Figure 2 The representative spectra obtained by conventioal EPSI, xSPEN spectroscopy and J-decouped xSPEN spectroscopy from the spatial location marked by the red dot in the phantom using a spectral bandwidth of 1000 Hz(a) and 2000 Hz(b)

Figure 3 (a) EPSI chemical shift maps from multiplets (b) The map of singlet from J-decoupled xSPEN spectroscopy.

Comparison between 3D metabolite volumes resulting from ADISE-MRSI and FID-MRSI acquisition sequences acquired subsequently in one volunteer. Bottom, two sample spectra at same location for both sequences are shown on the same scale and exhibit a slightly lower signal with ADISE-MRSI sequence, consequence of the longer TE. Signal loss due to B0 inhomogeneity in frontal lobe is present with both sequences.

Comparison of spectral quality parameters between Fast ADISE-MRSI and FID-MRSI sequences on the same session. Left, the signal loss due to the longer TE for ADISE-MRSI is visible over the whole brain in the SNR map. FWHM maps exhibits no marked difference. Right, the histograms of the Cramer-Rao Lower Bound (CRLB) resulting from both sequences are displayed side to side. Most metabolites show a slight shift towards higher CRLB values for ADISE-MRSI. This is particularly visible for Glu+Gln that are known to be more difficult to quantify at longer TE due to J-coupling modulations.

Figure 1: Schematic representation of the DW-sL-EPSI sequence showing RF pulses with bipolar DW gradients placed around the slice selective refocusing HS RF pulses. δ = gradient duration, sum of the durations of four lobes; Δ = diffusion time, time between the first lobe of the dephasing diffusion gradient group and the first lobe of the re-phasing diffusion gradient group. Water suppression was performed with WET. An EPI-based readout was used to capture the k-t data.

Figure 2: Results from a brain phantom scan. (A) T₁-weighted localization image showing the VOI; also shown is the DW-sL-EPSI spectra obtained from the 3x3 region within the VOI at the b-values (B) 36 s/mm² and (C) 3996 s/mm².

Figure 2: a) Two-dimensional J-resolved MC semiLASER spectrum (TE_start: 24 ms, TR: 6000 ms, $$$n$$$=85, $$$∆t$$$=2 ms) acquired at 9.4T from a Braino phantom. Lactate peaks at 1.31 and 4.09 ppm (maximum separated in the upfield proton spectrum) were considered to calculate reduction in the intensity of the J-refocused peaks according to the equation given in Lin et al¹⁷. This resulted in 86% reduction in the intensity and hence, there are barely any J-refocused peaks in the spectrum. b) Two-dimensional J-resolved MC semiLASER spectrum from a representative subject acquired at 9.4T.

Figure 1: a) 2D J-resolved MC semiLASER sequence implemented at 9.4 T. The excitation and adiabatic pulse bandwidths are 8000Hz. This leads to a chemical shift displacement of 10% between NAA (2.008 ppm) and mI (4.05 ppm). This means that even after accounting for the displacement in all three directions still there is a 73% voxel overlap occurring in the voxels for the two mentioned resonances. b) High-resolution MP2RAGE images showing the voxel positioning for the acquisition of in vivo data. Tissue segmentation resulted in GM/WM/CSF content: 67.3 ± 8.6/ 28.5 ± 8.6/ 3.7 ± 1.5%.

Figure 1 MR spectra acquired in the motor cortex using (A) MEGA-sSPECIAL and (B) sSPECIAL sequences. The edit-on, edit-off, and difference spectra are illustrated in (A). The absence of choline peak at 3.2 ppm implies that creatine is completely subtracted and two sub-spectra were well corrected and aligned to each other.

Table 1 Reproducibility test results for sSPECIAL and MEGA-sSPECIAl sequence.

Figure 2: Stimulated echo spectra comparison for different diffusion-weighting values. A-B) spectra acquired during the same experimental session, respectively with STE using broad pulse (BP) and STE using selective pulse (SP). C-D) Lactate peaks as extracted with LCModel. E) Average S/S0 ratio over four blocks of 32 averages as a function of diffusion weighting (b). F) CoV of S/S0 for each b-value and each metabolites. G) Calculated ADC with STE BP data and STE SP data.

Figure 4: Stimulated echo using BP versus spin echo using SP. A-B) spectra acquired respectively with STE using BP and SE using SP. C-D) Lactate peaks as extracted with LCModel. E) Average S/S(b=0) = S/S0 ratio over four blocks of 32 averages as a function of diffusion weighting (b). F) CoV of S/S0 for each b-value and each metabolites. G) Calculated ADC with STE BP data and SE SP data.

Figure 4. MRSI data acquired (TE/TR = 22.2/2500 ms, 10.2 min acquisition time, 1 x 1 cm² grid) with IR and no-IR methods. (A) The axial slice imaged, with the nine voxel regions overlaid. (B-C) NAA maps from both methods. (D) Voxel locations from the grid illustrated in (A). Both methods demonstrate high quality spectra, despite the overall reduced amplitude with the IR method. The IR data demonstrate minimal macromolecular resonances evident by the flat baseline, compared to the No-IR data.

Figure 5. Summary of MRSI (TE/TR = 22.2/2500 ms) data in Figure 4 with LCModel fitting of the IR data. (A) The corresponding axial slice image, with four voxel locations marked. (B) LCModel fitting of spectral locations in (A). In each panel the residual, fitted spectra overlaid on the measured spectra, and the baseline are illustrated. (C-F) Metabolic maps referenced to water for NAA, tCr, Ins, and Glx. (G-J) illustrate corresponding CRLB maps for the metabolic maps in (C-F).

Figure 1: Illustration of the T2* calculation procedure. (A) A set of FIDs with different time-shifts (Δt) was generated (shift between 0ms and 30ms in 5ms interval) by progressively discarding the first points (represented in grey) of the originally acquired FID. (B) FIDs were Fourier transformed (spectra shown in black) and fitted with LCModel (fits shown in red). A basis-set was generated using a Matlab® routine for each Δt. (C) A linear regression was used to fit the logarithm of the signal of five brain metabolites as a function of Δt. T2* values were estimated as -1/slope of the fit.

Figure 3: (A) Logarithm of the signal of metabolites was quantified at all time-shifts (Δt) and fitted with a linear regression. The data (circle) and fit (black line) for the mean over all participants is shown. The error bars represent the standard deviation over subjects and the dashed grey line indicates the 95% confidence interval. (B) T2* values of five brain metabolites are shown, suggesting lower values in astrocytes cells. Paired Student’s t-test was used to estimate differences (*p< 0.05, ***p< 0.001). The error bars represent the standard deviation over subjects.

Figure 3. Example of spectra without processing (upper) and with the proposed method (lower) where the black line is the modelled peaks. It appears to be less noise with the proposed method.

Figure 1. Positioning of the volume of interest (red box and the yellow box is the shifted water volume) inside the disc and the four saturation slabs around the disc. Sagittal (left), coronal (middle) and axial (right).

Figure 5. NIfTI MRS will be supported from the start by eight MRS analysis packages, covering five major programming languages. Several packages (FSL, SUSPECT and spant shown here) already can load NIfTI format data.

Figure 1. Schematic of the NIfTI MRS format. The NIfTI header is retained and used for its original purpose. Additional MRS specific meta-data is stored in a JSON formatted NIfTI header extension. Complex time-domain data is stored in the fourth dimension, after three spatial dimensions, and before three optional flexible-use dimensions.

Figure 1: Pulse sequence diagram of the EPSI sequence showing semi-adiabatic point-resolved spectroscopy (PRESS) sequence and bi-polar echo-planar readout.

Figure 4: Fully-reconstructed data showing spatially-resolved spectra with peaks of Creatine (Cr), Choline (Cho) and N-acetyl aspartate (NAA) visible and labeled in one spectrum. Horizontal axes are in parts-per-million (ppm) and vertical axes in arbitrary units representing signal amplitude.

Figure 1. The proposed spectroscopy acquisition at 10.5T using (a) a double spin-echo sequence with (b) 3D SPSP adiabatic pulses for refocusing. The design of the 3D SPSP pulse was shown in (b), where a train of pTx spiral sub-pulses are modulated by an adiabatic envelope. With pTx, the peak amplitude can be effectively reduced and hard constrained by optimal control method as shown in (c). To further increase the spectral bandwidth at 10.5T, an inhomogeneous spatial profile can be used for the sub-pulse while still achieving a homogeneous inversion by the 3D SPSP pulses as shown in (d).

Figure 2. A brief summary of the 3D SPSP pulse performance. The phantom setup was shown in (a), where FOV and VOI were indicated by the white and yellow box. The B0 mapping was shown in (b). By simulation, the pulse provided an approximately 920 Hz for the 95% passband along with stopband at ±750 Hz for water and lipid suppression as shown in (c), with overall mild chemical shift displacement errors as shown in (d), (e). The spatially resolved spectra acquired with the proposed method as shown in (f) matched with the simulated profiles.

Figure1: (a.) EPSI pulse sequence using spatial selective amplitude modulated excitation and refocusing RF-pulses. (b.) Proposed EPSI variant of this abstract: the slice selective Mao pulse typed refocusing pulse is replaced by a chemical shift selective adiabatic complex hyperbolic-secant 2π-pulse pair. All the measurements were performed with a volume of interest of 280 X 220 X 100 mm.

Figure 2: (a-d) water maps: comparison of non-adiabatic excitation and refocusing using Mao pulses (a,c) with complex hyperbolic secant RF-pulses (b,d). (a’-d’) corresponding histograms of the images (a-d) over the phantom area. TE = 82 ms, TR = 1500 ms, BW = 1.4 kHz with a resolution of 4.3 X 11 X 13.8 mm.

Figure 1. The diagram for double-band MRSI acquisition with atlas prescription and adaptive Hadamard pulses. A special atlas template was designed to cover superior and deep gray matter regions. After prescription, Hadamard pulses were automatically generated to excite top slice and bottom slice in S/I direction. Finally, 2D MRSI can be reconstructed from a two-echo Hadamard-encoded acquisition.

Figure 5. Hadamard 2D GABA+/Cr map of top slices and bottom slices in all three subjects overlaying T1-weighted images. Voxels with GABA+ fitting error > 30% or GABA FWHM > 30 Hz were all excluded.

Figure 1. (a) Three-dimensional T1-weighted anatomical images were acquired using MPRAGE. Green boxes covering two voxels illustrate the shimming volume in first scan. ACC (blue box) and PCC (red box) regions were selected for ¹H MRS acquisition. (b) Localized water suppressed ¹H spectrum (blue) along with spectral fit (orange), residual (black) and baseline (red) obtained from LCModel quantification.

Figure 2. (a) Green boxes covering two voxels illustrate the shimming volume in second scan in the anatomical MPRAGE image. GM-rich (red box) and WM-rich (blue box) regions were selected for ¹H MRS acquisition. (b) Localized water suppressed ¹H spectrum (blue) along with spectral fit (orange), residual (black) and baseline (red) obtained from LCModel quantification.

Fig.2: Simulated inversion profiles for a) HS b) FOCI5 c) GOIA-W(16,4) and GOIA-W(50,10) at 15 μT maximum B₁ field and for 0,1 and 2 ppm off-resonance at 7T. GOIA-W(50,10) shows compromise between passband ripple and CSD for 4.5ms.

Fig.4: Single-voxel semi-LASER MRS on a brain metabolite phantom (after line broadening) using three different adiabatic inversion pulses a) GOIA-W(50,10) b) FOCI5 and c) HS resulting in a minimum echo time of 23, 31 and 37 ms respectively.

Figure 1. Schematic of interleaved water referencing (IWR) and spectral registration (SR) for real-time center frequency (F₀) updating of MEGA-PRESS acquisitions. IWR and acquisition of the SR reference, S_ref(t), occur every ith and ith + 1 TRs, depending on the desired number of unsuppressed water reference acquisitions. For example, for a MEGA-PRESS scan with 320 water-suppressed averages and 8 unsuppressed water references, IWR will occur every 40th TR. OVS, outer-volume saturation; WS, water suppression.

Figure 2. Phantom experimental results. Top row: Relative changes in center frequency (ΔF₀) over each of the four ~5-min GABA-edited MEGA-PRESS scans before and after an ~8-min EPI scan with and without interleaved water referencing (IWR) and spectral registration (SR). Bottom row: GABA-edited difference spectra for each of the four scans. The corresponding SNR of the 3.0 ppm edited GABA signal is shown.

Figure 1: EPSI-SLOW spectral editing sequence scheme. a) Chemical selectively refocusing the full range of interested spins. b) Chemical selectively refocusing the partial range of interested spins.

Figure 2: a) Simulation of the adiabatic pulse (used as inversion pulse in the simulation for simplicity). The passband and transition band are indicated by blue/orange and light blue/orange respectively for editing full and editing partial pulses. b) The editing full/partial pulse bandwidth is 840 Hz but with a different carrier frequency. TR = 1500 ms, volume of interest (VOI) = 280 X 220 X 100 mm, voxel size = 4.3 X 11 X 13.8 mm, and total measurement time = 6 mins.

Figure 4. Resulting water-scaled in vivo difference spectra.

Figure 2. Simulations compared to Phantom measurements. For visualization purposes, the simulated data have been line-broadened to match the linewidth of the difference spectrum for the phantom data.

3. (a) Voxel location in the OCC and example spectra in two different subjects acquired with and without prior DWI. In both cases, the WS-MEGA and MC-MEGA spectra are qualitatively similar to one another. (b) Voxel location in the medial prefrontal cortex and example spectra in two subjects. In one case, the WS-MEGA spectrum displays a significantly larger Cho artifact than the MC-MEGA spectrum.

4. Metrics of the water frequency across subjects. (a) Boxplots comparing the magnitude average ΔF0 between the MC-MEGA and WS-MEGA scans. The average ΔF0 is 68% lower in the MC-MEGA scans than in the WS-MEGA scans in the OCC. In the mPFC, the average ΔF0 is 65% lower in the MC-MEGA scans than in the WS-MEGA scans (b) Boxplots comparing the standard deviation of the water frequency between WS-MEGA and MC-MEGA experiments. The water frequency standard deviation is 26% lower in the MC-MEGA scans than in the WS-MEGA scans in the OCC and 75% lower in the MC-MEGA scans than in the WS-MEGA in the mPFC.

Fig 2. Cohort-averaged downfield spectra from 10 subjects each, plotted in the range between 6.5 and 10 ppm. The cohort averages were formed after scaling by unsuppressed water to assure equal weight for each subject. Appropriate scaling was also applied to guarantee a comparable scale between techniques. For better visibility of the NAD⁺ signals spectra are plotted with 6x vertical scale on the right-hand side along with the simulated NAD+ pattern (peaks at 8.2 and 8.4 ppm removed to minimize interference with larger overlapping signals). Dashed lines indicate the NAD+ peaks fitted.

Table 1. NAD⁺ concentrations and Cramer Rao lower bounds and their cohort standard deviations (SD) as obtained with all three localization techniques, without and with correction for T₂ relaxation with an assumed T₂ of 80 ms (assumption based on Ref 12 reporting 54±5 ms at 11.7 T). For a fair comparison considering equal scan times for all methods, the CRLB for MC semiLASER and 2D ICSE should be reduced by 30%, which yields almost the same CRLB for both semiLASER approaches.

Fig.1 – A – 2D Spin echo MRSI sequence with binomial spectro-spatial excitation (red) and selective refocusing (green). B – Placement of the MRSI FOV in vivo.

Fig. 4 – An example of MRSI downfield spectra from three subjects shown for grey-matter rich (red voxel) and white-matter rich (white voxel) voxels. 3Hz Gaussian line-broadening was applied. Spectral pattern consists of resonances at 6.1, 6.8, 7.1, 7.3, 7.5, 7.9 and 8.2 ppm peaks.

Figure 2. Simulated voxel profiles a) pulse 1 and b) pulse 2. Spatial offsets range from 0, 2, .., 12 cm. The vertical dotted lines show the Nyquist frequencies.

Figure 1. Point to point phase increments of two popular GOIA-WURST(16-4) adiabatic pulses, number of points, sample interval, bandwidth range, B1 max level, and gradient amplitude modulation factor: a) pulse1: 175, 20 us, -10 kHz … 10 kHz, 817 Hz, 0.90 from (3), and b) pulse2: 450, 10 us, 5 kHz … 5 kHz, 640 Hz, 0.85) from (1). The Nyquist limit at 180 degrees is shown as the dotted line. The number at the left in the plot indicate the spatial shift of the pulse in cm.

Figure 1. The architecture of DHMF. (a) the general process of the k-th block, (b) P and Q modules with time domain convolution in the basic DHMF, (c) P and Q modules with frequency domain convolution in the enhanced DHMF, (d) dense convolutional neural network.

Figure 2. The reconstructed spectra and singular values at each block. (a) fully sampled spectrum, (b-f) the reconstructed spectrum by the 1st to 5th blocks, (g) the nuclear norm of Hankel matrix of time-domain signal, and (h-l) denote corresponding singular values of the output of each block. Note: To show small singular value clearly, there exists a break from 0.084 to 0.085 in Y axis of (h-l).

Fig. 1. A schematic of the optimization of the AnoGAN. First, the generator G and the discriminator D are simultaneously trained. Second, using the trained G and D, the noise vector in the latent space is iteratively optimized by latent space mapping. Third, the NMSE and 2SD are obtained for all data in the validation sets. Then, the optimal threshold NMSE and 2SD values in the classification of spectra into normal and abnormal classes are determined from the NMSE-2SD space. Finally, the optimal threshold NMSE and 2SD values are used on the test sets.

Fig. 2. The representative query, AnoGAN-generated, and residual spectra for the abnormal spectra groups. (A)-(G) The input (query) spectra to the AnoGAN from (A) Spec­_ano.SNR, (B) Spec­_ano.LW, (C) Spec_ano.GABA, (D) Spec_ano.mI, (E) Spec_ano.NAA, (F) Spec_{ano.multimeta}, and (G) Spec_­ano.all. (H)-(N) The corresponding AnoGAN-generated spectra. (O)-(U) The residual spectra between the input and the AnoGAN-generated spectra. The abnormal spectral parameters and their values in the simulation are shown in (A)-(G) (the unit of the metabolite concentration is mmol/L).

Figure 1: The proposed DCCAE and training strategy. X denotes the collection of multi-TE FID training data with length T and M TEs. Complex units are used where different TEs are treated as different channels in the input. For each complex convolution block, data dimensions were reduced by half while the channel dimension (K) increased by a small amount. The fully connected part followed an encoder-decoder structure and a middle feature layer with dimension $$$L$$$ (referred to as the model order). Errors between $$$\textbf{X}$$$ and $$$\hat{\textbf{X}}$$$ is minimized.

Figure 2: Representation efficiency of the learned model: a) Relative $$$\ell_2$$$ errors of the proposed model approximation with different model orders $$$L$$$’s for 3-TE data (orange curve), compared to linear subspace models (TE-combined subspace in the blue curve and TE-dependent subspace in a yellow curve). For the TE-dependent subspaces, $$$L$$$ is the total dimension of the three subspaces. b) Approximations of a test spectra at different TEs (30, 80, and 130 ms) using the three models with $$$L = 42$$$. A more accurate representation is achieved by our learned model.

1. (a) K-space undersampling schemes for the originally proposed 6x and 9x-acceleration (first row) as well as the newly proposed variable-density CAIPIRINHA schemes for 5x and 6x acceleration. (b) Schematic for augmenting the MRSI data with water-removed NWS data to provide more k-space points as well as a larger k-space region for training the neural networks based off the lipid behavior.

5. Glutamate + glutamine (Glx) maps over total creatine (tCr) in one subject across different sampling schemes and reconstruction methods. Of the maps featured, the Glx/tCr maps from the variable-density CAIPIRINHA schemes are most similar to the Glx/tCr map from the fully-sampled dataset.

Figure 5 - Metabolic maps of tNAA/tCr and tCho/tCr and example spectra from two locations are presented for both coil combination methods. The contrast of the ratio maps appear similar in all three orthogonal projection for both methods. The position are marked with the small letters. The spectra in the same column belong to the same coil combination method. The appearance of the spectra for different methods differ mainly in the course of the baseline.

Figure 2 – Comparison of kspCC and cCC maps of the spectral data quality. Both methods produced similar results in terms of spatial distribution of parameters. The SNR values for kspCC are a bit lower compared to the cCC but approximately the same volume is covered. The FWM maps look very similar and from the maps themselves no underperformance can be observed.

Figure 1: T1-weighted MR images showing cerebellar atrophy. Defaced coronal and sagittal MRI slices (MNI space: x=0) of (A) patient presenting with late-onset Tay-Sachs disease showing profound cerebellar atrophy, (B) patient presenting with late-onset Sandhoff disease, and (C) healthy control.

Table 1: Participant demographics and clinical assessment scores reported as mean ± standard deviation.

Figure 1. a) Fit of Marchenko-Patstur distribution to the lowest eigenvalues from PCA. B) Mean value of the standard deviation of noise (last 300 points of the FID) from all 120 spectra before and after denoising (upper and lower graphs, respectively). c) The noise distribution of 6 random selected spectra before and after denoising.

Figure 2. A sub-set (5x8) of the full image matrix demonstrates the quality of the spectra before and after denoising.

fCSF corrected NAA concentration map and its overlay onto reference T2w MRI (figure 5a) and ROI analysis of an example dataset on 400 brain parcellations defined on 17 rs-fMRI networks (figure 5b).

Segmentation module shows fCSF, fWM and fGM maps for a selected metabolite (NAA+NAAG) at different slices.

Fig. 2: Fit results for the baseline simulations are shown. The blue line shows the input spectrum; the black line the input baseline. Fitted baselines (dashed lines) and resulting residuals (continuous lines) are shown in red for LCModel and purple for ProFit-v3. Offsets used for plotting are indicated on the right of each subplot. Inlays show the mAIC curves for the ProFit-v3 fitting. These spectra show a simulated zero baseline, an in-phase (φ₀ = 0°) and an out of phase (φ₀ = 90°) lipid peak at 1.3 ppm, but also an extracted baseline from a previous LCModel fit of an in vivo spectrum.

Fig. 1 A: The ProFit-v3 algorithm is depicted with the successive optimization steps: first preprocessing steps affect the spectrum to be fit while the fitting iterations optimize the linear combination of the basis sets. In later iterations, more metabolites are added, and additional metabolite specific local degrees of freedom are allowed while keeping the previously optimized global parameters. B: Metabolite weighting envelopes are displayed in red. Summing the weights of active metabolites for the fit iteration gives the weights of the spectral residual R_X shown on the right.

Figure 4: 3D concentration maps for tCho/tCr, Glu/tCr, NAA/tCr, mI/tCr in arbitrary units showing the brain coverage achieved in this study with the optimized set-up using L2-regularization and including a simulated macromolecular baseline in the LCModel fit. The metabolite maps are underlayed with the anatomical images.

Figure 5: Mean number of voxels fitted with CRLB < 100 % for each slice for NAA and Glu for one measurement of all volunteers. The test-retest figure in b) shows the mean concentration for each slice. Data is shown for all five volunteers and five different metabolites (Cho = red dots, NAA = black dots, tCr = green dots, Glu = purple dots, mI = blue dots). The black line is the curve fitted to the data with y = 0.96x + 0.03 and r2 = 0.94; the gray dotted line is the identity line with y = x. In c) the absolute difference of the dots in the test-retest figure to the ideal case of y = x is shown for five metabolites.

Fig. 3. In vivo scan-rescan spectra from 4 voxels within the red box.

Fig. 5. In vivo scan-rescan reproducibility: scan-rescan voxel-wise concentration correlation plots ((a), (b) and (c)), Bland Altman plots ((d), (e) and (f))

Figure 4: Metabolite maps for the four approaches used for fitting MRSI data. Maps are reported with T₁-relaxation corrections and in units of mmol / kg. It is apparent that using simulated MM basis vectors performs best generally when considering the poor fits of NAAG, mI, and Gln from Approach A and Approach B.

Figure 1: The relaxation-corrected, sequence-specific MM simulation model algorithm diagram. Voigt lines are simulated using measured Gaussian and Lorentzian lineshapes. Voigt lines are then scaled by measured concentrations of MM from 9.4T and further processed with single-spin Bloch simulations to simulate a universal base MM spectrum which is then attenuated by sequence specific relaxation effects to yield a sequence specific MM basis vector.

Fig 2. Top: Representative spectrum following raw data reconstruction and spectral registration. Bottom: Fit results using default preprocessing (left, TARQUIN) and proposed preprocessing pipeline (right, Matlab). Inline images display the effects of the phase correction step on the baseline.

Fig 1. Preprocessing pipeline (Matlab), including spectra alignment, eddy current correction and the proposed automatic zero and first order phase correction.

Figure 1: Illustration of the IDEAL SPIRAL spectral encoding scheme. It consists of Radiofrequency (RF) pulses applied during an excitation time (t₁), and acquisition with spiral-OUT spatial encoding (t₃-t₂) applied after an echo time (TE=t₂-t₁). Several shots are used to encode the spectral information, which is targeted during the evolution time (TE), while slightly increasing the TE after each shot (TE_m is the echo time of the m^th shot). Three shots are presented, but this pulse sequence is true for m shots.

Figure 2: Illustration of the different cases of the emission/reception frequency switching during the pulse sequence timing, leading to different frequency dependence during the evolution times. Acq-Switch case: f_e-f_r switch before the acquisition at t₂, and the CS behaviour detection is done in reference to f_e. RF-Switch case: f_e-f_r switch before the evolution time at t₁, hence CS behaviour detection done in reference to f_r. Double 0-Switch case: f_e-0 switch for the evolution time at t₁, 0-f_r switch at the end of it at t₂.

Fig. 1. Partial derivatives of linear combination model with respect to complex baseline shapes for Fisher information matrix calculation. Shown here are the Fourier transforms of example real and imaginary polynomial and spline baseline components incorporated into the Fisher information matrix used to estimate Cramér-Rao Lower Bounds (CRLB) for linear combination model fits to simulated in vivo sLASER (T_E 20.1 ms) metabolite proton spectra. Each shape is scaled by its corresponding polynomial coefficient for direct calculation of relative CRLBs. ppm: parts per million.

Fig. 5. Baseline Cramér-Rao Lower Bounds (CRLB) improved metabolite CRLB accuracy. Calculating amplitude CRLBs for polynomial or spline baselines directly from the Fisher information matrix improved correspondence between metabolite amplitude CRLBs and parameter estimate standard deviations (S.D.) by SNR (before=blue; after=black). Correspondent with Fig. 4, non-normal distributions (pink), for which S.D. may not be an appropriate measure of parameter variability, were observed more often for fits using spline than polynomial baselines. ppm: parts per million.

Figure 2: Top: cohort distribution with unbounded fitting algorithm and pertinent formulae. µ: ground truth mean, σ: ground truth std. µ_TR: mean of right truncated distribution, µ_TL: mean of left truncated distribution. Bottom: cohort distribution with 0+ fitting boundary. Limiting parameter space skews the Gaussian distribution. The negative tail is mapped to a small interval around 0+. Assuming its contribution to equal 0, the true mean can be reconstructed from its distorted version.

Figure 3: histogram of estimated concentrations for GABA in three different parameter space settings. Cohort 1 is depicted in the left column and cohort 2 in the right. µ_GT: ground truth concentration. µ_distr: distribution estimated concentration.

Table 1: Comparison of published [3] vs. optimized chemical shift positions and J-couplings for myo-inositol

Figure 1: Examples of individual 3T, PRESS TR=2000ms, TE=35ms spectra of abnormal tissue with prominent mI (A) and of normal grey matter (B). C: Myo-inositol basis spectra before and after optimization.

Figure 2: Example spectrum measured with GE’s standard product implementation of the PRESS sequence and fitted with four different PRESS basis sets of matched T_E 35 ms. The original data are in black, the fit is depicted in red. The upper part of the figures represents the residual signal after fitting. A – Matched GE basis set; B – Basis set based on GE timings, but using hard-pulses; C – Basis set for Philips’ PRESS; D – Basis set for the Siemens’ PRESS. Individual fits were printed from LCModel.

Figure 3: Example spectrum measured with Siemens’s standard product implementation of the PRESS sequence and fitted with four different PRESS basis sets of matched T_E 35 ms. The original data are in black, the fit is depicted in red. The upper part of the figures represents the residual signal after fitting. A – Matched Siemens basis set; B – Basis set based on Siemens timings, but using hard-pulses; C – Basis set for Philips’ PRESS; D – Basis set for the GE’s PRESS. Individual fits were printed from LCModel.

Figure 1. The training of the BCNN and the estimation of metabolite content and corresponding uncertainty. The metabolite content is estimated by multiple regression using the metabolite basis set and the predictive mean spectrum that is the mean spectrum over the BCNN-predicted metabolite-only spectra (number of spectra = T (number of inferences)). The uncertainty in metabolite content is estimated by multiple regression using the 2SD spectrum. In this case, the metabolite basis set is used in absolute mode in accordance with the 2SD-spectrum.

Figure 2. (A) 4 representative simulated spectra (BCNN input). (B) Ground truth (GT) spectra. (C) BCNN-predicted spectra. (D) Reconstructed spectra using the estimated metabolite content and metabolite bases. (E) Difference spectra (GT – Predicted). (F) Difference spectra (Predicted – reconstructed). (G) Total uncertainty spectra (= (H) aleatoric + (I) epistemic uncertainty) (BCNN-predicted spectra shown in dotted line). (J) 2SD spectra. (K) Reconstructed 2SD spectra using the estimated uncertainty and metabolite bases. (L) Difference spectra (2SD – reconstructed 2SD).

Figure 1. Schematic overview illustrating the generation of dataset and the proposed network architecture featuring consecutive three convolutional blocks. A pair of 1D convolutional layer and batch normalization layer act as a fundamental component with four times repetitions for completing each block. Network training was conducted with pairs of ground truth spectra and progressively degraded spectra while minimizing the mean squared error using Adam optimization algorithm. Learning rate was set to 10^-4.

Figure 2. Numerically calculated ¹H MRS spectra at low SNR (left column) and high SNR (right column). CNN-predicted spectra, difference spectra (ground truth – predicted), and NMSE illustrate the impact from using different training sizes in CNN.

Figure 1. The convolutional neuronal network diagram for taking 3 tiles separated real and magnitude spectra as inputs. The final output value indicates the probability for bad label.

Figure 2. Models with different spectra inputs and tiles and the tested ACC and AUC results. No difference was found between including or not tissue ratios.

Figure 3 Reconstructed spectra from the neural network (dotted blue lines), compared with the spectra from human brain obtained 15, 45, 75 and 105 minutes post oral ingestion of deuterated glucose (solid red lines).

Figure 1 Autoencoder architecture used for denoising and fitting the spectrum.

Figure 3: Metabolite concentration mapping for Ace, Choline, and Creatine in rows 1, 2, and 3 respectively. Obtained by the three different methods, in (a) healthy brain spectra while (b) is a brain tumor.

Figure 1: Representation of both implemented neural networks, an CNN (a) and a ResNet (b). In both cases, the input and output are exactly the same, and all the convolutional layers have the same kernel size of 3.

Figure 3: The first column displays the GT peak area maps as found by TDFDFit. The second column displays the RF-regressor predicted maps for the noise level 0.5 of the in vivo semiLASER data sets. The third and the fourth column show the predicted maps of noise level = 4 and noise level = 0.5. Example signals with very poor and extreme poor SNR are displayed in Figure 4.

Figure 4: This figure shows the x-y-scatter plots for NAA, Cho, Cr, and Glu peak area parameters: horizontally the GT value obtained with TDFDFit, and vertically the RF-regressor predicted area parameter values. For NAA the coefficient of determination is best namely R²=0.991, for Cho -> R²=0.988 ,for Cr -> R²=0.989 and for Glu the worst namely R²=0.975. Note that the slope of all linear regression lines is between 0.96 for NAA and maximum 1.26 for Glu, in accordance with Cramér-Rao minimum variance bounds.

Figure 1a: Proposed strategy to learn the entire end-to-end inverse function and low dimensional representations of spectroscopic signals – (from left to right) Building the training database: The 27 metabolites FIDs were simulated with a sLASER pulse sequence with metabolic cycling and B₀ variations. The simulated metabolites FIDs were used to create the training database by combining metabolites, water signal, phase modulations and 20-50dB of gaussian noise. The input/output to the network was the real and imaginary component of metabolic cycle FIDs/spectra (see Methods).

Figure 3: In vivo cerebellum MRSI reconstruction with AUTOMAP. (from top to bottom) The AUTOMAP and NUFFT reconstructed summed image from the 1st time point are shown. The metabolite-only spectra with a range from 0.5 to 4.2 ppm from the 9 different voxels (represented by the black box in the images) are displayed in blue for AUTOMAP and in black for NUFFT. At the bottom an enlarged spectra with the corresponding metabolite peaks (total Choline (tCho), NAA (tNAA) and Creatine (tCr) is represented.

Figure 4. The mean metabolite concentrations across the whole group of subjects, for methods M₁ (a), M₃ (b), and the CRLB values (c). Total concentrations tCho=GPC+PCh, tNAA=NAA+NAAG, tCr=Cr+PCr and Glx=Glu+Gln are additionally shown.

Figure 3. Linear regression (green line) estimated for tCr (a), Glu (b), GSH (c), Ins (d), NAA (e), tCho (f) using pooled 3T and 7T data. Metabolite concentrations of individual subjects determined from pooled results (3T and 7T) and the calculated α value for each metabolite. Different shapes represent different brain areas (o: striatum; ⧠: frontal WM; ◊: parietal WM; *: occipital WM). Blue and red points represent data from 7T and 3T, respectively. The green shaded area highlights the 95% confidence band.

Fig.1: Frequency correction fidelity for SR and RSR with two increments of direct averaging. A frequency correction fidelity of 1 indicates perfect correction, 0 indicates correction was as effective as no correction, and a value less than 0 is worse than no correction. RSR performs better for low b data than high b-value data, indicating a potential for bias in diffusion fits. While DA provides a marginal gain in the effective domain of both SR and RSR, it compromises the fidelity of higher SNR data.

Fig.4: Histograms of the percentage deviation from known the ADC. Data are pooled from the fits of TNAA, TCho, and MyI, and diffusion fits with $$$R^2$$$<0.75 were excluded. The blue bars represent fits of all data, while orange bars are data fit after excluding points with SNR < 2. Here a negative value indicates an underestimation of the ADC, while a positive value indicates overestimation. All methods tended to overestimation, suggesting that higher b-values were disproportionately affected by incoherent averaging. However, filtering based on SNR remedies this to an extent.