Simulation studies of ultrasonic backscattering and B-mode images of liver using acoustic microscopy data

Experimental validation of a convolution- based ultrasound image formation model using a planar arrangement of micrometer-scale scatterers

The shift-invariant convolution model of ultrasound is widely used in the literature, for instance to generate fast simulations of ultrasound images. However, comparison of the resulting simulations with experiments is either qualitative or based on aggregate descriptors such as envelope statistics or spectral components. In the current work, a planar arrangement of 49-μm polystyrene microspheres was imaged using macrophotography and a 4.7-MHz ultrasound linear array. The macrophotograph allowed estimation of the scattering function (SF) necessary for simulations. Using the coefficient of determination R(2) between real and simulated ultrasound images, different estimates of the SF and point spread function (PSF) were tested. All estimates of the SF performed similarly, whereas the best estimate of the PSF was obtained by Hanningwindowing the deconvolution of the real ultrasound image with the SF: this yielded R(2) = 0.43 for the raw simulated image and R(2) = 0.65 for the envelope-detected ultrasound image. R(2) was highly dependent on microsphere concentration, with values of up to 0.99 for regions with scatterers. The results validate the use of the shift-invariant convolution model for the realistic simulation of ultrasound images. However, care needs to be taken in experiments to reduce the relative effects of other sources of scattering such as from multiple reflections, either by increasing the concentration of imaged scatterers or by more careful experimental design.

Estimation of trabecular thickness using ultrasonic backcatter

We present a method to estimate trabecular thickness (Tb.Th) in trabecular bones from ultrasound backscatter measurements. The estimation scheme is based on a nonlinear adjustment of predictions from a model to experimental data. The model assumes weak scattering from bone, where scattering is assumed to arise from the elastic solid trabeculae. The fluctuations of acoustical properties between bone tissue and the saturating fluid are assumed to be random and are described by the 3-D spatial autocorrelation function of the medium. In this paper, a Gaussian autocorrelation function is used. The inversion procedure is applied to a set of data measured on 33 femoral bone specimens. Results show that the model can predict both the magnitude and the frequency-dependence of the backscatter coefficient (root mean square error RMSE = 1 dB). The estimated trabecular thickness values are compared to the true trabecular thickness measured on high resolution microcomputed tomography 3-D reconstruction of bones microarchitecture. A close agreement is obtained on average over the group of specimens between predictions and the reference values: true Tb.Th is 132 +/- 12 microm and estimated Tb.Th is 134 +/- 15 microm. However, a moderate correlation between actual and estimated Tb.Th values is found (R2 = 0.44, p<10(-4), RMSE = 8.7 microm) suggesting a modest predictability at the individual level. Sources for the variability of the estimator are studied. Using synthetic rf signals, we demonstrate that the fundamental limitation of the estimator due to speckle noise is approximately 5 microm. Taking into account the measurement errors, the total uncertainty on Tb.Th estimates is of the order of 7 microm. The influence of the attenuation compensation function used to derive the backscatter coefficient is studied. In particular, we demonstrate the necessity of compensating for the effect of the gating time window. The results are discussed with respect to their meaningful clinical value. The requirements to be fulfilled by the performance of the technique change with regard to the question being posed. Two different strategies are examined: 1. characterize trabecular thickness without consideration of bone quantity (or bone mineral density) and 2. estimate trabecular thickness after adjustment for BMD. Considering the first strategy, a comparison between the precision of our estimator and the biological variability leads us to the conclusion that our estimator should only permit to distinguish between micro-architectures characterized by extreme values of trabecular thickness (i.e., very thin or very thick trabecular thickness). In this respect, it would be interesting to test whether the estimator is able to discriminate between rod-like (thin) and plate-like (thick) structures that are known to influence differently bone strength. The second strategy is more demanding in terms of technique performance and our estimator is not able yet to catch small differences in Tb.Th values expected after adjustment to bone density. Progress in the field will require a significant reduction in speckle noise and measurement errors and/or the development of other and more efficient microstructural estimators.

Analysis and correction of ultrasonic wavefront distortion based on a multilayer phase-screen model

A model is introduced that incorporates the cumulative wavefront distortion effects caused by spatial heterogeneities along the path of propagation, and a corresponding model-based wavefront distortion-correction method is presented. In the proposed model, a distributed heterogeneous medium is lumped into a series of parallel phase screens. The distortion effects can be compensated--without a priori knowledge of the distorting structure--by backpropagation of received wavefronts through hypothetical multiple phase screens located between the imaging system and targets, while each pointwise time shift is adjusted iteratively to maximize a specified image quality factor at the final layer. Theoretical analyses indicate that the mean speckle brightness decreases monotonically with the root-mean-square value of distributed phase distortions; therefore, the speckle brightness can be used as an image quality factor. Experimental one-dimensional (1-D) array data with simulated distortion effects based on a real 2-D abdominal-tissue map were used to evaluate the performance of the proposed method and existing aberration-correction techniques. The simulated characteristics of wavefront distortion and relative performance of existing correction techniques were similar to reports based on abdominal-wall data and breast data. This investigation shows that the proposed method provides better compensation for wavefront distortion.

Simulation of ultrasonic pulse propagation through the abdominal wall

Ultrasonic pulse propagation through the abdominal wall has been simulated using a model for two-dimensional propagation through anatomically realistic tissue cross sections. The time-domain equations for wave propagation in a medium of variable sound speed and density were discretized to obtain a set of coupled finite-difference equations. These difference equations were solved numerically using a two-step MacCormack scheme that is fourth-order accurate in space and second-order accurate in time. The inhomogeneous tissue of the abdominal wall was represented by two-dimensional matrices of sound speed and density values. These values were determined by processing scanned images of abdominal wall cross sections stained to identify connective tissue, muscle, and fat, each of which was assumed to have a constant sound speed and density. The computational configuration was chosen to simulate that of wavefront distortion measurements performed on the same specimens. Qualitative agreement was found between those measurements and the results of the present computations, indicating that the computational model correctly depicts the salient characteristics of ultrasonic wavefront distortion in vivo. However, quantitative agreement was limited by the two-dimensionality of the computation and the absence of detailed tissue microstructure. Calculations performed using an asymptotic straight-ray approximation showed good agreement with time-shift aberrations predicted by the full-wave method, but did not explain the amplitude fluctuations and waveform distortion found in the experiments and the full-wave calculations. Visualization of computed wave propagation within tissue cross sections suggests that amplitude fluctuations and waveform distortion observed in ultrasonic propagation through the abdominal wall are associated with scattering from internal inhomogeneities such as septa within the subcutaneous fat. These observations, as well as statistical analysis of computed and observed amplitude fluctuations, suggest that weak fluctuation models do not fully describe ultrasonic wavefront distortion caused by the abdominal wall.

Experimental assessment of spectrum analysis of ultrasonic echoes as a method for estimating scatterer properties

In vitro experiments using weak scatterers ranging in size from mean longest diameter of 26.9 to 83.0 microns were performed to test the validity of theoretical predictions for scatterer size and concentration derived from normalized power spectrum parameters of ultrasonic backscatterer echoes. Scatterers consisting of cell clusters were suspended in collagen gel and scanned by a 10 MHz transducer system. Optical measurements validated theoretical predictions that (1) slope value is a function solely of scatterer size; (2) intercept value is a function of scatterer size and concentration; and (3) midband fit value increases as scatterer concentration increases, and, to a lesser extent, as size increases. These results were obtained under relatively ideal conditions of minimal attenuation and scatterer spacing (not closer than two scatterer diameters) and were consistent with the assumptions underlying the scattering theory.

Effect of perfusion and blood content on ultrasonic backscattering of liver tissue

The purpose of this study was to determine the effect of blood flow perfusion and red cell content on ultrasonic scattering by liver tissue. Data acquisition for ultrasonic tissue characterization (UTC) employing analysis of the backscattered echoes from the power spectrum was obtained from the same region of pig liver tissue under four conditions: 1) normal perfusion in situ, 2) ischemia in situ in the living pig, 3) ischemia in situ immediately postmortem, and 4) immediately after excision of the liver. Discriminant function analysis was used to evaluate differences in the two basic parameters from the normalized power spectrum: slope and intercept. Normal perfused liver had significantly higher intercept values and lower slope values than liver under the other three conditions. Excised liver showed the lowest intercept and highest slope values (p < 0.01). These experiments indicate that differences in perfusion produce significant differences in ultrasonic scattering by liver tissue (ischemia caused a 3 dB drop in intercept amplitude). Normal or ischemic in vivo and in vitro liver tissue is associated with different patterns of ultrasonic scattering, and scattering data under these various circumstances are not equivalent.