Defining optimal axial and lateral resolution for estimating scatterer properties from volumes using ultrasound backscatter

The rf signals used to construct conventional ultrasound B-mode images contain frequency-dependent information that can be examined through the backscattered power spectrum. Typically, the backscattered power spectrum is calculated from a region of interest (ROI) within some larger volume. The dimensions of the ROI are defined axially by the spatial length corresponding to the time gate and laterally by the number of scan lines included in the ROI. Averaging the backscattered power spectra from several independent scan lines can reduce the presence of noise caused by electronics and by the random scatterer spacings, but also decreases the lateral resolution of the interrogation region. Furthermore, larger axial gate lengths can be used to reduce the effects of noise and improve the precision and accuracy of scatterer property estimates but also decreases the axial resolution. A trade-off exists between the size of the ROI (the number of scan lines used, the separation distance between each scan line, the axial gate length) and the accuracy and precision of scatterer property estimates. A series of simulations and measurements from physical phantoms were employed to examine these trade-offs. The simulations and phantom measurements indicated the optimal lateral and axial sizes of the ROI, where estimate accuracy and precision were better than 10% and 5%, respectively, occurred at 4 to 5 beamwidths laterally and 15 to 20 spatial pulse lengths axially.     

Method of improved scatterer size estimation and application to parametric imaging using ultrasound

The frequency dependence of RF signals backscattered from random media (tissues) has been used to describe the microstructure of the media. The frequency dependence of the backscattered RF signal is seen in the power spectrum. Estimates of scatterer properties (average scatterer size) from an interrogated medium are made by minimizing the average squared deviation (MASD) between the measured power spectrum and a theoretical power spectrum over an analysis bandwidth. Estimates of the scatterer properties become increasingly inaccurate as the average signal to noise ratio (SNR) over the analysis bandwidth becomes smaller. Some frequency components in the analysis bandwidth of the measured power spectrum will have smaller SNR than other frequency components. The accuracy of estimates can be improved by weighting the frequency components that have the smallest SNR less than the frequencies with the largest SNR in the MASD. A weighting function is devised that minimizes the noise effects on the estimates of the average scatterer sizes. Simulations and phantom experiments are conducted that show the weighting function gives improved estimates in an attenuating medium. The weighting function is applied to parametric images using scatterer size estimates of a rat that had developed a spontaneous mammary tumor.     

A novel power spectrum calculation method using phase-compensation and weighted averaging for the estimation of ultrasound attenuation

An estimation of ultrasound attenuation in soft tissues is critical in the quantitative ultrasound analysis since it is not only related to the estimations of other ultrasound parameters, such as speed of sound, integrated scatterers, or scatterer size, but also provides pathological information of the scanned tissue. However, estimation performances of ultrasound attenuation are intimately tied to the accurate extraction of spectral information from the backscattered radiofrequency (RF) signals. In this paper, we propose two novel techniques for calculating a block power spectrum from the backscattered ultrasound signals. These are based on the phase-compensation of each RF segment using the normalized cross-correlation to minimize estimation errors due to phase variations, and the weighted averaging technique to maximize the signal-to-noise ratio (SNR). The simulation results with uniform numerical phantoms demonstrate that the proposed method estimates local attenuation coefficients within 1.57% of the actual values while the conventional methods estimate those within 2.96%. The proposed method is especially effective when we deal with the signal reflected from the deeper depth where the SNR level is lower or when the gated window contains a small number of signal samples. Experimental results, performed at 5 MHz, were obtained with a one-dimensional 128 elements array, using the tissue-mimicking phantoms also show that the proposed method provides better estimation results (within 3.04% of the actual value) with smaller estimation variances compared to the conventional methods (within 5.93%) for all cases considered.     

Identifying ultrasonic scattering sites from three-dimensional impedance maps

Ultrasonic backscattered signals contain frequency-dependent information that is usually discarded to produce conventional B-mode images. It is hypothesized that parametrization of the quantitative ultrasound frequency-dependent information (i.e., estimating scatterer size and acoustic concentration) may be related to discrete scattering anatomic structures in tissues. Thus, an estimation technique is proposed to extract scatterer size and acoustic concentration from the power spectrum derived from a three-dimensional impedance map (3DZM) of a tissue volume. The 3DZM can be viewed as a computational phantom and is produced from a 3D histologic data set. The 3D histologic data set is constructed from tissue sections that have been appropriately stained to highlight specific tissue features. These tissue features are assigned acoustic impedance values to yield a 3DZM. From the power spectrum, scatterer size and acoustic concentration estimates were obtained by optimization. The 3DZM technique was validated by simulations that showed relative errors of less than 3% for all estimated parameters. Estimates using the 3DZM technique were obtained and compared against published ultrasonically derived estimates for two mammary tumors, a rat fibroadenoma and a 4T1 mouse mammary carcinoma. For both tumors, the relative difference between ultrasonic and 3DZM estimates was less than 10% for the average scatterer size.     

Experimental study of the Doppler shift generated by a vibrating scatterer

We report an experimental study of the backscattering of a sound wave of frequency f by a surface vibrating harmonically at frequency F (F < f) and amplitude A in the regime where the Doppler effect overcomes bulk nonlinear effects. When the duration to of the analyzed time series of the scattered wave is small compared to the vibration period, the power spectrum of the backscattered wave is proportional to the probability density function of the scatterer velocity, which presents two peaks shifted from f by roughly 2fAomega/c (omega = 2piF). On the contrary, when t0 > F(-1), sidebands at frequencies f +/- nF (n integer) appear in the power spectrum, which are due to the phase modulation of the backscattered wave induced by its reflection on a moving boundary. We use the backscattered power spectrum to validate the phase modulation theory of the Doppler effect in the latter case for 2kA < 1 and 2kA approximately > 1 (k = 2pif/c, where c is the wave velocity) and we test the validity of an acoustic nonintrusive estimator of A as a function of power spectrum bandwidth and of A itself.     

Impact of local attenuation approximations when estimating correlation length from backscattered ultrasound echoes

Estimating the characteristic correlation length of tissue microstructure from the backscattered power spectrum could improve the diagnostic capability of medical ultrasound. Previously, size estimates were obtained after compensating for source focusing, the frequency-dependent attenuation along the propagation path (total attenuation), and the frequency-dependent attenuation in the scattering region (local attenuation). In this study, the impact of approximations of the local attenuation on the scatterer size estimate was determined using computer simulations and theoretical analysis. The simulations used Gaussian impedance distributions with an effective radius of 25 microm randomly positioned in a homogeneous half-space sonified by a spherically focused source (f/1 to f/4). The approximations of the local attenuation that were assessed neglected local attenuation (i.e., assume 0 dB/cm-MHz) neglected frequency dependence of the local attenuation, and assumed a finite frequency dependence (i.e., 0.5 dB/cm-MHz) independent of the true attenuation of the medium. Errors in the scatterer size estimate due to the local attenuation approximations increased with increasing window length, increasing true local attenuation and increasing f number. The most robust estimates were obtained when the local attenuation was approximated by a tissue-independent attenuation value that was greater than 70% of the largest attenuation expected in the tissue region of interest.     

Time and frequency parameters of bottlenose dolphin whistles as predictors of surface behavior in the Mississippi Sound

In this study, an algorithm previously developed for estimating the total ultrasonic attenuation along the propagation path from the surface of the transducer to a region of interest (ROI) in tissue, was modified to make it more practical for use in clinical settings. Specifically, the algorithm was re-derived for when a tissue mimicking phantom rather than a planar reflector is used to obtain the reference power spectrum. The reference power spectrum is needed to compensate for the transfer function of the transmitted pulse, the transfer function of transducer, and the diffraction effects that result from focusing/beam forming. The modified algorithm was tested on simulated radio frequency (RF) echo lines obtained from two samples that have different scatterer sizes and different attenuation coefficient slopes, one of which was used as a reference. The mean and standard deviation of the percent errors in the attenuation coefficient estimates (ACEs) were less than 5% and 10%, respectively, for ROIs that contain more than 10 pulse lengths and more than 25 independent echo lines. The proposed algorithm was also tested on two tissue mimicking phantoms that have attenuation coefficient slopes of 0.7 dB/cm-MHz and 0.5 dB/cm-MHz respectively, the latter being the reference phantom. When a single element spherically focused source was used, the mean and standard deviation of the percent errors in the ACEs were less than 5% and 10% respectively for windows that contain more than 10 pulse lengths and more than 17 independent echo lines. When a clinical array transducer was used, the mean and standard deviation of the percent errors in the ACEs were less than 5% and 25%, respectively, for windows that contain more than 12 pulse lengths and more than 45 independent echo lines.     

Compton-Polarimeter für 2 MeV-Bremsstrahlung

A polarimeter for bremsstrahlung must simultaneously perform two functions: it must select photons within a small energy interval out of the continuous bremsstrahlung spectrum and it must measure the polarization of these photons. The polarimeter depends on the polarization sensitivity of the Compton process with a 5 mm Si(Li-drift) detector as scatterer and a plastic scintillator as photon detector. To improve the energy resolution of the polarimeter a second 0,5 mm Si(Li-drift) detector behind the scatterer has been placed in anticoincidence with the scatterer.     

Fourier-domain low-coherence interferometry for light-scattering spectroscopy

We present a novel method for obtaining depth-resolved spectra for determining scatterer size through elastic-scattering properties. Depth resolution is achieved with a white-light source in a Michelson interferometer with the mixed signal and reference fields dispersed by a spectrograph. The spectrum is Fourier transformed to yield the axial spatial cross correlation between the signal and reference fields with near 1-microm depth resolution. Spectral information is obtained by windowing to yield the scattering amplitude as a function of wave number. The technique is demonstrated by determination of the size of polystyrene microspheres in a subsurface layer with subwavelength accuracy. Application of the technique to probing the size of cell nuclei in living epithelial tissues is discussed.     

Modeling the frequency dependence (5-120 MHz) of ultrasound backscattering by red cell aggregates in shear flow at a normal hematocrit

The frequency dependence of the ultrasound signal backscattered by blood in shear flow was studied using a simulation model. The ultrasound backscattered signal was computed with a linear model that considers the characteristics of the ultrasound system and tissue acoustic properties. The tissue scattering properties were related to the position and shape of the red blood cells (RBCs). A 2D microrheological model simulated the RBC dynamics in a Couette shear flow system. This iterative model, described earlier [Biophys. J. 82, 1696-1710 (2002)], integrates the hydrodynamic effect of the flow, as well as adhesive and repulsive forces between RBCs. RBC aggregation was simulated at 40% hematocrit and shear rates of 0.05-2 s(-1). The RBC aggregate sizes ranged, on average, from 3.3 RBCs at 2 s(-1) to 33.5 cells at 0.05 s(-1). The ultrasound backscattered power was studied at frequencies between 5-120 MHz and insonification angles between 0-180 degrees. At frequencies below approximately 30 MHz, the ultrasound backscattered power increased as the shear rate was decreased and the size of the aggregates was raised. A totally different scattering behavior was noted above 30 MHz. Typical spectral slopes of the backscattered power (log-log scale) between 5-25 MHz equaled 3.8, whereas slopes down to 0.6 were measured at 0.05 s(-1), between 40-60 MHz. The ultrasound backscattered power was shown to be angle dependent at low frequencies (5-25 MHz). The anisotropy persisted at high frequencies (>25 MHz) for small aggregates (at 2 s(-1)). In conclusion, this study sheds some light on the blood backscattering behavior with an emphasis on the non-Rayleigh regime. Additional experimental studies may be necessary to validate the simulation results, and to fully understand the relation between the ultrasound backscattered power, level of RBC aggregation, shear rate, frequency, and insonification angle.     

A theoretical comparison of attenuation measurement techniques from backscattered ultrasound echoes

Accurate characterization of tissue pathologies using ultrasonic attenuation is strongly dependent on the accuracy of the algorithm that is used to obtain the attenuation coefficient estimates. In this paper, computer simulations were used to compare the accuracy and the precision of the three methods that are commonly used to estimate the local ultrasonic attenuation within a region of interest (ROI) in tissue; namely, the spectral log difference method, the spectral difference method, and the hybrid method. The effects of the inhomgeneities within the ROI on the accuracy of the three algorithms were studied, and the optimal ROI size (the number of independent echoes laterally and the number of pulse lengths axially) was quantified for each method. The three algorithms were tested for when the ROI was homogeneous, the ROI had variations in scatterer number density, and the ROI had variations in effective scatterer size. The results showed that when the ROI was homogeneous, the spectral difference method had the highest accuracy and precision followed by the spectral log difference method and the hybrid method, respectively. Also, when the scatterer number density varied, the spectral difference method completely failed, while the log difference method and hybrid method still gave good results. Lastly, when the scatterer size varied, all of the methods failed.     

Backscattering from different objects in turbulent media

Abstract

The connection between diffraction characteristics of the scatterer and distribution of average backscattered intensity of a spherical wave is considered. In experiments with an ‘infinite’ plane mirror it is shown that the distribution of average backscattered intensity coincides with the correlation function of the intensity fluctuation of a virtual point source located at the mirror and observed from the real source plane. Non-monotonic dependence (with a minimum at the Fresnel number of scattered mirror?1) between the enhancement factor and the size of reflected mirror is observed in experiments.     

Study of a Microwave Radar Signal Backscattered at Small Incidence Angles: In-Situ Measurements

We present the results of data processing of the field experiment devoted to a study of a microwave signal backscattered by a rough water surface and compare them with the theoretical estimates. The measurements were conducted sequentially using a radar with parabolic and knife-beam antennas. The radar was mounted on the Molitovsky bridge at a height of 40 m across the Oka river in Nizhny Novgorod, Russia. For the radar with knife-shaped antenna pattern, we examined the reflected-signal power and the shift and width of the Doppler spectrum as functions of the azimuthal angle for the nadir sounding. For the parabolic antenna, we studied the reflected-signal power as a function of the incidence angle. Comparison with the experimental data shows that the developed theoretical model of a Doppler spectrum is in good agreement with the observations. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 48, No. 8, pp. 661–673, August 2005.     

Errors in ultrasonic scatterer size estimates due to phase and amplitude aberration

Current ultrasonic scatterer size estimation methods assume that acoustic propagation is free of distortion due to large-scale variations in medium attenuation and sound speed. However, it has been demonstrated that under certain conditions in medical applications, medium inhomogeneities can cause significant field aberrations that lead to B-mode image artifacts. These same aberrations may be responsible for errors in size estimates and parametric images of scatterer size. This work derives theoretical expressions for the error in backscatter coefficient and size estimates as a function of statistical parameters that quantify phase and amplitude aberration, assuming a Gaussian spatial autocorrelation function. Results exhibit agreement with simulations for the limited region of parameter space considered. For large values of aberration decorrelation lengths relative to aberration standard deviations, phase aberration errors appear to be minimal, while amplitude aberration errors remain significant. Implications of the results for accurate backscatter and size estimation are discussed. In particular, backscatter filters are suggested as a method for error correction. Limitations of the theory are also addressed. The approach, approximations, and assumptions used in the derivation are most appropriate when the aberrating structures are relatively large, and the region containing the inhomogeneities is offset from the insonifying transducer.     

一种平行栅碳纳米管阵列阴极的场发射特性研究

建立一种平行栅碳纳米管阵列阴极,利用悬浮球模型和镜像电荷法进行计算,给出碳纳米管顶端表面电场与电场增强因子的解析式. 在此基础上,进一步分析器件各类参数以及接触电阻对阴极电子发射性能的影响. 分析表明,碳纳米管间距大约为2倍碳纳米管高度时阵列阴极的分布密度最佳,靠边缘部位的碳纳米管发射电子能力比其中心部位的大;除碳纳米管的长径比之外,栅极宽度和栅极间距也对电场增强因子有一定作用;接触电阻的存在大幅度降低碳纳米管顶端表面电场与发射电流,而接触电阻高于800 kΩ时,器件对阳极驱动电压的要求更高. 关键词： 平行栅碳纳米管阵列 悬浮球 场增强因子 接触电阻     

On the estimation of backscatter coefficients using single-element focused transducers

The ultimate goal of quantitative ultrasound (QUS) imaging methods based on backscatter coefficient (BSC) estimates is to obtain system-independent structural information about samples. In the current study, three BSC estimation methods were compared and evaluated using the same backscattered pressure datasets in order to assess their consistency. BSC estimates were obtained from two phantoms with embedded glass spheres and compared to theoretical BSCs calculated using size distributions estimated using optical microscopy. Effective scatterer diameter and concentration estimates of the glass spheres were also obtained from the estimated BSCs. One estimation method needed to be compensated by more than an order of magnitude in amplitude in order to produce BSCs comparable to the other two methods. All calibration methods introduced different frequency-dependent effects, which could have noticeable effects on the bias of QUS estimates derived from experimental BSCs. Although in most cases the experimental QUS estimates obtained with all three methods were observed to differ by less than 10%, larger differences are expected depending on both the pressure focusing gain of the transducer (proportional to the ratio of the square of the aperture radius to the product of the wavelength and focal length) and ka range used in the estimation.     

Free Path Lengths in Quasi Crystals

The Lorentz gas is a model for a cloud of point particles (electrons) in a distribution of scatterers in space. The scatterers are often assumed to be spherical with a fixed diameter d, and the point particles move with constant velocity between the scatterers, and are specularly reflected when hitting a scatterer. There is no interaction between point particles. An interesting question concerns the distribution of free path lengths, i.e. the distance a point particle moves between the scattering events, and how this distribution scales with scatterer diameter, scatterer density and the distribution of the scatterers. It is by now well known that in the so-called Boltzmann–Grad limit, a Poisson distribution of scatterers leads to an exponential distribution of free path lengths, whereas if the scatterer distribution is periodic, the free path length distribution asymptotically behaves as a power law.     

Time reversal of speckle noise

Focusing a wave in an unknown inhomogeneous medium is an open problem in wave physics. This work presents an iterative method able to focus in pulse-echo mode in an inhomogeneous medium containing a random distribution of scatterers. By performing a coherent summation of the random echoes backscattered from a set of points surrounding the desired focus, a virtual bright pointlike reflector is generated. A time-reversal method enables an iterative convergence towards the optimal wave field focusing at the location of this virtual scatterer. Thanks to this iterative time-reversal process, it is possible to focus at any arbitrary point in the heterogeneous medium even in the absence of pointlike source. An experimental demonstration is given for the correction of strongly distorted images in the field of medical ultrasound imaging. This concept enables envisioning many other applications in wave physics.     

Energy spectra of electrons backscattered from bulk solid targets

Energy distribution spectra of backscattered electrons in the range 5–25 keV are obtained experimentally. An inverse problem of the reconstruction of the true electron spectrum is solved taking into account the instrument response function of the spectrometer; on the basis of the obtained solution, we specify functions of the real energy distribution of the electrons backscattered from homogeneous and layered samples.     

Quantum confinements in highly asymmetric sub-micrometer device structures

With the ongoing miniaturization of MOSFET structures into the nanometer domain, experimental results suggest there are physical limits up to which one can reduce the gate lengths. Furthermore, it becomes progressively more difficult to overcome the short channel effects at small gate lengths. This has led the researchers in the industry to look for alternative device technologies. One solution to the problem are the asymmetric device structures. In this work, we have simulated a 50 nm asymmetric MOS device structure using a two-dimensional Monte Carlo Poisson particle-based solver, in which quantum effects have been taken into account via the effective potential scheme. The quantum effects in these small device structures lead to strong quantum confinement of the carriers at the semiconductor/oxide interface, thus affecting the device drive current and the threshold voltage. We also show that the Silvaco Atlas simulations performed on the same device structure using the energy balance model were strongly affected by the choice of the energy relaxation times.