{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,9]],"date-time":"2026-10-09T12:52:35Z","timestamp":1791550355112,"version":"4.3.4"},"reference-count":27,"publisher":"MDPI AG","issue":"19","license":[{"start":{"date-parts":[[2026,10,8]],"date-time":"2026-10-08T00:00:00Z","timestamp":1791417600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2026,10,8]],"date-time":"2026-10-08T00:00:00Z","timestamp":1791417600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Diagnostics"],"abstract":"<jats:p>Background\/Objectives: In this paper, we propose ultrasound normalized weighted cumulative residual entropy (NWCRE) imaging, a novel quantitative ultrasound (QUS) technique derived from the information-theoretic weighted cumulative residual entropy (WCRE) for hepatic steatosis characterization. Methods: The proposed ultrasound NWCRE imaging method adopted cumulative distribution function (CDF)-driven non-parametric estimation, and parallel computing was implemented to improve computational efficiency. For a comparison study, the previously reported ultrasound normalized cumulative residual entropy (NCRE) imaging was also implemented. We further mathematically derived the finite upper bound of integrals for both NWCRE and NCRE to convert improper integrals into proper integrals for numerical calculation. Phantom simulations with varied scatterer number densities and two groups of clinical datasets for hepatic steatosis assessment were investigated for validation. Results: Phantom results demonstrated that both NWCRE and NCRE values decreased with increasing scatterer concentrations. For clinical group A (72 liver donors; magnetic resonance spectroscopy-measured hepatic fat fraction (HFF) served as the reference), NWCRE imaging exhibited a slightly stronger correlation with log10(HFF) (Spearman r = \u22120.6749, p &lt; 0.0001) than NCRE (Spearman r = \u22120.6695, p &lt; 0.0001). For clinical group B (204 chronic hepatitis B patients; liver biopsy served as the histopathological ground-truth reference), NWCRE imaging yielded comparable diagnostic performance to NCRE for discriminating hepatic steatosis grades (all p &gt; 0.05), with area under the receiver operating characteristic curve (AUC) values of 0.78, 0.85 and 0.86 for \u2265G1, \u2265G2 and \u2265G3 steatosis, respectively. Across phantom simulations and both clinical groups, the dynamic ranges of NWCRE imaging were statistically significantly higher than those of NCRE imaging (all p &lt; 0.0001). Conclusions: The proposed parallelized ultrasound NWCRE imaging delivers diagnostic performance comparable to NCRE imaging while improving the dynamic range over NCRE imaging, providing a potential CDF-based QUS tool for quantitative evaluation of hepatic steatosis.<\/jats:p>","DOI":"10.3390\/diagnostics16193253","type":"journal-article","created":{"date-parts":[[2026,10,8]],"date-time":"2026-10-08T15:16:52Z","timestamp":1791472612000},"page":"3253","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Ultrasound Normalized Weighted Cumulative Residual Entropy Imaging: A New Quantitative Ultrasound Method for Characterizing Hepatic Steatosis"],"prefix":"10.3390","volume":"16","author":[{"given":"Huilin","family":"Si","sequence":"first","affiliation":[{"name":"School of Computer and Artificial Intelligence, Beijing Technology and Business University, Beijing 100048, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"methodology","vocabulary":"credit"},{"role":"software","vocabulary":"credit"},{"role":"formal-analysis","vocabulary":"credit"},{"role":"investigation","vocabulary":"credit"},{"role":"writing-original-draft","vocabulary":"credit"},{"role":"visualization","vocabulary":"credit"}]},{"given":"Ruiyang","family":"Gao","sequence":"additional","affiliation":[{"name":"Department of Biomedical Engineering, College of Chemistry and Life Science, Beijing University of Technology, Beijing 100124, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"methodology","vocabulary":"credit"},{"role":"validation","vocabulary":"credit"},{"role":"formal-analysis","vocabulary":"credit"},{"role":"data-curation","vocabulary":"credit"},{"role":"writing-original-draft","vocabulary":"credit"},{"role":"visualization","vocabulary":"credit"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1054-1583","authenticated-orcid":false,"given":"Dar-In","family":"Tai","sequence":"additional","affiliation":[{"name":"Department of Gastroenterology and Hepatology, Chang Gung Memorial Hospital at Linkou, Chang Gung University, Taoyuan 333423, Taiwan"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"validation","vocabulary":"credit"},{"role":"formal-analysis","vocabulary":"credit"},{"role":"resources","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"}]},{"given":"Po-Hsiang","family":"Tsui","sequence":"additional","affiliation":[{"name":"Department of Biomedical Engineering and Environmental Sciences, National Tsing Hua University, Hsinchu 300044, Taiwan"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"conceptualization","vocabulary":"credit"},{"role":"methodology","vocabulary":"credit"},{"role":"formal-analysis","vocabulary":"credit"},{"role":"resources","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"},{"role":"supervision","vocabulary":"credit"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0570-8473","authenticated-orcid":false,"given":"Zhuhuang","family":"Zhou","sequence":"additional","affiliation":[{"name":"Department of Biomedical Engineering, College of Chemistry and Life Science, Beijing University of Technology, Beijing 100124, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"conceptualization","vocabulary":"credit"},{"role":"methodology","vocabulary":"credit"},{"role":"software","vocabulary":"credit"},{"role":"validation","vocabulary":"credit"},{"role":"investigation","vocabulary":"credit"},{"role":"data-curation","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"},{"role":"supervision","vocabulary":"credit"}]}],"member":"1968","published-online":{"date-parts":[[2026,10,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"7083","DOI":"10.1038\/s41598-025-91312-5","article-title":"Global burden of MAFLD, MAFLD related cirrhosis and MASH related liver cancer from 1990 to 2021","volume":"15","author":"Guo","year":"2025","journal-title":"Sci. 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