Hepatic Fat Quantification Using Beta Distribution and a Probabilistic Neural Network in a Prepubertal Male Cohort

Background/Objectives: High liver fat content is closely associated with hepatic disease and multiple comorbidities including cancer, diabetes and cardiovascular accidents. Therefore, accurate quantification of hepatic steatosis, especially of borderline cases, is essential for clinical management. Although MRI non-invasively assesses hepatic steatosis, current approaches remain limited by the data variability introduced through use of region-of-interest measurements or classification models that predict discrete fat grades without providing uncertainty estimates. This study proposes a probabilistic approach for hepatic steatosis quantification based on combining a neural network and beta distribution, enabling prediction of hepatic fat percentage with corresponding confidence intervals. Methods: Single in-phase Dixon MRI liver images from a cohort of prepubertal males (n = 84) were used as input to a probabilistic neural network combined with a beta distribution framework to estimate hepatic fat content along with associated confidence intervals. The predicted fat fractions were then compared against reference MRI-derived measurements (ground truth). Results: The methodology achieved a low prediction error and demonstrated good performance for the test set, with predicted values in good agreement with the ground truth measurements. This was reflected by the mean absolute error (MAE = 0.44 percentage points) and the coefficient of determination (R² = 0.98). The empirical standard deviation of the prediction errors on a logarithmic scale was σ = 0.0609. Conclusions: By incorporating uncertainty quantification into hepatic steatosis estimation, this probabilistic framework provides an interpretable measure of variability alongside point estimates. The approach is demonstrated in a specific cohort and requires further validation in broader populations.