Tsubota Ken-ichi, Suzuki Yusuke, Yamada Tomonori, Hojo Masaki, Makinouchi Akitake, Adachi Taiji
Department of Mechanical Engineering, Chiba University, Yayoi, Inage, Japan.
J Biomech. 2009 May 29;42(8):1088-94. doi: 10.1016/j.jbiomech.2009.02.030. Epub 2009 Apr 29.
Ever since Julius Wolff proposed the law of bone transformation in the 19th century, it has been widely known that the trabecular structure of cancellous bone adapts functionally to the loading environment. To understand the mechanism of Wolff's law, a three-dimensional (3D) computer simulation of trabecular structural changes due to surface remodeling was performed for a human proximal femur. A large-scale voxel finite element model was constructed to simulate the structural changes of individual trabeculae over the entire cancellous region. As a simple remodeling model that considers bone cellular activities regulated by the local mechanical environment, nonuniformity of local stress was assumed to drive the trabecular surface remodeling to seek a uniform stress state. Simulation results demonstrated that cell-scale ( approximately 10microm) remodeling in response to mechanical stimulation created complex 3D trabecular structures of the entire bone-scale ( approximately 10cm), as illustrated in the reference of Wolff. The bone remodeling reproduced the characteristic anisotropic structure in the coronal cross section and the isotropic structures in other cross sections. The principal values and axes of a structure characterized by fabric ellipsoids corresponded to those of the apparent stress of the structure. The proposed large-scale computer simulation indicates that in a complex mechanical environment of a hierarchical bone structure of over 10(4) length scale (from approximately 10microm to approximately 10cm), a simple remodeling at the cellular/trabecular levels creates a highly complex and functional trabecular structure, as characterized by bone density and orientation.
自19世纪朱利叶斯·沃尔夫提出骨转化定律以来，松质骨的小梁结构在功能上适应负荷环境这一观点已广为人知。为了理解沃尔夫定律的机制，对人类近端股骨进行了表面重塑引起的小梁结构变化的三维（3D）计算机模拟。构建了一个大规模体素有限元模型，以模拟整个松质区域内单个小梁的结构变化。作为一个考虑由局部力学环境调节的骨细胞活动的简单重塑模型，假定局部应力的不均匀性驱动小梁表面重塑以寻求均匀应力状态。模拟结果表明，响应机械刺激的细胞尺度（约10微米）重塑产生了整个骨尺度（约10厘米）的复杂3D小梁结构，如沃尔夫文献中所示。骨重塑再现了冠状截面中的特征性各向异性结构以及其他截面中的各向同性结构。由织物椭球体表征的结构的主值和轴与该结构的表观应力的主值和轴相对应。所提出的大规模计算机模拟表明，在超过10⁴长度尺度（从约10微米到约10厘米）的分层骨结构的复杂力学环境中，细胞/小梁水平的简单重塑产生了高度复杂且具有功能的小梁结构，其特征为骨密度和方向。
