INTEMA-School of Engineering, CONICET-National University of Mar del Plata, Av. Juan B. Justo 4302, B7608FDQ, Mar del Plata, Argentina.
Laboratoire Modélisation et Simulation Multiéchelle, UMRS CNRS 8208, CNRS, 61 avenue du gal de Gaulle, 94010, Creteil, France.
Biomech Model Mechanobiol. 2017 Oct;16(5):1485-1502. doi: 10.1007/s10237-017-0901-y. Epub 2017 Apr 3.
Bone tissue mechanical properties and trabecular microarchitecture are the main factors that determine the biomechanical properties of cancellous bone. Artificial cancellous microstructures, typically described by a reduced number of geometrical parameters, can be designed to obtain a mechanical behavior mimicking that of natural bone. In this work, we assess the ability of the parameterized microstructure introduced by Kowalczyk (Comput Methods Biomech Biomed Eng 9:135-147, 2006. doi: 10.1080/10255840600751473 ) to mimic the elastic response of cancellous bone. Artificial microstructures are compared with actual bone samples in terms of elasticity matrices and their symmetry classes. The capability of the parameterized microstructure to combine the dominant isotropic, hexagonal, tetragonal and orthorhombic symmetry classes in the proportions present in the cancellous bone is shown. Based on this finding, two optimization approaches are devised to find the geometrical parameters of the artificial microstructure that better mimics the elastic response of a target natural bone specimen: a Sequential Quadratic Programming algorithm that minimizes the norm of the difference between the elasticity matrices, and a Pattern Search algorithm that minimizes the difference between the symmetry class decompositions. The pattern search approach is found to produce the best results. The performance of the method is demonstrated via analyses for 146 bone samples.
骨组织力学性能和小梁微结构是决定松质骨生物力学性能的主要因素。人工松质微观结构通常可以通过减少几个几何参数来设计，以获得模仿天然骨的力学行为。在这项工作中，我们评估了 Kowalczyk 提出的参数化微观结构（Comput Methods Biomech Biomed Eng 9:135-147, 2006. doi: 10.1080/10255840600751473）模拟松质骨弹性响应的能力。从弹性矩阵及其对称类的角度比较了人工微观结构和实际骨样本。结果表明，参数化微观结构能够以松质骨中存在的比例组合主导的各向同性、六方、四方和正交对称类。基于这一发现，设计了两种优化方法来找到更好地模拟目标天然骨样本弹性响应的人工微观结构的几何参数：一种是最小化弹性矩阵之间差异的范数的序列二次规划算法，另一种是最小化对称类分解之间差异的模式搜索算法。结果发现，模式搜索方法产生了最好的结果。该方法的性能通过对 146 个骨样本的分析得到了验证。
