In vivo diffusion-weighted MRS using semi-LASER in the human brain at 3 T: methodological aspects and clinical feasibility

Diffusion ‐ weighted (DW ‐ ) MRS investigates non ‐ invasively microstructural properties of tissue by probing metabolite diffusion in vivo. Despite the growing interest in DW ‐ MRS for clinical applications, little has been published on the reproducibility of this technique. In this study, we explored the optimization of a single ‐ voxel DW ‐ semi ‐ LASER sequence for

Diffusion-weighted (DW-) MRS investigates non-invasively microstructural properties of tissue by probing metabolite diffusion in vivo.Despite the growing interest in DW-MRS for clinical applications, little has been published on the reproducibility of this technique.In this study, we explored the optimization of a single-voxel DWsemi-LASER sequence for clinical applications at 3 T, and evaluated the reproducibility of the method under different experimental conditions.DW-MRS measurements were carried out in 10 healthy participants and repeated across three sessions.
Metabolite apparent diffusion coefficients (ADCs) were calculated from monoexponential fits (ADC exp ) up to b = 3300 s/mm 2 , and from the diffusional kurtosis approach (ADC K ) up to b = 7300 s/mm 2 .The inter-subject variabilities of ADCs of N-acetylaspartate + N-acetylaspartylglutamate (tNAA), creatine + phosphocreatine, choline containing compounds, and myo-inositol were calculated in the posterior cingulate cortex (PCC) and in the corona radiata (CR).We explored the effect of physiological motion on the DW-MRS signal and the importance of cardiac gating and peak thresholding to account for signal amplitude fluctuations.Additionally, we investigated the dependence of the intra-subject variability on the acquisition scheme using a bootstrapping resampling method.Coefficients of variation were lower in PCC than CR, likely due to the different sensitivities to motion artifacts of the two regions.
Finally, we computed coefficients of repeatability for ADC exp and performed power calculations needed for designing clinical studies.The power calculation for ADC exp of tNAA showed that in the PCC seven subjects per group are sufficient to detect a difference of 5% between two groups with an acquisition time of 4 min, suggesting that ADC exp of tNAA is a suitable marker for disease-related intracellular alteration even in small case-control studies.In the CR, further work is needed to evaluate the voxel size and location that minimize the motion artifacts and variability of the ADC measurements.
Abbreviations: ADC, apparent diffusion coefficient; C R , coefficient of repeatability; Cr, creatine; CR, corona radiata; CRLB, Cramér-Rao lower bound; C V , coefficient of variation; δ, diffusion gradient duration; DW, diffusion weighted; GM, gray matter; mIns, myo-inositol; PCC, posterior cingulate cortex; PCr, phosphocreatine; rANOVA, repeated analysis of variance; SD, standard deviation; SNR, signal-to-noise ratio; tCho, choline containing compounds; tCr, creatine + phosphocreatine; td, diffusion time; tNAA, N-acetylaspartate + N-acetylaspartylglutamate; VAPOR, variable power with optimized relaxation delays; VOI, volume of interest; WM, white matter 2][3][4] Similarly to conventional MRS, DW-MRS exploits the specific compartmentalization of metabolites in different cell types, thus enabling differentiation between physiological or pathological mechanisms affecting brain tissue.The addition of magnetic field gradient pulses to MRS sequences allows sensitization of the NMR signal to diffusion, and quantification of metabolite displacement in tissue at a given time-scale.
From metabolite diffusion measures, it is possible to derive information on cell size and morphology, [5][6][7][8] as well as on the properties of the intracellular environment, such as viscosity and molecular crowding. 91][12][13] Although very promising, the application of DW-MRS techniques in clinical studies is challenging due to the intrinsic low signal-to-noise ratio (SNR) of metabolites, especially when the spectra are acquired at high diffusion-weightings.To overcome the issue of low SNR at high b-values, DW-MRS often requires long acquisition times, which are not always feasible in a clinical setting.In addition, obtaining robust and reproducible DW-MRS data is hampered by the high sensitivity of this technique to bulk and physiological motion, affecting both the phase and the amplitude of individual DW-MRS acquisitions.These deleterious effects increase dramatically the variance in DW-MRS calculated measures, resulting in low reproducibility and in significantly overestimated diffusion coefficients. 4,14All these factors point towards the need for accurate post-processing procedures, in addition to effective acquisition strategies.
Currently, the most commonly used techniques for DW-MRS are based on stimulated echo acquisition mode (STEAM), 15 point-resolved spectroscopy (PRESS), 16 and localization by adiabatic selective refocusing (LASER), 17 with magnetic field gradient pulses added in variable configurations for diffusion sensitization. 4 DW-STEAM allows for long diffusion times keeping a short echo time (T E ), and is thus ideal for exploration of the time dependence of metabolite diffusion. 5,9,18,19DW-STEAM has also been shown to better quantify diffusion of J-coupled metabolites compared with DW-PRESS. 20Spin-echo sequences provide higher SNR for a given T E , and, when equipped with a full bipolar diffusion gradient scheme, they allow maximization of the achievable b-value.These characteristics are highly beneficial, especially for applications on clinical scanners, where the maximum available gradient strength is limited by hardware constraints.Fully adiabatic LASER 17 or partially adiabatic semi-LASER 21 coupled with diffusion gradients (DW-semi-LASER) have the additional advantages of reducing signal losses related to B 1 field inhomogeneities and lower chemical shift displacement error compared with STEAM and PRESS sequences with standard RF pulses. 22Despite the increasing number of studies reporting different applications of DW-MRS to investigate brain tissue, and the importance of the evaluation of the reliability of the method for a study design, to our knowledge only two reports so far have tested the reproducibility of DW-MRS methods.In contrast to our study, one of these reports focused on a specific model of metabolite diffusion in the human corpus callosum employing a DW-PRESS sequence at both 3 T and 7 T. 23 In the second report, a DW-STEAM sequence was employed to measure metabolite apparent diffusion coefficients (ADCs) at 3 T, and the reproducibility of the method was tested in the subcortical white matter (WM) in a small group of three subjects. 24Yet, the long acquisition time employed in this study is not suitable for clinical applications.
The goal of the present study was to optimize the acquisition and post-processing procedures for single-voxel DW-MRS experiments, and to evaluate the feasibility of clinical studies using a DW-semi-LASER sequence at 3 T.To this aim, we report the variability of ADCs of Nacetylaspartate + N-acetylaspartylglutamate (tNAA), creatine + phosphocreatine (tCr), choline containing compounds (tCho), and myo-inositol (mIns), measured using DW-semi-LASER in two brain regions containing mostly gray matter (GM) or WM.In order to explore the impact of a series of methodological issues on the variability of metabolite ADCs, the reproducibility of the diffusion measures was evaluated for different experimental conditions across repeated measurements of the same subject, and across subjects.In particular, the effect of physiological motion on the DW-MRS signal and the importance of cardiac gating and peak thresholding to account for signal amplitude fluctuations were investigated.The ADCs were calculated using mono-exponential functions up to moderately high b-values (b = 3300 s/mm 2 ), as well as using a kurtosis model for measurements up to high b-values (b = 7300 s/mm 2 ).Finally, based on the variance of the metabolite ADCs, we provide power calculations that can be used for planning clinical studies, and discuss the suitability of DW-MRS for case-control studies in disease populations.

| Human subjects
Ten healthy volunteers (seven males, three females; mean age ± standard deviation (SD) 25 ± 3 years, range 20-29 years) participated in this study.Each subject underwent the same MRI/MRS examination during three different sessions (S1, S2, and S3), each on a different day, with a maximum delay between sessions of three weeks.All subjects provided informed consent according to local procedures prior to the study.The study was approved by the local ethics committee.

| MRI hardware
All subjects were scanned on a 3 T whole-body Siemens MAGNETOM Prisma Fit MRI scanner (Siemens Medical Solutions, Erlangen, Germany).
The scanner was equipped with gradient coils capable of reaching 80 mT/m on each of the three orthogonal axes.The standard RF body-coil was used for excitation and a 64-channel receive-only head coil for reception.
The DW-MRS acquisitions were performed using a single-voxel semi-LASER sequence with diffusion gradients added in a bipolar configuration, as shown in Figure 1.Using the bipolar configuration of the diffusion gradients minimizes eddy currents as well as cross terms between the diffusion gradients and gradients rising from inhomogeneities of the B 0 field. 25DW-MRS data were acquired in two VOIs of 20 × 20 × 20 mm 3 located in the posterior cingulate cortex (PCC), from here on referred to as VOI PCC (Figure 2A), and in the corona radiata (CR), from here on referred to as VOI CR (Figure 2C).In the CR, data were acquired in eight subjects also in a smaller VOI (VOI' CR ) of 15 (foothead) × 20 (anterior-posterior) × 15 (right-left) mm 3 , with the same center as VOI CR (in two subjects it was not possible to perform the measurement in VOI' CR for technical reasons).For all VOIs, sequence parameters were T E = 120 ms, spectral width = 3 kHz and number of complex points = 2048.All resonances were excited using a slice-selective 90°pulse (pulse length of 2.52 ms) followed by two pairs of slice-selective adiabatic refocusing pulses in the other two dimensions (HS1, R = 24, pulse length 7 ms).The 64-channel signals were combined on-line using a reference water scan, after appropriate phase adjustment and amplitude weighting of each channel for optimal SNR combination.All acquisitions were synchronized with cardiac cycle using a pulse-oximeter device, in order to start each acquisition every three heart beats, while maintaining a minimum T R of 2.5 s.To verify the effect of cardiac gating on signal fluctuations, an additional acquisition was performed in one subject without a pulse-oximeter device at T R = 2.5 s.Diffusion-weighting was applied in three orthogonal directions ( nograms of the pulse sequence, and therefore accounted for all gradients present in the sequence, including slice-selective and crusher gradients.A non-DW condition with diffusion gradient amplitude set to zero was also acquired: b 0 = 11 s/mm 2 , where the small b-value originates from the slice-selective and crusher gradients.Forty averages were collected for each diffusion-weighting condition and saved as individual free induction decays for further post-processing.Water suppression was performed using variable power with optimized relaxation delays (VAPOR) and outer volume suppression. 26The delays used for VAPOR were 150, 100, 146, 105, 106, 68, 80, and 22 ms. 27Unsuppressed water reference scans were acquired from the same VOIs using the same parameters as water suppressed spectra for eddy current corrections.B 0 shimming was performed using a fast automatic shimming technique with echo-planar signal trains utilizing mapping along projections, FAST (EST) MAP. 28GURE 1 Schematic diagram of the DWsemi-LASER sequence.The RF pulses are shown together with the DW gradients, but without slice-selective or crusher gradients.t d is the time between the first lobe of the dephasing diffusion gradient group (in gray) and the first lobe of the re-phasing diffusion gradient group (in green).The total gradient duration δ corresponds to the sum of the durations of four lobes, and is identical for dephasing and re-phasing groups The total DW-MRS scan time for VOI PCC and VOI CR was about 17 min for each VOI.In VOI' CR , an additional shorter acquisition was performed using only b 0 and b 2 (the latest applied in the three orthogonal directions) and 24 averages per diffusion condition (about 4 min), to evaluate, under these experimental conditions, the effect of voxel size on data variability.

| Spectral processing
All spectra were processed with an in-house written routine in MATLAB release R2016b (MathWorks, Natick, MA, USA).DW-MRS data were first corrected for eddy currents using water reference scans.Zero-order phase fluctuations and frequency drifts were corrected on single averages before summation using an area minimization and penalty algorithm and a cross-correlation algorithm, respectively. 29A peak-thresholding procedure was applied, for each diffusion condition, to discard the single averages with artifactual low SNR caused by non-translational tissue motion, which is not justified by gaussian noise alone (see Supplementary Material S1).The remaining spectra, for each condition, were averaged.Finally, the averaged spectra were analyzed with LCModel 30 for metabolite quantification.The basis set was simulated with an in-house written routine in MATLAB based on the density matrix formalism 31 and using previously reported chemical shifts and J-couplings. 32,33The basis set included alanine, ascorbate, aspartate, creatine (Cr), γ-aminobutyric acid, glucose, glutamate, glutamine, glutathione, glycerophosphorylcholine, mIns, lactate, N-acetylaspartate (NAA), N-acetylaspartylglutamate, phosphocreatine (PCr), phosphorylcholine, phosphorylethanolamine, scyllo-inositol, and taurine.Independent spectra for the CH 3 and CH 2 groups of NAA, Cr, and PCr were simulated and included in the basis set.

| Metabolite diffusion measures
Based on the LCModel data, metabolite diffusivity properties for tNAA, tCr, tCho, and mIns were calculated in each VOI.ADCs were computed assuming a mono-exponential decay of the signal up to b 2 (Figure 3) in each diffusion direction: where S i (b) is the signal measured at a given b-value in direction i, S 0 is the signal measured at b 0 , and ADC i exp is the corresponding apparent diffusion coefficient estimated in direction i.Since the signal decay obtained up to b 3 was not mono-exponential, the signal decay up to this b-value was evaluated using the kurtosis approach 34,35 (Figure 3): where ADC i K is the apparent diffusion coefficient for direction i and K i is the kurtosis parameter in the same direction.The quality of both monoexponential and kurtosis fits up to b 3 was assessed using a chi-square (χ 2 ) goodness-of-fit test for the residuals, using the Cramér-Rao lower bounds (CRLBs) provided by LCModel as SDs for the metabolite signal amplitudes.

| Inter-subject variability
The inter-subject variability of the diffusion measures was evaluated for all four metabolites and all VOIs.Coefficients of variation (C V ) were calculated as ratios between SDs and mean values of the diffusion parameters.SDs and mean values were estimated across subjects for each session separately, as well as across subjects and sessions, and were consequently used for the C V evaluations.
First the effects of peak thresholding, diffusion-weighting direction, and VOI size on the mean values and variability of tNAA diffusion measures were evaluated.Subsequently the C V values were calculated for metabolite ADC exp , ADC K , and K estimated using peak thresholding and averaged over three diffusion directions.

| Intra-subject variability
The intra-subject variability analysis was carried out on ADC exp , ADC K , and K of tNAA and tCho derived from VOI PCC and VOI CR .The dependence of the intra-subject variability of the diffusion measures on the acquisition time was evaluated by computing the diffusivity parameters for each subject, considering different diffusion-weighting schemes and different numbers of spectral averages per diffusion condition.For this purpose, a bootstrapping subsampling procedure was used: the datasets from each session were randomly resampled with replacement prior to averaging.For each resampled subset, the averaged spectra needed for calculation of the diffusion metrics were obtained.The bootstrapping procedure was repeated 200 times for each subset size to obtain a bootstrap population.From the bootstrap populations, mean values and SDs of the diffusivity parameters were obtained and utilized for intra-subject C V calculations.

| Reproducibility and sample size analysis
A one-way repeated analysis of variance (rANOVA) model (MATLAB release R2016b) was performed to evaluate the within-subject variability (σ) of metabolite ADC exp averaged over the diffusion directions.σ was used for repeatability coefficient (C R ) and power/sample size calculations.C R within the 95% confidence interval was defined as C R ¼ 1:96 ffiffiffi 2 p σ. 36 It was assumed that the means were normally distributed and the variances of the two groups were the same (σ 1 = σ 2 = σ).The linearity of the signal logarithm attenuation for the acquisition scheme b [0-2] was very good for all metabolites in both GM and WM (R 2 > 0.9 for all fits).In contrast, for the acquisition scheme b [0-3] a significant deviation from linearity was observed in about 30% of the fits (p < 0.05 for the χ 2 goodness-of-fit test for the residuals), and the signal decay was better fitted by the kurtosis model: for all fits, the null hypothesis of the χ 2 goodness-of-fit test was accepted with p > 0.9.
Tissue segmentation results showed that the average WM fraction was 88 ± 4% in VOI CR and 94 ± 4% in VOI' CR , while the average GM fraction in VOI PCC was 72 ± 5%.

| Peak thresholding
The average numbers of spectra rejected after peak thresholding were 3 for b 0 and b 1 , 4 for b 2 , and 5 for b 3 in VOI PCC , and 2, 6, 10, and 12, respectively, in VOI CR .In VOI' CR , 1 and 2 spectra on average were rejected for b 0 and b 2 , respectively.Figure 5 shows an example of 40 averages acquired at b 3 in VOI CR , plotted without post-processing (A), after eddy current, phase, and frequency corrections (B), and after peak thresholding (C).
Figure 6 shows ADC exp (A, B), ADC K (C, D), and K (E, F) of tNAA measured in VOI PCC and VOI CR for each diffusion direction, from all subjects and all sessions, with and without peak thresholding.In VOI PCC , decreases in both the mean values and the variability of ADC exp were observed when peak thresholding was applied (Figure 6A).The C V of ADC exp decreased after peak thresholding by 26% in dir 1 , 14% in dir 2 , and 35% in dir 3 .
In contrast, no differences in the C V of ADC K were observed in any of the three directions when peak thresholding was applied.In VOI CR the mean values and the C V of ADC exp decreased strongly in each direction when peak thresholding was applied: 33% in dir 1 , 41% in dir 2 , and 39% in dir 3 (Figure 6B).Similarly, in this region the C V of ADC K decreased by 25%, 36%, and 21% in dir 1 , dir 2 , and dir 3 , respectively (Figure 6D).In both VOIs, no differences in the variability of K were observed when peak thresholding was applied (Figure 6E and 6F).The diffusion metrics and their C V reported from here on were calculated with peak thresholding.

| DW direction
In VOI PCC , the variability of ADC exp and ADC K of tNAA was very similar for the three directions: mean C V = 9% and 12% for the two metrics, respectively (Figure 6A and 6C).In contrast, in VOI CR , the variabilities of ADC exp , ADC K , and K of tNAA (C V = 10%, 14%, and 27%, respectively) were lower in dir 3 with respect to the other two directions (C V = 18%, 22%, and 38% for both dir 1 and dir 2 ) (Figures 6B, 6D and 6F).

| Voxel size
Figure 7 shows the ADC exp of tNAA derived in VOI CR and VOI' CR , plotted for all subjects and all sessions, and for each DW direction.In both voxels, ADC exp values were estimated using scheme b [0,2] and 24 averages per diffusion condition.In contrast to VOI CR , the variability estimated from VOI' CR did not present any significant dependence on the diffusion-weighting direction (averaged C V = 16%).The C V values calculated in VOI' CR in dir 1 and dir 2 dropped by 19% with respect to those derived from VOI CR in the same directions, while they were comparable in dir 3 .Similar behavior with respect to peak thresholding, DW direction, and VOI size was observed for the variability of tCr, tCho, and mIns diffusion measures (data not shown).

| Inter-subject variability
tNAA, tCr, tCho, and mIns diffusivity measures averaged across diffusion directions and subjects are reported for each session, with the associated SD and C V values, in Tables 1 and 2, for VOI PCC and for VOI CR and VOI' CR , respectively.No significant differences in diffusivity measures of the metabolites across the sessions were observed (rANOVA).
In VOI PCC , the C V values estimated for ADC exp and ADC K of all metabolites ranged from 6% to 14% and from 8% to 18%, respectively, while the C V of K ranged from 11% to 34% (Table 1).In VOI CR , the C V of ADC exp and ADC K were higher than those calculated in VOI PCC , ranging from 7% to 32%, while the C V of K ranged from 15% to 38% (Table 2).Finally, in the VOI' CR the C V of tNAA, tCr, and tCho ADC exp ranged from 8% to 19% (Table 2).In Figure 8, all diffusivity measures computed for all metabolites from all subjects and all sessions for the two VOIs are shown.after post-processing without peak thresholding (eddy current, phase, and frequency corrections) (B), and after post-processing with peak thresholding (C).Blue lines correspond to the average spectra.In this example, fourteen spectra had artifactual low SNR and were discarded.D, comparison of the average spectra obtained with and without peak thresholding scheme.The C V of K of tNAA were below 20% when 150 and 250 averages (scanning times of 7 and 11 min) were used in VOI PCC and VOI CR , respectively.Similar trends were observed for tCr and tCho (data not shown).

| Effect of acquisition time on intra-subject variability
In addition, the diffusion metrics' variabilities as a function of the SNR estimated at b 0 are shown in Figure 4S of the Supplementary Material.

| Reproducibility and sample size analysis
C R values for ADC exp of all metabolites were calculated in VOI PCC and VOI CR for different acquisition schemes (b [0,1,2] and b [0,2] ) and acquisition times (12, 7, and 4 min), and reported as percentages of ADC exp mean values (Table 3).The C R were much lower in VOI PCC than in VOI CR , indicating higher repeatability in the first region.Interestingly, while C R values for VOI CR gradually increased when reducing the acquisition time, in VOI PCC for all metabolites the C R obtained for scheme b [0,2] and acquisition time of 4 min were smaller than those for the same scheme and acquisition time of 7 min.
For each of the acquisition schemes reported in Table 3, power calculations were performed for ADC exp of tNAA to reflect the number of subjects per group required to detect a difference between two groups with a power of 80% and significance level 5% (Figure 10).A 5% difference can be detected with 6 and 29 subjects per group in VOI PCC and VOI CR , respectively, with scheme b [0,1,2] and a scanning time of 12 min (Figure 10 A).With scheme b [0,2] and a scanning time of 7 min, a 5% difference can be detected with 17 and 29 subjects per group in VOI PCC and in VOI CR , respectively (Figure 10B).With b [0,2] and a reduced scanning time of 4 min, a 5% difference can be detected with 7 and 31 subjects per group in VOI PCC and in VOI CR , respectively (Figure 10C).Diffusion-attenuation curves were fitted to mono-exponential functions up to b 2 = 3300 s/mm 2 and to a kurtosis model (Equation 2) up to b 3 = 7300 s/mm 2 .The χ 2 goodness-of-fit test revealed that the mono-exponential fit was not able to explain 30% of the metabolite signal decays up to b 3 , whereas the kurtosis approach was found to be more accurate (the null hypothesis was accepted for all fits with p > 0.9).The non-monoexponential behavior of the signal decay at high b-values may originate from non-gaussian, restricted diffusion within individual compartments, distributions of diffusion coefficients associated with multiple gaussian compartments, fiber dispersion, exchange effects, or a combination of these processes. 38Sampling DW-MRS data at high b-values is necessary to derive information on tissue morphology at the microscopic scale. 6,39though reaching ultra-high b-values greater than 15000 s/mm 2 would be desirable for accurate modeling of DW-MRS signals and extraction of microstructural parameters, this may be very challenging in a clinical context with stringent limitations in the acquisition times.In the present study, we evaluated the possibility of capturing deviations from mono-exponentiality using the kurtosis approach, with a reasonably high b-value of 7300 s/mm 2 and a relatively short acquisition protocol.Significantly higher K mean values in GM compared with WM for all metabolites confirmed previous results suggesting greater diffusional heterogeneity in GM. 40 Coefficients of variation for K were much higher than those obtained for the ADCs.

| Inter-subject and intra-subject variability
The inter-subject variability calculated from full datasets was less than 16% for ADC exp and ADC K of all metabolites under investigation in VOI PCC (Table 1), while it was higher in VOI CR (<16% for tNAA, tCr, and tCho, <27% for mIns) (Table 2).In contrast, the inter-subject variability of K was less than 27% for all metabolites in both VOIs.
The robustness of the DW-MRS acquisition was evaluated by exploring the variability of the diffusion measures associated with different subsamplings of the data.The procedure was repeated for different numbers of averages per DW condition and different diffusion-weighting schemes, corresponding to different acquisition times.In both VOIs, the coefficients of variation for tNAA, tCr, and tCho ADCs were lower than 10% when 60 or more averages were considered using scheme b [0,2] , corresponding to acquisition times of at least 3 min (Figure 9A  DW-MRS can be used to characterize microstructural alterations affecting brain tissue in a variety of diseases.Previous clinical and preclinical studies reported differences greater than 20% in the diffusion of several metabolites in patients with ischemic stroke or tumor, compared with healthy subjects. 41,42Wood et al reported differences of almost 20% in the tNAA diffusivity in the corpus callosum of patients with multiple sclerosis, 13 while differences in tCho and tCr ADCs of more than 15% were observed in systemic lupus erythematosus. 11Our results on ADC exp repeatability (Table 3) suggest that for investigation of tNAA, tCr, tCho, and mIns diffusion abnormalities in pathologies where the expected ADC exp differences are greater than 10%, it is sufficient to keep the acquisition time per region of interest below 5 min, with a group size of about 30 subjects.In contrast, to explore more subtle microstructural abnormalities in normal aging or neurological diseases at the very early stage, longer acquisition times are probably desirable, and need to be evaluated case by case depending on the location and size of the brain region under investigation and the expected differences in the diffusion metrics.

| CONCLUSIONS
We have evaluated the performance of a DW-semi-LASER sequence at 3 T and demonstrated the feasibility of this method in a clinical setting, providing that all procedures from experimental planning (choice of b-values and number of averages), execution (cardiac triggering), and postprocessing (peak thresholding in addition to standard phase and frequency corrections) are carefully performed.Altered metabolite diffusion in tissue has been shown to reflect specific structural damage in disease.In particular, the diffusion of the neuronal marker tNAA has been suggested to reflect pure intra-axonal damage in WM diseases, while the diffusion of tCho and tCr represents potential markers of inflammation and glial cell alterations.DW-semi-LASER may allow the exploration of microscopic cellular alterations in different pathological conditions, providing useful insights into the pathogenesis and evolution of the disease, and eventually helping to choose the most appropriate temporal window for tailored therapies and to monitor treatment response.

FIGURE 2
FIGURE 2 DW spectra and VOIs.The locations of the VOIs in the PCC (a) and the CR (C) are shown on T 1 -weighted images together with examples of DW spectra acquired at different b-values in VOI PCC (B) and VOI CR (D) Each subset consisted respectively of10, 15, 20, 25, 30, 35, and 40 averages per diffusion condition (e.g. per b-value and diffusion direction).In addition, the ADC exp and their variabilities were estimated from different diffusion-weighting schemes: scheme b [0,1,2] employs b 0 , b 1 , and b 2 ; scheme b [0,2] employs b 0 and b 2 ; scheme b [0,1] employs b 0 and b 1 .The K were estimated using all b-values, b 0 , b 1 , b 2, and b 3 (scheme b [0-3] ).

FIGURE 3
FIGURE 3 tNAA attenuation curves.Natural logarithm of tNAA normalized signal decay plotted as a function of b-value.The attenuation curve was fitted to a mono-exponential function (solid line) up to b 2 = 3300 s/mm 2 and to a kurtosis model (dashed line) up to b 3 = 7300 s/mm 2

3 | RESULTS 3 . 1 |
DW spectra qualityRepresentative DW spectra acquired in VOI PCC and VOI CR of one subject at all b-values applied in one diffusion gradient direction (dir 1 ) are shown in Figure2Band 2D, respectively.The CRLBs of tNAA calculated from all subjects, all b-values, all directions, and all VOIs ranged from 2 to 7%, while the CRLBs of tCr and of tCho ranged from 3 to 12%.The CRLBs of mIns were lower than 20% for all b-values in VOI PCC and lower than 35% for all b-values up to b 2 in VOI CR , whereas for b 3 in VOI CR they were higher than 50% for 5 out of 30 datasets and were therefore excluded from the kurtosis analysis.In VOI' CR , the CRLBs of mIns at b 2 were greater than 35% for more than half of the datasets; therefore, these signals were not considered for further analysis.The mean SNR, based on the tNAA peak (averaged over all sessions and DW directions), was 24 for b 0 and 14 for b 3 in VOI PCC .In VOI CR , the mean SNR was 23 for b 0 and 9 for b 3 .Both in VOI PCC and in VOI CR , no differences in SNR were observed between different DW directions.The SNRs were considerably lower in VOI' CR than in VOI CR for each direction and both b-values: SNR = 14 for b 0 and SNR = 8 for b 2 .

3. 2 |
Figure4Aand 4B shows the SNR of tNAA for single averages (40 averages for each diffusion condition) with and without cardiac gating, respectively.Mean SNRs derived with and without cardiac gating at b 1 , b 2 , and b 3 were plotted for each diffusion direction (Figure4C).The SNRs were normalized to the SNR calculated at b 0 = 11 s/mm 2 (SNR 0 ), in order to remove effects due to fluctuations in T R in the acquisitions with cardiac gating.The mean SNRs of the spectra acquired with cardiac gating were higher for each b-value and diffusion condition.The associated SDs were slightly lower with heartbeat trigger, except for b 1 in dir 2 .

Figure 9 FIGURE 4 FIGURE 5
Figure9shows the C V of ADC exp and K of tNAA calculated as a function of the number of averages acquired in VOI PCC (Figure9Aand 9C) and in VOI CR (Figure9Band 9D), based on data resampling from all subjects and sessions.The C V of ADC exp of tNAA was evaluated for different

FIGURE 6 FIGURE 7
FIGURE 6 Effect of peak thresholding on the variability of tNAA diffusion measures.Diffusivity measures of tNAA derived in VOI PCC (A, C, E) and VOI CR (B, D, F) from all subjects and sessions, displayed separately for each diffusion direction.Mean values (central bars) and SDs (outer bars) are plotted for each parameter and direction

FIGURE 10
FIGURE 10 Reproducibility analysis.Number of subjects (per group) required to detect a difference in the ADC exp of tNAA (as a percentage of the mean) with significance level α = 0.05 and power of 1 − β = 0.80.The power was calculated in VOI PCC and VOI CR for the full dataset including all b-values up to b 2 = 3300 s/mm 2 (scheme b [0,1,2] ), corresponding to an acquisition time of 12 min (a), and sub-sampled datasets using b 0 = 11 s/ mm 2 and b 2 = 3300 s/mm 2 (scheme b [0,2] ) and different numbers of averages (B, C), corresponding to acquisition times of 7 and 4 min, respectively scheme b [0,1,2] , the same variability could be reached with at least 90 averages, indicating that acquiring spectra at the low b-value of 850 s/mm 2 does not add stability to the ADC calculation.Finally, using scheme b [0,1] should be avoided, since it does not provide sufficient diffusion-weighting for proper ADC estimations.Figure4S(Supplementary Material) shows the behavior of the diffusion metrics' variabilities as a function of the SNR estimated at b 0 .These plots report the non-DW SNR necessary to obtain a certain variability of the diffusion measures in the brain regions under investigation, providing that all acquisition and post-processing steps are properly performed, and can be useful to translate our results to data acquired on different experimental setups.However, depending on the effect of motion and other factors such phase and amplitude fluctuations on the DW signal detected in the region of interest, the SNR at b 0 cannot be directly linked to the robustness of the measurements, and these results should be adapted with caution to different experimental conditions.

TABLE 1
Mean SD and C V of ADC exp , ADC K , and K values calculated for each session (S1 to S3) in VOI PCC (scheme b [0,1,2] and 40 averages per diffusion condition)

TABLE 2
Average, SD, and C V of ADC exp , ADC K , and K values calculated for each session (S1 to S3) in VOI CR (scheme b [0,1,2] and 40 averages per diffusion condition) and average, SD, and C V of ADC exp calculated for each session in VOI' CR (scheme b [0,2] and 24 averages per diffusion condition).Inter-subject variability.ADC exp , ADC K , and K of all metabolites from all subjects and sessions derived in VOI PCC(A, C) and VOI CR (B, D) averaged over all diffusion directions.Mean values (central bars) and SDs (outer bars) are displayed for each parameterFIGURE 9 Intra-subject variability.Coefficients of variation for ADC exp and K of tNAA, calculated in VOI PCC (A, C) and in VOI CR (B, D), from a bootstrapping subsampling procedure.The datasets from each subject and session were randomly resampled with replacement prior to averaging.Each subset consisted of 10, 15, 20, 25, 30, 35, and 40 averages per diffusion condition.The ADC exp were estimated from different diffusionweighting schemes: b [0,1,2] , b [0,2] , and b [0,1] .The K were estimated using all b-values (scheme b [0-3] )

TABLE 3 C
R and variance (σ 2 ) of ADC exp values calculated for different acquisition schemes and acquisition times, in VOI PCC and VOI CR .Power analysis can be performed using the σ 2 values reported in the table and equation 4