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。      

空间频率域超声背散射参量用于骨质状况的评价*

在超声背散射骨质评价中,不同测量感兴趣区域(ROI)的超声背散射信号会有波动,致使诊断准确度降低。该文目的是研究超声背散射信号随测量区域的变化规律。采用空间扫描方法离体测量了35块骨样本,将超声背散射参数从空间域变换到空间频率域。结果表明,超声背散射参数的主要空间频率成分集中于低频部分;空间频率域超声背散射参量最大值(MASF)与骨矿密度等参数具有中高度显著相关性(R2=0.45~0.83,p0.001);空间频率域超声背散射参量衰减系数(AC)也与松质骨密度及结构特征有显著相关性(R2=0.41~0.72,p0.001)。研究表明空间频率域变换方法有助于明确超声背散射信号随测量ROI的变化规律,空间频率域的超声背散射相关新参量评价松质骨状况具有可行性。     

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.     

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.     

超声背散射法评价松质骨状况的研究

超声背散射法评价松质骨状况及诊断骨质疏松症是近年来医学超声领域内的研究热点之一,现已取得了显著的进展。本文将介绍近年来超声背散射法及其参量评价松质骨状况的研究进展,并分析超声背散射相关参量频谱质心偏移量（SCS）和平均骨小梁间距（TbSp）与骨矿密度（BMD）的相关性。研究结果表明,超声背散射参量与BMD有较高的相关性。最后提出了将来研究中需要努力的方向。     

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.     

Amplitude modulation excitation for cancellous bone evaluation using a portable ultrasonic backscatter instrumentation

The ultrasonic backscatter (UB) has the advantage of non-invasively obtaining bone density and structure, expected to be an assessment tool for early diagnosis osteoporosis. All former UB measurements were based on exciting a short single-pulse and analyzing the ultrasonic signals backscattered in bone. This study aims to examine amplitude modulation (AM) ultrasonic excitation with UB measurements for predicting bone characteristics. The AM multiple lengths excitation and backscatter measurement (AM-UB) functions were integrated into a portable ultrasonic instrument for bone characterization. The apparent integrated backscatter coefficient in the AM excitation (AIB_AM) was evaluated on the AM-UB instrumentation. The correlation coefficients of the AIB_AM estimating volume fraction (BV/TV), structure model index (SMI), and bone mineral density (BMD) were then analyzed. Significant correlations (|R| = 0.82-0.93, p < 0.05) were observed between the AIB_AM, BV/TV, SMI, and BMD. By growing the AM excitation length, the AIB_AM values exhibit more stability both in 1.0-MHz and 3.5-MHz measurements. The recommendations in AM-UB measurement were that the avoided length (T1) should be lower than AM excitation length, and the analysis length (T2) should be enough long but not more than AM excitation length. The authors conducted an AM-UB measurement for cancellous bone characterization. Increasing the AM excitation length could substantially enhance AIB_AM values stability with varying analyzed signals. The study suggests the portable AM-UB instrument with the integration of real-time analytics software that might provide a potential tool for osteoporosis early screening.     

超声表观积分背散射系数评价新生儿骨状况的可行性研究

新生儿骨发育状况的超声评价有重要意义。本文研究用超声背散射信号来评价新生儿骨发育状况的可行性。提出将超声表观积分背散射系数(AIB)用于评价新生儿松质骨状况,研究了不同超声频率下AIB与婴儿体重、出生天数之间的关系。研究结果表明,足月儿的AIB明显大于早产儿的AIB;足月儿的体重和AIB相关性较弱;早产儿的AIB参数和出生天数具有较高的正相关性(R=0.633)。说明超声背散射信号及其参数AIB可用于评价新生儿松质骨发育状况。      

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.     

Ultrasonic backscatter coefficient quantitative estimates from high-concentration Chinese Hamster Ovary cell pellet biophantoms

Previous work estimated the ultrasonic backscatter coefficient (BSC) from low-concentration (volume density <3%) Chinese Hamster Ovary (CHO, 6.7-μm cell radius) cell pellets. This study extends the work to higher cell concentrations (volume densities: 9.6% to 63%). At low concentration, BSC magnitude is proportional to the cell concentration and BSC frequency dependency is independent of cell concentration. At high cell concentration, BSC magnitude is not proportional to cell concentration and BSC frequency dependency is dependent on cell concentration. This transition occurs when the volume density reaches between 10% and 30%. Under high cell concentration conditions, the BSC magnitude increases slower than proportionally with the number density at low frequencies (ka<1), as observed by others. However, what is new is that the BSC magnitude can increase either slower or faster than proportionally with number density at high frequencies (ka>1). The concentric sphere model least squares estimates show a decrease in estimated cell radius with number density, suggesting that the concentric spheres model is becoming less applicable as concentration increases because the estimated cell radius becomes smaller than that measured. The critical volume density, starting from when the model becomes less applicable, is estimated to be between 10% and 30% cell volume density.     

Characterization of dense bovine cancellous bone tissue microstructure by ultrasonic backscattering using weak scattering models

A weak scattering model was proposed for the ultrasonic frequency-dependent backscatter in dense bovine cancellous bone, using two autocorrelation functions to describe the medium: one with discrete homogeneities (spherical distribution of equal spheres) and another, which considers tissue as an inhomogeneous continuum (densely populated medium). The inverse problem to estimate trabecular thickness of bone tissue has been addressed. A combination of the two autocorrelation functions was required to closely approximate the backscatter from bovine bone with various microarchitecture, given that the shape of trabeculae ranges from a rodlike to a platelike shape. Because of the large variation in trabecular thickness, both at an intraspecimen and an interspecimen level, thickness distributions for individual trabeculae for each bone specimen were obtained, and dominant trabecular sizes were determined. Comparison of backscatter measurements to theoretical predictions indicated that there were more than one dominant trabecular sizes that scatter sound for most specimens. Linear regression, performed between dominant trabecular thickness and estimated correlation length, showed significant linear correlation (R(2)=0.81). Attenuation due to scattering by a continuous distribution of scatterers was predicted to be linear over a frequency range from 0.3 to 0.9 MHz, suggesting a possibility that scattering may be a significant source of attenuation.     

Relationships of quantitative ultrasound parameters with cancellous bone microstructure in human calcaneus in vitro

Ultrasound parameters (attenuation, phase velocity, and backscatter), bone mineral density (BMD), and microarchitectural features were measured on 29 human cancellous calcaneus samples in vitro. Regression analysis was performed to predict ultrasound parameters from BMD and microarchitectural features. The best univariate predictors of the ultrasound parameters were the indexes of bone quantity: BMD and bone volume fraction (BV/TV). The most predictive univariate models for attenuation, phase velocity, and backscatter coefficient yielded adjusted squared correlation coefficients of 0.69-0.73. Multiple regression models yielded adjusted correlation coefficients of 0.74-0.83. Therefore attenuation, phase velocity, and backscatter are primarily determined by bone quantity, but multiple regression models based on bone quantity plus microarchitectural features achieve slightly better predictive performance than models based on bone quantity alone.     

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).     

Application of Biot's theory to ultrasonic characterization of human cancellous bones: determination of structural, material, and mechanical properties

This paper is devoted to the experimental determination of distinctive macroscopic structural (porosity, tortuosity, and permeability) and mechanical (Biot-Willis elastic constants) properties of human trabecular bones. Then, the obtained data may serve as input parameters for modeling wave propagation in cancellous bones using Biot's theory. The goal of the study was to obtain experimentally those characteristics for statistically representative group of human bones (35 specimens) obtained from a single skeletal site (proximal femur). The structural parameters were determined using techniques devoted to the characterization of porous materials: electrical spectroscopy, water permeametry, and microcomputer tomography. The macroscopic mechanical properties, Biot-Willis elastic constants, were derived based on the theoretical consideration of Biot's theory, micromechanical statistical models, and experimental results of ultrasonic studies for unsaturated cancellous bones. Our results concerning structural parameters are consistent with the data presented by the other authors, while macroscopic mechanical properties measured within our studies are situated between the other published data. The discrepancies are mainly attributed to different mechanical properties of the skeleton frame, due to strong structural anisotropy varying from site to site. The results enlighten the difficulty to use Biot's theory for modeling wave propagation in cancellous bone, implying necessity of individual evaluation of input parameters.     

Numerical investigation of ultrasound reflection and backscatter measurements in cancellous bone on various receiving areas

In this study, new ultrasound reflection and backscatter measurements in cancellous bone using a membrane-type hydrophone are proposed. A membrane hydrophone made of a piezoelectric polymer film mounted on an annular frame allows an incident ultrasound wave to pass through its aperture because it has no backing material. Therefore, in measurements using the membrane hydrophone, the receiving area could be located independently from the transmitting area. In addition, the size and shape of the receiving area, which corresponded to those of the electrode deposited on the piezoelectric film, could be arranged in various ways. To investigate the validity of the proposed measurements, before bench-top experiments, the reflected and backscattered waves from cancellous bone were numerically simulated using a finite-difference time-domain method. The reflection and backscatter parameters were measured on various receiving areas, and their correlation coefficients with the structural parameters in the cancellous bone were derived. The simulated results suggested that appropriate receiving areas for the reflection and backscatter measurements could exist and that the proposed measurements could be more effective for evaluating bone properties than conventional measurements.     

The spectrum entropy estimation method for ultrasonic backscattering signal in cancellous bones

In the application of cancellous bone ultrasound diagnosis based on backscattering method,it is of great importance to estimate fast and accurately whether the valid backscattering signal exists in the received signal.We propose a fast estimation method based on spectrum entropy method.With 984 records of adult calcaneus clinical data,we estimate the validity of the backscatter signal using this method.The results of the proposed method and the results of experience-base judgement were compared and analyzed.And two key parameters,the signal range length and the segment number of the spectrum entropy,were analyzed.The results show when the signal range length is 13 us and the segment number is 15-20,this method can get the best result(accuracy95%,sensitivity99%,specificity87%),while taking little calculation time(1.5 ms).Therefore,this spectrum entropy method can satisfy the accuracy and real-time requirements in the ultrasonic estimation for cancellous 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.     

松质骨超声背散射信号的谱信息熵判断方法

在松质骨超声背散射评价的实际应用中,如何快速准确地判断接收到的信号中是否包含有效背散射信号是一个重要问题。提出一种基于谱信息熵的背散射信号判断方法。对在体采集的984例成人跟骨处临床数据,采用该方法判断背散射信号的有效性,将判断结果与经验判断结果进行对照分析,并分析该方法中的信号区间长度和谱信息熵分段数对判断结果的影响。结果表明,当信号区间长度为13μs,谱信息熵分段数为15~20时,该方法可以获得最佳的判断结果(准确度〉95%,灵敏度〉99%,特异度〉87%),并且计算时间极短(1.5 ms)。因此采用谱信息熵方法判断背散射信号的有效性,可以满足超声骨质评价中对准确性和实时性的要求。      

骨小梁中超声背散射信号的频率分析及其微结构的估计

骨质疏松症是一种骨强度下降的全身性骨骼疾病,骨强度的下降是骨量减少和骨微结构退化的共同结果。相比于传统的超声透射方法,超声背散射法可提供更多的骨微结构信息,而对于松质骨结构的建模能有助于结构信息的获取。本文将骨小梁简化为单圆柱模型(圆柱状的单根骨小梁浸于骨髓中),并基于此模型对超声背散射与频率的关系进行分析。用铝线代替骨小梁做仿体实验,通过实验与理论结果的比较来验证单圆柱模型的可行性。     

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.