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Quantification of peak velocity is important in the assessment of stenotic flow jets in patients with congenital heart disease. Phase-contrast magnetic resonance underestimates peak velocities. Hence, clinically Doppler ultrasound is used as the reference standard for assessing stenoses. It is possible to accurately measure peak velocity in MR using Fourier velocity encoding (FVE). In this study, a fast, high-resolution slice-selective FVE sequence was developed with the use of spiral trajectories, parallel imaging, and partial Fourier in the velocity dimension and a novel velocity-unwrap technique. The resulting sequence was acquired within a short breath-hold (more than 15 heartbeats) making this FVE technique clinically achievable. Peak velocities were compared from Doppler ultrasound, phase-contrast magnetic resonance, and FVE. Experiments were carried out in vitro and in vivo in 25 patients with congenital heart disease with stenoses. It was shown that in vitro and in vivo phase-contrast magnetic resonance tended to underestimate peak velocity when compared with Doppler ultrasound, whereas FVE agreed well with Doppler ultrasound.