# 4DFlowNet: Super-Resolution 4D Flow MRI using Deep Learning and Computational Fluid Dynamics

arXiv: https://arxiv.org/abs/2004.07035 · HTML: https://mlsanity.com/paper/2004.07035/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Apr 2020.

## Built on by (most cited first, 19 of 19)

- [Physics-Driven Deep Learning for Computational Magnetic Resonance Imaging](https://mlsanity.com/paper/2203.12215/) (2022)
- [Physics-informed deep-learning applications to experimental fluid mechanics](https://mlsanity.com/paper/2203.15402/) (2022)
- [Implicit neural representations for unsupervised super-resolution and denoising of 4D flow MRI](https://mlsanity.com/paper/2302.12835/) (2023)
- [Physics-informed compressed sensing for PC-MRI: an inverse Navier-Stokes problem](https://mlsanity.com/paper/2207.01466/) (2022)
- [Transient Hemodynamics Prediction Using an Efficient Octree-Based Deep Learning Model](https://mlsanity.com/paper/2302.06557/) (2023)
- [Bayesian inverse Navier-Stokes problems: joint flow field reconstruction and parameter learning](https://mlsanity.com/paper/2406.18464/) (2024)
- [Rotationally Equivariant Super-Resolution of Velocity Fields in Two-Dimensional Fluids Using Convolutional Neural Networks](https://mlsanity.com/paper/2202.11099/) (2022)
- [Coarse-Super-Resolution-Fine Network (CoSF-Net): A Unified End-to-End Neural Network for 4D-MRI with Simultaneous Motion Estimation and Super-Resolution](https://mlsanity.com/paper/2211.11144/) (2022)
- [Generalized super-resolution 4D Flow MRI unicodex2013 using ensemble learning to extend across the cardiovascular system](https://mlsanity.com/paper/2311.11819/) (2023)
- [CPT-Interp: Continuous sPatial and Temporal Motion Modeling for 4D Medical Image Interpolation](https://mlsanity.com/paper/2405.15385/) (2024)
- [Enhanced Vascular Flow Simulations in Aortic Aneurysm via Physics-Informed Neural Networks and Deep Operator Networks](https://mlsanity.com/paper/2503.17402/) (2025)
- [Non-invasive hemodynamic analysis for aortic regurgitation using computational fluid dynamics and deep learning](https://mlsanity.com/paper/2111.11660/) (2021)
- [Unsupervised 4D Flow MRI Velocity Enhancement and Unwrapping Using Divergence-Free Neural Networks](https://mlsanity.com/paper/2604.00205/) (2026)
- [Automated Diagnosis of Cardiovascular Diseases from Cardiac Magnetic Resonance Imaging Using Deep Learning Models: A Review](https://mlsanity.com/paper/2210.14909/) (2022)
- [Adaptive Plane Reformatting for 4D Flow MRI using Deep Reinforcement Learning](https://mlsanity.com/paper/2506.00727/) (2025)
- [Potential and challenges of generative adversarial networks for super-resolution in 4D Flow MRI](https://mlsanity.com/paper/2508.14950/) (2025)
- [Distributional Deep Learning for Super-Resolution of 4D Flow MRI under Domain Shift](https://mlsanity.com/paper/2602.15167/) (2026)
- [Attention-guided super-resolution of 4D flow MRI in carotid arteries](https://mlsanity.com/paper/2609.04891/) (2026)
- [Interactive 4D Volumetric Liquid Forecasting under Moving-Solid Interaction](https://mlsanity.com/paper/2610.16167/) (2026)

## Abstract (arXiv)

4D-flow magnetic resonance imaging (MRI) is an emerging imaging technique where spatiotemporal 3D blood velocity can be captured with full volumetric coverage in a single non-invasive examination. This enables qualitative and quantitative analysis of hemodynamic flow parameters of the heart and great vessels. An increase in the image resolution would provide more accuracy and allow better assessment of the blood flow, especially for patients with abnormal flows. However, this must be balanced with increasing imaging time. The recent success of deep learning in generating super resolution images shows promise for implementation in medical images. We utilized computational fluid dynamics simulations to generate fluid flow simulations and represent them as synthetic 4D flow MRI data. We built our training dataset to mimic actual 4D flow MRI data with its corresponding noise distribution. Our novel 4DFlowNet network was trained on this synthetic 4D flow data and was capable in producing noise-free super resolution 4D flow phase images with upsample factor of 2. We also tested the 4DFlowNet in actual 4D flow MR images of a phantom and normal volunteer data, and demonstrated comparable results with the actual flow rate measurements giving an absolute relative error of 0.6 to 5.8% and 1.1 to 3.8% in the phantom data and normal volunteer data, respectively.