Ultrasonic field modeling: a comparison of analytical, semi-analytical, and numerical techniques

Modeling ultrasonic fields in front of a transducer in the presence and absence of a scatterer is a fundamental problem that has been attempted by different techniques: analytical, semi-analytical, and numerical. However, a comprehensive comparison study among these techniques is currently missing in the literature. The objective of this paper is to make this comparison for different ultrasonic field modeling problems with various degrees of difficulty. Four fundamental problems are considered: a flat circular transducer, a flat square transducer, a circular concave transducer, and a point focused transducer (concave lens) in the presence of a cavity. The ultrasonic field in front of a finite-sized transducer can be obtained by Huygens-Fresnel superposition principle that integrates the contributions of several point sources distributed on the transducer face. This integral which is also known as the Rayleigh integral or Rayleigh-Sommerfeld integral (RSI) can be evaluated analytically for obtaining the pressure field variation along the central axis of the transducer for simple geometries, such as a flat circular transducer. The semi-analytical solution is a newly developed mesh-free technique called the distributed point source method (DPSM). The numerical solution is obtained from finite element analysis. Note that the first three problems study the effect of the transducer size and shape, whereas the fourth problem computes the field in presence of a scatterer.     

Ultrasonic beam steering through inhomogeneous layers with a timereversal mirror

Adaptive time delay focusing techniques allow an efficient correction of the effects due to an inhomogeneous layer close to the transducer array. If the layer is far from the array, these techniques are no longer appropriate to correct the diffraction effects between the layer and the transducer array. This problem was overcome by the use of acoustic time reversal mirrors. In this technique, the Green's function of a dominant scatterer available in the medium is recorded in digital memories and used to focus on the scatterer in both transmit and receive modes. We present in this paper an extension of this technique to focus, in the presence of an aberrating layer, not only on the dominant scatterer, but also around it in order to image the surrounding zone. From the knowledge of the Green's function needed to focus on the initial scatterer, we calculate the new Green's function matched to the new point of interest. The algorithm uses the concept of time reversal propagation, and we shall present here theoretical and experimental results obtained with this technique. Finally, the knowledge of each Green's function matched to each new desired focal point allows the realization of a B-scan image of the zone surrounding the reflector     

Improved parametric imaging of scatterer size estimates using angular compounding

The feasibility of estimating and imaging scatterer size using backscattered ultrasound signals and spectral analysis techniques was demonstrated previously. In many cases, size estimation, although computationally intensive, has proven to be useful for monitoring, diagnosing, and studying disease. However, a difficulty that is encountered in imaging scatterer size is the large estimator variance caused by statistical fluctuations in echo signals from random media. This paper presents an approach for reducing these statistical uncertainties. Multiple scatterer size estimates are generated for each image pixel using data acquired from several different directions. These estimates are subsequently compounded to yield a single estimate that has a reduced variance. In this feasibility study, compounding was achieved by translating a sectored-array transducer in a direction parallel to the acquired image plane. Angular compounding improved the signal-to-noise ratio (SNR) in scatterer size images. The improvement is proportional to the square root of the effective number of statistically independent views available for each image pixel.     

Reversible back-propagation imaging algorithm for postprocessing of ultrasonic array data

The paper describes a method for processing data from an ultrasonic transducer array. The proposed algorithm is formulated in such a way that it is reversible, i.e., the raw data set can be recovered from the image. This is of practical significance because it allows the raw-data to be spatially filtered using the image to extract, for example, only the raw data associated with a particular scatterer. The method is tested on experimental data obtained from a commercial 64-element, 5.5-MHz array on an aluminum specimen that contains several machined slots and side-drilled holes. The raw transmitter-receiver data corresponding to each scatterer is extracted, and the scattering matrices of different scatterers are reconstructed. This allows the signals from 1-mm-long slot and a 1-mm-diameter hole to be clearly distinguished and the orientation and the size of the slots to be determined.     

Intervening attenuation affects first-order statistical properties of ultrasound echo signals

Previous studies show that first-order statistical properties of ultrasound echo signals are related to the effective number of scatterers in the "resolution cell" of a pulse-echo ultrasound system. When the effective number of scatterers is large (~10 or more) this results in echo signals whose amplitude follows a Rayleigh distribution, with the RF echo signal obeying Gaussian statistics; deviation from Rayleigh or Gaussian statistics yields information on scatterer number densities. In this paper, the influence of the medium's attenuation on non-Gaussian properties of the echo signal is considered. Preferential attenuation of higher frequency components of a pulsed ultrasound beam effectively broadens the beam and increases the resolution cell size. Thus, the resultant non-Gaussian parameter for broad bandwidth excitation of the transducer depends not only on the scatterer number density but also on the attenuation in the medium. These effects can be reduced or eliminated by using narrow-band experiments.     

A simple scheme for self-focusing of an array

A self-focusing technique and its application to a linear array system are presented in this paper. By application of the technique the system is capable of both sonification and reception focusing. The array is first excited as an unfocused array. Next a cross-correlation technique is used to determine time delays of reception of the largest amplitude backscattered signals at the elements of the array. The original transducer signal is then reemitted with the appropriate time delays to achieve sonification focusing on the scatterer producing the largest signal. This process is repeated in an iterative mode to focus energy on the strongest scatterer. Once insonification focusing has been achieved the last time-delay calculations are used once more for reception focusing, i.e., to correct the signals received by the individual elements for differences in arrival times. A low cost linear array has been constructed to implement the self-focusing technique. Examples demonstrate the capability of the technique to focus on the largest hole of sets of three holes in an aluminum specimen.     

A novel coded excitation scheme to improve spatial and contrast resolution of quantitative ultrasound imaging

Quantitative ultrasound (QUS) imaging techniques based on ultrasonic backscatter have been used successfully to diagnose and monitor disease. A method for improving the contrast and axial resolution of QUS parametric images by using the resolution enhancement compression (REC) technique is proposed. Resolution enhancement compression is a coded excitation and pulse compression technique that enhances the ?6-dB bandwidth of an ultrasonic imaging system. The objective of this study was to combine REC with QUS (REC-QUS) and evaluate and compare improvements in scatterer diameter estimates obtained using the REC technique to conventional pulsing methods. Simulations and experimental measurements were conducted with a single-element transducer (f/4) having a center frequency of 10 MHz and a ?6-dB bandwidth of 80%. Using REC, the -6-dB bandwidth was enhanced to 155%. Images for both simulation and experimental measurements contained a signal-to-noise ratio of 28 dB. In simulations, to monitor the improvements in contrast a software phantom with a cylindrical lesion was evaluated. In experimental measurements, tissue-mimicking phantoms that contained glass spheres with different scatterer diameters were evaluated. Estimates of average scatterer diameter in the simulations and experiments were obtained by comparing the normalized backscattered power spectra to theory over the ?6-dB bandwidth for both conventional pulsing and REC. Improvements in REC-QUS over conventional QUS were quantified through estimate bias and standard deviation, contrast-to-noise ratio, and histogram analysis of QUS parametric images. Overall, a 51% increase in contrast and a 60% decrease in the standard deviation of average scatterer diameter estimates were obtained during simulations, while a reduction of 34% to 71% was obtained in the standard deviation of average scatterer diameter for the experimental results.     

A new transducer receive transfer function calibration method: application to microbubble backscattering cross-section measurements at high frequency

When comparing acoustic scattering experiments with theory, the relationship between the pressure generated by a scatterer at the surface of a transducer and the induced voltage must be known. Methods have been previously proposed to measure the receive transfer function that rely on several assumptions. A new, experimental method for measuring the acoustic response of a spherically-focused transducer, using a hydrophone at twice the focal distance, is proposed that requires a minimum number of assumptions and calculations. The receive transfer function of a spherically-focused, high-frequency transducer was calculated, and found to be within 10% of the receive transfer function calculated assuming reciprocity. Further, using the receive transfer function, the effective backscattering cross-section of bound microbubbles interrogated at 30 MHz was measured to be, on average, 65% of the geometric backscattering cross-section, with significant size-independent variability. These results give insight into selecting the optimal microbubble size distribution for linear microbubble imaging at high frequencies.     

First-order statistics of pulsed-sinusoid backscatter from randommedia: basic elements of an exact treatment

In ultrasonic imaging systems, the instantaneous pressure at the transducer face during echo reception is typically comprised of many superimposed reflections of a pulse resembling an amplitude-modulated sinusoid. Generally, these reflections are randomly shifted in phase and randomly scaled in amplitude. Moreover, each reflected pulse may have been distorted by passage through a nonuniform medium. The first-order amplitude statistics of such a waveform have long been considered of interest. The backscatter formation process has often been modeled as a random walk in two dimensions. For simplicity, the effects of amplitude-phase dependence and scatterer size distribution have not been fully included in previous work. In most cases of interest this is physically justified; but, given a strongly non-Rayleigh random medium, experience has shown that more accurate expressions may be required. This paper points to the essentials of such an improved analysis. The effects of pulse structure and scatterer size distribution on the statistical properties of the individual step of the random walk are considered de novo. Simulation results are described     

圆柱阵主动声纳空时混响仿真及空时特性分析

经典的单元散射模型混响仿真方法无法应用于主动声纳空时自适应处理（space-time adaptive processing,STAP）算法研究。提出了一种基于单元散射模型的适合主动声纳STAP算法研究的圆柱阵混响仿真方法。根据声纳发射信号的距离和多普勒分辨力将海洋空间划分成若干个散射单元,将每个散射单元对各个通道混响的贡献在时域分别进行求和,得到各个通道的混响时间序列。仿真综合考虑了多种影响混响的因素,包括发射信号的参数、声呐平台的运动、海洋环境等。对仿真结果的空时特性进行了分析,结果表明仿真数据能够满足STAP算法研究的需要。     

The scattering of surface acoustic waves by electrical effects in two-dimensional metal film structures

A theory is presented for the scattering of surface acoustic waves by electrical effects in thin metal films of arbitrary shape on the surface of a piezoelectric material. A Green's function approach is used, and an expression for the two-dimensional Green's function appropriate to the problem is given. General expressions are obtained for the far-field radiation pattern and for the response of an interdigital transducer to a single scatterer. Expressions for the reflection and velocity perturbation due to periodic arrays of scatterers are also presented. Good agreement is found when the theoretical predictions are compared with a wide range of experimental results on lithium niobate.     

Simple algorithms for sonar imaging and bathymetry with a linear swept-frequency (chirp) source

This article describes a digital implementation of time-delay sonar imaging for linear swept-frequency (chirp) sources. The technique, based on phase-shifting of match-filtered individual transducer echoes, is a direct equivalent of analog phased-array processing. Computing and sampling costs are minimized by sparse population of the receiver aperture, using a separate transmission array with controlled beamwidth to suppress grating lobes. Synthetic-aperture processing uses essentially the same computation, and is carried out for a chirp signal without frequency decomposition. When different arrays are used for transmission and reception, azimuthal resolution depends on transmission array length, but maximum movement between pings without aliasing is set by the length of the receiver array, so high resolution is compatible with fast survey. This article describes how a closely related algorithm can be used for swath bathymetric depth estimation, and presents simulation results using a random surface scatterer model. © 1997 John Wiley & Sons, Inc. Int J Imaging Syst Technol, 8, 359–376, 1997     

Characterization of reperfused infarcted myocardium from high-frequency intracardiac ultrasound imaging using homodyned K distribution

Myocardial changes caused by infarction/reperfusion (contraction band necrosis, hemorrhage, edema, etc.) may result in an increased scatterer density and a variation in scatterer arrangement. This paper, for the first time, models most of the scattering conditions resulting from the interaction of ultrasound and normal/reperfused infarcted myocardium using the homodyned K distribution. Furthermore, this method is used to characterize the change in scatterer density by calculating the effective scatterer number per resolution cell. The reliability and the effects of attenuation and scan conversion on effective scatterer number estimation are discussed. We used in vivo data acquired using high-frequency intracardiac ultrasound imaging (8.5 MHz) from the left and right ventricles of open-chest pigs in an acute infarction/reperfusion model. The results show that the homodyned K distribution describes the statistical distribution of backscattered signal from both normal and abnormal myocardium. A significant increase in scatterer density occurs in the infarcted region after reperfusion compared with the same region at baseline (normal myocardium prior to occlusion). The scatterer density of the normal region does not change significantly after reperfusion. We conclude that the homodyned K distribution may characterize normal and reperfused infarcted myocardium using high-frequency intracardiac ultrasound images.     

Quantitative modeling of the anisotropy of ultrasonic backscatterfrom canine myocardium

Reports extensions and new results of the First Time Domain Born approximation model used by Mottley and Miller (1982) to describe the anisotropy of ultrasonic backscatter measured in canine myocardium. The interaction of an ultrasonic plane wave impulse with a single cylindrical scatterer using time and frequency domain approaches is reviewed. Myocardial tissue is modeled as a suspension of aligned cylindrically shaped scatterers uniformly distributed in a homogeneous medium. The authors propose extensions to this model to deal with nonideal scatterer orientation, by introducing axial distribution functions and scatterer size distributions based on histology, modeled as a uniform distribution. The backscatter coefficient in the range 2.0-8.0 MHz is calculated. An algorithm to compute the average differential scattering cross section is presented. Ultrasonic elastic properties of myocardial tissue are discussed. Results of the anisotropy of the numerically computed backscatter parameters for model media having nominal mechanical and acoustic properties of canine myocardial tissue are presented and compared to available experimental data along with discussion of possible conclusions     

Wave equation-based imaging of mode converted waves in ultrasonic NDI, with suppressed leakage from nonmode converted waves

The value of imaging techniques in ultrasonic nondestructive inspection (NDI) to find and characterize defects in steel components has already been demonstrated. The imaging techniques based on the integral representation of the wave equation, the Rayleigh integrals for wave field extrapolation, are becoming feasible and attractive due to advances in array technology and due to faster computers. Known implementations are the total focusing method (TFM), the synthetic aperture focusing method (SAFT), and the inverse wave field extrapolation method (IWEX). In principle, these techniques compensate propagation effects from sources to a scatterer such as a defect and propagation effects from the scatterer to receivers. Currently, this approach is applied to wave fronts of single modes (pure longitudinal or pure transversal). In practice, multiple wave fronts from the scatterer will be received as a result of mode conversion. These arrivals will not have the same arrival time because of the difference in sound velocity between longitudinal and transversal waves. Images of mode converted waves are obtained by choosing the appropriate sound velocity that corresponds with the mode-converted scattered wave in the imaging process. Therefore, the nonmode converted waves will image as leakage artifacts in the mode-converted images, and vice versa. This may lead to false interpretations. In this paper, such artifacts will be identified and explained with the help of an analytical example. Measurements from steel test pieces with a 4 MHz linear array transducer with 64 elements will be used to demonstrate the artifacts. Furthermore, a procedure to predict the artifacts and the subsequent suppression from the input measurements will be presented and demonstrated.     

Ultrasonic backscatter imaging by shear-wave-induced echo phase encoding of target locations

We present a novel method for ultrasound backscatter image formation wherein lateral resolution of the target is obtained by using traveling shear waves to encode the lateral position of targets in the phase of the received echo. We demonstrate that the phase modulation as a function of shear wavenumber can be expressed in terms of a Fourier transform of the lateral component of the target echogenicity. The inverse transform, obtained by measurements of the phase modulation over a range of shear wave spatial frequencies, yields the lateral scatterer distribution. Range data are recovered from time of flight as in conventional ultrasound, yielding a B-mode-like image. In contrast to conventional ultrasound imaging, where mechanical or electronic focusing is used and lateral resolution is determined by aperture size and wavelength, we demonstrate that lateral resolution using the proposed method is independent of the properties of the aperture. Lateral resolution of the target is achieved using a stationary, unfocused, single-element transducer. We present simulated images of targets of uniform and non-uniform shear modulus. Compounding for speckle reduction is demonstrated. Finally, we demonstrate image formation with an unfocused transducer in gelatin phantoms of uniform shear modulus.     

Scattering of a plane harmonic SH wave by a completely embedded corrugated scatterer

Anti‐plane‐strain model for steady‐state scattering of elastic waves by a rough inclusion or a cavity embedded in a half space is considered by using a direct boundary integral equation method. The roughness of the scatterer is assumed to be periodic with arbitrary amplitude and period. Detailed testing of the numerical results is presented. The motion along the half‐space surface is evaluated for different corrugations, frequencies and impedance contrast of the materials. The importance of the scatterer roughness upon the displacement field is clearly demonstrated. It was shown that larger corrugation amplitudes, shorter corrugation periods and higher frequencies may produce significant change in the displacement field when compared with the corresponding smooth scatterer result. This effect strongly depends upon the impedance contrast of the materials. Copyright © 2008 John Wiley & Sons, Ltd.     

Diffuse reflectance spectroscopy of human adenomatous colon polyps in vivo

Diffuse reflectance spectra were collected from adenomatous colon polyps (cancer precursors) and normal colonic mucosa of patients undergoing colonoscopy. We analyzed the data by using an analytical light diffusion model, which was tested and validated on a physical tissue model composed of polystyrene beads and hemoglobin. Four parameters were obtained: hemoglobin concentration, hemoglobin oxygen saturation, effective scatterer density, and effective scatterer size. Normal and adenomatous tissue sites exhibited differences in hemoglobin concentration and, on average, in effective scatterer size, which were in general agreement with other studies that employ standard methods. These results suggest that diffuse reflectance can be used to obtain tissue information about tissue structure and composition in vivo.     

Tissue characterization based on scatterer number density estimation

The authors propose a robust model for characterizing the statistical nature of signals obtained from ultrasonic backscatter processes. The model can accommodate frequency-dependent attenuation, spatially varying media statistics, arbitrary beam geometries, and arbitrary pulse shapes. On the basis of this model, statistical schemes are proposed for estimating the scatterer number density (SND) of tissues. The algorithm for estimating the scatterer number incorporates measurements of both the statistical moments of the backscattered signals and the point spread function of the acoustic system. The number density algorithm has been applied to waveforms obtained from ultrasonic phantoms with known number densities and in vitro mammalian tissues. There is an excellent agreement among theoretical, histological, and experimental results. The application of this technique for noninvasive clinical tissue characterization is discussed.     

Estimating mean scatterer spacing with the frequency-smoothedspectral autocorrelation function

The quasiperiodicity of regularly spaced scatterers results in characteristic patterns in the spectra of backscattered ultrasonic signals from which the mean scatterer spacing can be estimated. The mean spacing has been considered for classifying certain biological tissue. This paper addresses the problem of estimating the mean scatterer spacing from backscattered ultrasound signals using the frequency-smoothed spectral autocorrelation (SAC) function. The SAC function exploits characteristic differences between the phase spectrum of the resolvable quasiperiodic scatterers and the unresolvable uniformly distributed (diffuse) scatterers to improve estimator performance over other estimators that operate directly on the magnitude spectrum. Mean scatterer spacing estimates are compared for the frequency-smoothed SAC function and a cepstral technique using an AR model. Simulation results indicate that SAC-based estimates converge more reliably over smaller amounts of data than cepstrum-based estimates. An example of computing an estimate from liver tissue scans is also presented for the SAC function and the AR cepstrum