Synopsis

Multi-shot diffusion-weighted (msDW) imaging schemes can improve the spatial resolution of DWIs. However, the multi-shot readout spans multiple TRs which reduce the time efficiency of msDWI. Hence the practical utility of multi-shot methods for high angular resolution imaging for fiber tracking purposes currently remains limited. To improve the time efficiency of msDWI, SMS acceleration can be employed. However, the DWIs from SMS-accelerated msDW acquisition will exhibit severe artifacts due to slice aliasing and inter-shot phase inconsistencies arising from the msDW encoding. We present a novel navigator-free reconstruction method to simultaneously slice unfold and jointly recover multi-shot diffusion data from an SMS-accelerated msDW acquisition. The method is shown to effectively reconstruct 4-shot DW data accelerated at a multi-band factor of 3.

Introduction

EPI-based diffusion imaging using single-shot readout methods are prone to geometric distortions and blurring, which preclude its utility for high-resolution imaging. Multi-shot diffusion-weighted (msDW) imaging overcomes the above problems by splitting the single long readout into multiple shorter readouts that are acquired over multiple TRs. The shorter k-space readout duration limits the geometric distortions and blurring and achieves a shorter echo-time suitable for high-resolution diffusion imaging. However, the acquisition spanning multiple TRs to cover a single k-space reduce the time efficiency of multi-shot methods. Hence the practical utility of multi-shot methods for high angular resolution studies currently remains limited.

Simultaneous multi-slice^1,2 (SMS) imaging acceleration techniques can improve the time efficiency of msDW imaging without sacrificing SNR. A blipped-CAIPI³ EPI trajectory modified for multi-shot acquisitions coupled with a multi-band RF pulse can simultaneously encode and acquire k-space data from multiple slice locations. However, the reconstruction of this data is extremely challenging. The images from the above acquisition will be not only slice aliased, but will exhibit severe artifacts due to inter-shot phase inconsistencies arising from the msDW encoding. Reconstruction of artifact-free DWIs from the above acquisition requires simultaneous phase compensation and slice unfolding. Existing methods depend on explicit⁴ or implicit^5,6 navigators to calibrate the phase associated with each shot which is then used in a simultaneous slice-unfolding and phase-compensation reconstruction. We present a novel navigator-free reconstruction method, SMS MUSSELS, to achieve the above.

Methods

The proposed method exploits the low-rank property that exists between the multi-shot diffusion data. The MUSSELS⁷ formulation for the navigator-free reconstruction of msDW data proved the existence of annihilation relationships between multi-shot data of the form:

\begin{equation} \label{eq_8} {\bf{\cal H}}(\widehat{m_{i}})\cdot \widehat{\phi_j}[{\bf{k}}]- {\bf{\cal H}}(\widehat{m_{j}})\cdot\widehat{\phi_i}[{\bf{k}}]=0, \end{equation}

where $$$m_i(x), m_j(x)$$$ and $$$\phi_i(x), \phi_j(x)$$$ denote the DWI from shots $$$i, j$$$ and their phases respectively, $$$\widehat{m_i}[k], \widehat{m_j}[k],\widehat{\phi_i[k]}, \widehat{\phi_j[k]}$$$ denote the corresponding Fourier samples, and $$${\bf{\cal H}}$$$ represents the construction of the Hankel-structured convolution matrix. The existence of such linear relations assert that the block-Hankel matrix

\begin{equation}{\bf{H_1}}=[{\bf{\cal H}}(\widehat{m_{1}})\hspace{5mm}~{\bf{\cal H}}(\widehat{m_{2}}) \hspace{5mm}\cdots~\hspace{5mm}{\bf{\cal H}}(\widehat{m_{N_s}})],\end{equation}

formed out of the k-space data of each shots is rank-deficient. Here, $$$N_s$$$ denote the number of shots. In the SMS setting where $$$L$$$ slices are simultaneously excited, the above relation holds true independently for the shot data corresponding to each slice. Thus, we can state that

\begin{equation}{\bf{H}}_l=[{\bf{\cal H}}(\widehat{m_{1,l}})\hspace{5mm}~{\bf{\cal H}}(\widehat{m_{2,l}}) \hspace{5mm}\cdots\hspace{5mm}{\bf{\cal H}}(\widehat{m_{N_s,l}})];~~ l=1:L\end{equation}

is rank-deficient. We propose to make use of the above property to reconstruct the slice unaliased DWIs from the SMS-accelerated acquisition that are unaffected by phase artifacts. We pose the reconstruction of the slice unalised k-space data corresponding to each shot and each slice, $$${\bf{\widehat{m}}}$$$, as

\begin{equation}\label{use Hankel}\widehat{\tilde {\bf m}}= argmin_{{\bf{\widehat{m}}}} \underbrace{||{\mathcal{A}}\left({\bf{\widehat{m}}}\right)-{\bf{\widehat{y}}}||^2_{\ell_2}}_{\mbox{slice unfolding}} + \lambda\underbrace{\sum_{l=1}^{L}||{\bf H}_l({\bf{\widehat{{m}}}})||_*.}_{\mbox{low rank penalty}}\end{equation}

The operator $$${\mathcal{A}}\left({\bf{\widehat{m}}}\right)$$$ incorporates SMS slice folding and enforces data consistency with the measured k-space data, $$$\bf{\widehat y}$$$, of dimension $$$N_1\times N_2/N_s \times N_c\times N_{s}$$$. Here, $$$N_1\times N_2$$$ represents the size of the DWIs, and $$$N_c$$$ represents the number of channels. The different steps involved in the computation of $$${\mathcal A}\left({\bf{\widehat{m}}}\right)$$$ are illustrated in figure 1. The second term in eq. [4] enforces the low-rank property of the block-Hankel matrix for each slice by minimizing its nuclear norm. $$$ \lambda$$$ is a regularization parameter. The above cost function can be minimized using alternating minimization⁷ schemes that alternate between the data consistency term and the rank penalty term.

To test the proposed reconstruction, we collected diffusion data using a multi-shot blipped-CAIPI EPI sequence at various multi-shot and multi-band (MB) factors. A Stajeskal-Tanner sequence with b-value=700 s/mm², 25 diffusion directions and one non-DWI was used for data acquisition using a 32 channel coil on 3T MRI. MB=2,3 and Ns=2,4 were tested. Other imaging parameters were: FOV= 210mm; slice thickness=2mm, NEX=1 with matrix sizes of 128x88 and 192x120. The proposed reconstructions were compared with SMS-MUSE⁶, another navigator-free reconstruction method.

Results

Conclusion

Acknowledgements

References

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