intends to be a comprehensive review of phase-field models of individual and collective cell migration. We describe a numerical implementation, based on isogeometric analysis, which successfully deals with the challenges associated with phase-field problems. We present numerical simulations that illustrate the unique capabilities of the phase-field approach for cell migration. In particular, we show 2D and 3D simulations of individual cell migration in confined and fibrous environments that highlight the mechanochemical interplay between the cell and the extracellular environment. We also show 2D simulations of cell co-attraction in non-confluent multicellular systems, in which the use of the phase-field method is crucial to capture the dynamics of the multicellular system.