In Magnetic Resonance Spectroscopic Imaging (MRSI), full volume coverage with a sufficiently small voxel size suffers from either long acquisition times or poor SNR. EPSI¹ is a technique capable of reducing the scan time considerably by simultaneously encoding spatial and spectral information. This enables fast 3D-MRSI acquisitions which are of great interest for human brain research and diagnosis.

In this work, a target-driven overdiscrete reconstruction^2,3 is applied to in-vivo 3D-EPSI data in order to increase SNR and reduce voxel bleeding. This is achieved via optimization of the Spatial Response Function (SRF) and correction of B₀ field variations that cause spectral shifts and incoherent signal averaging. Additionally, we show that the residual water peak in the acquired signal can be used to extract a sufficiently accurate B₀ map needed for the spectral correction.

In an overdiscrete reconstruction², the SRF of every spatial voxel is optimized by solving the minimization problem $$\triangle_{\pi}=\parallel (FE - T)_{\pi}\parallel_{2},$$ with its analytical solution leading to the reconstruction matrix $$F=T\theta E^{H} (E\theta E^{H})^{+},$$ where T represents the target SRF matrix and E the encoding matrix, both expressed at a higher than nominal resolution, θ corresponds to a spatial weighting factor and (⁺) denotes the pseudo-inverse. As an intermediate step, B₀ inhomogeneity correction in the high resolution spatial grid can be applied to achieve coherent signal averaging and SNR enhancement^4,5. The spectral shifts are performed in time domain multiplying the FIDs of individual subvoxels by $$$e^{-i2 \pi t \triangle f_{0}(r)}$$$, where Δf₀(r) corresponds to the local frequency shift in Hz at position r.

Data acquisition: A 3D-EPSI dataset of the brain of a healthy volunteer was acquired using a 3T-HDxt system (GE-Healthcare) with an 8-channel head receive coil (Invivo, Gainesville, USA). PRESS localization and CHESS water suppression were used as part of the sequence. The acquisition parameters were: FOV=220x220x80mm³, voxel size=10x10x10mm³, TE=144ms, TR=2000ms, spectral bandwidth=4kHz, with a total scan duration of 6 minutes. A B₀ field map, the coil sensitivity maps and a non-water suppressed 3D-EPSI measurement with the same settings were also acquired.

Data Processing: Spatial and spectral apodization for line broadening was initially performed on the EPSI raw dataset (22x22x8 voxels). The data was zero filled and spatially transformed to obtain an intermediate high resolution image, overdiscretized by a factor of ζ=3 in AP and LR directions (66x66x8 voxels). Coil combination was done and frequency shift correction was performed on the intermediate image as described above. A Gaussian target function with σ=1.5 subvoxels, was applied to the combined MRSI data to optimize the SRF and return to the nominal resolution. Finally, a spectral transform was computed. For the reconstruction, uncorrelated noise between coil elements was assumed and no SENSE acceleration was used.

B0 Estimation: B₀ field maps were obtained in three different ways. (1) A high resolution B₀ field map was measured at the time of the acquisition, using a standard double-echo gradient echo sequence. Furthermore, two maps were extracted using the residual water signal in the standard-reconstructed (2) water-suppressed (WS) and (3) non-water suppressed (non-WS) EPSI datasets, subsequently every slice was linearly interpolated to a ζ²=9 resolution (66x66x8 voxels). Under the assumption that the B₀ field variations are continuous and smooth, the interpolated maps can be used for frequency shift correction at subvoxel level.

The acquired and the auto calibrated B₀ maps are shown in Figure 1. For the region within the PRESS voxel the estimated B₀ maps were comparable to the one measured, as sufficient water signal and no abrupt B₀ variations were present in the analyzed volume. In Figure 3, the increase in SNR_NAA for two different voxels of a reconstructed slice is shown. The SNR_NAA was calculated as the ratio between the maximum of the real NAA peak at 2ppm, versus the standard deviation of the signal at the negative end of the ppm scale after baseline correction, considering all the voxels of the reconstructed slice. Additionally, a comparison between the frequency shift corrected spectra, using the different extracted B₀ maps, is presented. The mean SNR_NAA of the voxels in the ROI after the different reconstructions is shown in Figure 4. The largest increase in mean SNR_NAA was obtained with the reconstruction using the estimated B₀ from the WS-EPSI dataset.A target-driven overdiscrete reconstruction was applied to in-vivo 3D-EPSI leading to a mean SNR_NAA increase of 1.7 to 2.8. The B₀ field map extraction from the residual water signal in the EPSI dataset was proposed, showing similar reconstruction results and avoiding the need of an extra B₀ measurement during the scanning protocol.