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.     

Effect of thermal noise on random lasers in diffusion regime

In this paper, we study the effects of thermal noise on the time evolution of a weak light pulse (probe) in the presence of a strong light pulse (pump) within a gain medium which includes random scatterer particles. Suitable thermal noise term is added to a set of four coupled equations including three diffusion equations for energy densities and a rate equation for the upper level population in a four-level gain medium. These equations have been solved simultaneously by Crank–Nicholson numerical method. The main result is that the back-scattered output probe light is increased as the thermal noise strength is increased and simultaneously, with the same rate, the amplified spontaneous emission is decreased. Therefore, the amplified response of the random laser in diffusion regime for the input probe pulse is enhanced due to effect of the thermal noise.     

Estimation of scatterer size from backscattered ultrasound: a simulation study

The reliability of the estimation of the size of scattering structures is assessed by realistic simulations and phantom experiments. The acoustic tissue model used in the simulation studies comprised a constant sound speed, homogeneous attenuation, and isotropic scattering. The scattering models considered were a discrete (spherical) model and two inhomogeneous-continuum models. The latter were characterized by an exponential and a Gaussian autocorrelation function, respectively. The backscattering spectra were, over the range from 5 to 10 MHz, fitted to linear, power, and autocorrelation functions of the three scattering models. The effects of the fitting function, the attenuation-either in an intervening layer or within the region of interest (ROI)-of the transmission pulse, and a spread in the scatterer sizes on the accuracy and the precision of the size estimates were assessed. The attenuation in the intervening tissue layer(s) as well as in the ROI itself has a significant effect on the accuracy of the size estimates and needs to be corrected. When performing the attenuation correction the inaccuracy of the attenuation estimate of the intervening layer leads to a large bias in the estimated scatterer size. Experimental results support the conclusion that scatterer size is a feasible tissue characterization parameter.     

Improved scatterer property estimates from ultrasound backscatter using gate-edge correction and a pseudo-Welch technique

Quantitative ultrasound (QUS) techniques have been widely used to estimate the size, shape and mechanical properties of tissue microstructure for specified regions of interest (ROIs). For conventional methods, an ROI size of 4 to 5 beamwidths laterally and 15 to 20 spatial pulse lengths axially has been suggested to estimate accuracy and precision better than 10% and 5%, respectively. A new method is developed to decrease the standard deviation of the quantitative ultrasound parameter estimate in terms of effective scatterer diameter (ESD) for small ROIs. The new method yielded estimates of the ESD within 10% of actual values at an ROI size of five spatial pulse lengths axially by two beamwidths laterally, and the estimates from all the ROIs had a standard deviation of 15% of the mean value. Such accuracy and precision cannot be achieved using conventional techniques with similar ROI sizes.     

Statistical properties of the penetration of photons into a semi-infinite turbid medium: a random-walk analysis

Statistical properties of the expected amount of time spent by a photon at different depths of a semi-infinite turbid medium are derived with formalism based on the continuous-time random walk. The formalism is applied to the study of both cw and time-gated experiments. Earlier analytical results relating to cw experiments are reproduced with a single approximation, rather than the more complicated approach used in earlier research based on the discrete-time random walk. The distribution of the occupancy of different depths in a time-gated experiment is found to have a convenient scaling form.     

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.     

A uniform amplitude spectrum generator for test of the maximum effective pulse rate of MCAs

This paper describes a two dimensional random pulse generator with output pulses which are both random in time and amplitude. It creates a pulse amplitude spectrum with statistically uniform distribution. Besides, a high resolution stable pulse (reference peak) is also produced just beyond the high end of the spectrum. This generator is designed to replace the radioactive source in testing MCAs or computerized data acquisition and processing systems. Especially, the shift of channel address and the resolution of pulse amplitude of MCAs can be measured precisely and easily by this generator at various input pulse rate.     

A pseudopotential approach to scattering

Scalar wave scattering is discussed using pseudopotentials. These are singular, wavefunction-dependent source terms subsuming the scattering properties of the object. The latter can be an impenetrable body or an inhomogeneity. In this approach, the boundary condition on the scatterer does not enter into computations explicitly, but the scattering amplitude in an unbounded medium appears in the Helmholtz equation. The pseudopotential gives the correct solution of the scattering problem outside the smallest sphere circumscribing the scatterer. If the scattering medium is spatially limited by a boundary (e.g., a waveguide or an enclosure), then the pseudopotentials decouple the scatterer boundary condition from that on the limiting surface. This simplifies the problem in that only the Green’s function for the limiting boundary needs to be considered. The formulation is entirely in terms of the free-space Green’s function, and hence is independent of any particular assumption or specific expression of the incident field. Numerical results are presented for a spherical inhomogeneity in a spherical Dirichlet enclosure. The pseudopotential formulation is anticipated to be useful in situations involving multiple scattering centers, and extraneous bounding surfaces.     

Antenna Gain Measurements by an Extended Version of the NBS Extrapolation Method

A General Extrapolation Technique which corrects for the effects of ground reflections in absolute gain measurements is described. It utilizes the Extrapolation Method developed at NBS which, in its present form, utilizes only amplitude versus distance data. However, for broadbeam antennas such as those encountered below 1 GHz, ground reflections may produce unwanted oscillations in the amplitude versus distance data. Hence the data are not amenable to the curve-fitting procedure of the Extrapolation Method. This problem can be overcome by including phase versus distance information to reduce the effects of ground reflections.     

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     

Emergence of an optimal search strategy from a simple random walk

In reports addressing animal foraging strategies, it has been stated that Lévy-like algorithms represent an optimal search strategy in an unknown environment, because of their super-diffusion properties and power-law-distributed step lengths. Here, starting with a simple random walk algorithm, which offers the agent a randomly determined direction at each time step with a fixed move length, we investigated how flexible exploration is achieved if an agent alters its randomly determined next step forward and the rule that controls its random movement based on its own directional moving experiences. We showed that our algorithm led to an effective food-searching performance compared with a simple random walk algorithm and exhibited super-diffusion properties, despite the uniform step lengths. Moreover, our algorithm exhibited a power-law distribution independent of uniform step lengths.     

Application of the MFS to inverse obstacle scattering problems

In this paper, the method of fundamental solutions (MFS) is used to detect the shape, size and location of a scatterer embedded in a host acoustic homogeneous medium from scant measurements of the scattered acoustic pressure in the vicinity of the obstacle. A nonlinear constrained minimization regularized MFS technique is proposed for the numerical solution of the inverse problem in question. The stability of the technique is investigated by inverting measurements contaminated by random noise. The results of several numerical experiments are presented.     

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.     

Size-dependent effective dynamic properties of unidirectional nanocomposites with interface energy effects

This article studies the size effect on wave propagation characteristics of plane longitudinal and transverse elastic waves in a two-phase nanocomposite consisting of transversely isotropic and unidirectionally oriented identical cylindrical nanofibers embedded in a transversely isotropic homogeneous matrix. The surface elasticity theory is employed to incorporate the interfacial stress effects. The effect of random distribution of nanofibers in the composite medium is taken into account via a generalized self-consistent multiple scattering model. The phase velocities and attenuations of longitudinal and shear waves along with the associated dynamic effective elastic constants are calculated for a wide range of frequencies and fiber concentrations. The numerical results reveal that interface elasticity at nanometer length scales can significantly alter the overall dynamic mechanical properties of nanofiber-reinforced composites. Limiting cases are considered and excellent agreements with solutions available in the literature have been obtained.     

Quantitative ultrasound estimates from populations of scatterers with continuous size distributions

Although quantitative ultrasound imaging based on backscattering coefficients has proven potential for tissue characterization, the scattering models used in most studies assume distributions of identical scatterers. However, actual tissues may exhibit multiple levels of spatial scales. Therefore, the objective of the present study is to analyze the effects of scatterer size distributions when using a fluid-sphere model for estimating values of effective scatterer diameter (ESD) through both simulations and experiments. For simulations, ESD estimates were obtained at several analysis frequencies between 1 and 40 MHz from populations of scatterers with diameters ranging between 25 and 100 μm, 25 and 50 μm, 50 and 100 μm, and 50 and 75 μm. For sufficiently high analysis frequencies, the ESD estimates obtained through simulations were approximately inversely proportional to frequency and mostly independent of the underlying scatterer size distribution. Asymptotic expressions for the expected ESD estimates at low- and high-frequency limits were derived. Experiments were conducted using two gelatin phantoms with contrast agent spheres ranging in diameter from 30 to 140 μm and 70 to 140 μm, and 5-, 7.5-, 10-, and 13-MHz focused transducers. Not only was the asymptotic behavior of ESD versus frequency estimates observed experimentally, but also the experimental ESD estimates using the 10- and 13-MHz transducers were lower than the smallest scatterers present in the second phantom. These results may have a direct impact on how scatterer size estimates corresponding to specimens with different subresolution spatial scales should be interpreted.     

Design and performance of Huffman sequences in medical ultrasound coded excitation

This paper deals with coded-excitation techniques for ultrasound medical echography. Specifically, linear Huffman coding is proposed as an alternative approach to other widely established techniques, such as complementary Golay coding and linear frequency modulation. The code design is guided by an optimization procedure that boosts the signal-to-noise ratio gain (GSNR) and, interestingly, also makes the code robust in pulsed-Doppler applications. The paper capitalizes on a thorough analytical model that can be used to design any linear coded-excitation system. This model highlights that the performance in frequency-dependent attenuating media mostly depends on the pulse-shaping waveform when the codes are characterized by almost ideal (i.e., Kronecker delta) autocorrelation. In this framework, different pulse shapers and different code lengths are considered to identify coded signals that optimize the contrast resolution at the output of the receiver pulse compression. Computer simulations confirm that the proposed Huffman codes are particularly effective, and that there are scenarios in which they may be preferable to the other established approaches, both in attenuating and non-attenuating media. Specifically, for a single scatterer at 150 mm in a 0.7-dB/(MHz·cm) attenuating medium, the proposed Huffman design achieves a main-to-side lobe ratio (MSR) equal to 65 dB, whereas tapered linear frequency modulation and classical complementary Golay codes achieve 35 and 45 dB, respectively.     

Utilization of prior flaw information in ultrasonic NDE: An analysis of flaw scattering amplitude as a random variable

Probabilistic approaches to flaw detection, classification, or characterization often assume prior knowledge of the flaw distribution. It is implicit that there is a scattering amplitude distribution associated with the flaw distribution. In a number of previously published probabilistic analyses, it has been assumed that scattering amplitude is an uncorrelated, Gaussian random variable with zero mean and known variance. In the work reported here, these assumptions are evaluated for the case of a lognormal distribution of spherical flaws. The correlation, mean, variance, and nature of the scattering amplitude distribution are considered as a function of frequency and as a function of the breadth of the assumed flaw distribution. It is shown for the assumed flaw distributions that scattering amplitude is not uncorrelated and does not have zero mean. It is shown that errors in estimating the flaw distribution variance affect both the scattering amplitude mean and variance. Using both analytical and numerical procedures, the scattering amplitude distribution is shown to be lognormal at long wavelength for a lognormal distribution of spherical scatterers. At high frequency, the distribution is shown to have a bimodal character.     

X-ray analysis of different starch granules

Crystal sizes and lattice distortion parameters for root, pulse and cereal starch granules have been determined using observed X-ray diffraction reflections by Fourier method. Enthalpy for the formation of the lattice in root, pulse and cereal starches has been estimated and compared. It is found that the crystal size is normally high in root starch compared to pulse and cereal starches.     

Nonuniform phase distribution in ultrasound speckle analysis. I. Background and experimental demonstration

In some cases, the statistical properties of the phase of ultrasound speckle in B-scan images differ from the uniform distribution characteristic exhibited by the fully developed speckle. This phenomenon has been noted when examining scattering structures with a somewhat regular spacing using wideband pulse excitation. It is shown by computer simulation and experiments on phantoms that when the mean scatterer spacing is equal to multiples of a half wavelength at the reference frequency of the receiver quadrature demodulator, the center of the echo phase distribution, plotted on the complex plane, will shift away from the origin. When the spacing is equal to an odd multiple of a quarter wavelength, the phase distribution will have a figure ;8' shape. By noticing those noncircular phase distributions while changing the demodulation frequency, the mean scatterer spacing can be estimated.