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.

Methods for bone quality assessment in human bone tissue: a systematic review

Background

For biomechanical investigations on bone or bone implants, bone quality represents an important potential bias. Several techniques for assessing bone quality have been described in the literature. This study aims to systematically summarize the methods currently available for assessing bone quality in human bone tissue, and to discuss the advantages and limitations of these techniques.

Methods

A systematic review of the literature was carried out by searching the PubMed and Web of Science databases from January 2000 to April 2021. References will be screened and evaluated for eligibility by two independent reviewers as per PRISMA (Preferred Reporting Items for Systematic Reviews and Meta-Analyses) guidelines. Studies must apply to bone quality assessment with imaging techniques, mechanical testing modalities, and compositional characterization. The terms used for the systematic search were: “(bone quality”. Ti,ab.) AND “(human bone specimens)”.

Results

The systematic review identified 502 relevant articles in total. Sixty-eight articles met the inclusion criteria. Among them, forty-seven articles investigated several imaging modalities, including radiography, dual-energy X-ray absorptiometry (DEXA), CT-based techniques, and MRI-based methods. Nineteen articles dealt with mechanical testing approaches, including traditional testing modalities and novel indentation techniques. Nine articles reported the correlation between bone quality and compositional characterization, such as degree of bone mineralization (DBM) and organic composition. A total of 2898 human cadaveric bone specimens were included.

Conclusions

Advanced techniques are playing an increasingly important role due to their multiple advantages, focusing on the assessment of bone morphology and microarchitecture. Non-invasive imaging modalities and mechanical testing techniques, as well as the assessment of bone composition, need to complement each other to provide comprehensive and ideal information on the bone quality of human bone specimens.

Supplementary Information

The online version contains supplementary material available at 10.1186/s13018-022-03041-4.

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.

Wireless Module for Nondestructive Testing/Structural Health Monitoring Applications Based on Solitary Waves

In recent years, there has been an increasing interest in the use of highly nonlinear solitary waves (HNSWs) for nondestructive evaluation and structural health monitoring applications. HNSWs are mechanical waves that can form and travel in highly nonlinear systems, such as granular particles in Hertzian contact. The easiest setup consists of a built-in transducer in drypoint contact with the structure or material to be inspected/monitored. The transducer is made of a monoperiodic array of spherical particles that enables the excitation and detection of the solitary waves. The transducer is wired to a data acquisition system that controls the functionality of the transducer and stores the time series for post-processing. In this paper, the design and testing of a wireless unit that enables the remote control of a transducer without the need to connect it to sophisticated test equipment are presented. Comparative tests and analyses between the measurements obtained with the newly designed wireless unit and the conventional wired configuration are provided. The results are corroborated by an analytical model that predicts the dynamic interaction between solitary waves and materials with different modulus. The advantages and limitations of the proposed wireless platform are given along with some suggestions for future developments.

Axial stress determination using highly nonlinear solitary waves

This article presents a nondestructive evaluation (NDE) method to infer the neutral temperature and the axial stress in thick beams. The method relies on the propagation of highly nonlinear solitary waves generated at one end of a chain of spherical particles in a dry point contact with the beam to be evaluated. The waves are reflected back to the chain and the research hypothesis is that the axial stress, which influences the beam's stiffness, affects the amplitude and speed of the reflected waves. To verify this hypothesis a general finite element model of thermally stressed beams was developed and coupled to a discrete particle model able to predict the propagation of the waves along an L-shaped granular medium. The models were validated experimentally to quantify the repeatability of the setup, the sensitivity of the wave features on the thermal stress, and the independence of the wave features on the neutral temperature of the beam. The hypothesis was proven valid by both the numerical and the experimental results. In the future, these findings may be used to refine a NDE method to assess stress in columns, to infer the neutral temperature of continuous welded rails, and to prevent thermal buckling of critical structures.