PURPOSE: To develop a model-based reconstruction technique for real-time phase-contrast flow MRI with improved spatiotemporal accuracy in comparison to methods using phase differences of two separately reconstructed images with differential flow encodings. METHODS: The proposed method jointly computes a common image, a phase-contrast map, and a set of coil sensitivities from every pair of flow-compensated and flow-encoded datasets obtained by highly undersampled radial FLASH. Real-time acquisitions with five and seven radial spokes per image resulted in 25.6 and 35.7 ms measuring time per phase-contrast map, respectively. The signal model for phase-contrast flow MRI requires the solution of a nonlinear inverse problem, which is accomplished by an iteratively regularized Gauss-Newton method. Aspects of regularization and scaling are discussed. The model-based reconstruction was validated for a numerical and experimental flow phantom and applied to real-time phase-contrast MRI of the human aorta for 10 healthy subjects and 2 patients. RESULTS: Under all conditions, and compared with a previously developed real-time flow MRI method, the proposed method yields quantitatively accurate phase-contrast maps (i.e., flow velocities) with improved spatial acuity, reduced phase noise and reduced streaking artifacts. CONCLUSION: This novel model-based reconstruction technique may become a new tool for clinical flow MRI in real time. Magn Reson Med 77:1082-1093, 2017.
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