Super-resolution Y-Net for simultaneous ¹H MRF/²³Na MRI

📌 Overview

This project introduces a Y-Net super-resolution neural network that generates high-resolution sodium (²³Na) images from simultaneously acquired ¹H MRF/²³Na MRI data. The method addresses the challenge of low resolution in sodium MRI, which has been a major barrier to its clinical translation despite its valuable metabolic information content.

Key Features

✅ Super-resolution for Sodium MRI: Enhances low-resolution ²³Na images using simultaneously acquired high-resolution ¹H data
✅ Y-Net Architecture: Dual-encoder design leveraging both ¹H multi-contrast and ²³Na information ✅ Clinical Translation: Enables practical sodium MRI with improved resolution for clinical applications
✅ Comprehensive Framework: Built on Lightning-Hydra template for robust experimentation

🔬 Scientific Background

Sodium (²³Na) MRI can reveal valuable metabolic information, making it potentially useful for clinical diagnosis. However, its low natural abundance in the human body and low gyromagnetic ratio practically prohibit the acquisition of high-resolution (HR) ²³Na images.

This work addresses this limitation by developing a post-processing method that leverages simultaneously acquired ¹H MRF data to enhance ²³Na image resolution, making sodium MRI more viable for clinical practice.

Authors

Gonzalo Gabriel Rodriguez¹,², Hector Lise de Moura², Ilias Giannakopoulos², Riccardo Lattanzi²,³,⁴, Ravinder Regatte²,³, and Guillaume Madelin²,³

¹ NMR Signal Enhancement, Max Planck Institute for Multidisciplinary Sciences, Göttingen, Germany
² Bernard and Irene Schwartz Center for Biomedical Imaging, Department of Radiology, New York University School of Medicine, New York, NY, United States
³ Vilcek Institute of Graduate Biomedical Sciences, New York University School of Medicine, New York, NY, United States
⁴ Center for Advanced Imaging Innovation and Research, New York University School of Medicine, New York, NY, United States

🚀 Key Results

Method	SSIM	RMSE	PSNR
Y-Net (Ours)	0.935	0.034	28.8
PLS	0.916	0.040	28.0
Bi-cubic Interpolation	0.928	0.058	24.3

Performance Highlights

• High Similarity: SSIM of 0.935 compared to ground truth HR ²³Na images
• Superior Performance: Outperforms both PLS and bi-cubic interpolation methods
• Fast Inference: ~1.2s on A100 GPU vs ~616s for PLS method
• Clinical Viability: Enables online implementation for clinical use

📊 Visual Results

Figure 1: Network Architecture

Schematic diagram of the Y-Net super-resolution architecture showing the dual-encoder design with ¹H multi-contrast and ²³Na inputs.

Figure 2: Input Data

Center slice showing the initial ¹H and ²³Na data acquired with 3D simultaneous ¹H MRF/²³Na MRI and the ground truth HR ²³Na acquired with 3D stack-of-stars GRE.

Figure 3: Super-resolution Results

Comparison of acquired LR and HR (ground truth) ²³Na images, the generated HR ²³Na images, and the differences between ground truth and generated HR images for four central slices of the test subject.

Figure 4: Method Comparison

Comparison between the Y-Net, PLS and bi-cubic interpolation methods for the central slice of the test subject.

Figure 5: Statistical Analysis

Statistical parameters calculated for each method over the 3D volume showing the superior performance of the Y-Net approach.

🛠️ Technical Approach

Y-Net Architecture

The Y-Net is a deep convolutional neural network architecture similar to U-Net but with two encoder paths:

• ¹H Path: Processes multi-contrast images (proton density, T₁, T₂ maps)
• ²³Na Path: Processes low-resolution sodium density images
• Shared Decoder: Combines features from both paths with skip connections

Dataset

• Acquisition: 7T MAGNETOM (Siemens) with 16-channel-Tx/Rx dual-tuned head coil
• Subjects: 8 healthy volunteers (2 females, 32±12 years old)
• Resolution: ¹H: 1.5×1.5×5 mm³, ²³Na: 2.85×2.85×5 mm³
• Training/Validation: 7 subjects (1540 images: 1386 training, 154 validation)
• Testing: 1 subject (22 images)
• Resolution Ratio: 1.9× enhancement in both in-plane directions

Training Details

• Input Size: 160×160 patches
• Optimizer: AdamW with learning rate 0.01
• Scheduler: 20% reduction every 10 epochs
• Epochs: 300 total
• Loss Function: Structural Similarity Index Measure (SSIM)
• Data Augmentation: Rotation and additive Gaussian noise

📁 Project Structure

├── configs/                   # Hydra configuration files
│   ├── callbacks/            # Callback configurations
│   ├── data/                 # Data module configurations
│   ├── experiment/           # Experiment configurations
│   ├── logger/               # Logger configurations
│   ├── model/                # Model configurations
│   ├── trainer/              # Trainer configurations
│   └── ...
├── data/                     # Project data directory
├── logs/                     # Training logs and outputs
├── notebooks/                # Jupyter notebooks for analysis
├── src/                      # Source code
│   ├── data/                 # Data loading and processing
│   ├── models/               # Model implementations
│   ├── utils/                # Utility functions
│   ├── train.py             # Training script
│   └── eval.py              # Evaluation script
├── tests/                    # Unit tests
├── mnf_readme/              # Figures and documentation
│   ├── fig1.jpg             # Network architecture diagram
│   ├── fig2.jpg             # Input data visualization
│   ├── fig3.jpg             # Super-resolution results
│   ├── fig4.jpg             # Method comparison
│   └── fig5.jpg             # Statistical analysis
└── README.md                # This file

🏃‍♂️ Quick Start

Environment Setup

# Clone the repository
git clone <repository-url>
cd MNF_SR_hydra

# Create conda environment
conda env create -f environment.yaml
conda activate mnf_sr

# Or install with pip
pip install -r requirements.txt

Training

# Train with default configuration
python src/train.py

# Train with specific experiment config
python src/train.py experiment=ynet_super_resolution

# Train with custom parameters
python src/train.py model.lr=1e-4 trainer.max_epochs=300

Evaluation

# Evaluate trained model
python src/eval.py ckpt_path="/path/to/checkpoint.ckpt"

# Evaluate with specific metrics
python src/eval.py experiment=eval_super_resolution

Hyperparameter Optimization

# Run hyperparameter search
python src/train.py -m hparams_search=ynet_optuna experiment=ynet

📊 Experiments and Configurations

The project includes several pre-configured experiments:

• ynet: Main Y-Net training configuration
• ablation_single_ynet: Single Y-Net (non-cascaded) ablation study

🔍 Key Innovations

1. Dual-Modal Learning: Leverages both ¹H and ²³Na information simultaneously
2. Cascaded Refinement: Two-stage processing for enhanced quality
3. Clinical Optimization: Fast inference suitable for clinical workflow
4. Robust Framework: Built on proven Lightning-Hydra architecture
5. Comprehensive Evaluation: Thorough comparison with existing methods

📈 Clinical Impact

This super-resolution method enables:

• Enhanced Sodium MRI Resolution: From 2.85×2.85×5 mm³ to effective 1.5×1.5×5 mm³
• Clinical Translation: Fast inference times suitable for clinical implementation
• Improved Diagnostics: Better visualization of metabolic processes
• Reduced Scan Time: No need for additional high-resolution sodium acquisitions

🔧 Advanced Usage

Custom Model Training

# Train with custom data module
python src/train.py data=custom_sodium_data

# Use different loss functions
python src/train.py model.loss_fn=l1_loss

# Multi-GPU training
python src/train.py trainer=ddp trainer.devices=4

Monitoring and Logging

# Train with Weights & Biases logging
python src/train.py logger=wandb

# Train with TensorBoard
python src/train.py logger=tensorboard

📚 Citation

If you use this work in your research, please cite:

@article{rodriguez2025super,
  title={Super-resolution Y-Net for simultaneous ¹H MRF/²³Na MRI},
  author={Rodriguez, Gonzalo Gabriel and de Moura, Hector Lise and Giannakopoulos, Ilias and Lattanzi, Riccardo and Regatte, Ravinder and Madelin, Guillaume},
  journal={Magnetic Resonance in Medicine},
  year={2025},
  note={In preparation}
}

🙏 Acknowledgements

The research reported in this publication was supported by the NIH/NIBIB grant R01 EB026456, and performed under the rubric of the Center for Advanced Imaging Innovation and Research, a NIBIB Biomedical Technology Resource Center (P41 EB017183).

📜 References

1. Madelin G, & Regatte R R. Biomedical applications of sodium MRI in vivo. J. Magn. Reson. Imag., 2013;38:511-529.

2. Yu, Z., Hodono, S., Dergachyova, O., et al. Simultaneous 3D acquisition of ¹H MRF and ²³Na MRI. Mag. Res. in Med., 2021, 83(6), 00:1-14.

3. Wang, B, Zhang, B., Yu, Z., et al. A radially interleaved sodium and proton coil array for brain MRI at 7T. NMR Biomed. 2021, e4608.

4. Do W., Seo S., Han Y., et al. Reconstruction of multicontrast MR images through deep learning. Med. Phys., 2020, 47 (3).

5. Wang, Z., Bovik, A.C., Sheikh, H.R., Simoncelli, E.P. Image quality assessment: from error visibility to structural similarity. IEEE Trans. on Imag. Process. 2004;13(4),600–612.

6. Rodriguez G.G., Yu Z., Shaykevich S., et al. Super-resolution of sodium images from simultaneous ¹H MRF/²³Na MRI acquisition. NMR Biomed., 2023, vol 36, e4959.

📞 Contact

For questions and collaboration:

• Hector Lise de Moura: [hector.demoura@nyulangone.org]
• Guillaume Madelin: [guillaume.madelin@nyulangone.org]

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NYU School of Medicine | Center for Biomedical Imaging | Max Planck Institute