Researchers interested in image accelerationNew k-space trajectories and reconstruction techniques offer the possibility of large acceleration factors in the slice direction (in the case of SMS) [1,2] or in either of the two phase encoding directions in volumetric imaging [3,4]. While 2D and 3D reconstructions can be seen on a common framework [5], it is not straightforward to, in conventional multi-slice imaging, have more than 3-4 fold inplane acceleration.In standard 2D Grappa reconstruction of an Ry accelerated acquisition the non-sampled signal at the k-space coordinate $$$(k_x,k_y+m\delta_{k_y})$$$ of coil i is given by: $$ S_i(k_x,k_y+m\delta_{k_y},z) = \sum_{coils}\sum_{\delta_x} \sum_{\delta_y} w_{m,i,z}(coils,\delta_x,\delta_y) S(k_x+\delta_x\delta_{k_x},k_y+\delta_yR_y\delta_{k_y},z)$$ Where m=1,…,Ry-1, $$$\delta_{kx},\delta_{ky} $$$ the k-space steps, the range of $$$\delta_x,\delta_y $$$ defines the GRAPPA kernel size, and the coefficients $$$w$$$ are the GRAPPA weights. In this manuscript we propose to extend the grappa kernel to a 3rd dimension in the hybrid space, $$$(k_x,k_y,z)$$$ $$ S_i(k_x,k_y+m\delta_{k_y},z)=\sum_{coils}\sum_{\delta_x}\sum_{\delta_y}\sum_{\delta_z}w_{m,i, z}(coils,\delta_x,\delta_y,\delta_z)S(k_x+\delta_x\delta_{k_x},k_y+\delta_yR_y\delta_{k_y},z+\delta_z ) $$ For the sake of completeness we also explored the possibility of using the same kernels as in figure 1 but applying it in the $$$(x,k_y,z)$$$. To make optimum use of the extra dimension, its information should be as independent from that in the current plane. For this effect, we propose different shifts of the acquired readout lines in phase encoding direction are used (see Fig. 1).One subject was scanned, after giving informed consent, on a 3T scanner (Magnetom Prisma, Siemens Healthcare, Germany) using a 32 channel head coil. One 2D-TSE sequence with the following parameters was acquired: TR/TE=3000/100ms, FOV=220x220mm, 0.35x0.35mm in plane resolution, slice=3.9mm, 20 slices, tacq=3min34s. Standard additional reference data volume coil images were acquired Raw data were compressed in the coil dimension to 12 channels using PCA and were subsequently decimated to simulate different resolutions, acceleration factors and number of reference lines. This was then used to compare the performance of 2Dk_xk_y GRAPPA (Eq.1) vs 3Dk_xk_yz GRAPPA (Eq.2). The kernel size was 3x3 and 3x3x3 for the 2D and 3D method respectively. On the z direction, only the points from the same kx plane as the target points were used as source points in order to down-weight the information of the neighboring slices (See Fig. 1). Experiment 1: g-factor maps were calculated using pseudo replica (100 repetitions) on a dataset decimated to an inplane matrix size of 160x160 (64x64 ACS lines were used). Acceleration factors were varied from Ry=3,4,6,8, and PEshift factors varied from 0 to Ry/2 (the corresponding sampling patterns were applied to th fully sampled data). Experiment 2: Coil sensitivities were computed using the scanner volume coil. Synthetic signal was added to the acquired k-space data. The synthetic data consisted of 4 rectangles positioned in one single slice with a maximum amplitude of ~10% of the local signal (see top panel of Fig. 4) and a predefined timecourse. The data were decimated using different sampling strategies (Ry 3, 4, 6, 8 and different PE shifts). Once reconstructed a GLM was applied. .

Figure 2 shows examples of g-factor maps obtained for equivalent acceleration factors, using 2D or 3D GRAPPA and the implications of combining 3DGRAPPA with PE shifts. It is visible that the 3D GRAPPA does not provide any significant advantage (2nd column) if not combined with PE shifts (3rd and 4th column). While the benefits are minimal for Ry=3-4 , they increase significantly for 6 and 8 (Fig.3) with various fine resolution and contrast being preserved in the regions of greater g-noise amplification.

Figure 4 shows that some of the improvements seen in Fig. 2 and 3 were not translatable into reduced aliasing and came at a price of a small degree of smoothing in the z direction and much reduced detectability for 3Dxk_yz GRAPPA. ForR_y=8 the amount of power on successive slices was 5 and 20% for the 3Dk_xk_yz and 3Dxk_yz GRAPPA respectively, while the power aliased was of 5, 7 and 16% for 2Dk_xk_y, 3Dk_xk_yz and 3Dxk_yz.

The presented 3Dk_xk_yz GRAPPA provides a new mean to accelerate imaging or increase in plane resolution in multi-slice imaging using sequences such as TSE. Because the current formulation is done in a hybrid space it is not straight forward to visualise the prior knowledge/ regularization that is being imposed on the data that is effectively reducing temporal instability as assessed by the g-factor and visual image assessment. Yet, the method does introduce a certain degree of smoothing in the adjacent slice on the z-direction, see Fig. 4, this is relatively benign and limited to the adjacent slices.