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

Quantitative Load Dependency Analysis of Local Trabecular Bone Microstructure to Understand the Spatial Characteristics in the Synthetic Proximal Femur

Analysis of the dependency of the trabecular structure on loading conditions is essential for understanding and predicting bone structure formation. Although previous studies have investigated the relationship between loads and structural adaptations, there is a need for an in-depth analysis of this relationship based on the bone region and load specifics. In this study, the load dependency of the trabecular bone microstructure for twelve regions of interest (ROIs) in the synthetic proximal femur was quantitatively analyzed to understand the spatial characteristics under seven different loading conditions. To investigate the load dependency, a quantitative measure, called the load dependency score (LDS), was established based on the statistics of the strain energy density (SED) distribution. The results showed that for the global model and epiphysis ROIs, bone microstructures relied on the multiple-loading condition, whereas the structures in the metaphysis depended on single or double loads. These results demonstrate that a given ROI is predominantly dependent on a particular loading condition. The results confirm that the dependency analysis of the load effects for ROIs should be performed both qualitatively and quantitatively.

Detection of defects in cellular solids using highly nonlinear solitary waves: a numerical study of the proximal femur

This study investigates the suitability of a relatively new non-destructive evaluation (NDE) technique for the detection of non-visible defects in cellular solids using highly nonlinear solitary waves (HNSWs) in a one-dimensional granular chain. Specifically, the HNSW-based NDE approach is employed to identify the existence of micro-fractures in trabecular bone within the femoral neck (FN) and the intertrochanteric (IT) region of the proximal femur which are fracture-prone sites due to their relatively low bone density, particularly in osteoporosis patients. The availability of a HNSW-based bone quality assessment tool could not only help in early diagnosis of osteoporosis but also affect surgical decisions and improve clinical outcomes in joint replacement surgeries which motivated this study. To obtain a realistic representation of the trabecular microstructure, high-resolution finite-element (FE) models of the FN and the IT region are first constructed using a topology optimization-based bone reconstruction scheme. Then, artificial defects in the form of fractured ligaments are generated in the FN and IT models by selectively disconnecting various struts within the trabecular network. Using the FE models as the inspection medium, hybrid discrete-element/finite-element (DE/FE) simulations are performed to examine the interaction of the HNSWs with the cellular bone samples through two different inspection modes, i.e., inspection via direct contact with the sample and indirect contact through an adequately chosen face sheet inserted between the cellular sample and the granular chain. The delays and amplitudes of the HNSWs are used to estimate the effective elastic moduli of the cellular samples and these estimates were found to be reasonably accurate only in case the face sheet was applied. For the latter case, it was shown that the HNSW-based modulus estimates can be used as indicators for defect detection, allowing to discern between pristine and damaged cellular solids. These results suggest that HNSW-based NDE is a reliable and cost-effective technique for the identification of defects in cellular solids, and is expected to find applications in various fields, such as non-invasive screening of bone diseases and fractures, or damage detection in additively manufactured cellular structures.

Topology Optimization-Based Localized Bone Microstructure Reconstruction for Image Resolution Enhancement: Accuracy and Efficiency

Topology optimization is currently the only way to provide bone microstructure information by enhancing a 600 μm low-resolution image into a 50 μm high-resolution image. Particularly, the recently proposed localized reconstruction method for the region of interest has received much attention because it has a high possibility to overcome inefficiency such as iterative large-scale problems of the conventional reconstruction. Despite the great potential, the localized method should be thoroughly validated for clinical application. This study aims to quantitatively validate the topology optimization-based localized bone microstructure reconstruction method in terms of accuracy and efficiency by comparing the conventional method. For this purpose, this study re-constructed bone microstructure for three regions of interest in the proximal femur by localized and conventional methods, respectively. In the comparison, the dramatically reduced total progress time by at least 88.2% (20.1 h) as well as computational resources by more than 95.9% (54.0 gigabytes) were found. Moreover, very high reconstruction accuracy in the trabecular alignment (up to 99.6%) and morphometric indices (up to 2.71%) was also found. These results indicated that the localized method could reconstruct bone microstructure, much more effectively preserving the originality of the conventional method.

Predictions of the elastic modulus of trabecular bone in the femoral head and the intertrochanter: a solitary wave-based approach

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.