Verified and validated finite element analyses of humeri

Background: Although ~200,000 emergency room visits per year in the US alone are associated with fractures of the proximal humerus, only limited studies exist on their mechanical response. We hypothesise that for the proximal humeri (a) the mechanical response can be well predicted by using inhomogeneous isotropic material properties, (b) the relation between bone elastic modulus and ash density (E(ρ_ash)) is similar for the humerus and the femur, and may be general for long bones, and (c) it is possible to replicate a proximal humerus fracture in vitro by applying uniaxial compression on humerus' head at a prescribed angle. Methods: Four fresh frozen proximal humeri were CT-scanned, instrumented by strain-gauges and loaded at three inclination angles. Thereafter head displacement was applied to obtain a fracture. CT-based high order (p-) finite element (FE) and classical (h-) FE analyses were performed that mimic the experiments and predicted strains were compared to the experimental observations. Results: The E(ρ_ash) relationship appropriate for the femur is equally appropriate for the humeri: predicted strains in the elastic range showed an excellent agreement with experimental observations with a linear regression slope of m=1.09 and a coefficient of regression R²=0.98. p-FE and h-FE results were similar for the linear elastic response. Although fractures of the proximal humeri were realised in the in vitro experiments, the contact FE analyses (FEA) were unsuccessful in representing properly the experimental boundary conditions. Discussion: The three hypotheses were confirmed and the linear elastic response of the proximal humerus, attributed to a stage at which the cortex bone is intact, was well predicted by the FEA. Due to a large post-elastic behaviour following the cortex fracture, a new non-linear constitutive model for proximal humerus needs to be incorporated into the FEA to well represent proximal humerus fractures. Thereafter, more in vitro experiments are to be performed, under boundary conditions that may be well represented by the FEA, to allow a reliable simulation of the fracture process.