Introduction

For high resolution diffusion weighted (DW) EPI, interleaved segmentation provides substantially improved image quality. One drawback of such segmentation is the vulnerability to phase fluctuations. Multiplexed sensitivity encoding¹ enables robust high-resolution DWI by formulating a joint SENSE reconstruction. Such joint reconstruction was already applied to k-space based algorithms^2,3. However, these required navigators to estimate the segments’ phases. In this work, an operator for joint reconstruction of interleaved segmented DW data in k-space without phase navigation is investigated.

Methods

Figure 1 visualizes the general idea of the ASeDiWA operator. First, (fig.1a) an ordinary interleaved combination is displayed, leading to substantial ghosting artifacts.
Figure 1b shows the GRAPPA reconstruction of each individual segment. Missing samples are reconstructed according to:
$$x_{is0}(r)=\sum_j g_{rji}^*(\widetilde{R}_{rs}x_{js}),\color{white}{.....}[1]$$
where for each segment ($$$s$$$) the nonacquired k-space value at a position $$$r$$$ in the $$$i$$$-th coil $$$x_{is0}(r)$$$ is calculated from the acquired data of all coils of this segment selected by an operator $$$\widetilde{R}_{rs}$$$ about the position $$$r$$$. $$$g_{rji}^*$$$ denotes a set of weights calculated from reference data obtained from the unweighted (B0) scans.
In fig.1c, the ASeDiWA operator reconstructs missing samples in one segment, using data from all segments. For this operation, new reference data are generated by combining the phase information of each segment reconstructed in Eq.1 with the absolute value of the original reference data in image space:
$$x'_{isn}=IFFT\left\{abs\left\{FFT\left\{x_i\right\}\right\}*phase\left\{FFT\left\{x_{isn} \right\}\right\}\right\},\color{white}{.....}[2]$$
where $$$x'_{isn}$$$ is the modified reference data of a segment $$$s$$$ in the $$$i$$$-th coil.
Given the augmented reference data ($$$x'_{isn}$$$) a second calibration is formulated:
$$\min_{g_{risn}}\sum_{p \epsilon Calib}\left\| \sum_t \sum_j g^*_{rjitsn}(\widetilde{R}_{pt}x'_{jtn}) - x'_{isn}(p) \right\|^2,\color{white}{.....}[3]$$
where the operator $$$\widetilde{R}_{pt}$$$ selects sampled k-space locations from all segments and coils about the positions $$$p$$$.
This set of weights ($$$g^*_{rjitsn}$$$) is used for the second reconstruction step:
$$x_{is(n+1)}(r)=\sum_t\sum_j g_{rjitsn}^*(\widetilde{R}_{rt}x_{jt})\color{white}{.....}[4]$$
To reconstruct a k-space location in one segment $$$x_{is(n+1)}(r)$$$, data from all segments are used.
ASeDiWA reconstructs a full k-space dataset for each segment and coil ($$$x_{is(n+1)}(r)$$$), including information of the object phase. Thus, the steps described in Eq. 2-4 can be iterated as denoted by the index n. Note, that the dataset $$$x_{is(n+1)}(r)$$$ is still reconstructed from the acquired data.

Measurements and Simulations

DWI data with 4 interleaves were acquired on a 3T system with 32-channel head coil (Tim Trio, Siemens Healthcare). Settings: TE/TR = 107/4000ms, FOV = 220×220×3.0mm³, Matrix = 256×260, 1 B0 scan, 3 b-values (500, 1000, and 2000 s/mm²). Data were reconstructed using the three algorithms visualized in fig.1.
To evaluate the parallel imaging algorithms, g-factor maps were generated. For different segmentation factors (2, 3, and 4), data were reconstructed with GRAPPA, ASeDiWA, and ASeDiWA_n (n denoting the number of additional iterations). Simulations were performed on fully sampled FLASH data, acquired on a 7T system with a 4-channel coil (BioSpec, Bruker BioSpin). Settings: TE/TR = 2.576/500ms, FOV = 20×20×1.0mm³, Matrix = 128×128.
DTI processing was applied on a preclinical dataset with different reconstruction settings. Data were acquired on a 9.4T system with a four-channel cryogenic coil (BioSpec , Bruker BioSpin). Settings: TE/TR = 22/2000ms, FOV = 25×25×0.8mm³, Matrix = 128×128×5, 4 segments, 5 B0 scans, b-value 650 s/mm², 30 directions, with phase navigation.

Results

Figure 2 compares the FFT reconstruction of the human data with the results of the GRAPPA reconstruction and ASeDiWA. For all b-values, the FFT reconstruction shows ghosting. Ghosting is corrected by GRAPPA as well as ASeDiWA. The comparison between GRAPPA and ASeDiWA shows improved results of the ASeDiWA reconstruction.
Figure 3 shows results of the g-factor simulations. The left side of each image contains the magnitude image, the right side displays the g-factor maps. From left to right each reconstruction establishes the phase estimate for the following reconstruction step, improving reconstruction results over iterations.
Figure 4 shows fractional anisotropy and corresponding color maps of the preclinical measurement. The first column (a) shows the standard FFT including the phase information of the navigator. In Figure 4b the navigator information was discarded, resulting in ghosting. Figure 4c displays the GRAPPA reconstruction. While artifacts from ghosting are reduced, a substantial loss in SNR can be observed. In fig.4d, ASeDiWA shows improved quality of the DTI maps, compared to GRAPPA. Further improvement can be observed in fig.4e, displaying ASeDiWA₂ with two additional iterations.

Discussion

An algorithm for joint reconstruction of segmented DWI without navigators was presented. Phase estimates of each segment were calculated using a kernel calculated from an unweighted scan of the same experiment. Particularly an iterative reconstruction was shown to improve the g-factor and result in robust DWI, even with a small number of receivers. While the number of receivers limits the approach to a few segments, this constraint is relaxed by iteratively improving phase estimates. The method was applied to several in-vivo datasets, rodents as well as human.

Conclusion

The presented ASeDiWA algorithm allows for robust reconstruction of segmented DWI data without additional navigation or calibration measurements. In comparison to GRAPPA reconstruction approaches, the method reduces parallel imaging artifacts and improves SNR. An iterative variant was shown to further improve image quality and to provide robust results especially in the case of a small number of receiver channels.

Acknowledgements

No acknowledgement found.