Introduction

Multi-shot DWI techniques are entering clinical practice overcoming current technical limitations in resolution and SNR of the prevalent single-shot EPI acquisitions¹. The motion sensitive and rather lengthy multi-shot diffusion-weighted scans suffer from shot phase variations and gross motion¹. In-plane gross motion can be addressed by dedicated model-based image reconstructions², but through-plane motion remains challenging. At the same time, simultaneous multi-slice (SMS) acquisitions with controlled aliasing schemes offer scan time reductions at moderate g-factor penalty for interleaved EPI^3,4 and provide data support for motion estimation in the through-plane direction per EPI-shot. Recently, SMS-to-volume registration approaches have been proposed for fMRI⁵ and DTI modeling⁶ to obtain and correct for shot-wise 3D rigid motion parameters. In this work, we introduce such a method for DWI image reconstruction and propose an algorithm, termed motion-aware SMS-accelerated and interleaved image creation (MoSaIC), with navigated 3D rigid motion correction in the brain.

Methods

Image Reconstruction Model
An SMS extension⁴ of a navigated Stejskal-Tanner sequence⁷ is used to acquire interleaved high-resolution image data at the first spin echo and moderately undersampled low-resolution navigator data at the second. The SENSE-based⁸ data discrepancy functional for interleaved SMS DWI is stated as
$$\underset{\boldsymbol{\rho}}{\mathrm{minimize}}\quad\lVert{M}\,{F}\,{\Theta}\,{C}\,{\Phi}\,{H}\,{\Omega}\;{\boldsymbol{\rho}}-\boldsymbol{b}\rVert_2^2 + {\alpha}\,\lVert{W}\boldsymbol{\rho}\rVert_2^2,$$ where $$$\boldsymbol{\rho}\in\mathbb{C}^{N_p}$$$ is the image volume with $$$N_{p}=N_{x}N_{y}N_{z}$$$ pixels and $$$\boldsymbol{b}\in\mathbb{C}^{N_b}$$$ is the acquired k-space data. The forward model contains the macroscopic motion operator $$$\Omega$$$ ($$$N_{shots}N_p{\times}N_p$$$) applying the shot transformation. The slice sampling operator $$$H$$$ ($$$N_{shots}N_{MB}N_{y}N_{x}{\times}N_{shots}N_{p}$$$) selects the $$$N_{MB}$$$ SMS slices per shot. The SMS slices are weighted by the diffusion phases using $$$\Phi$$$ ($$$N_{shots}N_{MB}N_{y}N_{x}{\times}N_{shots}N_{MB}N_{y}N_{x}$$$) and the $$$N_{c}$$$ coil sensitivities using $$$C$$$ ($$$N_{c}N_{shots}N_{MB}N_{y}N_{x}{\times}N_{shots}N_{MB}N_{y}N_{x}$$$). The CAIPI operator $$$\Theta$$$ ($$$N_{c}N_{shots}N_{y}N_{x}{\times}N_{c}N_{shots}N_{MB}N_{y}N_{x}$$$) applies CAIPI shifts and adds the SMS slices. For EPI (with gridded ramp samples), $$$F$$$ applies the Fourier transform along the phase-encoding direction and $$$M$$$ the sampling mask ($$$N_{b}{\times}N_{c}N_{shots}N_{y}N_{x}$$$). A weighted Tikhonov regularization is added with parameter $$$\alpha$$$ and a weight matrix $$$W=\mathrm{diag}(w_{p}^{-1})$$$ with a reference image $$$\boldsymbol{w}\in\mathbb{R}^{N_p}$$$. The shot parameters for $$$\Phi$$$ and $$$\Omega$$$ are estimated from low-resolution image navigator data, sampled for each SMS interleaf⁷, so that the full-volume reconstruction is convex.

Navigated Algorithm
The algorithm, visualized in Fig. 1, comprises three main steps, namely: navigator reconstruction, shot parameter estimation from the navigators, and full-volume reconstruction. First, the navigator data, which is undersampled in phase-encoding and slice direction, is unfolded by 2D-SENSE⁹. Second, the simultaneous navigator slices are registered to a reference volume by a SMS-to-volume (SMS2Vol) registration scheme, which is implemented in SimpleITK¹⁰ and shown schematically in Fig. 2, yielding the 3D rigid shot motion parameters. The low-resolution navigator phases are extracted for shot- and slice-wise physiological motion correction. Shots whose l2-norm energy of the navigator signal drops below 5 times the median absolute deviation over all diffusion-weighted shots are rejected.
The full-volume reconstruction is solved by conjugate gradients with intensity correction⁸. The rigid motion operator is constructed as proposed by Cordero-Grande et al.¹¹. The algorithm is compared to a navigated SMS-MUSE³ implementation without intra-volume gross motion correction, called SMS-IRIS. Fractional anisotropy (FA) maps were calculated after affine alignment of the volumes per diffusion direction using Dipy¹².

Acquisition
DTI with 4 EPI interleaves, 3 simultaneous slices and 15 diffusion directions at 1000 s/mm² was performed on a 3T Philips Ingenia scanner with a 32-channel head coil. Image echo parameters were FOV (R x P x S) = 232 x 228 x 120 mm³, resolution = 1.0 x 1.0 x 4.0 mm³, TR = 3 s, TE = 70 ms, FOV/3 CAIPI shift and partial Fourier factor 0.632. The navigator data was acquired at TEnav = 145 ms, 5 mm in-plane resolution, 1.62 in-plane acceleration and FOV/2 CAIPI shift. SPIR was used for fat suppression, and the total scan time was 3:30 min.
The DTI scans were performed twice in five healthy volunteers, first, without motion (static) and, second, with motion. For motion scans, the subjects were asked to remain still in the first third, perform in-plane head shake motion in the second and through-plane nodding motion in the third. Informed consent was attained according to the rules of the institution. Coil reference data was acquired in a gradient-echo prescan.

Results

Figure 3 shows the reconstruction and registration performance in different simulated motion scenarios generated from static in-vivo data. The low-resolution navigator analysis enables sub-millimeter target registration errors (TRE)¹³ and improved image quality for both in- and through-plane motion components. MoSaIC’s motion detection helps reducing errors and computational load in the absence of motion. Motion-corrected in-vivo DWI image volumes and the rigid shot motion parameters are presented in Fig. 4 for different motion cases. Figure 5 compares FA results for in-vivo DTI.

Discussion

SMS-to-volume registration, which is itself challenging, is further complicated by the multi-contrast and low-SNR nature of DWI. The presented registration achieves improved image quality over all investigated motion scenarios. Reducing the slice thickness leads to insufficient SNR for the presented method, which currently prevents isotropic DWI and could be addressed in future work by improved slice encoding strategies¹⁴.

Conclusion

The navigated MoSaIC algorithm integrates the through-plane motion problem to support retrospective full 3D rigid motion correction in interleaved SMS DWI reconstructions, improving image quality in the presence of head motion.

Acknowledgements

No acknowledgement found.