Numerical predictions of the interaction between highly nonlinear solitary waves and the microstructure of trabecular bone in the femoral head

The unique properties of highly nonlinear solitary waves in granular chains have prompted extensive research in the area of non-destructive testing and led to the development of new diagnostic schemes with potential applications in the healthcare industry. Here, we study numerically the interaction between highly nonlinear solitary waves in a granular chain and the microstructure of trabecular bone in the femoral head. High-resolution finite element models of bone microstructures with varying bone volume fraction are generated using a topology optimization-based bone microstructure reconstruction scheme. The obtained FE models of the trabecular bone were then used to develop a hybrid discrete/finite element model able to simulate the propagation of highly nonlinear solitary waves in a vertical array of steel particles, and their interaction with the adjacent bone microstructure model was studied. Two test modes were considered, one where the granular chain was placed in direct contact with the bone microstructure model, while in the second test mode, a face sheet was included between the chain and the bone model. For both test modes, we found that the characteristic features of the reflected solitary waves are sensitive to the effective compressive modulus of the bone microstructure models and follow similar trends than those obtained for a homogeneous, non-porous solid. It was also found that the use of the face sheet substantially reduces the sensitivity of the predictions to small changes in the bone topology, making it a robust and reliable method for non-destructive evaluation of the effective elastic modulus of cellular materials with small structural dimensions, as it is required for the site-specific evaluation of the mechanical properties of trabecular bone.