Relation between mechanical and densimetric properties to fractal dimension in human rib cortical bone

• Published in: Medical engineering & physics 2023-07, Vol.117, p.104004-104004, Article 104004
• Main Authors: García-Vilana, S., Sánchez-Molina, D., Velázquez-Ameijide, J., Llumà, J., Arregui-Dalmases, C.
• Format: Article
• Language: English
• Subjects: Biomechanical Phenomena; Bone Density; Cortical bone; Cortical Bone - diagnostic imaging; Density; Fractal dimension; Fractals; Humans; Mechanical properties; Mineral content; Ribs
• ISSN: 1350-4533; 1873-4030
• DOI: 10.1016/j.medengphy.2023.104004

Numerous prior studies hypothesized a power-law relationship (E∝ρα) 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 (fmin), organic (forg) and water (fwat) 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. •Tensile properties, fractal dimension and density of cortical bone coupons were obtained.•A high number of specimens from 21 to 91 years old were tested.•Equations relating mechanical properties with density, mineral and Fractal Dimension are given.•Density is related with Young Modulus with an exponent of 2, linking the behavior with porous ceramics theory.•Fractal Dimension decrease when density increases, interpreting FD as an alternative to porosity.