Ultrasonic Evaluation of Liver Fibrosis Coexisting with Hepatic Steatosis Using the Homodyned K Distribution Combined with Noise-modulated Empirical Mode Decomposition

Abstract

The Homodyne <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathbf{K}$</tex> (HK) distribution is a generalized model of ultrasound backscattering, with its parameters <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$k$</tex> (the ratio of the coherent to diffuse signal) and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\alpha$</tex> (the effective number of scatterers per resolution cell). When liver fibrosis and hepatic steatosis coexist, the backscattered signal contributed by fibrous liver tissue could not be highlighted, as the signal components (SCs) contributed by fatty liver have a much larger amplitude than those by fibrous liver. In this situation, characterizing liver fibrosis by using the HK distribution is quite challenging. In this study, we proposed using the HK distribution combined with noise-modulated empirical mode decomposition (NEMD) for ultrasonic assessment of liver fibrosis. Clinical ultrasound radiofrequency (RF) data of liver fibrosis used in our previous study [Tsai et al. Ultrasound Med. Biol. 47 (2021) 84–94] were revisited <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$(n=237)$</tex> . This study was approved by the Institutional Review Board of Chang Gung Memorial Hospital in Taiwan to reuse clinical data for the purpose of data analysis. The RF data were divided into liver fibrosis with no hepatic steatosis <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$(n=94)$</tex> and liver fibrosis with mild to severe hepatic steatosis <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$(n=143)$</tex> . The latter 143 cases of RF data (F0 = 13, F1 = 34, F2 = 18, F3 = 25, F4 = 41) were included in this study. The RF data were decomposed by NEMD, where artificial noises were added to EMD. The NEMD technique was used to separate liver fibrosis SCs from fatty liver SCs. The NEMD-decomposed second intrinsic mode function (IMF2) signals were envelope-detected and sliding-window-processed to construct parametric images of the HK distribution. The XU estimator was used for estimating HK model parameters <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$k$</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\alpha$</tex> . The average values of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$k$</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\alpha$</tex> within the region of interest in IMF2 parametric images (denoted by <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$k_{\mathbf{IMF}2}$</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$a_{\mathbf{IMF}2})$</tex> were used to evaluate the diagnostic performance of liver fibrosis. When fatty liver coexisted, the areas under the receiver operating characteristic curve obtained using <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\alpha$</tex> and α <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">IMF2</inf> were 0.69, 0.71, 0.69, 0.67 and 0.81, 0.76, 0.70, 0.60 for diagnosing liver fibrosis ≥F1, ≥ F2, ≥ F3, ≥ F4, respectively. Those using <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$k$</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\boldsymbol{k}_{\mathbf{IMF}2}$</tex> were 0.51, 0.53, 0.59, 0.55 and 0.55, 0.56, 0.51, 0.53, respectively. The NEMD-decomposed IMF <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> signals may contain large-amplitude SCs such as fatty liver, while the IMF2 signals are mostly contributed by liver fibrosis. This was confirmed in our experiments. Therefore, IMF2 SCs were used in this study. NEMD-HK improves the performance of liver fibrosis detection when fatty liver coexists, especially for early detection of liver fibrosis.