仿骨小梁力学性能的多孔结构拓扑优化设计

目的 基于动物骨小梁结构设计多孔植入物，阐述骨小梁结构的力学性能特点，说明使用仿骨小梁多孔结构植入物在临床治疗中的重要意义。方法 基于动物骨小梁结构的各向异性力学性能，利用拓扑优化技术进行多孔结构设计。根据骨功能原理提出分区、分块重建原则，利用 Micro-CT 图像重建动物骨小梁模型结构；根据代表体元法对模型施加边界约束和外载荷，以求解的力学性能作为优化的目标函数，利用拓扑优化中的变密度法和均匀化方法进行多孔结构设计及优化。结果 骨小梁结构具有各向异性的力学特点。求解发现，松质骨的体积分数在同一截面的边缘到中间主压力位置呈现递增趋势；泊松比无明显变化规律，均匀分布在0.17～0.30 之间；而弹性模量和剪切模量在松质骨主压力位置明显大于其他位置；基于上述结果进行拓扑优化设计，结果显示，优化后模型的泊松比分布在 0.17～0.30，弹性模量误差在 14%以下，最小的仅为 3%，剪切模量误差范围在 8%以下，基本符合最初的设计目标。结论 利用拓扑优化方法设计的多孔结构具有与动物松质骨相同的各向异性特点，同时减少应力集中现象，可以实现特定性能的多孔结构设计，为后续设计临床应用的多孔植入物提供一种合理有效的方法。
Objective Based on structure of animal trabecular bone, implants with porous structure were designed to describe mechanical properties of trabecular structure and explain significance of bionic trabecular porous implants in clinical treatment. Methods Based on anisotropic mechanical properties of animal trabecular bone, a porous structure was designed using the topology optimization method. The principles of partition and block reconstruction were first proposed according to bone function theory. The trabecular structure was then reconstructed based on micro-CT images. The boundary constraint and external load were applied on this model according to the respective-volume-element (RVE) method. Taking the solved mechanical properties as objective functions of optimization, the porous structure design and optimization were conducted using the variable density method and the homogenization method. Results The trabecular bone possessed the anisotropic mechanical properties. It was found that the volume fraction showed an increasing trend from the edge to the middle across the same section of trabecular bone. But there was no obvious regular pattern in Poisson’s ratio, which was evenly distributed in the range between 0.17 and 0.30. As to the values of elastic modulus and shear modulus, they were both significantly higher in the main pressure position compared with those in the other positions. After topography optimization based on these mechanical properties, the Poisson’s ratio of the optimized model was in the same range as the animal trabecular bone. The elastic modulus error was less than 14%， with the minimum being only 3%. In addition, the shear modulus error was below 8%， which ultimately complied with criteria of the original goal. Conclusions The designed porous structure based on topology optimization had the same anisotropic characteristics as animal trabecular bone, while reducing the stress concentration phenomenon, which could achieve the specific design for porous structure, thus providing a reasonable and effective method for