Deep Learning Analysis of Ultrasonic Guided Waves for Cortical Bone Characterization

Robust guided wave inversion for estimating bone thickness and elasticity

Accurately characterizing bone properties using quantitative ultrasound remains a significant challenge due to the dispersive nature of guided waves, limited observations, irregularity of bone structure, and heterogeneity of bone tissues. In this paper, an inversion technique is proposed that combines weighted mean absolute criteria and the simulated annealing algorithm to extract the thicknesses and elastic properties of a bilayer bone model. By utilizing the L1 norm with an appropriate weighting parameter, this method effectively reduces the influence of outliers and noises commonly encountered in ultrasonic data, leading to more accurate estimation. This paper also introduces an asymptotic scheme to significantly reduce the search domain, improving the speed and precision of the inversion process. This approach employs a spectral collocation method as a forward modeling technique to simulate guided waves in a bone plate coated by a soft tissue layer. This paper validates the inversion using simulated and ex vivo data and demonstrates its ability to estimate features of cortical bone and soft tissue with high accuracy. Results are presented for the isotropic model. These findings hold great promise for the accurate characterization of bone properties using quantitative ultrasound, with potential applications in clinical diagnosis and treatment of bone-related diseases and injuries.

Cortical bone plate properties assessment using inversion of axially transmitted low frequency ultrasonic guided waves

Over the past few decades, early osteoporosis detection using ultrasonic bone quality evaluation has gained prominence. Specifically, various studies focused on axial transmission using ultrasonic guided waves and have highlighted this technique's sensitivity to intrinsic properties of long cortical bones. This work aims to demonstrate the potential of low-frequency ultrasonic guided waves to infer the properties of the bone inside which they are propagating. A proprietary ultrasonic transducer, tailored to transmit ultrasonic guided waves under 500 kHz, was used for the data collection. The gathered data underwent two-dimensional fast Fourier transform processing to extract experimental dispersion curves. The proposed inversion scheme compares experimental dispersion curves with simulated dispersion curves calculated through the semi-analytical iso-geometric analysis (SAIGA) method. The numerical model integrates a bone phantom plate coupled with a soft tissue layer on its top surface, mimicking the experimental bone phantom plates. Subsequently, the mechanical properties of the bone phantom plates were estimated by reducing the misfit between the experimental and simulated dispersion curves. This inversion leaned heavily on the dispersive trajectories and amplitudes of ultrasonic guided wave modes. Results indicate a marginal discrepancy under 5% between the mechanical properties ascertained using the SAIGA-based inversion and those measured using bulk wave pulse-echo measurements.

Bi-Directional Axial Transmission measurements applied in a clinical environment

Accurate measurement of cortical bone parameters may improve fracture risk assessment and help clinicians on the best treatment strategy. Patients at risk of fracture are currently detected using the current X-Ray gold standard DXA (Dual XRay Absorptiometry). Different alternatives, such as 3D X-Rays, Magnetic Resonance Imaging or Quantitative Ultrasound (QUS) devices, have been proposed, the latter having advantages of being portable and sensitive to mechanical and geometrical properties. The objective of this cross-sectional study was to evaluate the performance of a Bi-Directional Axial Transmission (BDAT) device used by trained operators in a clinical environment with older subjects. The device, positioned at one-third distal radius, provides two velocities: VFAS (first arriving signal) and VA0 (first anti-symmetrical guided mode). Moreover, two parameters are obtained from an inverse approach: Ct.Th (cortical thickness) and Ct.Po (cortical porosity), along with their ratio Ct.Po/Ct.Th. The areal bone mineral density (aBMD) was obtained using DXA at the femur and spine. One hundred and six patients (81 women, 25 men) from Marien Hospital and St. Anna Hospital (Herne, Germany) were included in this study. Age ranged from 41 to 95 years, while body mass index (BMI) ranged from 16 to 47 kg.m-2. Three groups were considered: 79 non-fractured patients (NF, 75±13years), 27 with non-traumatic fractures (F, 80±9years) including 14 patients with non-vertebral fractures (NVF, 84±7years). Weak to moderate significant Spearman correlations (R ranging from 0.23 to 0.53, p < 0.05) were found between ultrasound parameters and age, BMI. Using multivariate Partial Least Square discrimination analyses with Leave-One-Out Cross-Validation (PLS-LOOCV), we found the combination of VFAS and the ratio Ct.Po/Ct.Th to be predictive for all non traumatic fractures (F) with the odds ratio (OR) equals to 2.5 [1.6-3.4] and the area under the ROC curve (AUC) equal to 0.63 [0.62-0.65]. For the group NVF, combination of four parameters VA0. Ct.Th, Ct.Po and Ct.Po/Ct.Po, along with age provides a discrimination model with OR and AUC equals to 7.5 [6.0-9.1] and 0.75 [0.73-0.76]. When restricted to a smaller population (87 patients) common to both BDAT and DXA, BDAT ORs and AUCs are comparable or slightly higher to values obtained with DXA. The fracture risk assessment by BDAT method in older patients, in a clinical setting, suggests the benefit of the affordable and transportable device for the routine use.

Influence of optical transmissivity on signal characteristics of photoacoustic guided waves in long cortical bone

Long cortical bone allows axial transmission of ultrasonic guided waves, which has been utilized for osteoporosis evaluation. Benefiting structural and molecular sensitivity, photoacoustic has been used for tissue composition characterization. However, photoacoustic guided waves (PAGWs) in long cortical bone as well as the influence of optical transmissivity on PAGWs have not been thoroughly investigated. In the study, the influence of optical transmissivity on the signal characteristics of PAGWs was experimentally studied with a 1064 nm pulsed laser ultrasonic system and a tunable laser system (wavelength range: 650-2600 nm). Results show that dispersion curves of PAGWs are not significantly affected by the optical transmissivity; while photoacoustic guided modes and signal spectrum are sensitive to the optical transmissivity in cortical bone. In experiments, the lasers with high transmissivity can emit pure A₀ mode PAGWs at the low frequency, around 22 kHz, in the relatively thick 6.2 mm bone plate; on the contrary, both A₀ and S₀ modes are generated. The slope of power spectrum density (PSD) of PAGWs decreases with the increase of transmissivity, and the decline rate is around -0.229. The study proves the correlation between the signal characteristics of PAGWs and the optical transmissivity, it is helpful for the development of PAGWs in long cortical bone towards the osteoporosis evaluation.

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.

A review of ultrasonic sensing and machine learning methods to monitor industrial processes

Supervised machine learning techniques are increasingly being combined with ultrasonic sensor measurements owing to their strong performance. These techniques also offer advantages over calibration procedures of more complex fitting, improved generalisation, reduced development time, ability for continuous retraining, and the correlation of sensor data to important process information. However, their implementation requires expertise to extract and select appropriate features from the sensor measurements as model inputs, select the type of machine learning algorithm to use, and find a suitable set of model hyperparameters. The aim of this article is to facilitate implementation of machine learning techniques in combination with ultrasonic measurements for in-line and on-line monitoring of industrial processes and other similar applications. The article first reviews the use of ultrasonic sensors for monitoring processes, before reviewing the combination of ultrasonic measurements and machine learning. We include literature from other sectors such as structural health monitoring. This review covers feature extraction, feature selection, algorithm choice, hyperparameter selection, data augmentation, domain adaptation, semi-supervised learning and machine learning interpretability. Finally, recommendations for applying machine learning to the reviewed processes are made.

Deep Learning Empowered Structural Health Monitoring and Damage Diagnostics for Structures with Weldment via Decoding Ultrasonic Guided Wave

Welding is widely used in the connection of metallic structures, including welded joints in oil/gas metallic pipelines and other structures. The welding process is vulnerable to the inclusion of different types of welding defects, such as lack of penetration and undercut. These defects often initialize early-age cracking and induced corrosion. Moreover, welding-induced defects often accompany other types of mechanical damage, thereby leading to more challenges in damage detection. As such, identification of weldment defects and interaction with other mechanical damages at their early stage is crucial to ensure structural integrity and avoid potential premature failure. The current strategies of damage identification are achieved using ultrasonic guided wave approaches that rely on a change in physical parameters of propagating waves to discriminate as to whether there exist damaged states or not. However, the inherently complex nature of weldment, the complication of damages interactions, and large-scale/long span structural components integrated with structure uncertainties pose great challenges in data interpretation and making an informed decision. Artificial intelligence and machine learning have recently become emerging methods for data fusion, with great potential for structural signal processing through decoding ultrasonic guided waves. Therefore, this study aimed to employ the deep learning method, convolutional neural network (CNN), for better characterization of damage features in terms of welding defect type, severity, locations, and interaction with other damage types. The architecture of the CNN was set up to provide an effective classifier for data representation and data fusion. A total of 16 damage states were designed for training and calibrating the accuracy of the proposed method. The results revealed that the deep learning method enables effectively and automatically extracting features of ultrasonic guided waves and yielding high precise prediction for damage detection of structures with welding defects in complex situations. In addition, the effectiveness and robustness of the proposed methods for structure uncertainties using different embedding materials, and data under noise interference, was also validated and findings demonstrated that the proposed deep learning methods still exhibited a high accuracy at high noise levels.

Improved Unsupervised Learning Method for Material-Properties Identification Based on Mode Separation of Ultrasonic Guided Waves

Numerical methods, including machine-learning methods, are now actively used in applications related to elastic guided wave propagation phenomena. The method proposed in this study for material-properties characterization is based on an algorithm of the clustering of multivariate data series obtained as a result of the application of the matrix pencil method to the experimental data. In the developed technique, multi-objective optimization is employed to improve the accuracy of the identification of particular parameters. At the first stage, the computationally efficient method based on the calculation of the Fourier transform of Green’s matrix is employed iteratively and the obtained solution is used for filter construction with decreasing bandwidths providing nearly noise-free classified data (with mode separation). The filter provides data separation between all guided waves in a natural way, which is needed at the second stage, where a more laborious method based on the minimization of the slowness residuals is applied to the data. The method might be further employed for material properties identification in plates with thin coatings/interlayers, multi-layered anisotropic laminates, etc.

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.

Index-Rotated Fast Ultrasound Imaging of Cortical Bone Based on Predicted Velocity Model

Due to the significant acoustic impedance contrast at cortical boundaries, highly inside attenuation, and the unknown sound velocity distribution, accurate ultrasound cortical bone imaging remains a challenge, especially for the traditional pulse-echo modalities using unique sound velocity. Moreover, the large amounts of data recorded by multielement probe results in a relatively time-consuming reconstruction process. To overcome these limitations, this article proposed an index-rotated fast ultrasound imaging method based on predicted velocity model (IR-FUI-VP) for cortical cross section ultrasound tomography (UST) imaging, utilizing ray-tracing synthetic aperture (RTSA). In virtue of ring probe, the sound velocity model was predicted in advance using bent-ray inversion (BRI). With the predicted velocity model, index-rotated fast ultrasound imaging (IR-FUI) was further applied to image the cortical cross sections in the sectors corresponding to the dynamic apertures (DAs) and ring center. The final result was merged by all sector images. One cortical bone phantom and two ex vivo bovine femurs were utilized to demonstrate the performance of the proposed method. Compared to the conventional synthetic aperture (SA) imaging, the method can not only accurately image the outer cortical boundary but also precisely reconstruct the inner cortical surface. The mean relative errors of the predicted sound velocity in the region of interest (ROI) were all smaller than 7%, and the mean errors of cortical thickness are all less than 0.31 mm. The reconstructed images of bovine femurs were in good agreement with the reference images scanned by micro-computed tomography ( μ CT) with respect to the morphology and thickness. The speed of IR-FUI is about 3.73 times faster than the traditional SA. It is proved that the proposed IR-FUI-VP-based UST is an effective way for fast and accurate cortical bone imaging.

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.

Fourier-Domain Ultrasonic Imaging of Cortical Bone Based on Velocity Distribution Inversion

There is a significant acoustic impedance contrast between the cortical bone and the surrounding soft tissue, resulting in difficulty for ultrasound penetration into bone tissue with high frequency. It is challenging for the conventional pulse-echo modalities to give accurate cortical bone images using uniform sound velocity model. To overcome these limitations, an ultrasound imaging method called full-matrix Fourier-domain synthetic aperture based on velocity inversion (FM-FDSA-VI) was developed to provide accurate cortical bone images. The dual linear arrays were located on the upper and lower sides of the imaging region. After full-matrix acquisition with two identical linear array probes facing each other, travel-time inversion was used to estimate the velocity distribution in advance. Then, full-matrix Fourier-domain synthetic aperture (FM-FDSA) imaging based on the estimated velocity model was applied twice to image the cortical bone, utilizing the data acquired from top and bottom linear array, respectively. Finally, to further improve the image quality, the two images were merged to give the ultimate result. The performance of the method was verified by two simulated models and two bone phantoms (i.e., regular and irregular hollow bone phantom). The mean relative errors of estimated sound velocity in the region-of-interest (ROI) are all below 12%, and the mean errors of cortical section thickness are all less than 0.3 mm. Compared to the conventional synthetic aperture (SA) imaging, the FM-FDSA-VI method is able to accurately image cortical bone with respect to the structure. Moreover, the result of irregular bone phantom was close to the image scanned by microcomputed tomography ( μ CT) in terms of macro geometry and thickness. It is demonstrated that the proposed FM-FDSA-VI method is an efficient way for cortical bone ultrasonic imaging.

In vivopulse-echo measurement of apparent broadband attenuation andQfactor in cortical bone: a preliminary study

Quantitative ultrasound (QUS) methods have been introduced to assess cortical bone health at the radius and tibia through the assessment of cortical thickness (Ct.Th), cortical porosity and bulk wave velocities. Ultrasonic attenuation is another QUS parameter which is not currently used. We assessed the feasibility ofin vivomeasurement of ultrasonic attenuation in cortical bone with a broadband transducer with 3.5 MHz center frequency. Echoes from the periosteal and endosteal interfaces were fitted with Gaussian pulses using sparse signal processing. Then, the slope of the broadband ultrasonic attenuation (Ct.nBUA) in cortical bone and quality factorQ11-1were calculated with a parametric approach based on the center-frequency shift. Five human subjects were measured at the one-third distal radius with pulse-echo ultrasound, and reference data was obtained with high-resolution x-ray peripheral computed tomography (Ct.Th and cortical volumetric bone mineral density (Ct.vBMD)). Ct.Th was used in the calculation of Ct.nBUA whileQ11-1is obtained solely from ultrasound data. The values of Ct.nBUA (6.7 ± 2.2 dB MHz^-1.cm^-1) andQ11-1(8.6 ± 3.1%) were consistent with the literature data and were correlated to Ct.vBMD (R2=0.92,p<0.01, RMSE = 0.56 dB.MHz^-1.cm^-1, andR2=0.93,p<0.01, RMSE = 0.76%). This preliminary study suggests that the attenuation of an ultrasound signal propagating in cortical bone can be measuredin vivoat the one-third distal radius and that it provides an information on bone quality as attenuation values were correlated to Ct.vBMD. It remains to ascertain that Ct.nBUA andQ11-1measured here exactly reflect the true (intrinsic) ultrasonic attenuation in cortical bone. Measurement of attenuation may be considered useful for assessing bone health combined with the measurement of Ct.Th, porosity and bulk wave velocities in multimodal cortical bone QUS methods.