Time domain attenuation estimation method from ultrasonic backscattered signals

Pulse-echo ultrasound attenuation tomography

Objective.We present the first fully two-dimensional attenuation imaging technique developed for pulse-echo ultrasound systems. Unlike state-of-the-art techniques, which use line-by-line acquisitions, our method uses steered emissions to constrain attenuation values at each location with multiple crossing wave paths, essential to resolve the spatial variations of this tissue property.Approach.At every location, we compute normalized cross-correlations between the beamformed images that are obtained from emissions at different steering angles. We demonstrate that their log-amplitudes provide the changes between attenuation-induced amplitude losses undergone by the different incident waves. This allows us to formulate a linear tomographic problem, which we efficiently solve via a Tikhonov-regularized least-squares approach.Main results.The performance of our tomography technique is first validated in numerical examples and then experimentally demonstrated in custom-made tissue-mimicking phantoms with inclusions of varying size, echogenicity, and attenuation. We show that this technique is particularly good at resolving lateral variations in tissue attenuation and remains accurate in media with varying echogenicity.Significance.Based on a similar principle, this method can be easily combined with computed ultrasound tomography in echo mode for speed-of-sound imaging, paving the way towards a multi-modal ultrasound tomography framework characterizing multiple acoustic tissue properties simultaneously.

Estimation of Tissue Attenuation from Ultrasonic B-Mode Images-Spectral-Log-Difference and Method-of-Moments Algorithms Compared

We report on results from the comparison of two algorithms designed to estimate the attenuation coefficient from ultrasonic B-mode scans obtained from a numerical phantom simulating an ultrasound breast scan. It is well documented that this parameter significantly diverges between normal tissue and malignant lesions. To improve the diagnostic accuracy it is of great importance to devise and test algorithms that facilitate the accurate, low variance and spatially resolved estimation of the tissue’s attenuation properties. A numerical phantom is realized using k-Wave, which is an open source Matlab toolbox for the time-domain simulation of acoustic wave fields that facilitates both linear and nonlinear wave propagation in homogeneous and heterogeneous tissue, as compared to strictly linear ultrasound simulation tools like Field II. k-Wave allows to simulate arbitrary distributions, resolved down to single voxel sizes, of parameters including the speed of sound, mass density, scattering strength and to include power law acoustic absorption necessary for simulation tasks in medical diagnostic ultrasound. We analyze the properties and the attainable accuracy of both the spectral-log-difference technique, and a statistical moments based approach and compare the results to known reference values from the sound field simulation.

Finite element modeling of grain size effects on the ultrasonic microstructural noise backscattering in polycrystalline materials

The correlation between ultrasonic wave propagation and polycrystalline microstructures has significant implications in nondestructive evaluation. An original numerical approach using the finite element method to quantify in both time and frequency domains the ultrasonic noise scattering due to the elastic heterogeneity of polycrystalline microstructures is presented. Based on the reciprocity theorem, it allows the scattering evaluation using mechanical data recorded only on the boundary of polycrystal instead of within its volume and is applicable to any polycrystalline aggregate regardless of its crystallographic or morphological characteristics. Consequently it gives a more realistic and accurate access of polycrystalline microstructures than the classical analytical models developed under the assumption of single scattering and the Born approximation. The numerical approach is proposed within the same unified theoretical framework as the classical analytical models, so it is possible to validate it in the cases of idealized microstructures for which the considered analytical models remain relevant. As an original result, assuming single phase, untextured and equiaxed microstructures, two-dimensional (2D) theoretical formulas are developed and a frequency-dependent coefficient is found compared to the classical three-dimensional (3D) formulas. 2D numerical simulations are then performed for idealized microstructures composed of hexagonal grains with a uniform grain-size. Three grain sizes are considered herein and involve different scattering regions. Good comparisons are obtained between theoretical and numerical estimates of the backscattering coefficient, which validate the numerical approach. Effects of the grain boundary orientations are analyzed by modeling an irregular hexagonal grain morphology and a random grain morphology generated by an established Voronoi approach. The origin of the significant oscillation level of backscattering is then investigated and discussed.

Transverse-to-transverse diffuse ultrasonic scattering

Ultrasonic scattering occurs when elastic waves interact with interfaces within heterogeneous media. Diffuse ultrasonic backscatter measurements are used to capture the effective grain scattering within a polycrystal for extracting microstructural information. Recently, a mode-conversion scattering model was developed to describe the longitudinal-to-transverse ultrasonic scattering within polycrystalline materials and successfully applied to determine the material spatial correlation length L by fitting experimental results with the theoretical model. The mode-conversion model may allow additional microstructural information, such as grain shape, to be assessed. In this article, a theoretical extension of the previous mode-conversion ultrasonic scattering model is presented. The transverse-to-transverse (T-T) scattering can be measured by an experimental configuration with both source and receiving transducers oriented at angles between the first and second critical angles, including pitch-catch and pulse-echo measurements. The model is used to determine the correlation length from a sample of 1040 steel through pulse-echo T-T scattering measurements using 7.5 and 10 MHz transducers. The results show that the derived T-T model works well for lower frequencies but the results for higher frequencies reveal deficiencies in the model.

Lower Bound on Estimation Variance of the Ultrasonic Attenuation Coefficient Using the Spectral-Difference Reference-phantom Method

Ultrasonic attenuation is one of the primary parameters of interest in Quantitative Ultrasound (QUS). Non-invasive monitoring of tissue attenuation can provide valuable diagnostic and prognostic information to the physician. The Reference Phantom Method (RPM) was introduced as a way of mitigating some of the system-related effects and biases to facilitate clinical QUS applications. In this paper, under the assumption of diffuse scattering, a probabilistic model of the backscattered signal spectrum is used to derive a theoretical lower bound on the estimation variance of the attenuation coefficient using the Spectral-Difference RPM. The theoretical lower bound is compared to simulated and experimental attenuation estimation statistics in tissue-mimicking (TM) phantoms. Estimation standard deviation (STD) of the sample attenuation in a region of interest (ROI) of the TM phantom is measured for various combinations of processing parameters, including Radio-Frequency (RF) data block length (i.e., window length) from 3 to 17 mm, RF data block width from 10 to 100 A-lines, and number of RF data blocks per attenuation estimation ROI from 3 to 10. In addition to the Spectral-Difference RPM, local attenuation estimation for simulated and experimental data sets was also performed using a modified implementation of the Spectral Fit Method (SFM). Estimation statistics of the SFM are compared to theoretical variance predictions from the literature.1 Measured STD curves are observed to lie above the theoretical lower bound curves, thus experimentally verifying the validity of the derived bounds. This theoretical framework benefits tissue characterization efforts by isolating processing parameter ranges that could provide required precision levels in estimation of the ultrasonic attenuation coefficient using Spectral Difference methods.

Review of Quantitative Ultrasound: Envelope Statistics and Backscatter Coefficient Imaging and Contributions to Diagnostic Ultrasound

Conventional medical imaging technologies, including ultrasound, have continued to improve over the years. For example, in oncology, medical imaging is characterized by high sensitivity, i.e., the ability to detect anomalous tissue features, but the ability to classify these tissue features from images often lacks specificity. As a result, a large number of biopsies of tissues with suspicious image findings are performed each year with a vast majority of these biopsies resulting in a negative finding. To improve specificity of cancer imaging, quantitative imaging techniques can play an important role. Conventional ultrasound B-mode imaging is mainly qualitative in nature. However, quantitative ultrasound (QUS) imaging can provide specific numbers related to tissue features that can increase the specificity of image findings leading to improvements in diagnostic ultrasound. QUS imaging can encompass a wide variety of techniques including spectral-based parameterization, elastography, shear wave imaging, flow estimation, and envelope statistics. Currently, spectral-based parameterization and envelope statistics are not available on most conventional clinical ultrasound machines. However, in recent years, QUS techniques involving spectral-based parameterization and envelope statistics have demonstrated success in many applications, providing additional diagnostic capabilities. Spectral-based techniques include the estimation of the backscatter coefficient (BSC), estimation of attenuation, and estimation of scatterer properties such as the correlation length associated with an effective scatterer diameter (ESD) and the effective acoustic concentration (EAC) of scatterers. Envelope statistics include the estimation of the number density of scatterers and quantification of coherent to incoherent signals produced from the tissue. Challenges for clinical application include correctly accounting for attenuation effects and transmission losses and implementation of QUS on clinical devices. Successful clinical and preclinical applications demonstrating the ability of QUS to improve medical diagnostics include characterization of the myocardium during the cardiac cycle, cancer detection, classification of solid tumors and lymph nodes, detection and quantification of fatty liver disease, and monitoring and assessment of therapy.

Scatterer number density considerations in reference phantom-based attenuation estimation

Attenuation estimation and imaging have the potential to be a valuable tool for tissue characterization, particularly for indicating the extent of thermal ablation therapy in the liver. Often the performance of attenuation estimation algorithms is characterized with numerical simulations or tissue-mimicking phantoms containing a high scatterer number density (SND). This ensures an ultrasound signal with a Rayleigh distributed envelope and a signal-to-noise ratio (SNR) approaching 1.91. However, biological tissue often fails to exhibit Rayleigh scattering statistics. For example, across 1647 regions of interest in five ex vivo bovine livers, we obtained an envelope SNR of 1.10 ± 0.12 when the tissue was imaged with the VFX 9L4 linear array transducer at a center frequency of 6.0 MHz on a Siemens S2000 scanner. In this article, we examine attenuation estimation in numerical phantoms, tissue-mimicking phantoms with variable SNDs and ex vivo bovine liver before and after thermal coagulation. We find that reference phantom-based attenuation estimation is robust to small deviations from Rayleigh statistics. However, in tissue with low SNDs, large deviations in envelope SNR from 1.91 lead to subsequently large increases in attenuation estimation variance. At the same time, low SND is not found to be a significant source of bias in the attenuation estimate. For example, we find that the standard deviation of attenuation slope estimates increases from 0.07 to 0.25 dB/cm-MHz as the envelope SNR decreases from 1.78 to 1.01 when estimating attenuation slope in tissue-mimicking phantoms with a large estimation kernel size (16 mm axially × 15 mm laterally). Meanwhile, the bias in the attenuation slope estimates is found to be negligible (<0.01 dB/cm-MHz). We also compare results obtained with reference phantom-based attenuation estimates in ex vivo bovine liver and thermally coagulated bovine liver.