Introduction

EPI ¹, despite its rapid imaging capability, is prone to distortions from magnetic-field-inhomogeneity and related issues ².
Postprocessing solutions such as TOPUP ^3,4 is effective at gross-scale mitigation but can cause compromised resolution, particularly in image compression areas. To overcome this, high inplane-acceleration (R_inplane) can be employed (Figure1.b) , but can lead to large $$$g\sqrt{R_{inplane}}$$$ SNR-penalty ⁵, especially beyond R_inplane =3.
This work introduces an ensemble of k-t GRAPPA ⁶ kernels (EnKT-GRAPPA) approach for use on moderately-accelerated EPI, to fill missing-kspace and correct for cumulative-phase of field-inhomogeneity in one step, where phase/distortion correction level can be flexibly tuned to tradeoff distortion mitigation vs. noise amplification. We show that such an approach improves the trade-off between distortion mitigation and SNR-reduction in accelerated-EPI.

Methods

In this abstract, R_inplane denotes the inplane undersampling performed during acquisition, while R_recon represents the equivalent factor in terms of distortion-mitigation achieved through EnKT-GRAPPA reconstruction.
We validate the proposed EnKT-GRAPPA approach through comparing reconstructions performed on simulated k-t data generated from a ground truth GRE and a B0 map (used to simulate phase-accumulation along the EPI-readout) ⁷. The data were collected on a healthy volunteer using a 3T scanner with 48-channel coils. For our target brain-imaging application, R_inplane = 2 was chosen for use with EnKT-GRAPPA for 1mm EPI-acquisition, where the echo-spacing was assumed to be 1ms (Figure2) . This choice effectively curtails the amount of phase-accumulation that needs to be mitigated, while preserving a good level of SNR due to reasonably low $$$g\sqrt{R_{inplane}}$$$ SNR-penalty (Figure1.c). Based on this, we trained spatio-temporal GRAPPA kernels in a confined self-calibration region of k-space, achieving results with minimal distortion. We delve into three key facets:

• Training a Spatio-Temporal GRAPPA-Kernel for Magnetic-Field-Inhomogeneity Correction（Figure1.d）

Using a 3 $$$\times$$$ 3 kernel (k_x $$$\times$$$ k_y) for illustration, nine points are sourced from each coil-channel within three proximate-rows and time-slots, forming the source-points (3 $$$\times$$$ 3 $$$\times$$$ coil-number). Data points from each channel at the 3 $$$\times$$$ 3-grid's center location at the target time-point are selected as target-points. Once the kernel is trained, a linear correlation between the source and target is formulated:[target] = [kernel] * [source]
This trained kernel can correct B₀-inhomogeneity phase-accumulation of the calibration area at a specific time-point to the phase at the target time-point. Utilizing EnKT-GRAPPA kernels, each data point sampled at a specific temporal-instance can be synchronized to a chosen target time-point. This creates a consistent phase across different rows within the EPI-dataset. By applying these kernels to various rows, we align the phase of data points from disparate temporal-coordinates to a common reference-time. This harmonization effectively eliminates inter-row phase discrepancies, thus preventing distortion in the aggregated-data.

• Using EnKT-GRAPPA Kernel for Concurrent Image Distortion-Correction & K-space Filling（Figure1.e）

For k_y lines that are sampled during EPI acquisition (red-dots), we use specialized kernels solely for phase-correction. For unsampled ky lines (green-dots), we apply a different set of EnKT-GRAPPA kernels to estimates the missing-kspace values while simultaneously performs phase-correction. In this case, our EnKT-GRAPPA not only fills gaps but corrects temporal k-space along echo-times.

• Determining the Optimal Phase-Correction Magnitude（Figure1.f）

Distortion-correction level can be tweaked by adjusting the phase states of the target-points during kernel training. For instance, the figure depicts the use of EnKT-GRAPPA to perform distortion-mitigated reconstruction for R_inplane =2 EPI-data, at different level of distortion mitigation R_recon = 4,8, and 16, with larger mitigation requiring the k-t kernels to perform larger interpolation along t to rewind phase error, which resulted in a more ill-posed reconstruction.

Results

The distortion mitigation outcomes from EnKT-GRAPPA demonstrate superior-corrections compared to conventional-GRAPPA , particularly as the R_recon value increases. This is particularly evident in the compressed air-tissue interface region with large B0-inhomogeneity, circled in red.
Figure 4 shows comparison of GRAPPA vs EnKT-GRAPPA reconstructed images for various simulated-EPI acquisitions with added-noise at different level of R_inplane accelerations; all reconstructed to the same level of image-distortion (R_recon 4). GRAPPA reconstruction of R_inplane 4 acquisition resulted undesirably large noise-amplification and artifacts. EnKT-GRAPPA reconstruction of R_inplane 1 data, reconstructed to R_recon 4 achieves improved results with less noise. However, the large amount of phase-correction, required by k-t GRAPPA kernels, can cause reconstruction errors as seen by prominent stripes in the red boxes. The synergistic use of R_inplane 2 acquisition-acceleration, with a further 2x distortion mitigation via EnKT-GRAPPA to achieve R_recon 4 provide the best trade-off with high quality reconstruction.

Conclusion and Discussion

Our simulation results demonstrate that EnKT-GRAPPA can efficiently address missing k-line fillings and phase-correction. By merging parallel imaging with phase-correction through a unified kernel-set, we maintain high-SNR, reduced-distortion, and a minimized g-factor, ensuring more enhanced noise-management.

Acknowledgements

This work is partially supported by R01MH116173, R01EB019437, U01EB025162, P41EB030006, R01EB033206, U24NS129893.