This study examines the relationship between apparent density and Young’s modulus of human femoral cortical bone. The tested samples are segments of human femurs subjected to three-point bending, from which elastic stiffness can be derived from experimental load-displacement curves. These segments were previously scanned to obtain a voxelized density field. This field is transferred to a finite element (FE) mesh of the actual bone geometry, reconstructed in three dimensions. A geometric alignment method and a point location algorithm enable accurate mapping of density values onto the FE model. The relationship between Young’s modulus and density is modeled using a power law, with parameters identified by minimizing the difference between experimental and numerically simulated stiffness values. The analysis of ten femurs reveals that an exponent ranging from 3.54 to 4 provides a good fit to the data (R 2 ≈0.987). These findings are consistent with certain values reported in the literature and highlight the importance of a local approach in linking density to mechanical properties.
Godio-Raboutet et al. (Wed,) studied this question.