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.     

Multi-parameter acoustic imaging of uniform objects in inhomogeneous soft tissue

The problem studied in this paper is ultrasound image reconstruction from frequency-domain measurements of the scattered field from an object with contrast in attenuation and sound speed. The case in which the object has uniform but unknown contrast in these properties relative to the background is considered. Background clutter is taken into account in a physically realistic manner by considering an exact scattering model for randomly located small scatterers that vary in sound speed. The resulting statistical characteristics of the interference are incorporated into the imaging solution, which includes application of a total-variation minimization-based approach in which the relative effect of perturbation in sound speed to attenuation is included as a parameter. Convex optimization methods provide the basis for the reconstruction algorithm. Numerical data for inversion examples are generated by solving the discretized Lippman-Schwinger equation for the object and speckle-forming scatterers in the background. A statistical model based on the Born approximation is used for reconstruction of the object profile. Results are presented for a two-dimensional problem in terms of classification performance and compared with minimum-l2-norm reconstruction. Classification using the proposed method is shown to be robust down to a signal-to-clutter ratio of less than 1 dB.     

Three-dimensional ultrasound imaging system for prostate cancerdiagnosis and treatment

Prostate cancer is the most commonly diagnosed cancer in men in North America. Although two-dimensional (2-D) transrectal ultrasound imaging is widely used for the evaluation of prostate disease, it suffers from limitations that limit its use in diagnosis and therapy of prostate cancer. The use of conventional ultrasound requires that the diagnosticians mentally integrate a series of 2-D images in order to develop an impression of the three-dimensional (3-D) anatomy, and to estimate the volume of the prostate. This approach depends of the expertise of the physician resulting in variability. We have developed a 3-D ultrasound imaging approach that overcomes this problem. In this paper, we describe a 3-D ultrasound imaging system for use in prostate imaging and report on its performance. The system consists of a conventional ultrasound machine, a microcomputer with a video frame grabber, and a custom-built assembly for rotating the ultrasound transducer. A typical scan of 100 2-D B-mode images takes 8 s. These images are then reconstructed into a 3-D image, which can be displayed and interactively manipulated using 3-D visualization software. We also show that manual planimetry of prostates in the 3-D images can be used to estimate volumes in vitro with an accuracy of 2.6%, and a precision of 2.5%; and in vivo with 5.1% intra-observer variability and 11.4% interobserver variability. Thus, 3-D ultrasound imaging overcomes some of the limitations of conventional imaging of the prostate, and has great potential as a tool in the diagnosis and treatment of prostate disease     

Synthetic aperture focusing for a single-element transducer undergoing helical motion

This paper describes the application of 3-D synthetic aperture focusing (SAF) to a single-element trans-rectal ultrasound transducer. The transducer samples a 3-D volume by simultaneous rotation and translation, giving a helical motion. Two different 3-D SAF methods are investigated, a direct and a two-step approach. Both methods perform almost identically for simulated scatterers and give a significant improvement in azimuth resolution and a constant resolution in elevation. Side lobes below -60 dB are achievable for both methods. Validation of the method is achieved by scanning a simple wire phantom and a complex phantom containing wires in azimuth and elevation. The simple wire phantom shows the same results as that found through simulation. The complex phantom shows simultaneous focusing in azimuth and elevation for the wire scatterers. Consideration of the processing requirements for both 3-D SAF methods shows that the two-step approach can give equivalent performance using an order of magnitude fewer calculations. This reduction requires a temporary storage of 9.1 GB of data for the investigated setup.     

Three-dimensional multiexcitation magnetoacoustic tomography with magnetic induction

Magnetoacoustic tomography with magnetic induction (MAT-MI) is a hybrid imaging modality proposed to image electrical conductivity contrast of biological tissue with high spatial resolution. This modality combines magnetic excitations with ultrasound detection through the Lorentz force based coupling mechanism. However, previous studies have shown that MAT-MI method with single type of magnetic excitation can only reconstruct the conductivity boundaries of a sample. In order to achieve more complete conductivity contrast reconstruction, we proposed a multiexcitation MAT-MI approach. In this approach, multiple magnetic excitations using different coil configurations are applied to the object sequentially and ultrasonic signals corresponding to each excitation are collected for conductivity image reconstruction. In this study, we validate the new multiexcitation MAT-MI method for three-dimensional (3D) conductivity imaging through both computer simulations and phantom experiments. 3D volume data are obtained by utilizing acoustic focusing and cylindrical scanning under each magnetic excitation. It is shown in our simulation and experiment results that with a common ultrasound probe that has limited bandwidth we are able to correctly reconstruct the 3D relative conductivity contrast of the imaging object. As compared to those conductivity boundary images generated by previous single-excitation MAT-MI, the new multiexcitation MAT-MI method provides more complete conductivity contrast reconstruction, and therefore, more valuable information in possible clinical and research applications.     

Optical tomographic image reconstruction from ultrafast time-sliced transmission measurements

Optical imaging and localization of objects inside a highly scattering medium, such as a tumor in the breast, is a challenging problem with many practical applications. Conventional imaging methods generally provide only two-dimensional (2-D) images of limited spatial resolution with little diagnostic ability. Here we present an inversion algorithm that uses time-resolved transillumination measurements in the form of a sequence of picosecond-duration intensity patterns of transmitted ultrashort light pulses to reconstruct three-dimensional (3-D) images of an absorbing object located inside a slab of a highly scattering medium. The experimental arrangement used a 3-mm-diameter collimated beam of 800-nm, 150-fs, 1-kHz repetition rate light pulses from a Ti:sapphire laser and amplifier system to illuminate one side of the slab sample. An ultrafast gated intensified camera system that provides a minimum FWHM gate width of 80 ps recorded the 2-D intensity patterns of the light transmitted through the opposite side of the slab. The gate position was varied in steps of 100 ps over a 5-ns range to obtain a sequence of 2-D transmitted light intensity patterns of both less-scattered and multiple-scattered light for image reconstruction. The inversion algorithm is based on the diffusion approximation of the radiative transfer theory for photon transport in a turbid medium. It uses a Green s function perturbative approach under the Rytov approximation and combines a 2-D matrix inversion with a one-dimensional Fourier-transform inversion to achieve speedy 3-D image reconstruction. In addition to the lateral position, the method provides information about the axial position of the object as well, whereas the 2-D reconstruction methods yield only lateral position.     

Noninvasive OCT imaging of the retinal morphology and microvasculature based on the combination of the phase and amplitude method

To implement the optical coherence tomography (OCT) angiography on the low scanning speed OCT system, we developed a joint phase and amplitude method to generate 3-D angiograms by analysing the frequency distribution of signals from non-moving and moving scatterers and separating the signals from the tissue and blood flow with high-pass filter dynamically. This approach firstly compensates the sample motion between adjacent A-lines. Then according to the corrected phase information, we used a histogram method to determine the bulk non-moving tissue phases dynamically, which is regarded as the cut-off frequency of a high-pass filter, and separated the moving and non-moving scatters using the mentioned high-pass filter. The reconstructed image can visualize the components of moving scatters flowing, and enables volumetric flow mapping combined with the corrected phase information. Furthermore, retinal and choroidal blood vessels can be simultaneously obtained by separating the B-scan into retinal part and choroidal parts using a simple segmentation algorithm along the RPE. After the compensation of axial displacements between neighbouring images, three-dimensional vasculature of ocular vessels has been visualized. Experiments were performed to demonstrate the effectiveness of the proposed method for 3-D vasculature imaging of human retina and choroid. The results revealed depth-resolved vasculatures in retina and choroid, suggesting that our approach can be used for noninvasive and three-dimensional angiography with a low-speed clinical OCT, and it has a great potential for clinic application.     

Fast Computation of the Acoustic Field for Ultrasound Elements

A fast method for computing the acoustic field of ultrasound transducers is presented with application to rectangular elements that are cylindrically focused. No closed-form solutions exist for this case but several numerical techniques have been described in the ultrasound imaging literature. Our motivation is the rapid calculation of imaging kernels for physics-based diagnostic imaging for which current methods are too computationally intensive. Here, the surface integral defining the acoustic field from a baffled piston is converted to a 3-D spatial convolution of the element surface and the Green's function. A 3-D version of the overlap-save method from digital signal processing is employed to obtain a fast computational algorithm based on spatial Fourier transforms. Further efficiency is gained by using a separable approximation to the Green's function through singular value decomposition and increasing the effective sampling rate by polyphase filtering. The tradeoff between accuracy and spatial sampling rate is explored to determine appropriate parameters for a specific transducer. Comparisons with standard tools such as Field II are presented, where nearly 2 orders of magnitude improvement in computation speed is observed for similar accuracy.     

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.     

Ultrasound speckle reduction using harmonic oscillator models

A speckle reduction algorithm called the harmonic imaging (HI) algorithm is presented. It is based on a multicomponent scattering model for medical ultrasonics. The backscattered ultrasound quadrature signal is modeled as the sum of three components after demodulation. The first component represents nonresolvable diffuse scatterers, while the second component represents subresolvable quasi-periodic scatterers. The third component represents resolvable quasi-periodic scatterers and mirroring surfaces. Since the second component gives rise to the most long range destructive interference effects it is eliminated in the HI algorithm to reduce speckle. Due to its slow spatial variation, it can be almost completely eliminated simply by differentiating the backscattered demodulated quadrature signal. Lissajous-like figures are observed in complex plots of the signals from ultrasound beams going through tissues with quasi-periodic components and sometimes in areas with only diffuse scatterers. Therefore the sum of the complex signals from the resolvable and nonresolvable scatterers within a resolution cell is modeled by two orthogonal and independent harmonic oscillators. The estimated, total energy of these two oscillators determines the gray level value of the HI image within the resolution cell. The HI images produced using radio frequency data from a phantom and from tissues in vivo are more blurred than ordinary envelope images, but the signal to noise ratio and tissue contrast were higher for the HI images     

A frequency domain model for generating B-mode images with array transducers

A frequency domain B-mode imaging model applicable to linear and phased array transducers was developed for simulating ultrasound images of random media. Computations are based on an approximation that is less restrictive than the Fresnel approximation. The model is compared with the exact time domain impulse response method, regarded as the "gold standard". In a typical application, errors in simulated rf waveforms are less than 1% regardless of the steering angle for distances greater than 2 cm, yet computation times are on the order of 1/150 of those using the exact method. This model takes into account the effects of frequency-dependent attenuation, backscattering, and dispersion. Modern beam-forming techniques such as apodization, dynamic aperture, elevational focusing, multiple transmit focusing and dynamic receiving focusing also can be simulated.     

Phase-aberration correction using signals from point reflectors and diffuse scatterers: measurements

A method for phase-aberration correction of phased-array images is tested using a model of near-field velocity inhomogeneities. A set of grooved room-temperature vulcanizing plates was constructed to simulate near-field aberrations encountered in clinical ultrasound imaging. As expected, large image distortion was experienced when grooved plates producing significant aberrations were placed near the surface of the array. An iterative aberration correction procedure based on cross-correlation measures between neighboring elements in a phased array, using signals reflected from diffuse scatterers, significantly reduced the effects of these aberrations, producing images nearly identical to those generated in the absence of aberrations. The results suggest that a practical phase-aberration correction system can be constructed for medical ultrasound imaging and possibly all coherent imaging systems by using a sampled aperture.     

Quantitative 3-d diagnostic ultrasound imaging using a modified transducer array and an automated image tracking technique

An approach for acquiring dimensionally accurate three-dimensional (3-D) ultrasound data from multiple 2-D image planes is presented. This is based on the use of a modified linear-phased array comprising a central imaging array that acquires multiple, essentially parallel, 2-D slices as the transducer is translated over the tissue of interest. Small, perpendicularly oriented, tracking arrays are integrally mounted on each end of the imaging transducer. As the transducer is translated in an elevational direction with respect to the central imaging array, the images obtained by the tracking arrays remain largely coplanar. The motion between successive tracking images is determined using a minimum sum of absolute difference (MSAD) image matching technique with subpixel matching resolution. An initial phantom scanning-based test of a prototype 8 MHz array indicates that linear dimensional accuracy of 4.6% (2 /spl sigma/) is achievable. This result compares favorably with those obtained using an assumed average velocity [31.5% (2 /spl sigma/) accuracy] and using an approach based on measuring image-to-image decorrelation [8.4% (2 /spl sigma/) accuracy]. The prototype array and imaging system were also tested in a clinical environment, and early results suggest that the approach has the potential to enable a low cost, rapid, screening method for detecting carotid artery stenosis. The average time for performing a screening test for carotid stenosis was reduced from an average of 45 minutes using 2-D duplex Doppler to 12 minutes using the new 3-D scanning approach.     

PSF dedicated to estimation of displacement vectors for tissue elasticity imaging with ultrasound

This paper investigates a new approach devoted to displacement vector estimation in ultrasound imaging. The main idea is to adapt the image formation to a given displacement estimation method to increase the precision of the estimation. The displacement is identified as the zero crossing of the phase of the complex cross-correlation between signals extracted from the lateral direction of the ultrasound RF image. For precise displacement estimation, a linearity of the phase slope is needed as well as a high phase slope. Consequently, a particular point spread function (PSF) dedicated to this estimator is designed. This PSF, showing oscillations in the lateral direction, leads to synthesis of lateral RF signals. The estimation is included in a 2-D displacement vector estimation method. The improvement of this approach is evaluated quantitatively by simulation studies. A comparison with a speckle tracking technique is also presented. The lateral oscillations improve both the speckle tracking estimation and our 2-D estimation method. Using our dedicated images, the precision of the estimation is improved by reducing the standard deviation of the lateral displacement error by a factor of 2 for speckle tracking and more than 3 with our method compared to using conventional images. Our method performs 7 times better than speckle tracking. Experimentally, the improvement in the case of a pure lateral translation reaches a factor of 7. Finally, the experimental feasibility of the 2-D displacement vector estimation is demonstrated on data acquired from a Cryogel phantom.     

Continuous wave ultrasonic tomography

As an object rotates with respect to a stationary ultrasonic beam, the scattering centers within the object return echoes that are Doppler-shifted in frequency by amounts depending on the velocities of the individual scatterers. The scattering centers that lie on a line of constant cross-range all have the same effective velocity in the direction pointing toward the transducer; therefore, the backscattered echo amplitude at any particular frequency is the line integral of the scattered radiation at the cross-range corresponding to that frequency. The amplitudes of the returned signals at other frequencies give the line integrals for the scatterers at the corresponding cross-ranges. The amplitude as a function of frequency can be interpreted as a tomographic projection. A continuum of the projections at different positions is generated while the object is rotating. A tomographic reconstruction algorithm can produce an image of the distribution of scattering centers in the insonified object from these projections. A microscanner was developed to investigate the approach of using continuous wave (CW) ultrasound for cross-sectional imaging. The resolution is limited by the target size and the ultrasonic wavelength.     

Beam transformation techinques for ultrasonic medical imaging

Data acquisition rates in pulsed ultrasound scanners are limited by the speed of sound in the human body. This poses severe limitations to the design of future ultrasound equipment, such as 3-D imaging scanners. The authors describe a technique for higher data acquisition rates based on the simultaneous transmission of multiple beams. By using a linear combination of the received beams, interbeam interference due to the sidelobe energy of the transmitting beams can be significantly reduced. The transformation coefficients are found by using a least squares minimization criterion. A simulation environment used for the evaluation of the authors' methodologies and various simulation results are presented.     

The effect of including myocardial anisotropy in simulated ultrasound images of the heart

We have examined the effect of incorporating tissue anisotropy in simulated ultrasound images of the heart. In simulation studies, the cardiac muscle (myocardium) is usually modeled as a cloud of uncorrelated point scatterers. Although this approach successfully generates a realistic speckle pattern, it fails to reproduce any effects of image anisotropy seen in real ultrasound images. We hypothesize that some of this effect is caused by the varying orientation of anisotropic myocardial structures relative to the ultrasonic beam and that this can be taken into account in simulations by imposing an angle dependent correlation of the scatterer points. Ultrasound images of a porcine heart were obtained in vitro, and the dominating fiber directions were estimated from the insonification angles that gave rise to the highest backscatter intensities. A cylindrical sample of the myocardium was then modeled as a grid of point scatterers correlated in the principal directions of the muscle fibers, as determined experimentally. Ultrasound images of the model were simulated by using a fast k-space based convolution approach, and the results were compared with the in vitro recordings. The simulated images successfully reproduced the insonification dependent through-wall distribution of backscatter intensities in the myocardial sample, as well as a realistic speckle pattern.     

Real-time ultrasound simulation using the GPU

Ultrasound simulators can be used for training ultrasound image acquisition and interpretation. In such simulators, synthetic ultrasound images must be generated in real time. Anatomy can be modeled by computed tomography (CT). Shadows can be calculated by combining reflection coefficients and depth dependent, exponential attenuation. To include speckle, a pre-calculated texture map is typically added. Dynamic objects must be simulated separately. We propose to increase the speckle realism and allow for dynamic objects by using a physical model of the underlying scattering process. The model is based on convolution of the point spread function (PSF) of the ultrasound scanner with a scatterer distribution. The challenge is that the typical field-of-view contains millions of scatterers which must be selected by a virtual probe from an even larger body of scatterers. The main idea of this paper is to select and sample scatterers in parallel on the graphic processing unit (GPU). The method was used to image a cyst phantom and a movable needle. Speckle images were produced in real time (more than 10 frames per second) on a standard GPU. The ultrasound images were visually similar to images calculated by a reference method.     

Reduced peak-hopping artifacts in ultrasonic strain estimation using the Viterbi algorithm

Internal strain resulting from tissue deformation can be estimated by correlation processing of speckle patterns within complex (i.e., radio frequency) ultrasound images acquired during deformation. At large deformations, the magnitude of the correlation coefficient peak can be significantly lower than unity, so that random speckle correlations will exceed the true peak. This effect is called ?peak hopping? and causes significant errors in displacement and deformation estimates. Here we investigate the Viterbi algorithm, a dynamic programming procedure, to overcome peak-hopping artifacts by finding the most likely sequence of hidden states in a sequence of observed events. It is well suited to motion estimation in elasticity- imaging studies because adjacent tissue elements remain adjacent following deformation. Particularly, tissue elements along an ultrasonic beam in one image lie along a 3-D continuous curve in the next image instant. The observed event in this case is the correlation coefficient of a pixel at a certain displacement. Radio-frequency data were generated before and after deformation with an average strain of 6%. Simulations were performed for a homogenous medium and for a medium with a stiffer inclusion. Results show that Viterbi processing of speckle-tracking outputs can significantly reduce peak-hopping artifacts.