Ultrasonic scattering from cancellous bone: a review

Statistics of the envelope of ultrasonic backscatter from human trabecular bone

The paper describes the investigations intended to compare the results of experimental measurements of backscattering properties of the trabecular bone with the results of computer simulations. Ultrasonic RF echoes were collected using two bone scanners operating at 0.58 and 1.3 MHz. The simulations of the backscattered RF echoes were performed using the scattering model of the trabecular bone that consisted of cylindrical and spherical elements uniformly distributed in water-like medium. For each measured or simulated RF backscatter the statistical properties of the signal envelope were determined. Experimental results suggest deviations of the backscattering properties from the Rayleigh distribution. The results of simulation suggest that deviation from Rayleigh distribution depends on the variation of trabeculae diameters and the number of thin trabeculae. Experimentally determined deviations corresponded well to the deviations calculated from simulated echoes assuming trabeculae thickness variation equaled to the earlier published histomorphometric study results.

Effect of the cortex on ultrasonic backscatter measurements of cancellous bone

Ultrasonic backscatter techniques offer a promising new approach for detecting changes in bone caused by osteoporosis. However, several challenges impede clinical implementation of backscatter techniques. This study examines how the dense outer surface of bone (the cortex) affects backscatter measurements of interior regions of porous (cancellous) bone tissue. Fifty-two specimens of bone were prepared from 13 human femoral heads so that the same region of cancellous bone could be ultrasonically interrogated through the cortex or along directions that avoided the cortex. Backscatter signals were analyzed over a frequency range of 0.8-3.0 MHz to determine two ultrasonic parameters: apparent integrated backscatter (AIB) and frequency slope of apparent backscatter (FSAB). The term 'apparent' means that the parameters are sensitive to the frequency-dependent effects of diffraction and attenuation. Significant (p < 0.001) changes in AIB and FSAB indicated that measurements through the cortex decreased the apparent backscattered power and increased the frequency dependence of the power. However, the cortex did not affect the correlation of AIB and FSAB with the x-ray bone mineral density of the specimens. This suggests that results from many previous in vitro backscatter studies of specimens of purely cancellous bone may be extrapolated with greater confidence to in vivo conditions.

Quantitative ultrasound measurement of the calcaneus in Southeast Asian children with thalassemia: comparison with dual-energy X-ray absorptiometry

OBJECTIVES

The purpose of this study was to test the hypothesis that quantitative ultrasound properties of the calcaneus in Southeast Asian children treated for thalassemia have different characteristics than those of their healthy counterparts and thereby can be used for assessing the risk of osteoporosis.

METHODS

Broadband ultrasound attenuation and the speed of sound were measured from groups of thalassemic and healthy children and compared with bone mineral density (BMD) estimated from dual-energy X-ray absorptiometry to determine intergroup and intragroup dependencies of the measurements and variations with differences in sex and anthropometric characteristics.

RESULTS

Broadband ultrasound attenuation and speed of sound measurements were found to be independent of sex but dependent on age in the thalassemic children. Consistently, broadband ultrasound attenuation had lower values and the speed of sound had higher values compared with those of the healthy children in each age group. Broadband ultrasound attenuation correlated well with the speed of sound and also with age, weight, and height, but the speed of sound did not show an association with these parameters. Broadband ultrasound attenuation correlated moderately with BMD in the lumbar spine and whole body, but the corresponding association was much weaker for the speed of sound. In the thalassemic children, both broadband ultrasound attenuation and BMD increased with age as they grew older but not fast enough compared with the healthy children, and the risk of osteoporosis was greater at older ages.

CONCLUSIONS

Calcaneal quantitative ultrasound may be used as a diagnostic screening tool for assessing the bone status in thalassemic Southeast Asian children and for deciding whether further dual-energy X-ray absorptiometry is needed, particularly in those who are at a greater risk for osteoporosis as identified by low body weight and height.

Multiridge-based analysis for separating individual modes from multimodal guided wave signals in long bones

Quantitative ultrasound has great potential for assessing human bone quality. Considered as an elastic waveguide, long bone supports propagation of several guided modes, most of which carry useful information, individually, on different aspects of long bone properties. Therefore, precise knowledge of the behavior of each mode, such as velocity, attenuation, and amplitude, is important for bone quality assessment. However, because of the complicated characteristics of the guided waves, including dispersion and mode conversion, the measured signal often contains multiple wave modes, which yields the problem of mode separation. In this paper, some novel signal processing approaches were introduced to solve this problem. First, a crazy-climber algorithm was used to separate time-frequency ridges of individual modes from time-frequency representations (TFR) of multimodal signals. Next, corresponding time domain signals representing individual modes were reconstructed from the TFR ridges. It was found that the separated TFR ridges were in agreement with the theoretical dispersion, and the reconstructed signals were highly representative of the individual guided modes as well. The validations of this study were analyzed by simulated multimodal signals, with or without noise, and by in vitro experiments. Results of this study suggest that the ridge detection and individual reconstruction method are suitable for separating individual modes from multimodal signals. Such a method can improve the analysis of skeletal guided wave signals by providing accurate assessment of mode-specific ultrasonic parameters, such as group velocity, and indicate different bone quality properties.

Density imaging using a multiple-frequency DBIM approach

Current inverse scattering methods for quantitative density imaging have limitations that keep them from practical experimental implementations. In this work, an improved approach, termed the multiple-frequency distorted Born iterative method (MF-DBIM) algorithm, was developed for imaging density variations. The MF-DBIM approach consists of inverting the wave equation by solving for a single function that depends on both sound speed and density variations at multiple frequencies. Density information was isolated by using a linear combination of the reconstructed single-frequency profiles. Reconstructions of targets using MF-DBIM from simulated data were compared with reconstructions using methods currently available in the literature, i.e., the dual-frequency DBIM (DF-DBIM) and T-matrix approaches. Useful density reconstructions, i.e., root mean square errors (RMSEs) less than 30%, were obtained with MF-DBIM even with 2% Gaussian noise in the simulated data and using frequency ranges spanning less than an order of magnitude. Therefore, the MFDBIM approach outperformed both the DF-DBIM method (which has problems converging with noise even an order of magnitude smaller) and the T-matrix method (which requires a ka factor close to unity to achieve convergence). However, the convergence of all the density imaging algorithms was compromised when imaging targets with object functions exhibiting high spatial frequency content.

Acoustic backscattering enhancements resulting from the interaction of an obliquely incident plane wave with an infinite cylinder

BACKGROUND AND OBJECTIVE

The analysis of the acoustic backscattering enhancements from tilted cylinders is of particular importance in determining some of the (visco)elastic properties of the cylinder, and/or its surrounding fluid in ultrasonic non-destructive evaluation (NDE) and imaging (NDI) applications. Previous related investigations on an aluminum cylinder limited to incidence angles varying from 0 degrees to 40 degrees , revealed the existence of an anomalous "pseudo-Rayleigh" mode (above the critical Rayleigh angle) identified as the rigid-body translational dipole (n=1) mode. The objective here is to provide a complete investigation on the backscattering enhancements for incidence angles larger than 40 degrees for various elastic and viscoelastic cylinder materials.

METHOD

Using the partial-wave series solution for the linear scattering by an infinite circular cylinder, the acoustic backscattering from isotropic elastic and viscoelastic (polymer-type) cylinders excited by an obliquely incident plane acoustic wave is investigated. Total and resonance backscattering form functions are calculated for several elastic and viscoelastic cylinder materials immersed in water versus the angle of incidence 0 degrees alpha < 90 degrees . The "pure" resonance peaks are isolated by subtracting a rigid background from the total form function, so the associated resonance modes are properly identified.

RESULTS AND CONCLUSION

The plots of the partial-wave series reveal acoustic backscattering enhancements (not shown in previous investigations) generally occurring at ka less, similar 0.1 at a critical angle alpha(c) bounded by the longitudinal and shear waves coupling angles theta(L)=sin(-1)(c/c(L)) and theta(S)=sin(-1)(c/c(S)) such that theta(L) < alpha(c) < theta(S) (where c(L) and c(S) are the phase velocities of the longitudinal and shear waves inside the elastic cylinder, and c is the speed of sound in the surrounding medium). It is shown here that the backscattering enhancements with a critical angle theta(L) < alpha(c) < theta(S) result from the excitation of the monopole (n=0) resonance mode. Moreover, additional acoustic backscattering enhancements still occur in the range 1 less, similar ka less similar 6 even though the angle of tilt is greater than the Rayleigh wave coupling angle theta(R)=sin(-1)(c/c(R)) (where c(R) is the Rayleigh wave velocity in an elastic half-space). The resonance scattering theory shows that such additional enhancements are associated with the excitation of a dipole (n=1) resonance mode which may result from the interference of meridional and/or helical waves propagating along the cylinder's surface. It is therefore essential to consider tilt angles ranging from normal to end-on incidence for a complete analysis of the backscattering by elastic and viscoelastic cylinders.

A-Mode ultrasound guidance for pedicle screw advancement in ovine vertebral bodies

BACKGROUND CONTEXT

In pedicle screw fixation surgery, rigid instruments are inserted into a vertebral body. When the instruments are misdirected within the pedicle or advanced too far beyond it, perforations of the inner or outer cortex can cause damage to the spinal nerve roots and spinal cord. These complications can occur despite the use of imaging modalities, such as radiographs, fluoroscopy, and computerized axial tomography (CAT) scans. A-Mode ultrasound (US), a nonionizing modality, merits study for its possible use in such a type of surgery.

PURPOSE

The purpose of the study was to determine the utility of A-mode US during pedicle screw placement, to characterize the approach to the marrow-cortex interface, and to obtain the signature profiles of cortex perforations.

STUDY DESIGN

A-Mode data were generated on insertion of a forward-viewing transducer (FVT) and a side-viewing transducer (SVT) to successively greater drilled depths along the insertion pathway. A-Mode broadband US backscatter (BUB) pedicle screw emulation experiments were conducted with transducers inserted into drilled sheep vertebral bodies. BUB amplitude patterns were observed and analyzed. Descriptive statistics were used.

METHODS

In vitro acoustic experiments on vertebral bodies in a water bath were performed with two 1-MHz unfocused transducers to measure sound speed, broadband US attenuation, and backscatter coefficients. Micro-CAT scan three-dimensional (3-D) images of 10 disarticulated vertebral bodies were obtained pre- and postdrilling done in 5-mm depth increments with a flat-bottom drill. BUB patterns were noted of transducers inserted through rostral outer cortex, through the pedicle, and advanced to the ventral marrow-cortex interface. 2.5-MHz FVT and SVT were co-advanced in successive 5-mm increments along the insertion pathway, with BUBs measured at each point and the echoes composited into a single figure. Deliberate perforations of ventral cortex were made.

RESULTS

Evident patterns or measures indicating the proximity of the ventral marrow-cortex interface were: 1) marrow BUB values increasing in amplitude over three distal peaks in most FVT cases (7 out of 10) and SVT cases (9 out of 10); 2) BUB ratio of marrow-cortex interface to the smallest marrow value greater than 2, in all FVT cases (10 out of 10) with FVT mean of 4.00+/-1.82 (2.25-8.33); and 3) a ratio of distal BUB value to starting cortex BUB in the 0. 82 to 1.62 range (mean, 0.98+/-0.30) in 80% of FVT cases. Ventral FVT perforations resulted in a major drop in the BUB value.

CONCLUSIONS

The increase in the BUB amplitudes in the distal insertion pathway suggests that, at least with a 2.5-MHz transducer, an approximate 1.5-cm US window exists in most cases, by which close approach of the ventral marrow-cortex interface could be anticipated. Other ratios may serve as stop criteria to prevent further drilling. A precipitous drop in BUB amplitude may be an indication of a cortex perforation.

Numerical analysis of uncertainties in dual frequency bone ultrasound technique

Quantitative ultrasound (QUS) measurements are used in the diagnostics of osteoporosis. However, the variation in the thickness and composition of the overlying soft tissue causes significant errors to the bone QUS parameters and diminishes the reliability of the technique in vivo. Recently, the dual frequency ultrasound (DFUS) technique was introduced to minimize the errors related to soft tissue effects. In this study, the significance of soft tissue induced errors and their elimination with the DFUS technique were simulated using the finite difference time domain technique. Furthermore, we investigated the potential of the DFUS corrected integrated reflection coefficient (IRC) of bone to detect changes in the cortical bone density. The effects of alterations in the thickness of fat and lean tissue layers and the inclination between the soft-tissues and between the soft tissue-bone layers were simulated. When the angle of the soft tissue interface was zero, i.e., perpendicular to the incident ultrasound beam, the DFUS-calculated soft tissue composition correlated highly linearly with the true soft tissue composition. The inclination between the soft tissue-bone layers was found to be critical. Even a 2-degree inclination between the soft tissue and the bone surface induced an almost 18% relative error in the corrected IRC. Increasing the inclination between the soft tissue layers increased the error in the DFUS-calculated lean and fat tissue thickness. This error was especially significant at inclination angles greater than 20 degrees. The significant soft tissue induced errors in IRC values (>300 %) could be effectively minimized (<10%) by means of the DFUS correction. Importantly, after the DFUS correction, physiologically relevant variation in the cortical bone density could be detected (p<0.05).

Influence of the filling fluid on frequency-dependent velocity and attenuation in cancellous bones between 0.35 and 2.5 MHz

The paper is focused on experiments on human cancellous bones filled with different fluids with the goal of evaluating their contribution to velocity dispersion, absorption, and scattering mechanisms. The specimens were measured first filled with marrow and subsequently, after marrow removal, with water and alcohol. No significant influence of the fluids was evidenced on the attenuation coefficient. Given the absence of impact of viscosity of the saturating fluid, the authors hypothesized that the source of attenuation is associated with viscoelastic absorption in the solid trabeculae and with scattering. Alteration of scattering obtained by changing the acoustic impedance mismatch between the fluid (alcohol vs water) and the trabeculae was reflected neither in the attenuation nor in its slope. This led the authors to suggest that longitudinal-to-shear scattering together with absorption in the solid phase are candidates as main sources for the attenuation. The differences in velocity values indicate that the elastic properties of the fluid are main determinants of the phase velocity. This finding is particularly significant in the context of /in vivo/ measurements, because it demonstrates that the subject-dependent properties of marrow may partly explain the inter-subject variability of speed of sound values.

Relationship between ultrasonic parameters and apparent trabecular bone elastic modulus: a numerical approach

The physical principles underlying quantitative ultrasound (QUS) measurements in trabecular bone are not fully understood. The translation of QUS results into bone strength remains elusive. However, ultrasound being mechanical waves, it is likely to assess apparent bone elasticity. The aim of this study is to derive the sensitivity of QUS parameters to variations of apparent bone elasticity, a surrogate for strength. The geometry of 34 human trabecular bone samples cut in the great trochanter was reconstructed using 3-D synchrotron micro-computed tomography. Finite-difference time-domain simulations coupled to 3-D micro-structural models were performed in the three perpendicular directions for each sample and each direction. A voxel-based micro-finite element linear analysis was employed to compute the apparent Young's modulus (E) of each sample for each direction. For the antero-posterior direction, the predictive power of speed of sound and normalized broadband ultrasonic attenuation to assess E was equal to 0.9 and 0.87, respectively, which is better than what is obtained using bone density alone or coupled with micro-architectural parameters and of the same order of what can be achieved with the fabric tensor approach. When the direction of testing is parallel to the main trabecular orientation, the predictive power of QUS parameters decreases and the fabric tensor approach always gives the best results. This decrease can be explained by the presence of two longitudinal wave modes. Our results, which were obtained using two distinct simulation tools applied on the same set of samples, highlight the potential of QUS techniques to assess bone strength.

Semi-empirical bone model for determination of trabecular structure properties from backscattered ultrasound

A novel semi-empirical scattering model of trabecular bone facilitating its characterization and allowing optimization of the interrogating pulse-echo transducer performance was developed. The model accounts for spatial density distribution of the trabeculae and includes measurement conditions such as pressure-time waveform of the probing ultrasound wave, the emitted field structure, and the transfer function and limited bandwidth of the acoustic source operating in pulse-echo mode. These measurement conditions are of importance as they modify the scattered echoes, which in turn are linked to the micro-architecture of the bone. The bone was modeled by a random distribution of long and thin cylindrical scatterers having randomly varying diameters and mechanical properties, and oriented perpendicularly to the ultrasound beam axis. To mimic clinically encountered conditions the relevant empirical data obtained at 1 MHz were input to the model. The data included pulse-echo source pressure field distribution in the focal zone and the above mentioned transfer function. With these data the model allowed frequency dependent backscattering coefficient of the simulated bone structure and its statistical properties to be determined. The results obtained indicated that the computer simulation is of particular relevance in studying scattering properties of the cancellous bone and holds promise as a tool to determine the relationship between the physical dimensions and shape of the scatterers and for monitoring of osteoporosis. The results of simulations also indicated that the new bone model proposed is well suited to mimic clinically relevant conditions. In contrast to the existing bone models, which usually assume scatterers to be randomly distributed as infinitely long identical cylinders with a cross-section much smaller than the probing ultrasound wave, the new model includes two populations of scatterers having different physical dimensions and also allows the mechanical properties of the scatterers to be varied.

Analysis of frequency dependence of ultrasonic backscatter coefficient in cancellous bone

The ultrasonic scattering mechanism in cancellous bone is investigated theoretically and a model describing the frequency dependence of ultrasonic scattering from cancellous bone is presented. The ultrasonic backscatter coefficient (BSC) of bovine tibiae, human calcanei in vitro and in vivo, were measured and discussed. The data of BSC were also fitted by polynomial. The results demonstrate that BSC is a nonlinear function of frequency and increases with frequency. A good agreement was obtained between BSC values from theory and experiment. Also, the high correlation coefficient between BSC and bone mineral density was obtained, r=0.85+/-0.07 (mean+/-SD) (n=15, p<0.001). Based on the values of BSC, the status of cancellous bone and the degree of osteoporotic fracture risk may be assessed.

Comparison of the Faran Cylinder Model and the Weak Scattering Model for predicting the frequency dependence of backscatter from human cancellous femur in vitro

This letter presents the first side-by-side comparison of the Faran Cylinder Model and the Weak Scattering Model for predicting backscatter from human femur. Both models are applied to the same dataset of frequency-dependent backscatter coefficients from 26 human femur cancellous bone samples in vitro. The Faran Cylinder Model predicts a slightly slower rate of increase of backscatter with frequency than the Weak Scattering Model, but both models are in reasonable agreement with the data and with each other, given the uncertainty in the measurements.

A new quality of bone ultrasound research

Quantitative ultrasound (QUS) methods have strong power to predict osteoporotic fractures, but they are also very relevant for the assessment of bone quality. A representative sample of recent studies addressing these topics can be found in this special issue. Further pursuit of these methods will establish micro-QUS imaging methods as tools for measuring specific aspects of bone quality. Once this is achieved, we will be able to link such data to the clinical QUS methods used in vivo to determine which aspects of bone quality cause QUS to be a predictor of fracture risk that is independent of bone mineral density (BMD). Potentially this could lead to the development of a new generation of QUS devices for improved and expanded clinical assessment. Good quality of basic science work will thus lead to good quality of clinical patient examinations on the basis of a more detailed assessment of bone quality.

Instrumentation for in vivo ultrasonic characterization of bone strength

Although it has been more than 20 years since the first recorded use of a quantitative ultrasound (QUS) technology to predict bone fragility, the field has not yet reached its maturity. QUS has the potential to predict fracture risk in several clinical circumstances and has the advantages of being nonionizing, inexpensive, portable, highly acceptable to patients, and repeatable. However, the wide dissemination of QUS in clinical practice is still limited and suffering from the absence of clinical consensus on how to integrate QUS technologies in bone densitometry armamentarium. Several critical issues need to be addressed to develop the role of QUS within rheumatology. These include issues of technologies adapted to measure the central skeleton, data acquisition, and signal processing procedures to reveal bone properties beyond bone mineral quantity and elucidation of the complex interaction between ultrasound and bone structure. This article reviews the state-of-the art in technological developments applied to assess bone strength in vivo. We describe generic measurement and signal processing methods implemented in clinical ultrasound devices, the devices and their practical use, and performance measures. The article also points out the present limitations, especially those related to the absence of standardization, and the lack of comprehensive theoretical models. We conclude with suggestions of future lines and trends in technology challenges and research areas such as new acquisition modes, advanced signal processing techniques, and modelization.