An investigation to determine if a single validated density–elasticity relationship can be used for subject specific finite element analyses of human long bones

Subject-specific FE-models of human long bones have to predict mechanical parameters with sufficient accuracy to be applicable in a clinical setting. One of the main aspects in subject-specific FE-models of bones regarding accuracy is the modeling of the material inhomogeneity. The goal of this study was therefore to develop FE-models of human femurs and investigate if a single validated density–elasticity relationship can be used for subject specific finite element analyses of human long bones, when the task is to predict the bone's mechanical response to load. To this aim, 23 human cadaver femurs were tested in axial compression with a load of 1000 N. Strains, local displacements, and axial bone stiffness were determined. Subject-specific FE-models were developed for each bone based on quantitative CT-scans. Three different density–elasticity relationships were retrieved from the literature, and were implemented in the FE-models. The predicted mechanical values depended largely on the used equation. The most reasonable equation showed a mean error of −11% in strain prediction, a mean error of −23% in local displacement prediction, and a mean error of +23% in axial stiffness prediction. The scatter of the predictions was very low in all three categories of measurements with a 1.96 standard deviation of about 30% to the mean errors. In conclusion, a framework for subject-specific FE-models was developed that was able to predict surface strains and bone deformation with good accuracy by using a single density–elasticity relationship. However, it was also found that the most appropriate density–elasticity relationship was specimen-specific.