Unsupervised Learning-Based Measurement of Ultrasonic Axial Transmission Velocity in Neonatal Bone.

OBJECTIVES: To develop a robust algorithm for estimating ultrasonic axial transmission velocity from neonatal tibial bone, and to investigate the relationships between ultrasound velocity and neonatal anthropometric measurements as well as clinical biochemical markers of skeletal health. METHODS: This study presents an unsupervised learning approach for the automatic detection of first arrival time and estimation of ultrasonic velocity from axial transmission waveforms, which potentially indicates bone quality. The proposed method combines the ReliefF algorithm and fuzzy C-means clustering. It was first validated using an in vitro dataset measured from a Sawbones phantom. It was subsequently applied on in vivo signals collected from 40 infants, comprising 21 males and 19 females. The extracted neonatal ultrasonic velocity was subjected to statistical analysis to explore correlations with the infants' anthropometric features and biochemical indicators. RESULTS: The results of in vivo data analysis revealed significant correlations between the extracted ultrasonic velocity and the neonatal anthropometric measurements and biochemical markers. The velocity of first arrival signals showed good associations with body weight (ρ = 0.583, P value <.001), body length (ρ = 0.583, P value <.001), and gestational age (ρ = 0.557, P value <.001). CONCLUSION: These findings suggest that fuzzy C-means clustering is highly effective in extracting ultrasonic propagating velocity in bone and reliably applicable in in vivo measurement. This work is a preliminary study that holds promise in advancing the development of a standardized ultrasonic tool for assessing neonatal bone health. Such advancements are crucial in the accurate diagnosis of bone growth disorders.

Signal Processing Techniques Applied to Axial Transmission Ultrasound.

A new application of ultrasonography has been emerging in the bone quantitative ultrasound arena in the last twenty years: cortical bone characterization using axial transmission ultrasound (ATU). Although challenged by the complicated cortical tissue-ultrasonic wave interaction, ATU has proved to have promising potential to be a valuable diagnostic tool in the assessment of cortical bones. This chapter reviews the main landmarks of axial transmission signal processing in the past decade to provide a guide to the diversity of available techniques. In order to increase the readability of the chapter, the signal processing methods are categorized based on the experimental settings: single and multiple transmitter-receiver configuration. The review considers the key stages required for the analysis of bone guided-wave ultrasound data namely dispersion energy imaging, modal filtering, dispersion curve inversion, and measurement automation with integrated artificial intelligence concepts. Besides discussing the recent signal processing advances in the field of bone assessment by axial transmission, this communication offers developments that might be anticipated in the near future.

Single Versus Multi-channel Dispersion Analysis of Ultrasonic Guided Waves Propagating in Long Bones.

Ultrasonic guided wave techniques have been applied to characterize cortical bone for osteoporosis assessment. Compared with the current gold-standard X-ray-based diagnostic methods, ultrasound-based techniques pose some advantages such as compactness, low cost, lack of ionizing radiation, and their ability to detect the mechanical properties of the cortex. Axial transmission technique with a source-receiver offset is employed to acquire the ultrasound data. The dispersion characteristics of the guided waves in bones are normally analyzed in the transformed domains using the dispersion curves. The transformed domain can be time-frequency map using a single channel or wavenumber-frequency (or phase velocity-frequency) map with multi-channels. In terms of acquisition effort, the first method is more cost- and time-effective than the latter. However, it remains unclear whether single-channel dispersion analysis can provide as much quantitative guided-wave information as the multi-channel analysis. The objective of this study is to compare the two methods using numerically simulated and ex vivo data of a simple bovine bone plate and explore their advantages and disadvantages. Both single- and multi-channel signal processing approaches are implemented using sparsity-constrained optimization algorithms to reinforce the focusing power. While the single-channel data acquisition and processing are much faster than those of the multi-channel, modal identification and analysis of the multi-channel data are straightforward and more convincing.

Multichannel filtering and reconstruction of ultrasonic guided wave fields using time intercept-slowness transform.

Multichannel ultrasonic axial-transmission data are multimodal by nature. As guided waves are commonly used in nondestructive material testing, wave field filtering becomes important because the analysis is usually limited to a few lower-order modes and requires their extraction. An application of the Radon transform to enhance signal-to-noise ratio and separate wave fields in ultrasonic records is presented. The method considers guided wave fields as superpositions of plane waves defined by ray parameters (p) and time intercepts (τ) and stacks the amplitudes along linear trajectories, mapping time-offset (t - x) data to a τ - p or Radon panel. The transform is implemented using a least-squares strategy with Cauchy-norm regularization that serves to enhance the focusing power. The method was verified using simulated data and applied to an uneven spatially sampled bovine-bone-plate data set. The results demonstrate the Radon panels show isolated amplitude clusters and the Cauchy-norm constraint provides a more focused Radon image than the damped least-squares regularization. Wave field separation can be achieved by selectively windowing the τ - p signals and inverse transformation, which is illustrated by the successful extraction of the A0 mode in bone plate. In addition, the method effectively attenuates noise, enhances the coherency of the guided wave modes, and reconstructs the missing records. The proposed transform presents a powerful signal-enhancement tool to process guided waves for further analysis and inversion.

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.

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.

Spectrogram decomposition of ultrasonic guided waves for cortical thickness assessment using basis learning.

Due to its multimode and dispersive nature, ultrasonic guided waves (UGWs) usually consist of overlapped wave packets, which challenge accurate bone characterization. To overcome this obstacle, a classic idea is to separate individual modes and to extract the corresponding dispersion curves. Reported single-channel mode separation algorithms mainly focused on offering a time-frequency representation (TFR) where the energy distributions of individual modes were apart from each other. However, such approaches are still limited to identifying the modes without significant overlapping in time-frequency domain. In this study, a spectrogram decomposition technique was developed based on a combination strategy of generalized separable nonnegative matrix factorization (GS-NMF) and adaptive basis learning, towards the automatic mode extraction under severe overlapping and low signal-to-noise ratio (SNR). The extracted modes were further used for cortical thickness estimation. The method was verified using broadband simulated and experimental datasets. Experiments were conducted on a bone-mimicking plate and bovine cortical bone plates. For simulated data, the relative errors between extracted and theoretical dispersion curves are 1.33% (SNR = ∞), 1.43% (SNR = 10 dB) and 0.88% (SNR = 5 dB). The root-mean-square errors of the estimated thickness for 3.10 mm-thick bone-mimicking plate, 3.83 mm- and 4.00 mm-thick bovine cortical bone plates are 0.039 mm, 0.049 mm, and 0.052 mm, respectively. It is demonstrated that the proposed method is capable of separating multimodal UGWs even under significantly overlapping and low SNR conditions, further facilitating the UGW-based cortical thickness assessment.

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.

Sensitivity analysis of ultrasonic guided waves propagating in trilayered bone models: a numerical study.

The fundamental ultrasonic guided modes are consistently observed in long bones ex vivo and in vivo. However, the responses of ultrasonic guided waves to the changes of cortical thickness, cortical elastic parameters, and thickness of the overlying soft tissues are not comprehensively understood. This paper systematically presents a sensitivity analysis of leaky Lamb modes to the geometry and material characteristics of layered bone model by means of semi-analytical finite element modeling. The stratified bone model is consisted of a transversely isotropic cortex with an overlying soft tissue and underlying marrow. The study is important as it offers guidance to the parameter inversion process about the optimal selection of guided modes and regions of sensitivity for better inversion results.

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

We present a semi-analytical finite element (SAFE) scheme for accurately computing the velocity dispersion and attenuation in a trilayered system consisting of a transversely-isotropic (TI) cortical bone plate sandwiched between the soft tissue and marrow layers. The soft tissue and marrow are mimicked by two fluid layers of finite thickness. A Kelvin-Voigt model accounts for the absorption of all three biological domains. The simulated dispersion curves are validated by the results from the commercial software DISPERSE and published literature. Finally, the algorithm is applied to a viscoelastic trilayered TI bone model to interpret the guided modes of an ex-vivo experimental data set from a bone phantom.

Imaging ultrasonic dispersive guided wave energy in long bones using linear radon transform.

Multichannel analysis of dispersive ultrasonic energy requires a reliable mapping of the data from the time-distance (t-x) domain to the frequency-wavenumber (f-k) or frequency-phase velocity (f-c) domain. The mapping is usually performed with the classic 2-D Fourier transform (FT) with a subsequent substitution and interpolation via c = 2πf/k. The extracted dispersion trajectories of the guided modes lack the resolution in the transformed plane to discriminate wave modes. The resolving power associated with the FT is closely linked to the aperture of the recorded data. Here, we present a linear Radon transform (RT) to image the dispersive energies of the recorded ultrasound wave fields. The RT is posed as an inverse problem, which allows implementation of the regularization strategy to enhance the focusing power. We choose a Cauchy regularization for the high-resolution RT. Three forms of Radon transform: adjoint, damped least-squares, and high-resolution are described, and are compared with respect to robustness using simulated and cervine bone data. The RT also depends on the data aperture, but not as severely as does the FT. With the RT, the resolution of the dispersion panel could be improved up to around 300% over that of the FT. Among the Radon solutions, the high-resolution RT delineated the guided wave energy with much better imaging resolution (at least 110%) than the other two forms. The Radon operator can also accommodate unevenly spaced records. The results of the study suggest that the high-resolution RT is a valuable imaging tool to extract dispersive guided wave energies under limited aperture.

Excitation of ultrasonic Lamb waves using a phased array system with two array probes: phantom and in vitro bone studies.

Long bones are good waveguides to support the propagation of ultrasonic guided waves. The low-order guided waves have been consistently observed in quantitative ultrasound bone studies. Selective excitation of these low-order guided modes requires oblique incidence of the ultrasound beam using a transducer-wedge system. It is generally assumed that an angle of incidence, θi, generates a specific phase velocity of interest, co, via Snell's law, θi=sin(-1)(vw/co) where vw is the velocity of the coupling medium. In this study, we investigated the excitation of guided waves within a 6.3-mm thick brass plate and a 6.5-mm thick bovine bone plate using an ultrasound phased array system with two 0.75-mm-pitch array probes. Arranging five elements as a group, the first group of a 16-element probe was used as a transmitter and a 64-element probe was a receiver array. The beam was steered for six angles (0°, 20°, 30°, 40°, 50°, and 60°) with a 1.6-MHz source signal. An adjoint Radon transform algorithm mapped the time-offset matrix into the frequency-phase velocity dispersion panels. The imaged Lamb plate modes were identified by the theoretical dispersion curves. The results show that the 0° excitation generated many modes with no modal discrimination and the oblique beam excited a spectrum of phase velocities spread asymmetrically about co. The width of the excitation region decreased as the steering angle increased, rendering modal selectivity at large angles. The phenomena were well predicted by the excitation function of the source influence theory. The low-order modes were better imaged at steering angle ⩾30° for both plates. The study has also demonstrated the feasibility of using the two-probe phased array system for future in vivo study.

Analysis of ultrasonic waves propagating in a bone plate over a water half-space with and without overlying soft tissue.

Recent in vitro studies have shown that guided waves can characterize bone properties. However, for clinical applications to be viable, the soft-tissue layer should be considered. This study examined the effect of soft tissue on guided waves using a bovine bone plate over a water half-space and overlaid by a 4-mm gelatin-based soft-tissue mimic. The data (with and without soft tissue) clearly show a high-frequency, fast-propagating wave packet and a low-frequency, delayed phase group. The presence of soft tissue attenuates the signals significantly and increases mode density and number as predicted by theory. The data retain higher frequency content than the bone-plate data at large offsets. Using theoretical dispersion curves, the guided modes can be identified with mode 1 (similar to the A0 Lamb mode) minimally affected by the addition of soft tissue. There is infiltration of high-frequency, late-arriving energy within the low-velocity guided-wave regime. Results of travel-time calculation suggest that P-wave and PP-reflections/multiples within the soft tissue may be responsible for the high-frequency oscillations.