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4DFlowNet: Super-Resolution 4D Flow MRI using Deep Learning and Computational Fluid Dynamics
Edward Ferdian, Avan Suinesiaputra, David Dubowitz, Debbie Zhao, Alan Wang, Brett Cowan, Alistair Young
TL;DR
Limited 4D-flow MRI resolution constrains accurate assessment of some hemodynamic parameters. 4DFlowNet trains on synthetic MRI-like data generated from CFD, producing noise-free super-resolution phase images at an upsampling factor of 2. Tests on phantom and volunteer data showed agreement with flow measurements, while the training set’s three aortic geometries limit its scope.
Problem
Limited 4D-flow MRI resolution makes some hemodynamic parameters, including wall shear stress, difficult to calculate accurately.
Source: §1 · p. 2Method
4DFlowNet learns to map noisy low-resolution data to noise-free high-resolution phase images using synthetic MRI-like data generated from CFD solutions.
Source: §1 · p. 2Results
The network produced noise-free super-resolution phase images at an upsampling factor of 2, with phantom flow-rate relative errors of -0.6% at the inlet, 3.3% at the bifurcation, and 5.8% at the outlet.
Source: §3.2 · p. 17, §4.4 · p. 21Takeaways & Limitations
The noise-free super-resolution phase images can potentially be used to delineate regions of interest and automatically calculate flow parameters.
Source: §4.4 · p. 21The training dataset used only three aortic geometries and limited boundary conditions.
Source: §4.3 · p. 21
Abstract
from arXiv · showhide
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.
1 Introduction
4D-flow MRI captures volumetric blood flow, but its limited resolution constrains accurate calculation of some hemodynamic parameters. This study uses CFD-generated synthetic data to train a deep-learning network for super-resolution and evaluates it on phantom and volunteer scans.
1 Introduction
- Limited 4D-flow MRI resolution prevents accurate calculation of some hemodynamic parameters, including wall shear stress.The technique also has limitations associated with SNR and VENC.Source: §1 · p. 2
- CFD offers higher spatial and temporal resolution than 4D-flow MRI, but depends on accurate geometry and personalized inlet and outlet boundary conditions.The study uses CFD to generate high-resolution flow images for a super-resolution task.Source: §1 · p. 2
- Prior deep-learning super-resolution studies did not address velocity fields or 4D-flow MRI phase and magnitude representations.The task remains challenging and ill-posed.Source: §1 · p. 2
- The proposed network learns to map noisy low-resolution data to noise-free high-resolution phase images using synthetic 4D-flow MR data generated from CFD solutions.The synthetic data were made consistent with MRI image representations and physics; evaluation included phantom and normal-volunteer data.Source: §1 · pp. 2–3
2 Methods
The method builds paired synthetic 4D-flow MRI data from CFD and trains 4DFlowNet to map noisy low-resolution phase images to noise-free high-resolution velocity images. It evaluates the network with velocity-gradient and relative-speed-error measures.
2.1 Generating Training Data
- CFD simulations of three aortic geometries generated velocity fields, with volunteer-derived inlet waveforms and pressure boundary conditions used to produce training data.The geometries included one from a healthy volunteer and two with aortic coarctation; the simulations assumed rigid vessel walls and laminar flow.Source: §2.1 · pp. 3–5
2.1.1 Bridging the “CFD-4D Flow” gap – downsampling in the frequency domain
- Synthetic MRI-equivalent images were formed by encoding velocity as phase, then downsampling complex images in 3D k-space and adding Gaussian noise to target the desired SNR.The downsampling factor was 2; phase and magnitude images were reconstructed after inverse Fourier transformation.Source: §2.1.1 · pp. 6–7
2.1.2 Data augmentation and patch generation
- Randomized VENC, fluid intensity, and SNR augmented the data; rotated patches yielded 14,200 training patches, while aorta03 supplied validation and test data.Actual phantom acquisitions at 4 mm and 2 mm isotropic resolution and a volunteer acquisition were also used for evaluation.Source: §2.1.2 · pp. 7–9
2.2 Network architecture and Training
- 4DFlowNet uses magnitude-derived anatomical inputs and three velocity-component inputs, with residual blocks before and after upsampling to predict super-resolved velocity components.The anatomical path includes PC-MRA, speed, and magnitude channels; the velocity path receives Vx, Vy, and Vz.Source: §2.2 · pp. 9–10
2.3 Loss function and accuracy metrics
- Training combines voxel-wise mean squared error with a weighted velocity-gradient loss to emphasize vessel-wall predictions and encourage low-divergence solutions.The gradient term uses first-order differences between neighboring vectors.Source: §2.3 · p. 11
2.3.1 Evaluation metric – relative speed error
- Relative speed error compares predicted and actual speed within the fluid region, excluding non-fluid voxels and adding ε=10^-5 to the denominator.The validation-set relative speed error was used to select the model checkpoint.Source: §2.3.1 · pp. 11–12
3 Results
Tests covered synthetic 4D flow MRI, a bifurcation phantom, and a normal volunteer. 4DFlowNet reduced noise in predicted images, with reported flow-rate comparisons on synthetic and phantom data and flow-rate differences measured in the volunteer.
3 Results
- The evaluation tested 71 synthetic CFD frames, one phantom frame upsampled from 4 mm to 2 mm, and one volunteer frame; performance metrics were available only for synthetic and phantom data.Comparisons included linear, cubic spline, and sinc interpolation.Source: §3 · p. 12
3.1 Tests on synthetic 4D flow MR images
- On synthetic patches, predictions were close to ground truth and reduced noise; predicted gradients and divergence fields were smoother and closer to ground truth than interpolation results.Interpolation methods were more affected by noise and non-uniformity, and noise from LR images appeared in fluid and non-fluid regions.Source: §3.1 · pp. 13–14, Figure 6 · p. 13
- On synthetic data, 4DFlowNet and sinc interpolation performed comparably in systole, while 4DFlowNet performed better for low-velocity predictions during diastole.The evaluated sequence included 71 frames; relative errors were higher for low velocities compared with VENC.Source: §3.1 · pp. 14–15, Figure 7 · p. 14
- Synthetic flow-rate measurements showed comparable results and small differences between 4DFlowNet and interpolation methods across three planes, with higher error in systole than diastole.The authors report that the network did not introduce error in flow rates, an important clinical quantity.Source: §3.1 · p. 16, Figure 9 · p. 16
3.2 Tests on actual 4D flow MRI data– bifurcation phantom
- At the phantom inlet, relative error was -0.6% vs 7% for 4DFlowNet and sinc interpolation; at the bifurcation it was 3.3% vs 4.3%, and at the outlet both were 5.8%.Flow rates were measured at three cross-sections within the masked fluid region.Source: Figure 10 · p. 17, §3.2 · p. 17
3.3 Tests on actual 4D flow MRI data– normal volunteer data
- The volunteer’s peak-flow differences were 10.7 mL/s (2.6%), -2 mL/s (-1.1%), and -4.8 mL/s (-3.8%) at the ascending aorta, aortic arch, and descending aorta, respectively.The volunteer dataset was upsampled by a factor of 2; no HR ground truth was available.Source: §3.3 · pp. 17–18, Figure 11 · p. 18
4 Discussion
4DFlowNet produced higher-resolution, noise-reduced flow images and encouraging predictions in phantom and healthy-volunteer data. The discussion describes the synthetic training data and patch-based design, while noting limits in simulation scope and validation.
4 Discussion
- Flow predictions agreed with simulations and phantom MRI, while phase images showed clearer vessel boundaries, less noise, and improved divergence-free flow fields.The authors also report relatively small velocity bias versus CFD ground truth and smoother predictions than other interpolation methods.Source: §4 · p. 19
4.1 CFD as synthetic 4D flow MRI dataset
- Synthetic training data addressed the lack of economically feasible real MRI acquisitions and the altered noise distribution caused by downsampling; simulations nevertheless omitted several physical factors.The CFD did not model accurate boundary conditions, nonlinear viscosity, fluid–structure interactions, or transitions to turbulence. Only one cardiac cycle was simulated, although negligible differences were observed in a five-cycle comparison for one geometry.Source: §4.1 · pp. 19–20
4.2 Network design
- Patch-based training obscured global geometry and flow context while retaining local patch information, and inference supported arbitrary cube sizes within memory limits.The authors used conventional bilinear upsampling after PixelShuffle and nearest-neighbor initialization performed poorly for 3D velocity images; full-volume prediction took roughly 40–90 seconds.Source: §4.2 · pp. 20–21
4.3 Limitations and Future Work
- The training set used only three aortic geometries and limited boundary conditions, and the network still requires validation on more 4D Flow MRI cases.Whether it reproduces strongly helical flow in patients with coarctation and bicuspid aortic valves remains future work; wall-shear-stress estimation assumptions and optimizations also need investigation.Source: §4.3 · p. 21
4.4 Conclusion
- The network achieved 2× upsampling with reduced noise and clear anatomical regions, with demonstrated utility in phantom and normal-anatomy MRI.The authors note potential for further improvement with more synthetic or real MRI training data; using noise-free images to delineate regions of interest and calculate flow parameters is a potential application.Source: §4.4 · p. 21
5 Conflict of Interest
The disclosure reports financial support for EF.
5 Conflict of Interest
- Siemens Healthineers provided working expenses and partial stipend for EF.Source: §5 · p. 22
6 Author Contributions
All authors contributed to study design and interpretation; EF drafted the first manuscript and led network and data-analysis work.
6 Author Contributions
- All authors participated in study conception and design, data interpretation, manuscript revision, and final approval.Source: §6 · p. 22
- EF wrote the first draft of the manuscript.Source: §6 · p. 22
- EF designed the network architecture and performed the data analysis.Source: §6 · p. 22