Multicellular simulations with shape and volume constraints using optimal transport

Many living and physical systems such as cell aggregates, tissues, or bacterial colonies behave as unconventional systems of particles that are strongly constrained by volume exclusion and shape interactions. Understanding how these constraints lead to macroscopic self-organized structures is a fundamental question in, e.g., developmental biology. Here, we introduce a framework to model particle systems with arbitrary volumes, dynamical shapes, and deformability properties. Our method is grounded in optimal transport theory and its recent applications in incompressible fluid flows, crowd dynamics, and material sciences. Our approach supports a wide range of interaction and deformation mechanisms, while automatically taking care of the volume exclusion constraint with state-of-the-art numerical performance. We showcase the versatility of this approach through a series of experiments, demonstrating how it extends and refines results from previous approaches, with a special focus on challenging 3D situations in biophysics.