This paper deals with the numerical prediction of the elastic modulus of trabecular bone in the femoral head (FH) and the intertrochanteric (IT) region via site-specific bone quality assessment using solitary waves in a one-dimensional granular chain. For accurate evaluation of bone quality, high-resolution finite element models of bone microstructures in both FH and IT are generated using a topology optimization-based bone microstructure reconstruction scheme. A hybrid discrete element/finite element (DE/FE) model is then developed to study the interaction of highly nonlinear solitary waves in a granular chain with the generated bone microstructures. For more robust and reliable prediction of the bone’s mechanical properties, a face sheet is placed at the interface between the last chain particle and the bone microstructure, allowing more bone volume to be engaged in the dynamic deformation during interaction with the solitary wave. The hybrid DE/FE model was used to predict the elastic modulus of the IT and FH by analysing the characteristic features of the two primary reflected solitary waves. It was found that the solitary wave interaction is highly sensitive to the elastic modulus of the bone microstructure and can be used to identify differences in bone density. Moreover, it was found that the use of a relatively stiff face sheet significantly reduces the sensitivity of the wave interaction to local stiffness variations across the test surface of the bone, thereby enhancing the robustness and reliability of the proposed method. We also studied the effect of the face sheet thickness on the characteristics of the reflected solitary waves and found that the optimal thickness that minimizes the error in the modulus predictions is 4 mm for the FH and 2 mm for the IT, if the primary reflected solitary wave is considered in the evaluation process. We envisage that the proposed diagnostic scheme, in conjunction with 3D-printed high-resolution bone models of an actual patient, could provide a viable solution to current limitations in site-specific bone quality assessment.

本文通过使用一维颗粒链中的孤立波进行位点特异性骨质量评估，对股骨头 (FH) 和转子间 (IT) 区域骨小梁的弹性模量进行数值预测。为了准确评估骨骼质量，使用基于拓扑优化的骨骼微结构重建方案生成 FH 和 IT 中骨骼微结构的高分辨率有限元模型。然后开发了混合离散元/有限元 (DE/FE) 模型来研究颗粒链中的高度非线性孤立波与生成的骨微结构的相互作用。为了更稳健和可靠地预测骨骼的机械性能，面板被放置在最后一个链颗粒和骨骼微结构之间的界面处，在与孤立波相互作用期间，允许更多的骨量参与动态变形。混合DE/FE模型通过分析两个主反射孤立波的特征来预测IT和FH的弹性模量。研究发现，孤立波相互作用对骨微结构的弹性模量高度敏感，可用于识别骨密度的差异。此外，发现使用相对刚性的面板显着降低了波相互作用对骨骼测试表面的局部刚度变化的敏感性，从而提高了所提出方法的稳健性和可靠性。我们还研究了面板厚度对反射孤立波特性的影响，发现如果初级反射孤立波，使模量预测误差最小化的最佳厚度是 FH 为 4 mm，IT 为 2 mm在评估过程中考虑波。我们设想，所提出的诊断方案与实际患者的 3D 打印高分辨率骨骼模型相结合，可以为当前特定部位骨骼质量评估的局限性提供可行的解决方案。