Fast ultrasound imaging simulation in K-space

Most available ultrasound imaging simulation methods are based on the spatial impulse response approach. The execution speed of such a simulation is of the order of days for one heart-sized frame using desktop computers. For some applications, the accuracy of such rigorous simulation approaches is not necessary. This work outlines a much faster 3-D ultrasound imaging simulation approach that can be applied to tasks like simulating 3-D ultrasound images for speckle-tracking. The increased speed of the proposed simulation method is based primarily on the approximation that the point spread function is set to be spatially invariant, which is a reasonably good approximation when using polar coordinates for simulating images from phased arrays with constant aperture. Ultrasound images are found as the convolution of the PSF and an object of sparsely distributed scatterers. The scatterers are passed through an anti-aliasing filter before insertion into a regular beam-space grid to reduce the bandwidth and significantly reduce the amount of data. A comparison with the well-established simulation software package field II has been made. A simulation of a cyst image using the same input object was found to be in the order of 7000 times slower than the presented method. Following these considerations, the proposed simulation method can be a rapid and valuable tool for working with 3-D ultrasound imaging and in particular 3-D speckle-tracking.     

FEM/BEM for simulation of LSAW devices

This paper presents a modeling of the propagation of surface acoustic, leaky acoustic, and surface skimming bulk waves in piezoelectrics with a finite array of metallic electrodes over their surface. A combined method of matrix Green's function and the finite element method for computation of all acoustic wave fields is an effective tool for simulation of the propagation of acoustic waves in such structures. The proposed method is optimized in the speed of computation of all matrix Green's function components originally obtained. The Fourier transformations of Green's function from kappa-space domain to real space domain are performed by combined trapezoidal and Filon's integration methods for rapidly oscillating functions. The trapezoidal integration method is used on a distance from a point source from zero to a few wavelengths long, but the other has the advantage for a distance from some wavelength to infinity. That allows one, by selectively condensing computation grids around branch and singular points of the sharp behavior of Green's function, to maximize speed and accuracy of computation of integrals. FEM is used, modified originally to achieve acceleration without loss accuracy. Because of the simple geometry of the electrodes, unknown elastic fields are presented as a series of known eigenfunctions with unknown coefficients over the whole region of electrodes. All unknown coefficients are determined by applying the Galerkin method. There is good agreement between numerical and experimental conductances of acoustic wave transducers on materials such as lithium niobate and lithium tantalate.     

Toward a real-time simulation of ultrasound image sequences based on a 3-D set of moving scatterers

Data simulation is an important research tool to evaluate algorithms. Two types of methods are currently used to simulate medical ultrasound data: those based on acoustic models and those based on convolution models. The simulation of ultrasound data sequences is very time-consuming. In addition, many applications require accounting for the out-ofplane motion induced by the 3-D displacement of scatterers. The purpose of this paper is to propose a model adapted to a fast simulation of ultrasonic data sequences with 3-D moving scatterers. Our approach is based on the convolution model. The scatterers are moved in a 3-D continuous medium between each pair of images and then projected onto the imaging plane before being convolved. This paper discusses the practical implementation of the convolution that can be performed directly or after a grid approximation. The grid approximation convolution is obviously faster than the direct convolution but generates errors resulting from the approximation to the grid?s nodes. We provide the analytical expression of these errors and then define 2 intensity-based criteria to quantify them as a function of the spatial sampling. The simulation of an image requires less than 2 s with oversampling, thus reducing these errors. The simulation model is validated with first- and second-order statistics. The positions of the scatterers at each imaging time can be provided by a displacement model. An example applied to flow imaging is proposed. Several cases are used to show that this displacement model provides realistic data. It is validated with speckle tracking, a well-known motion estimator in ultrasound imaging.     

Quantitative flaw reconstruction from ultrasonic surface wavefields measured by electronic speckle pattern interferometry

A new method for imaging flaws in plate and shell structures is presented. The method employs two-dimensional ultrasonic surface wave data obtained by optical electronic speckle pattern interferometry (ESPI) techniques. In the imaging method, the measured out-of-plane displacement field associated with an externally excited ultrasonic Lamb wave is processed to obtain the spatial frequency domain spectrum of the wavefield. A free space Green's function is then deconvolved from the wavefield to obtain quantitative images of effective scattering sources. Because the strength of these effective sources is directly dependent on local variations in sample thickness and material properties, these images provide a direct map of internal inhomogeneities. Simulation results show that the method accurately images flaws for a wide range of sizes and material contrast ratios. These results also demonstrate that flaw features much smaller than an acoustic wavelength can be imaged, consistent with the theoretical capability of the imaging method to employ scattered evanescent waves. Reconstructions are also obtained from ultrasonic Lamb wave displacement fields recorded by ESPI in a flawed aluminum plate. These reconstructions indicate that the present method has potential for imaging flaws in complex structures for which ESPI wavefield measurements cannot be straightforwardly interpreted     

Surface Green's function of a piezoelectric half-space

The computation of the two-dimensional harmonic spatial-domain Green's function at the surface of a piezoelectric half-space is discussed. Starting from the known form of the Green's function expressed in the spectral domain, the singular contributions are isolated and treated separately. It is found that the surface acoustic wave contributions (i.e., poles in the spectral Green's function) give rise to an anisotropic generalization of the Hankel function H0(2), the spatial Green's function for the scalar two-dimensional wave equation. The asymptotic behavior at infinity and at the origin (for the electrostatic contribution) also are explicitly treated. The remaining nonsingular part of the spectral Green's function is obtained numerically by a combination of fast Fourier transform and quadrature. Illustrations are given in the case of a substrate of Y-cut lithium niobate.     

Green's function method in the radiative transfer problem. II. Spatially heterogeneous anisotropic surface

The most recent theoretical studies have shown that three-dimensional (3-D) radiation effects play an important role in the optical remote sensing of atmospheric aerosol and land surface reflectance. These effects may contribute notably to the error budget of retrievals in a broad range of sensor resolutions, introducing systematic biases in the land surface albedo data sets that emerge from the existing global observation systems. At the same time, 3-D effects are either inadequately addressed or completely ignored in data processing algorithms. Thus there is a need for further development of the radiative transfer theory that can rigorously treat both 3-D and surface anisotropy effects and yet be flexible enough to permit the development of fast forward and inversion algorithms. We describe a new theoretical solution to the 3-D radiative transfer problem with an arbitrary nonhomogeneous non-Lambertian surface. This solution is based on an exact semianalytical solution derived in operator form by the Green's function method. The numerical implementation is based on several parameterizations that accelerate the solution dramatically while keeping its accuracy within several percent under most general conditions.     

Extended high-frame rate imaging method with limited-diffraction beams

Fast three-dimensional (3-D) ultrasound imaging is a technical challenge. Previously, a high-frame rate (HFR) imaging theory was developed in which a pulsed plane wave was used in transmission, and limited-diffraction array beam weightings were applied to received echo signals to produce a spatial Fourier transform of object function for 3-D image reconstruction. In this paper, the theory is extended to include explicitly various transmission schemes such as multiple limited-diffraction array beams and steered plane waves. A relationship between the limited-diffraction array beam weighting of received echo signals and a 2-D Fourier transform of the same signals over a transducer aperture is established. To verify the extended theory, computer simulations, in vitro experiments on phantoms, and in vivo experiments on the human kidney and heart were performed. Results show that image resolution and contrast are increased over a large field of view as more and more limited-diffraction array beams with different parameters or plane waves steered at different angles are used in transmissions. Thus, the method provides a continuous compromise between image quality and image frame rate that is inversely proportional to the number of transmissions used to obtain a single frame of image. From both simulations and experiments, the extended theory holds a great promise for future HFR 3-D imaging.     

Adaptive fast multipole boundary element method for three-dimensional half-space acoustic wave problems

A new adaptive fast multipole boundary element method (BEM) for solving 3-D half-space acoustic wave problems is presented in this paper. The half-space Green's function is employed explicitly in the boundary integral equation (BIE) formulation so that a tree structure of the boundary elements only for the boundaries of the real domain need to be applied, instead of using a tree structure that contains both the real domain and its mirror image. This procedure simplifies the implementation of the adaptive fast multipole BEM and reduces the CPU time and memory storage by about a half for large-scale half-space problems. An improved adaptive fast multipole BEM is presented for the half-space acoustic wave problems, based on the one developed recently for the full-space problems. This new fast multipole BEM is validated using several simple half-space models first, and then applied to model 3-D sound barriers and a large-scale windmill model with five turbines. The largest BEM model with 557470 elements was solved in about an hour on a desktop PC. The accuracy and efficiency of the BEM results clearly show the potential of the adaptive fast multipole BEM for solving large-scale half-space acoustic wave problems that are of practical significance.     

High frequency ultrasound imaging with optical arrays

Dynamically focused and steered high frequency ultrasound imaging systems require arrays with fine element spacing, wide bandwidths, and large apertures. However, these characteristics are difficult to achieve at frequencies greater than 30 MHz using conventional array construction methods. Optical schemes offer a solution. Focused laser beams incident on a suitable surface can generate and detect acoustic radiation. Precisely controlling the position and size of the beams defines points of transmission and detection, making it possible for pulse-echo image formation by synthetic aperture methods. An optical detection array was built, relying on a conventional piezoelectric transducer as an ultrasound source. The detection system, with near optimal resolution over a wide depth of field, demonstrates the potential for high frequency array implementation using optical techniques. A possible application is in pathology, where 2-D or 3-D fine resolution pulse-echo imaging can be performed in situ without the need for biopsies.     

Fast characterization of aluminum plates with TV-holography measurements of the frequency spectrum of multimode, quasi- monochromatic Lamb waves

We introduce a novel approach for measuring the frequency spectrum of Lamb waves and, subsequently, for obtaining the thickness and the bulk wave velocities of isotropic, homogeneous plates. It is based on Fourier transforming a set of spatial and temporal samples of the acoustic displacement but, in contrast to the traditional approach that employs dense temporal sampling and a reduced set of spatial sampling locations, our data set is a sequence of 2-D high-resolution maps of the instantaneous out-of-plane displacement obtained with TV holography. We have devised three variants to obtain a set of points of the wavenumber-frequency space, based, respectively, on the spatial (1-D or 2-D) and on the spatio-temporal (3-D) Fourier transforms. The whole process to obtain these points can be easily automated and substantial time savings can be achieved, compared with other full-field techniques that require human intervention or with pointwise scanned probes. Experimental demonstration of the three variants with quasimonochromatic multimode Lamb waves in aluminum plates is presented. The characteristic parameters of the plates are calculated by fitting the theoretical model to the experimental points of the frequency spectrum. The analysis of the uncertainties shows that the accuracy of the method is only slightly lower than the accuracy of a previously reported method based on measuring the wavelength of single-modes, for which the data acquisition procedure is much slower.     

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.     

Fast ultrasound beam prediction for linear and regular two-dimensional arrays

Real-time beam predictions are highly desirable for the patient-specific computations required in ultrasound therapy guidance and treatment planning. To address the longstanding issue of the computational burden associated with calculating the acoustic field in large volumes, we use graphics processing unit (GPU) computing to accelerate the computation of monochromatic pressure fields for therapeutic ultrasound arrays. In our strategy, we start with acceleration of field computations for single rectangular pistons, and then we explore fast calculations for arrays of rectangular pistons. For single-piston calculations, we employ the fast near-field method (FNM) to accurately and efficiently estimate the complex near-field wave patterns for rectangular pistons in homogeneous media. The FNM is compared with the Rayleigh-Sommerfeld method (RSM) for the number of abscissas required in the respective numerical integrations to achieve 1%, 0.1%, and 0.01% accuracy in the field calculations. Next, algorithms are described for accelerated computation of beam patterns for two different ultrasound transducer arrays: regular 1-D linear arrays and regular 2-D linear arrays. For the array types considered, the algorithm is split into two parts: 1) the computation of the field from one piston, and 2) the computation of a piston-array beam pattern based on a pre-computed field from one piston. It is shown that the process of calculating an array beam pattern is equivalent to the convolution of the single-piston field with the complex weights associated with an array of pistons. Our results show that the algorithms for computing monochromatic fields from linear and regularly spaced arrays can benefit greatly from GPU computing hardware, exceeding the performance of an expensive CPU by more than 100 times using an inexpensive GPU board. For a single rectangular piston, the FNM method facilitates volumetric computations with 0.01% accuracy at rates better than 30 ns per field point. Furthermore, we demonstrate array calculation speeds of up to 11.5 X 10(9) field-points per piston per second (0.087 ns per field point per piston) for a 512-piston linear array. Beam volumes containing 256(3) field points are calculated within 1 s for 1-D and 2-D arrays containing 512 and 20(2) pistons, respectively, thus facilitating future real-time thermal dose predictions.     

Phase-aberration correction with a 3-D ultrasound scanner: feasibility study

We tested the feasibility of using adaptive imaging, namely phase-aberration correction, with two-dimensional (2-D) arrays and real-time, 3-D ultrasound. Because of the high spatial frequency content of aberrators, 2-D arrays, which generally have smaller pitch and thus higher spatial sampling frequency, and 3-D imaging show potential to improve the performance of adaptive imaging. Phase-correction algorithms improve image quality by compensating for tissue-induced errors in beamforming. Using the illustrative example of transcranial ultrasound, we have evaluated our ability to perform adaptive imaging with a real-time, 3-D scanner. We have used a polymer casting of a human temporal bone, root-mean-square (RMS) phase variation of 45.0 ns, full-width-half-maximum (FWHM) correlation length of 3.35 mm, and an electronic aberrator, 100 ns RMS, 3.76 mm correlation, with tissue phantoms as illustrative examples of near-field, phase-screen aberrators. Using the multilag, least-squares, cross-correlation method, we have shown the ability of 3-D adaptive imaging to increase anechoic cyst identification, image brightness, contrast-to-speckle ratio (CSR), and, in 3-D color Doppler experiments, the ability to visualize flow. For a physical aberrator skull casting we saw CSR increase by 13% from 1.01 to 1.14, while the number of detectable cysts increased from 4.3 to 7.7.     

结合横向振荡和空间正交的向量血流速度测量

传统的彩色多普勒成像只能测量与超声波束平行的血流速度分量,且依赖于超声波束与血管之间的夹角。超声向量血流成像是一种更加先进的血流成像技术,该方法可以直接获得血流速度的实际大小和方向,因此不依赖于超声波束与血管之间的夹角。本文从向量血流测量方法之一的横向声场法入手,简要概括了横向振荡(Transverse Oscillation, TO)法和空间正交(Spatial Quadrature, SQ)法两种方法的基本原理、成像过程及各自的优缺点,并提出了一种互相结合的方法,即奇偶振荡法(Odd Even Oscillation, OEO),该方法利用SQ法快速进行波束合成,利用TO法计算最终的速度矢量,克服了TO法和SQ法各自的缺点,能够有效解决TO法成像计算量大以及SQ法出现混叠和对噪声灵敏度高的问题。     

Three-dimensional imaging based on Gray-code light projection: characterization of the measuring algorithm and development of a measuring system for industrial applications

A three-dimensional (3-D) imaging system based on Gray-code projection is described; it is thought to be used as an integration to the already developed profilometer based on the projection of multifrequency gratings. The Gray-code method allows us to evaluate the 3-D profile of objects that present even marked discontinuities of the surface, thus increasing the flexibility of the measuring system as to the topology of the objects that can be measured. The basic aspects of Gray-code projection for 3-D imaging and profiling are discussed, with particular emphasis devoted to the study of the resolution of the method and to the analysis of the systematic errors. The results of this study allow us to determine the optimal setting of the parameters of the measurement and to develop a suitable calibration procedure. The procedures for implementing the Gray-code method are presented, and some interesting experimental results are reported. Calibration of the system reveals an accuracy of 0.2 mm, corresponding to 0.1% of the field of view.     

Numerical study of the spectral 3-D green's function singularities for piezoelectric SAW components

This article deals with the numerical study of the singularities appearing in the spectral 3-D Green's function associated with the piezoelectric surface acoustic wave components (so-called SAW components). These electrical units are currently used today in several devices produced by the telecommunications industry (radio, TV, radar, and digital telecommunication systems). The need to improve their performance has motivated engineers and researchers to use mathematical modeling intensively, in particular the integral equations technique here used, which requires the computing of the associated Green's function and the study of its properties.     

Two-dimensional ultrasound receive array using an angle-tuned Fabry-Perot polymer film sensor for transducer field characterization and transmission ultrasound imaging

A 2-D optical ultrasound receive array has been investigated. The transduction mechanism is based upon the detection of acoustically induced changes in the optical thickness of a thin polymer film acting as a Fabry-Perot sensing interferometer (FPI). By illuminating the sensor with a large-area laser beam and mechanically scanning a photodiode across the reflected output beam, while using a novel angle-tuned phase bias control system to optimally set the FPI working point, a notional 2-D ultrasound array was synthesized. To demonstrate the concept, 1-D and 2-D ultrasound field distributions produced by planar 3.5-MHz and focused 5-MHz PZT ultrasound transducers were mapped. The system was also evaluated by performing transmission ultrasound imaging of a spatially calibrated target. The "array" aperture, defined by the dimensions of the incident optical field, was elliptical, of dimensions 16 x 12 mm and spatially sampled in steps of 0.1 mm or 0.2 mm. Element sizes, defined by the photodiode aperture, of 0.8, 0.4, and 0.2 mm were variously used for these experiments. Two types of sensor were evaluated. One was a discrete 75-microm-thick polyethylene terephthalate FPI bonded to a polymer backing stub which had a wideband peak noise-equivalent pressure of 6.5 kPa and an acoustic bandwidth 12 MHz. The other was a 40-microm Parylene film FPI which was directly vacuum-deposited onto a glass backing stub and had an NEP of 8 kPa and an acoustic bandwidth of 17.5 MHz. It is considered that this approach offers an alternative to piezoelectric ultrasound arrays for transducer field characterization, transmission medical and industrial ultrasound imaging, biomedical photoacoustic imaging, and ultrasonic nondestructive testing.     

The Green's Function for the Two-Dimensional Helmholtz Equation in Periodic Domains

Analytical techniques are described for transforming the Green's function for the two-dimensional Helmholtz equation in periodic domains from the slowly convergent representation as a series of images into forms more suitable for computation. In particular methods derived from Kummer's transformation are described, and integral representations, lattice sums and the use of Ewald's method are discussed. Green's functions suitable for problems in parallel-plate acoustic waveguides are also considered and numerical results comparing the accuracy of the various methods are presented.