PurposeTo develop a free‐breathing hepatic fat and quantification method by extending a previously described stack‐of‐stars model‐based fat‐water separation technique with additional modeling of the transverse relaxation rate .MethodsThe proposed technique combines motion‐robust radial sampling using a stack‐of‐stars bipolar multi‐echo 3D GRE acquisition with iterative model‐based fat‐water separation. Parallel‐Imaging and Compressed‐Sensing principles are incorporated through modeling of the coil‐sensitivity profiles and enforcement of total‐variation (TV) sparsity on estimated water, fat, and parameter maps. Water and fat signals are used to estimate the confounder‐corrected proton‐density fat fraction (PDFF). Two strategies for handling respiratory motion are described: motion‐averaged and motion‐resolved reconstruction. Both techniques were evaluated in patients (n = 14) undergoing a hepatobiliary research protocol at 3T. PDFF and parameter maps were compared to a breath‐holding Cartesian reference approach.ResultsLinear regression analyses demonstrated strong (r > 0.96) and significant (P ≪ .01) correlations between radial and Cartesian PDFF measurements for both the motion‐averaged reconstruction (slope: 0.90; intercept: 0.07%) and the motion‐resolved reconstruction (slope: 0.90; intercept: 0.11%). The motion‐averaged technique overestimated hepatic values (slope: 0.35; intercept: 30.2 1/s) compared to the Cartesian reference. However, performing a respiratory‐resolved reconstruction led to better value consistency (slope: 0.77; intercept: 7.5 1/s).ConclusionsThe proposed techniques are promising alternatives to conventional Cartesian imaging for fat and quantification in patients with limited breath‐holding capabilities. For accurate estimation, respiratory‐resolved reconstruction should be used.