Introduction.

Diagnostic ultrasound imaging has gained wide acceptance for a broad range of clinical uses. In many cases, ultrasonography is the first-line imaging modality selected for its ease of access and absence of ionizing radiation. Over the last decades, ultrasonography has considerably evolved and is currently contributing to important improvements in patient diagnosis and treatment. Modern ultrasound imaging can provide soft tissue anatomical (shape, size…) and functional information (tissue movements, blood flow) in 3D and 4D, characterization and distinction among tissues (echostructure) and quantification of tissue properties (microstructure, tissue stiffness). Soft tissue quantitative ultrasound (QUS) refers to methods specifically developed to assess quantitative variables reflecting tissue physical properties, usually by analyzing the raw radiofrequency signals and/or its spectral characteristics.

Clinical Devices for Bone Assessment.

Although it has been over 30 years since the first recorded use of quantitative ultrasound (QUS) technology to predict bone strength, the field has not yet reached its maturity. Among several QUS technologies available to measure cortical or cancellous bone sites, at least some of them have demonstrated potential to predict fracture risk with an equivalent efficiency compared to X-ray densitometry techniques, and the advantages of being non-ionizing, inexpensive, portable, highly acceptable to patients and repeatable. In this Chapter, we review instrumental developments that have led to in vivo applications of bone QUS, emphasizing the developments occurred in the decade 2010-2020. While several proposals have been made for practical clinical use, there are various critical issues that still need to be addressed, such as quality control and standardization. On the other side, although still at an early stage of development, recent QUS approaches to assess bone quality factors seem promising. These include guided waves to assess mechanical and structural properties of long cortical bones or new QUS technologies adapted to measure the major fracture sites (hip and spine). New data acquisition and signal processing procedures are prone to reveal bone properties beyond bone mineral quantity and to provide a more accurate assessment of bone strength.

Axial Transmission: Techniques, Devices and Clinical Results.

Recent progress in quantitative ultrasound have sparked increasing interest towards the measurement of long cortical bones (e.g., radius or tibia), because their ability to sustain loading and resist fractures is known to be related to their mechanical properties at different length scales. In particular, applying guided waves for the assessment of cortical bone is inspired by widely used techniques developed earlier in the field of nondestructive testing and evaluation of different waveguide structures. This approach is based on the experimental evidence that the cortex of long bones can act as a natural waveguide for ultrasound, despite its irregular geometry, attenuation, and heterogeneous material properties. Because guided waves could yield the characterization of several bone properties (e.g., cortical thickness, anisotropic stiffness or porosity) at the mesoscopic level by fitting the dispersion characteristics of a waveguide model to the measured dispersion curves (i.e., solving an inverse problem), this method has a strong clinical potential as a tool for bone status assessment. This chapter revisits the roadmap that allowed the so-called bidirectional axial transmission technique to progress from a pure laboratory concept to a diagnostic tool of clinical interest over the second decade of the twenty-first century and discusses the current clinical challenges associated with cortical bone characterization by ultrasound guided waves.

Dispersive Radon transform.

Dispersion results in the spreading and overlapping of the wave-packets, which often limits the capability of signal interpretation; on the other hand, such a phenomenon can also be used for structure or media evaluation. In this study, the authors propose an original dispersive Radon transform (DRT), which is formulated as integration transform along a set of dispersion curves. Multichannel dispersive signals of each individual mode can be concentrated to a well localized region in the DRT domain. The proposed DRT establishes the sparse projection of the dispersive components and provides an efficient solution for mode separation, noise filtering, and missing data reconstruction. Particularly the DRT method allows projecting the temporal signals of dispersive waves on the space of parameters of interest, which can be used to solve the inverse problem for waveguide or media property estimation. The least-square procedure and sparse scheme of the DRT are introduced. A high-resolution DRT is designed based on an iterative reweighting inversion scheme, which resembles the infinite-aperture velocity gather. The proposed method is applied by analyzing ultrasonic guided waves in plate-like structures and in a human radius specimen. The results suggest that the DRT method can significantly enhance the interpretation of dispersive signals.

Quantification of stiffness measurement errors in resonant ultrasound spectroscopy of human cortical bone.

Resonant ultrasound spectroscopy (RUS) is the state-of-the-art method used to investigate the elastic properties of anisotropic solids. Recently, RUS was applied to measure human cortical bone, an anisotropic material with low Q-factor (20), which is challenging due to the difficulty in retrieving resonant frequencies. Determining the precision of the estimated stiffness constants is not straightforward because RUS is an indirect method involving minimizing the distance between measured and calculated resonant frequencies using a model. This work was motivated by the need to quantify the errors on stiffness constants due to different error sources in RUS, including uncertainties on the resonant frequencies and specimen dimensions and imperfect rectangular parallelepiped (RP) specimen geometry. The errors were first investigated using Monte Carlo simulations with typical uncertainty values of experimentally measured resonant frequencies and dimensions assuming a perfect RP geometry. Second, the exact specimen geometry of a set of bone specimens were recorded by synchrotron radiation micro-computed tomography. Then, a "virtual" RUS experiment is proposed to quantify the errors induced by imperfect geometry. Results show that for a bone specimen of ∼1° perpendicularity and parallelism errors, an accuracy of a few percent ( <6.2%) for all the stiffness constants and engineering moduli is achievable.

Measurement of dispersion curves of circumferential guided waves radiating from curved shells: Theory and numerical validation.

A method is proposed to evaluate in a non-contact way the phase velocity dispersion curves of circumferential waves around a shell of arbitrary shape immersed in a fluid. No assumptions are made about the thickness or the material of the shell. A geometrical model is derived to describe the shape of the radiated wavefronts in the surrounding fluid, and predict the positions of its centers of curvature. Then the time-reversal principle is applied to recover these positions and to calculate the phase velocity of the circumferential waves. Numerical finite-difference simulations are performed to evaluate the method on a circular and on an elliptic thin shell. Different dispersion curves can be recovered with an error of less than 10%.

Multichannel processing for dispersion curves extraction of ultrasonic axial-transmission signals: Comparisons and case studies.

Some pioneering studies have shown the clinical feasibility of long bones evaluation using ultrasonic guided waves. Such a strategy is typically designed to determine the dispersion information of the guided modes to infer the elastic and structural characteristics of cortical bone. However, there are still some challenges to extract multimode dispersion curves due to many practical limitations, e.g., high spectral density of modes, limited spectral resolution and poor signal-to-noise ratio. Recently, two representative signal processing methods have been proposed to improve the dispersion curves extraction. The first method is based on singular value decomposition (SVD) with advantages of multi-emitter and multi-receiver configuration for enhanced mode extraction; the second one uses linear Radon transform (LRT) with high-resolution imaging of the dispersion curves. To clarify the pros and cons, a face to face comparison was performed between the two methods. The results suggest that the LRT method is suitable to separate the guided modes at low frequency-thickness-product ( fh) range; for multimode signals in broadband fh range, the SVD-based method shows more robust performances for weak mode enhancement and noise filtering. Different methods are valuable to cover the entire fh range for processing ultrasonic axial transmission signals measured in long cortical bones.

Distribution of mesoscale elastic properties and mass density in the human femoral shaft.

Cortical bone properties are determined by tissue composition and structure at several hierarchical length scales. In this study, the spatial distribution of micro- and mesoscale elastic properties within a human femoral shaft has been investigated. Microscale tissue degree of mineralization (DMB), cortical vascular porosity Ct.Po and the average transverse isotropic stiffness tensor C(Micro) of cylindrical-shaped samples (diameter: 4.4 mm, N = 56) were obtained from cortical regions between 20 and 85% of the total femur length and around the periphery (anterior, medial, posterior and lateral quadrants) by means of synchrotron radiation µCT (SRµCT) and 50-MHz scanning acoustic microscopy (SAM). Within each cylinder, the volumetric bone mineral density (vBMD) and the mesoscale stiffness tensor C(Meso) were derived using a numerical homogenization approach. Moreover, microelastic maps of the axial elastic coefficient c33 measured by SAM at distinct cross-sectional locations along the femur were used to construct a 3-D multiscale elastic model of the femoral shaft. Variations of vBMD (6.1%) were much lower than the variations of mesoscale elastic coefficients (11.1-21.3%). The variation of DMB was only a minor predictor for variations of the mesoscale elastic properties (0.05 ≤ R(2) ≤ 0.34). Instead, variations of the mesoscale elastic properties could be explained by variations of cortical porosity and microscale elastic properties. These data were suitable inputs for numerical evaluations and may help to unravel the relations between structure and composition on the elastic function in cortical bone.

A free plate model can predict guided modes propagating in tubular bone-mimicking phantoms.

The goal of this work was to show that a non-absorbing free plate model can predict with a reasonable accuracy guided modes measured in bone-mimicking phantoms that have circular cross-section. Experiments were carried out on uncoated and coated phantoms using a clinical axial transmission setup. Adjustment of the plate model to the experimental data yielded estimates for the waveguide characteristics (thickness, bulk wave velocities). Fair agreement was achieved over a frequency range of 0.4 to 1.6 MHz. A lower accuracy observed for the thinnest bone-mimicking phantoms was caused by limitations in the wave number measurements rather than by the model itself.

Ultrasound to assess bone quality.

Bone quality is determined by a variety of compositional, micro- and ultrastructural properties of the mineralized tissue matrix. In contrast to X-ray-based methods, the interaction of acoustic waves with bone tissue carries information about elastic and structural properties of the tissue. Quantitative ultrasound (QUS) methods represent powerful alternatives to ionizing x-ray based assessment of fracture risk. New in vivo applicable methods permit measurements of fracture-relevant properties, [eg, cortical thickness and stiffness at fragile anatomic regions (eg, the distal radius and the proximal femur)]. Experimentally, resonance ultrasound spectroscopy and acoustic microscopy can be used to assess the mesoscale stiffness tensor and elastic maps of the tissue matrix at microscale resolution, respectively. QUS methods, thus, currently represent the most promising approach for noninvasive assessment of components of fragility beyond bone mass and bone microstructure providing prospects for improved assessment of fracture risk.

Resonant ultrasound spectroscopy for viscoelastic characterization of anisotropic attenuative solid materials.

Resonant ultrasound spectroscopy (RUS) is an accurate measurement method in which the full stiffness tensor of a material is assessed from the free resonant frequencies of a small sample, and the viscoelastic damping is measured from the resonant peaks width. High viscoelastic damping causes the resonant peaks to overlap and therefore complicate the measurement of the resonant frequencies and the inverse identification of material properties. For that reason, RUS has been known to be fully applicable only to low damping materials. The purpose of this work is to adapt RUS for the characterization of highly attenuating viscoelastic materials. Spectrum measurement using shear transducers combined with dedicated signal processing is employed to retrieve the resonant frequencies despite overlapping. A probabilistic (Bayesian) formulation of the inverse problem, tackling the problem of correctly pairing the measured and predicted frequencies, is proposed. Applications to polymethylmethacrylate (isotropic) and glass/epoxy transversely isotropic samples are presented. The full set of viscoelastic properties is obtained with good repeatability. Particularly, elastic moduli of the isotropic samples are obtained within 1%.

Measuring the wavenumber of guided modes in waveguides with linearly varying thickness.

Measuring guided waves in cortical bone arouses a growing interest to assess skeletal status. In most studies, a model of waveguide is proposed to assist in the interpretation of the dispersion curves. In all the reported investigations, the bone is mimicked as a waveguide with a constant thickness, which only approximates the irregular geometry of cortical bone. In this study, guided mode propagation in cortical bone-mimicking wedged plates is investigated with the aim to document the influence on measured dispersion curves of a waveguide of varying thickness and to propose a method to overcome the measurement limitations induced by such thickness variations. The singular value decomposition-based signal processing method, previously introduced for the detection of guided modes in plates of constant thickness, is adapted to the case of waveguides of slowly linearly variable thickness. The modification consists in the compensation at each frequency of the wavenumber variations induced by the local variation in thickness. The modified method, tested on bone-mimicking wedged plates, allows an enhanced and more accurate detection of the wavenumbers. Moreover, the propagation in the directions of increasing and decreasing thickness along the waveguide is investigated.

Circumferential guided wave measurements of a cylindrical fluid-filled bone-mimicking phantom.

In the context of hip fracture risk prediction, measurement of guided waves could improve the assessment of cortical femoral neck properties. The decomposition of the time reversal operator (DORT) method was previously shown to be efficient to measure circumferential guided modes in an empty cortical bone-mimicking tube of circular cross section. In this study, an adaptation of the DORT method is proposed to probe the same bone-mimicking tube but filled with a marrow-mimicking fluid. The contributions to the backscattered field of waves multiply reflected in the cavity of the tube interfere with those of circumferential guided waves. The former contributions are eliminated in the backpropagation image using ad hoc criterion determined with simulation. Eight portions of different guided modes were observed from experimental and simulated data. They were identified by comparison with theoretical predictions. This work confirms the feasibility of measuring guided waves in a fluid-filled tube of bone-mimicking material with the DORT method.

Accurate measurement of guided modes in a plate using a bidirectional approach.

Measuring guided wave propagation in long bones is of interest to the medical community. When an inclination exists between the probe and the tested specimen surface, a bias is introduced on the guided mode wavenumbers. The aim of this study was to generalize the bidirectional axial transmission technique initially developed for the first arriving signal. Validation tests were performed on academic materials such a bone-mimicking plate covered with either a silicon or fat-mimicking layer. For any inclination, the wavenumbers measured with the probe parallel to the waveguide surface can be obtained by averaging the wavenumbers measured in two opposite directions.

Three-dimensional quantitative ultrasound for detecting lymph node metastases.

PURPOSE: Detection of metastases in lymph nodes (LNs) is critical for cancer management. Conventional histological methods may miss metastatic foci. To date, no practical means of evaluating the entire LN volume exists. The aim of this study was to develop fast, reliable, operator-independent, high-frequency, quantitative ultrasound (QUS) methods for evaluating LNs over their entire volume to effectively detect LN metastases. METHODS: We scanned freshly excised LNs at 26 MHz and digitally acquired echo-signal data over the entire three-dimensional (3D) volume. A total of 146 LNs of colorectal, 26 LNs of gastric, and 118 LNs of breast cancer patients were enrolled. We step-sectioned LNs at 50-µm intervals and later compared them with 13 QUS estimates associated with tissue microstructure. Linear-discriminant analysis classified LNs as metastatic or nonmetastatic, and we computed areas (Az) under receiver-operator characteristic curves to assess classification performance. The QUS estimates and cancer probability values derived from discriminant analysis were depicted in 3D images for comparison with 3D histology. RESULTS: Of 146 LNs of colorectal cancer patients, 23 were metastatic; Az = 0.952 ± 0.021 (95% confidence interval [CI]: 0.911-0.993); sensitivity = 91.3% (specificity = 87.0%); and sensitivity = 100% (specificity = 67.5%). Of 26 LNs of gastric cancer patients, five were metastatic; Az = 0.962 ± 0.039 (95% CI: 0.807-1.000); sensitivity = 100% (specificity = 95.3%). A total of 17 of 118 LNs of breast cancer patients were metastatic; Az = 0.833 ± 0.047 (95% CI: 0.741-0.926); sensitivity = 88.2% (specificity = 62.5%); sensitivity = 100% (specificity = 50.5%). 3D cancer probability images showed good correlation with 3D histology. CONCLUSIONS: These results suggest that operator- and system-independent QUS methods allow reliable entire-volume LN evaluation for detecting metastases. 3D cancer probability images can help pathologists identify metastatic foci that could be missed using conventional methods.

Nonlinear ultrasound: potential of the cross-correlation method for osseointegration monitoring.

Recently the concept of probing nonlinear elasticity at an interface prosthesis/bone has been proposed as a promising method to monitor the osseointegration/sealing of a prosthesis. However, the most suitable method to achieve this goal is a point of debate. To this purpose, two approaches termed the scaling subtraction method and the cross-correlation method are compared here. One nonlinear parameter derived from the cross-correlation method is as sensitive as a clinical device based on linear elasticity measurement. Further, this study shows that cross-correlation based methods are more sensitive than those based on subtraction/addition, such like pulse inversion and similar methods.

Comparative investigation of elastic properties in a trabecula using micro-Brillouin scattering and scanning acoustic microscopy.

Micro-Brillouin scattering (µ-BR) and a 200 MHz scanning acoustic microscope (SAM) with similar spatial resolutions were applied to evaluate tissue elastic properties in two directions in a trabecula. Acoustic impedance measured by SAM was in the range of 5-9 Mrayl. Wave velocities determined by µ-BR were in the range of (4.75-5.11) × 10(3) m/s. Both exhibited a similar trend of variation across the trabecula and were significantly correlated (R(2) = 0.63-0.67, p < 0.01). µ-BR is useful for the evaluation of tissue stiffness within a trabecula. Combined with SAM or nanoindentation, it can provide additional information to assess elastic anisotropy at the micro-scale.

Time reversed elastic nonlinearity diagnostic applied to mock osseointegration monitoring applying two experimental models.

This study broadens vibration-like techniques developed for osseointegration monitoring to the nonlinear field. The time reversed elastic nonlinearity diagnostic is applied to two mock models. The first one consists of tightening a dental implant at different torques in a mock cortical bone; the second one allows one to follow glue curing at the interface between a dental implant and a mock jaw. Energy is focused near the implant interface using the time reversal technique. Two nonlinear procedures termed pulse inversion and the scaling subtraction method, already used successfully in other fields such as contrast agents and material characterization, are employed. These two procedures are compared for both models. The results suggest that nonlinear elasticity can provide new information regarding the interface, complementary to the linear wave velocity and attenuation. The curing experiment exhibits an overall low nonlinear level due to the fact that the glue significantly damps elastic nonlinearity at the interface. In contrast, the torque experiment shows strong nonlinearities at the focus time. Consequently, a parallel analysis of these models, both only partially reflecting a real case, enables one to envisage future in vivo experiments.

Characterization of circumferential guided waves in a cylindrical cortical bone-mimicking phantom.

The femoral neck cortical shell was recently demonstrated to act like a waveguide for circumferential waves. Femoral neck assessment with ultrasound could be enhanced by guided waves measurement. In this study, the decomposition of the time reversal operator (DORT) method is used to measure the phase velocities of circumferential guided modes in a circular tube with dimensions characteristic of femoral neck. The tube is made of a bone-mimicking material. Five guided modes are obtained and compared to theoretical predictions. The work substantiates the feasibility of measuring guided waves in a relatively thick tube of attenuating material with the DORT method.

Inverse Problem in Resonant Ultrasound Spectroscopy With Sampling and Optimization: A Comparative Study on Human Cortical Bone.

The Bayesian inference with prior knowledge has been proposed recently to solve the inverse problem in resonant ultrasound spectroscopy. It allows inferring the elastic properties of high damping materials, such as cortical bone with less dependence on the initial guessed values. In this method, the estimation of the stiffness coefficients is expressed as a probabilistic solution to the inverse problem, which can be achieved by sampling or optimization methods. However, the detailed performance comparison of these two strategies applied to high damping materials has not been fully studied. In this work, the full stiffness tensor of 52 transversely isotropic cortical bone specimens was obtained using Markov chain Monte Carlo (MCMC) sampling and particle swarm optimization (PSO), respectively. Results showed that the local probability distributions of stiffness coefficients estimated by the two methods are consistent. Compared with MCMC, the average calculation speed of PSO is ten times faster [614 s ± 59 s (MCMC) versus 53 s ± 22 s (PSO)]. The mean standard error between theoretical and experimental resonant frequencies was slightly smaller for PSO compared with MCMC. In conclusion, PSO, a global optimization strategy, is suitable to solve the inverse problem for high damping materials.