Many biological 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. To this end, various types of computational models have been developed: phase fields, cellular automata, vertex models, level-set, finite element simulations, etc. We introduce a new framework based on optimal transport theory to model particle systems with arbitrary dynamical shapes and deformability. Our method builds upon the pioneering work of Brenier on incompressible fluids and its recent applications to materials science. It lets us specify the shapes of individual cells and supports a wide range of interaction mechanisms, while automatically taking care of the volume exclusion constraint at an affordable numerical cost. We showcase the versatility of this approach by reproducing several classical systems in computational biology. Our Python code is freely available at: www.github.com/antoinediez/ICeShOT

翻译：许多生物系统，如细胞聚集体、组织或细菌菌落，其行为类似于受体积排斥和形状相互作用强烈约束的非传统粒子系统。理解这些约束如何导致宏观自组织结构，是发育生物学等领域的一个基本问题。为此，人们开发了多种计算模型：相场、元胞自动机、顶点模型、水平集、有限元模拟等。我们引入了一个基于最优输运理论的新框架，用于模拟具有任意动态形状和可变形性的粒子系统。该方法建立在Brenier关于不可压缩流体的开创性工作及其在材料科学中的近期应用之上。它允许我们指定单个细胞的形状，并支持多种相互作用机制，同时以可承受的计算成本自动处理体积排斥约束。通过复现计算生物学中的几个经典系统，我们展示了该方法的通用性。我们的Python代码可在www.github.com/antoinediez/ICeShOT免费获取。