Elsevier

Magnetic Resonance Imaging

Volume 66, February 2020, Pages 9-21
Magnetic Resonance Imaging

Original contribution
Coil-combined split slice-GRAPPA for simultaneous multi-slice diffusion MRI

https://doi.org/10.1016/j.mri.2019.11.017Get rights and content

Abstract

Objective: To develop a kernel optimization method called coil-combined split slice-GRAPPA (CC-SSG) to improve the accuracy of the reconstructed coil-combined images for simultaneous multi-slice (SMS) diffusion weighted imaging (DWI) data.

Methods: The CC-SSG method optimizes the tuning parameters in the k-space SSG kernels to achieve an optimal trade-off between the intra-slice artifact and inter-slice leakage after the root-sum-of-squares (rSOS) coil combining of the de-aliased SMS DWI data. A detailed analysis is conducted to evaluate the contributions of the intra-slice artifact and inter-slice leakage to the total reconstruction error after coil combining.

Results: Comparisons of the proposed CC-SSG method with the slice-GRAPPA (SG) and split slice-GRAPPA (SSG) methods are provided using two in-vivo readout-segmented (RS) EPI datasets collected from stroke patients. The CC-SSG method demonstrates improved accuracy of the reconstructed coil-combined images and the estimated diffusion tensor imaging (DTI) maps.

Conclusion: CC-SSG strikes a good balance between the intra-slice artifact and inter-slice leakage for rSOS coil combining, and so can yield better reconstruction performance compared to SG and SSG for rSOS reconstruction. The optimal trade-off between the two artifacts is robust to the contrast of SMS data and the choice of the coil combining method.

Introduction

Diffusion-weighted imaging is a well-established magnetic resonance imaging (MRI) technique to study microstructure of the brain and other organs and is extensively used in clinical applications. Single-shot two-dimensional (2D) echo-planar imaging (EPI) is commonly used to acquire diffusion-weighted images (DWIs). However, due to physics such as T2* decay and off-resonant spins, single-shot DW-EPI suffers from image distortion and blurring artifacts [1] and offers a limited spatial resolution. Furthermore, when doing diffusion spectrum imaging (DSI) [2] or high angular resolution diffusion imaging (HARDI) [3], a large number of DWIs are needed, which are relatively slow to acquire. Therefore, the long scan time associated with high-resolution full-brain coverage would benefit from being shortened. Conventional 2D parallel imaging techniques [1,4,5] try to reduce the repetition time (TR) by cutting out some of the phase encoding (PE) steps during the acquisition, though for diffusion prepared EPI, TR can not be reduced significantly. On the other hand, multi-shot acquisitions such as readout-segmented (RS) EPI [6] and multiplexed sensitivity-encoding (MUSE) [7] reduce the artifacts and allow for higher resolution DWIs at the cost of increasing the scan time.

Simultaneous multi-slice (SMS) acquisition can reduce the scan time by imaging multiple slices at the same readout time. Unlike the conventional accelerated 2D parallel imaging methods, SMS acquisitions do not suffer from R reduction in signal-to-noise ratio (SNR) when compared with a time matched 2D acquisition. In order to separate simultaneously acquired slices more efficiently, SMS is combined with controlled aliasing in parallel imaging results in higher acceleration (CAIPIRINHA) techniques [[8], [9], [10]]. The CAIPIRINHA scheme proposed in Ref. [8] is not compatible with EPI, but the scheme presented in Ref. [9] solves this problem, yet it introduces voxel tilting artifacts. The blipped-CAIPI scheme proposed in Ref. [10] allows for shifting of simultaneous slices in the PE direction with small tilting artifacts and enables SMS acquisitions with low g-factor penalties. The SMS acquisitions combined with blipped-CAIPI have been used to reduce the scan time for both single-shot [10,11] and multi-shot EPI [12].

Image reconstruction for SMS have been extensively studied in the literature [[8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18]], among which the k-space GRAPPA-based methods including slice-GRAPPA (SG) [10] and split slice-GRAPPA (SSG) [16] are commonly used. In the SG method, individual k-space kernels are fitted using non-SMS calibration data to separate each of the simultaneously acquired slices with the objective being to minimize the mean-square-error (MSE) between reconstructed and ground truth coil images. The SSG method in Ref. [16] improves the SG method by designing k-space kernels that perform an unbiased estimate and hence are more robust to phase differences between SMS slices. In particular, the SSG method imposes separate constraints on intra-slice artifact and inter-slice leakage to control them simultaneously as opposed to the SG method which minimizes the total error caused by the combined effect of the two artifacts. In Ref. [16], the suppression of the two artifacts are weighted equally. Although the possibility of using different weights is suggested in Ref. [16], no detailed study on how to adjust those weights or the impact of the weights on the image reconstruction quality was provided.

While equally-weighted suppression of intra-slice artifact and inter-slice leakage in SSG results in the minimization of the reconstruction error for individual coil images, it is not necessarily optimal for coil-combined images because coil combining can alter the interactions between the two artifacts. This is particularly important for diffusion-weighted imaging where diffusion parameters are extracted from coil-combined magnitude images. In this work, we aim to improve the SMS reconstruction quality for coil-combined images by optimizing SSG kernels to balance the intra-slice artifact and inter-slice leakage after coil combining. Specifically, we propose a new method termed coil-combined split slice-GRAPPA (CC-SSG) [19] to train k-space kernels such that the mean-square-error between reconstructed and ground truth coil-combined images are minimized. The CC-SSG kernels are an extended form of SSG kernels that allow for an optimal trade-off between intra-slice artifact and inter-slice leakage through some tuning parameters. We also present a sub-optimal CC-SSG method that has a lower computational complexity compared to that of optimal CC-SSG while achieving a similar performance.

In this work, we primarily focus on the commonly used root-sum-of-squares (rSOS) coil combining which does not require prior knowledge of coil sensitivity profiles. This is in line with k-space de-aliasing methods such as SG and SSG which also do not require knowledge of coil sensitivities. For rSOS coil combining, we provide a detailed characterization of various components of the reconstruction error due to the two artifacts and show how they are balanced by adjusting the tuning parameters in the proposed CC-SSG. Controlling intra-slice artifact and inter-slice leakage is particularly important for rSOS coil combining because these can not be suppressed by sensitivity-weighted coil combining as in the case when coil sensitivities are known. While the concept of CC-SSG is applicable to other coil combining methods beyond rSOS, we note that other methods such as sensitivity encoding (SENSE) can be less sensitive to the trade-off between intra-slice artifact and inter-slice leakage because the linear coil combining operation in such methods can largely suppress these artifacts. As a result, for such methods minimizing the reconstruction error for individual coil images is similar to that for the coil-combined images.

Since this work focuses on improving the quality of the reconstructed rSOS coil-combined images, the proposed CC-SSG does not necessarily optimize the MSE of individual coil images. The primary reason for the optimization of coil-combined images is that in diffusion MRI individual coil images are typically noisy with low SNR and hence coil-combining is necessary to improve the SNR of the final reconstruction. Usually, final qualitative and quantitative interpretations of data including fitting to the diffusion tensor imaging (DTI) model are performed using coil-combined magnitude images. This motivates our work to design CC-SSG kernels which directly minimize the MSE for rSOS coil-combined images rather than for the individual coil images.

We processed two in-vivo multi-shot readout-segmented (RS) EPI datasets from stroke patients to evaluate CC-SSG and compare it with SG and SSG methods. The results show that using the optimized kernels designed for coil combining, the CC-SSG produces more accurate reconstructed single slice DWIs and DTI maps than those of the SG and SSG.

Section snippets

Theory

In this section, we provide a mathematical description of the proposed CC-SSG. Consider a set of multi-coil and multi-slice DWIs with Nc coils, Ns slices, and Nd diffusion-encoded directions. Let mi,z,n(x,y) denote the DWI acquired by the i-th coil, for the z-th slice, and the n-th diffusion direction, where i = 1,⋯ ,Nc, z = 1,⋯ ,Ns, and n = 1,⋯ ,Nd. Similarly, we let mi,z,0(x,y) denote the baseline images corresponding to b = 0. Also, let Mi,z,n(kx,ky) denote the k-space representation of mi,z,

Methods

To compare optimized and sub-optimal CC-SSG with conventional SG/SSG we processed two multi-shot RS-EPI datasets. Fully sampled RS-EPI diffusion MR data were acquired from a Siemens 3T Verio scanner with a 32-channel head coil. Two stroke patients with IRB approval and informed consent were imaged. For each dataset, one b = 0 and twenty DWIs with a b-value of 2000 s/mm2 were acquired with TR = 3.5 s, TE = 100 ms, number of shots = 7, number of slices = 16 with a slice thickness of 2.1 mm, and

Results

In Fig. 2, the nRMSE between reconstructed and ground truth single slices are shown for both training and diffusion-weighted SMS data from the first dataset. The top sub-figure shows the nRMSE of reconstructed coil images, averaged over all 32 coils. The bottom sub-figure shows the nRMSE of rSOS coil-combined reconstructed images. In each sub-figure, six groups of error bars are shown, corresponding to six different settings with different Ns and R values. Here, Ns denotes the number of

Analysis of artifacts for CC-SSG with rSOS coil combining

In this section, we present a detailed analysis on the contributions of intra-slice artifact and inter-slice leakage towards the total error between reconstructed and ground truth rSOS coil-combined images for SSG and sub-optimal CC-SSG. After applying kernels on the SMS data, the reconstructed single-slice coil images for a given diffusion direction n can be written as m^i,z,n=mi,z,n+ξi,z,n+νi,z,n,where mi,z,n=F1{Mi,z,n} is the ground truth coil image for i-th coil, slice z, and diffusion

Conclusion

In this work, we propose a CC-SSG method to improve the accuracy of the reconstruction of rSOS coil-combined images by applying optimized SSG kernels to de-alias the SMS DWI data. By optimizing tuning parameters that control the trade-off between intra-slice artifact and inter-slice leakage, the CC-SSG kernels strike a good balance in suppressing the two artifacts for rSOS coil combining and hence outperform SSG with αi,z = 1. Sub-optimal CC-SSG gives similar good performance for estimation of

References (1)

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      Image reconstruction for SMS acquisition has been extensively studied in the literature (Breuer et al., 2005; Nunes et al., 2006; Setsompop et al., 2012b; Larkman et al., 2001; Zahneisen et al., 2015; Martin et al., 2006; Moeller et al., 2014; Zhu et al., 2012; Cauley et al., 2014; HashemizadehKolowri et al., 2020; Zhu et al., 2016; Park et al., 2019; Olson et al., 2019).

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