Ultrasound Normalized Weighted Cumulative Residual Entropy Imaging: A New Quantitative Ultrasound Method for...

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 = -0.6749, p < 0.0001) than NCRE (Spearman r = -0.6695, p < 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 > 0.05), with area under the receiver operating characteristic curve (AUC) values of 0.78, 0.85 and 0.86 for ≥G1, ≥G2 and ≥G3 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 < 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.