Ultrasound k-nearest neighbor entropy imaging: Theory, algorithm, and applications

Ultrasound information entropy is a flexible approach for analyzing ultrasound backscattering. Shannon entropy imaging based on probability distribution histograms (PDHs) has been implemented as a promising method for tissue characterization and diagnosis. However, the bin number affects the stability of entropy estimation. In this study, we introduced the k-nearest neighbor (KNN) algorithm to estimate entropy values and proposed ultrasound KNN entropy imaging. The proposed KNN estimator leveraged the Euclidean distance between data samples, rather than the histogram bins by conventional PDH estimators. We also proposed cumulative relative entropy (CRE) imaging to analyze time-series radiofrequency signals and applied it to monitor thermal lesions induced by microwave ablation (MWA). Computer simulation phantom experiments were conducted to validate and compare the performance of the proposed KNN entropy imaging, the conventional PDH entropy imaging, and Nakagami-m parametric imaging in detecting the variations of scatterer densities and visualizing inclusions. Clinical data of breast lesions were analyzed, and porcine liver MWA experiments ex vivo were conducted to validate the performance of KNN entropy imaging in classifying benign and malignant breast tumors and monitoring thermal lesions, respectively. Compared with PDH, the entropy estimation based on KNN was less affected by the tuning parameters. KNN entropy imaging was more sensitive to changes in scatterer densities and performed better visualizable capability than typical Shannon entropy (TSE) and Nakagami-m parametric imaging. Among different imaging methods, KNN-based Shannon entropy (KSE) imaging achieved the higher accuracy in classification of benign and malignant breast tumors and KNN-based CRE imaging had larger lesion-to-normal contrast when monitoring the ablated areas during MWA at different powers and treatment durations. Ultrasound KNN entropy imaging is a potential quantitative ultrasound approach for tissue characterization.

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.