Thermodynamics of strong coupling superconductors including the effect of anisotropy

The thermodynamics of several elemental superconductors is computed from isotropic Eliashberg theory formulated on the imaginary frequency axis. A symmary of the available experimental literature is presented and a comparison with theory is given. The small disagreements that are found are all in the direction expected from anisotropy effects. We calculate the effect of a small amount of model anisotropy on the critical temperature, critical field, and high-temperature specific heat from an exact solution of the anisotropic Eliashberg equations. These are the first such results below the critical temperature; unlike previous analytical work, we include retardation, anisotropy in the mass enhancement, and the effect of the Coulomb repulsion in enhancing anisotropy, all of which are significant. We derive a new formula independent of any model anisotropy for the rate of decrease with impurity lifetime of the critical temperature. Finally we demonstrate how the commonly used formulas of Markowitz and Kadanoff and of Clem may give entirely misleading estimates of the gap anisotropy when used to interpret certain experiments.Research supported by the Natural Sciences and Engineering Research Council of Canada.     

Despeckling of medical ultrasound images

Speckle noise is an inherent property of medical ultrasound imaging, and it generally tends to reduce the image resolution and contrast, thereby reducing the diagnostic value of this imaging modality. As a result, speckle noise reduction is an important prerequisite, whenever ultrasound imaging is used for tissue characterization. Among the many methods that have been proposed to perform this task, there exists a class of approaches that use a multiplicative model of speckled image formation and take advantage of the logarithmical transformation in order to convert multiplicative speckle noise into additive noise. The common assumption made in a dominant number of such studies is that the samples of the additive noise are mutually uncorrelated and obey a Gaussian distribution. The present study shows conceptually and experimentally that this assumption is oversimplified and unnatural. Moreover, it may lead to inadequate performance of the speckle reduction methods. The study introduces a simple preprocessing procedure, which modifies the acquired radio-frequency images (without affecting the anatomical information they contain), so that the noise in the log-transformation domain becomes very close in its behavior to a white Gaussian noise. As a result, the preprocessing allows filtering methods based on assuming the noise to be white and Gaussian, to perform in nearly optimal conditions. The study evaluates performances of three different, nonlinear filters--wavelet denoising, total variation filtering, and anisotropic diffusion--and demonstrates that, in all these cases, the proposed preprocessing significantly improves the quality of resultant images. Our numerical tests include a series of computer-simulated and in vivo experiments.     

Three-dimensional blind deconvolution of ultrasound images

Three-dimensional ultrasound images are blurred by the ultrasound pulse through the convolution between the 3-D tissue signal and the 3-D pulse. The blurring reduces the spatial resolution of the 3-D ultrasound images and, consequently, their diagnostic value. This paper presents a method for 3-D blind homomorphic deconvolution of medical 3-D ultrasound images to improve their spatial resolution. The blind estimate of the 3-D pulse is necessary because the pulse changes in spatial extent and frequency composition as it passes through the tissues and because the pulse is not separable in its spatial dimensions. The method was tested on a 3-D image of a phantom with anechoic spheres of known size in a uniform diffuse scattering matrix. The spheres were clearly better defined and had volumes much closer to the true volume in the deconvolved image than in the original image     

Statistical characterization of diffuse scattering in ultrasound images

The marginal statistics for the diffused ultrasound speckle echo has been postulated as exhibiting circularly symmetric Gaussian behavior similar to the laser speckle for monochromatic illumination under the assumption of a large number of unresolvable scatterers per resolution cell. This is known in the literature as the Rayleigh scattering condition. This paper presents a formal statistical test, the Kolmogorov-Smirnov nonparametric goodness of fit statistical test, to test the hypothesis that the unresolvable part (diffuse part) of the backscatter echo follows a Rayleigh scattering condition, and obtain numerical values for the scatterer concentration required for the Rayleigh condition to be valid. In addition, it presents a formal statistical test, the Kolmogorov-Smirnov nonparametric homogeneity statistical test, to compare two regions of interest with different scattering concentrations without prior knowledge of the nature of the scattering conditions (Rayleigh or non-Rayleigh scattering). Unlike all previous parametric testing methods that treat the A-scan or B-scan echo as a random sample, the authors' method presents formal tests based on the colored nature of the diffuse backscattered echo which is a more realistic model of the diffuse scattering component. The tests are demonstrated on simulations of RF scans with different scatterer concentrations per resolution cell as well as on phantom data which mimic tissue.     

The effect of inhomogeneity and anisotropy on Stoneley waves

Summary In this paper we study the dispersion equation of Stoneley waves that are travelling in an inhomogeneous elastic half-space over an anisotropic homogeneous elastic half-space.The phase velocity is calculated as a function of the wave number. The results indicate that the effect of anisotropy on such waves is small and can be neglected, while the effect of inhomogeneity is very pronounced. The results show that Stoneley waves do not exist after some cut-off value of the wave number.     

Two-dimensional noise-robust blind deconvolution of ultrasound images

This paper presents a new method for 2-D blind homomorphic deconvolution of medical B-scan ultrasound images. The method is based on noise-robust 2-D phase unwrapping and a noise-robust procedure to estimate the pulse in the complex cepstrum domain. Ordinary Wiener filtering is used in the subsequent deconvolution. The resulting images became much sharper with better defined tissue structures compared with the ordinary images. The deconvolved images had a resolution gain of the order of 3 to 7, and the signal-to-noise ratio (SNR) doubled for many of the images used in our experiments. The method gave stable results with respect to noise and gray levels through several image sequences     

The effect of the measurement frequency on the elastic anisotropy of fibre laminates

Static tests and ultrasonic measurements (2.25 MHz) have been carried out on a series of composite laminates of glass fibres in a polypropylene matrix. A range of angle ply laminates were prepared for this study, with laminate angles θ of ±0, 10, 20, 30 and 40^∘. The high frequency measurements were made using the ultrasonic immersion technique, which allows the determination of a complete set of the elastic constants of a material. The relationship between the ultrasonically determined elastic constants of the angle ply laminates was found to be in excellent agreement with theoretical predictions, as previously validated for carbon fibre/epoxy angle ply laminates. A comparison between the ultrasonic and statically measured values was made for two of the angle ply laminates (θ = 0 and 20^∘). It was found that the static values were lower than those measured at ultrasonic frequency, particularly those constants that were more matrix dominated (for example the transverse moduli of the laminates). Measurements on a pure polypropylene sample at both testing frequencies confirmed that the change in matrix properties with frequency was the cause of this difference. The change in properties with test frequency is likely to be much larger in this system than in other composite materials because the glass transition temperature of polypropylene is close to ambient temperature. Dynamic mechanical tests (1 Hz) were carried out on a sample of pure polypropylene to assess this effect. We also give an appropriate method of estimating the dependence of glass transition temperature on frequency. The results for polypropylene are compared with those for other commonly used polymer matrix materials: epoxy resin, nylon and polyetheretherketone (PEEK): DMTA measurements were also made on these samples. The effect of test frequency on matrix properties, for the glass/PP laminates, was further investigated by examining the relationship of the Poisson's ratios with laminate angle using a mixture of ultrasonic experiments and theoretical predictions. Previously we have shown that the degree of anisotropy between the reinforcing fibre and the matrix phase is paramount in determining whether the material will show a negative Poisson's ratio at a critical laminate angle. The ultrasonic measurements carried out in this study on the glass/PP laminates showed a minimum in one of the Poisson's ratio at a laminate angle of 32°, but the value did not become negative. However, theoretical predictions showed that for a static frequency measurement (1 Hz), where the matrix is softer and hence the anisotropy of each laminate ply is higher, the laminate will show a negative Poisson's ratio with a minimum at a laminate angle of around 28°.     

The effects of heterogeneity and anisotropy on the size effect in cracked polycrystalline films

A model is developed for quantifying the size effect due to heterogeneity and anisotropy in polycrystalline films. The Monte Carlo finite element calculations predict the average and standard deviation of the microscopic (local) stress intensity factors and energy release rate of a crack in a columnar aggregate of randomly orientated, perfectly bonded, orthotropic crystals (grains) under plane deformation. The boundary of the near-tip region is subjected to displacement boundary conditions associated with a macroscopic (far field or nominal) Mode-I stress intensity factor and average elastic constants calculated for the uncracked film with a large number of grains. The average and standard deviation of the microscopic stress intensity factors and energy release rate, normalized with respect to the macroscopic parameters, are presented as functions of the number of grains within the near-tip region, and the parameters that quantify the level of crystalline anisotropy. It is shown that for a given level of anisotropy, as long as the crack tip is surrounded by at least ten grains, then the expected value and standard deviation of the crack tip parameters are insensitive to the number of crystals. For selected values of crystalline anisotropy, the probability distributions of Mode-I stress intensity factor and stress ahead of the crack are also presented. The results suggest that the size effect due to heterogeneity and anisotropy is weak; crack initiation load and direction are governed only by the details of the grains in the immediate vicinity of the crack tip. This revised version was published online in July 2006 with corrections to the Cover Date.     

Fermi-surface anisotropy in potassium and the effect of hydrostatic pressure

The anisotropy of the Fermi surface (FS) of potassium has been determined with improved precision. The anisotropy and absolute value of the pressure coefficient for the potassium FS in the 25-bar pressure range have also been measured. The pressure coefficient anisotropy is some eight times greater than, and of similar form to, the FS anisotropy. The mean value of the (area) pressure coefficient is 1.720±0.008×10^-2/kbar, which is some 5% lower than that predicted from the bulk modulus. No obvious reason has been found for the discrepancy between our result and that obtained from high-pressure measurements.     

Two-dimensional blind Bayesian deconvolution of medical ultrasound images

A new approach to 2-D blind deconvolution of ultrasonic images in a Bayesian framework is presented. The radio-frequency image data are modeled as a convolution of the point-spread function and the tissue function, with additive white noise. The deconvolution algorithm is derived from statistical assumptions about the tissue function, the point-spread function, and the noise. It is solved as an iterative optimization problem. In each iteration, additional constraints are applied as a projection operator to further stabilize the process. The proposed method is an extension of the homomorphic deconvolution, which is used here only to compute the initial estimate of the point-spread function. Homomorphic deconvolution is based on the assumption that the point-spread function and the tissue function lie in different bands of the cepstrum domain, which is not completely true. This limiting constraint is relaxed in the subsequent iterative deconvolution. The deconvolution is applied globally to the complete radiofrequency image data. Thus, only the global part of the point-spread function is considered. This approach, together with the need for only a few iterations, makes the deconvolution potentially useful for real-time applications. Tests on phantom and clinical images have shown that the deconvolution gives stable results of clearly higher spatial resolution and better defined tissue structures than in the input images and than the results of the homomorphic deconvolution alone.     

Interactive volume rendering of real-time three-dimensional ultrasound images

Real-time, three-dimensional (RT3D) ultrasound allows video frame rate volumetric imaging. The ability to acquire full three-dimensional (3-D) image data in real-time is particularly helpful for applications such as cardiac imaging, which require visualization of complex and dynamic 3-D anatomy. Volume rendering provides a method for intuitive graphical display of the 3-D image data, but capturing the RT3D echo data and performing the necessary processing to generate a volumetric image in real time poses a significant technical challenge. We present a data capture and rendering implementation that uses off-the-shelf components to real-time volume render RT3D ultrasound images. Our approach allowed live, interactive volume rendering of RT3D ultrasound scans.     

Higher order spectra based deconvolution of ultrasound images

We address the problem of improving the spatial resolution of ulrasound images through blind deconvolution. The ultrasound image formation process in the RF domain can be expressed as a spatio-temporal convolution between the tissue response and the ultrasonic system response, plus additive noise. Convolutional components of the dispersive attenuation and aberrations introduced by propagating through the object being imaged are also incorporated in the ultrasonic system response. Our goal is to identify and remove the convolutional distortion in order to reconstruct the tissue response, thus enhancing the diagnostic quality of the ultrasonic image. Under the assumption of an independent, identically distributed, zero-mean, non-Gaussian tissue response, we were able to estimate distortion kernels using bicepstrum operations on RF data. Separate 1D distortion kernels were estimated corresponding to axial and lateral image lines and used in the deconvolution process. The estimated axial kernels showed similarities to the experimentally measured pulse-echo wavelet of the imaging system. Deconvolution results from B-scan images obtained with clinical imaging equipment showed a 2.5-5.2 times gain in lateral resolution, where the definition of the resolution has been based on the width of the autocovariance function of the image. The gain in axial resolution was found to be between 1.5 and 1.9     

Restoration of medical ultrasound images using two-dimensionalhomomorphic deconvolution

Describes how two-dimensional (2D) homomorphic deconvolution can be used to improve the lateral and radial resolution of medical ultrasound images recorded by a sector scanner. The recorded radio frequency ultrasound image in polar coordinates is considered as a 2D sequence of angle and depth convolved with a 2D space invariant point-spread function (PSF). Each polar coordinate sequence is transformed into the 2D complex cepstrum domain using the fast Fourier transform for Cartesian coordinates. The low-angle and low-depth portion of this sequence is taken as an estimate of the complex cepstrum representation of the PSF. It is transformed back to the Fourier frequency domain and is used to compute the deconvolved angle and depth sequence by 2D Wiener filtering. Two-dimensional homomorphic deconvolution produced substantial improvement in the resolution of B-mode images of a tissue-mimicking phantom in vitro and of several human tissues in vivo. It was better than lateral or radial homomorphic deconvolution alone, and better than 2D Wiener filtering with a PSF recorded in vitro     

Connecting fractional anisotropy from medical images with mechanical anisotropy of a hyperviscoelastic fibre-reinforced constitutive model for brain tissue

Brain tissue modelling has been an active area of research for years. Brain matter does not follow the constitutive relations for common materials and loads applied to the brain turn into stresses and strains depending on tissue local morphology. In this work, a hyperviscoelastic fibre-reinforced anisotropic law is used for computational brain injury prediction. Thanks to a fibre-reinforcement dispersion parameter, this formulation accounts for anisotropic features and heterogeneities of the tissue owing to different axon alignment. The novelty of the work is the correlation of the material mechanical anisotropy with fractional anisotropy (FA) from diffusion tensor images. Finite-element (FE) models are used to investigate the influence of the fibre distribution for different loading conditions. In the case of tensile–compressive loads, the comparison between experiments and simulations highlights the validity of the proposed FA–k correlation. Axon alignment affects the deformation predicted by FE models and, when the strain in the axonal direction is large with respect to the maximum principal strain, decreased maximum deformations are detected. It is concluded that the introduction of fibre dispersion information into the constitutive law of brain tissue affects the biofidelity of the simulations.     

High contrast ultrasound images of defects in food package seals

Previous work to detect defects in food packaging seals using pulse-echo ultrasound inspired the backscattered amplitude integral (BAI) imaging technique, which could reliably identify channels with diameters 38 mum or larger at a center frequency of 17.3 MHz (lambda=86 mum). The current study presents two new processing techniques that more reliably reveal smaller channels ( approximately 6 mum in diameter). The RF sampling technique (RFS) displays a single, time-gated, pressure value from the received (not envelope-detected) RF waveform at each transducer position. The RF correlation technique (RFC) calculates the correlation coefficients of the RF signals with a reference signal that does not pass through a channel. The correlation coefficient can be calculated for the entire RF signal (RFCE) or over a short segment of the RF signal (RFCS). The performance of these imaging methods for detecting channel defects is investigated for plastic and aluminum foil trilaminate films with 6, 10, 15, 38, and 50 mum channels filled with water or air. Data are collected with a focused ultrasound transducer (17.3 MHz, 6.35 mm in diameter, f/2, 173 mum -6 dB pulse-echo lateral beamwidth at the focus) scanned over a rectangular grid, keeping the package in the focus. Performance is measured using detection rates, image contrast, and contrast-to-noise ratio (CNR). Both RFS and RFCS have improved detection rates relative to BAI for channels 15 mum or smaller. The RFCS technique is the most effective at smoothing the background, leading to the greatest CNR improvements.     

The effect of ultrasound on the parameters of metal-dielectric-semiconductor structures

Data on the effect of ultrasound on the metal-oxide-semiconductor structures preliminary irradiated by γ-quanta are presented. It is demonstrated that the ultrasonic action results in a decrease of the radiation-induced charge in the dielectric layer of the structures under study. The observed effects are explained using a mechanism of the ultrasound-stimulated diffusion of radiation defects in the field of elastic stresses in the layer of silicon dioxide.     

WOLD decomposition of the backscatter echo in ultrasound images of soft tissue organs

Deals with a method of detecting and estimating the scatterer spacing between the regularly spaced resolvable coherent scatterers in tissue. Scatterer spacing has been successfully used in classifying tissue structure, in differentiating between normal and cirrhotic liver, and in detecting diffuse liver disease. This paper presents a WOLD decomposition of the radio frequency (RF) field into its diffused and coherent components from which maximum likelihood estimates (MLE) or minimum mean square error (MMSE) estimates of the scattering spacing are easily computed. The MLE are efficient and for relatively long record are unbiased. They result in accurate estimates in low signal-to-noise (SNR) ratios. Unfortunately, they require nonlinear minimization and knowledge of the probability density associated with the RF backscatter echo. The MMSE estimates, on the other hand, are computationally simple, yield unique closed form solutions, do not require a-priori knowledge of the probability distribution function of the backscatter echo, and result in accurate estimates in low SNR ratios. This paper also presents an unbiased decision rule to detect whether or not an RF echo exhibits any specular scattering relative to the wavelength of the interrogating ultrasonic pulse. The approach has been tried on simulations as well as on in-vivo scans of liver data, and appears to perform well.     

The effect of an electric field on the surface energy anisotropy in alkali metal alloys

The effect of an electric field on the surface energy anisotropy in alloys is considered for the first time with an allowance for the surface segregation.     

Superresolution of ultrasound images using the first and second harmonic signal

This paper presents a new method of blind two-dimensional (2-D) homomorphic deconvolution and speckle reduction applied to medical ultrasound images. The deconvolution technique is based on an improved 2-D phase unwrapping scheme for pulse estimation. The input images are decomposed into minimum-phase and allpass components. The 2-D phase unwrapping is applied only to the allpass component. The 2-D phase of the minimum-phase component is derived by a Hilbert transform. The accuracy of 2-D phase unwrapping is also improved by processing small (16 x 16 pixels) overlapping subimages separately. This takes the spatial variance of the ultrasound pulse into account. The deconvolution algorithm is applied separately to the first and second harmonic images, producing much sharper images of approximately the same resolution and different speckle patterns. Speckle reduction is made by adding the envelope images of the deconvolved first and second harmonic images. Neither the spatial resolution nor the frame rate decreases, as the common compounding speckle reduction techniques do. The method is tested on sequences of clinical ultrasound images, resulting in high-resolution ultrasound images with reduced speckle noise.     

The cross algorithm for phase-aberration correction in medical ultrasound images formed with two-dimensional arrays

Common-midpoint signals in the near-field signal-redundancy (NFSR) algorithm for one-dimensional arrays are acquired using three consecutive transducer elements. An all-row-plus-two-column algorithm has been proposed to implement the one-dimensional NFSR algorithm on two dimensional arrays. The disadvantage of this method is that its ambiguity profile is not linear and a timeconsuming iterative method has to be used to linearize the ambiguity profile. An all-row-plus-two-column-and-a-diagonal algorithm has also been proposed. Its ambiguity profile is linear, but it is very sensitive to noise and cannot be used. In this paper, a novel cross algorithm is proposed to implement the NFSR algorithm on two-dimensional arrays. In this algorithm, common-midpoint signals are acquired using four adjacent transducer elements, which is not available in one-dimensional arrays. Its advantage includes a linear ambiguity profile and a higher measurement signal-to-noise ratio. The performance of the cross algorithm is evaluated theoretically. The region of redundancy is analyzed. The procedure for deriving the phaseaberration profile from peak positions of cross-correlation functions between common-midpoint signals is discussed. This algorithm is tested with a simulated data set acquired with a two-dimensional array, and the result shows that the cross algorithm performs better than the all-row plus-twocolumn NFSR algorithm.