Two Scale FE‐FFT‐Based Modeling of Cancellous Bone

ABSTRACT Osteoporosis is characterized by a loss of volume percentage of cortical bone, which reduces the loading capacity of this organ and increases its likelihood for fractures. The disease has the highest prevalence of any bone disease worldwide, with a particularly high incidence among the elderly. Currently, dual‐energy x‐ray absorptiometry is the gold standard in diagnostics. However, sonography could emerge as a potential less invasive and less costly future early detection method. Numerical simulations can support the development of this tool and increase the understanding of measured effects. In this contribution, we present several advancements regarding the accuracy and performance of simulations modeling the early detection of osteoporosis affecting cancellous bone. We introduce a dimensionless formulation of the underlying system of partial differential equations (PDEs), which improves the numerical stability in the context of finite element method (FEM) simulations. We explore a simplified unidirectional coupled model, which may allow a solution of the PDE system in a staggered manner. Finally, we resolve the microstructure using the fast Fourier transform (FFT) method. The numerical results obtained from this study demonstrate that the FFT method is a rapid and effective alternative to the previously used FEM to solve the microscale problem and could be used in future studies in conjunction with real computer tomography (CT) imaging data.