Colabella Lucas, Cisilino Adriáan, Fachinotti Victor, Capiel Carlos, Kowalczyk Piotr
Instituto de Investigaciones en Ciencia y Tecnología de Materiales (INTEMA), Universidad Nacional de Mar del Plata (UNMdP)/Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Av. Juan B. Justo, 4302, Mar del Plata, Argentina.
Instituto de Investigaciones en Ciencia y Tecnología de Materiales (INTEMA), Universidad Nacional de Mar del Plata (UNMdP)/Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Av. Juan B. Justo, 4302, Mar del Plata, Argentina.
J Mech Behav Biomed Mater. 2020 Aug;108:103748. doi: 10.1016/j.jmbbm.2020.103748. Epub 2020 Apr 15.
Cancellous bone is a highly porous, heterogeneous, and anisotropic material which can be found at the epiphyses of long bones and in the vertebral bodies. The hierarchical architecture makes cancellous bone a prime example of a lightweight natural material that combines strength with toughness. Better understanding the mechanics of cancellous bone is of interest for the diagnosis of bone diseases, the evaluation of the risk of fracture, and for the design of artificial bones and bone scaffolds for tissue engineering. A multiscale optimization method to maximize the stiffness of artificial bones using biomimetic cellular microstructures described by a finite set of geometrical micro-parameters is presented here. The most outstanding characteristics of its implementation are the use of: an interior point optimization algorithm, a precalculated response surface methodology for the evaluation of the elastic tensor of the microstructure as an analytical function of the micro-parameters, and the adjoint method for the computation of the sensitivity of the macroscopic mechanical response to the variation of the micro-parameters. The performance and effectiveness of the tool are evaluated by solving a problem that consists in finding the optimal distribution of the microstructures for a proximal end of a femur subjected to physiological loads. Two strategies for the specification of the solid volume fraction constraints are assessed. The results are compared with data of a computed tomography study of an actual human bone. The model successfully predicts the main features of the spatial arrangement of the trabecular and cortical microstructures of the natural bone.
松质骨是一种高度多孔、非均质且各向异性的材料，存在于长骨的骨骺和椎体中。这种层次结构使松质骨成为兼具强度与韧性的轻质天然材料的典型代表。更好地理解松质骨的力学性能对于骨疾病的诊断、骨折风险评估以及组织工程中人工骨和骨支架的设计都具有重要意义。本文提出了一种多尺度优化方法，该方法利用由一组有限的几何微观参数描述的仿生细胞微结构来最大化人工骨的刚度。其实现过程最显著的特点是使用了：一种内点优化算法、一种预先计算的响应面方法，用于将微观结构的弹性张量评估为微观参数的解析函数，以及伴随方法来计算宏观力学响应相对于微观参数变化的灵敏度。通过解决一个问题来评估该工具的性能和有效性，该问题是为承受生理载荷的股骨近端寻找微观结构的最佳分布。评估了两种用于指定固体体积分数约束的策略。将结果与实际人体骨骼的计算机断层扫描研究数据进行了比较。该模型成功预测了天然骨小梁和皮质微观结构空间排列的主要特征。
