Ultrasonic Evaluation of Liver Fibrosis Using the Homodyned K Distribution with an Artificial Neural Network Estimator

Abstract

Early detection of liver fibrosis is of critical importance. The homodyned K (HK) distribution is a generalized model with the most physical meaning of ultrasonic backscattering. The stage of liver fibrosis can be evaluated by estimating its parameters k and a. However, the estimation of the parameters is complicated. Recently, we have proposed an artificial neural network (ANN) estimator for the HK distribution. In this work, we proposed an improved ANN estimator. Monte Carlo computer simulation was used to generate independent and identically distributed envelope signals of HK distribution, which were used to train an ANN model. Signal-to-noise ratio (SNR) R, skewness S, kurtosis K, X-, and U-statistics were calculated from envelope signals as feature parameters. The inputs of our previous ANN estimator were R <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> , S <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> , K <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> , X and U. In this work, the proposed ANN estimator took parameters R <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0.72</inf> , S <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0.72</inf> , K <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0.72</inf> , R <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0.88</inf> , S <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0.88</inf> , K <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0.88</inf> , X and U as the inputs. Clinical ultrasound radiofrequency (RF) data were divided into Group I (n = 94; liver fibrosis with no hepatic steatosis) and Group II (n = 143; liver fibrosis with mild to severe hepatic steatosis). The RF data were envelope-detected and the eight feature parameters were calculated as the input to the trained ANN model to obtain the estimated k and a values. The receiver operating characteristic (ROC) curve was used for evaluating the diagnostic values of k and a based on the ANN estimator, which were compared with those based on the XU estimator. Computer simulation results show that the proposed ANN estimator outperforms the previous ANN estimator. For Group I, the area under the ROC curve obtained using the k parameter based on the proposed ANN and conventional XU estimators were (0.80, 0.67, 0.60, 0.65) and (0.75, 0.62, 0.59, 0.67) for diagnosing liver ≥F1, ≥F2, ≥F3, ≥F4, respectively. For Group II, compared with the XU estimator, the ANN estimator had comparable diagnostic performance of liver fibrosis. The coexistence of hepatic steatosis affected the detection and diagnosis of liver fibrosis by the HK distribution.