Synopsis

Keywords: Artifacts, fMRI, Geometrid Distortion, B0 inhomogeneity

GDCNet is a “self-consistent” deep learning (DL) model for distortion correction of EPI fMRI images and field map estimation. It only requires the EPI images for correction, saving acquisition time and avoiding motion-related correction errors. The two supervised U-Nets for forward modelling and distortion correction have been tested in silico and in vivo on a publicly-available and a prospectively-acquired dataset. The in silico models demonstrated generalization capabilities and achieved a mean RMSE of 2.56 x10^-2 as self-conistency metric. Inference in vivo showed modest correction in the prefrontal cortex and similar estimated field map compared to the acquired ground truth.

Introduction

Echo planar imaging (EPI)’s high temporal resolution makes it the trajectory of choice for functional MRI due to its sensitivity to BOLD signal changes¹. However, phase errors accumulate along its long readout duration, causing geometric distortions and signal loss in areas of local field inhomogeneities such as air-tissue interfaces². State-of-the-art correction methods leverage a voxel shift map (VSM) to mitigate distortions and intensity errors³. For its calculation a double echo-time GRE field map or two sets of EPI images with opposite phase encoding direction⁴ are required. Both approaches are time-consuming as they require one additional sequence acquisition. Furthermore, the long acquisition times characteristic of fMRI make it prone to subject motion during or between sequences, leading to registration errors and potential inaccuracies during distortion correction⁵. For these reasons, most studies do not perform any distortion correction. Within the 25 most downloaded fMRI datasets in OpenNeuro⁶, only 23% include a field map, and 9% double-encoded EPI data. Here we present GDCNet, a “self-consistent” deep learning (DL) model for distortion correction of EPI fMRI images. This method only requires the raw EPI images for correction, saving acquisition time and avoiding motion-related correction errors.

Methods

We trained two types of supervised U-Nets⁷ to learn geometric distortion correction (inverse2) and forward simulation using Tensorflow-Keras⁸. Figure 1 shows both model architectures and the implementation details. We leveraged two datasets for the models training, validation, and testing. First, we experimented on an in silico dataset generated using a 3D Shepp-Logan phantom corrupted using OCTOPUS⁹ along a 64x64 single-shot EPI trajectory with different field maps and off-resonance ranges of up to ±250 Hz. Second, we trained two other models using retrospective in vivo BOLD fMRI data and the corresponding field map from 10 subjects of an OpenNeuro dataset¹⁰. For both datasets, we generated 10,000 slices and split 80-20% among the training and testing sets. Additionally, 20% of the training sets were used for validation. The multi-frequency interpolation (MFI)¹¹ and FSL’s FUGUE¹² corrected images, together with the field maps, were used as ground truth for the in silico and in vivo inverse2 models, respectively. We experimented with FUGUE’s intensity correction option but opted to avoid it due to poor performance. We concatenated the in silico models (inverse2forward) to ensure correction ¨self-consistency¨ and calculated the RMSE between input and output. This experiment aimed at model expainability. Finally, we tested the in vivo inverse2 model on a prospective dataset acquired on a GE 3T scanner. We also acquired a field map for this experiment to compare with the predictions of the model.

Results and discussion

After training each model for 100 epochs (Figure 2) we evaluated their performance on the test sets. The hyperparameters used for the loss functions were ɑ=0.84 and λ=3. The in silico inverse2 model achieved 0.009 loss and RMSE values of 0.0061 and 0.0085 for the image, and field map outputs, respectively, while the forward model obtained 0.0235 loss and 0.0095 RMSE. The in vivo inverse2 model reached 0.0436 loss, image RMSE of 0.0095, and field map RMSE of 0.0049 whereas the forward model obtained 0.021 loss and 0.007 RMSE. Figure 3 shows in silico inference cases concatenating the inverse2 and forward models for different types of field maps and distortions. We chose to use a DL model (forward) to explain the results and ensure the self-consistency of the inverse2 model for processing speed reasons. Forward modelling using the forward DL model took 1 second for 2,000 slices while OCTOPUS takes 41 minutes. The mean RMSE between $$$I_{corrupted}$$$ and $$$\hat{I}_{corrected}$$$ was 2.56x10^-2±0.0098 and 1.23x10^-2±0.004 for the in silico and in vivo test sets, repectively. Furthermore, we confirmed the generalization capabilities of the in silico models by feeding them the undistorted Shepp-Logan phantom image, which resulted in no distortion and a uniform field map with 0 off-resonance from the inverse2 model. The forward model induced some ringing artifact characteristic of the MFI-corrected images used as ground truth during training.
In vivo inference outputs (Figure 4-5) show modest geometric accuracy recovery in the orbitofrontal prefrontal cortex. The difference images between the inverse2 inputs and outputs show higher voxel displacement (red and blue pixels) in areas of the field map with higher off-resonance values. The correction performance, however, is limited to FUGUE’s performance as these correction results have been used as ground truth during training. Figure 4B shows how the model recovers the distorted frontal region but the intensity of the recovered voxels is not correct. Current work includes bypassing these ground-truth limitations and improving generalization and performance of the inverse2 model on prospective data (Figure 5) by implementing smoothness constraint into the field map branch loss function. The acquired and estimated field maps are similar overall although they present a slight difference in magnitude. The acquired field map is smoother and shows higher off-resonance in the prefrontal region (red arrows in Figure 5) where geometric distortions occur.

Conclusion

GDCNet demonstrated good performance and self-consistency in silico and in a retrospective in vivo dataset. The benefit of using this approach includes the ability of geometric distortion correction of EPI fMRI data without any extra sequence acquisition.

Acknowledgements

This study was funded [in part] by the Seed Grant Program for MR Studies and the Technical Development Grant Program for MR Studies of the Zuckerman Mind Brain Behavior Institute at Columbia University and Columbia MR Research Center site.