Measuring anisotropy of elastic wave velocity with ultrasound imaging and an autofocus method: application to cortical bone.

This work investigates the feasibility of estimating the parameters of an exact transverse isotropy model in cortical bone. The model describes the anisotropy of the velocity of compressional and shear bulk elastic waves. We propose to achieve this with ultrasound imaging relying on the transmission of unfocused beams and with an autofocus method. The latter is based on the principle that the reconstructed ultrasound image shows optimal quality if the velocity model is correct. The autofocus approach is applied to a composite image of the interface between cortical bone and marrow. It is obtained by incoherent summation of four types of images exploiting four different ray paths in the cortical bone layer, three of them involving mode-converted shear waves. If the parameters of the model are correct, spatial co-localization of the interface appears in the four images. As a result, intensity and sharpness in the composite image are maximal. The five parameters of the model of transverse isotropy are successfully estimated in a tube made of a bone-mimicking material. The estimates are in good agreement with resonant ultrasound spectroscopy (RUS) measurements. The tube thickness is recovered with an error smaller than 0.3%. In vivo results at the forearm of a volunteer are promising, four parameters could be estimated and are in good agreement with ex vivo RUS measurements. Moreover x-ray peripheral computed tomography corroborates the thickness of the cortical bone layer in the ultrasound image. Weak-anisotropy and exact transverse isotropy models provide very close measurements of the thickness of the tube and the radius bone. Thus, we recommend using the model of weak transverse isotropy for real-time anatomical imaging because more computationally efficient. For material characterization however, the model of exact transverse isotropy is preferred because the elastic anisotropy of cortical bone is moderate, rather than weak.

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.

Combined estimation of thickness and velocities using ultrasound guided waves: a pioneering study on in vitro cortical bone samples.

This paper reports for the first time on inverse estimation of several bone properties from guided-wave measurements in human bone samples. Previously, related approaches have focused on ultrasonic estimation of a single bone property at a time. The method is based on two steps: the multi-Lamb mode response is analyzed using the singular value decomposition signal processing method recently introduced in the field, then an identification procedure is run to find thickness and anisotropic elastic properties of the considered specimen. Prior to the measurements on bone, the method is validated on cortical bone-mimicking phantoms. The repeatability and the trueness of the estimated parameters on bone-mimicking phantoms were found around a few percent. Estimation of cortical thickness on bone samples was in good agreement with cortical thickness derived from high-resolution peripheral quantitative computed tomography data analysis of the samples.

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.

Non-destructive assessment of human ribs mechanical properties using quantitative ultrasound.

Advanced finite element models of the thorax have been developed to study, for example, the effects of car crashes. While there is a need for material properties to parameterize such models, specific properties are largely missing. Non-destructive techniques applicable in vivo would, therefore, be of interest to support further development of thorax models. The only non-destructive technique available today to derive rib bone properties would be based on quantitative computed tomography that measures bone mineral density. However, this approach is limited by the radiation dose. Bidirectional ultrasound axial transmission was developed on long bones ex vivo and used to assess in vivo health status of the radius. However, it is currently unknown if the ribs are good candidates for such a measurement. Therefore, the goal of this study is to evaluate the relationship between ex vivo ultrasonic measurements (axial transmission) and the mechanical properties of human ribs to determine if the mechanical properties of the ribs can be quantified non-destructively. The results show statistically significant relationships between the ultrasonic measurements and mechanical properties of the ribs. These results are promising with respect to a non-destructive and non-ionizing assessment of rib mechanical properties. This ex vivo study is a first step toward in vivo studies to derive subject-specific rib properties.

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.

Probing heterogeneity of cortical bone with ultrasound axial transmission.

In clinical examination of long cortical bones based on ultrasound axial transmission, the parameter currently used as indicator of bone fragility is the velocity of the first arriving signal (VFAS). VFAS is inherently related to the material properties of the bone site. However, experimental uncertainties may hide the true sensitivity of VFAS to elastic characteristics of bone. Measurements are performed with a multi-element compact array placed in contact with the bone. Therefore, VFAS measurements may be biased by variability imposed by geometrical irregularities of the sample below the probe and/or by probe misalignment. In this paper, we test the assumption that despite experimental errors, VFAS variations resulting from material properties can be measured. The methodology was to compare VFAS and velocities of compression bulk waves (VBWs) on carefully matched sites around the circumference of a test sample (bovine femur). VBW was mapped on bone cross-sections using a through-transmission technique. VBW and VFAS were highly correlated [R² = 0.80, root mean square error = 23 m·s⁻¹, p < 10⁻5] and the slope of the linear regression was close to 1 except in a part of the circumference with a pronounced curvature. In measurements performed with the same protocol as for clinical measurements, regions with different material properties (reflected by VBW) could be identified. This work demonstrates that within-specimen variations of material properties can be assessed with a technique available for in vivo measurements.

Measurement of guided mode wavenumbers in soft tissue-bone mimicking phantoms using ultrasonic axial transmission.

Human soft tissue is an important factor that influences the assessment of human long bones using quantitative ultrasound techniques. To investigate such influence, a series of soft tissue-bone phantoms (a bone-mimicking plate coated with a layer of water, glycerol or silicon rubber) were ultrasonically investigated using a probe with multi-emitter and multi-receiver arrays in an axial transmission configuration. A singular value decomposition signal processing technique was applied to extract the frequency-dependent wavenumbers of several guided modes. The results indicate that the presence of a soft tissue-mimicking layer introduces additional guided modes predicted by a fluid waveguide model. The modes propagating in the bone-mimicking plate covered by the soft-tissue phantom are only slightly modified compared to their counterparts in the free bone-mimicking plate, and they are still predicted by an elastic transverse isotropic two-dimensional waveguide. Altogether these observations suggest that the soft tissue-bone phantoms can be modeled as two independent waveguides. Even in the presence of the overlying soft tissue-mimicking layer, the modes propagating in the bone-mimicking plate can still be extracted and identified. These results suggest that our approach can be applied for the purpose of the characterization of the material and structural properties of cortical bone.

Cortical bone quality assessment using quantitative ultrasound on long bones.

The potential of ultrasonic guided waves to identify geometrical and elastic properties of long cortical bone was tested in this feasibility study. In this paper, we present the general framework of the inversion process applied to guided waves measurements performed on test cases and on one in vitro sample of human long cortical bone (forearm). Test cases were flat plates of bone mimicking material. Cortical thickness and direction dependent elastic properties of a long cortical bone were identified from ultrasound guided waves measurements. While the results need to be confirmed on a large set of bone specimens, this study opens new perspectives for axial transmission technique, due to the fact that measurements were performed under actual conditions of clinical measurements, i.e. with a probe and a signal processing dedicated to clinical use.

High-accuracy acoustic detection of nonclassical component of material nonlinearity.

The aim is to assess the nonclassical component of material nonlinearity in several classes of materials with weak, intermediate, and high nonlinear properties. In this contribution, an optimized nonlinear resonant ultrasound spectroscopy (NRUS) measuring and data processing protocol applied to small samples is described. The protocol is used to overcome the effects of environmental condition changes that take place during an experiment, and that may mask the intrinsic nonlinearity. External temperature fluctuation is identified as a primary source of measurement contamination. For instance, a variation of 0.1 °C produced a frequency variation of 0.01%, which is similar to the expected nonlinear frequency shift for weakly nonlinear materials. In order to overcome environmental effects, the reference frequency measurements are repeated before each excitation level and then used to compute nonlinear parameters. Using this approach, relative resonant frequency shifts of 10(-5) can be measured, which is below the limit of 10(-4) often considered as the limit of NRUS sensitivity under common experimental conditions. Due to enhanced sensitivity resulting from the correction procedure applied in this work, nonclassical nonlinearity in materials that before have been assumed to only be classically nonlinear in past work (steel, brass, and aluminum) is reported.

Experimental and simulation results on the effect of cortical bone mineralization in ultrasound axial transmission measurements: a model for fracture healing ultrasound monitoring.

Ultrasound axial transmission (UAT), a technique using propagation of ultrasound waves along the cortex of cortical bones, has been proposed as a diagnostic technique for the evaluation of fracture healing. Quantitative ultrasound parameters have been reported to be sensitive to callus changes during the regeneration process. The aim of this work was to identify the specific effect of cortical bone mineralization on UAT measurements by means of numerical simulations and experiments using a reverse fracture healing approach. A cortical bovine femur sample was used, in which a 3mm fracture gap was drilled. A 3mm thick cortical bone slice, extracted from another location in the bone sample, was submitted to a progressive demineralization process with EDTA during 12 days. UAT measurements and simulations using a 1MHz probe were performed with the demineralized slice placed into the fracture gap to mimic different stages of mineralization during the healing process. The calcium loss of the slice due to the EDTA treatment was recorded everyday, and its temporal evolution could be modeled by an exponential law. A 50MHz scanning acoustic microscopy was also used to assess the mineralization degree of the bone slice at the end of the intervention. These data were used in the numerical simulations to derive a model of the time evolution of bone slice mechanical properties. From both the experiments and the simulations, a significant and progressive increase in the time of flight (TOF; p<0.001) of the propagating waves measured by UAT was observed during the beginning of the demineralization process (first 4 days). Although the simulated TOF values were slightly larger than the experimental ones, they both exhibited a similar time-dependence, validating the simulation approach. Our results suggest that TOF measured in axial transmission is affected by local changes of speed of sound induced by changes in local mineralization. TOF may be an appropriate indicator to monitor callus maturation.

Impact of attenuation on guided mode wavenumber measurement in axial transmission on bone mimicking plates.

Robust signal processing methods adapted to clinical measurements of guided modes are required to assess bone properties such as cortical thickness and porosity. Recently, an approach based on the singular value decomposition (SVD) of multidimensional signals recorded with an axial transmission array of emitters and receivers has been proposed for materials with negligible absorption, see Minonzio et al. [J. Acoust. Soc. Am. 127, 2913-2919 (2010)]. In presence of absorption, the ability to extract guided mode degrades. The objective of the present study is to extend the method to the case of absorbing media, considering attenuated plane waves (complex wavenumber). The guided mode wavenumber extraction is enhanced and the order of magnitude of the attenuation of the guided mode is estimated. Experiments have been carried out on 2 mm thick plates in the 0.2-2 MHz bandwidth. Two materials are inspected: polymethylacrylate (PMMA) (isotropic with absorption) and artificial composite bones (Sawbones, Pacific Research Laboratory Inc, Vashon, WA) which is a transverse isotropic absorbing medium. Bulk wave velocities and bulk attenuation have been evaluated from transmission measurements. These values were used to compute theoretical Lamb mode wavenumbers which are consistent with the experimental ones obtained with the SVD-based approach.

Computational evaluation of the compositional factors in fracture healing affecting ultrasound axial transmission measurements.

This work aimed at computationally evaluating the compositional factors in fracture healing affecting ultrasound axial transmission (UAT), using four numerical daily-changing healing models, representing more realistic clinical conditions. Using two-dimensional (2-D) simulations, a 1-MHz source and a receiver were positioned parallel to the bone surface to detect the first arriving signal (FAS). The time-of-flight of the FAS (TOF(FAS)) was found to be sensitive only to superficial modifications in the propagation path. It was also shown that callus mature bone better explained alone the variation in TOF(FAS) (R(2) >or= 0.70, p < 0.001). Better TOF(FAS) predictions are obtained when using the callus composition inside cortical fracture gap (R(2) = 0.98, p < 0.01). Callus composition could not well explain the changes in energy attenuation. These results suggest that UAT may be an important clinical tool for fracture healing assessment, identifying callus degree of mineralization and possible consolidation delays and nonunions.

Influence of viscoelastic and viscous absorption on ultrasonic wave propagation in cortical bone: Application to axial transmission.

Cortical bone and the surrounding soft tissues are attenuating and heterogeneous media, which might affect the signals measured with axial transmission devices. This work aims at evaluating the effect of the heterogeneous acoustic absorption in bone and in soft tissues on the bone ultrasonic response. Therefore, a two-dimensional finite element time-domain method is derived to model transient wave propagation in a three-layer medium composed of an inhomogeneous transverse isotropic viscoelastic solid layer, sandwiched between two viscous fluid layers. The model couples viscous acoustic propagation in both fluid media with the anisotropic viscoelastic response of the solid. A constant spatial gradient of material properties is considered for two values of bone thicknesses (0.6 and 4 mm). In the studied configuration, absorption in the surrounding fluid tissues does not affect the results, whereas bone viscoelastic properties have a significant effect on the first arriving signal (FAS) velocity. For a thin bone, the FAS velocity is governed by the spatially averaged bone properties. For a thick bone, the FAS velocity may be predicted using a one-dimensional model.

Analysis of the most energetic late arrival in axially transmitted signals in cortical bone.

Axial transmission techniques are particularly suitable for the ultrasonic assessment of cortical bone. The generic term "axial transmission technique" indicates a measurement configuration in which emitters and receivers are placed on the same side of the skeletal site, along the bone axis. Whereas axially transmitted signals are composed of several contributions, only the first arriving signal was shown to be a robust indicator of bone status, because its velocity discriminates osteoporotic from healthy patients in clinical studies. Later arrivals may provide additional bone indicators enhancing diagnostic value, but the precise determination of their velocities is challenging. In this paper, we focus on the most energetic contribution and we applied a singular-value decomposition-based extraction method not yet employed in the domain of bone assessment with the aim of determining the velocity of this contribution. Signals acquired in vitro on human radii, together with academic models, were used to reveal the relationship between the velocity of the most energetic component and bone properties. The velocity of the most energetic component is highly correlated to cortical layer thickness in the in vitro database (R(2)= 0.6, P < 10(-5) compared with R(2)= 0.20, P < 10-(2) for the first arriving signal), consistent with a flexural type of wave on regular tubes or plates. Conclusions are in agreement with published papers based on other axial transmission and signal processing approaches.

Influence of a gradient of material properties on ultrasonic wave propagation in cortical bone: application to axial transmission.

The aim of this work is to evaluate the effect of a spatial gradient of material properties (mass density and stiffness coefficients) of cortical bone on its ultrasonic response obtained with an axial transmission device. Therefore, a two-dimensional finite element time-domain method is derived to model transient wave propagation in a three-layer medium composed of an inhomogeneous transverse isotropic solid layer sandwiched between two acoustic fluid layers and excited by an acoustic linear source located in one fluid layer, delivering broadband ultrasonic pulses. The model couples the acoustic propagation in both fluid media with the elastodynamic response of the solid layer. A constant spatial gradient of material properties is considered for two values of bone thicknesses corresponding to relatively thick and thin bone widths. For a thin bone (0.6 mm) compared to wavelength (around 4 mm at 1 MHz), the results are in good agreement with a S(0) Lamb wave assuming a homogeneous material with spatially averaged material properties. For a thick bone (4 mm), the results are in agreement with the propagation of a lateral wave and allow the derivation of an equivalent contributing depth in the case of a transverse isotropic inhomogeneous solid layer.

Determination of the random anisotropic elasticity layer using transient wave propagation in a fluid-solid multilayer: model and experiments.

The aim of this paper is to introduce a simplified model for an uncertain solid layer sandwiched between two acoustic fluid layers and using the ultrasonic characterization with an acoustic source placed in one fluid layer. Uncertainties are taken into account with a probabilistic model of the elasticity tensor. Its parameters are the mean value of the random tensor and a dispersion parameter that controls the statistical fluctuation level. The characterization of the solid layer given a database of actual measurements consists in the determination of the (i) elastic parameters of the mean elasticity model, (ii) the dispersion parameter, and (iii) mass density of the solid. This is performed with a numerical solver of wave propagation and for in vivo data collected previously. The model is representative of measurements of human bone properties with the so-called axial transmission technique. The capability of the model to predict the velocity of the first experimental arriving signal in the statistical sense is proved. The identified anisotropic elasticity tensor of cortical bone from actual data based on the simplified model is given.

Modeling the impact of soft tissue on axial transmission measurements of ultrasonic guided waves in human radius.

Recent in vitro and simulation studies have shown that guided waves measured at low ultrasound frequencies (f=200 kHz) can characterize both material properties and geometry of the cortical bone wall. In particular, a method for an accurate cortical thickness estimation from ultrasound velocity data has been presented. The clinical application remains, however, a challenge as the impact of a layer of soft tissue on top of the bone is not yet well established, and this layer is expected to affect the dispersion and relative intensities of guided modes. The present study is focused on the theoretical modeling of the impact of an overlying soft tissue. A semianalytical method and finite-difference time domain simulations were used. The models developed were shown to predict consistently real in vivo data on human radii. As a conclusion, clinical guided wave data are not consistent with in vitro data or related in vitro models, but use of an adequate in vivo model, such as the one introduced here, is necessary. A theoretical model that accounts for the impact of an overlying soft tissue could thus be used in clinical applications.

Singular value decomposition-based wave extraction in axial transmission: application to cortical bone ultrasonic characterization.

A singular value decomposition-based extraction algorithm is designed in order to recover the group velocity of an energetic contribution measured with an axial transmission device developed previously for cortical bone assessment. Its performance is evaluated on synthetic data mimicking in vivo signals, and it is compared with classical methods.

Ultrasonically determined thickness of long cortical bones: Three-dimensional simulations of in vitro experiments.

It was reported in a previous study that simulated guided wave axial transmission velocities on two-dimensional (2D) numerically reproduced geometry of long bones predicted moderately real in vitro ultrasound data on the same bone samples. It was also shown that fitting of ultrasound velocity with simple analytical model yielded a precise estimate (UTh) for true cortical bone thickness. This current study expands the 2D bone model into three dimensions (3D). To this end, wave velocities and UTh were determined from experiments and from time-domain finite-difference simulations of wave propagation, both performed on a collection of 10 human radii (29 measurement sites). A 3D numerical bone model was developed with tuneable fixed material properties and individualized geometry based on X-ray computed tomography reconstructions of real bones. Simulated UTh data were in good accordance (root-mean-square error was 0.40 mm; r(2)=0.79, p<0.001) with true cortical thickness, and hence the measured phase velocity can be well estimated by using a simple analytical inversion model also in 3D. Prediction of in vitro data was improved significantly (by 10% units) and the upgraded bone model thus explained most of the variability (up to 95% when sites were carefully matched) observed in in vitro ultrasound data.