UPC-EEBE, Eduard Maristany, 14, 08019 Barcelona, Spain.
UPC-EEBE, Eduard Maristany, 14, 08019 Barcelona, Spain.
Med Eng Phys. 2023 Jul;117:104004. doi: 10.1016/j.medengphy.2023.104004. Epub 2023 Jun 5.
Numerous prior studies hypothesized a power-law relationship (E∝ρ) between cortical bone Young's modulus (E) and density (ρ) with an exponent 2.3≤α≤3.0, that has not been previously justified in the literature on a theoretical level. Moreover, despite the fact microstructure have been extensively studied, the material correlate of Fractal Dimension (FD) as a descriptor of bone microstructure was not clear in previous studies.
This study examined the effect of mineral content and density on the mechanical properties of a large number of human rib cortical bone samples. The mechanical properties were calculated using Digital Image Correlation and uniaxial tensile tests. CT scans were used to calculate the Fractal Dimension (FD) of each specimen. For each specimen, the mineral (f), organic (f) and water (f) weight fractions were determined. In addition, density was measured after a drying-and-ashing process. Then, Regression Analysis was employed to investigate the relationship between anthropometric variables, weight fractions, density and FD, as well as its impact on the mechanical properties.
Young's modulus exhibited a power-law relationship with an exponent of α>2.3 when using the conventional density (wet density), but α=2 when using dry density (desecated specimens). In addition, FD increases with decreasing cortical bone density. A significant relationship has been found between FD and density, whereby FD is correlated with the embedding of low density regions in cortical bone.
This study provides a new insight in the exponent value of the power-law relation between Young's Modulus and density, and relates bone behavior with the fragile fracture theory in ceramic materials. Moreover, the results suggest that Fractal Dimension is related to presence of low-density regions.
许多先前的研究假设皮质骨杨氏模量 (E) 和密度 (ρ) 之间存在幂律关系 (E∝ρ)，其指数为 2.3≤α≤3.0，但在文献中尚未从理论上证明这一点。此外，尽管微观结构已经得到广泛研究，但作为骨微观结构描述符的分形维数 (FD) 的材料相关性在以前的研究中并不明确。
本研究检查了大量人肋骨皮质骨样本的矿物质含量和密度对力学性能的影响。使用数字图像相关和单轴拉伸试验计算力学性能。使用 CT 扫描计算每个标本的分形维数 (FD)。对于每个标本，确定矿物质 (f)、有机物质 (f) 和水 (f) 的重量分数。此外，在干燥和灰化过程后测量密度。然后，回归分析用于研究人体测量变量、重量分数、密度和 FD 之间的关系，以及它们对力学性能的影响。
当使用常规密度（湿密度）时，杨氏模量表现出幂律关系，指数为 α>2.3，但当使用干燥密度（去湿标本）时，α=2。此外，FD 随皮质骨密度的降低而增加。发现 FD 与密度之间存在显著关系，即 FD 与皮质骨中低密度区域的嵌入有关。
本研究为杨氏模量与密度之间幂律关系的指数值提供了新的见解，并将骨行为与陶瓷材料中的易碎断裂理论联系起来。此外，结果表明分形维数与低密度区域的存在有关。
