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The objectives of this study were to develop a new method for free-breathing contrast-enhanced multiphase liver magnetic resonance imaging (MRI) using a combination of compressed sensing, parallel imaging, and radial k-space sampling and to demonstrate the feasibility of this method by performing image quality comparison with breath-hold cartesian T1-weighted (conventional) postcontrast acquisitions in healthy participants.This Health Insurance Portability and Accountability Act–compliant prospective study received approval from the institutional review board. Eight participants underwent 3 separate contrast-enhanced fat-saturated T1-weighted gradient-echo MRI examinations with matching imaging parameters: conventional breath-hold examination with cartesian k-space sampling volumetric interpolate breath hold examination (BH-VIBE) and free-breathing acquisitions with interleaved angle-bisection and continuous golden-angle radial sampling schemes. Interleaved angle-bisection and golden-angle data from each 100 consecutive spokes were reconstructed using a combination of compressed sensing and parallel imaging (interleaved-angle radial sparse parallel [IARASP] and golden-angle radial sparse parallel [GRASP]) to generate multiple postcontrast phases.Arterial- and venous-phase BH-VIBE, IARASP, and GRASP reconstructions were evaluated by 2 radiologists in a blinded fashion. The readers independently assessed quality of enhancement (QE), overall image quality (IQ), and other parameters of image quality on a 5-point scale, with the highest score indicating the most desirable examination. Mixed model analysis of variance was used to compare each measure of image quality.Images of BH-VIBE and GRASP had significantly higher QE and IQ values compared with IARASP for both phases (P < 0.05). The differences in QE between BH-VIBE and GRASP for the arterial and venous phases were not significant (P > 0.05). Although GRASP had lower IQ score compared with BH-VIBE for the arterial (3.9 vs 4.8; P < 0.0001) and venous (4.2 vs 4.8; P = 0.005) phases, GRASP received IQ scores of 3 or more in all participants, which was consistent with acceptable or better diagnostic image quality.Contrast-enhanced multiphase liver MRI of diagnostic quality can be performed during free breathing using a combination of compressed sensing, parallel imaging, and golden-angle radial sampling.