Introduction

Off-resonance artifacts in MRI lead to geometric distortions and blurring for non-Cartesian acquisitions. Model-based image reconstruction (MBIR) using accurate fieldmaps can correct for these effects¹, but such fieldmaps conventionally require a multi-echo acquisition and are often done separately before acquiring fMRI data. However, for dynamic imaging such as BOLD fMRI, having a fieldmap for every timepoint could improve image quality, especially in changing $$$B_0$$$ fields due to respiration or motion. Prior work has shown off-resonance correction on individual images using an entropy metric², a piecewise linear estimate³, or with convolutional neural networks (CNNs)^4,5. Here we use a residual UNet, called FieldMapNet, that, given a prior estimate of the fieldmap and image phase from an earlier timepoint, dynamically estimates fieldmaps from the phase of each timeseries image. The fMRI timeseries is then corrected using MBIR⁶, reducing the effects of potential network artifacts on the final images.

Methods

MRI Acquisition
We acquired human in vivo data for network training and test fMRI experiments on a 3T GE MR750 scanner with a Nova 32-channel head coil using the TOPPE pulse sequence programming language⁷. For both sets of data we acquired 80 slices of 2D single-shot fully sampled spiral-in images, with volume FOV=240×240×240mm³ and resolution=3×3×3mm³ (matrix size=80×80×80). We also acquired a conventional GRE field map (1:37s) prior to acquiring the spiral-in data.

Multiecho Training Data Parameters: To create the dynamic ground-truth off-resonance maps used for training the network, we acquired three sequential spiral-in images at each slice with TE=26.7/27.7/28.9ms ($$$\Delta$$$TE=1,2.3ms), FA=10°, volume TR=9.9s, # frames=20 (3:18min).

Testing Data Parameters: TE=26.7ms, volume TR=3.1s, # frames=65 (3:21min), FA=84°. The experiment was repeated with deep breathing to investigate the impact of large changes in off-resonance.

FieldMapNet Structure
FieldMapNet (Fig. 1) maps 5 input channels, $$$[\cos (\boldsymbol{\phi}_n^{TE1}), \sin (\boldsymbol{\phi}_n^{TE1}), \cos (\boldsymbol{\phi}_0^{TE1}), \sin (\boldsymbol{\phi}_0^{TE1}), \boldsymbol{\omega}_0]$$$ to a single output of $$$\boldsymbol{\omega}_n$$$, where $$$\boldsymbol{\phi}_n^{TE1}$$$ is the phase of the first TE image at timepoint $$$n$$$, $$$\boldsymbol{\phi}_0^{TE1}$$$ is the phase of the first TE image at some initial timepoint, $$$\boldsymbol{\omega}_0$$$ is a fieldmap calculated from $$$\boldsymbol{\phi}_0^{TE1}$$$, $$$\boldsymbol{\phi}_0^{TE2}$$$, and $$$\boldsymbol{\phi}_0^{TE3}$$$, and $$$\boldsymbol{\omega}_n$$$ is the fieldmap at timepoint $$$n$$$. We use cosine and sine of the phase to accommodate phase wraps. For the three-TE training data we used the first volume for $$$\phi_0^{TE1}$$$ and $$$\boldsymbol{\omega}_0$$$, and for the single-echo time test data we used the last timepoint from the most recent training data scan (this prior fieldmap takes 9.9s to acquire and could also be added to be beginning of the single-TE scan). We used a residual single-level UNet by passing $$$\boldsymbol{\omega}_0$$$ to the output as a skip connection, with 5×5 convolutional filters, MAE loss , learning rate=10^-4, and the Adam optimizer, implemented in Keras.

FieldMapNet Training Data
We reconstructed images from the three TE data using a model-based image reconstruction (MBIR) as described in the section below. The images from the three TEs were used to calculate the fieldmaps $$$\boldsymbol{\omega}_n$$$ at each frame using a regularized iterative algorithm⁸. We used 10 subjects for network training and two subjects unseen by the network for testing. For training we selected slices within the brain region of the imaging volume, yielding 176 slices across all subjects, and 3520 unique image to fieldmaps pairs (from the 20 frames). We augmented the data using translations, rotations, and random bulk phase, leading to 22528/5632 training/validation pairs.

Model-based Image Reconstruction
Images at each timepoint are generated from an edge-preserving regularized reconstruction using a second-order finite difference operator, $$$\boldsymbol{C}$$$, and a Fair potential function $$$\psi$$$. The forward model, $$$\boldsymbol{A}$$$, includes sensitivity maps calculated using the sigpy.mri⁹ implementation of joint-sense^10,11, a gridding operator, and the fieldmap $$$\boldsymbol{\omega}$$$⁶
$$ \boldsymbol{\hat{x}} = \mathop{\mathrm{arg\,min}}_{\boldsymbol{x}} \frac{1}{2} \| \boldsymbol{A}(\boldsymbol{\omega}) \boldsymbol{x}-\boldsymbol{y} \|_2^2+\beta R(\boldsymbol{x}) \hspace{10pt} \text{where} \hspace{10pt} R(\boldsymbol{x})=\sum_k \psi ([\boldsymbol{Cx}]_k)$$
with $$$\beta$$$ empirically set to 30. The images are first reconstructed using the GRE fieldmaps, and these images are input to FieldMapNet. Dynamic fieldmaps are then generated from the network and the images are re-reconstructed with the fieldmap at that timepoint. All reconstructions used the MATLAB implementation of MIRT¹². Fig. 2 gives an overview of the method. This approach mitigates potential network hallucinations affecting the image by using a physics-based reconstruction as the final step.

Results

Fig. 3 shows fieldmaps generated using the iterative three-echo model-based method⁸ (ground truth) and the proposed FieldMapNet. Fig. 4A shows image reconstruction results compared to the 3-TE ground truth, Fig. 4B shows the % RMSE across slices, and Fig. 4C shows the summary statistics. Fig. 5A shows image results from the deep breathing experiment, reconstructed using the standard GRE fieldmap versus the dynamic fieldmaps from FieldMapNet, with reduced blurring using FieldMapNet. Fig. 5B shows the changes in B₀ over the course of the scan detected by FieldMapNet, with more off-resonance detected in deep breathing vs. normal breathing, as expected.

Discussion & Conclusions

We have demonstrated the potential to dynamically estimate a fieldmap from a single TE image using a prior fieldmap estimate and a residual one-level UNet. Using FieldMapNet with MBIR can correct for off-resonance while avoiding ML artifacts in the final image. We expect this method to improve the quality of fMRI experiments, especially in moving subjects where the fieldmap can change as a subject moves through the FOV.

Acknowledgements

This work was supported by the National Institutes of Health Grants U01EB026977 and F32EB029289.