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Purpose To develop a deep learning‐based method for rapid liver proton‐density fat fraction (PDFF) and R2* 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 R2* 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 R2* 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 R2* (−0.37 s−1). Compared with breath‐holding Cartesian MRI results, UP‐Net achieved low MD for liver PDFF (0.53%) and R2* (6.75 s−1). UP‐Net uncertainty scores predicted absolute liver PDFF and R2* 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 R2* maps from self‐gated free‐breathing stack‐of‐radial MRI. The pixel‐wise uncertainty maps from UP‐Net predict quantification errors in the liver.

Background Magnetic resonance (MR) elastography of the liver measures hepatic stiffness, which correlates with the histopathological staging of liver fibrosis. Conventional Cartesian gradient-echo (GRE) MR elastography requires breath-holding, which is challenging for children. Non-Cartesian radial free-breathing MR elastography is a potential solution to this problem. Objective To investigate radial free-breathing MR elastography for measuring hepatic stiffness in children. Materials and methods In this prospective pilot study, 14 healthy children and 9 children with liver disease were scanned at 3 T using 2-D Cartesian GRE breath-hold MR elastography (22 s/slice) and 2-D radial GRE free-breathing MR elastography (163 s/slice). Each sequence was acquired twice. Agreement in the stiffness measurements was evaluated using Lin’s concordance correlation coefficient (CCC) and within-subject mean difference. The repeatability was assessed using the within-subject coefficient of variation and intraclass correlation coefficient (ICC). Results Fourteen healthy children and seven children with liver disease completed the study. Median (±interquartile range) normalized measurable liver areas were 62.6% (±26.4%) and 44.1% (±39.6%) for scan 1, and 60.3% (±21.8%) and 43.9% (±44.2%) for scan 2, for Cartesian and radial techniques, respectively. Hepatic stiffness from the Cartesian and radial techniques had close agreement with CCC of 0.89 and 0.94, and mean difference of 0.03 kPa and −0.01 kPa, for scans 1 and 2. Cartesian and radial techniques achieved similar repeatability with within-subject coefficient of variation=1.9% and 3.4%, and ICC=0.93 and 0.92, respectively. Conclusion In this pilot study, radial free-breathing MR elastography was repeatable and in agreement with Cartesian breath-hold MR elastography in children.