Computer simulations of speckle in B-scan images

CNN-Based Image Reconstruction Method for Ultrafast Ultrasound Imaging

Ultrafast ultrasound (US) revolutionized biomedical imaging with its capability of acquiring full-view frames at over 1 kHz, unlocking breakthrough modalities such as shear-wave elastography and functional US neuroimaging. Yet, it suffers from strong diffraction artifacts, mainly caused by grating lobes, sidelobes, or edge waves. Multiple acquisitions are typically required to obtain a sufficient image quality, at the cost of a reduced frame rate. To answer the increasing demand for high-quality imaging from single unfocused acquisitions, we propose a two-step convolutional neural network (CNN)-based image reconstruction method, compatible with real-time imaging. A low-quality estimate is obtained by means of a backprojection-based operation, akin to conventional delay-and-sum beamforming, from which a high-quality image is restored using a residual CNN with multiscale and multichannel filtering properties, trained specifically to remove the diffraction artifacts inherent to ultrafast US imaging. To account for both the high dynamic range and the oscillating properties of radio frequency US images, we introduce the mean signed logarithmic absolute error (MSLAE) as a training loss function. Experiments were conducted with a linear transducer array, in single plane-wave (PW) imaging. Trainings were performed on a simulated dataset, crafted to contain a wide diversity of structures and echogenicities. Extensive numerical evaluations demonstrate that the proposed approach can reconstruct images from single PWs with a quality similar to that of gold-standard synthetic aperture imaging, on a dynamic range in excess of 60 dB. In vitro and in vivo experiments show that trainings carried out on simulated data perform well in experimental settings.

Assessing the performance of ultrasound imaging systems using images from relatively high-density random spherical void phantoms: A simulation study

BACKGROUND

The development of clinically meaningful, objective, and quantitative methods for assessing the performance of ultrasound imaging systems represents a continuing area of interest. One approach has been to image phantoms with randomly distributed spherical voids.

PURPOSE

The objectives of this study were: (1) to explore the potential of using relatively high-volume fraction random spherical void (RSV) phantoms as an approach for quantitatively assessing the performance of ultrasound imaging systems; (2) to identify potential metrics that can be used to provide quantitative assessments of images obtained from relatively high-volume fraction RSV phantoms; and (3) to demonstrate changes in the quantitative metrics that can occur as image features are degraded.

METHODS

A series (10 each) of computer-simulated RSV phantoms with a range of RSV volume fractions (0.05, 0.15, and 0.25) were generated. To determine the number of image planes necessary to provide robust measurements, a series of consecutive planes (ranging from 1 to 150) within each type of simulated phantom were analyzed. The observed circular cross-section radii histogram distributions (representing the intersection of each plane with the local distribution of spherical voids) were compared with the theoretical histogram distribution. Simulated phantom images were produced by adding speckle and degradation of imaging system performance was modeled by averaging 1 to 9 neighboring planes to represent increasing elevation plane thicknesses. Quantification of the performance of the imaging system was determined by measuring the: (1) mean number of circular cross-sections detected per image frame; (2) mean fractional area of circular cross-sections detected per image frame; (3) agreement of observed circular cross-section radii histogram distribution with the theoretical distribution (Chi-square statistic); and (4) contrast and contrast-to-noise ratio as a function of observed circular cross-section radius.

RESULTS

Results suggest that analyses of a sufficient number of image planes (providing over approximately 3000 total circular cross-sectional areas) provides excellent agreement between the observed and theoretical histogram distributions (mean Chi-square < 0.004). For the 0.15 volume fraction series of simulated RSV phantoms, using 150 image plane analyses, phantom images show decreasing mean number of circle cross-sections detected per frame (31.5 ± 0.3, 28.4 ± 0.3, 28.2 ± 0.3, 26.3 ± 0.3, and 25.3 ± 0.3); decreasing mean fractional area of circle cross-sections per frame (0.157 ± 0.002, 0.133 ± 0.001, 0.133 ± 0.001, 0.111 ± 0.001, and 0.108 ± 0.001); and a decreasing agreement with the theoretical histogram distribution of radii (Chi-square values: 0.070 ± 0.004, 0.140 ± 0.005, 0.149 ± 0.007, 0.379 ± 0.011, and 0.518 ± 0.010) for 1, 3, 5, 7, and 9 plane averages, respectively. Contrast and contrast-to-noise measurements as a function of observed circular cross-section radius also demonstrate marked changes with simulated image degradation.

CONCLUSIONS

Results of this simulation study suggest that analyses of images obtained from relatively high-density RSV phantoms may offer a promising approach for assessing ultrasound imaging systems. The proposed measurements appear to provide reproducible, robust, quantitative metrics that can be compared with corresponding theoretical values to provide quantifiable, objective metrics of imaging system performance.

Insights into photoacoustic speckle and applications in tumor characterization

In ultrasound imaging, fully-developed speckle arises from the spatiotemporal superposition of pressure waves backscattered by randomly distributed scatterers. Speckle appearance is affected by the imaging system characteristics (lateral and axial resolution) and the random-like nature of the underlying tissue structure. In this work, we examine speckle formation in acoustic-resolution photoacoustic (PA) imaging using simulations and experiments. Numerical and physical phantoms were constructed to demonstrate that PA speckle carries information related to unresolved absorber structure in a manner similar to ultrasound speckle and unresolved scattering structures. A fractal-based model of the tumor vasculature was used to study PA speckle from unresolved cylindrical vessels. We show that speckle characteristics and the frequency content of PA signals can be used to monitor changes in average vessel size, linked to tumor growth. Experimental validation on murine tumors demonstrates that PA speckle can be utilized to characterize the unresolved vasculature in acoustic-resolution photoacoustic imaging.

Efficient Frequency-Domain Synthetic Aperture Focusing Techniques for Imaging With a High-Frequency Single-Element Focused Transducer

Synthetic aperture focusing techniques (SAFT) make the spatial resolution of the conventional ultrasound imaging from a single-element focused transducer more uniform in the lateral direction. In this work, two new frequency-domain (FD-SAFT) algorithms are proposed, which are based on the synthetic aperture radar's wavenumber algorithm, and 2-D matched filtering technique for the image reconstruction. The first algorithm is the FD-SAFT virtual source (FD-SAFT-VS) that treats the focus of a focused transducer as a virtual source having a finite size and the diffraction effect in the far-field is taken into consideration in the image reconstruction. The second algorithm is the FD-SAFT deconvolution (FD-SAFT-DE) that uses the simulated point spread function of the imaging system as a matched filter kernel in the image reconstruction. The performance of the proposed algorithms was studied using a series of simulations and experiments, and it was compared with the conventional B-mode and time-domain SAFT (TD-SAFT) imaging techniques. The image quality was analyzed in terms of spatial resolution, sidelobe level, signal-to-noise ratio (SNR), contrast resolution, contrast-to-speckle ratio, and ex vivo image quality. The results showed that the FD-SAFT-VS had the smallest spatial resolution and FD-SAFT-DE had the second smallest spatial resolution. In addition, FD-SAFT-DE had generally the largest SNR. The computation run time of FD-SAFT-VS and FD-SAFT-DE, depending on the image size, was lower by 4 to 174 times and 4 to 189 times, respectively, compared to the TD-SAFT-virtual point source.

Meshfree simulations of ultrasound vector flow imaging using smoothed particle hydrodynamics

Before embarking on a series of in vivo tests, design of ultrasound-flow-imaging modalities are generally more efficient through computational models as multiple configurations can be tested methodically. To that end, simulation models must generate realistic blood flow dynamics and Doppler signals. The current in silico ultrasound simulation techniques suffer mainly from uncertainty in providing accurate trajectories of moving ultrasound scatterers. In mesh-based Eulerian methods, numerical truncation errors from the interpolated velocities, both in the time and space dimensions, can accumulate significantly and make the pathlines unreliable. These errors can distort beam-to-beam inter-correlation present in ultrasound flow imaging. It is thus a technical issue to model a correct motion of the scatterers by considering their interaction with boundaries and neighboring scatterers. We hypothesized that in silico analysis of emerging ultrasonic imaging modalities can be implemented more accurately with meshfree approaches. We developed an original fluid-ultrasound simulation environment based on a meshfree Lagrangian CFD (computational fluid dynamics) formulation, which allows analysis of ultrasound flow imaging. This simulator combines smoothed particle hydrodynamics (SPH) and Fourier-domain linear acoustics (SIMUS  =  simulator for ultrasound imaging). With such a particle-based computation, the fluid particles also acted as individual ultrasound scatterers, resulting in a direct and physically sound fluid-ultrasonic coupling. We used the in-house algorithms for fluid and ultrasound simulations to simulate high-frame-rate vector flow imaging. The potential of the particle-based method was tested in 2D simulations of vector Doppler for the intracarotid flow. The Doppler-based velocity fields were compared with those issued from SPH. The numerical evaluations showed that the vector flow fields obtained by vector Doppler components were in good agreement with the original SPH velocities, with relative errors less than 10% and 2% in the cross-beam and axial directions, respectively. Our results showed that SPH-SIMUS coupling enables direct and realistic simulations of ultrasound flow imaging. The proposed coupled algorithm has also the advantage to be 3D compatible and parallelizable.

High frequency ultrasound imaging and simulations of sea urchin oocytes

High frequency ultrasound backscatter signals from sea urchin oocytes were measured using a 40 MHz transducer and compared to numerical simulations. The Faran scattering model was used to calculate the ultrasound scattered from single oocytes in suspension. The urchin oocytes are non-nucleated with uniform size and biomechanical properties; the backscatter from each cell is similar and easy to simulate, unlike typical nucleated mammalian cells. The time domain signal measured from single oocytes in suspension showed two distinct peaks, and the power spectrum was periodic with minima spaced approximately 10 MHz apart. Good agreement to the Faran scattering model was observed. Measurements from tightly packed oocyte cell pellets showed similar periodic features in the power spectra, which was a result of the uniform size and consistent biomechanical properties of the cells. Numerical simulations that calculated the ultrasound scattered from individual oocytes within a three dimensional volume showed good agreement to the measured signals and B-scan images. A cepstral analysis of the signal was used to calculate the size of the cells, which was 78.7 μm (measured) and 81.4 μm (simulated). This work supports the single scattering approximation, where ultrasound is discretely scattered from single cells within a bulk homogeneous sample, and that multiple scattering has a negligible effect. This technique can be applied towards understanding the complex scattering behaviour from heterogeneous tissues.

A model for reflectivity enhancement due to surface bound submicrometer particles

Submicrometer particles filled with liquid perfluorocarbon have been shown to increase the ultrasound reflectivity of surfaces onto which they bind and, consequently, are seen as potential targeted contrast agents. The objective of this study is to explain the reflectivity enhancement as a result of the presence of randomly distributed particles on a surface. A model is presented where the diffraction-weighted scattering of all particles is summed over the exposed surface. Experiments were performed at frequencies ranging from 15 MHz to 60 MHz, with glass microbeads and perfluorohexane particles deposited on the surface of agar and Aqualene, a rubber closely matched to water, to confirm the validity of the model. Results showed that the model predicts the surface density and the frequency dependence of the reflectivity enhancement up to a density corresponding to twice the maximum packing of spheres on a surface (200% confluence fraction) for glass beads and a fifth (20% confluence fraction) for perfluorohexane particles. This suggests the possibility of predicting signal enhancement due to a bound contrast agent in simple geometries.

A model based upon pseudo regular spacing of cells combined with the randomisation of the nuclei can explain the significant changes in high-frequency ultrasound signals during apoptosis

Recent ultrasound (US) experiments on packed myeloid leukaemia cells have shown that, at frequencies from 32 to 40 MHz, significant increases of signal amplitude were observed during apoptosis. This paper is an attempt to explain these signal increases based upon a simulation of the backscattered signals from the cells nuclei. The simulation is an expansion of work in which a condensed sample of cells, with fairly regular sizes, could be considered as an imperfect crystal. Thus, destructive interference could occur and this would be observed as a large reduced value of backscattered signals compared with the values obtained from a similar, but random, scattering source. This current paper explores the possibility that simple changes in the nuclei, such as their observed condensation or the small loss of nuclei scatterers from cells, could cause a significant increase in the observed backscattered signals. This model indicates that the greater backscattered signals can be explained by further randomisation of the average positions of the scattering sources in each cell. When these "microechoes" are added together, so that the destructive interference is reduced, a large increase in the signal is predicted. The simplified model strongly suggests that much of observed large increases of the backscattered signals could be simply explained by the randomisation of the position of the condensed nuclei during apoptosis, and the destruction of the nuclei could produce further signal amplitude changes due to disruption of the cloud of backscattered waves.

The diffraction response interpolation method

Computer modeling of the output voltage in a pulse-echo system is computationally very demanding, particularly when considering reflector surfaces of arbitrary geometry. A new, efficient computational tool, the diffraction response interpolation method (DRIM), for modeling of reflectors in a fluid medium, is presented. The DRIM is based on the velocity potential impulse response method, adapted to pulse-echo applications by the use of acoustical reciprocity. Specifically, the DRIM operates by dividing the reflector surface into planar elements, finding the diffraction response at the corners of the elements, calculating the response integrated over the surface element by time-domain convolutions with analytically determined filters, and summing the responses from the individual surface elements. As the method is based on linearity, effects such as shadowing, higher-order diffraction, nonlinear propagation, cannot be directly incorporated in the modeling. The DRIM has been compared to other modeling tools when possible. Excellent agreement between the results obtained with the DRIM and the alternative techniques have been found, and the DRIM offers reductions in computation time in the range from 30 to 400 times. Experimental results obtained using a planar circular transducer together with cylindrical reflectors were compared to DRIM results and fairly good agreement was observed.

Phase insensitive homomorphic image processing for speckle reduction

Speckle appears in all conventional ultrasound images and is caused by the use of a phase-sensitive transducer. Speckle is an undesirable property as it can mask small but perhaps diagnostically significant image features. In this paper a homomorphic, hybrid nonlinear processing method, based on cancellation of scattering interference, is developed and examined. Experiments with synthetic and real ultrasound imagery show that the proposed method improves the contrast-to-noise ratio in both lesion and cyst areas and preserves edge clarity.

Simulation of ultrasonic imaging with linear arrays in causal absorptive media

Rigorous and efficient numerical methods are presented for simulation of acoustic propagation in a medium where the absorption is described by relaxation processes. It is shown how FFT-based algorithms can be used to simulate ultrasound images in pulse-echo mode. General expressions are obtained for the complex wavenumber in a relaxing medium. A fit to measurements in biological media shows the appropriateness of the model. The wavenumber is applied to three FFT-based extrapolation operators, which are implemented in a weak form to reduce spatial aliasing. The influence of the absorptive medium on the quality of images obtained with a linear array transducer is demonstrated. It is shown that, for moderately absorbing media, the absorption has a large influence on the images, whereas the dispersion has a negligible effect on the images.

The subtleties of ultrasound images of an ensemble of cells: simulation from regular and more random distributions of scatterers

Significant differences in the backscatter amplitudes which are correlated with different tissue morphology have been observed in ultrasound images of tissue. While many factors could be linked to subtle changes in the images, the purpose of this paper is to explore the possibility that backscatter signals are linked to the organization of the spatial distribution of individual cells that produce an ensemble of scattering sources. Simple one- and two-dimensional simulations of backscatter signals produced by weak scatters separated by << lambda to < lambda in regular, random, and pseudo-random distributions in a "sample" are performed. Both regular and pseudo-random distributions produce large boundary signals, and in the central regions of the sample, the square root of the backscatter power is directly related to the amount of randomization, R, over a large range. Large changes in backscattering intensities are predicted for the same density of scatterers with differing R in different regions of the same sample. Thus, the subtle differences in the scattering distribution should show significant changes in the backscatter images.

Simulation of two-dimensional ultrasonic imaging of biological tissues in the presence of phase aberrations

A simulator of phase aberrations for mathematical modeling of two-dimensional (2-D) ultrasonic medical imaging is developed. Principal characteristics of expected phase aberrations were put into the model to investigate the distorting influence of intervening tissues on the quality of conventional medical B-scan images. Information necessary for numerical simulations, including the form of the phase correlation function, correlation length and distortion magnitude, was obtained from analysis of known experimental data on abdominal and breast imaging in vivo. Examples of simulated acoustical images of some simple phantoms are presented. Improvement of image quality due to one simple phase adaptation algorithm is also presented.

A computer model for simulating ultrasonic scattering in biological tissues with high scatterer concentration

Scattering of ultrasonic waves by biological tissues at different scatterer concentrations is investigated using one- and two-dimensional computer simulation models. The backscattered power as a function of scatterer concentrations is calculated using two types of incident waves, a Gaussian shaped pulse and a continuous wave (CW). The simulation results are in good agreement with the Percus-Yevick packing theory within the scatterer concentrations, from 0% to 100% in one-dimensional (1D) space, and 0% to 46% in two-dimensional (2D) space. In all cases, the simulation results from a pulsed incident wave show a much smaller standard deviation (SD) than those from an incident CW. The simulation can serve as a useful tool to verify scattering theories, simulate different experimental conditions, and to investigate the interaction between the scatterer properties and the scattering of ultrasonic waves. More importantly, the 2D simulation procedure serves as an initial step toward the final realization of a true three-dimensional (3D) simulation of ultrasonic scattering in biological tissues.

Potential of fractal analysis for lesion detection in echographic images

The application of fractal analysis to parametric imaging of B-mode echograms and to differentiation of echographic speckle textures was investigated. Echograms were obtained from realistic simulations and from a clinical study on diffuse liver disease. The simulations comprised tissue models with randomly positioned scatterers in a 3-D volume in which the number density was varied over a range from 0.5 to 25 mm-3. The clinical echograms comprised both normals and patients with liver cirrhosis. Three methods of estimating the fractal dimension were investigated, two in the spatial image domain and one in the spatial frequency domain. The results of these methods are compared and the applicability and the limitations of texture differentiation using fractal analysis is discussed. The main conclusion is that fractal analysis offers no obvious advantage over statistical analysis of the texture of echographic images. Its use for parametric imaging is further limited by the need to use relatively large windows for local estimation of the fractal dimension.

An efficient computer model of three-dimensional speckle patterns in dynamically focused annular array

This paper describes an efficient computer method for generating three-dimensional (3-D) ultrasonic speckle patterns for sector scans of an annular array with dynamic focusing in both transmit and receive. Assuming random scatterers in an attenuating medium, the system synthesizes the waveform for each scan line using echo data received at all annular elements of the transducer when short pulses are transmitted by one annulus after another. The amount of echo data needed to synthesize one waveform is tremendously reduced by reducing the 3-D distributions of scatterers to line distributions and by representing scatterers on a small line segment by a single equivalent scatterer taking into account the two-way travel time differences. Furthermore, by a judicious 3-D arrangement of the scatterer lines and scan lines, it is possible to synthesize the waveform for a new scan line with negligible computation overhead. The waveforms of the scan lines are detected to obtain a B-mode image or speckle patterns. The patterns obtained on several differently-oriented image planes showed a good statistical agreement with experimentally obtained patterns.

Correction of phase aberrations for sectored annular array ultrasound transducers

Two methods for correction of unknown phase aberrations induced by inhomogeneous acoustic velocities in tissues are explored for the two dimensional geometry of a sectored annular array system. The methods employed are adaptations of a cross correlation technique and a speckle brightness maximization technique. The methods correct phase distortions via the introduction of phase shifts in the timing sequence at the beamformer stage of a sectored annular array transducer. The techniques are investigated employing software models and a computer controlled automated scanning system. A 65-element sectored annular array is modelled via a rotating 5 element transducer. Tissue equivalent materials were moulded into a double layer aberrating medium to simulate phase distortions encountered in the rectus abdominis muscle in vivo. A comparison of the effectiveness of the two correction methods is presented. Contrast of an anechoic region is increased from 0.34 +/- 0.08 to 0.48 +/- 0.06 for the cross correlation technique, and up to 0.62 +/- 0.05 for the speckle brightness maximization method. The performance of these correction techniques on target phantoms suggests that considerable improvements in image quality should be possible for clinical systems.

Mathematical simulation of pressure pulse propagation in biological tissues

The propagation of pressure pulses of arbitrary time form in inhomogeneous attenuating media with characteristics similar to real biological tissues is considered. A mathematical model using the quasi-optical approximation is developed to solve the wave equation. Such a model proves to be convenient for computer realization. A spectral analysis of known experimental data on frequency dependent backscatter is realized to separate coherent and incoherent components of backscatter from tissues and determine their parameters. The characteristics of the scattering are utilized for digital simulations of ultrasound propagation from an interrogated tissue volume. The results presented describe the expected space distribution of the pressure amplitude and phase near the transducer focus in the presence of an aberrating layer with parameters characteristic of abdominal imaging.

Nonlinear receiver compression effects on the amplitude distribution of backscattered ultrasonic signals

Nonlinear receiver compression effects on the amplitude distribution of backscattered ultrasonic signals are investigated by using digitized RF signals that have been compressed in a commercially made ultrasonic B-scan imaging instrument. Amplitude distributions of compressed RF and video signals were obtained from regions of B-scan images that correspond to approximately the same physical region in a random medium model with known backscatter amplitude characteristics. The amplitude distribution of the signal before compression was obtained by using a table constructed from measurements of the imaging instrument compression characteristics as a function of time gain compensation. While the results indicate the general form of the decompressed data agrees with single parameter model curves that are predicted by a widely employed Gaussian random process model, the signal-to-noise ratios of the decompressed envelope vary up to 20% from the 1.91 value predicted that model. This implies that effects such as nonlinearities, envelope smoothing, and noise which all may be present in varying degrees in practical ultrasonic imaging instrumentation can cause appreciable departures from theoretical data even under highly controlled conditions.

Properties of acoustical speckle in the presence of phase aberration. Part II: Correlation lengths

In recent years, analysis of the second order statistics of ultrasound speckle has led to accurate prediction and measurements of the average speckle size in the transducer focal zone. In this paper, that work has been extended to the average speckle size as determined by the normalized autocovariance in the presence of transducer phase aberrations. In general, a phase aberration causes a narrowing of the main lobe of the normalized autocovariance in the lateral direction. However, the lateral speckle autocovariance also showed significant side lobes in the presence of phase aberrations, indicating that individual speckles in a region of interest are not independent but are correlated so that less information is present for the task of signal detection when a transducer phase aberration exists. The same evidence of correlated speckle was found in the near field of a transducer in the region of fine speckle texture. This explanation satisfies the quandary of poor detectability in the near field region where the speckle is fine but the lateral resolution is quite degraded. The axial speckle in the presence of phase aberrations showed a small increase in main lobe widths and no evidence of side lobes. Beginning in 1978, the analysis of the second order statistics of speckle images for the purpose of spatial compounding led to accurate measurement and prediction of the cross-correlation curve as a function of transducer aperture translation for purposes of spatial compounding. In this paper, that work has been extended to the presence of transducer phase aberrations. The existence of transducer phase aberrations causes significant increases in the rate of decorrelation of speckle interference patterns as a transducer is translated. This indicates that spatial compounding will result in quite significant improvements in area-wise SNR and low contrast lesion detection for the case of severe random aberrators or focal point errors.

Fundamental correlation lengths of coherent speckle in medical ultrasonic images

Refinements to previous analyses of the natural correlation lengths within simple images and between images to be compounded are presented. Comparison of theoretical and experimental results show very good agreement for the case of Rayleigh scattering media: the correlation length within a simple image is comparable to the resolution cell size; the correlation length between images to be spatially compounded is comparable to, but smaller than, the transducer on array aperture; and the correlation length between images to be frequency-compounded becomes a frequency comparable to their bandwidth. Complications arising from the presence of specular scattering or due to the presence of just a few scatterers are considered. It is shown that straightforward solutions exist for either of these problems taken by itself. When they occur in combination, calibration techniques may lead to unambiguous identification of the contributions to the scattering from diffuse or incoherent scattering and from specular or coherent scattering, and to estimation of the density of diffuse scatterers.

Properties of acoustical speckle in the presence of phase aberration. Part I: First order statistics

The first order statistical properties of acoustical speckle patterns are studied as a function of several types of random and structured phase error. Such errors may arise from tissue velocity inhomogeneities or limitations in the acoustical imaging system. In this paper, we review the theory describing the statistical properties of speckle, describe a computer model which predicts the mean speckle brightness in the presence of phase aberrations, and report experiments in which we measure the effect of these aberrations on speckle brightness and variance. We find that the average speckle brightness is significantly reduced by even mild phase aberrations. The phase aberrations studied include focal point errors, random phase errors, and structured errors. Good agreement is found between experiment and computer simulation. We then discuss the implications of these results for imaging through aberrating media, tissue characterization and phase compensation methods.

Texture of B-mode echograms: 3-D simulations and experiments of the effects of diffraction and scatterer density

B-mode echograms were simulated by employing the impulse response method in transmission and reception using a discrete scatterer tissue model, with and without attenuation. The analytic signal approach was used for demodulation of the RF A-mode lines. The simulations were performed in 3-D space and compared to B-mode echograms obtained from experiments with scattering tissue phantoms. The average echo amplitude appeared to increase towards the focus and to decrease beyond it. In the focal zone, the average amplitude increased proportionally to the square root of the scatterer density. The signal to noise ratio (SNR) was found to be independent of depth, i.e., 1.91 as predicted for a Rayleigh distribution of gray levels, although a minimum was found in the focal zone at relatively low scatterer densities. The SNR continuously increased with increasing scatterer density and reached the limit of 1.91 at relatively high densities (greater than 10(4) cm-3). The lateral full width at half maximum (FWHM) of the two dimensional autocovariance function of the speckle increased continuously from the transducer face to far beyond the focus and decreased thereafter due to the diffraction effect. The lateral FWHM decreased proportionally to the logarithm of the scatterer density at low densities and reached a limit at high densities. Introduction of attenuation in the simulated tissue resulted in a much more pronounced depth dependence of the texture. The axial FWHM was independent of the distance to the transducer to a first approximation and decreased slightly with increasing scatterer density until a limit was reached at densities larger than 10(3) cm-3. This limit was in agreement with theory. The experiments confirmed the simulations and it can be concluded that the presented results are of great importance to the understanding of B-mode echograms and to the potential use of the analysis of B-mode texture for tissue characterization.

Quantitative echocardiographic image texture: normal contraction-related variability

Myocardial tissue characterization using ultrasound is a growing area of investigation which attempts to evaluate the structure of the myocardium by analysis of ultrasound signals. Our laboratory has been exploring the use of texture analysis for the determination of myocardial tissue properties from two-dimensional echocardiographic images. In the present study, we tested the hypothesis that echocardiographic image texture varies with cardiac contraction in normal human subjects. In 17 subjects, we obtained long-and short-axis images at end diastole and end systole. Echo image texture was assessed using three classes of quantitative texture measures: run length, gray level difference, and busyness statistics. These statistics measure various attributes of image texture. We found significant contraction-related changes in image texture for the left ventricular posterior wall. This observation is important in that future applications of texture analysis to echocardiographic image data will require that texture be measured at a consistent point in the cardiac cycle. Moreover, it is possible that alteration in the normal variation of texture with cardiac contraction may be a sensitive indicator of abnormal myocardium.

Ultrasound speckle size and lesion signal to noise ratio: verification of theory

We compare predictions from our published theory of speckle cell size with recently published experimental results and a three dimensional computer simulation for the case of Gaussian pulses from spherically focused transducers in random media. The agreement is very good. We also compare our published theoretical predictions of the signal-to-noise ratio for a circular lesion in a speckle background with published "contrast to speckle ratio" data for anechoic cylindrical lesions in tissue mimicking material. Again, agreement is very good. The verification of these theoretical predictions has important implications for the evaluation of B-scan image quality and the study of tissue characterization.