Multiphase-Field Models of Tissues

Abstract

Understanding how cells coordinate their behaviors to produce large-scale patterns and functions is central to deciphering biological processes ranging from tissue development and regeneration to cancer progression and morphogenesis. Despite advances in imaging and mechanical characterization, the role of physical forces in collective cell dynamics remains incompletely understood. Physics-based models are essential for complementing experimental data, offering access to high-resolution spatiotemporal fields, and enabling mechanistic insights into complex multicellular systems. This review focuses on dense, soft tissues, in which the mechanical deformation of one cell drives reorganization of its neighbors, giving rise to emergent behaviors such as orientational order and long-range force transmission. The multiphase-field model provides a powerful and versatile framework to investigate such systems, bridging biological phenomena and the nonequilibrium physics of active matter. We discuss the theoretical foundations of the model and its applications to a range of biological contexts, including cell migration, heterogeneous populations, confined geometries, and metastasis. We also emphasize the integration of simulations with experimental data, highlighting how this approach is reshaping our understanding of tissue mechanics, collective order, and force transmission. Finally, we outline current trends and future challenges in applying multiphase-field models to biology and soft matter physics.