Fatty liver evaluation with double-Nakagami model under low-resolution conditions

Ultrasound normalized cumulative residual entropy imaging: Theory, methodology, and application

BACKGROUND AND OBJECTIVE

Ultrasound information entropy imaging is an emerging quantitative ultrasound technique for characterizing local tissue scatterer concentrations and arrangements. However, the commonly used ultrasound Shannon entropy imaging based on histogram-derived discrete probability estimation suffers from the drawbacks of histogram settings dependence and unknown estimator performance. In this paper, we introduced the information-theoretic cumulative residual entropy (CRE) defined in a continuous distribution of cumulative distribution functions as a new entropy measure of ultrasound backscatter envelope uncertainty or complexity, and proposed ultrasound CRE imaging for tissue characterization.

METHODS

We theoretically analyzed the CRE for Rayleigh and Nakagami distributions and proposed a normalized CRE for characterizing scatterer distribution patterns. We proposed a method based on an empirical cumulative distribution function estimator and a trapezoidal numerical integration for estimating the normalized CRE from ultrasound backscatter envelope signals. We presented an ultrasound normalized CRE imaging scheme based on the normalized CRE estimator and the parallel computation technique. We also conducted theoretical analysis of the differential entropy which is an extension of the Shannon entropy to a continuous distribution, and introduced a method for ultrasound differential entropy estimation and imaging. Monte-Carlo simulation experiments were performed to evaluate the estimation accuracy of the normalized CRE and differential entropy estimators. Phantom simulation and clinical experiments were conducted to evaluate the performance of the proposed normalized CRE imaging in characterizing scatterer concentrations and hepatic steatosis (n = 204), respectively.

RESULTS

The theoretical normalized CRE for the Rayleigh distribution was π/4, corresponding to the case where there were ≥10 randomly distributed scatterers within the resolution cell of an ultrasound transducer. The theoretical normalized CRE for the Nakagami distribution decreased as the Nakagami parameter m increased, corresponding to that the ultrasound backscattered statistics varied from pre-Rayleigh to Rayleigh and to post-Rayleigh distributions. Monte-Carlo simulation experiments showed that the proposed normalized CRE and differential entropy estimators can produce a satisfying estimation accuracy even when the size of the test samples is small. Phantom simulation experiments showed that the proposed normalized CRE and differential entropy imaging can characterize scatterer concentrations. Clinical experiments showed that the proposed ultrasound normalized CRE imaging is capable to quantitatively characterize hepatic steatosis, outperforming ultrasound differential entropy imaging and being comparable to ultrasound Shannon entropy and Nakagami imaging.

CONCLUSION

This study sheds light on the theory and methodology of ultrasound normalized CRE. The proposed ultrasound normalized CRE can serve as a new, flexible quantitative ultrasound envelope statistics parameter. The proposed ultrasound normalized CRE imaging may find applications in quantified characterization of biological tissues. Our code will be made available publicly at https://github.com/zhouzhuhuang.

Clinical performance of ultrasonic backscatter parametric and nonparametric statistics in detecting early hepatic steatosis

Diagnosis of early hepatic steatosis would allow timely intervention. B-mode ultrasound imaging was in question for detecting early steatosis, especially with a variety of concomitant parenchymal disease. This study aimed to use the surgical specimen as a reference standard to elucidate the clinical performance of ultrasonic echogenicity and backscatter parametric and nonparametric statistics in real-world scenarios. Ultrasound radio-frequency (RF) signals of right liver lobe and patient data were collected preoperatively. Surgical specimen was then used to histologically determine staging of steatosis. A backscatter nonparametric statistic (h), a known backscatter parametric statistic, i.e., the Nakagami parameter (m), and a quantitative echo intensity (env) were calculated. Among the 236 patients included in the study, 93 were grade 0 (<5% fat) and 143 were with steatosis. All the env, m and h statistics had shown significant discriminatory power of steatosis grades (AUC = 0.643-0.907 with p-value < 0.001). Mann-Whitney U tests, however, revealed that only the backscatter statistics m and h were significantly different between the groups of grades 0 and 1 steatosis. The two-way ANOVA showed a significant confounding effect of the elevated ALT on env (p-value = 0.028), but no effect on m or h. Additionally, the severe fibrosis was found to be a significant covariate for m and h. Ultrasonic signals acquired from different scanners were found linearly comparable.

Relationship between transmission/reception conditions of high-frequency plane wave compounding and evaluation accuracy of extended amplitude envelope statistics

The double-Nakagami (DN) model provides a method for analyzing the amplitude envelope statistics of quantitative ultrasound (QUS). In this study, the relationship between the sound field characteristics and the robustness of QUS evaluation was evaluated using five HF linear array probes and tissue-mimicking phantoms. Compound plane-wave imaging (CPWI) was used to acquire echo data. Five phantoms containing two types of scatterers were used to mimic fatty liver tissue. After clarifying the relationship between the sound field characteristics of the probes and QUS parameters, DN QUS parameters in 10 rat livers with different lipidification were evaluated using one HF linear array probe. For both phantom and in situ liver analyses, correlations between fat content and multiple QUS parameters were confirmed, suggesting that the combination of CPWI using a HF linear array probe with the DN model is a robust method for quantifying fatty liver and has potential clinical diagnostic applications.

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.

Basic concept and clinical applications of quantitative ultrasound (QUS) technologies

In the field of clinical ultrasound, the full digitalization of diagnostic equipment in the 2000s enabled the technological development of quantitative ultrasound (QUS), followed by multiple diagnostic technologies that have been put into practical use in recent years. In QUS, tissue characteristics are quantified and parameters are calculated by analyzing the radiofrequency (RF) echo signals returning to the transducer. However, the physical properties (and pathological level structure) of the biological tissues responsible for the imaging features and QUS parameters have not been sufficiently verified as there are various conditions for observing living tissue with ultrasound and inevitable discrepancies between theoretical and actual measurements. A major issue of QUS in clinical application is that the evaluation results depend on the acquisition conditions of the RF echo signal as the source of the image information, and also vary according to the model of the diagnostic device. In this paper, typical examples of QUS techniques for evaluating attenuation, speed of sound, amplitude envelope characteristics, and backscatter coefficient in living tissues are introduced. Exemplary basic research and clinical applications related to these technologies, and initiatives currently being undertaken to establish the QUS method as a true tissue characterization technology, are also discussed.