Ex vivo cortical porosity and thickness predictions at the tibia using full-spectrum ultrasonic guided-wave analysis

Study of Ultrasonic Guided Wave Propagation in Bone Composite Structures for Revealing Osteoporosis Diagnostic Indicators

Tubular bones are layered waveguide structures composed of soft tissue, cortical and porous bone tissue, and bone marrow. Ultrasound diagnostics of such biocomposites are based on the guided wave excitation and registration by piezoelectric transducers applied to the waveguide surface. Meanwhile, the upper sublayers shield the diseased interior, creating difficulties in extracting information about its weakening from the surface signals. To overcome these difficulties, we exploit the advantages of the Green's matrix-based approach and adopt the methods and algorithms developed for the guided wave structural health monitoring of industrial composites. Based on the computer models implementing this approach and experimental measurements performed on bone phantoms, we analyze the feasibility of using different wave characteristics to detect hidden diagnostic signs of developing osteoporosis. It is shown that, despite the poor excitability of the most useful modes associated with the diseased inner layers, the use of the improved matrix pencil method combined with objective functions based on the Green's matrix allows for effective monitoring of changes in the elastic moduli of the deeper sublayers. We also note the sensitivity and monotonic dependence of the resonance response frequencies on the degradation of elastic properties, making them a promising indicator for osteoporosis diagnostics.

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.

Can guided wave ultrasound predict bone mechanical properties at the femoral neck in patients undergoing hip arthroplasty?

The bone quality of patients undergoing hip replacement surgery is poorly predicted by radiographs alone. With better bone quality information available to a surgeon, the operation can be performed more safely. The aim of this study was to investigate whether ultrasound signals of cortical bone at peripheral sites such as the tibia and radius can be used to predict the compressive mechanical properties of cortical bone at the femoral neck. We recruited 19 patients undergoing elective hip arthroplasty and assessed the radius and tibia of these patients with the Azalée guided wave ultrasound to estimate the porosity and thickness of the cortex. Excess bone tissues were collected from the femoral neck and the compressive mechanical properties of the cortex were characterised under a mechanical loading rig to determine stiffness, ultimate strength, and density. The correlations between the ultrasound measurements and mechanical properties were analysed using linear regression, Pearson correlation statistics, and multiple regression analysis. Cortical mechanical properties were weakly to moderately correlated with the ultrasound measurements at various sites (R2 = 0.00-0.36). The significant correlations found were not consistent across all 4 peripheral measurement sites. Additionally, weak to moderate ability of the ultrasound to predict mechanical properties at the neck of femur with multiple regression analysis was found (R2 = 0.00-0.48). Again, this was inconsistent across the different anatomical sites. Overall, the results demonstrate the need for ultrasound scans to be collected directly from clinically relevant sites such as the femoral neck due to the inconsistency of mechanical properties across various sites.

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.

Virtual segmentation of three-dimensional ultrasound images of morphological structures of an ex vivo ectopic pregnancy inside a fallopian tube

Ex vivo ultrasound (US) of human tissues has been used for decades on the study of the acoustic physical aspects of the US, to the study of the morphology of the organs. Using three-dimensional (3D) US, we demonstrate the possibilities to study surgical specimens from gynecological conditions. 3D images of the surgical specimen were collected and virtually segmented according to the contrast of its images, providing a 3D image of the ectopic pregnancy and its effects on the fallopian tube.

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.

Ultrasound Scattering in Cortical Bone

Recent advances in imaging of bone microstructure have led to a growing recognition of the role of cortical microstructure in osteoporosis. It is now accepted that the assessment of the microstructure of cortical porosity is essential to assess bone mechanical competence and predict fracture risk. Cortical porosity affects the propagation of ultrasound waves because pores act as ultrasound scatterers. Scattering by the porosity is an opportunity that should be leveraged to extract quantitative information about cortical microstructure. Scattering by the pores affects a number of ultrasound parameters that should be quantified, including attenuation, backscatter coefficient, ultrasound diffusivity, and their frequency dependence. Measuring these ultrasound parameters and developing models that describe their dependence upon parameters of cortical microstructure is the key to solve inverse problems that will allow the quantitative assessment of cortical porosity and ultimately will improve the non-invasive ultrasound-based evaluation of bone mechanical competence and fracture risk. In this chapter, we present recent advances in measuring and modeling those parameters in cortical bone.

Deep Learning Analysis of Ultrasonic Guided Waves for Cortical Bone Characterization

Ultrasonic guided waves (UGWs) propagating in the long cortical bone can be measured via the axial transmission method. The characterization of long cortical bone using UGW is a multiparameter inverse problem. The optimal solution of the inverse problem often includes a complex solving process. Deep neural networks (DNNs) are essentially powerful multiparameter predictors based on universal approximation theorem, which are suitable for solving parameter predictions in the inverse problem by constructing the mapping relationship between UGW and cortical bone material parameters. In this study, we investigate the feasibility of applying the multichannel crossed convolutional neural network (MCC-CNN) to simultaneously estimate cortical thickness and bulk velocities (longitudinal and transverse). Unlike the multiparameter estimation in most previous studies, the technique mentioned in this work avoids solving a multiparameter optimization problem directly. The finite-difference time-domain (FDTD) method is performed to obtain the simulated UGW array signals for training the MCC-CNN. The network that is exclusively trained on simulated data sets can predict cortical parameters from the experimental UGW data. The proposed method is confirmed by using FDTD simulation signals and experimental data obtained from four bone-mimicking plates and from ten ex vivo bovine cortical bones. The estimated root-mean-squared error (RMSE) in the simulated test data for the longitudinal bulk velocity ( V_L ), transverse bulk velocity ( V_T ), and cortical thickness (Th) is 97 m/s, 53 m/s, and 0.089 mm, respectively. The predicted RMSE in the bone-mimicking phantom experiments for V_L|| , V_T|| , and Th is 120 m/s, 80 m/s, and 0.14 mm, respectively. The experimental dispersion trajectories are matched with the theoretical dispersion curves calculated by the predicted parameters in ex vivo bovine cortical bone experiments. Our proposed method demonstrates a feasible approach for the accurate evaluation of long cortical bones based on UGW.

Estimation of Cortical Bone Microstructure From Ultrasound Backscatter

Multichannel pulse-echo ultrasound using linear arrays and single-channel data acquisition systems opens new perspectives for the evaluation of cortical bone. In combination with spectral backscatter analysis, it can provide quantitative information about cortical microstructural properties. We present a numerical study, based on the finite-difference time-domain method, to estimate the backscatter cross section of randomly distributed circular pores in a bone matrix. A model that predicts the backscatter coefficient using arbitrary pore diameter distributions was derived. In an ex vivo study on 19 human tibia bones (six males, 13 females, 83.7 ± 8.4 years), multidirectional ultrasound backscatter measurements were performed using an ultrasound scanner equipped with a 6-MHz 128-element linear array with sweep motor control. A normalized depth-dependent spectral analysis was performed to derive backscatter and attenuation coefficients. Site-matched reference values of tissue acoustic impedance Z , cortical thickness (Ct.Th), pore density (Ct.Po.Dn), porosity (Ct.Po), and characteristic parameters of the pore diameter (Ct.Po.Dm) distribution were obtained from 100-MHz scanning-acoustic microscopy images. Proximal femur areal bone mineral density (aBMD), stiffness S , and ultimate force Fu from the same donors were available from a previous study. All pore structure and material properties could be predicted using linear combinations of backscatter parameters with a median to high accuracy (0.28 ≤ adjusted R² ≤ 0.59). The combination of cortical thickness and backscatter parameter provided similar or better prediction accuracies than aBMD. For the first time, a method for the noninvasive assessment of the pore diameter distribution in cortical bone by ultrasound is proposed. The combined assessment of cortical thickness, sound velocity, and pore size distribution in a mobile, nonionizing measurement system could have a major impact on preventing osteoporotic fractures.

Bulk Wave Velocities in Cortical Bone Reflect Porosity and Compression Strength

The goal of this study was to evaluate whether ultrasonic velocities in cortical bone can be considered as a proxy for mechanical quality of cortical bone tissue reflected by porosity and compression strength. Micro-computed tomography, compression mechanical testing and resonant ultrasound spectroscopy were used to assess, respectively, porosity, strength and velocity of bulk waves of both shear and longitudinal polarisations propagating along and perpendicular to osteons, in 92 cortical bone specimens from tibia and femur of elderly human donors. All velocities were significantly associated with strength (r = 0.65-0.83) and porosity (r = -0.64 to -0.77). Roughly, according to linear regression models, a decrease in velocity of 100 m/s corresponded to a loss of 20 MPa in strength (which is approximately 10% of the largest strength value) and to an increase in porosity of 5%. These results provide a rationale for the in vivo measurement of one or several velocities for the diagnosis of bone fragility.

Estimation of Thickness and Speed of Sound in Cortical Bone Using Multifocus Pulse-Echo Ultrasound

Most bone loss during the development of osteoporosis occurs in cortical bone at the peripheral skeleton. Decreased cortical thickness (Ct.Th) and the prevalence of large pores at the tibia are associated with reduced bone strength at the hip. Ct.Th and cortical sound velocity, i.e., a surrogate marker for changes of cortical porosity (Ct.Po), are key biomarkers for the identification of patients at high fracture risk. In this study, we have developed a method using a conventional ultrasound array transducer to determine thickness (Ct.Th) and the compressional sound velocity propagating in the radial bone direction (Ct. ν₁₁ ) using a refraction-corrected multifocus imaging approach. The method was validated in-silico on porous bone plate models using a 2-D finite-difference time-domain method and ex vivo on plate-shaped plastic reference materials and on plate-shaped cortical bovine tibia samples. Plane-wave pulse-echo measurements provided reference values to assess precision and accuracy of our method. In-silico results revealed the necessity to account for inclination-dependent transmission losses at the bone surface. Moreover, the dependence of Ct. ν₁₁ on both porosity and pore density was observed. Ct.Th and Ct. ν₁₁ obtained ex vivo showed a high correlation ) with reference values. The ex-vivo accuracy and precision for Ct. ν₁₁ were 29.9 m/s and 0.94%, respectively, and those for Ct.Th were 0.04 mm and 1.09%, respectively. In conclusion, this numerical and experimental study demonstrates an accurate and precise estimation of Ct.Th and Ct. ν₁₁ . The developed multifocus technique may have high clinical potential to improve fracture risk prediction using noninvasive and nonionizing conventional ultrasound technology with image guidance.

Decreased Compressional Sound Velocity Is an Indicator for Compromised Bone Stiffness in X-Linked Hypophosphatemic Rickets (XLH)

Objectives: To assess the diagnostic potential of bidirectional axial transmission (BDAT) ultrasound, and high-resolution peripheral quantitative computed tomography (HR-pQCT) in X-linked hypophosphatemia (XLH, OMIM #307800), a rare genetic disorder of phosphate metabolism caused by mutations in the PHEX gene. Methods: BDAT bone ultrasound was performed at the non-dominant distal radius (33% relative to distal head) and the central left tibia (50%) in eight XLH patients aged between 4.2 and 20.8 years and compared to twenty-nine healthy controls aged between 5.8 and 22.4 years. In eighteen controls, only radius measurements were performed. Four patients and four controls opted to participate in HR-pQCT scanning of the ultradistal radius and tibia. Results: Bone ultrasound was feasible in patients and controls as young as 4 years of age. The velocity of the first arriving signal (ν_FAS) in BDAT ultrasound was significantly lower in XLH patients compared to healthy controls: In the radius, mean ν_FAS of XLH patients and controls was 3599 ± 106 and 3866 ± 142 m/s, respectively (-6.9%; p < 0.001). In the tibia, it was 3578 ± 129 and 3762 ± 124 m/s, respectively (-4.9%; p = 0.006). HR-pQCT showed a higher trabecular thickness in the tibia of XLH patients (+16.7%; p = 0.021). Conclusions: Quantitative bone ultrasound revealed significant differences in cortical bone quality of young XLH patients as compared to controls. Regular monitoring of XLH patients by a radiation-free technology such as BDAT might provide valuable information on bone quality and contribute to the optimization of treatment. Further studies are needed to establish this affordable and time efficient method in the XLH patients.

In Vivo Measurements of Cortical Thickness and Porosity at the Proximal Third of the Tibia Using Guided Waves: Comparison with Site-Matched Peripheral Quantitative Computed Tomography and Distal High-Resolution Peripheral Quantitative Computed Tomography

The aim of this study was to estimate cortical porosity (Ct.Po) and cortical thickness (Ct.Th) using 500-kHz bi-directional axial transmission (AT). Ct.Th_AT and Ct.Po_AT were obtained at the tibia in 15 patients from a 2-D transverse isotropic free plate model fitted to measured guided wave dispersion curves. The velocities of the first arriving signal (υ_FAS) and A₀ mode (υ_A0) were also determined. Site-matched peripheral quantitative computed tomography (pQCT) provided volumetric cortical bone mineral density (Ct.vBMD_pQCT) and Ct.Th_pQCT. Good agreement was found between Ct.Th_AT and Ct.Th_pQCT (R² = 0.62, root mean square error [RMSE] = 0.39 mm). Ct.vBMD_pQCT correlated with Ct.Po_AT (R² = 0.57), υ_FAS (R² = 0.43) and υ_A0 (R² = 0.28). Furthermore, a significant correlation was found between AT and distal high-resolution pQCT. The measurement ofcortical parameters at the tibia using guided waves might improve the prediction of bone fractures in a cost-effective and radiation-free manner.