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Navigator-free multi-shot EPI with shift-invariant kernel extraction in subspace
Rui Tian1, Martin Uecker2, and Klaus Scheffler1,3
1High-Field MR center, Max Planck Institute for Biological Cybernetics, Tuebingen, Germany, 2Institute of Biomedical Imaging, Graz University of Technology, Graz, Austria, 3Department for Biomedical Magnetic Resonance, University of Tuebingen, Tuebingen, Germany

Synopsis

Keywords: Image Reconstruction, Image Reconstruction

Motivation: In functional and diffusion MRI, multi-shot EPI enhances spatial resolution and minimizes distortion compared to single-shot scans. However, its vulnerability to shot-to-shot phase variations presents a significant challenge, with various proposed methods having drawbacks.

Goal(s): We propose a robust, navigator-free, computational efficient multi-shot method without SNR penalty.

Approach: In readout-segmented multi-shot EPI, we exploit the k-space overlapped regions between adjacent segments to extract relative phase fluctuations. This method, inspired by ESPIRiT and nonlinear gradient calibration, efficiently extracts shot-dependent phase variations in subspace.

Results: Our ex-vivo and in-vivo scans, including diffusion-weighted imaging, successfully achieves a high in-plane resolution of about 0.6mm without ghost artifacts.

Impact: Our proposed multi-shot technique eliminates the needs for time-consuming navigators, provides robust high-resolution diffusion and potentially functional imaging, and could be easily adapted for interleaved Cartesian and spiral EPI allowing robust phase error estimation from merely small k-space regions.

Introduction

For functional1–3 and diffusion4 MRI, multi-shot EPI5 offers enhanced spatial resolution and reduced geometric distortion compared to single-shot acquisitions; however, it introduces susceptibility to uncontrollable phase fluctuations between shots6,7, which could result from various factors (e.g., motions, respiration, heartbeat, scanner instability, diffusion gradients) and has attracted continuous research interests towards more sophisticated techniques.

One established approach uses a 2D navigator8–11 to explicitly estimate the phase inconsistency, which inevitably prolongs the scan time and may fail in some cases. The phase fluctuations can also be estimated through pure post-processing, however, only with fully sampled k-space center12 or when the EPI interleave number is below the maximum parallel imaging acceleration factor13.

Alternatively, iteratively reconstruction with a low-rank penalty term, formulated in either k-space14 or local image-space15, can be applied without explicit phase estimation. Unfortunately, this could lead to substantially increased computational complexity, or image artifacts given highly undersampled data. Lastly, the inter-shot phase variations can be eliminated in a magnitude-based super-resolution scan with subpixel modulation16–19, but at the cost of inevitable SNR loss.

To address these issues, we propose a navigator-free multi-shot technique without significant constraints. This approach accurately and efficiently extracts inter-shot phase fluctuations in subspace, as inspired by studies of ESPIRiT20 and nonlinear gradient calibration21.

Methods

Mathematically, shot-dependent phase fluctuations in image space can be represented as shift-invariant kernels convolved with k-space signals, similar to the GRAPPA kernel22 in parallel imaging22–24. In parallel imaging, the RF receivers’ sensitivity maps can be directly estimated in subspace with the ESPIRiT algorithm based on central k-space calibration scans20, which allows efficient and robust reconstruction.

A key insight for our technique is that, the calibration scans with commonly sampled (e.g., by distinct RF receivers, or different shots) k-space region need not be confined to the k-space center, thanks to the shift-invariant nature of the kernel across the entire k-space. For instance, in readout segmented EPI11 with a typical band overlapping ratio (e.g., 10%-20%) to avoid k-space holes, the kernel can be directly estimated using the subspace algorithm20 by treating the overlapped k-space pixels from different shots as from distinct RF receivers.

As illustrated in Figure 1, a multi-shot readout segmented EPI (A) is programmed in Pulseq25 and tested on a 3T Siemens Prisma scanner with a 64-element RF array. The opposite readout gradient polarity between neighboring segments ensures consistent T2 decay between overlapped k-space pixels. After pre-processing the data from the scanner (e.g., re-gridding, gradient calibration, or optional, parallel imaging), a calibration matrix (C) is constructed by selecting data in the overlapped regions between two adjacent k-space segments, using a sliding window with a specified kernel size (B). Notably, the data from different RF coils are treated analogously to the kernel data sliding across different k-space locations (C), as different than ESPIRiT for estimating RF sensitivity maps. Based on this calibration matrix, the phase maps between every two adjacent EPI segments can be estimated using a similar mathematical principle as ESPIRiT20, including subspace thresholding (D) and pixel-wise eigenvector extraction in image space along the shot dimension (E).

Additionally, when applying the estimated phase maps for correction, the Gibbs ringing in each low-resolution segment image can propagate to the finally reconstructed image. Hence, a Kaiser window is applied to filter each segment in k-space suppressing the ringing, and an inverse filter is utilized to undo the modulation transfer function (F), as a reconstruction treatment used in phaseless encoding MRI18,19.

Results

In Figures 2 and 5, our technique is experimentally validated with multi-slice ex-vivo phantom26,27 and in-vivo brain scans. Compared to uncorrected images, the corrected multi-shot (here, 7-shot) reconstruction achieves significant resolution enhancement (0.56 mm2/0.66mm2) than the single-shot acquisitions (1.33 mm2/1.67mm2) without ghost artifacts.

Additionally, in Figure 3, a moderate apodization for each segment proves useful for images with sharp edges, but appeared unnecessary for high b-value scans. Furthermore, in Figure 4, different kernel sizes and subspace cutoff thresholds are investigated, and empirically, a kernel size of 6x6 to 10x10 pixels with moderate thresholding will be sufficient to correct the inter-shot phase fluctuations.

Discussions/Conclusion

Our subspace estimation technique successfully achieves high-resolution non-diffusion and diffusion-weighted imaging with multi-shot readout-segmented EPI without navigators, by extracting the phase fluctuations as shift-invariant kernel convolved in k-space, from only about 90 (phase) x10 (read) overlapped k-space pixels between adjacent segments. This technique can also be adapted for interleaved Cartesian or spiral EPI to achieve robust phase error estimation from merely a small k-space region commonly sampled during different shots.

Acknowledgements

This study is supported by ERC Advanced Grant No 834940.

The ex-vivo brain phantom was with courtesy of the Institute of Clinical Anatomy and Cell Analysis, Department of Anatomy, Eberhard Karls University of Tübingen. The first author thanks Dr. Thomas Shiozawa (Institute of Clinical Anatomy and Cell Analysis) for assistance with sample preparation, and Dr. Gisela Hagberg for assistance in scanning this phantom.

The first author thanks Dr. Sebastian Mueller, Dr. Felix Glang, Praveen Iyyappan Valsala, and Dana Ramadan for experimental assistance.

References

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Figures

Figure 1. A. The k-space trajectory for readout segmented EPI, with opposite readout polarity between adjacent segments. B. Selecting k-space patches from overlapped regions. C. Structuring patches into a calibration matrix, where the convolution filters between two neighboring segments to be extracted are contained in vectorized patches along the horizontal dimension, and remain shift-invariant along the vertical dimension. D. The calibration matrix with subspace cutoff using SVD. E. Reshaping data. Applying pixel-wise SVD to estimate maps with the primary eigenvector.

Figure 2. The multi-slice ex-vivo scans comparing single-shot EPI and navigator-free 7-shot readout segmented EPI. For both b = 0 s/mm2 and 2000 s/mm2, the 7-shot EPI reaches significantly higher in-plane resolution (0.56 mm2) than the single-shot ones (1.33 mm2), resolving more fine details. As expected, ghost artifacts are observed in the conventional multi-shot EPI images without navigator corrections. These artifacts are effectively removed using the phase fluctuation maps estimated in subspace.

Figure 3. Comparing k-space apodization strengths for filtering low-resolution segments to suppress Gibbs ringing propagated to the final image after phase map corrections. For b = 0 s/mm2 ex-vivo image with sharp edges, a Kaiser filter with Kaiser coefficient 3.0 applied to the low-resolution segment leads to high-quality reconstruction without noticeable Gibbs ringing artifacts, which can be observed if no filter or a very strong one (i.e., Kaiser coefficient 5.0) is used. For = 2000 s/mm2, the filter is unnecessary given smoother signal representation in image space.

Figure 4. Comparing reconstruction quality with different kernel sizes and cutoff thresholds for subspace estimation of phase errors. Here, a 20-pixel k-space overlapping along the readout dimension is used, allowing varying kernel sizes from 6x6 to 20x20 pixels. For both b = 0 s/mm2 and b = 2000 s/mm2 images, a moderate subspace cutoff will be sufficient for high-quality reconstruction with kernel size in 6, 10, and 20. Thus, a 10-pixel k-space overlapping is sufficient for our experiments. Moreover, the subspace cutoff is critical for diffusion-weighted images due to low SNR.

Figure 5. Multi-slice In-vivo scans comparing single-shot and multi-shot EPI without and with our proposed phase correction technique. The conventional multi-shot EPI without navigators suffers from ghost artifacts similar to Figure 2. However, with our subspace-estimated phase maps, the shot-to-shot phase variations can be directly accessed from the acquisition data and used to reconstruct artifact-free images. The proposed technique produces a substantially higher in-plane resolution (0.66 mm2) than single-shot acquisitions (1.67 mm2) without the needs of navigators.

Proc. Intl. Soc. Mag. Reson. Med. 32 (2024)
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DOI: https://doi.org/10.58530/2024/1081