发表机构
TU Dresden; Center for Systems Biology Dresden (CSBD); Cluster of Excellence Physics of Life (PoL)（德累斯顿工业大学; 德累斯顿系统生物学中心; 生命物理学卓越集群）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对上皮组织的固体-流体双重特性，提出表面浅水波-赫耳弗里克模型，引入厚度场替代不可伸长约束，开发表面有限元数值格式，经测试可用于模拟形态发生过程中表面形状的演化。
AI 中文摘要
上皮组织在形态发生中发挥基础作用，从力学角度可视为兼具固体与流体双重特性的薄软材料。表面纳维-斯托克斯-赫耳弗里克模型通过结合弯曲特性与表面流体动力学来描述这些性质。为考虑细胞厚度的变化，我们借鉴浅水波方程的思路引入厚度场，该厚度场定义在（自演化的）表面上，替代了二维流体的不可伸长约束，同时将表面积守恒替换为薄膜流体的不可压缩约束，允许表面积发生变化。我们开发了基于表面有限元的数值格式，进行了收敛性测试，展示了在封闭表面包围体积恒定的情况下厚度变化对形状演化的影响，并探讨了其在形态发生建模中的意义。
英文摘要
Epithelial tissues play a fundamental role in morphogenesis. Mechanically they can be viewed as thin soft materials exhibiting a solid-fluid duality. The Surface Navier-Stokes-Helfrich model accounts for these properties by combining bending and surface hydrodynamics. In order to account for varying cell thickness we incorporate a thickness field in the spirit of a shallow-water equation, but defined on the (self-)evolving surface. This replaces the inextensibility constraint of the two-dimensional fluid and with it the conservation of surface area by an incompressibility constraint of the thin film fluid allowing for changes in surface area. We develop a numerical scheme based on surface finite elements, perform convergence tests, demonstrate the impact on shape evolution of closed surfaces with a constant enclosed volume and discuss implications on modeling morphogenesis.
