Free of speckle ultrasound images of small tissue structures

By using the Born approximation deconvolved inverse scattering method instead of the traditional pulse-echo method for analyzing ultrasound pulse reflections from plastic phantoms and soft tissue specimens, improvement in image resolution is shown to be possible provided these targets are fair approximations to layered media. These images are free of speckle and are more vivid than the usual pulse-echo images.     

Non-linear inverse scattering: high resolution quantitative breast tissue tomography

Recent published results in inverse scattering generally show the difficulty in dealing with moderate to high contrast inhomogeneities when employing linearized or iteratively linearized algorithms (e.g., distorted Born iterative method). This paper presents a fully nonlinear algorithm utilizing full wave field data, that results in ultrasound computed tomographic images from a laboratory breast scanner, and shows several such unique images from volunteer subjects. The forward problem, data collection process and inverse scattering algorithm used are discussed. A functional that represents the "best fit" between predicted and measured data is minimized, and therefore requires a very fast forward problem solver, Jacobian calculation, and gradient estimation, all of which are described. The data collection device is described. The algorithm and device yield quantitative estimates of human breast tissue in vivo. Several high resolution images, measuring ～150 by 150 wavelengths, obtained from the 2D inverse scattering algorithms, using data collected from a first prototype, are shown and discussed. The quantitative values are compared with previous published work.     

Distribution of backscattered intensity in the distorted Born approximation: Application to C-band SAR images of woodland

Abstract

The intensity distribution in synthetic aperture radar (SAR) images of woodland is known to depend upon imaging conditions. Whilst phenomenological models can be used to match observed backscatter distributions, a physical model is needed to explain their origins. Images of woodland obtained during airborne SAR trials are analysed and shown to exhibit non-exponential intensity distributions. Expressions are derived for the moments of the intensity distribution using discrete scattering models based on the Born and distorted Born approximations. The predictions of the Born approximation are such that, at all but extremely high resolutions, the intensity statistics reflect only fluctuations in the number of discrete scatterers in resolution cells. In the distorted Born approximation it is revealed that, even at modest resolutions, fluctuations in both number and cross section of objects can influence intensity distributions. This is shown to be a direct consequence of the incorporation of attenuation effects in the distorted Born model. The theory is applied to scattering from a model woodland canopy and shown to yield intensity moments in close agreement with observations. The consequences of the model for other scattering situations are discussed.     

In vivo biomicroscopy with ultrasound

We propose the use of inverse scattering theory methods to analyse high frequency ultrasound reflection data to provide high resolution images of living tissue. Conventional ultrasound imaging uses the pulse-echo method which can only resolve structures which are large compared to the wavelength of the ultrasound. Inverse scattering analysis, on the other hand, can image details as small as a quarter wavelength. This makes possible a significant improvement in resolution and has many potential applications in the detection and study of disease. We report here results obtained using this method to produce images of the retina, where we were able to resolve details as small as 50 micron in a 300 micron layer.     

An extended Rytov approximation and its significance for remote sensing and inverse scattering

The Born approximation has been shown by Wolf to be particularly convenient for formulating inverse scattering problems. The Rytov approximation is known to be more widely applicable than the Born approximation. We introduce an improvement that further increases the range of validity of the Rytov approximation. It transpires that our extension of the Rytov approximation is as convenient for inverse scattering as the Born approximation.     

Shadow effects in simulated ultrasound images derived from computed tomography images using a focused beam tracing model

Simulation of ultrasound images based on computed tomography (CT) data has previously been performed with different approaches. Shadow effects are normally pronounced in ultrasound images, so they should be included in the simulation. In this study, a method to capture the shadow effects has been developed, which makes the simulated ultrasound images appear more realistic. The method using a focused beam tracing model gives diffuse shadows that are similar to the ones observed in measurements on real objects. Ultrasound images of a cod (Gadus morhua) were obtained with a BK Medical 2202 ProFocus ultrasound scanner (BK Medical, Herlev, Denmark) equipped with a dedicated research interface giving access to beamformed radio frequency data. CT images were obtained with an Aquilion ONE Toshiba CT scanner (Toshiba Medical Systems Corp., Tochigi, Japan). CT data were mapped from Hounsfield units to backscatter strength, attenuation coefficients, and characteristic acoustic impedance. The focused beam tracing model was used to create maps of the transmission coefficient and scattering strength maps. Field II was then used to simulate an ultrasound image of 38.9 × 55.3 × 4.5 mm, using 10(6) point scatterers. As there is no quantitative method to assess quality of a simulated ultrasound image compared to a measured one, visual inspection was used for evaluation.     

Calculation of acoustic scattering of a nonrigid surface using physical acoustic method

In this paper the physical acoustic method or the Kirchhoff approxima-tion is extended to treat the scattering of a nonrigid surface in order to estimatethe target strength of targets with absorbing coatings.By using the locally planewave approximation,the relationship between the sound pressure and its normalderivative on the surface can be represented by the plane wave reflectioncoefficient and the acoustic impedance of the surface.The resulting modifiedKirchhoff approximation involves the plane wave reflection coefficient.For aimpedance sphere,a comparison between the physical acoustic method and theexact solution shows that the physical acoustic method still is a good approxima-tion at higher κα values.     

On multidimensional ultrasonic scattering in an inhomogeneous elastic background.

This work is concerned with the modeling of elastic wave scattering by solid or fluid-filled objects embedded in an inhomogeneous elastic background. The medium is probed by a monochromatic force and the scattered field is computed (forward problem) or observed (inverse problem) at some known receiver locations. Based on vector integral equations for elastic scattering, a general framework is developed, independent of both the problem geometry and the transmitter-receiver characteristics. This framework encompasses both forward and inverse modeling. In the forward model, a Born approximation for an inhomogeneous background is applied to obtain a closed form expression for the scattered field. In the inverse model, this approximation is also invoked to linearize for the multiparameter characteristic of the object. Finally, an iterative inversion scheme alternating forward and inverse modeling is proposed to improve the resolution and accuracy of the reconstruction algorithm.     

Three-dimensional impedance map analysis of rabbit liver

Three-dimensional impedance maps (3DZMs) are computational models of acoustic impedance of tissue constructed from histology images. 3DZMs can be analyzed to estimate model-based quantitative ultrasound parameters such as effective scatterer diameter (ESD). In this study, 3DZMs were constructed from normal and fatty rabbit livers. Estimates of ESD were made using the fluid-filled sphere scattering model. Weighting toward smaller scatterer sizes produced ESD estimates of 7.5 ± 1.3 and 7.0 ± 0.3 μm for normal and fatty liver, respectively, approximately the size of a liver cell nucleus. This suggests the nucleus could be a primary source of scattering in liver.     

Finite element analysis of broadband acoustic pulses through inhomogenous media with power law attenuation

Acoustic waves in tissues and weakly attenuative fluids often have an attenuation parameter, alpha(omega), satisfying alpha(omega)= alpha0omegay in which alpha0 is a constant, omega is the frequency, and y is between 1 and 2. This power law attenuation is not predicted by the classical thermoviscous wave equation and researchers have proposed different modified viscous wave equations in which the loss term is a convolution operator or a fractional spatial or temporal derivative. In this paper, acoustic waves undergoing power law attenuation are modeled by a modification to the thermoviscous wave equation in which the time derivative of the viscous term is replaced by a fractional time derivative. An explicit time domain, finite element formulation leads to a stable algorithm capable of simulating axisymmetric, broadband acoustic pulses propagating through attenuative and dispersive media. The algorithm does not depend on the Born approximation, long wavelength limit, or plane wave assumptions. The algorithm is validated for planar and focused transducers and results include radiation patterns from a viscous scatterer in a lossless background and signals reflected from a viscous layer. The program can be used to determine scattering parameters for large, strong, possibly viscous scatterers, in either a lossless or viscous background, for which analytic results are scarce.     

Tissue self-affinity and polarized light scattering in the born approximation: a new model for precancer detection

Light scattered from biological tissues can exhibit an inverse power law spectral component. We develop a model based on the Born approximation and von Karman (self-affine) spatial correlation of submicron tissue refractive index to account for this. The model is applied to light scattering spectra obtained from excised esophagi of normal and carcinogen-treated rats. Power law exponents used to fit dysplastic tissue site spectra are significantly smaller than those from normal sites, indicating that changes in tissue self-affinity can serve as a potential biomarker for precancer.     

Quantitative ultrasound brain imaging with multiscale deconvolutional waveform inversion

High-resolution images of human brain are critical for monitoring the neurological conditions in a portable and safe manner. Sound speed mapping of brain tissues provides unique information for such a purpose. In addition, it is particularly important for building digital human acoustic models, which form a reference for future ultrasound research. Conventional ultrasound modalities can hardly image the human brain at high spatial resolution inside the skull due to the strong impedance contrast between hard tissue and soft tissue. We carry out numerical experiments to demonstrate that the time-domain waveform inversion technique, originating from the geophysics community, is promising to deliver quantitative images of human brains within the skull at a sub-millimeter level by using ultra-sound signals. The successful implementation of such an approach to brain imaging requires the following items: signals of sub-megahertz frequencies transmitting across the inside of skull, an accurate numerical wave equation solver simulating the wave propagation, and well-designed inversion schemes to reconstruct the physical parameters of targeted model based on the optimization theory. Here we propose an innovative modality of multiscale deconvolutional waveform inversion that improves ultrasound imaging resolution, by evaluating the similarity between synthetic data and observed data through using limited length Wiener filter. We implement the proposed approach to iteratively update the parametric models of the human brain. The quantitative imaging method paves the way for building the accurate acoustic brain model to diagnose associated diseases, in a potentially more portable, more dynamic and safer way than magnetic resonance imaging and x-ray computed tomography.     

Reconstructing the adhesion stiffness distribution in a laminated elastic plate: Exact and approximate inverse scattering solutions

This paper formulates and solves a time harmonic inverse scattering problem to reconstruct the effective stiffness distribution of an adhesive bond in a layered elastic plate. The motivation is based on the assumption that localized adhesion flaws that diminish bond stiffness also tend to diminish bond strength. The formulation is based on the invariant imbedding method, applies to isotropic and anisotropic elastic layers, and is essentially that of identifying embedded acoustic sources in elastic layered structures. This paper presents two solutions for the inverse problem: the Born approximation and the exact solution. The example calculations compare the two solutions and show that when imperfections are too large in either magnitude or extent the accuracy of the Born approximation breaks down. The impact of noise and uncertainties in the background properties in the inversion is also investigated. A regularization strategy is introduced in the exact solution that controls solution sensitivity in regions with low signal to noise ratio.     

Three-dimensional modeling of acoustic backscattering from fluid-like zooplankton

Scattering models that correctly incorporate organism size and shape are a critical component for the remote detection and classification of many marine organisms. In this work, an acoustic scattering model has been developed for fluid-like zooplankton that is based on the distorted wave Born approximation (DWBA) and that makes use of high-resolution three-dimensional measurements of the animal's outer boundary shape. High-resolution computerized tomography (CT) was used to determine the three-dimensional digitizations of animal shape. This study focuses on developing the methodology for incorporating high-resolution CT scans into a scattering model that is generally valid for any body with fluid-like material properties. The model predictions are compared to controlled laboratory measurements of the acoustic backscattering from live individual decapod shrimp. The frequency range used was 50 kHz to 1 MHz and the angular characteristics of the backscattering were investigated with up to a 1 degree angular resolution. The practical conditions under which it is necessary to make use of high-resolution digitizations of shape are assessed.     

Contrast harmonic imaging

The behavior of ultrasound contrast agents depends highly on the acoustic pressure of the insonified ultrasound wave. For low pressure the expansion and compression is linear to the pressure, for medium acoustic pressure nonlinear behavior starts to occur and for high pressures, but still in the diagnostic range transient scattering can be noticed, resulting in an enhanced scattering followed by a disappearance of the bubble. The nonlinear and transient regime can be utilized for imaging of the contrast agent in or nearby tissue. The magnitude of the nonlinear signal from the contrast has to compete with the nonlinear component of the ultrasound wave, which is generated during propagation. It is shown that contrast is superior to tissue when using low frequencies and imaging the third or fourth harmonic of the transmitted frequency.     

The scattering of ultrasound by cylinders: implications for diffraction tomography

The validity of wave equations employed as system models in acoustical diffraction tomography is investigated using simulations and measurements of the scattering of plane ultrasound waves by cylinders. It is demonstrated by simulation and experiment that it can be appropriate to neglect density fluctuations and shear waves, implying that the commonly used form of the wave equation suitably describes scattering by fluctuations of acoustic speed and absorption. Diffraction tomographic reconstructions of simulated data reveal the importance of absorption, the behavior of the real and imaginary parts of the reconstructed refractive index, and the relative advantages and limitations of the Born and Rytov approximate transformations.     

A systematic comparison between born approximation and distorted wave Born approximation for inelastic electron scattering

The correction factors for Coulomb effects in inelastic electron scattering are given for electric quadrupole transitions. The cross sections in Born approximation and distorted wave Born approximation are calculated in the liquid drop model for electron energies between 20 and 80 MeV and nuclei up toZ=26.     

Model for continuously scanning ultrasound vibrometer sensing displacements of randomly rough vibrating surfaces

An analytic model is developed for the time-dependent ultrasound field reflected off a randomly rough vibrating surface for a continuously scanning ultrasound vibrometer system in bistatic configuration. Kirchhoff's approximation to Green's theorem is applied to model the three-dimensional scattering interaction of the ultrasound wave field with the vibrating rough surface. The model incorporates the beam patterns of both the transmitting and receiving ultrasound transducers and the statistical properties of the rough surface. Two methods are applied to the ultrasound system for estimating displacement and velocity amplitudes of an oscillating surface: incoherent Doppler shift spectra and coherent interferometry. Motion of the vibrometer over the randomly rough surface leads to time-dependent scattering noise that causes a randomization of the received signal spectrum. Simulations with the model indicate that surface displacement and velocity estimation are highly dependent upon the scan velocity and projected wavelength of the ultrasound vibrometer relative to the roughness height standard deviation and correlation length scales of the rough surface. The model is applied to determine limiting scan speeds for ultrasound vibrometer measuring ground displacements arising from acoustic or seismic excitation to be used in acoustic landmine confirmation sensing.     

Modification to first-order Born approximation for improved prediction of scattered sound from weakly scattering objects

When deriving the Fourier diffraction theorem based on the first-order Born approximation,the difference between wave number of the scattering object and that of the surrounding medium is ignored,causing substantial errors in sound scattering prediction.This paper modifies the Born approximation by taking into account the amplitude and phase changes between the scattering object and the water due to the wave number difference.By changing the radius and center position of the sampling circle in the Fourier domain,accuracy of the predicted sound scattering is improved.With the modified Born approximation,the computed far-field directional pattern of the scattered sound from a circular cylinder is in good agreement with the rigorous solution.Numerical calculations for several objects with different shapes are used to show applicability and effectiveness of the proposed method.     

Scatterer size estimation in pulse-echo ultrasound using focused sources: theoretical approximations and simulation analysis

The speckle in ultrasound images has long been thought to contain information related to the tissue microstructure. Many different investigators have analyzed the frequency characteristics of the backscattered signals to estimate the scatterer acoustic concentration and size. Previous work has been mostly restricted to unfocused or weakly focused ultrasound sources, thus limiting its implementation with diagnostically relevant fields. Herein, we derive equations capable of estimating the size of a scatterer for any reasonably focused source provided that the velocity potential field in the focal region can be approximated as a three-dimensional Gaussian beam, scatterers are a sufficient distance from the source, and the field is approximately constant across the scatterer. The calculations show that, when estimating the scatterer size, correcting for focusing requires a generalized attenuation-compensation function that includes both attenuation and focusing along the beam axis. The Gaussian approximation is validated by comparing the ideal velocity potential field for three spherically focused sources with f-numbers of 1, 2, and 4 to the Gaussian approximation for frequencies from 2 to 14 MHz. The theoretical derivations are evaluated by simulating the backscatter by using spherically focused sources (f-numbers of 1, 2, and 4) adjacent to attenuating media (0.05 to 1 dB/cm/MHz) that contain scatterers with Gaussian impedance distributions. The generalized attenuation-compensation function yielded results accurate to 7.2% while the traditional attenuation-compensation functions that neglected focusing had errors as high as 103%.