Investigation of a local modulus-density relationship for human femoral cortical bone

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.