In silico, cell based approaches for modeling biological morphogenesis are used to test and validate our understanding of the biological and mechanical processes that are at work during the growth and the organization of multi-cell tissues. As compared to in vivo experiments, computer based frameworks dedicated to tissue modeling allow us to easily test different hypotheses, and to quantify the impact of various biophysically relevant parameters. Here, we propose a formalism based on a detailed, yet simple, description of cells that accounts for intra-, inter- and extra-cellular mechanisms. More precisely, cell growth and division are described through the space and time evolution of the membrane vertices. These vertices follow a Newtonian dynamics, meaning that their evolution is controlled by different types of forces: a membrane force (spring and bending), an adherence force (inter-cellular spring), external and internal pressure forces. Different evolution laws can be applied to the internal pressure, depending on the intra-cellular mechanism of interest. In addition to the cells dynamics, our formalism further relies on a lattice Boltzmann method, using the Palabos library, to simulate the diffusion of chemical signals. The latter aims at driving the growth and migration of a tissue by simply changing the state of the cells. All of this leads to an accurate description of the growth and division of cells, with realistic cell shapes and where membranes can have different properties. While this work is mainly of methodological nature, we also propose to validate our framework through simple, yet biologically relevant benchmark tests at both single-cell and full tissue scales. This includes free and chemically controlled cell tissue growth in an unbounded domain. The ability of our framework to simulate cell migration, cell compression and morphogenesis under external constraints is also investigated in a qualitative manner.

在计算机上，用于建模生物形态发生的基于细胞的方法用于测试和验证我们对多细胞组织的生长和组织过程中起作用的生物学和机械过程的理解。与体内实验相比，专门用于组织建模的基于计算机的框架使我们能够轻松测试不同的假设，并量化各种生物物理相关参数的影响。在这里，我们基于对细胞进行解释的简单而又详细的描述，提出了一种形式主义，解释了细胞内，细胞间和细胞外的机制。更准确地说，通过膜顶点的时空演化来描述细胞的生长和分裂。这些顶点遵循牛顿动力学，这意味着它们的演化受不同类型的力控制：膜力（弹簧和弯曲），粘附力（细胞间弹簧），外部和内部压力。根据所关注的细胞内机制，可以将不同的演化规律应用于内部压力。除了细胞动力学外，我们的形式主义还依赖于使用Palabos库的格子Boltzmann方法来模拟化学信号的扩散。后者旨在通过简单地改变细胞状态来驱动组织的生长和迁移。所有这些都导致对细胞生长和分裂的准确描述，具有逼真的细胞形状以及膜可能具有不同特性的位置。虽然这项工作主要是方法论性的，但我们也建议通过简单，在单细胞和整个组织规模上仍具有生物学相关性的基准测试。这包括在无界域中自由和化学控制的细胞组织生长。我们的框架在外部约束下模拟细胞迁移，细胞压缩和形态发生的能力也以定性的方式进行了研究。