OBJECTIVE: Focal liver lesion (FLL) is a prevalent finding in cross-sectional imaging, and distinguishing between benign and malignant FLLs is crucial for liver health management. While shear wave elastography (SWE) serves as a conventional quantitative ultrasound tool for evaluating FLLs, ultrasound tissue scatterer distribution imaging (TSI) emerges as a novel technique, employing the Nakagami statistical distribution parameter to estimate backscattered statistics for tissue characterization. In this prospective study, we explored the potential of TSI in characterizing FLLs and evaluated its diagnostic efficacy with that of SWE.
METHODS: A total of 235 participants (265 FLLs; the study group) were enrolled to undergo abdominal examinations, which included data acquisition from B-mode, SWE, and raw radiofrequency data for TSI construction. The area under the receiver operating characteristic curve (AUROC) was used to evaluate performance. A dataset of 20 patients (20 FLLs; the validation group) was additionally acquired to further evaluate the efficacy of the TSI cutoff value in FLL characterization.
RESULTS: In the study group, our findings revealed that while SWE achieved a success rate of 49.43 % in FLL measurements, TSI boasted a success rate of 100 %. In cases where SWE was effectively implemented, the AUROCs for characterizing FLLs using SWE and TSI stood at 0.84 and 0.83, respectively. For instances where SWE imaging failed, TSI achieved an AUROC of 0.78. Considering all cases, TSI presented an overall AUROC of 0.81. There was no statistically significant difference in AUROC values between TSI and SWE (p > 0.05). In the validation group, using a TSI cutoff value of 0.67, the AUROC for characterizing FLLs was 0.80.
CONCLUSIONS: In conclusion, ultrasound TSI holds promise as a supplementary diagnostic tool to SWE for characterizing FLLs.

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.

OBJECTIVE: The purpose of this study is to accurately monitor temperature during microwave hyperthermia. We propose a temperature estimation model BP-Nakagami based on neural network for Nakagami distribution.
METHODS: In this work, we designed the microwave hyperthermia experiment of fresh ex vivo pork tissue and phantom, collected ultrasonic backscatter data at different temperatures, modeled these data using Nakagami distribution, and calculated Nakagami distribution parameter m. A neural network model was built to train the relationship between Nakagami distribution parameter m and temperature, and a BP-Nakagami temperature model with good fitting was obtained. The temperature model is used to draw the two-dimensional temperature distribution map of biological tissues in microwave hyperthermia. Finally, the temperature estimated by the model is compared with the temperature measured by thermocouples.
RESULTS: The error between the temperature estimated by the temperature model and the temperature measured by the thermocouple is within 1°C in the range of 25°C-50°C for ex vivo pork tissue, and the error between the temperature estimated by the temperature model and the temperature measured by the thermocouple is within 0.5°C in the range of 25°C-50°C for phantom.
CONCLUSIONS: The results show that the temperature estimation model proposed by us is an effective model for monitoring the internal temperature change of biological tissues.

In this study we investigate the potential of parametric images formed from ultrasound B-mode scans using the Nakagami distribution for non-invasive classification of breast lesions and characterization of breast tissue. Through a sliding window technique, we generated seven types of Nakagami images for each patient scan in our dataset using basic and as well as derived parameters of the Nakagami distribution. To determine the suitable window size for image generation, we conducted an empirical analysis using 4 windows, which includes 3 column windows of lengths 0.1875 mm, 0.45 mm and 0.75 mm and widths of 0.002 mm, along with the standard square window with sides equal to three times the pulse length of incident ultrasound. From the parametric image sets generated using each window, we extracted a total of 72 features that consisted of morphometric, elemental and hybrid features. To our knowledge no other literature has conducted such a comprehensive analysis of Nakagami parametric images for the classification of breast lesions. Feature selection was performed to find the most useful subset of features from each of the parametric image sets for the classification of breast cancer. Analyzing the classification accuracy and Area under the Receiver Operating Characteristic (ROC) Curve (AUC) of the selected feature subsets, we determined that the selected features acquired from Nakagami parametric images generated using a column window of length 0.75 mm provides the best results for characterization of breast lesions. This optimal feature set provided a classification accuracy of 93.08%, an AUC of 0.9712, a False Negative Rate (FNR) of 0%, and a very low False Positive Rate (FPR) of 8.65%. Our results indicate that the high accuracy of such a procedure may assist in the diagnosis of breast cancer by helping to reduce false positive diagnoses.

BACKGROUND: Considerable progress of ultrasound simulation on blood has enhanced the characterizing of red blood cell (RBC) aggregation.
OBJECTIVE: A novel simulation method aims at modeling the blood with different RBC aggregations and concentrations is proposed.
METHODS: The modeling process is as follows: (i) A three-dimensional scatterer model is first built by a mapping with a Hilbert space-filling curve from the one-dimensional scatterer distribution. (ii) To illustrate the relationship between the model parameters and the RBC aggregation level, a variety of blood samples are prepared and scanned to acquire their radiofrequency signals in-vitro. (iii) The model parameters are determined by matching the Nakagami-distribution characteristics of envelope signals simulated from the model with those measured from the blood samples.
RESULTS: Nakagami metrics m estimated from 15 kinds of blood samples (hematocrits of 20%, 40%, 60% and plasma concentrations of 15%, 30%, 45%, 60%, 75%) are compared with metrics estimated by their corresponding models (each with different eligible parameters). Results show that for the three hematocrit levels, the mean and standard deviation of the root-mean-squared deviations of m are 0.27 ± 0.0026, 0.16 ± 0.0021, 0.12 ± 0.0018 respectively.
CONCLUSIONS: The proposed simulation model provides a viable data source to evaluate the performance of the ultrasound-based methods for quantifying RBC aggregation.

OBJECTIVE: Our previous studies demonstrate that the variation in ultrasonic envelope statistics is correlated with the temperature change inside scattering media. This variation is identified as the change in the scatterer structure during thermal expansion or contraction. However, no specific evidence has been verified to date. This study numerically reproduces the change in the scatterer distribution during thermal expansion or contraction using finite element simulations and also investigates how the situation is altered by different material properties.
METHODS: The material properties of a linear elastic solid depend on the thermal expansion coefficient, thermal conductivity, specific heat, and initial scatterer number density. Three-dimensional displacements, calculated in the simulation, were sequentially used to update the positions of the randomly distributed scatterers. Ultrasound signals from the scatterer distribution were generated by simulating a 7.5-MHz linear array transducer whose specifications were the same as those in the experimental measurements of several phantoms and excised porcine livers. To represent the change in the envelope statistical feature, the absolute value of the ratio change in the logarithmic Nakagami (NA) parameter, Δ m , at each time was calculated as a value normalized with the initial NA parameter.
RESULTS: The change in the scatterer number density relates to the volume change during temperature elevation. The magnitude of the Δ m shift against the temperature change increases depending on the higher thermal expansion coefficient. In contrast, the relationship between Δ m and the scatterer number density is similar with any material property. Additionally, the changes in Δ m obtained by several experimental phantoms with low to high scatterer number densities are comparable with the numerical simulation results.
CONCLUSIONS: The change in Δ m is indirectly related to the change in the scatterer number density owing to the volume change during thermal expansion or contraction.

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.

BACKGROUND: Lymphedema is a disease in which tissue swelling is caused by interstitial fluid retention in subcutaneous tissue. It is caused by a compromised lymphatic system. Lymphoscintigraphy is the current and primary modality used to assess lymphatic system dysfunction. Ultrasound elastography is a complementary tool used for evaluating the tissue stiffness of the lymphedematous limb. Tissue stiffness implies the existence of changes in tissue microstructures. However, ultrasound features related to tissue microstructures are neglected in clinical assessments of lymphedematous limbs. In this study, we aimed to evaluate the lymphedematous diagnostic values of ultrasound Nakagami and entropy imaging, which are, respectively, model- and nonmodel-based backscattered statistical analysis methods for scatterer characterization.
METHODS: A total of 60 patients were recruited, and lymphoscintigraphy was used to score the patient\'s clinical severity of each of their limb lymphedema (0: normal; 1: partial lymphatic obstruction; and 2: total lymphatic obstruction). We performed ultrasound examinations to acquire ultrasound backscattered signals for B-mode, Nakagami, and entropy imaging. The envelope amplitude, Nakagami, and entropy values, as a function of the patients\' lymphatic obstruction grades, were expressed in terms of their median and interquartile range (IQR). The values were then used in both an independent t test and a receiver operating characteristic (ROC) curve analysis.
RESULTS: For each increase in a patient\'s score from 0 to 2, the envelope amplitude values were 405.44 (IQR: 238.72-488.17), 411.52 (IQR: 298.53-644.25), and 476.37 (IQR: 348.86-648.16), respectively. The Nakagami parameters were 0.16 (IQR: 0.14-0.22), 0.26 (IQR: 0.23-0.34), and 0.24 (IQR: 0.16-0.36), respectively, and the entropy values were 4.55 (IQR: 4.41-4.66), 4.86 (IQR: 4.78-4.99), and 4.87 (IQR: 4.81-4.97), respectively. The P values between the normal control and lymphedema groups obtained from B-mode and Nakagami analysis were larger than 0.05; whereas that of entropy imaging was smaller than 0.05. The areas under the ROC curve for B-mode, Nakagami, and entropy imaging were 0.64 (sensitivity: 70%; specificity: 47.5%), 0.75 (sensitivity: 70%; specificity: 75%), and 0.94 (sensitivity: 95%; specificity: 87.5%), respectively.
CONCLUSIONS: The current findings demonstrated the diagnostic values of ultrasound Nakagami and entropy imaging techniques. In particular, the use of non-model-based entropy imaging enables for improved performance when characterizing limb lymphedema.

We propose a novel joint segmentation and characterization algorithm for the assessment of skin aging using 50 MHz high-frequency ultrasound images. The proposed segmentation method allows a fine determination of the envelope signal\'s statistics in the dermis as a function of depth. The sequence of statistical estimates obtained is then combined into a single aging score. The segmentation is based on tailored recursive non-linear filters. The epidermis and the dermis are jointly segmented with a non-parametric active contour combining a texture criterion, an epidermis indicator map and the geometric constraint of horizontal continuity. The algorithm is designed to apply to 2D and 3D images as well. We evaluated skin photo-aging on ultrasound images with an experimental study on a cohort of 76 women separated into 2 groups of different ages. Two aging scores are computed from the images: local dermal contrast and skin roughness. We show that these scores are much better at identifying the two groups (p-value ≈10-6) than the previously used MGVR indicator (p-value 0.046). Moreover, we find that a combined score more reliably evaluates skin photo-aging, with 84% success, than a scoring of the ultrasound images by 4 experts.

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 (MLEgw) for comparisons. The simulation results demonstrated that, compared with the MBE and MLE1, the MLE2 and MLEgw 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 MLEgw could simultaneously differentiate various scatterer concentrations with lower standard deviations and reliably reflect physical meanings associated with the backscattered statistics. Therefore, the MLE2 and MLEgw are suggested as estimators for the development of Nakagami-based methodologies for ultrasound tissue characterization.