Multiscale stiffness characterisation of both healthy and osteoporotic bone tissue using subject-specific data

Severe bone fractures are often treated by appending internal fixations. In unhealthy or osteoporotic patients, post-implantation bone fractures can occur due to external impact (e.g. from a fall), day-to-day activities in highly-osteoporotic cases and mismatches in the stiffness of bone and the implant's biomaterial, since this causes stress concentrations. One approach to alleviating this problem is to use biomaterials that closely mimic the effective stiffness of real bone, thereby more seamlessly integrating the fixation. This requires to know the properties target (bone properties) and therefore, it highlights the relevance of the evaluation of the bone's mechanical properties which is impractical via direct measurement. This work presents a methodology (multistage homogenisation) for predicting the anisotropic stiffness of bone given the porosity and mineral fraction, both of which are more readily obtained than the mechanical properties themselves. Unlike previous work we: (i) account for finger-like morphology of the mineral phase at the nanoscale; (ii) use microscopy data to model the osteon geometry and its curvilinear anisotropy at the microscale, and (iii) use data to define the trabecular (microCT) and cortical (microscopy) bone geometries at the mesoscale. The predicts have been shown to agree favourably with experimental data in the literature as well as previous modelling works. The results are summarised in a database containing anisotropic stiffness tensors applicable to a broad range of degrees of bone health (e.g. mineral fractions and mesoscale porosities); thus, this work is a contribution towards being able to design more robust patient-specific bone implants in practice.