Quantitative ultrasound estimates from populations of scatterers with continuous size distributions: effects of the size estimator algorithm

Effects of Size Polydispersity and Dense Media on Quantitative Ultrasound Estimates

Quantitative ultrasound (QUS) techniques based on the backscatter coefficient (BSC) aim to characterize the scattering properties of biological tissues. A scattering model is fit to the measured BSC, and the fitted QUS parameters can provide local tissue microstructure, namely, scatterer size and acoustic concentration. However, these techniques may fail to provide a correct description of tissue microstructure when the medium is polydisperse and/or dense. The objective of this study is to investigate the effects of scatterer size polydispersity in sparse or dense media on the QUS estimates. Four scattering models (i.e., the monodisperse and polydisperse sparse models, and the monodisperse and polydisperse concentrated models based on the structure factor) are compared to assess their accuracy and reliability in quantifying the QUS estimates. Simulations are conducted with different scatterer size distributions for sparse, moderately dense, and dense media (volume fractions of 1%, 20%, and 73%, respectively). The QUS parameters are estimated by using model-based inverse methods at different center frequencies between 8 and 50 MHz. Experimental data are also analyzed using colon adenocarcinoma HT29 cell pellet biophantoms to further validate the results obtained from simulations at the volume fraction of 73%. Our findings reveal that the choice of scattering model has a significant impact on the accuracy of QUS estimates. For sufficiently high frequencies and dense media, the polydisperse concentrated model outperforms the other models and enables more accurate quantification. Furthermore, our results contribute to advancing our understanding of the complexities associated with scatterer size polydispersity and dense media in spectral-based QUS techniques.

Simulation of ultrasonic scattering from scatterer size distributions using Field II

Quantitative analysis of radio frequency (RF) signals obtained from ultrasound scanners can yield objective parameters that are gaining clinical relevance as imaging biomarkers. These include the backscatter coefficient (BSC) and the effective scatterer diameter (ESD). Biomarker validation is typically performed in phantoms which do not provide the flexibility of systematic variation of scattering properties. Computer simulations, such as those from the ultrasound simulator Field II, can allow more flexibility. However, Field II does not allow simulation of RF data from a distribution of scatterers with finite size. In this work, a simulation method is presented which builds upon previous work by including Faran theory models representative of distributions of scatterer size. These are systematically applied to RF data simulated in Field II. The method is validated by measuring the root mean square error of the estimated BSC and percent bias of the ESD and comparing to experimental results. The results indicate the method accurately simulates distributions of scatterer sizes and provides scattering similar to that seen in data from clinical scanners. Because Field II is widely used by the ultrasound community, this method can be adopted to aid in validation of quantitative ultrasound imaging biomarkers.

Extracting Quantitative Ultrasonic Parameters from the Backscatter Coefficient

The ultrasonic backscatter coefficient (BSC) is a fundamental quantitative ultrasound (QUS) parameter that contains rich information about the underlying tissue. Deriving parameters from the BSC is essential for fully utilizing the information contained in BSC for tissue characterization. In this chapter, we review two primary approaches for extracting parameters from the BSC versus frequency curve: the model-based approach and the model-free approach, focusing on the model-based approach, where a scattering model is fit to the observed BSC to yield model parameters. For this approach, we will attempt to unite commonly used models under a coherent theoretical framework. We will focus on the underlying assumptions and conditions for various BSC models. Computer code is provided to facilitate the use of some of the models. The strengths and weaknesses of various models are also discussed.

US Backscatter for Liver Fat Quantification: An AIUM-RSNA QIBA Pulse-Echo Quantitative Ultrasound Initiative

Nonalcoholic fatty liver disease (NAFLD) is believed to affect one-third of American adults. Noninvasive methods that enable detection and monitoring of NAFLD have the potential for great public health benefits. Because of its low cost, portability, and noninvasiveness, US is an attractive alternative to both biopsy and MRI in the assessment of liver steatosis. NAFLD is qualitatively associated with enhanced B-mode US echogenicity, but visual measures of B-mode echogenicity are negatively affected by interobserver variability. Alternatively, quantitative backscatter parameters, including the hepatorenal index and backscatter coefficient, are being investigated with the goal of improving US-based characterization of NAFLD. The American Institute of Ultrasound in Medicine and Radiological Society of North America Quantitative Imaging Biomarkers Alliance are working to standardize US acquisition protocols and data analysis methods to improve the diagnostic performance of the backscatter coefficient in liver fat assessment. This review article explains the science and clinical evidence underlying backscatter for liver fat assessment. Recommendations for data collection are discussed, with the aim of minimizing potential confounding effects associated with technical and biologic variables.

Estimation of polydispersity in aggregating red blood cells by quantitative ultrasound backscatter analysis

Quantitative ultrasound techniques based on the backscatter coefficient (BSC) have been commonly used to characterize red blood cell (RBC) aggregation. Specifically, a scattering model is fitted to measured BSC and estimated parameters can provide a meaningful description of the RBC aggregates' structure (i.e., aggregate size and compactness). In most cases, scattering models assumed monodisperse RBC aggregates. This study proposes the Effective Medium Theory combined with the polydisperse Structure Factor Model (EMTSFM) to incorporate the polydispersity of aggregate size. From the measured BSC, this model allows estimating three structural parameters: the mean radius of the aggregate size distribution, the width of the distribution, and the compactness of the aggregates. Two successive experiments were conducted: a first experiment on blood sheared in a Couette flow device coupled with an ultrasonic probe, and a second experiment, on the same blood sample, sheared in a plane-plane rheometer coupled to a light microscope. Results demonstrated that the polydisperse EMTSFM provided the best fit to the BSC data when compared to the classical monodisperse models for the higher levels of aggregation at hematocrits between 10% and 40%. Fitting the polydisperse model yielded aggregate size distributions that were consistent with direct light microscope observations at low hematocrits.

Scatterer size estimation using the center frequency assessed from ultrasound time domain data

Scatterer size estimation is useful when characterizing tissue using ultrasound. In all previous studies on scatterer size, the estimations are performed in the frequency domain and are thus subjected to a trade off in time-frequency resolution. This study focused on the feasibility of estimating scatterer size in the time domain using only the ultrasound center frequency, assuming a Gaussian-shaped pulse. A model for frequency normalization was derived and the frequency-dependent attenuation was compensated. Five phantoms with well-defined sizes of spherical glass beads were made and scanned with two different linear array transducers with variable center frequencies. A strong correlation (r = 0.99, p < 10^-19) between the backscattered center frequency and the product between the wave number and scatterer radius was demonstrated. On average the scatterer diameter was underestimated by 6% ± 24%. These results suggest that estimation of scatterer size is possible using only the center frequency assessed in the time domain.

Heterogeneous Tissue Characterization Using Ultrasound: A Comparison of Fractal Analysis Backscatter Models on Liver Tumors

Assessment of tumor tissue heterogeneity via ultrasound has recently been suggested as a method for predicting early response to treatment. The ultrasound backscattering characteristics can assist in better understanding the tumor texture by highlighting the local concentration and spatial arrangement of tissue scatterers. However, it is challenging to quantify the various tissue heterogeneities ranging from fine to coarse of the echo envelope peaks in tumor texture. Local parametric fractal features extracted via maximum likelihood estimation from five well-known statistical model families are evaluated for the purpose of ultrasound tissue characterization. The fractal dimension (self-similarity measure) was used to characterize the spatial distribution of scatterers, whereas the lacunarity (sparsity measure) was applied to determine scatterer number density. Performance was assessed based on 608 cross-sectional clinical ultrasound radiofrequency images of liver tumors (230 and 378 representing respondent and non-respondent cases, respectively). Cross-validation via leave-one-tumor-out and with different k-fold methodologies using a Bayesian classifier was employed for validation. The fractal properties of the backscattered echoes based on the Nakagami model (Nkg) and its extend four-parameter Nakagami-generalized inverse Gaussian (NIG) distribution achieved best results-with nearly similar performance-in characterizing liver tumor tissue. The accuracy, sensitivity and specificity of Nkg/NIG were 85.6%/86.3%, 94.0%/96.0% and 73.0%/71.0%, respectively. Other statistical models, such as the Rician, Rayleigh and K-distribution, were found to not be as effective in characterizing subtle changes in tissue texture as an indication of response to treatment. Employing the most relevant and practical statistical model could have potential consequences for the design of an early and effective clinical therapy.

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.

Experimental evaluation of spectral-based quantitative ultrasound imaging using plane wave compounding

Quantitative ultrasound (QUS) based on backscatter coefficient (BSC) estimation has shown potential for tissue characterization. Beamforming using plane wave compounding has advantages for echographic, Doppler, and elastographic imaging; however, to date, plane wave compounding has not been experimentally evaluated for the purpose of BSC estimation. In this study, two BSC-derived parameters (i.e., the BSC midband fit and intercept) were estimated from experimental data obtained using compound plane wave beamforming. For comparison, QUS parameters were also estimated from data obtained using both fixed focus and dynamic receive beamforming. An ultrasound imaging system equipped with a 9-MHz center frequency, 64-element array was used to collect data up to a depth of 45 mm. Two gelatin phantoms with randomly distributed 20-μm inclusions with a homogeneous scatterer concentration and a two-region scatterer concentration were used for assessing the precision and lateral resolution of QUS imaging, respectively. The use of plane wave compounding resulted in accurate QUS estimation (i.e., bias in the BSC parameters of less than 2 dB) and relatively constant lateral resolution (i.e., BSC midband fit 10% to 90% rise distance ranging between 1.0 and 1.5 mm) throughout a 45 mm field of view. Although both fixed focus and dynamic receive beamforming provided the same performance around the focal depth, the reduction in SNR away from the focus resulted in a reduced field of view in the homogeneous phantom (i.e., only 28 mm). The lateral resolution also degraded away from the focus, with up to a 2-fold and 10-fold increase in the rise distance at 20 mm beyond the focal depth for dynamic receive and fixed focus beamforming, respectively. These results suggest that plane wave compounding has the potential to improve the performance of spectral-based quantitative ultrasound over other conventional beamforming strategies.