Multi-phase-field Models of Biological Tissues

The development of complex multicellular organisms from a single parent cell is a highly orchestrated process that cells conduct collectively without central guidance, creating intricate dynamic patterns essential for development and regeneration. Despite significant advances in imaging spatiotemporal dynamics of cell collectives and mechanical characterization techniques, the role of physical forces in biological functions remains poorly understood. Physics-based models are crucial in complementing experiments, providing high-resolution spatiotemporal fields in three dimensions. This review focuses on dense, soft multicellular systems, such as tissues, where mechanical deformation of one cell necessitates the re-organization of neighboring cells. The multi-phase-field model offers a rich physics-based framework to advance our understanding of biological systems and provides a robust playground for non-equilibrium physics of active matter. We discuss the foundational aspects of the multi-phase-field model and their applications in understanding physics of active matter. We also explore the integration of biological physics with experimental data, covering cell migration, heterogeneous cell populations, and confined systems. Finally, we highlight current trends, the importance of multi-phase-field models in biological and physics research, and future challenges.