Source-linked AI summary
MR fingerprinting Deep RecOnstruction NEtwork (DRONE)
Ouri Cohen, Bo Zhu, Matthew S. Rosen
TL;DR
Multi-dimensional MRF reconstruction faces exponentially growing dictionaries and associated technical issues. This paper uses a feedforward neural network informed by time-dependent Bloch-equation modeling, achieving fast reconstruction with sparse dictionaries and approximately 300-fold faster operation than conventional dictionary matching.
Problem
Multi-dimensional MRF reconstruction is challenged by the exponential growth of dictionaries with increasing dimensions.
Method
A four-layer feedforward neural network models the time-dependent Bloch equations used in MRF sequences and reconstructs data using sparse dictionaries.
Results
Approximately 300-fold faster reconstruction was achieved than with conventional dictionary matching, while maintaining fast and accurate reconstruction with sparse dictionaries.
Takeaways & Limitations
The approach addresses technical issues inherent to exponentially growing multi-dimensional dictionaries while requiring limited storage.
Takeaways & Limitations
Increasing the number of acquisitions by 10–100 fold will likely require longer network training.
Abstract
from arXiv · showhide
PURPOSE: Demonstrate a novel fast method for reconstruction of multi-dimensional MR Fingerprinting (MRF) data using Deep Learning methods. METHODS: A neural network (NN) is defined using the TensorFlow framework and trained on simulated MRF data computed using the Bloch equations. The accuracy of the NN reconstruction of noisy data is compared to conventional MRF template matching as a function of training data size, and quantified in a both simulated numerical brain phantom data and acquired data from the ISMRM/NIST phantom. The utility of the method is demonstrated in a healthy subject in vivo at 1.5 T. RESULTS: Network training required 10 minutes and once trained, data reconstruction required approximately 10 ms. Reconstruction of simulated brain data using the NN resulted in a root-mean-square error (RMSE) of 3.5 ms for T1 and 7.8 ms for T2. The RMSE for the NN trained on sparse dictionaries was approximately 6 fold lower for T1 and 2 fold lower for T2 than conventional MRF dot-product dictionary matching on the same dictionaries. Phantom measurements yielded good agreement (R2=0.99) between the T1 and T2 estimated by the NN and reference values from the ISMRM/NIST phantom. CONCLUSION: Reconstruction of MRF data with a NN is accurate, 300 fold faster and more robust to noise and undersampling than conventional MRF dictionary matching.
Introduction
MRF enables simultaneous quantitative tissue mapping but creates dictionaries whose size and computational burden grow exponentially with dimensionality. The paper proposes learning a compact signal-to-parameter mapping from sparse dictionary entries to address this reconstruction challenge.
- MRF produces multiple quantitative tissue parameter maps from a single experiment, potentially reducing total scan time.
- Dictionary size grows exponentially as the number of tissue parameters increases, creating substantial memory, storage, and computational demands.
- Reducing dictionary density limits the a priori accuracy of reconstruction before experimental factors are considered.
- Existing compression methods require generating the full fine-grained dictionary before computationally expensive SVD decomposition.
- The proposed method learns a function mapping acquired signal magnitudes to tissue parameters using a sparse set of dictionary entries.
- The learned reconstruction function is approximately 20 times smaller than typical MRF dictionaries and about 300-fold faster than conventional dictionary matching.
Methods
The study trains a TensorFlow neural network on Bloch-equation-simulated MRF dictionary data and evaluates reconstruction across sparse dictionaries, simulations, phantoms, and in vivo imaging. The network is designed to accommodate different MRF pulse sequences and input types.
- A four-layer fully connected neural network was implemented with input and output layers plus two hidden layers.
- The network was trained with ADAM using mean squared error and tanh hidden-layer activations with a sigmoid output layer.
- A roughly 79,900-entry dictionary of T1 and T2 values was simulated with Bloch equations using Extended Phase Graph formalism.
- Zero-mean Gaussian noise with 2% standard deviation was added to training data to promote robust learning.
- The method was assessed using a numerical brain phantom, the ISMRM/NIST phantom, and a healthy subject scanned at 1.5 T.
- Networks trained on dictionaries subsampled from 2- to 60-fold were compared with conventional dictionary matching under noisy reconstruction conditions.
Results
The neural network reconstructed simulated, phantom, and in vivo MRF data accurately while substantially reducing reconstruction time and maintaining lower error than conventional matching for sparse dictionaries. Errors increased at extreme T1/T2 values and in selected phantom compartments.
- Short T1/T2 values near the EPI echo time and very long T2 values above 1000 ms showed increased deviation from true values.
- 3.5 ms for T1 and 7.8 ms for T2 were the RMSEs for reconstruction of the simulated brain phantom.
- 5–7 fold smaller T1 RMSE and 2 fold smaller T2 RMSE were obtained with the neural network than with conventional dictionary matching across undersampling factors.
- 72 ms T1 RMSE and 88 ms T2 RMSE were calculated for the included phantom analysis before additional exclusions.
- ~10 ms was required to reconstruct 128×128 T1 and T2 maps, compared with ~3 s for conventional matching using a 79,900-entry dictionary.
Discussion
The NN replaces discrete dictionary matching with a compact, continuous signal-to-parameter mapping that is faster, less storage-intensive, and more robust to noise. Its current proof-of-concept scope leaves optimization, sequence scaling, additional parameters, and activation-function effects for future work.
- Motivation: MRF enables quantitative tissue mapping quickly but requires increased memory, storage, and computational resources for dictionary matching.Large dictionaries are a practical constraint because storage and memory are less accessible than scanner time.
- Method and novelty: The NN produces continuous-valued parameter outputs instead of matching acquired signals only to discrete dictionary entries.Its functional representation maps signals to parameters within the network rather than relying solely on dictionary-entry similarity.
- Robustness: Training on noisy signals yielded smaller T1 and T2 errors than conventional dictionary matching using the same noisy dictionaries.Conventional normalization can amplify noisy signals, whereas the network was trained to handle noise.
- Efficiency: 300-fold faster reconstruction and approximately 5% of the storage and memory requirements distinguish the NN from conventional dot-product dictionary matching.The fixed feedforward topology keeps reconstruction time independent of the number of training-dictionary entries.
- Training data: Simulated training data can be generated arbitrarily and still supports accurate reconstruction of measured data despite noise and other measurement errors.This reduces reliance on large, expensive clinical datasets for training.
- Limitations and future work: The study is an initial proof of concept, and alternative sequences with 10–100-fold more acquisitions or simultaneous additional-parameter reconstruction may require longer training or deeper networks.The current architecture may need further optimization for broader parameter estimation and more demanding sequences.
Conclusion
The study demonstrates that deep-learning reconstruction of MRF data is fast and accurate while requiring limited storage despite sparse dictionaries. The approach addresses technical issues caused by the exponential growth of multi-dimensional dictionaries.
- Deep learning networks enabled fast and accurate reconstruction of MRF data with limited storage requirements.
- The proposed approach resolves technical issues inherent to the exponential growth of multi-dimensional dictionaries.
Table 1
The study describes a neural-network pipeline that maps optimized MRF data to tissue parameters and evaluates it through training, simulated phantom, physical phantom, and in vivo results. The reconstructed T1 and T2 values closely matched reference or true values, including under noisy and undersampled conditions.
- Reconstruction method: The four-layer neural network receives optimized MRF EPI data voxelwise and outputs tissue parameters including T1 and T2.Additional parameters such as M0, B0, and B1 can also be obtained by training with a suitable dictionary.
- Network training: Approximately 10 minutes were required to train the network for 1000 epochs on an Nvidia K80 GPU.Most training-cost reduction occurred within the initial 400 epochs, suggesting shorter training may be possible.
- Simulated data: The reconstructed training data showed excellent agreement with true T1 and T2 values, with a correlation coefficient of R2=0.99.The reported minimal biases were 10 ms for T1 and 3.1 ms for T2.
- Simulated data: T1 and T2 RMSEs for the numerical brain phantom were 3.5 ms and 7.8 ms, respectively.The true and reconstructed maps showed close agreement, with the errors displayed in an associated error map.
- Noise and undersampling: The neural network retained lower reconstruction error than conventional dictionary matching despite increased dictionary undersampling.The comparison used noisy data reconstructed either by direct matching or by a network trained on undersampled dictionaries.