Can the diverse elastic properties of trabecular and cortical bone be attributed to only a few tissue-independent phase properties and their interactions? Arguments from a multiscale approach
Can the diverse elastic properties of trabecular and cortical bone be attributed to only a few tissue-independent phase properties and their interactions? Arguments from a multiscale approach
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DOI：
10.1007/s10237-004-0040-0
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发表时间：
2004-06-01
影响因子：
3.5
通讯作者：
Dormieux, Luc
中科院分区：
文献类型：
--
作者：
Hellmich, Christian;Ulm, Franz-Josef;Dormieux, Luc
作为皮质骨和小梁骨的组织非依赖性阶段的候选者，我们考虑（i）羟基磷灰石，（ii）胶原蛋白，（iii）超微结构水和非胶原有机物质，以及（iv）填充哈弗氏管和小梁间空间的骨髓（水）。从文献中报道的实验，我们分配这些阶段的刚度属性在这些相定义的基础上，我们在连续介质微观力学的框架内开发了两步均匀化过程：（i）在100-200 nm的长度尺度下，羟基磷灰石（HA）晶体形成晶体泡沫，（“多晶”），水和非胶原有机物填充晶间空间（均质化步骤I）;（ii）在矿化组织的超微结构尺度上（5-10微米），由胶原分子组成的胶原组装体嵌入晶体泡沫中，机械地充当圆柱形模板。在5-10 mm的扩大材料规模下，第二均质化步骤还将骨小梁间隙调节为圆柱形孔内含物（哈弗氏管和鲍曼管，骨小梁间隙），其适用于骨小梁和皮质骨。该微观力学模型的输入是HA、胶原和微囊空间的组织特异性体积分数。输出的是组织特异性的超微结构和微观结构（=宏观=表观）弹性张量。第二个独立的实验集（成分数据和实验刚度值）被用来验证所提出的模型。我们报告一个小的平均预测误差的宏观刚度值。该验证表明，羟基磷灰石、胶原和水是组织独立相，通过其机械相互作用定义了所有骨（无论是皮质骨还是小梁骨）的弹性。
As candidates for tissue-independent phases of cortical and trabecular bone we consider (i) hydroxyapatite, (ii) collagen, (iii) ultrastructural water and non-collagenous organic matter, and (iv) marrow (water) filling the Haversian canals and the intertrabecular space. From experiments reported in the literature, we assign stiffness properties to these phases (experimental set I).On the basis of these phase definitions, we develop, within the framework of continuum micromechanics, a two-step homogenization procedure: (i) at a length scale of 100-200 nm, hydroxyapatite (HA) crystals build up a crystal foam ("polycrystal"), and water and non-collagenous organic matter fill the intercrystalline space (homogenization step I); (ii) at the ultrastructural scale of mineralized tissues (5-10 microns), collagen assemblies composed of collagen molecules are embedded into the crystal foam, acting mechanically as cylindrical templates. At an enlarged material scale of 5-10 mm, the second homogenization step also accommodates the micropore space as cylindrical pore inclusions (Haversian and Volkmann canals, inter-trabecular space) that are suitable for both trabecular and cortical bone. The inputs for this micromechanical model are the tissue-specific volume fractions of HA, collagen, and of the micropore space. The outputs are the tissue-specific ultrastructural and microstructural (=macroscopic=apparent) elasticity tensors.A second independent experimental set (composition data and experimental stiffness values) is employed to validate the proposed model. We report a small mean prediction error for the macroscopic stiffness values. The validation suggests that hydroxyapatite, collagen, and water are tissue-independent phases, which define, through their mechanical interaction, the elasticity of all bones, whether cortical or trabecular.