Influence of microarchitecture alterations on ultrasonic backscattering in an experimental simulation of bovine cancellous bone aging

An experimental model which can simulate physical changes that occur during aging was developed in order to evaluate the effects of change of mineral content and microstructure on ultrasonic properties of bovine cancellous bone. Timed immersion in hydrochloric acid was used to selectively alter the mineral content. Scanning electron microscopy and histological staining of the acid-treated trabeculae demonstrated a heterogeneous structure consisting of a mineralized core and a demineralized layer. The presence of organic matrix contributed very little to normalized broadband ultrasound attenuation (nBUA) and speed of sound. All three ultrasonic parameters, speed of sound, nBUA and backscatter coefficient, were sensitive to changes in apparent density of bovine cancellous bone. A two-component model utilizing a combination of two autocorrelation functions (a densely populated model and a spherical distribution) was used to approximate the backscatter coefficient. The predicted attenuation due to scattering constituted a significant part of the measured total attenuation (due to both scattering and absorption mechanisms) for bovine cancellous bone. Linear regression, performed between trabecular thickness values and estimated from the model correlation lengths, showed significant linear correlation, with R(2)=0.81 before and R(2)=0.80 after demineralization. The accuracy of estimation was found to increase with trabecular thickness.     

Influence of the precision of spectral backscatter measurements on the estimation of scatterers size in cancellous bone

The goal of this study is to propose a model for the ultrasonic frequency-dependent backscatter coefficient in femoral cancellous bone. This model has been developed with success to predict backscatter in human calcaneal bone [Jenson, Ultr. Med. Biol. 2003]. A weak scattering model is used and the backscatter coefficient is expressed in terms of a Gaussian autocorrelation function of the medium. The backscatter coefficient is computed and comparison is made with experimental data for 37 specimens and for frequency ranging from 0.4 to 1.2 MHz. An excellent agreement between experimental data and predictions is found for both the magnitude and the frequency-dependence of the backscatter coefficient. Then, a nonlinear regression is performed for each specimen, and the mean trabecular thickness is estimated. Experimental data and theoretical predictions are averaged over the 37 specimens. We also find a close agreement between theoretical predictions obtained using the Gaussian autocorrelation function (scatterer size=134+/-15 microm) and the mean trabecular thickness (Tb.Th=132+/-12 microm) derived from the analysis of bone 3-D micro-architecture using high-resolution micro-tomography. However, the correlation between individual experimental and estimated Tb.Th values is moderate (R(2)=0.44). The performance of the estimator are limited mainly by two factors: interference noise due to random positioning of the scatterers and attenuation. We show that the fundamental limitation of our estimator due to the speckle noise is around 5 microm for trabecular thickness estimation. This limitation is lower than the observed biological variability which is around 30 microm and should not be a limiting factor for individual prediction. A second limitation is the tremendous attenuation encountered in highly scattering media such as cancellous bone, which results in highly damped backscatter signals. The compensation for attenuation is difficult to perform, and it may be a critical point that limits the precision of the estimator.     

Prediction of backscatter coefficient in trabecular bones using a numerical model of three-dimensional microstructure

A model of ultrasonic backscattering for cancellous bone saturated by water is proposed. This model assumes that scattering is caused by the solid trabeculae and describes the cancellous bone as a weak scattering medium. The backscatter coefficient is related to the spatial Fourier transform of bone microarchitecture and to the density and compressibility fluctuations between the solid trabeculae and the saturating fluid. The computations of the model make use of three-dimensional numerical images of bone microarchitecture, obtained by tomographic reconstructions with a 10 microm spatial resolution. With this model, the predictions of the frequency dependence and of the magnitude of the backscatter coefficient are reasonably accurate. The theoretical predictions are compared to experimental data obtained on 19 specimens. An accuracy error of approximately 1 dB was found (difference between the averaged experimental values and theoretical predictions). One limit of the model may come from inaccurate values of trabecular bone characteristics needed for the computations (density and longitudinal velocity), which are yet to be precisely determined for human trabecular bone. However, the model is only slightly sensitive to variations of bone material properties. It was found that an accuracy error of 2.2 dB at maximum resulted from inaccurate a priori values of bone material properties. A computation of the elastic mean free path in the medium suggests that multiple scattering plays a minor role in the working frequency bandwidth (0.4-1.2 MHz). It follows from these results that a weak scattering medium model may be appropriate to describe scattering from trabecular bone.     

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.     

Study on the mean trabecular bone spacing based on fundamental frequency estimation method

Ultrasonic backscatter signals from the cancellous bone can be used to diagnose osteoporosis effectively due to its ability to provide the information of bone microstructure. Mean trabecular bone spacing(MTBS)is one of the important parameters for characterization of bone microstructure.This paper proposed a MTBS estimating method based on the fundamental frequency estimation,which was applied to backscatter signals from simulations, and in vitro bovine trabeculae.The estimated MTBS were compared with those of simplified inverse filter tracking(SIFT)algorithm and autoregressive(AR)cepstrum method.The results demonstrated that the proposed method is very robust for the MTBS estimation with more precise estimates and smaller estimated variance in the presence of a small signal-to-noise ratio (SNR),and a large scattering strength ratio of diffuse scatterers to regular ones.     

Modeling and analysis of multiple scattering of acoustic waves in complex media: application to the trabecular bone

The integral equations that describe scattering in the media with step-rise changing parameters have been numerically solved for the trabecular bone model. The model consists of several hundred discrete randomly distributed elements. The spectral distribution of scattering coefficients in subsequent orders of scattering has been presented. Calculations were carried on for the ultrasonic frequency ranging from 0.5 to 3 MHz. Evaluation of the contribution of the first, second, and higher scattering orders to total scattering of the ultrasounds in trabecular bone was done. Contrary to the approaches that use the μCT images of trabecular structure to modeling of the ultrasonic wave propagation condition, the 3D numerical model consisting of cylindrical elements mimicking the spatial matrix of trabeculae, was applied. The scattering, due to interconnections between thick trabeculae, usually neglected in trabecular bone models, has been included in calculations when the structure backscatter was evaluated. Influence of the absorption in subsequent orders of scattering is also addressed. Results show that up to 1.5 MHz, the influence of higher scattering orders on the total scattered field characteristic can be neglected while for the higher frequencies, the relatively high amplitude interference peaks in higher scattering orders clearly occur.     

Frequency dependence of ultrasonic backscatter from human trabecular bone: theory and experiment

A model describing the frequency dependence of backscatter coefficient from trabecular bone is presented. Scattering is assumed to originate from the surfaces of trabeculae, which are modeled as long thin cylinders with radii small compared with the ultrasonic wavelength. Experimental ultrasonic measurements at 500 kHz, 1 MHz, and 2.25 MHz from a wire target and from trabecular bone samples from human calcaneus in vitro are reported. In both cases, measurements are in good agreement with theory. For mediolateral insonification of calcaneus at low frequencies, including the typical diagnostic range (near 500 kHz), backscatter coefficient is proportional to frequency cubed. At higher frequencies, the frequency response flattens out. The data also suggest that at diagnostic frequencies, multiple scattering effects on the average are relatively small for the samples investigated. Finally, at diagnostic frequencies, the data suggest that absorption is likely to be a larger component of attenuation than scattering.     

Effect of trabecular bone material properties on ultrasonic backscattering signals

In this study, ultrasonic backscattering signals in cancellous bones were obtained by finite difference time domain （FDTD） simulations, and the effect of trabecular material properties on these signals was analyzed. The backscatter coefficient （BSC） and integrated backscatter coefficient （IBC） were numerically investigated for varying trabecular bone material properties, including density, Lame coefficients, viscosities, and resistance coefficients. The results show that the BSC is a complex function of trabecular bone density, and the IBC increases as density increases. The BSC and IBC increase with the first and second Lame coefficients. While not very sensitive to the second viscosity of the trabeculae, the BSC and IBC decrease as the first viscosity and resistance coefficients increase. The results demonstrate that, in addition to bone mineral density （BMD） and microarchitecture, trabecular material properties significantly influence ultrasonic backseattering signals in cancellous bones. This research furthers the understanding of ultrasonic backscattering in cancellous bones and the characterization of cancellous bone status.     

Fundamental precision limitations for measurements of frequency dependence of backscatter: applications in tissue-mimicking phantoms and trabecular bone.

Various models for ultrasonic scattering from trabecular bone have been proposed. They may be evaluated to a certain extent by comparison with experimental measurements. In order to appreciate limitations of these comparisons, it is important to understand measurement precision. In this article, an approach proposed by Lizzi and co-workers is adapted to model precision of estimates of frequency-dependent backscatter for scattering targets (such as trabecular bone) that contain many scatterers per resolution cell. This approach predicts uncertainties in backscatter due to the random nature of the interference of echoes from individual scatterers as they are summed at the receiver. The model is validated in experiments on a soft-tissue-mimicking phantom and on 24 human calcaneus samples interrogated in vitro. It is found that while random interference effects only partially explain measured variations in the magnitude of backscatter, they are virtually entirely responsible for observed variations in the frequency dependence (exponent of a power law fit) of backscatter.     

Compensation for receiver bandpass effects on ultrasonic backscatter power spectra using a random medium reference

A linear model of an ultrasonic pulse-echo system is used to express the measured power spectrum as the product of a scattering medium power spectrum and a transfer function accounting for system effects. Transfer functions are experimentally determined for multiple ranges using a random medium reference. Measured power spectra normalized by these functions are shown to be in close agreement with theoretical power spectra both in shape and absolute magnitude. The results indicate that the model allows scattering media to be distinguished when the media backscatter characteristics differ in the bandwidth of the measurement system.     

The dependencies of phase velocity and dispersion on trabecular thickness and spacing in trabecular bone-mimicking phantoms

Frequency-dependent phase velocity was measured in trabecular-bone-mimicking phantoms consisting of two-dimensional arrays of parallel nylon wires (simulating trabeculae) with thicknesses ranging from 152 to 305 microm and spacings ranging from 700 to 1000 microm. Phase velocity varied approximately linearly with frequency over the range from 400 to 750 kHz. Dispersion was characterized by the slope of a linear least-squares regression fit to phase velocity versus frequency data. The increase in phase velocity (compared with that in water) at 500 kHz was approximately proportional to the (1) square of trabecular thickness, (2) inverse square of trabecular spacing, and (3) volume fraction occupied by nylon wires. The first derivative of phase velocity with respect to frequency was negative and exhibited nonlinear, monotonically decreasing dependencies on trabecular thickness and volume fraction. The dependencies of phase velocity and its first derivative on volume fraction in the phantoms were consistent with those reported in trabecular bone.     

Anisotropy of ultrasonic backscatter and attenuation from human calcaneus: implications for relative roles of absorption and scattering in determining attenuation

Although bone sonometry has been demonstrated to be useful in the diagnosis of osteoporosis, much remains to be learned about the processes governing the interactions between ultrasound and bone. In order to investigate these processes, ultrasonic attenuation and backscatter in two orientations were measured in 43 human calcaneal specimens in vitro at 500 kHz. In the mediolateral (ML) orientation, the ultrasound propagation direction is approximately perpendicular to the trabecular axes. In the anteroposterior (AP) orientation, a wide range of angles between the ultrasound propagation direction and trabecular axes is encountered. Average attenuation slope was 18% greater while average backscatter coefficient was 50% lower in the AP orientation compared with the ML orientation. Backscatter coefficient in both orientations approximately conformed to a cubic dependence on frequency, consistent with a previously reported model. These results support the idea that absorption is a greater component of attenuation than scattering in human calcaneal trabecular bone.     

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.     

Helmholtz-pair transmit coil with integrated receive array for high-resolution MRI of trabecular bone in the distal tibia at 7T

A Helmholtz-pair local transmit RF coil with an integrated four-element receive array RF coil and foot immobilization platform was designed and constructed for imaging the distal tibia in a whole-body 7T MRI scanner. Simulations and measurements of the B(1) field distribution of the transmit coil are described, along with SAR considerations for operation at 7T. Results of imaging the trabecular bone of three volunteers at 1.5T, 3T and 7T are presented, using identical 1.5T and 3T versions of the 7T four-element receive array. The spatially registered images reveal improved visibility for individual trabeculae and show average gains in SNR of 2.8× and 4.9× for imaging at 7T compared to 3T and 1.5T, respectively. The results thus display an approximately linear dependence of SNR with field strength and enable the practical utility of 7T scanners for micro-MRI of trabecular bone.     

Frequency-dependent attenuation and backscatter coefficients in bovine trabecular bone from 0.2 to 1.2 MHz

The frequency-dependent attenuation and backscatter coefficients were measured in 25 bovine femoral trabecular bone samples from 0.2 to 1.2 MHz. When the average attenuation coefficient was fitted to a nonlinear power law α(f)=α(0)+α(1)f(n), the exponent n was found to be 1.65. In contrast, the average backscatter coefficient was fitted to a power law η(f)=η(1)f(n) and the exponent n was measured as 3.25. The apparent bone density was significantly correlated with the parameter α(1) (0.2-0.7 MHz: r = 0.852, 0.6-1.2 MHz: r = 0.832) as well as the backscatter coefficient (0.5 MHz: r = 0.751, 1.0 MHz: r = 0.808).     

Theoretical and experimental study of the ultrasonic attenuation in bovine cancellous bone

In this study a theoretical approach for the estimation of ultrasonic attenuation is proposed. The approach combines two models which take into account both absorption and scattering. Attenuation due to absorption is studied by using the Biot’s analytical model whereas that due to scattering is described by means of a generalized weak scattering model which is formulated for binary mixtures. The scattering model takes account of the density fluctuation of the porous medium in addition to the propagation velocity fluctuation. For the calculation of the attenuation coefficient due to absorption, experimental values have been used to link size of pores to porosity. The theoretical results have been compared with experimental data obtained on bovine cancellous bone samples filled with water. Using an immersion acoustic transmission method, the ultrasonic attenuation has been measured at a frequency range between 0.1 and 1.0 MHz for 12 bovine cancellous bone samples with a porosity range between 40% and 70%. The prediction of attenuation with this model appears to correspond more closely to its experimentally observed behavior. This study indicates that scattering is the predominant mechanism which is responsible for attenuation in trabecular bone. Furthermore, it shows that the density fluctuations contribute significantly to the phenomenon of attenuation and cannot thus be neglected.     

骨小梁材料特性对超声背散射信号的影响

基于时域有限差分法(FDTD)建立了松质骨的超声背散射仿真系统,研究了骨小梁材料特性对超声背散射信号的影响。首次得到松质骨中的超声背散射系数(BSC)和积分背散射系数(IBC)随骨小梁材料参数(密度、拉梅常数、黏度系数及声阻抗系数)的变化关系。研究结果表明,IBC随骨小梁密度的增加而增加;BSC和IBC随拉梅常数的增加而增加、随第一黏度系数的增加而近似线性地减小,第二黏度的变化对背散射信号的影响很小;背散射参数随阻抗系数的增加而减小。说明松质骨中的超声背散射特性不仅受骨矿密度(BMD)和骨微结构的影响,还与骨小梁的材料参数密切相关。研究结果有利于理解松质骨中超声的背散射特性,对松质骨骨质状况的评价有一定帮助。      

Vertebral cancellous bone turn-over: microcallus and bridges in backscatter electron microscopy

Backscatter electron microscopy (BSE) is a powerful technique for investigating cancellous bone structure. Its main function is to offer information regarding the degree of mineralization of the tissue within individual trabeculae.

To illustrate the qualitative information that can be drawn from BSE imaging technique, we present a study on human vertebral cancellous bone. This tissue is continuously remodeled through osteoclastic resorption and osteoblastic new bone apposition. It is thought that osteoclastic resorption pits are especially deleterious for vertebral bone architecture since they often perforate the thin trabeculae; the osteoblasts being unable to repair the gap. In addition, excessive stress may also disrupt the architecture in case of trabecular fracture or damage accumulation.

Waves of new bone formation were easy to identify in BSE. Often these waves were connecting both edges of a perforation and called bridges. Additionally, we present a few images of microcallus formations. A microcallus is described as a small mass of woven bone that generally repairs a trabecula. The microstructural aspects of different microcalluses are presented and discussed. Both bridges and microcallus should be considered as examples of the repair porcess since they obviously preserve the connectivity of the trabeculae. However, bridges were much more frequent than microcallus (396 vs 15). Both mechanisms probably illustrate the normal response to different local stimuli.     

Measures of complexity for 3D image analysis of trabecular bone

Based on fractal properties and spatial auto-correlation, the measures of complexity lacunarity, Moran's I and Geary's C index are defined for 3D image analysis. Their abilities to investigate translational invariance, characteristic length scales, spatial correlation and shapes of 3D micro-structures are demonstrated on proto-typical examples. Finally, using these measures of complexity, 3D images of trabecular bone are analysed. The main findings are that the complexity of the trabecular structure decreases and the plate-like shapes of the trabeculae change to mainly rod-like shapes during bone loss. These results and the proposed measures could have a great impact for medicine and for space exploration.     

In vitro estimation of fast and slow wave parameters of thin trabecular bone using space-alternating generalized expectation-maximization algorithm

In testing cancellous bone using ultrasound, two types of longitudinal Biot’s waves are observed in the received signal. These are known as fast and slow waves and their appearance depend on the alignment of bone trabeculae in the propagation path and the thickness of the specimen under test (SUT). They can be used as an effective tool for the diagnosis of osteoporosis because wave propagation behavior depends on the bone structure. However, the identification of these waves in the received signal can be difficult to achieve.In this study, ultrasonic wave propagation in a 4 mm thick bovine cancellous bone in the direction parallel to the trabecular alignment is considered. The observed Biot’s fast and slow longitudinal waves are superimposed; which makes it difficult to extract any information from the received signal. These two waves can be separated using the space alternating generalized expectation maximization (SAGE) algorithm. The latter has been used mainly in speech processing.In this new approach, parameters such as, arrival time, center frequency, bandwidth, amplitude, phase and velocity of each wave are estimated. The B-Scan images and its associated A-scans obtained through simulations using Biot’s finite-difference time-domain (FDTD) method are validated experimentally using a thin bone sample obtained from the femoral-head of a 30 months old bovine.