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Deep variational network for rapid 4D flow MRI reconstruction


Phase-contrast magnetic resonance imaging (MRI) provides time-resolved quantification of blood flow dynamics that can aid clinical diagnosis. Long in vivo scan times due to repeated three-dimensional (3D) volume sampling over cardiac phases and breathing cycles necessitate accelerated imaging techniques that leverage data correlations. Standard compressed sensing reconstruction methods require tuning of hyperparameters and are computationally expensive, which diminishes the potential reduction of examination times. We propose an efficient model-based deep neural reconstruction network and evaluate its performance on clinical aortic flow data. The network is shown to reconstruct undersampled 4D flow MRI data in under a minute on standard consumer hardware. Remarkably, the relatively low amounts of tunable parameters allowed the network to be trained on images from 11 reference scans while generalizing well to retrospective and prospective undersampled data for various acceleration factors and anatomies.

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Fig. 1: Breathing-resolved 4D flow data acquisition.
Fig. 2: FlowVN architecture and training.
Fig. 3: Reconstruction results on retrospectively undersampled data.
Fig. 4: Retrospective reconstruction of the data from a patient with abnormal flow pattern.
Fig. 5: Quantitative flow evaluation of reconstruction methods on prospectively undersampled data (12.4 ≤ R ≤ 13.8) from seven healthy volunteers.

Data availability

The code for the network training and inference used in this study as well as network weights are available online from CodeOcean together with volunteer data: The code for analysis is available on CodeOcean from


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The authors acknowledge funding from the European Unions Horizon 2020 research and innovation programme under grant agreement no. 668039 and under EuroStars UNIFORM as well as funding of the Platform for Advanced Scientific Computing of the Council of the Federal Institutes of Technology (ETH Board), Switzerland.

Author information




J.W., V.V. and S.K. conceived the study. V.V. implemented the machine-learning reconstruction algorithms. J.W. conducted MR acquisition experiments and data preprocessing. J.W. and V.V. analysed experimental data under the supervision of S.K. All authors discussed the results and contributed to writing the manuscript.

Corresponding author

Correspondence to Valery Vishnevskiy.

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The authors declare no competing interests.

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Supplementary Fig. 1, algorithm (1) and tables 1 and 2.

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Vishnevskiy, V., Walheim, J. & Kozerke, S. Deep variational network for rapid 4D flow MRI reconstruction. Nat Mach Intell 2, 228–235 (2020).

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