Lower Bound Prediction of Femur Collapse Load Through a CT-Based Limit Analysis Strategy: A Sensitivity Analysis to Modelling Choices

The prediction of femur fracture risk, especially in the case of elderly people suffering from osteoporosis or other bone pathologies, is a relevant clinical problem. To provide a solution, many studies, typically based on the analysis of specific indicators, such as the bone mineral density in presence of osteoporosis, have been developed. However, if such indicators are accounted for without a reliable knowledge of the effective mechanical behavior of the femur, their use fall short in predicting fracture. Moreover, several patient-specific numerical approaches have also been developed resulting often very complex for practical clinical applications, especially if they involve 3D modeling and fracture or damage propagation description. In the present work an alternative method is promoted. The proposed approach is oriented to the prediction of the collapse load of the human femur by means of a limit analysis static approach. In particular, a lower bound to the femur collapse load is evaluated using the so-called elastic compensation method and a Tsai–Wu–type yield criterion. This method is applied in combination with the information provided by Computed Tomography (CT) images to obtain reliable femur geometry reconstruction as well as precise local evaluation of bone density values, the latters linkable to material strength limit values affecting, together with the finite element (FE) description, the numerical outcomings. A first validation of the CT-based limit analysis is performed by comparing the numerical results with experimental ones on a fresh-frozen human cadaveric femur. To enhance the understanding of how modeling choices can affect the prediction of femur collapse loads, a sensitivity analysis is performed to different relationships between strength limit values and bone density distribution. By tuning these choices, it is shown how it is possible to improve the reliability of CT-based limit analysis predictions acting both on the FE geometrical modeling and on the bone strength values detection, eventually leading to a better and reliable femur fracture risk assessment to be used in clinical practice.