Simultaneous estimation of cortical bone thickness and acoustic wave velocity using a multivariable optimization approach: Bone phantom and in-vitro study

Recycled windshield glass as new material for producing ultrasonic phantoms of cortical bone-healing stages

The quantitative ultrasound technique was used to evaluate bone-mimicking phantoms; however, these phantoms do not mimic the intermediate stages of cortical bone healing. We propose using windshield glass as an original material to produce phantoms that mimic the characteristics of three different stages of cortical bone healing. This material was processed via a route that included breaking, grinding, compacting, drying, and sintering in four temperature groups: 625 °C, 645 °C, 657 °C, and 663 °C. The parameters evaluated were the ultrasonic longitudinal phase velocity (cL), corrected (αc) ultrasonic attenuation coefficient, and bulk density (ρs). The results showed that the mean values ofcL,αc,andρsvaried from 2, 398 to 4, 406 m·s^-1, 3 to 10 dB·cm^-1, and 1, 563 to 2, 089 kg·m^-3, respectively. The phantoms exhibited properties comparable with the three stages of cortical bone healing and can be employed in diagnostic and therapeutic studies using ultrasound.

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.

Full wave 3D inverse scattering transmission ultrasound tomography in the presence of high contrast

We present here a quantitative ultrasound tomographic method yielding a sub-mm resolution, quantitative 3D representation of tissue characteristics in the presence of high contrast media. This result is a generalization of previous work where high impedance contrast was not present and may provide a clinically and laboratory relevant, relatively inexpensive, high resolution imaging method for imaging in the presence of bone. This allows tumor, muscle, tendon, ligament or cartilage disease monitoring for therapy and general laboratory or clinical settings. The method has proven useful in breast imaging and is generalized here to high-resolution quantitative imaging in the presence of bone. The laboratory data are acquired in ~ 12 min and the reconstruction in ~ 24 min-approximately 200 times faster than previously reported simulations in the literature. Such fast reconstructions with real data require careful calibration, adequate data redundancy from a 2D array of 2048 elements and a paraxial approximation. The imaging results show that tissue surrounding the high impedance region is artifact free and has correct speed of sound at sub-mm resolution.

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.

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.

Improving broadband ultrasound attenuation assessment in cancellous bone by mitigating the influence of cortical bone: Phantom and in-vitro study

The purpose of this work was to present a new approach that allows the influence of cortical bone on noninvasive measurement of broadband ultrasound attenuation (BUA) to be corrected. The method, implemented here at 1 MHz makes use of backscattered signal and once refined and clinically confirmed, it would offer an alternative to ionizing radiation based methods, such as DEXA (Dual-energy X-ray absorptiometry), quantitative computed tomography (QCT), radiographic absorptiometry (RA) or single X-ray absorptiometry (SXA), which are clinically approved for assessment of progress of osteoporosis. In addition, as the method employs reflected waves, it might substantially enhance the applicability of BUA - from being suitable to peripheral bones only it would extend this applicability to include such embedded bones as hip and femoral neck. The proposed approach allows the cortical layer parameters used for correction and the corrected value and parameter of the cancellous bone (BUA) to be determined simultaneously from the single (pulse-echo) bone backscattered wave; to the best of the authors' knowledge such approach was not previously reported. The validity of the method was tested using acoustic data obtained from a custom-designed bone-mimicking phantom and a calf femur. The relative error of the attenuation coefficient assessment was determined to be 3.9% and 4.7% for the bone phantom and calf bone specimens, respectively. When the cortical shell influence was not taken into account the corresponding errors were considerably higher 8.3% (artificial bone) and 9.2% (calf femur). As indicated above, once clinically proven, the use of this BUA measurement technique in reflection mode would augment diagnostic power of the attending physician by permitting to include bones, which are not accessible for transmission mode evaluation, e.g. hip, spine, humerus and femoral neck.