Motivation

Single-shot 2D SPEN is carried out in a hybrid mode, where “blips” sample the low-bandwidth domain in image space. In most instances a sufficiently dense sampling of the SPEN domain is unfeasible, but the ensuing loss in spatial resolution can be offset by the acquisition of multiple interleaved scans [1]. Unlike EPI interleaving, where the aim of the blips is to increase the sampling density so as to cover the FOV_y without folding artifacts [2], SPEN interleaving samples regions in space that had been skipped by the original rasterization. Still, whether sampling k_y or y, interleaved EPI and SPEN share the common need for performing multiple scans. Techniques such as SMASH/SENSE/GRAPPA can be used to fill missing lines in k-space [3-5] –either alone or in combination with compressed-sensing (CS) [6-7]. The present study exploits this to achieve a resolution enhancement that is identical to that afforded by interleaved SPEN, but can be completed in a single scan.

Theory

The SPEN pulse sequence used in this work (Figure 1) imparts a parabolic phase on the spins along their y axis. By spatially advancing this parabola, the acquisition gradient G_a manages to image the full FOV_y. Ideally, G_a blips would be fine enough to maximize the ensuing image resolution, which for fully-refocused SPEN [8,9] demands blipping $$$N^{max}_{SPEN}=2\gamma G_aFOV_yT_e$$$ times [2,10]. While this is hard to achieve in a single shot, multiple sensors can make up for this deficit. To visualize this notice that although they are implemented for different purposes, both SPEN and EPI interleaving premodulate acquisitions by a certain factor $$$\exp[-iΔk(l-1)y]$$$, over $$$1 ≤ l ≤ Nshot$$$ interleaved scans. According to the SMASH formalism [3] such spatial phase variations can, if sufficiently slow, be mimicked by summing signals arising from multiple coils: $$$\exp[-ih\Delta k\cdot y] =\sum_cn^h_cS_c(y)$$$ , where $$$n^h_c$$$ are suitable weighting coefficients for harmonic h and $$$S_c$$$ are sensitivity maps for the various c-coils. Such formalism is usually of limited usefulness since the weighting coefficients need to hold throughout the entire FOV_y (Figure 1B); in SPEN however, where signals stem from a localized spatial neighborhood, it is simple and robust to extend such formalism for the sake of computing the “missing” interleaved data. To do so we look for a RO and SPEN (x and y) set of localized coefficients , such that the coils will satisfy, for that particular y-neighborhood, $$\sum_{c=1}^{n_c}n^h_{c,y}W(y)S_c(x,y) = W(y)\exp[-ih\Delta k\cdot y],\ \ \ y\in FOV_y$$ where N_c is the number of coils and $$$W(y)$$$ is a weighting function which emphasizes the interpolated location. This enables one to faithfully synthesize localized harmonics up to a high resolution-enhancement factor R (Figure 1C). It is feasible to incorporate into this formalism, SENSE- and GRAPPA-based reconstruction algorithms. In the former case one can also search numerically for an image I satisfying A(I)=Data, where A is an operator which includes the quadratic phase and the sensors’ sensitivities. This was here implemented using CS reconstruction with a total-variation filter [7], leading to Super-resolved SPEN with SENSE (SUSPENSE). SUSPENSE, like SMASH, requires a coil sensitivity map. The direct-space sampling of SPEN, however, implies that despite its undersampling, unfolded low-resolution images carrying their respective sensitivity maps will arise; this renders the method completely self-referenced and fully auto-calibrated. Additionally, and also unlike the EPI case, the R-factor can be set in post-processing; the maximal R is limited by the sensors coverage over the FOV, and should be limited to $$$N^{max}_{SPEN}/Npe$$$.

Methods

SUSPENSE was validated on a phantom with a stripe pattern of sub-mm separation and on healthy human volunteers, using a 3T Siemens with a 32-channel head coil. Applications involved DWI imaging at sub-mm resolution.

Results and Discussion

Figure 2 shows phantom image reconstructions performed for increasing R-factors. In the original single-shot resolution (0.94mm) the phantom stripes are blurred, but higher Rs succeed to resolve these pattern. Notice that R-factors ≥3 do not increase the effective resolution, as with it $$$N^{max}_{SPEN}$$$ has been reached. Figure 3 shows a DWI experiment acquired at a native in-plane resolution of 4.5x1mm (SPENxRO) with a high $$$N^{max}_{SPEN}=200 $$$ value (FOV=18cm). Reconstruction using SUSPENSE with R=5 results in a final 0.9x1mm in-plane resolution. The high bandwidth used provides high robustness to inhomogeneities, otherwise noticeable at the frontal tissue-air border region.

Conclusions

SUSPENSE provides robust, high resolution anatomical and ADC maps, free from multi-shot complications.

Acknowledgements

Funding by grants ISF 795/13, ERC-2014-PoC # 633888, Minerva Foundation #712277, and the Kimmel Institute of Magnetic Resonance (Weizmann), is acknowledged. ML acknowledges a Visiting Faculty Program Fellowship (Weizmann). We are also grateful to Dr. Sagit Shushan (Wolfson Medical Center), and the Weizmann MRI team (Edna Furman-Haran, Fanny Attar and Nachum Stern).