Motivation

Spiral k-space trajectories provide unique advantages including efficient centre-out k-space coverage, straightforward variable density interleaves, and resilience to motion artefacts¹. However, despite these advantages, spiral imaging still lacks popularity in clinical routine. One important limiting factor is that spiral images are prone to off-resonance related blurring due to the rather long readouts and the gradients which are simultaneously varied in two directions¹.
Traditional field map-based methods are time consuming and rely heavily on field map's quality². Recent studies have shown that using convolutional neural networks (CNN) to correct for off-resonance artefacts in spiral images may be a feasible alternative ^3,4. While these recent studies have successfully trained off-resonance correction CNNs by using data acquired with off-resonance, in this work we demonstrate that an off-resonance correction CNN can be trained using simulated diffusion tensor cardiovascular MR (DTCMR) images.

Methods

The available data for this research consists of mid-ventricular short-axis images acquired with a STEAM-EPI sequence⁵ at 2.8x2.8x8mm³ resolution. 1750 images from 15 subjects and two cardiac phases are included ^6,7. Additionally, 7 field maps acquired in patients with myocardial infarction using a STEAM-spiral DTCMR sequence⁸ are used as basis for simulated field maps⁹.
As the 7 available field maps are not co-registered with the EPI images, we generate simulated field maps by segmenting the heart in the 7 field maps and fitting the data within the segmented region to 3^rd order polynomial surfaces which are extrapolated over the whole field of view (Figure 1).
We simulate off-resonance blurred spiral images using the original EPI images and simulated field maps as input. Off-resonance simulation was based on the frequency-segmented correction method². The input EPI images are resampled along spiral trajectories using an inverse gridding algorithm. Spiral data are replicated and spatially invariant off-resonance artefacts for different frequencies are simulated for each replicate by adding phase errors to each sampling point:
$$\Delta \phi_{\text {off-resonance }}=2 \pi \cdot \mathrm{i} \cdot \mathrm{T} \cdot f_{n}$$
where i indicates the index of the sampling point, T is the time interval between adjacent sampling points, and $$$f_{n}$$$ is the n^th constant off-resonance frequency in the range of [-250,250] Hz in steps of 10 Hz. We then grid the spiral data with phase errors to Cartesian image space with constant off-resonance artefacts.
The final step of simulation is to pixel-wise select the data from the constant off-resonance images based on simulated field maps. For example, if the off-resonance frequency at $$$(x,y)$$$ in a field map is 50 Hz, then we copy the value at $$$(x,y)$$$ from the 50 Hz constant off-resonance image to $$$(x,y)$$$ in the final image. As field map values do not, in general, correspond exactly with the constant off-resonance frequencies used, linear interpolation between two closest constant frequencies images is used.
Subsequently we set the original images as ground truth and the simulated blurred versions as input to train a deblurring auto-encoder CNN which consists of 6 2D-convolution layers (encoder) and 6 up-sampling layers (decoder). We use mean square error (MSE) as the loss function and ADAM as the optimizer. The dataset is split 80/20 into training and validation sets. Learning rate is set as 0.0003 with 66 epochs.
CNN-based deblurring performance is assessed by applying it to uncorrected STEAM DTCMR data acquired with spiral trajectories in 4 healthy volunteers⁸ in the same imaging plane and at the same spatial resolution as the training data. Sharpness was measured at the endocardial border¹⁰. CNN-corrected images are compared to data corrected with a field map-based frequency segmented correction.

Results

The CNN can effectively remove blurring in the training dataset (see Figure 3). In the test data acquired with spiral trajectories, the CNN-corrected data shows reduced blurring relative to the uncorrected data and avoids artefacts present in the field map-corrected images, introduced by imperfections in the field map (see Figure 4).
Figure 5 shows the sharpness measured in the uncorrected data, the field map-corrected data and the CNN-corrected data. From the 24 randomly selected cases, the mean±standard deviation sharpness is 0.048±0.014, 0.057±0.017 and 0.062±0.015 for the uncorrected, field map corrected and CNN corrected data respectively, showing the superior performance of CNN.

Discussion

The proposed CNN-based method trained using simulated images alone for off-resonance correction in spiral cardiac MRI performed at least as well as the field map-based correction. Sharpness values are highest for the CNN-based method and correction performance is visually excellent. In contrast to the field map-based correction, the CNN-based method does not introduce additional artefacts in the background and near the edge of myocardium. Finally, the CNN-based method may be timesaving as acquisition of field maps is not required.
Future work will enhance the CNN’s generalization by using a larger training dataset containing data from other types of acquisitions and using more realistic field maps. We also aim to make use of the multiple frames available in many CMR studies (e.g., b-values, directions, and averages in DTCMR) when training our CNN to improve performance and investigate its performance for correcting other spiral artefacts including T2* related blurring.

Acknowledgements

This work was funded by British Heart Foundation Program Grant RG/19/1/34160.

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