无适应有限元建模用于动物细胞中表面-体部粘性流的模拟
Unfitted finite element modelling of surface-bulk viscous flows in animal cells
AI总结：
本文提出一种新的无适应有限元框架，用于模拟时间依赖域中的耦合表面-体部问题，重点研究动物细胞中肌动蛋白-肌球蛋白皮层与细胞质之间的流体-流体相互作用。通过结合迹有限元方法和聚合有限元方法，实现固定笛卡尔网格上的准确稳定模拟，捕捉自组织图案形成、曲率驱动松弛和细胞裂解等现象。
摘要：
本文提出了一种新的无适应有限元框架，用于模拟时间依赖域中的耦合表面-体部问题，重点研究动物细胞中肌动蛋白-肌球蛋白皮层与细胞质之间的流体-流体相互作用。皮层是细胞膜下的薄层，提供结构完整性并通过生成类似张力的表面收缩力驱动形状变化。皮层收缩会产生马兰戈尼样表面流，并诱导细胞质内的流体流动，这对于细胞分裂、迁移和极化等过程至关重要，尤其是在大动物细胞中。尽管其重要性，皮层-细胞质相互作用的时空调控仍不明确，计算建模极具挑战性，因为表面-体部动力学常导致大细胞变形。为解决这些挑战，我们提出了一种尖界面框架，将迹有限元方法用于表面流，将聚合有限元方法用于体部流。该方法使在固定笛卡尔网格上进行准确稳定模拟成为可能，无需重新网格化。该模型还通过表面传输分子调节剂来纳入机械化学反馈。我们使用基于水平集的方法在固定笛卡尔网格上求解由此产生的混合维系统，以跟踪演化的表面。数值实验验证了该方法的准确性和稳定性，捕捉了自组织图案形成、曲率驱动松弛和细胞裂解等现象。该新框架为研究动物细胞中日益复杂的形态发生过程提供了强大且可扩展的工具。
英文摘要：
This work presents a novel unfitted finite element framework to simulate coupled surface-bulk problems in time-dependent domains, focusing on fluid-fluid interactions in animal cells between the actomyosin cortex and the cytoplasm. The cortex, a thin layer beneath the plasma membrane, provides structural integrity and drives shape changes by generating surface contractile forces akin to tension. Cortical contractions generate Marangoni-like surface flows and induce intracellular cytoplasmic flows that are essential for processes such as cell division, migration, and polarization, particularly in large animal cells. Despite its importance, the spatiotemporal regulation of cortex-cytoplasm interactions remains poorly understood and computational modelling can be very challenging because surface-bulk dynamics often lead to large cell deformations. To address these challenges, we propose a sharp-interface framework that uniquely combines the trace finite element method for surface flows with the aggregated finite element method for bulk flows. This approach enables accurate and stable simulations on fixed Cartesian grids without remeshing. The model also incorporates mechanochemical feedback through the surface transport of a molecular regulator of active tension. We solve the resulting mixed-dimensional system on a fixed Cartesian grid using a level-set-based method to track the evolving surface. Numerical experiments validate the accuracy and stability of the method, capturing phenomena such as self-organised pattern formation, curvature-driven relaxation, and cell cleavage. This novel framework offers a powerful and extendable tool for investigating increasingly complex morphogenetic processes in animal cells.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
