Martin E. Anderson

Speckle tracking for multi-dimensional flow estimation.

Speckle tracking methods overcome the major limitations of current Doppler methods for flow imaging and quantification: angle dependence and aliasing. In this paper, we review the development of speckle tracking, with particular attention to the advantages and limitations of two-dimensional algorithms that use a single transducer aperture. Ensemble tracking, a recent speckle tracking method based upon parallel receive processing, is described. Experimental results with ensemble tracking indicate the ability to measure laminar flow in a phantom at a beam-vessel angle of 60 degrees, which had not been possible with previous 2D speckle tracking methods. Finally, important areas for future research in speckle tracking are briefly summarized.

The impact of sound speed errors on medical ultrasound imaging

The results of a quantitative study of the impact of sound speed errors on the spatial resolution and amplitude sensitivity of a commercial medical ultrasound scanner are presented in the context of their clinical significance. The beamforming parameters of the scanner were manipulated to produce sound speed errors ranging over +/-8% while imaging a wire target and an attenuating, speckle-generating phantom. For the wire target, these errors produced increases in lateral beam width of up to 320% and reductions in peak echo amplitude of up to 10.5 dB. In the speckle-generating phantom, these errors produced increases in speckle intensity correlation cell area of up to 92% and reductions in mean speckle brightness of up to 5.6 dB. These results are applied in statistical analyses of two detection tasks of clinical relevance. The first is of low contrast lesion detectability, predicting the changes in the correct decision probability as a function of lesion size, contrast, and sound speed error. The second is of point target detectability, predicting the changes in the correct decision probability as function of point target reflectivity and sound speed error. Representative results of these analyses are presented and their implications for clinical imaging are discussed. In general, sound speed errors have a more significant impact on point target detectability over lesion detectability by these analyses, producing up to a 22% reduction in correct decisions for a typical error.

The direct estimation of sound speed using pulse–echo ultrasound

A method for the direct estimation of the longitudinal speed of sound in a medium is presented. This estimator derives the speed of sound through analysis of pulse-echo data received across a single transducer array following a single transmission, and is analogous to methods used in exploration seismology. A potential application of this estimator is the dynamic correction of beamforming errors in medical imaging that result from discrepancy between the assumed and actual biological tissue velocities. The theoretical basis of this estimator is described and its function demonstrated in phantom experiments. Using a wire target, sound-speed estimates in water, methanol, ethanol, and n-butanol are compared to published values. Sound-speed estimates in two speckle-generating phantoms are also compared to expected values. The mean relative errors of these estimates are all less than 0.4%, and under the most ideal experimental conditions are less than 0.1%. The relative errors of estimates based on independent regions of speckle-generating phantoms have a standard deviation on the order of 0.5%. Simulation results showing the relative significance of potential sources of estimate error are presented. The impact of sound-speed errors on imaging and the potential of this estimator for phase aberration correction and tissue characterization are also discussed.

The detection of breast microcalcifications with medical ultrasound

Microcalcifications are small crystals of calcium apatites which form in human tissue through a number of mechanisms. The size, morphology, and distribution of microcalcifications are important indicators in the mammographic screening for and diagnosis of various carcinomas in the breast. Although x-ray mammography is currently the only accepted method for detecting microcalcifications, its efficacy in this regard can be reduced in the presence of dense parenchyma. Current ultrasound scanners do not reliably detect microcalcifications in the size range of clinical interest. The results of theoretical, simulation, and experimental studies focused on the improvement of the ultrasonic visualization of microcalcifications are presented. Methods for estimating the changes in microcalcification detection performance which result from changes in aperture geometry or the presence of an aberrator are presented. An analysis of the relative efficacy of spatial compounding and synthetic receive aperture geometries in the detection of microcalcifications is described. The impact of log compression of the detected image on visualization is discussed. Registered high resolution ultrasound and digital spot mammography images of microcalcifications in excised breast carcinoma tissue and results from the imaging of suspected microcalcifications in vivo are presented.

A novel interpolation strategy for estimating subsample speckle motion

Multidimensional, high-resolution ultrasonic imaging of rapidly moving tissue is primarily limited by sparse sampling in the lateral dimension. In order to achieve acceptable spatial resolution and velocity quantization, interpolation of laterally sampled data is necessary. We present a novel method for estimating lateral subsample speckle motion and compare it with traditional interpolation methods. This method, called grid slopes, requires no a priori knowledge and can be applied to data with as few as two samples in the lateral dimension. Computer simulations were performed to compare grid slopes with two conventional interpolation schemes, parabolic fit and cubic spline. Results of computer simulations show that parabolic fit and cubic spline performed poorly at translations greater than 0.5 samples, and translations less than 0.5 samples were subject to an estimation bias. Grid slopes accurately estimated translations between 0 and 1 samples without estimation bias at high signal-to-noise ratios. Given that the grid slopes interpolation technique performs well at high signal-to-noise ratios, one pertinent clinical application might be tissue motion tracking.

Ensemble tracking for 2D vector velocity measurement: Experimental and initial clinical results

We describe a new method, called ensemble tracking, for estimating two-dimensional velocities with ultrasound. Compared to previous speckle tracking techniques, ensemble tracking measures motion over smaller times and distances, increasing maximum velocities and reducing errors due to echo decorrelation. Ensemble tracking uses parallel receive processing, 2D pattern matching, and interpolation of the resulting tracking grid to estimate sub-pixel speckle translations between successive ultrasonic acquisitions. In this study, small translations of a tissue mimicking phantom were quantified at transducer angles of 0/spl deg/, 45/spl deg/, and 90/spl deg/. Measurements over three parallel beam spacings and all transducer angles had mean errors from -4% to +11%, when parallel beam amplitudes were normalized. Such amplitude normalization substantially improved results at 45/spl deg/ and 90/spl deg/. The amplitude, spacing, and correlation between the parallel beams were quantified, and their effects on the accuracy and precision of estimates are discussed. Finally, initial clinical results demonstrate the ability to track and display blood flow in the carotid artery.

Microcalcifications as elastic scatterers under ultrasound

One of the fundamental limitations of medical ultrasound in the imaging of the breast is the inability of current practice to reliably visualize microcalcifications in the size range of clinical interest. Microcalcifications (MCs) are small crystals of calcium phosphates that form in human tissue through a number of mechanisms. The size, morphology, and distribution of MCs are important indicators in the mammographic screening for and diagnosis of various carcinomas in the breast. The authors are investigating the imaging of MCs under ultrasound in the interest of extending the utility of medical ultrasound in the breast clinic. They present an analysis of the acoustic properties of MCs modeled as elastic spheres based on the Faran model that considers the predicted complex spectra and spatial coherence of echoes from MCs. They have found the predictions of the model to be similar to ultrasound echoes from suspected MCs in vivo. They also present breast phase aberration estimates and spatial and frequency compounding results based on the echoes from these targets.

A heterodyning demodulation technique for spatial quadrature

Conventional flow estimation techniques quantify the axial component of blood or tissue velocity by either directly or indirectly estimating any Doppler shift of the frequency of the reflected ultrasound pulse. We have previously described a means of extending flow estimation to two dimensions through a method known as spatial quadrature. This technique creates a lateral complex modulation in the ultrasound beam, and hence in the echoes of scatterers moving through the beam, that can be used to estimate the lateral component of the flow velocity. The introduction of this lateral modulation creates the need for a means to distinguish the conventional axial modulation of the ultrasound pulse from this new lateral modulation. We demonstrate a novel vector velocity estimator based on spatial quadrature that uses heterodyning to achieve axial-only and lateral-only demodulation, and demonstrate its function using experimental data captured in real time in a vessel phantom under laminar flow conditions. This estimator was used to construct velocity profiles with peak velocities between 8 and 55 cm/s at Doppler angles of 90/spl deg/ and 60/spl deg/. Flow velocity profiles across the vessel were integrated to estimate flow rates that agreed with the known flow rates to within 3% and 6% relative error for flow at 90/spl deg/ and 60/spl deg/ Doppler angles.

2-D motion estimation using two parallel receive beams

We describe a method for estimating 2-D target motion using ultrasound. The method is based on previous ensemble tracking techniques, which required at least four parallel receive beams and 2-D pattern matching. In contrast, the method described requires only two parallel receive beams and 1-D pattern matching. Two 1-D searches are performed, one in each lateral direction. The direction yielding the best match indicates the lateral direction of motion. Interpolation provides sub-pixel magnitude resolution. We compared the two beam method with the four beam method using a translating speckle target at three different parallel beam steering angles and transducer angles of 0, 45, and 90/spl deg/. The largest differences were found at 90 degrees, where the two beam method was generally more accurate and precise than the four beam method and also less prone to directional errors at small translations. We also examined the performance of both methods in a laminar flow phantom. Results indicated that the two beam method was more accurate in measuring the flow angle when the flow velocity was small. Computer simulations supported the experimental findings. The poorer performance of the four beam method was attributed to differences in correlation among the parallel beams. Specifically, center beams 2 and 3 correlated better with each other than with the outer beams. Because the four beam method used a comparison of a kernel region in beam pair 2-3 with two different beam pairs 1-2 and 3-4, the 2-to-1 and 3-to-4 components of this comparison increased the incidence of directional errors, especially at small translations. The two beam method used a comparison between only two beams and so was not subject to this source of error. Finally, the two beam method did not require amplitude normalization, as was necessary for the four beam method, when the two beams were chosen symmetric to the transmit axis. We conclude that two beam ensemble tracking can accurately estimate motion using only two parallel receive beams.

A 2D nonlinear wave propagation solver written in open-source MATLAB code

We describe a MATLAB implementation of a 2D wave solver capable of simulating the linear and nonlinear propagation of ultrasonic waves through an attenuating medium modeled as a 2D spatial grid, the acoustic properties of which can be arbitrarily assigned at each node. The object of this work is to create a freely distributed nonlinear wave solver that is useful for both ultrasound research and the instruction of nonlinear and ultrasound acoustics, and that is written in a popular interpreted language so that the model can be quickly and easily modified to address a range of simulation tasks. The solver is based on a pseudospectral derivative, time-domain integration algorithm previously described by Wojcik, et al. (1997), and models frequency-dependent attenuation through the application of multiple relaxation mechanisms. Forcing functions can be applied over simulation time to nodes on the calculation surface to simulate arbitrary ultrasound array geometries. The time record of any parameters can also be stored in order to, for example, measure the magnitude of harmonics or determine an arrays point spread function. We present results from the solver, discuss its theoretical basis and structure, describe its calculation requirements given a variety of grid geometries and acoustic conditions, and provide the contact information needed to obtain the code.