Computing dispersion curves of elastic/viscoelastic transversely-isotropic bone plates coupled with soft tissue and marrow using semi-analytical finite element (SAFE) method

Ultrasonic Guided Waves in Bone: A Decade of Advancement in Review

The use of guided wave ultrasonography as a means to assess cortical bone quality has been a significant practice in bone quantitative ultrasound for more than 20 years. In this article, the key developments within the technology of ultrasonic guided waves (UGW) in long bones during the past decade are documented. The covered topics include data acquisition configurations available for measuring bone guided waveforms, signal processing techniques applied to bone UGW, numerical modeling of ultrasonic wave propagation in cortical long bones, formulation of inverse approaches to extract bone properties from observed ultrasonic signals, and clinical studies to establish the technology's application and efficacy. The review concludes by highlighting specific challenging problems and future research directions. In general, the primary purpose of this work is to provide a comprehensive overview of bone guided-wave ultrasound, especially for newcomers to this scientific field.

Meta-Learning Analysis of Ultrasonic Guided Waves for Coated Cortical Bone Characterization

Due to its sensitivity to geometrical and mechanical properties of waveguides, ultrasonic guided waves (UGWs) propagating in cortical bones play an important role in the early diagnosis of osteoporosis. However, as impacts of overlaid soft tissues are complex, it remains challenging to retrieve bone properties accurately. Meta-learning, i.e., learning to learn, is capable of extracting transferable features from a few data and, thus, suitable to capture potential characteristics, leading to accurate bone assessment. In this study, we investigate the feasibility to apply the multichannel identification neural network (MCINN) to estimate the thickness and bulk velocities of coated cortical bone. It minimizes the effects of soft tissue by extracting specific features of UGW, which shares the same cortical properties, while the overlaid soft tissue varies. Distinguished from most reported methods, this work moves from the hand-design inversion scheme to data-driven assessment by automatically mapping features of UGW to the space of bone properties. The MCINN was trained and validated using simulated datasets produced by the finite-difference time-domain (FDTD) method and then applied to experimental data obtained from cortical bovine bone plates overlaid with soft tissue mimics. A good match was found between experimental trajectories and theoretical dispersion curves. The results demonstrated that the proposed method was feasible to assess the thickness of coated cortical bone plates.

Analysis of Ultrasonic Guided Wave Propagation in Multilayered Bone Structure With Varying Soft-Tissue Thickness in View of Cortical Bone Characterization

Noninvasive characterization of cortical long bones using axial transmission ultrasound is a promising diagnostic technology for osteoporotic cortical thinning assessment. However, the soft tissue-bone coupling effect remains to be a challenge and an ambiguity especially in vivo. The influence of the overlying soft tissue layer with a varying thickness on the propagation of ultrasonic guided waves in cortical bone is studied experimentally and theoretically in this article. The wave propagation is characterized based on waveform comparison, spectral density and decomposition, dispersion energy imaging, and particle displacement analysis. Good agreement between experimental observations with theoretical predictions by semi-analytical finite element simulations is observed. The sensitivity of propagation characteristics in response to the coupled tissue thickness is elucidated. As the thickness of the loading soft tissue grows, the guided wave signals exhibit greater attenuated amplitude and delayed arrival time; more complex dispersive wave patterns emerge; and the modal number and density increase. The research findings advance the fundamental comprehension of ultrasonic-guided-wave excitation and interaction in long bones and facilitate further technical development and clinical utility of quantitative guided-wave ultrasonography in routine healthcare services as a nondestructive imaging modality for cortical bone examination.

Ex Vivo Assessment of Cortical Bone Properties Using Low-Frequency Ultrasonic Guided Waves

The early diagnosis of osteoporosis through bone quality assessment is a major public health challenge. Research in axial transmission using ultrasonic guided waves has shown the method to be sensitive to the geometrical and mechanical properties of the cortical layer in long bones. However, because of the asymmetric nature of cortical bone, the introduction of a more elaborate numerical model than the analytical plate and cylinder models, as well as its inversion, continues to be challenging. The aim of this article is, therefore, to implement a bone-like geometry using semianalytical finite-element (SAFE) modeling to perform the inverse characterization of ex vivo radii at low frequencies (< 60 kHz). Five cadaveric radiuses were taken from donors aged between 53 and 88 and tested using a typical axial transmission configuration at the middle of the diaphysis. The dispersion curves of the propagating modes were measured experimentally and then systematically compared with the solutions obtained with the SAFE method. For each sample, four parameters were estimated using a parameter identification procedure: 1) the bulk density; 2) the thickness; 3) the outer diameter; and 4) a shape factor (SF). The results showed a moderate agreement between the predicted bulk density and the average voxel value calculated from X-ray computed tomography images. Furthermore, a good agreement was observed between the geometrical parameters (thickness, outer diameter, and SF) and the reference images.

Ultrasound-Based Estimates of Cortical Bone Thickness and Porosity Are Associated With Nontraumatic Fractures in Postmenopausal Women: A Pilot Study

Recent ultrasound (US) axial transmission techniques exploit the multimode waveguide response of long bones to yield estimates of cortical bone structure characteristics. This pilot cross-sectional study aimed to evaluate the performance at the one-third distal radius of a bidirectional axial transmission technique (BDAT) to discriminate between fractured and nonfractured postmenopausal women. Cortical thickness (Ct.Th) and porosity (Ct.Po) estimates were obtained for 201 postmenopausal women: 109 were nonfractured (62.6 ± 7.8 years), 92 with one or more nontraumatic fractures (68.8 ± 9.2 years), 17 with hip fractures (66.1 ± 10.3 years), 32 with vertebral fractures (72.4 ± 7.9 years), and 17 with wrist fractures (67.8 ± 9.6 years). The areal bone mineral density (aBMD) was obtained using DXA at the femur and spine. Femoral aBMD correlated weakly, but significantly with Ct.Th (R = 0.23, p < 0.001) and Ct.Po (R = -0.15, p < 0.05). Femoral aBMD and both US parameters were significantly different between the subgroup of all nontraumatic fractures combined and the control group (p < 0.05). The main findings were that (1) Ct.Po was discriminant for all nontraumatic fractures combined (OR = 1.39; area under the receiver operating characteristic curve [AUC] equal to 0.71), for vertebral (OR = 1.96; AUC = 0.84) and wrist fractures (OR = 1.80; AUC = 0.71), whereas Ct.Th was discriminant for hip fractures only (OR = 2.01; AUC = 0.72); there was a significant association (2) between increased Ct.Po and vertebral and wrist fractures when these fractures were not associated with any measured aBMD variables; (3) between increased Ct.Po and all nontraumatic fractures combined independently of aBMD neck; and (4) between decreased Ct.Th and hip fractures independently of aBMD femur. BDAT variables showed comparable performance to that of aBMD neck with all types of fractures (OR = 1.48; AUC = 0.72) and that of aBMD femur with hip fractures (OR = 2.21; AUC = 0.70). If these results are confirmed in prospective studies, cortical BDAT measurements may be considered useful for assessing fracture risk in postmenopausal women. © 2019 American Society for Bone and Mineral Research.

Nonlinear Inversion of Ultrasonic Dispersion Curves for Cortical Bone Thickness and Elastic Velocities

In this study, a nonlinear grid-search inversion has been developed to estimate the thickness and elastic velocities of long cortical bones, which are important determinants of bone strength, from axially-transmitted ultrasonic data. The inversion scheme is formulated in the dispersive frequency-phase velocity domain to recover bone properties. The method uses ultrasonic guided waves to retrieve overlying soft tissue thickness, cortical thickness, compressional, and shear-wave velocities of the cortex. The inversion strategy requires systematic examination of a large set of trial dispersion-curve solutions within a pre-defined model space to match the data with minimum cost in a least-squares sense. The theoretical dispersion curves required to solve the inverse problem are computed for bilayered bone models using a semi-analytical finite-element method. The feasibility of the proposed approach was demonstrated by the numerically simulated data for a 1 mm soft tissue-5 mm bone bilayer and ex-vivo data from a bovine femur plate with an overlying 2 mm-thick soft-tissue mimic. The bootstrap method was employed to evaluate the inversion uncertainty and stability. Our results have shown that the cortical thickness and wave speeds could be recovered with fair accuracy.

Effect of intracortical bone properties on the phase velocity and cut-off frequency of low-frequency guided wave modes (20-85 kHz)

The assessment of intracortical bone properties is of interest since early-stage osteoporosis is associated with resorption in the endosteal region. However, understanding the interaction between ultrasonic guided waves and the cortical bone structure remains challenging. The purpose of this work is to investigate the effect of intracortical bone properties on the ultrasonic response obtained at low-frequency (<100 kHz) using an axial transmission configuration. The semi-analytical finite element method was used to simulate the propagation of guided waves in a waveguide with realistic geometry and material properties. An array of 20 receivers was used to calculate the phase velocity and cut-off frequency of the excited modes using the two-dimensional Fourier transform. The results show that the position of the emitter around the circumference of the bone is an important parameter to control since it can lead to variations of up to 10 dB in the amplitude of the transmitted modes. The cut-off frequency of the high order modes was, however, only slightly affected by the circumferential position of the emitter, and was sensitive mainly to the axial shear modulus. The phase velocity and cut-off frequency in the 20-85 kHz range are promising parameters for the assessment of intracortical properties.

Fatigue evaluation of long cortical bone using ultrasonic guided waves

Bone fatigue fracture is a progressive disease due to stress concentration. This study aims to evaluate the long bone fatigue damage using the ultrasonic guided waves. Two-dimensional finite-difference time-domain method was employed to simulate the ultrasonic guided wave propagation in the long bone under different elastic modulus. The experiment was conducted on a 3.8 mm-thick bovine bone plate. The phase velocities of two fundamental guided modes, A1 and S1, were measured by using the axial transmission technique. Simulation shows that the phase velocities of guided modes A1 and S1 decrease with the increasing of the fatigue damage. After 20,000 cycles of fatigue loading on the bone plate, the average phase velocities of A1 and S1 modes were 6.6% and 5.3% respectively, lower than those of the intact bone. The study suggests that ultrasonic guided waves can be potentially used to evaluate the fatigue damage in long bones.