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.     

Frequency-dependent ultrasonic differentiation of normal and diffusely diseased liver

The attenuation coefficient in 38 pathologically graded in vitro liver specimens was measured over a frequency range from 1.25-8 MHz and fitted to the power law model. The attenuation in the normal group (n = 17) exhibited a frequency dependence of the form 0.399f1.139; in the mild disease group (n = 13), it exhibited a dependence of the form 0.395f1.212; and in the moderate/severe disease group (n = 8), it exhibited a dependence of the form 0.391f1.325. Using a Student's t test, it is shown that, due to these differences in the frequency dependence, the statistical significance level at which the null hypothesis regarding the difference between the mean attenuation slopes of any two of these categories is rejected, is a strong function of frequency in the range of 1-4 MHz. The significance level relating to the difference between the normal and moderate/severe disease group is more than one order of magnitude better than the other categories. In all cases, no substantial improvement occurs beyond 4 MHz. It is also shown that attenuation slope values at 3 MHz confirm in vivo literature results obtained via different techniques.     

Anisotropy of the backscatter coefficient of formalin-fixed ovine myocardium

The objective of this study was to measure the backscatter coefficient of formalin-fixed myocardial tissue as a function of angle of insonification relative to the myocardial fiber direction. Backscatter measurements were performed on eight cylindrical formalin-fixed lamb myocardial specimens and compensated for attenuation and diffraction effects to determine the backscatter coefficient. The backscatter coefficient at 5 MHz was found to be maximum for insonification perpendicular to the predominant myofiber orientation and minimum for parallel insonification, with values of (17+/-14) and (1.2+/-0.7) x 10(-4) cm(-1) sr(-1) (mean+/-standard deviation), respectively.     

Identification of human myocardial infarction in vitro based on the frequency dependence of ultrasonic backscatter.

It has been reported previously that acute and mature myocardial infarction in dogs can be differentiated in vitro and in vivo by ultrasonic tissue characterization based on measurement of the frequency dependence of ultrasonic backscatter. To characterize human infarction with an index of the frequency dependence of backscatter that could be obtained in patients, cylindrical biopsy specimens from 7 normal regions and 12 regions of infarction of 6 fixed, explanted human hearts in 2-deg steps around their entire circumference with a 5-MHz broadband transducer were insonified. One to six consecutive transmural levels were studied for each specimen. The dependence of apparent (uncompensated for attenuation or beam width) backscatter, /B(f)/2, on frequency (f) was computed from spectral analyses of radio-frequency data as /B(f)/2 = afn, where from theoretical considerations the magnitude of n decreases as scatterer size increases. Apparent integrated backscatter was computed as the average of /B(f)/2 from 3 to 7 MHz. The average value for n for normal tissue (0.9 +/- 0.1) exceeded that for tissue from regions of infarction (0.6 +/- 0.1; p less than 0.05). Infarct manifested a significant decrease of n from epicardial to endocardial levels (epi----mid----endo: 0.9----0.7----0.2; p less than 0.05) whereas normal tissue manifested similar values for n at each transmural level (0.8----1.1----0.9; p = NS). Average integrated backscatter across all transmural levels for infarct was significantly greater than for normal tissue (-48.3 +/- 0.5 vs -53.4 +/- 0.4 dB, infarct versus normal; p less than 0.05). The presence of fibrosis was associated with smaller values of n and greater integrated backscatter.(ABSTRACT TRUNCATED AT 250 WORDS)     

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.     

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.     

Improved scatterer size estimation using backscatter coefficient measurements with coded excitation and pulse compression

Scatterer size estimates from ultrasonic backscatter coefficient measurements have been used to differentiate diseased tissue from normal. A low echo signal-to-noise ratio (eSNR) leads to increased bias and variance in scatterer size estimates. One way to improve the eSNR is to use coded excitation (CE). The normalized backscatter coefficient was measured from three tissue-mimicking phantoms by using CE and conventional pulsing (CP) techniques. The three phantoms contained randomly spaced glass beads with median diameters of 30, 45, and 82 mum, respectively. Measurements were made with two weakly focused, single-element transducers (f(0)=5 MHz and f(0)=10 MHz). For CE, a linear frequency modulated chirp with a time bandwidth product of 40 was used and pulse compression was accomplished by the use of a Wiener filter. Preliminary results indicated that improved estimation bias versus penetration depth was obtained by using CE compared to CP. The depth of penetration, where the accuracy of scatterer diameter estimates (absolute divergence <25%) were obtained with the 10 MHz transducer, was increased up to 50% by using CE versus CP techniques. In addition, for a majority of the phantoms, the increase in eSNR from CE resulted in a modest reduction in estimate variance versus depth of penetration.     

窄带脉冲信号测量横波衰减系数-频率曲线的方法

提出一种测量材料超声横波衰减-频率曲线(αs-f)的方法:应用窄带脉冲驱动接触式横波探头的脉冲反射方式,采用石英晶体作为耦合块,通过测量耦合块和被测试块耦合界面的声压反射和透射系数,并在衍射修正下测量得到单频率下的超声横波衰减系数;在探头有效带宽内改变发射频率并重复测量,得到不同频率下超声横波衰减系数数值;利用非线性最...     

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.     

Anisotropy of ultrasonic propagation and scattering properties in fresh rat skeletal muscle in vitro

The anisotropy of frequency-dependent backscatter coefficient, attenuation, and speed of sound is assessed in fresh rat skeletal muscle within 5 h post-mortem. Excised rat semimembranosus and soleus muscles are measured in 37 degrees C Tyrode solution, with the muscle fibers at 90 degrees and 45 degrees orientations to the incident sound beam. Reflected and through transmission signals from either a 6- or 10-MHz focused transducer give frequency dependent information in the 4-14 MHz range. The attenuation coefficient in each muscle is consistently a factor of 2.0 +/- 0.4 lower for propagation perpendicular to the fibers than at 45 degrees, whereas speed of sound shows a much milder anisotropy, and is slightly faster for the 90 degrees orientation. The largest anisotropy is seen in the backscatter coefficient, most notably in the semimembranosus where the magnitude at 90 degrees is over an order of magnitude greater than at 45 degrees, with the frequency dependence in both cases giving a power law between 1.5 and 2.0.     

脉冲Ti~（3＋）：Al_2O_3激光器的增益长度

脉冲激光束纵向泵浦Ｔｉ￣（３＋）：Ａｌ＿２Ｏ＿３晶体，根据晶体中增益区的分布情况和脉冲运转的特点，从获取高转换效率考虑，可用“损耗平衡”确定晶体长度。单纵向泵浦时晶体的长度１由式选取。式中α＿ｐ是晶体对泵浦光的吸收系数，β是ＦＯＭ值。双纵向泵浦时，“损耗平衡”表示为：是晶体长度。根据实际光路的调整状态，设双纵向泵浦参数基本对称，对高α＿ｐ晶体取Ｌ＝１．５ｌ。若α＿ｐ较低，且泵浦参数并不对称，则Ｌ在ｌ＜Ｌ＜１．５ｌ范围内取值。这一方法与实验系统运转情况相符。     

Frequency dependence of acoustic properties of aqueous glucose solutions in the VHF/UHF range

The bioultrasonic spectroscopy system was employed for measurements of velocity and attenuation coefficient of glucose solutions in the VHF/UHF range. The relation between the slope of the square of velocity and the relaxation parameters, and the relation between the frequency exponent on attenuation coefficient and the relaxation parameters are investigated. In order to carry out numerical calculations, a model for a single relaxation process is employed, wherein the attenuation coefficient is expressed as (A/( 1 + (f/falpha)2) + B)f2 where falpha is the attenuation relaxation frequency, and A and B are constants. The numerical calculations show that the slope of the square of the velocity is determined uniquely by the velocity relaxation frequency fv and v(infinity)2 - v(0)2 where v0 is the zero-frequency velocity and v(infinity) is the infinite-frequency velocity, and that the frequency exponent on the attenuation coefficient is determined uniquely by falpha and A/B. For experimental considerations, the velocities and the attenuation coefficients of 5, 15, and 25% concentration aqueous solutions of glucose were measured in the frequency range 20 to 700 MHz. The data for the 5 and 15% aqueous solutions can be explained using the single relaxation model. However, the data for the 25% aqueous solution suggest the existence of multirelaxation processes.     

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.     

毫米波辐照下大鼠脑电的长程相关性

通过脑电长程相关性的分析,定量研究了35 GHz毫米波辐照大鼠时产生的应激反应.通过退趋势分析法,得到反映高频成分的标度指数.显示在辐照前该成分具有布朗噪声的特性,辐照时具有长程相关性;而反映低频成分的标度指数显示在辐照前该成分具有长程相关性,辐照时成为布朗噪声.引进应激指标参量低频成份标度指标数/高频成份标度指标数,...     

Attenuation of ultrasound in post rigor bovine skeletal muscle

A pulse transmission method for measuring the attenuation of 1-7 MHz ultrasound in bovine skeletal muscle is described. Measurements of the attenuation coefficient at -20, 0, 20 and 40 degrees C conformed to the relation alpha = Afn, where A and n are temperature-dependent coefficients and f is the frequency. alpha/f varied slowly with frequency, and at 4 MHz and 20 degrees C mean values were 1.3 dB cm-1 MHz-1 along the fibres and 0.55 dB cm-1 MHz-1 across the fibres. These data are lower than most previous measurements of skeletal muscle, but comparable with recent measurements of canine heart muscle.     

Attenuation of ultrasound in skeletal muscle

Ultrasonic attenuation in fresh and 5% formalin fixed beef skeletal muscle has been measured, as a continuous function of frequency, in the range 1–8 MHz, for muscle fibre orientations both parallel and normal to the direction of propagation. Good agreement was found in all cases between two independent sets of measurements employing transmission and reflection techniques respectively. The data are consistent with a power law dependence of attenuation coefficient on frequency, with an exponent that is not significantly different from unity. For propagation normal to the fibres attenuation values are found as 1.1 ± 0.15 and 1.6 ± 0.15 dB cm^?1 MHz^?1 for fresh and fixed tissue respectively, the corresponding values for parallel propagation being 2.9 ± 0.23 and 4.1 ± 0.25 dB cm^?1 MHz^?1.     

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.     

Natural-Convection Thermosyphon Heat Transfer from a Stack of Horizontal Plates

Steady laminar natural convection of water about vertically stacked, two-sided, horizontal heated plates was studied experimentally over a range of plate gap to plate half-width ratio, H/a, from 0.078 to 0.94. Measurements were made of power input per plate, plate temperatures, and inlet and outlet bulk fluid temperatures. From these data were determined average Nusselt and Rayleigh numbers for each plate, which were correlated with a power law Nu = C Raⁿ for each gap height. The Nusselt numbers increased with gap height up to H/a 0.47 (from 8 to 48), and then became independent of H/a. The exponent n increased from n 0.2 at the lowest gap height tested (H/a 0.078), to a high value of n approximately equal to 0.4 at H/a = 0.24 and then decreased back to n = 0.2 for H/a greater than or equal to 0.47.     

Cs 39D态Rydberg原子Stark光谱的实验研究

本文从理论和实验上对Cs39D态Rydberg原子在弱电场作用下的Stark效应做了详细研究. 理论上利用数值方法计算了Cs原子39D态的Stark结构;实验上,采用两步激发超冷基态原子获得超冷Rydberg原子,通过场电离的方法获得了39D态的Stark光谱,测量获得α^5/2₂,α^5/2₀,α^3/2₂和α^3/2₀相应的极化率分别为：62(7),－146(13), 73(6) 和－106(20) MHz·V^-2cm²,实验结果与理论相符合. 关键词： Rydberg原子 Stark结构 场电离 极化率     

Relationships among calcaneal backscatter, attenuation, sound speed, hip bone mineral density, and age in normal adult women

The present study was undertaken in order to investigate the use of calcaneal ultrasonic backscatter for the application of diagnosis of osteoporosis. Broadband ultrasonic attenuation (BUA), speed of sound (SOS), the average backscatter coefficient (ABC), and the hip bone mineral density (BMD) were measured in calcanea in 47 women (average age: 58 years, standard deviation: 13 years). All three ultrasound variables had comparable correlations with hip BMD (around 0.5). As reported previously by others, BUA and SOS were rather highly correlated with each other. The logarithm of the ABC was only moderately correlated with the other two. The three ultrasound parameters exhibited similar moderate negative correlations with age. These results taken collectively suggest that the ABC may carry important diagnostic information independent of that contained in BUA and SOS and, therefore, may be useful as an adjunct measurement in the diagnosis of osteoporosis.