Functionally Graded Lattice (FGL) Models for Predicting the Mechanical Properties of Femur Spongy Bone

The cancellous tissue forming the inner layer of long bones is highly porous at the center, with porosity decreasing toward the outer layer, leading to gradual variations in mechanical properties. Hence, cancellous tissue can be regarded as a functionally graded material (FGM). This study investigates the mechanical properties of graded cancellous bone.

CT scan images combined with image processing techniques were used to extract gradients in mechanical properties of the femoral neck in bovine samples. Several unit cells were employed to model the microstructure of cancellous bone. The graded properties were validated through both numerical and experimental approaches. Cylindrical models are used for finite element analysis and complementary experimental tests were carried out on the femoral neck region.

Analytical relationships for mechanical properties of femur spongy bone have been presented. The Cubic and BCC unit cell structures, with $\frac{E_{\mathrm{ave}}}{E_s}I=187.11$ and $\frac{E_{ave}}{E_s}I=168.06m^4$ have maximum and minimum flexural stiffness values, respectively. Also, discrepancies between experimental, analytical, and numerical results were discussed.

The tesseract unit cell showed the most similarity with the cancellous bone properties, with only 0.11% difference in flexural stiffness, whereas the cubic unit cell, with an 8.48% difference, was the least suitable for modeling spongy bone.