Effects of Estimators on Ultrasound Nakagami Imaging in Visualizing the Change in the Backscattered Statistics from a Rayleigh Distribution to a Pre-Rayleigh Distribution

Multiple ultrasonic parametric imaging for the detection and monitoring of high-intensity focused ultrasound ablation

Numerous quantitative ultrasound imaging techniques have demonstrated superior monitoring performance for thermal ablation when compared to conventional ultrasonic B-mode imaging. However, the absence of comparative studies involving various quantitative ultrasound imaging techniques hinders further clinical exploration. In this study, we simultaneously reconstructed ultrasonic Nakagami imaging, ultrasonic horizontally normalized Shannon entropy (hNSE) imaging, and ultrasonic differential attenuation coefficient intercept (DACI) imaging from ultrasound backscattered envelope data collected during high-intensity focused ultrasound ablation treatment. We comprehensively investigated their performance differences through qualitative and quantitative analyses, including the calculation of contrast-to-noise ratios (CNR) for ultrasonic images, receiver operating characteristic (ROC) analysis with corresponding indicators, the analysis of lesion area fitting relationships, and computational time consumption comparison. The mean CNR of hNSE imaging was 10.98 ± 4.48 dB, significantly surpassing the 3.82 ± 1.40 dB (p < 0.001, statistically significant) of Nakagami imaging and the 2.45 ± 0.74 dB (p < 0.001, statistically significant) of DACI imaging. This substantial difference underscores that hNSE imaging offers the highest contrast resolution for lesion recognition. Furthermore, we evaluated the ability of multiple ultrasonic parametric imaging to detect thermal ablation lesions using ROC curves. The area under the curve (AUC) for hNSE was 0.874, exceeding the values of 0.848 for Nakagami imaging and 0.832 for DACI imaging. Additionally, hNSE imaging exhibited the strongest linear correlation coefficient (R = 0.92) in the comparison of lesion area fitting, outperforming Nakagami imaging (R = 0.87) and DACI imaging (R = 0.85). hNSE imaging also performs best in real-time monitoring with each frame taking 6.38 s among multiple ultrasonic parametric imaging. Our findings unequivocally demonstrate that hNSE imaging excels in monitoring HIFU ablation treatment and holds the greatest potential for further clinical exploration.

Hybrid QUS Radiomics: A Multimodal-Integrated Quantitative Ultrasound Radiomics for Assessing Ambulatory Function in Duchenne Muscular Dystrophy

BACKGROUND

Duchenne muscular dystrophy (DMD) is a neuromuscular disorder that affects ambulatory function. Quantitative ultrasound (QUS) imaging, utilizing envelope statistics, has proven effective in diagnosing DMD. Radiomics enables the extraction of detailed features from QUS images. This study further proposes a hybrid QUS radiomics and explores its value in characterizing DMD.

METHODS

Patients (n = 85) underwent ultrasound examinations of gastrocnemius through Nakagami, homodyned K (HK), and information entropy imaging. The hybrid QUS radiomics extracted, selected, and integrated the retained features derived from each QUS image for classification of ambulatory function using support vector machine. Nested five fold cross-validation of the data was conducted, with the rotational process repeated 50 times. The performance was assessed by averaging the areas under the receiver operating characteristic curve (AUROC).

RESULTS

Radiomics enhanced the average AUROC of B-scan, Nakagami, HK, and entropy imaging to 0.790, 0.911, 0.869, and 0.890, respectively. By contrast, the hybrid QUS radiomics using HK and entropy images for diagnosing ambulatory function in DMD patients achieved a superior average AUROC of 0.971 (p < 0.001 compared with conventional radiomics analysis).

CONCLUSIONS

The proposed hybrid QUS radiomics incorporates microstructure-related backscattering information from various envelope statistics models to effectively enhance the performance of DMD assessment.

Modified multi-Rayleigh model-based statistical analysis of ultrasound envelope for quantification of liver steatosis and fibrosis

PURPOSE

Quantitative diagnosis of the degree of fibrosis progression is currently a focus of attention for fatty liver in nonalcoholic steatohepatitis (NASH). However, previous studies have focused on either lipid droplets or fibrotic tissue, and few have reported the evaluation of both in patients whose livers contain adipose and fibrous features. Our aim was to evaluate fibrosis tissue and lipid droplets in the liver.

METHODS

We used an analytical method combining the multi-Rayleigh (MRA) model and a healthy liver structure filter (HLSF) as a technique for statistical analysis of the amplitude envelope to estimate fat and fibrotic volumes in clinical datasets with different degrees of fat and fibrosis progression.

RESULTS

Fat mass was estimated based on the non-MRA fraction corresponding to the signal characteristics of aggregated lipid droplets. Non-MRA fraction has a positive correlation with fat mass and is effective for detecting moderate and severe fatty livers. Progression of fibrosis was estimated using MRA parameters in combination with the HLSF. The proposed method was used to extract non-healthy areas with characteristics of fibrotic tissue. Fibrosis in early fatty liver suggested the possibility of evaluation. On the other hand, fat was identified as a factor that reduced the accuracy of estimating fibrosis progression in moderate and severe fatty livers.

CONCLUSION

The proposed method was used to simultaneously evaluate fat mass and fibrosis progression in early fatty liver, suggesting the possibility of quantitative evaluation for discriminating between lipid droplets and fibrous tissue in the early fatty liver.

Ultrasound image segmentation using Gamma combined with Bayesian model for focused-ultrasound-surgery lesion recognition

This study aims to investigate the feasibility of combined segmentation for the separation of lesions from non-ablated regions, which allows surgeons to easily distinguish, measure, and evaluate the lesion area, thereby improving the quality of high-intensity focused-ultrasound (HIFU) surgery used for the non-invasive tumor treatment. Given that the flexible shape of the Gamma mixture model (GΓMM) fits the complex statistical distribution of samples, a method combining the GΓMM and Bayes framework is constructed for the classification of samples to obtain the segmentation result. An appropriate normalization range and parameters can be used to rapidly obtain a good performance of GΓMM segmentation. The performance values of the proposed method under four metrics (Dice score: 85%, Jaccard coefficient: 75%, recall: 86%, and accuracy: 96%) are better than those of conventional approaches including Otsu and Region growing. Furthermore, the statistical result of sample intensity indicates that the finding of the GΓMM is similar to that obtained by the manual method. These results indicate the stability and reliability of the GΓMM combined with the Bayes framework for the segmentation of HIFU lesions in ultrasound images. The experimental results show the possibility of combining the GΓMM with the Bayes framework to segment lesion areas and evaluate the effect of therapeutic ultrasound.

A Study on a Parameter Estimator for the Homodyned K Distribution Based on Table Search for Ultrasound Tissue Characterization

OBJECTIVE

The homodyned K (HK) distribution is considered to be the most suitable distribution in the context of tissue characterization; therefore, the search for a rapid and reliable parameter estimator for HK distribution is important.

METHODS

We propose a novel parameter estimator based on a table search (TS) for HK parameter estimates. The TS estimator can inherit the strength of conventional estimators by integrating various features and taking advantage of the TS method in a rapid and easy operation. Performance of the proposed TS estimator was evaluated and compared with that of XU (the estimation method based on X and U statistics) and artificial neural network (ANN) estimators.

DISCUSSION

The simulation results revealed that the TS estimator is superior to the XU and ANN estimators in terms of normalized standard deviations and relative root mean squared errors of parameter estimation, and is faster. Clinical experiments found that the area under the receiver operating curve for breast lesion classification using the parameters estimated by the TS estimator could reach 0.871.

CONCLUSION

The proposed TS estimator is more accurate, reliable and faster than the state-of-the-art XU and ANN estimators and has great potential for ultrasound tissue characterization based on the HK distribution.

Information Entropy and Its Applications

Ultrasound is a first-line diagnostic tool for imaging many disease states. A number of statistical distributions have been proposed to describe ultrasound backscattering measured from tissues having different disease states. As an example, in this chapter we use nonalcoholic fatty liver disease (NAFLD), which is a critical health issue on a global scale, to demonstrate the capabilities of ultrasound to diagnose disease. Ultrasound interaction with the liver is typically characterized by scattering, which is quantified for the purpose of determining the degree of liver steatosis and fibrosis. Information entropy provides an insight into signal uncertainty. This concept allows for the analysis of backscattered statistics without considering the distribution of data or the statistical properties of ultrasound signals. In this chapter, we examined the background of NAFLD and the sources of scattering in the liver. The fundamentals of information entropy and an algorithmic scheme for ultrasound entropy imaging are then presented. Lastly, some examples of using ultrasound entropy imaging to grade hepatic steatosis and evaluate the risk of liver fibrosis in patients with significant hepatic steatosis are presented to illustrate future opportunities for clinical use.

An Improved Parameter Estimator of the Homodyned K Distribution Based on the Maximum Likelihood Method for Ultrasound Tissue Characterization

The homodyned K distribution (HK) can generally describe the ultrasound backscatter envelope statistics distribution with parameters that have specific physical meaning. However, creating robust and reliable HK parameter estimates remains a crucial concern. The maximum likelihood estimator (MLE) usually yields a small variance and bias in parameter estimation. Thus, two recent studies have attempted to use MLE for parameter estimation of HK distribution. However, some of the statements in these studies are not fully justified and they may hinder the application of parameter estimation of HK distribution based on MLE. In this study, we propose a new parameter estimator for the HK distribution based on the MLE (i.e., MLE1), which overcomes the disadvantages of conventional MLE of HK distribution. The MLE1 was compared with other estimators, such as XU estimator (an estimation method based on the first moment of the intensity and tow log-moments) and ANN estimator (an estimation method based on artificial neural networks). We showed that the estimations of parameters α and k are the best overall (in terms of the relative bias, normalized standard deviation, and relative root mean squared errors) using the proposed MLE1 compared with the others based on the simulated data when the sample size was N = 1000. Moreover, we assessed the usefulness of the proposed MLE1 when the number of scatterers per resolution cell was high (i.e., α up to 80) and when the sample size was small (i.e., N = 100), and we found a satisfactory result. Tests on simulated ultrasound images based on Field II were performed and the results confirmed that the proposed MLE1 is feasible and reliable for the parameter estimation from the ultrasonic envelope signal. Therefore, the proposed MLE1 can accurately estimate the HK parameters with lower uncertainty, which presents a potential practical value for further ultrasonic applications.

Autonomous Prostate Segmentation in 2D B-Mode Ultrasound Images

Prostate brachytherapy is a treatment for prostate cancer; during the planning of the procedure, ultrasound images of the prostate are taken. The prostate must be segmented out in each of the ultrasound images, and to assist with the procedure, an autonomous prostate segmentation algorithm is proposed. The prostate contouring system presented here is based on a novel superpixel algorithm, whereby pixels in the ultrasound image are grouped into superpixel regions that are optimized based on statistical similarity measures, so that the various structures within the ultrasound image can be differentiated. An active shape prostate contour model is developed and then used to delineate the prostate within the image based on the superpixel regions. Before segmentation, this contour model was fit to a series of point-based clinician-segmented prostate contours exported from conventional prostate brachytherapy planning software to develop a statistical model of the shape of the prostate. The algorithm was evaluated on nine sets of in vivo prostate ultrasound images and compared with manually segmented contours from a clinician, where the algorithm had an average volume difference of 4.49 mL or 10.89%.

Ultrasound Sample Entropy Imaging: A New Approach for Evaluating Hepatic Steatosis and Fibrosis

Objective: Hepatic steatosis causes nonalcoholic fatty liver disease and may progress to fibrosis. Ultrasound is the first-line approach to examining hepatic steatosis. Fatty droplets in the liver parenchyma alter ultrasound radiofrequency (RF) signal statistical properties. This study proposes using sample entropy, a measure of irregularity in time-series data determined by the dimension [Formula: see text] and tolerance [Formula: see text], for ultrasound parametric imaging of hepatic steatosis and fibrosis. Methods: Liver donors and patients were enrolled, and their hepatic fat fraction (HFF) ([Formula: see text]), steatosis grade ([Formula: see text]), and fibrosis score ([Formula: see text]) were measured to verify the results of sample entropy imaging using sliding-window processing of ultrasound RF data. Results: The sample entropy calculated using [Formula: see text] 4 and [Formula: see text] was highly correlated with the HFF when a small window with a side length of one pulse was used. The areas under the receiver operating characteristic curve for detecting hepatic steatosis that was [Formula: see text]mild, [Formula: see text]moderate, and [Formula: see text]severe were 0.86, 0.90, and 0.88, respectively, and the area was 0.87 for detecting liver fibrosis in individuals with significant steatosis. Discussion/Conclusions: Ultrasound sample entropy imaging enables the identification of time-series patterns in RF signals received from the liver. The algorithmic scheme proposed in this study is compatible with general ultrasound pulse-echo systems, allowing clinical fibrosis risk evaluations of individuals with developing hepatic steatosis.

Clinical Feasibility of Quantitative Ultrasound Imaging for Suspected Hepatic Steatosis: Intra- and Inter-examiner Reliability and Correlation with Controlled Attenuation Parameter

This study was aimed at investigating the clinical feasibility of quantitative ultrasound (QUS) imaging in the evaluation of suspected hepatic steatosis through assessment of the reliability of measurements and its correlation with the controlled attenuation parameter (CAP). This retrospective study included 117 patients who underwent liver B-mode ultrasound (US) with QUS imaging with a clinical US machine (RS85, Samsung Medison, Seoul, Korea) and CAP measurements between December 2019 and March 2020. For QUS examination, tissue attenuation imaging (TAI) and tissue scatter-distribution imaging (TSI) parameters were obtained. Intra- and inter-examiner reliability were assessed using intra-class correlation coefficients (ICCs), and QUS imaging parameters were correlated with CAP measurements using Spearman's correlation analysis. TAI and TSI revealed excellent intra- and inter-examiner reliability with ICCs of 0.994 and 0.975 and 0.991 and 0.947, respectively. Both TAI and TSI were significantly positively correlated with CAP values. QUS imaging provided good intra-and inter-observer reliability and correlated well with CAP in assessing suspected hepatic steatosis.

Detection of pediatric hepatic steatosis through ultrasound backscattering analysis

OBJECTIVES

Hepatic steatosis has become a considerable concern in the pediatric population. The objective of this study was to evaluate the feasibility of using ultrasound Nakagami imaging to produce a parametric image for analyzing the echo amplitude distribution to assess pediatric hepatic steatosis.

METHODS

A total of 68 pediatric participants were enrolled in healthy control (n = 26) and study groups (n = 42). Raw data from ultrasound imaging were acquired for each participant analysis using AmCAD-US, a software approved by the US Food and Drug Administration for ultrasound Nakagami imaging. The Nakagami parameters were compared with the hepatic steatosis index (HSI) and the steatosis grade (G0: HSI < 30; G1: 30 ≤ HSI < 36; G2: 36 ≤ HSI < 41.6; G3: 41.6 ≤ HSI < 43; G4: HSI ≥ 43) using correlation analysis, one-way analysis of variance (ANOVA), and receiver operating characteristic (ROC) curve analysis.

RESULTS

The Nakagami parameter increased from 0.53 ± 0.13 to 0.82 ± 0.05 with increasing severity of hepatic steatosis from G0 to G4 and were significantly different between the different grades of hepatic steatosis (p < .05). The areas under the ROC curves were 0.96, 0.92, 0.85, and 0.82 for diagnosing hepatic steatosis ≥ G1, ≥ G2, ≥ G3, and ≥ G4, respectively.

CONCLUSIONS

The Nakagami parameter value quantifies changes in the echo amplitude distribution of ultrasound backscattered signals caused by fatty infiltration, providing a novel, noninvasive, and effective data analysis technique to detect pediatric hepatic steatosis.

KEY POINTS

• Ultrasound Nakagami imaging enabled quantification of the echo amplitude distribution for tissue characterization. • The Nakagami parameter increased with the increasing severity of pediatric hepatic steatosis. • The Nakagami parameter demonstrated promising diagnostic performance in evaluating pediatric hepatic steatosis.

Nakagami imaging with related distributions for advanced thermogram pseudocolorization

Pseudocoloring algorithms embedded in the software of thermal cameras gradually colorize original intensity thermograms generated by detecting temperatures and contrast. Maximum and minimum based algorithms, however, executed by thresholding, applied to intensity thermograms for revealing and coloring the outliers instead. Although the common pseudocoloring protocols employed for general purposes may provide crucial information on the superficial contrast between radiation emitted by various sources; their common kernel is not sufficient for detecting and differentiating high radiated regions from surrounding areas, which is mandatory for recognition of abnormalities. Therefore, we propose novel imaging methodology based on Nakagami and related distributions, including gamma, Rayleigh, Weibull, chi-square and exponential, for enhancing thermal images and also for creating adequate discrimination. We initially define the boundaries of tumor and surrounding area in a synthetically generated breast thermogram already diagnosed as retroareolar tumor. Using Nakagami and transformations supported by mathematical foundations, we conducted several experiments to find the discrimination factor of the pseudocoloring techniques by calculating difference of average contrast between the tumor and the surrounding area. The performance is greatly encouraging that we achieved considerably better discrimination factor, designated for this study, up to 106.80 compared to the results of existing built-in pseudocolorization methods computed as 11.56.

Ultrasound Assessment of Hepatic Steatosis by Using the Double Nakagami Distribution: A Feasibility Study

Ultrasound imaging is a first-line assessment tool for hepatic steatosis. Properties of tissue microstructures correlate with the statistical distribution of ultrasound backscattered signals, which can be described by the Nakagami distribution (a widely adopted approximation of backscattered statistics). The double Nakagami distribution (DND) model, which combines two Nakagami distributions, was recently proposed for using high-frequency ultrasound to analyze backscattered statistics corresponding to lipid droplets in the fat-infiltrated liver. This study evaluated the clinical feasibility of the DND model in ultrasound parametric imaging of hepatic steatosis by conducting clinical experiments using low-frequency ultrasound dedicated to general abdominal examinations. A total of 204 patients were recruited, and ultrasound image raw data were acquired using a 3.5 MHz array transducer for DND parametric imaging using the sliding window technique. The DND parameters were compared with hepatic steatosis grades identified histologically. A receiver operating characteristic (ROC) curve analysis was used to evaluate the diagnostic performance. The results indicated that DND parametric imaging constructed using a sliding window with the side length of five times the pulse length of the transducer provided stable and reliable DND parameter estimations and visualized changes in the backscattered statistics caused by hepatic steatosis. The DND parameter increased with the hepatic steatosis grade. The areas under the ROC curve for identifying hepatic steatosis were 0.76 (≥mild), 0.81 (≥moderate), and 0.82 (≥severe). When using low-frequency ultrasound, DND imaging allows the clinical detection of hepatic steatosis and reflects information associated with lipid droplets in the fat-infiltrated liver.

Ultrasound Backscatter Envelope Statistics Parametric Imaging for Liver Fibrosis Characterization: A Review

Early detection and diagnosis of liver fibrosis is of critical importance. Currently the gold standard for diagnosing liver fibrosis is biopsy. However, liver biopsy is invasive and associated with sampling errors and can lead to complications such as bleeding. Therefore, developing noninvasive imaging techniques for assessing liver fibrosis is of clinical value. Ultrasound has become the first-line tool for the management of chronic liver diseases. However, the commonly used B-mode ultrasound is qualitative and can cause interobserver or intraobserver difference. Ultrasound backscatter envelope statistics parametric imaging is an important group of quantitative ultrasound techniques that have been applied to characterizing different kinds of tissue. However, a state-of-the-art review of ultrasound backscatter envelope statistics parametric imaging for liver fibrosis characterization has not been conducted. In this paper, we focused on the development of ultrasound backscatter envelope statistics parametric imaging techniques for assessing liver fibrosis from 1998 to September 2019. We classified these techniques into six categories: constant false alarm rate, fiber structure extraction technique, acoustic structure quantification, quantile-quantile probability plot, the multi-Rayleigh model, and the Nakagami model. We presented the theoretical background and algorithms for liver fibrosis assessment by ultrasound backscatter envelope statistics parametric imaging. Then, the specific applications of ultrasound backscatter envelope statistics parametric imaging techniques to liver fibrosis evaluation were reviewed and analyzed. Finally, the pros and cons of each technique were discussed, and the future development was suggested.

Monitoring of Adult Zebrafish Heart Regeneration Using High-Frequency Ultrasound Spectral Doppler and Nakagami Imaging

This paper reports the feasibility of Nakagami imaging in monitoring the regeneration process of zebrafish hearts in a noninvasive manner. In addition, spectral Doppler waveforms that are typically used to access the diastolic function were measured to validate the performance of Nakagami imaging. A 30-MHz high-frequency ultrasound array transducer was used to acquire backscattered echo signal for spectral Doppler and Nakagami imaging. The performances of both methods were validated with flow and tissue-mimicking phantom experiments. For in vivo experiments, both spectral Doppler and Nakagami imaging were simultaneously obtained from adult zebrafish with amputated hearts. Longitudinal measurements were performed for five zebrafish. From the experiments, the E/A ratio measured using spectral Doppler imaging increased at 3 days post-amputation (3 dpa) and then decreased to the value before amputation, which were consistent with previous studies. Similar results were obtained from the Nakagami imaging where the Nakagami parameter value increased at 3 dpa and decreased to its original value. These results suggested that the Nakagami and spectral Doppler imaging would be useful techniques in monitoring the regeneration of heart or tissues.

Considerations of Ultrasound Scanning Approaches in Non-alcoholic Fatty Liver Disease Assessment through Acoustic Structure Quantification

Non-alcoholic fatty liver disease (NAFLD) is a risk factor for hepatic fibrosis and cirrhosis. Acoustic structure quantification (ASQ), based on statistical analysis of ultrasound echoes, is an emerging technique for hepatic steatosis diagnosis. A standardized measurement protocol for ASQ analysis was suggested previously; however, an optimal ultrasound scanning approach has not been concluded thus far. In this study, the suitability of scanning approaches for the ASQ-based evaluation of hepatic steatosis was investigated. Hepatic fat fractions (HFFs; liver segments VIII, III and VI) of 70 living liver donors were assessed with magnetic resonance spectroscopy. A clinical ultrasound machine equipped with a 3-MHz convex transducer was used to scan each participant using the intercostal, epigastric and subcostal planes to acquire raw data for estimating two ASQ parameters (C_m² and focal disturbance [FD] ratio) of segments VIII, III and VI, respectively. The parameters were plotted as functions of the HFF for calculating the values of the correlation coefficient (r) and probability value (p). The diagnostic performance of the parameters in discriminating between the normal and steatotic (≥5 and ≥10%) groups was also compared using receiver operating characteristic (ROC) curves. The C_m² and FD ratio values measured using the epigastric and subcostal planes did not correlate with the severity of hepatic steatosis. However, intercostal imaging exhibited a higher correlation between the ASQ parameters and HFF (r = -0.64, p < 0.001). The diagnostic performance of C_m² and FD ratio in detecting hepatic steatosis using intercostal imaging was also satisfactory (areas under ROC curves >0.8). Intercostal imaging is an appropriate scanning approach for ASQ analysis of the liver.

Extraction of gray-scale intensity distributions from micro computed tomography imaging for femoral cortical bone differentiation between low-magnesium and normal diets in a laboratory mouse model

Previous studies have shown that the geometric development of femoral trabecular bone is affected by insufficient dietary intake of magnesium. However, it is not clear whether the development of femoral cortical bone can be quantitatively evaluated according to a diet with inadequate magnesium supplementation. Therefore, we used a micro computed tomography (CT) imaging approach with a laboratory mouse model to explore the potential application of texture analysis for the quantitative assessment of femoral cortical bones. C57BL/6J male mice were divided into two groups, where one group was fed a normal diet and the other group was fed a low-magnesium diet. We used a micro CT scanner for image acquisition, and the subsequent development of cortical bone was examined by texture analysis based on the statistical distribution of gray-scale intensities in which seven essential parameters were extracted from the micro CT images. Our calculations showed that the mean intensity increased by 7.20% (p = 0.000134), sigma decreased by 29.18% (p = 1.98E-12), skewness decreased by 19.52% (p = 0.0000205), kurtosis increased by 9.62% (p = 0.0877), energy increased by 24.19% (p = 3.32E-09), entropy decreased by 6.14% (p = 3.00E-10), and the Nakagami parameter increased by 104.32% (p = 4.13E-12) in the low-magnesium group when compared to the normal group. We found that the statistical parameters extracted from the gray-scale intensity distribution were able to differentiate between femoral cortical bone developments in the two different diet groups.

Hepatic Steatosis Assessment Using Quantitative Ultrasound Parametric Imaging Based on Backscatter Envelope Statistics

Hepatic steatosis is a key manifestation of non-alcoholic fatty liver disease (NAFLD). Early detection of hepatic steatosis is of critical importance. Currently, liver biopsy is the clinical golden standard for hepatic steatosis assessment. However, liver biopsy is invasive and associated with sampling errors. Ultrasound has been recommended as a first-line diagnostic test for the management of NAFLD. However, B-mode ultrasound is qualitative and can be affected by factors including image post-processing parameters. Quantitative ultrasound (QUS) aims to extract quantified acoustic parameters from the ultrasound backscattered signals for ultrasound tissue characterization and can be a complement to conventional B-mode ultrasound. QUS envelope statistics techniques, both statistical model-based and non-model-based, have shown potential for hepatic steatosis characterization. However, a state-of-the-art review of hepatic steatosis assessment using envelope statistics techniques is still lacking. In this paper, envelope statistics-based QUS parametric imaging techniques for characterizing hepatic steatosis are reviewed and discussed. The reviewed ultrasound envelope statistics parametric imaging techniques include acoustic structure quantification imaging, ultrasound Nakagami imaging, homodyned-K imaging, kurtosis imaging, and entropy imaging. Future developments are suggested.

Ex Vivo and In Vivo Monitoring and Characterization of Thermal Lesions by High-Intensity Focused Ultrasound and Microwave Ablation Using Ultrasonic Nakagami Imaging

The feasibility of ultrasonic Nakagami imaging to evaluate thermal lesions by high-intensity focused ultrasound and microwave ablation was explored in ex vivo and in vivo liver models. Dynamic changes of the ultrasonic Nakagami parameter in thermal lesions were calculated, and ultrasonic B-mode and Nakagami images were reconstructed simultaneously. The contrast-to-noise ratio (CNR) between thermal lesions and normal tissue was used to estimate the contrast resolution of the monitoring images. After thermal ablation, a bright hyper-echoic region appeared in the ultrasonic B-mode and Nakagami images, identifying the thermal lesion. During thermal ablation, mean values of Nakagami parameter showed an increasing trend from 0.72 to 1.01 for the ex vivo model and 0.54 to 0.72 for the in vivo model. After thermal ablation, mean CNR values of the ultrasonic Nakagami images were 1.29 dB (ex vivo) and 0.80 dB (in vivo), significantly higher ( ) than those for B-mode images. Thermal lesion size, assessed using ultrasonic Nakagami images, shows a good correlation to those obtained from the gross-pathology images (for the ex vivo model: length, = 0.96; width, = 0.90; for the in vivo model: length, = 0.95; width, = 0.85). This preliminary study suggests that ultrasonic Nakagami parameter may have a potential use in evaluating the formation of thermal lesions with better image contrast. Moreover, ultrasonic Nakagami imaging combined with B-mode imaging may be utilized as an alternative modality in developing monitoring systems for image-guided thermal ablation treatments.

Hepatic Steatosis Assessment with Ultrasound Small-Window Entropy Imaging

Nonalcoholic fatty liver disease is a type of hepatic steatosis that is not only associated with critical metabolic risk factors but can also result in advanced liver diseases. Ultrasound parametric imaging, which is based on statistical models, assesses fatty liver changes, using quantitative visualization of hepatic-steatosis-caused variations in the statistical properties of backscattered signals. One constraint with using statistical models in ultrasound imaging is that ultrasound data must conform to the distribution employed. Small-window entropy imaging was recently proposed as a non-model-based parametric imaging technique with physical meanings of backscattered statistics. In this study, we explored the feasibility of using small-window entropy imaging in the assessment of fatty liver disease and evaluated its performance through comparisons with parametric imaging based on the Nakagami distribution model (currently the most frequently used statistical model). Liver donors (n = 53) and patients (n = 142) were recruited to evaluate hepatic fat fractions (HFFs), using magnetic resonance spectroscopy and to evaluate the stages of fatty liver disease (normal, mild, moderate and severe), using liver biopsy with histopathology. Livers were scanned using a 3-MHz ultrasound to construct B-mode, small-window entropy and Nakagami images to correlate with HFF analyses and fatty liver stages. The diagnostic values of the imaging methods were evaluated using receiver operating characteristic curves. The results demonstrated that the entropy value obtained using small-window entropy imaging correlated well with log₁₀(HFF), with a correlation coefficient r = 0.74, which was higher than those obtained for the B-scan and Nakagami images. Moreover, small-window entropy imaging also resulted in the highest area under the receiver operating characteristic curve (0.80 for stages equal to or more severe than mild; 0.90 for equal to or more severe than moderate; 0.89 for severe), which indicated that non-model-based entropy imaging-using the small-window technique-performs more favorably than other techniques in fatty liver assessment.

Three-dimensional Visualization of Ultrasound Backscatter Statistics by Window-modulated Compounding Nakagami Imaging

In this study, the window-modulated compounding (WMC) technique was integrated into three-dimensional (3D) ultrasound Nakagami imaging for improving the spatial visualization of backscatter statistics. A 3D WMC Nakagami image was produced by summing and averaging a number of 3D Nakagami images (number of frames denoted as N) formed using sliding cubes with varying side lengths ranging from 1 to N times the transducer pulse. To evaluate the performance of the proposed 3D WMC Nakagami imaging method, agar phantoms with scatterer concentrations ranging from 2 to 64 scatterers/mm³ were made, and six stages of fatty liver (zero, one, two, four, six, and eight weeks) were induced in rats by methionine-choline-deficient diets (three rats for each stage, total n = 18). A mechanical scanning system with a 5-MHz focused single-element transducer was used for ultrasound radiofrequency data acquisition. The experimental results showed that 3D WMC Nakagami imaging was able to characterize different scatterer concentrations. Backscatter statistics were visualized with various numbers of frames; N = 5 reduced the estimation error of 3D WMC Nakagami imaging in visualizing the backscatter statistics. Compared with conventional 3D Nakagami imaging, 3D WMC Nakagami imaging improved the image smoothness without significant image resolution degradation, and it can thus be used for describing different stages of fatty liver in rats.

Effect of ultrasound frequency on the Nakagami statistics of human liver tissues

The analysis of the backscattered statistics using the Nakagami parameter is an emerging ultrasound technique for assessing hepatic steatosis and fibrosis. Previous studies indicated that the echo amplitude distribution of a normal liver follows the Rayleigh distribution (the Nakagami parameter m is close to 1). However, using different frequencies may change the backscattered statistics of normal livers. This study explored the frequency dependence of the backscattered statistics in human livers and then discussed the sources of ultrasound scattering in the liver. A total of 30 healthy participants were enrolled to undergo a standard care ultrasound examination on the liver, which is a natural model containing diffuse and coherent scatterers. The liver of each volunteer was scanned from the right intercostal view to obtain image raw data at different central frequencies ranging from 2 to 3.5 MHz. Phantoms with diffuse scatterers only were also made to perform ultrasound scanning using the same protocol for comparisons with clinical data. The Nakagami parameter-frequency correlation was evaluated using Pearson correlation analysis. The median and interquartile range of the Nakagami parameter obtained from livers was 1.00 (0.98-1.05) for 2 MHz, 0.93 (0.89-0.98) for 2.3 MHz, 0.87 (0.84-0.92) for 2.5 MHz, 0.82 (0.77-0.88) for 3.3 MHz, and 0.81 (0.76-0.88) for 3.5 MHz. The Nakagami parameter decreased with the increasing central frequency (r = -0.67, p < 0.0001). However, the effect of ultrasound frequency on the statistical distribution of the backscattered envelopes was not found in the phantom results (r = -0.147, p = 0.0727). The current results demonstrated that the backscattered statistics of normal livers is frequency-dependent. Moreover, the coherent scatterers may be the primary factor to dominate the frequency dependence of the backscattered statistics in a liver.

Evaluation of muscular changes by ultrasound Nakagami imaging in Duchenne muscular dystrophy

Duchenne muscular dystrophy (DMD) is the most common debilitating muscular disorder. Developing a noninvasive measure for monitoring the progression of this disease is critical. The present study tested the effectiveness of using ultrasound Nakagami imaging to evaluate the severity of the dystrophic process. A total of 47 participants (40 with DMD and 7 healthy controls) were recruited. Patients were classified into stage 1 (presymptomatic and ambulatory), stage 2 (early nonambulatory), and stage 3 (late nonambulatory). All participants underwent ultrasound examinations on the rectus femoris, tibialis anterior, and gastrocnemius. The results revealed that the ultrasound Nakagami parameter correlated positively with functional severity in the patients with DMD. The median Nakagami parameter of the gastrocnemius muscle increased from 0.50 to 0.85, corresponding to the largest dynamic range between normal and stage 3. The accuracy, sensitivity, and specificity of diagnosing walking function were 85.52%, 76.31%, and 94.73%, respectively. The Nakagami parameter of the rectus femoris and gastrocnemius muscles correlated negatively with the 6-minute walking distance in the ambulatory patients. Therefore, changes in the Nakagami parameter for the gastrocnemius muscle are suitable for monitoring disease progression in ambulatory patients and for predicting ambulation loss. Ultrasound Nakagami imaging shows potential for evaluating patients with DMD.

Detecting changes in ultrasound backscattered statistics by using Nakagami parameters: Comparisons of moment-based and maximum likelihood estimators

The Nakagami distribution is an approximation useful to the statistics of ultrasound backscattered signals for tissue characterization. Various estimators may affect the Nakagami parameter in the detection of changes in backscattered statistics. In particular, the moment-based estimator (MBE) and maximum likelihood estimator (MLE) are two primary methods used to estimate the Nakagami parameters of ultrasound signals. This study explored the effects of the MBE and different MLE approximations on Nakagami parameter estimations. Ultrasound backscattered signals of different scatterer number densities were generated using a simulation model, and phantom experiments and measurements of human liver tissues were also conducted to acquire real backscattered echoes. Envelope signals were employed to estimate the Nakagami parameters by using the MBE, first- and second-order approximations of MLE (MLE₁ and MLE₂, respectively), and Greenwood approximation (MLE_gw) for comparisons. The simulation results demonstrated that, compared with the MBE and MLE₁, the MLE₂ and MLE_gw enabled more stable parameter estimations with small sample sizes. Notably, the required data length of the envelope signal was 3.6 times the pulse length. The phantom and tissue measurement results also showed that the Nakagami parameters estimated using the MLE₂ and MLE_gw could simultaneously differentiate various scatterer concentrations with lower standard deviations and reliably reflect physical meanings associated with the backscattered statistics. Therefore, the MLE₂ and MLE_gw are suggested as estimators for the development of Nakagami-based methodologies for ultrasound tissue characterization.

Feasibility of Using Ultrasonic Nakagami Imaging for Monitoring Microwave-Induced Thermal Lesion in Ex Vivo Porcine Liver

The feasibility of using ultrasonic Nakagami imaging to evaluate thermal lesions induced by microwave ablation (MWA) in ex vivo porcine liver was explored. Dynamic changes in echo amplitudes and Nakagami parameters in the region of the MWA-induced thermal lesion, as well as the contrast-to-noise ratio (CNR) between the MWA-induced thermal lesion and the surrounding normal tissue, were calculated simultaneously during the MWA procedure. After MWA exposure, a bright hyper-echoic region appeared in ultrasonic B-mode and Nakagami parameter images as an indicator of the thermal lesion. Mean values of the Nakagami parameter in the thermal lesion region increased to 0.58, 0.71 and 0.91 after 1, 3 and 5 min of MVA. There were no significant differences in envelope amplitudes in the thermal lesion region among ultrasonic B-mode images obtained after different durations of MWA. Unlike ultrasonic B-mode images, Nakagami images were less affected by the shadow effect in monitoring of MWA exposure, and a fairly complete hyper-echoic region was observed in the Nakagami image. The mean value of the Nakagami parameter increased from approximately 0.47 to 0.82 during MWA exposure. At the end of the postablation stage, the mean value of the Nakagami parameter decreased to 0.55 and was higher than that before MWA exposure. CNR values calculated for Nakagami parameter images increased from 0.13 to approximately 0.61 during MWA and then decreased to 0.26 at the end of the post-ablation stage. The corresponding CNR values calculated for ultrasonic B-mode images were 0.24, 0.42 and 0.17. This preliminary study on ex vivo porcine liver suggested that Nakagami imaging have potential use in evaluating the formation of MWA-induced thermal lesions. Further in vivo studies are needed to evaluate the potential application.

Small-window parametric imaging based on information entropy for ultrasound tissue characterization

Constructing ultrasound statistical parametric images by using a sliding window is a widely adopted strategy for characterizing tissues. Deficiency in spatial resolution, the appearance of boundary artifacts, and the prerequisite data distribution limit the practicability of statistical parametric imaging. In this study, small-window entropy parametric imaging was proposed to overcome the above problems. Simulations and measurements of phantoms were executed to acquire backscattered radiofrequency (RF) signals, which were processed to explore the feasibility of small-window entropy imaging in detecting scatterer properties. To validate the ability of entropy imaging in tissue characterization, measurements of benign and malignant breast tumors were conducted (n = 63) to compare performances of conventional statistical parametric (based on Nakagami distribution) and entropy imaging by the receiver operating characteristic (ROC) curve analysis. The simulation and phantom results revealed that entropy images constructed using a small sliding window (side length = 1 pulse length) adequately describe changes in scatterer properties. The area under the ROC for using small-window entropy imaging to classify tumors was 0.89, which was higher than 0.79 obtained using statistical parametric imaging. In particular, boundary artifacts were largely suppressed in the proposed imaging technique. Entropy enables using a small window for implementing ultrasound parametric imaging.

Acoustic structure quantification by using ultrasound Nakagami imaging for assessing liver fibrosis

Acoustic structure quantification (ASQ) is a recently developed technique widely used for detecting liver fibrosis. Ultrasound Nakagami parametric imaging based on the Nakagami distribution has been widely used to model echo amplitude distribution for tissue characterization. We explored the feasibility of using ultrasound Nakagami imaging as a model-based ASQ technique for assessing liver fibrosis. Standard ultrasound examinations were performed on 19 healthy volunteers and 91 patients with chronic hepatitis B and C (n = 110). Liver biopsy and ultrasound Nakagami imaging analysis were conducted to compare the METAVIR score and Nakagami parameter. The diagnostic value of ultrasound Nakagami imaging was evaluated using receiver operating characteristic (ROC) curves. The Nakagami parameter obtained through ultrasound Nakagami imaging decreased with an increase in the METAVIR score (p < 0.0001), representing an increase in the extent of pre-Rayleigh statistics for echo amplitude distribution. The area under the ROC curve (AUROC) was 0.88 for the diagnosis of any degree of fibrosis (≥F1), whereas it was 0.84, 0.69, and 0.67 for ≥F2, ≥F3, and ≥F4, respectively. Ultrasound Nakagami imaging is a model-based ASQ technique that can be beneficial for the clinical diagnosis of early liver fibrosis.

Ultrasound window-modulated compounding Nakagami imaging: Resolution improvement and computational acceleration for liver characterization

Ultrasound Nakagami imaging is an attractive method for visualizing changes in envelope statistics. Window-modulated compounding (WMC) Nakagami imaging was reported to improve image smoothness. The sliding window technique is typically used for constructing ultrasound parametric and Nakagami images. Using a large window overlap ratio may improve the WMC Nakagami image resolution but reduces computational efficiency. Therefore, the objectives of this study include: (i) exploring the effects of the window overlap ratio on the resolution and smoothness of WMC Nakagami images; (ii) proposing a fast algorithm that is based on the convolution operator (FACO) to accelerate WMC Nakagami imaging. Computer simulations and preliminary clinical tests on liver fibrosis samples (n=48) were performed to validate the FACO-based WMC Nakagami imaging. The results demonstrated that the width of the autocorrelation function and the parameter distribution of the WMC Nakagami image reduce with the increase in the window overlap ratio. One-pixel shifting (i.e., sliding the window on the image data in steps of one pixel for parametric imaging) as the maximum overlap ratio significantly improves the WMC Nakagami image quality. Concurrently, the proposed FACO method combined with a computational platform that optimizes the matrix computation can accelerate WMC Nakagami imaging, allowing the detection of liver fibrosis-induced changes in envelope statistics. FACO-accelerated WMC Nakagami imaging is a new-generation Nakagami imaging technique with an improved image quality and fast computation.

Ultrasound characterization of the mastoid for detecting middle ear effusion: A preliminary clinical validation

Ultrasound detection of middle ear effusion (MEE) is an emerging technique in otolaryngology. This study proposed using ultrasound characterization of the mastoid to noninvasively measure MEE-induced mastoid effusion (ME) as a new strategy for determining the presence of MEE. In total, 53 patients were enrolled (Group I: normal, n = 20; Group II: proven MEE through both otoscopy and tympanometry, n = 15; Group III: patients with MEE having effusions observed during grommet surgery, n = 18). A 2.25-MHz delay-line transducer was used to measure backscattered signals from the mastoid. The Nakagami parameter was estimated using the acquired signals to model the echo amplitude distribution for quantifying changes in the acoustic structures of mastoid air cells. The median Nakagami parameter and interquartile range were 0.35 (0.34-0.37) for Group I, 0.39 (0.37-0.41) for Group II, and 0.43 (0.39-0.51) for Group III. The echo amplitude distribution observed for patients with MEE was closer to Rayleigh distribution than that without MEE. Receiver operating characteristic (ROC) curve analysis further revealed that the area under the ROC was 0.88, sensitivity was 72.73%, specificity was 95%, and accuracy was 81.13%. The proposed method has considerable potential for noninvasive and comfortable evaluation of MEE.