Effects of the Axial Variations of Porosity and Mineralization on the Elastic Properties of the Human Femoral Neck

This paper investigates the effects of the heterogeneous distribution of the Haversian Porosity (HP) and Tissue Mineral Density (TMD) on the elastic coefficients of bone in the human femoral neck. A bone specimen from the inferior femoral neck was obtained from a patient undergoing standard hemiarthroplasty. The specimen was imaged using 3-D synchrotron micro-computed tomography (voxel size of 10.13 mu m), leading to the determination of the anatomical distributions of HP and TMD. These experimental data were used to estimate the elastic coefficients of the bone using a three-step homogenization model based on continuum micromechanics: (i) At the tissue scale (characteristic length of several hundred micrometers), bone was modeled as cylindrical pores (Haversian canals) in a solid matrix called ultrastructure; (ii) At the scale of several micrometers, ultrastructure was modeled as collagen fibers embedded in a mineral foam; (iii) Eventually, at the scale of several hundred nanometers, mineral foam was modeled as a mixture of mineral and water. Effective elastic coefficients of the bone were computed accounting for the heterogeneous distributions of BP and TMD determined experimentally. The variations of RP, TMD and elastic coefficients were investigated along the axis of the femoral neck and at different distances from the periosteal surface of the sample. TMD was found to decrease from the distal to the proximal part of the femoral neck axis whereas no specific trend was found for the BP. Axial variations of the elastic coefficients were shown to be mainly related to the axial variations of TMD and HP in the dense and porous tissue, respectively. Therefore, this study underlines the importance of considering the actual spatial variations of TMD and HP to obtain accurate estimates of bone effective elastic properties.