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Abstract For 4D Flow MRI of mean and turbulent flow a compromise between spatiotemporal undersampling and velocity encodings needs to be found. Assuming a fixed scan time budget, the impact of trading off spatiotemporal undersampling versus velocity encodings on quantification of velocity and turbulence for aortic 4D Flow MRI was investigated. For this purpose, patient-specific mean and turbulent aortic flow data were generated using computational fluid dynamics which were embedded into the patient-specific background image data to generate synthetic MRI data with corresponding ground truth flow. Cardiac and respiratory motion were included. Using the synthetic MRI data as input, 4D Flow MRI was subsequently simulated with undersampling along pseudo-spiral Golden angle Cartesian trajectories for various velocity encoding schemes. Data were reconstructed using a locally low rank approach to obtain mean and turbulent flow fields to be compared to ground truth. Results show that, for a 15-min scan, velocity magnitudes can be reconstructed with good accuracy relatively independent of the velocity encoding scheme ( $$SSI{M}_{U}=0.938\pm 0.003)$$ S S I M U = 0.938 ± 0.003 ) , good accuracy ( $$SSI{M}_{U}\ge 0.933$$ S S I M U ≥ 0.933 ) and with peak velocity errors limited to 10%. Turbulence maps on the other hand suffer from both lower reconstruction quality ( $$SSI{M}_{TKE}\ge 0.323$$ S S I M TKE ≥ 0.323 ) and larger sensitivity to undersampling, motion and velocity encoding strengths ( $$SSI{M}_{TKE}=0.570\pm 0.110)$$ S S I M TKE = 0.570 ± 0.110 ) when compared to velocity maps. The best compromise to measure unwrapped velocity maps and turbulent kinetic energy given a fixed 15-min scan budget was found to be a 7-point multi- $${V}_{enc}$$ V enc acquisition with a low $${V}_{enc}$$ V enc tuned for best sensitivity to the range of expected intra-voxel standard deviations and a high $${V}_{enc}$$ V enc larger than the expected peak velocity.

Abstract We propose to synthesize patient-specific 4D flow MRI datasets of turbulent flow paired with ground truth flow data to support training of inference methods. Turbulent blood flow is computed based on the Navier–Stokes equations with moving domains using realistic boundary conditions for aortic shapes, wall displacements and inlet velocities obtained from patient data. From the simulated flow, synthetic multipoint 4D flow MRI data is generated with user-defined spatiotemporal resolutions and reconstructed with a Bayesian approach to compute time-varying velocity and turbulence maps. For MRI data synthesis, a fixed hypothetical scan time budget is assumed and accordingly, changes to spatial resolution and time averaging result in corresponding scaling of signal-to-noise ratios (SNR). In this work, we focused on aortic stenotic flow and quantification of turbulent kinetic energy (TKE). Our results show that for spatial resolutions of 1.5 and 2.5 mm and time averaging of 5 ms as encountered in 4D flow MRI in practice, peak total turbulent kinetic energy downstream of a 50, 75 and 90% stenosis is overestimated by as much as 23, 15 and 14% (1.5 mm) and 38, 24 and 23% (2.5 mm), demonstrating the importance of paired ground truth and 4D flow MRI data for assessing accuracy and precision of turbulent flow inference using 4D flow MRI exams.