Solitary wave-based site-specific bone quality assessment: A numerical study of the proximal femur

Abstract

We examine numerically the feasibility of using a relatively new solitary wave-based non-destructive test (NDT) method for site-specific bone quality assessment. Towards this end, we present numerical predictions of the effective elastic modulus of trabecular bone in the proximal femur using highly nonlinear solitary waves (HNSWs) propagating in a one-dimensional chain of spherical steel particles. A computational bone reconstruction technique, enabled through topology optimization, is developed to generate high-resolution finite-element models representing the complex architecture of the trabecular network in the femoral neck region of the proximal femur. The reconstructed bone microstructure models are then used as the inspection medium in a virtual NDT setup in the form of a hybrid discrete-element/finite-element (DE/FE) model, capable of simulating the propagation of HNSWs in the granular chain and their interaction with the bone microstructures. By inserting a face sheet between the granular chain and the porous trabecular bone model, our calculations evince that dynamic loading by the incident solitary wave results in nearly uniaxial deformation of the bone microstructure (rather than localized contact indentations), and this is shown to enhance the accuracy and reliability of the solitary wave-based prediction of the bone's effective elastic modulus. Using the delay of the primary reflected solitary wave in the estimation of the elastic modulus of bone, we are able to estimate the effective elastic moduli of the porous bone models with adequate accuracy. Based on these numerical findings, we believe that solitary wave-based non-destructive evaluation of computationally reconstructed artificial bone models could form the baseline for advanced bone quality assessment tools.