Triply periodic minimal surfaces (TPMS) are mathematically defined cellular structures whose geometry can be quickly adapted to target desired mechanical response (structural and fluid). This has made them desirable for a wide range of bioengineering applications; especially as bioinspired materials for bone replacement. The main objective of this study was to develop a novel analytical framework which would enable calculating permeability of TPMS structures based on the desired architecture, pore size and porosity. To achieve this, computer-aided designs of three TPMS structures (Fisher-Koch S, Gyroid and Schwarz P) were generated with varying cell size and porosity levels. Computational Fluid Dynamics (CFD) was used to calculate permeability for all models under laminar flow conditions. Permeability values were then used to fit an analytical model dependent on geometry parameters only. Results showed that permeability of the three architectures increased with porosity at different rates, highlighting the importance of pore distribution and architecture. The computed values of permeability fitted well with the suggested analytical model (R²>0.99, p<0.001). In conclusion, the novel analytical framework presented in the current study enables predicting permeability values of TPMS structures based on geometrical parameters within a difference <5%. This model, which could be combined with existing structural analytical models, could open new possibilities for the smart optimisation of TPMS structures for biomedical applications where structural and fluid flow properties need to be optimised.

三重周期性最小表面 (TPMS) 是数学定义的细胞结构，其几何形状可以快速适应目标所需的机械响应（结构和流体）。这使它们成为广泛的生物工程应用的理想选择。尤其是作为骨置换的仿生材料。本研究的主要目的是开发一种新的分析框架，能够根据所需的结构、孔径和孔隙率计算 TPMS 结构的渗透率。为了实现这一目标，生成了三种 TPMS 结构（Fisher-Koch S、Gyroid 和 Schwarz P）的计算机辅助设计，具有不同的单元尺寸和孔隙率水平。计算流体动力学 (CFD) 用于计算层流条件下所有模型的渗透率。然后使用渗透率值来拟合仅依赖于几何参数的分析模型。结果表明，三种结构的渗透率随着孔隙率的增加而增加，突出了孔隙分布和结构的重要性。渗透率的计算值与建议的分析模型 (R² > 0.99，p < 0.001）。总之，当前研究中提出的新型分析框架能够基于差异小于 5% 的几何参数预测 TPMS 结构的渗透率值。该模型可以与现有的结构分析模型相结合，可以为需要优化结构和流体流动特性的生物医学应用的 TPMS 结构智能优化开辟新的可能性。