Uncertainty-aware physics-driven deep learning network for free-breathing liver fat and R2 quantification using self-gated stack-of-radial MRI

Purpose: To develop a deep learning-based method for rapid liver proton-density fat fraction (PDFF) and R-2* quantification with built-in uncertainty estimation using self-gated free-breathing stack-of-radial MRI. Methods: This work developed an uncertainty-aware physics-driven deep learning network (UP-Net) to (1) suppress radial streaking artifacts because of undersampling after self-gating, (2) calculate accurate quantitative maps, and (3) provide pixel-wise uncertainty maps. UP-Net incorporated a phase augmentation strategy, generative adversarial network architecture, and an MRI physics loss term based on a fat-water and R-2* signal model. UP-Net was trained and tested using free-breathing multi-echo stack-of-radial MRI data from 105 subjects. UP-Net uncertainty scores were calibrated in a validation dataset and used to predict quantification errors for liver PDFF and R-2* in a testing dataset. Results: Compared with images reconstructed using compressed sensing (CS), UP-Net achieved structural similarity index > 0.87 and normalized root mean squared error < 0.18. Compared with reference quantitative maps generated using CS and graph-cut (GC) algorithms, UP-Net achieved low mean differences (MD) for liver PDFF (-0.36%) and R-2* (-0.37 s(-1)). Compared with breath-holding Cartesian MRI results, UP-Net achieved low MD for liver PDFF (0.53%) and R-2* (6.75 s(-1)). UP-Net uncertainty scores predicted absolute liver PDFF and R-2* errors with low MD of 0.27% and 0.12 s(-1) compared to CS + GC results. The computational time for UP-Net was 79 ms/slice, whereas CS + GC required 3.2 min/slice. Conclusion: UP-Net rapidly calculates accurate liver PDFF and R-2* maps from self-gated free-breathing stack-of-radial MRI. The pixel-wise uncertainty maps from UP-Net predict quantification errors in the liver.