Review of Envelope Statistics Models for Quantitative Ultrasound Imaging and Tissue Characterization.

The homodyned K-distribution and the K-distribution, viewed as a special case, as well as the Rayleigh and the Rice distributions, viewed as limit cases, are discussed in the context of quantitative ultrasound (QUS) imaging. The Nakagami distribution is presented as an approximation of the homodyned K-distribution. The main assumptions made are (1) the absence of log-compression or application of nonlinear filtering on the echo envelope of the radiofrequency signal and (2) the randomness and independence of the diffuse scatterers. We explain why other available models are less amenable to a physical interpretation of their parameters. We also present the main methods for the estimation of the statistical parameters of these distributions. We explain why we advocate the methods based on the X-statistics for the Rice and the Nakagami distributions and the K-distribution. The limitations of the proposed models are presented. Several new results are included in the discussion sections, with proofs in the appendix.

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.

Liver Fibrosis Assessment Using Radiomics of Ultrasound Homodyned-K imaging Based on the Artificial Neural Network Estimator.

The homodyned-K distribution is an important ultrasound backscatter envelope statistics model of physical meaning, and the parametric imaging of the model parameters has been explored for quantitative ultrasound tissue characterization. In this paper, we proposed a new method for liver fibrosis characterization by using radiomics of ultrasound backscatter homodyned-K imaging based on an improved artificial neural network (iANN) estimator. The iANN estimator was used to estimate the ultrasound homodyned-K distribution parameters k and α from the backscattered radiofrequency (RF) signals of clinical liver fibrosis (n = 237), collected with a 3-MHz convex array transducer. The RF data were divided into two groups: Group I corresponded to liver fibrosis with no hepatic steatosis (n = 94), and Group II corresponded to liver fibrosis with mild to severe hepatic steatosis (n = 143). The estimated homodyned-K parameter values were then used to construct k and α parametric images using the sliding window technique. Radiomics features of k and α parametric images were extracted, and feature selection was conducted. Logistic regression classification models based on the selected radiomics features were built for staging liver fibrosis. Experimental results showed that the proposed method is overall superior to the radiomics method of uncompressed envelope images when assessing liver fibrosis. Regardless of hepatic steatosis, the proposed method achieved the best performance in staging liver fibrosis ≥F1, ≥F4, and the area under the receiver operating characteristic curve was 0.88, 0.85 (Group I), and 0.85, 0.86 (Group II), respectively. Radiomics has improved the ability of ultrasound backscatter statistical parametric imaging to assess liver fibrosis, and is expected to become a new quantitative ultrasound method for liver fibrosis characterization.

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.

Detection of microwave ablation coagulation areas using ultrasound Nakagami imaging based on Gaussian pyramid decomposition: A feasibility study.

In this paper, we explored the feasibility of using ultrasound Nakagami-m parametric imaging based on Gaussian pyramid decomposition (GPD) to detect microwave ablation coagulation areas. Monte Carlo simulation and phantom simulation results demonstrated that a 2-layer GPD model was sufficient to achieve the same m parameter estimation accuracy, smoothness and resolution as 3-layer and 4-layer. The performances of GPD, moment-based estimator (MBE) and window-modulated compounding (WMC) algorithms were compared in terms of parameter estimation, smoothness, resolution and contrast-to-noise (CNR). Results showed that the m parameter estimation obtained by GPD algorithm was better than that of MBE and WMC algorithms except the small window size (27 × 5). When using a window size of >3 pulse lengths, GPD algorithm could achieve better smoothness and CNR than MBE and WMC algorithms, but there was a certain loss of axial resolution. The computation time of GPD algorithm was less than that of WMC algorithm, while about 2.24 times that of MBE algorithm. Experimental results of porcine liver microwave ablation ex vivo (n = 20) illustrated that the average areas under the operating characteristic curve (AUCs) of Nakagami mGPD, mMBE and mWMC parametric imaging and homodyned-K (HK) α and k parametric imaging to detect coagulation areas were significantly improved by polynomial approximation (PAX). Kruskal-Wallis test showed that the accuracy of coagulation area detection obtained by PAX imaging of mGPD parameter had no significant difference with that of mMBE, mWMC, HK_α and HK_k parameters. This preliminary study suggested that Nakagami imaging based on GPD algorithm may have the potential to detect microwave ablation coagulation areas.

Shear Wave Elastography and Quantitative Ultrasound as Biomarkers to Characterize Deep Vein Thrombosis In Vivo.

OBJECTIVE: Investigate shear wave elastography (SWE) and quantitative ultrasound (QUS) parameters in patients hospitalized for lower limb deep vein thrombosis (DVT). METHOD: Sixteen patients with DVT were recruited and underwent SWE and radiofrequency data acquisitions for QUS on day 0, day 7, and day 30 after the beginning of symptoms, in both proximal and distal zones of the clot identified on B-mode scan. SWE and QUS features were computed to differentiate between thrombi at day 0, day 7, and day 30 following treatment with heparin or oral anticoagulant. The Young's modulus from SWE was computed, as well as QUS homodyned K-distribution (HKD) parameters reflecting blood clot structure. Median and interquartile range of SWE and QUS parameters within clot were taken as features. RESULTS: In the proximal zone of the clot, the HKD ratio of coherent-to-diffuse backscatter median showed a significant decrease from day 7 to day 30 (P = .036), while the HKD ratio of diffuse-to-total backscatter median presented a significant increase from day 7 to day 30 (P = .0491). In the distal zone of the clot, the HKD normalized intensity of the echo envelope median showed a significant increase from day 0 to day 30 (P = .0062). No SWE features showed statistically significant differences over time. Nonetheless, a trend of lower median of Young's modulus within clot for patients who developed a pulmonary embolism was observed. CONCLUSION: QUS features may be relevant to characterize clot's evolution over time. Further analysis of their clinical interpretation and validation on a larger dataset would deserve to be studied.

[Monitoring microwave ablation using ultrasound backscatter homodyned K imaging: Comparison of estimators].

The feasibility of ultrasound backscatter homodyned K model parametric imaging (termed homodyned K imaging) to monitor coagulation zone during microwave ablation was investigated. Two recent estimators for the homodyned K model parameter, RSK (the estimation method based on the signal-to-noise ratio, the skewness, and the kurtosis of the amplitude envelope of ultrasound) and XU (the estimation method based on the first moment of the intensity of ultrasound, X statistics and U statistics), were compared. Firstly, the ultrasound backscattered signals during the microwave ablation of porcine liver ex vivo were processed by the noise-assisted correlation algorithm, envelope detection, sliding window method, digital scan conversion and color mapping to obtain homodyned K imaging. Then 20 porcine livers' microwave ablation experiments ex vivo were used to evaluate the effect of homodyned K imaging in monitoring the coagulation zone. The results showed that the area under the receiver operating characteristic curve of the RSK method was 0.77 ± 0.06 (mean ± standard deviation), and that of the XU method was 0.83 ± 0.08 (mean ± standard deviation). The accuracy to monitor the coagulation zone was (86 ± 10)% (mean ± standard deviation) by the RSK method and (90 ± 8)% (mean ± standard deviation) by the XU method. Compared with the RSK method, the Bland-Altman consistency for the coagulation zone estimated by the XU method and that of actual porcine liver tissue was higher. The time for parameter estimation and imaging by the XU method was less than that by the RSK method. We conclude that ultrasound backscatter homodyned K imaging can be used to monitor coagulation zones during microwave ablation, and the XU method is better than the RSK method.

Parameter estimation of the homodyned K distribution based on an artificial neural network for ultrasound tissue characterization.

The homodyned K (HK) distribution allows a general description of ultrasound backscatter envelope statistics with specific physical meanings. In this study, we proposed a new artificial neural network (ANN) based parameter estimation method of the HK distribution. The proposed ANN estimator took advantages of ANNs in learning and function approximation and inherited the strengths of conventional estimators through extracting five feature parameters from backscatter envelope signals as the input of the ANN: the signal-to-noise ratio (SNR), skewness, kurtosis, as well as X- and U-statistics. Computer simulations and clinical data of hepatic steatosis were used for validations of the proposed ANN estimator. The ANN estimator was compared with the RSK (the level-curve method that uses SNR, skewness, and kurtosis based on the fractional moments of the envelope) and XU (the estimation method based on X- and U-statistics) estimators. Computer simulation results showed that the relative bias was best for the XU estimator, whilst the normalized standard deviation was overall best for the ANN estimator. The ANN estimator was almost one order of magnitude faster than the RSK and XU estimators. The ANN estimator also yielded comparable diagnostic performance to state-of-the-art HK estimators in the assessment of hepatic steatosis. The proposed ANN estimator has great potential in ultrasound tissue characterization based on the HK distribution.

Ultrasound Detection of Liver Fibrosis in Individuals with Hepatic Steatosis Using the Homodyned K Distribution.

Acoustic structure quantification (ASQ) based on the analysis of ultrasound backscattered statistics has been reported to detect liver fibrosis without significant hepatic steatosis. This study proposed using ultrasound parametric imaging based on the parameter α of the homodyned K (HK) distribution for staging liver fibrosis in patients with significant hepatic steatosis. Raw ultrasound image data were acquired from patients (n = 237) to construct B-mode and HK α parametric images, which were compared with the focal disturbance (FD) ratio obtained from ASQ on the basis of histologic evidence (METAVIR fibrosis score and hepatic steatosis severity). The data were divided into group I (n = 173; normal to mild hepatic steatosis) and group II (n = 64; with moderate to severe hepatic steatosis) for statistical analysis through one-way analysis of variance and receiver operating characteristic (ROC) curve analysis. The results showed that the HK α parameter monotonically decreased as the liver fibrosis stage increased (p < .05); concurrently, the FD ratio increased (p < .05). For group I, the areas under the ROC (AUROCs) obtained using the FD ratio and the α parameter (AUROCFD and AUROCα) were, respectively, 0.56 and 0.55, 0.68 and 0.68, 0.64 and 0.64 and 0.62 and 0.62 for diagnosing liver fibrosis ≥F1, ≥F2, ≥F3 and ≥F4. The values of AUROCFD and AUROCα for group II were, respectively, 0.88 and 0.91, 0.81 and 0.81, 0.77 and 0.76 and 0.78 and 0.73 for diagnosing liver fibrosis ≥F1, ≥F2, ≥F3 and ≥F4. As opposed to previous studies, ASQ was found to fail in characterizing liver fibrosis in group I; however, it was workable for identifying liver fibrosis in patients with significant hepatic steatosis (group II). Compared with ASQ, HK imaging provided improved diagnostic performance in the early detection of liver fibrosis coexisting with moderate to severe hepatic steatosis. Ultrasound HK imaging is recommended as a strategy to evaluate early fibrosis risk in patients with significant hepatic steatosis.

Monitoring microwave ablation using ultrasound backscatter homodyned K imaging: Comparison of estimators / 生物医学工程学杂志

The feasibility of ultrasound backscatter homodyned K model parametric imaging (termed homodyned K imaging) to monitor coagulation zone during microwave ablation was investigated. Two recent estimators for the homodyned K model parameter, RSK (the estimation method based on the signal-to-noise ratio, the skewness, and the kurtosis of the amplitude envelope of ultrasound) and XU (the estimation method based on the first moment of the intensity of ultrasound,

In vivo Ultrafast Quantitative Ultrasound and Shear Wave Elastography Imaging on Farm-Raised Duck Livers during Force Feeding.

Shear wave elastography (speed and dispersion), local attenuation coefficient slope and homodyned-K parametric imaging were used for liver steatosis grading. These ultrasound biomarkers rely on physical interactions between shear and compression waves with tissues at both macroscopic and microscopic scales. These techniques were applied in a context not yet studied with ultrasound imaging, that is, monitoring steatosis of force-fed duck livers from pre-force-fed to foie gras stages. Each estimated feature presented a statistically significant trend along the feeding process (p values <10-3). However, whereas a monotonic increase in the shear wave speed was observed along the process, most quantitative ultrasound features exhibited an absolute maximum value halfway through the process. As the liver fat fraction in foie gras is much higher than that seen clinically, we hypothesized that a change in the ultrasound scattering regime is encountered for high-fat fractions, and consequently, care has to be taken when applying ultrasound biomarkers to grading of severe states of steatosis.

Value of homodyned K distribution in ultrasound parametric imaging of hepatic steatosis: An animal study.

Ultrasound is the first-line tool for screening hepatic steatosis. Statistical distributions can be used to model the backscattered signals for liver characterization. The Nakagami distribution is the most frequently adopted model; however, the homodyned K (HK) distribution has received attention due to its link to physical meaning and improved parameter estimation through X- and U-statistics (termed "XU"). To assess hepatic steatosis, we proposed HK parametric imaging based on the α parameter (a measure of the number of scatterers per resolution cell) calculated using the XU estimator. Using a commercial system equipped with a 7-MHz linear array transducer, phantom experiments were performed to suggest an appropriate window size for α imaging using the sliding window technique, which was further applied to measuring the livers of rats (n = 66) with hepatic steatosis induced by feeding the rats a methionine- and choline-deficient diet. The relationships between the α parameter, the stage of hepatic steatosis, and histological features were verified by the correlation coefficient r, one-way analysis of variance, and regression analysis. The phantom results showed that the window side length corresponding to five times the pulse length supported a reliable α imaging. The α parameter showed a promising performance for grading hepatic steatosis (p < 0.05; r2 = 0.68). Compared with conventional Nakagami imaging, α parametric imaging provided significant information associated with fat droplet size (p < 0.05; r2 = 0.53), enabling further analysis and evaluation of severe hepatic steatosis.

Ultrasound parametric imaging of hepatic steatosis using the homodyned-K distribution: An animal study.

Hepatic steatosis is an abnormal state where excess lipid mass is accumulated in hepatocyte vesicles. Backscattered ultrasound signals received from the liver contain useful information regarding the degree of steatosis in the liver. The homodyned-K (HK) distribution has been demonstrated as a general model for ultrasound backscattering. The estimator based on the first three integer moments (denoted as "FTM") of the intensity has potential for practical applications because of its simplicity and low computational complexity. This study explored the diagnostic performance of HK parametric imaging based on the FTM method in the assessment of hepatic steatosis. Phantom experiments were initially conducted using the sliding window technique to determine an appropriate window size length (WSL) for HK parametric imaging. Subsequently, hepatic steatosis was induced in male Wistar rats fed a methionine- and choline-deficient (MCD) diet for 0 (i.e., normal control), 1, 2, 4, 6, and 8 weeks (n = 36; six rats in each group). After completing the scheduled MCD diet, ultrasound B-mode and HK imaging of the rat livers were performed in vivo and histopathological examinations were conducted to score the degree of hepatic steatosis. HK parameters µ (related to scatterer number density) and k (related to scatterer periodicity) were expressed as functions of the steatosis stage in terms of the median and interquartile range (IQR). Receiver operating characteristic (ROC) curve analysis was conducted to assess the diagnostic performance levels of the µ and k parameters. The results showed that an appropriate WSL for HK parametric imaging is seven times the pulse length of the transducer. The median value of the µ parameter increased monotonically from 0.194 (IQR: 0.18-0.23) to 0.893 (IQR: 0.64-1.04) as the steatosis stage increased. Concurrently, the median value of the k parameter increased from 0.279 (IQR: 0.26-0.31) to 0.5 (IQR: 0.41-0.54) in the early stages (normal to mild) and decreased to 0.39 (IQR: 0.29-0.45) in the advanced stages (moderate to severe). The areas under the ROC curves obtained using (µ, k) were (0.947, 0.804), (0.914, 0.575), and (0.813, 0.604) for the steatosis stages of ≥mild, ≥moderate, and ≥severe, respectively. The current findings suggest that ultrasound HK parametric imaging based on FTM estimation has great potential for future clinical diagnoses of hepatic steatosis.

ESTIMATION METHOD OF THE HOMODYNED K-DISTRIBUTION BASED ON THE MEAN INTENSITY AND TWO LOG-MOMENTS.

The homodyned K-distribution appears naturally in the context of random walks and provides a useful model for the distribution of the received intensity in a wide range of non-Gaussian scattering configurations, including medical ultrasonics. An estimation method for the homodyned K-distribution based on the first moment of the intensity and two log-moments (XU method), namely the X and U-statistics previously studied in the special case of the K-distribution, is proposed as an alternative to a method based on the first three moments of the intensity (MI method) or the amplitude (MA method), and a method based on the signal-to-noise ratio (SNR), the skewness and the kurtosis of two fractional orders of the amplitude (labeled RSK method). Properties of the X and U statistics for the homodyned K-distribution are proved, except for one conjecture. Using those properties, an algorithm based on the bisection method for monotonous functions was developed. The algorithm has a geometric rate of convergence. Various tests were performed to study the behavior of the estimators. It was shown with simulated data samples that the estimations of the parameters 1/α and 1/(κ + 1) of the homodyned K-distribution are preferable to the direct estimations of the clustering parameter α and the structure parameter κ (with respective relative root mean squared errors (RMSEs) of 0.63 and 0.13 as opposed to 1.04 and 4.37, when N = 1000). Tests on simulated ultrasound images with only diffuse scatterers (up to 10 per resolution cell) indicated that the XU estimator is overall more reliable than the other three estimators for the estimation of 1/α, with relative RMSEs of 0.79 (MI), 0.61 (MA), 0.53 (XU) and 0.67 (RSK). For the parameter 1/(κ + 1), the relative RMSEs were equal to 0.074 (MI), 0.075 (MA), 0.069 (XU) and 0.100 (RSK). In the case of a large number of scatterers (11 to 20 per resolution cell), the relative RMSEs of 1/α were equal to 1.43 (MI), 1.27 (MA), 1.25 (XU) and 1.33 (RSK), and the relative RMSEs of 1/(κ + 1) were equal to 0.14 (MI), 0.16 (MA), 0.17 (XU) and 0.20 (RSK). The four methods were also tested on simulated ultrasound images with a variable density of periodic scatterers to test images with a coherent component. The addition of noise on ultrasound images was also studied. Results showed that the XU estimator was overall better than the three other ones. Finally, on the simulated ultrasound images, the average computation times per image were equal to 6.0 ms (MI), 8.0 ms (MA), 6.8 ms (XU) and 500 ms (RSK). Thus, a fast, reliable, and novel algorithm for the estimation of the homodyned K-distribution was proposed.