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

Abstract

Diffusion-weighted magnetic resonance spectroscopy (DW-MRS) investigates noninvasively 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 clinical applications at 3 T, and evaluated the reproducibility of the method under different experimental conditions. DW-MRS measurements were carried out in ten healthy participants and repeated across three sessions. Metabolite apparent diffusion coefficients (ADCs) were calculated from mono-exponential fits (ADC_exp) up to b-value = 3300 s/mm², and from the diffusional kurtosis approach (ADC_K) up to b-value = 7300 s/mm². The inter-subject variabilities of ADCs of N-acetylaspartate + N-acetylaspartylglutamate (tNAA), creatine + phosphocreatine (tCr), choline containing compounds (tCho), and myo-inositol (mIns) 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 sensitivity 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. Power calculation for ADC_exp of tNAA showed that in the PCC 7 subjects per group are sufficient to detect a difference of 5% between two groups with an acquisition time of 4 minutes, 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 voxel size and location that minimize motion artifacts and variability of the ADC measurements.

1. Introduction

Diffusion-weighted magnetic resonance spectroscopy (DW-MRS) explores metabolic and microstructural properties of healthy and diseased brains by probing the diffusion of several metabolites in vivo^1–4. Similarly to conventional MRS, DW-MRS exploits the specific compartmentalization of metabolites in different cell types, thus enabling differentiation between different 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^5–8, as well as on the properties of the intracellular environment, such as viscosity and molecular crowding⁹. When combined with diffusion-weighted imaging techniques, DW-MRS provides a unique way to differentiate between axonal degeneration, glial activation, and demyelination^10–13. 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 over-estimated diffusion coefficients^4,14. All 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 sensitization⁴. DW-STEAM allows for long diffusion times keeping short echo time (T_E), and is thus ideal for exploration of the time dependence of metabolite diffusion^5,9,18,19. DW-STEAM has also been shown to better quantify diffusion of J-coupled metabolites compared to DW-PRESS²⁰. Spin-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 LASER¹⁷ or partially adiabatic semi-LASER²¹ coupled with diffusion gradients (DW-semi-LASER) have the additional advantages of reducing signal losses related to B₁ field inhomogeneities and lower chemical shift displacement error compared to STEAM and PRESS sequences with standard radiofrequency pulses²². Despite 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 tested the reproducibility of DW-MRS methods. Differently from 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 T²³. 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 in a small group of three subjects²⁴. Yet, 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 N-acetylaspartate + 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 grey matter (GM) or white matter (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/mm²), as well as using kurtosis model for measurements up to high b-values (b = 7300 s/mm²). Finally, based on the variance of the metabolite ADCs, we provided power calculations that can be used for planning clinical studies, and discussed the suitability of DW-MRS for case-control studies in disease populations.

2. Material and Methods

2.1. Human subjects

Ten healthy volunteers (seven males, three females; mean age ± standard deviation: 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.

2.2. 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 radio-frequency body-coil was used for excitation and a 64-channel receive-only head coil for reception.

2.3. MRI/DW-MRS protocol

At the beginning of each scan, three-dimensional (3D) T₁-weighted magnetization-prepared rapid gradient echo (MPRAGE) images (field of view, 256 (anterior-posterior) × 256 (foot-head) × 231 (right-left) mm³; isotropic resolution, 0.9 mm; T_R/T_E, 2300/2.08 ms; total acquisition time, 5 min 17 s) were acquired to position the spectroscopic volumes of interest (VOIs) and to perform tissue segmentation.

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 B₀ field²⁵. DW-MRS data were acquired in two VOIs of 20 × 20 × 20 mm³ 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 (foot-head) × 20 (anterior-posterior) × 15 (right-left) mm³, with the same center as VOI_CR (in two subjects it was not possible to perform the measurement in VOI’_CR due to 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 of 7 ms). The 64-channels 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 3 heart beats, while keeping 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 pulse-oximeter device and T_R = 2.5 s. Diffusion-weighting was applied in three orthogonal directions (dir₁ = [1, 1, −0.5], dir₂ = [1, −0.5, 1], dir₃ = [−0.5, 1, 1] in the VOI coordinate system) with diffusion gradient duration (δ) = 18 ms, diffusion time (t_d) = 60 ms and three increasing gradient strengths resulting in the b-values b₁ = 850, b₂ = 3300 and b₃ = 7300 s/mm². The b-values were calculated using the chronograms of the pulse sequence, and therefore accounted for all gradients present in the sequence, including slice selective and crusher gradients. A non-diffusion-weighted condition with diffusion gradient amplitude set to zero was also acquired: b₀ = 11 s/mm², where the small b-value originates from the slice selective and crushers gradients. Forty averages were collected for each diffusion-weighting condition and saved as individual free induction decays (FID) for further post-processing. Water suppression was performed using variable power with optimized relaxation delays (VAPOR) and outer volume suppression²⁶. The delays used for VAPOR were 150, 100, 146, 105, 106, 68, 80, and 22 ms²⁷. Unsuppressed water reference scans were acquired from the same VOIs using the same parameters as water suppressed spectra for eddy current corrections. B₀ shimming was performed using a fast automatic shimming technique with echo-planar signal trains utilizing mapping along projections, FAST(EST)MAP²⁸.

Figure 1: Schematic of the DW-semi-LASER sequence.

The RF pulses are shown together with the diffusion-weighted gradients, but without slice-selective and crusher gradients. The diffusion time t_d is the time between the first lobe of the de-phasing diffusion gradient group (in grey) 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 de-phasing and re-phasing groups.

Figure 2: Diffusion-weighted spectra and VOIs.

The locations of the VOIs in (A) the PCC and (C) the CR are shown on T₁-weighted images together with examples of diffusion-weighted spectra acquired at different b-values in (B) VOI_PCC and (D) VOI_CR

The total DW-MRS scan time for VOI_PCC and VOI_CR was about 17 minutes for each VOI. In VOI’_CR, an additional shorter acquisition was performed using only b₀ and b₂ (the latest applied in the three orthogonal directions) and 24 averages per diffusion condition (about 4 minutes), to evaluate, at these experimental conditions, the effect of voxel size on data variability.

2.4. Spectral processing

All spectra were processed with 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, respectively²⁹. A peak thresholding procedure was applied, for each diffusion condition, to discard the single averages with artifactual low SNR caused by non-translational tissue motion, and 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 LCModel³⁰ for metabolite quantification. The basis set was simulated with an in-house written routine in MATLAB based on the density matrix formalism³¹ and using previously reported chemical shifts and J-couplings^32,33. The 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 CH₃ and CH₂ groups of NAA, Cr and PCr were simulated and included in the basis set.

2.5. 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 b₂ (Figure 3) in each diffusion direction:

$$ln\left[\frac{S^i\left(b\right)}{S_0}\right]=-b\cdot AD{C}_{exp}^i$$ (1)

where Sⁱ(b) is the signal measured at a given b-value in direction i, S₀ is the signal measured at b₀, and ADCⁱ_exp is the corresponding apparent diffusion coefficient estimated in direction i. Since the signal decay obtained up to b₃ was not mono-exponential, the signal decay up to this b-value was evaluated using the kurtosis approach^34,35 (Figure 3):

$$ln\left[\frac{S^i\left(b\right)}{S_0}\right]=-b\cdot AD{C}_K^i+\frac{K^i}{6}{\left(b\cdot AD{C}_K^i\right)}^2$$ (2)

where ADCⁱ_K is the apparent diffusion coefficient for the direction i and Kⁱ is the kurtosis parameter in the same direction. The quality of both mono-exponential and kurtosis fits up to b₃ was assessed using a chi-square (χ²) goodness-of-fit test for the residuals, using the Cramér-Rao lower bounds (CRLBs) provided by LCModel as standard deviations for the metabolite signal amplitudes.

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 b₂ = 3300 s/mm² and to a kurtosis model (dashed line) up to b₃ = 7300 s/mm².

2.6. 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 standard deviations (SD) and mean values of the diffusion parameters. SD 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.

At 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 were calculated for metabolite ADC_exp, ADC_K and K values estimated using peak-thresholding and averaged over three diffusion directions.

2.7. 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. Each subset consisted respectively of 10, 15, 20, 25, 30, 35 and 40 averages per diffusion condition (e.g., per b-value and diffusion direction). In addition, ADC_exp and their variabilities were estimated from different diffusion-weighting schemes: scheme b_[0,1,2] employs b₀, b₁, and b₂; scheme b_[0,2] employs b₀ and b₂; scheme b_[0,1] employs b₀ and b₁. K were estimated using all b-values b₀, b₁, b₂ and b₃ (scheme b_[0–3]).

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.

2.8. 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 $C_R=1.96 \times \sqrt{2} \times \sigma$³⁶.

Power calculations were performed to estimate the necessary sample size to detect a difference (Δ) in tNAA ADC_exp and K between two groups. These were based on a two-sided test with significance level α = 0.05 (z_1-α/2 = 1.96), and a power of 80% (1-β = 0.80, z_1-β = 0.84):

$$n=\frac{{\sigma }^2{\left(z_{1-\alpha /2}+z_{1-\beta }\right)}^2}{{\Delta }^2}.$$ (4)

It was assumed that the means were normally distributed and the variances of the two groups were the same for both groups (σ₁ = σ₂ = σ).

3. Results

3.1. Diffusion-weighted spectra quality

Representative diffusion-weighted spectra acquired in VOI_PCC and VOI_CR of one subject at all b-values applied in one diffusion gradient direction (dir₁) are shown in Figure 2B and 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 b₂ in VOI_CR, whereas for b₃ 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 b₂ were > 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 b₀ and 14 for b₃ in VOI_PCC. In VOI_CR, the mean SNR was 23 for b₀ and 9 for b₃. Both in VOI_PCC and in VOI_CR, no differences in SNR were observed between different DW directions. The SNRs in VOI’_CR were considerably lower than in VOI_CR for each direction and both b-values: SNR = 14 for b₀ and SNR = 8 for b₂.

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 (R² > 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 χ² 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 χ² 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, respectively, while the average grey matter fraction in VOI_PCC was 72 ± 5%.

3.2. Effect of acquisition strategy and post-processing on the variability of the diffusion measures

3.2.1. Cardiac gating

Figure 4A and 4B show 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 b₁, b₂ and b₃ were plotted for each diffusion direction (Figure 4C). The SNRs were normalized to the SNR calculated at b₀ = 11 s/mm² (SNR₀), in order to remove effects due to fluctuations in T_R in the acquisitions with cardiac gating. The mean SNR of the spectra acquired with cardiac gating were higher for each b-value and diffusion condition. The associated standard deviations were slightly lower with heartbeat trigger, except for b₁ in dir₂.

Figure 4: Effect of cardiac gating on tNAA SNR.

tNAA SNR calculated for single averages in one subject at all b-values and diffusion-weighted directions (A) with and (B) without cardiac gating. (C) Comparison of average SNR at different b-values (b₁, b₂ and b₃) and directions (dir₁, dir₂, dir₃) obtained with and without cardiac gating. The reported SNR were normalized to the SNR calculated at b₀ (SNR₀), in order to remove effects due to fluctuations in T_R in the acquisitions with cardiac gating. Error bars represent standard deviations.

3.2.2. Peak thresholding

The average number of spectra rejected after peak thresholding were 3 for b₀ and b₁, 4 for b₂, 5 for b₃ in VOI_PCC, and 2, 6, 10, 12, respectively, in VOI_CR. In VOI’_CR, 1 and 2 spectra on average were rejected for b₀ and b₂, respectively.

Figure 5 shows an example of 40 averages acquired at b₃ in VOI_CR, plotted without post-processing (5A), after eddy current, phase and frequency corrections (5B), and after peak thresholding (5C).

Figure 5. Post-processing.

Example of 40 averages acquired with cardiac gating at b₃ from VOI_CR, plotted (A) without post-processing, (B) after post-processing without peak thresholding (eddy current, phase and frequency corrections), and (C) after post-processing with peak thresholding. 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 (blue line) and without (red line) peak thresholding.

Figure 6 shows ADC_exp (6A, 6B), ADC_K (6C, 6D) and K (6E, 6F) 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 dir₁, 14% in dir₂ and 35% in dir₃, respectively. Instead, no differences in the C_V of ADC_K were observed in any of 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 dir₁, 41% in dir₂ and 39% in dir₃ (Figure 6B). Similarly, in this region the C_V of ADC_K decreased by 25%, 36% and 21% in dir₁, dir₂ and dir₃, 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.

Figure 6: Effect of peak thresholding on the variability of tNAA diffusion measures.

Diffusivity measures of tNAA derived in (A, C, E) VOI_PCC (squares) and (B, C, D) VOI_CR (dots) from all subjects and sessions, displayed separately for each diffusion direction. Mean values (central bars) and SDs (edge bars) are plotted for each parameter and direction. Blue markers: peak thresholding applied; red markers: no peak thresholding.

3.2.3. 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, 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 dir₃ with respect to the other two directions (C_V = 18%, 22% and 38% for both dir₁ and dir₂) (Figures 6B, 6D and 6F).

3.2.4. 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. Differently from VOI_CR, the variability estimated from the 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 dir₁ and dir₂ dropped by 19% with respect to those derived from VOI_CR in the same directions, while they were comparable in dir₃. 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).

Figure 7: Effect of the voxel size on the variability of tNAA diffusion measures.

ADC_exp derived from all subjects and sessions in VOI_CR (blue dots) and in VOI’_CR (green dots), displayed separately for each diffusion direction. Mean values (central bars) and SDs (edge bars) are plotted for each diffusion direction and VOI. ADC_exp values were estimated with scheme b_[0,2] and 24 averages per diffusion condition in both voxels. Voxel sizes were: VOI_CR = 20 × 20 × 20 mm³ and VOI’_CR = 15 × 20 × 15 mm³.

3.3. Inter-subject variability

tNAA, tCr, tCho and mIns diffusivity measures averaged across diffusion directions and subjects are reported for each session, with the associated SDs and C_V values, in Table 1 and 2, for VOI_PCC and VOI_CR and VOI’_CR, respectively. No significant differences in diffusivity measures of the metabolites across the sessions were observed (rANOVA).

Table 1.

Mean standard deviation (SD) and coefficient of variation (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).

VOIPCC		S1		S2		S3		Average
Diffusion Parameter	Metabolite	Mean (SD)	CV (%)	Mean (SD)	CV (%)	Mean (SD)	CV (%)	Mean (SD)	CV (%)
ADCexp	tNAA	0.126 (0.007)	6	0.120 (0.009)	7	0.124 (0.009)	7	0.123 (0.008)	7
(μm2/ms)	tCr	0.119 (0.010)	8	0.118 (0.013)	11	0.118 (0.010)	9	0.118 (0.011)	9
	tCho	0.106 (0.008)	8	0.106 (0.012)	12	0.107 (0.009)	9	0.106 (0.010)	9
	mIns	0.107 (0.015)	14	0.106 (0.015)	14	0.112 (0.015)	14	0.108 (0.015)	14
ADCK	tNAA	0.151 (0.011)	8	0.142 (0.014)	10	0.147 (0.014)	10	0.147 (0.013)	9
(μm2/ms)	tCr	0.141 (0.015)	11	0.139 (0.024)	18	0.135 (0.016)	12	0.140 (0.019)	13
	tCho	0.122 (0.012)	10	0.123 (0.020)	16	0.125 (0.013)	10	0.123 (0.015)	12
	mIns	0.134 (0.018)	14	0.133 (0.023)	17	0.141 (0.024)	17	0.136 (0.022)	16
K	tNAA	1.808 (0.204)	11	1.712 (0.211)	12	1.744 (0.266)	15	1.757 (0.227)	15
	tCr	1.689 (0.210)	12	1.692 (0.298)	18	1.552 (0.416)	27	1.645 (0.308)	19
	tCho	1.680 (0.486)	29	1.738 (0.262)	15	1.718 (0.291)	17	1.712 (0.346)	20
	mIns	1.533 (0.336)	22	1.522 (0.514)	34	1.817 (0.375)	21	1.624 (0.410)	25

Table 2.

Average, standard deviation (SD) and coefficient of variation (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). 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).

VOICR		S1		S2		S3		Average
Diffusion Parameter	Metabolite	Mean (SD)	CV (%)	Mean (SD)	CV (%)	Mean (SD)	CV (%)	Mean (SD)	CV (%)
ADCexp	tNAA	0.156 (0.017)	11	0.160 (0.020)	12	0.158 (0.020)	12	0.158 (0.019)	12
(μm2/ms)	tCr	0.156 (0.012)	7	0.174 (0.025)	14	0.173 (0.024)	14	0.168 (0.020)	12
	tCho	0.130 (0.015)	11	0.140 (0.025)	18	0.136 (0.023)	17	0.135 (0.023)	16
	mIns	0.126 (0.031)	22	0.156 (0.050)	32	0.130 (0.032)	24	0.137 (0.037)	27
ADCK	tNAA	0.186 (0.029)	16	0.180 (0.018)	10	0.189 (0.022)	12	0.185 (0.022)	12
(μm2/ms)	tCr	0.195 (0.025)	13	0.192 (0.031)	16	0.208 (0.026)	13	0.198 (0.031)	13
	tCho	0.162 (0.027)	16	0.146 (0.021)	15	0.156 (0.026)	17	0.155 (0.023)	15
	mIns	0.182 (0.033)	18	0.177 (0.056)	32	0.173 (0.036)	21	0.177 (0.039)	22
K	tNAA	1.308 (0.239)	18	1.238 (0.265)	21	1.190 (0.300)	25	1.246 (0.251)	20
	tCr	1.283 (0.243)	19	1.280 (0.218)	17	1.305 (0.192)	15	1.289 (0.204)	16
	tCho	1.507 (0.293)	19	1.166 (0.376)	32	1.238 (0.473)	38	1.304 (0.357)	27
	mIns	1.702 (0.425)	25	1.317 (0.230)	17	1.285 (0.453)	35	1.435 (0.346)	24
VOI’CR		S1		S2		S3		Average
Diffusion Parameter	Metabolite	Mean (SD)	CV (%)	Mean (SD)	CV (%)	Mean (SD)	CV (%)	Mean (SD)	CV (%)
	tNAA	0.185 (0.014)	8	0.179 (0.026)	15	0.163 (0.019)	12	0.176 (0.020)	11
ADCexp (μm2/ms)	tCr	0.148 (0.029)	19	0.168 (0.022)	13	0.165 (0.027)	16	0.160 (0.026)	16
	tCho	0.130 (0.013)	10	0.137 (0.026)	19	0.127 (0.012)	9	0.132 (0.017)	13

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.

Figure 8. Inter-subject variability.

ADC_exp, ADC_K and K of all metabolites from all subjects and sessions derived (A, C) in VOI_PCC (square markers) and (B, D) in VOI_CR (dot markers) averaged over all diffusion directions. Mean values (central bars) and SDs (edge bars) are displayed for each parameter.

3.4. Effect of acquisition time on intra-subject variability

Figure 9 shows the C_V of ADC_exp and K of tNAA calculated as a function of the number of averages acquired in VOI_PCC (Figure 9A and C) and in VOI_CR (Figure 9B and D), based on data resampling from all subjects and sessions. The C_V of ADC_exp of tNAA was evaluated for different acquisition schemes: b_[0,1,2], b_[0,2] and b_[0,1]. In both VOIs, C_V < 10% for ADC_exp of tNAA was observed with more than 60 and 90 averages acquired with schemes b_[0,2] and b_[0,1,2], respectively, corresponding to scanning times of 3 and 4 minutes. Notably, the C_V achieved for b_[0,2] with 160 averages (scanning time of 7 minutes) and for b_[0,1,2] with 280 total spectra (scanning time of 12 minutes) were comparable (~5% in VOI_PCC and ~7% in VOI_CR). Much higher values of C_V (> 15%) were observed for b_[0,1] in both VOIs, as expected given the low b-value utilized for this scheme. The C_Vs of K of tNAA were below 20% when 150 and 250 averages (scanning times of 7 and 11 minutes) were used in VOI_PCC and VOI_CR, respectively. Similar trends were observed for tCr and tCho (data not shown).

Figure 9. Intra-subject variability.

Coefficients of variation for ADC_exp and K of tNAA, calculated (A, C) in VOI_PCC and (B, D) in VOI_CR, from a bootstrapping subsampling procedure. The datasets from each subject and session were randomly resampled with replacement prior to averaging. Each subset consisted respectively of 10, 15, 20, 25, 30, 35 and 40 averages per diffusion condition. ADC_exp were estimated from different diffusion-weighting schemes: b_[0,1,2], b_{[0, 2]} and b_[0,1]. K were estimated using all b-values (scheme b_[0–3]).

In addition, the diffusion metrics’ variabilities as a function of the SNR estimated at b₀ are shown in Figure 4S of the Supplementary material.

3.5. 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 minutes), and reported as percentage of ADC_exp mean values (Table 3). The C_Rs 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 minutes were smaller than those for the same scheme and acquisition time of 7 minutes.

Table 3:

Repeatability coefficient (C_R) and variance (σ²) 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 σ² values reported in the table and Equation 4.

VOI	Metabolite	12 minute acquisition (scheme b[0,1,2])		7 minute acquisition (scheme b[0,2])		4 minute acquisition (scheme b[0,2])
		CR (%mean) (μm2/ms)	σ2 (x10−4) (μm4/ms2)	CR (%mean) (μm2/ms)	σ2 (x10−4) (μm4/ms2)	CR (%mean) (μm2/ms)	σ2 (x10−4) (μm4/ms2)
VOIPCC	tNAA	0.015 (12%)	0.3	0.026 (20%)	0.9	0.016 (13%)	0.3
	tCr	0.023 (20%)	0.7	0.032 (26%)	1.3	0.030 (25%)	1.1
	tCho	0.022 (20%)	0.6	0.040 (37%)	2.1	0.025 (23%)	0.8
	mIns	0.040 (37%)	2.1	0.066 (59%)	5.7	0.050 (46%)	3.3
VOICR	tNAA	0.042 (27%)	2.3	0.042 (26%)	2.3	0.045 (27%)	2.6
	tCr	0.040 (24%)	2.1	0.043 (25%)	2.4	0.052 (29%)	3.5
	tCho	0.044 (33%)	2.6	0.046 (33%)	2.7	0.050 (34%)	3.2
	mIns	0.104 (75%)	14.1	0.085 (62%)	9.4	0.101 (67%)	13.4

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 of 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 minutes (Figure 10A). With scheme b_[0,2] and a scanning time of 7 minutes, 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 minutes, a 5% difference can be detected with 7 and 31 subjects per group in VOI_PCC and in VOI_CR, respectively (Figure 10C).

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 (filled dots) and VOI_CR (empty squares) for (A) the full data-set including all b-values up to b₂ = 3300 s/mm² (scheme b_[0,1,2]), corresponding to an acquisition time of 12 minutes; (B, C) sub-sampled data-sets using b₀ = 11 s/mm² and b₂ = 3300 s/mm² (scheme b_[0,2]) and different number of averages, corresponding to acquisition times of 7 and 4 minutes, respectively.

In addition, C_R values for K of all metabolites were calculated in VOI_PCC and VOI_CR and reported as percentage of K mean values (Table 4S, Supplementary data). The power calculation for tNAA K revealed that a 10% difference can be observed with 11 and 21 subjects per group in VOI_PCC and VOI_CR, respectively.

4. Discussion

The variability of metabolite diffusion parameters measured with DW-semi-LASER across different subjects and sessions was evaluated in two brain regions of interest (PCC and CR) and with different acquisition and post-processing strategies. Our data showed that DW-MRS is feasible at 3 T with an excellent statistical power even employing a short acquisition protocol in small subject populations, providing that the proper choice of b-values, the execution with cardiac triggering, and the post-processing with peak thresholding are all taken carefully into account. The optimized acquisition and analysis pipeline allowed to obtain high quality DW-MR spectra for all subjects, sessions and VOIs, up to the highest b-value of b = 7300 s/mm² (Figure 2B, D), enabling the utilization of this method in clinically feasible acquisition times.

Nevertheless, the variance of the diffusion measures differed significantly across brain regions (despite the similar SNR at b₀), as they are affected by motion artifacts to different extents, and it also depended on the VOI size: while acquisitions in a larger VOI provide higher SNR, a smaller VOI may allow for more robust datasets and lower variability of the diffusion measures.

From power calculations we estimated that, under our experimental conditions, 5% differences in tNAA mean diffusion coefficient can be detected with a sample size of 7 and 31 subjects per group in the PCC and in the CR, respectively, with an acquisition time of 4 minutes. Remarkably, the measure of metabolite diffusion parameters was extremely robust and reproducible in the PCC, while much higher variability was observed in the CR when the VOI was located next to the ventricles.

4.1. Effect of physiological motion on the DW signal

Potential sources of bias in the evaluation of metabolite ADCs were identified, mainly attributed to the effect of physiological motion on the DW signal. Whilst artifacts induced by pure translational motion can be corrected by properly adjusting frequency and phase of the single averages before summation, small rotations or compressive motion due to cardiac and cerebrospinal fluid (CSF) pulsation may induce severe amplitude drops that are more difficult to address⁴.

To evaluate the effect of physiological motion on the DW signal, in one subject we investigated the influence of cardiac gating on tNAA SNR over time and across different directions. The mean normalized signal was higher when the acquisition was synchronized to the cardiac cycle at all b-values, while the associated standard deviations were always lower except for one condition (b = 850 s/mm², dir₂) (Figure 4C). This result highlights the importance of employing cardiac gating in DW-MRS experiments with high b-values, and the fact that the close proximity of the VOI to the ventricles may be detrimental for the DW signal. However, the assessment of the optimal trigger delay would require a more systematic investigation, since it may depend on the region of interest, DW-MRS sequence parameters, and cardiac gating device utilized. One possible limitation of using cardiac gating is that the effective T_R is slightly variable during the acquisition, thus possibly introducing another source of ADC variability. Moreover, it may differ from subject to subject, depending on the individual heart rate. Nevertheless, the intra-subject T_R fluctuations induced by irregular heart beatings were source of smaller signal amplitude variability compared to that observed without cardiac synchronization (Figure 4C).

In a previous study, the metabolite-cycling method and the use of the inherent water peak were proposed for compensation of significant signal loss³⁷. Peak thresholding represents an alternative way to overcome the issue of motion-related signal amplitude fluctuations, and becomes crucial especially at high diffusion-weighting values. This procedure avoids the risk of artificial overestimation of ADCs as a consequence of underestimation of the DW signal in the presence of significant drops in the signal amplitude due to non-translational motion. Although the removal of some of the spectra before averaging could introduce a relatively small artificial increase of SNR (see Supplementary material S1), as expected, in both VOIs the variability of ADCs across subjects and sessions was lower when peak thresholding was applied (Figure 6). Notably, the effect of peak thresholding was more pronounced in VOI_CR than VOI_PCC, suggesting that motion affects the diffusion-sensitized signal in the parietal WM more than in the PCC. In addition, the variability of the ADCs was much higher in two of the three DW directions (dir₁ and dir₂) in VOI_CR (Figure 6) indicating that motion is associated preferentially with specific directions, while in VOI_PCC there was no significant difference among directions. Interestingly, the ADC variability in the smaller voxel VOI’_CR did not depend on the diffusion direction (Figure 7), and, despite the intrinsic lower SNR related to voxel size, the ADC variability in VOI’_CR was lower than that in VOI_CR in dir₁ and dir₂, suggesting that in those directions the effect of motion is dominant with respect to noise, thus affecting to a higher extent the bigger VOI. In addition, the average number of rejected spectra after peak thresholding was smaller in VOI’_CR than in VOI_CR, further corroborating this hypothesis.

4.2. Metabolite kurtosis analysis

Diffusion-attenuation curves were fitted to mono-exponential functions up to b₂ = 3300 s/mm² and to a kurtosis model (Equation 2) up to b₃ = 7300 s/mm². The χ² goodness-of-fit test revealed that the mono-exponential fit was not able to explain 30% of the metabolite signal decays up to b₃, whereas the kurtosis approach was found to be more accurate (the null hypothesis was accepted for all fits with p > 0.9). The non mono-exponential behavior of the signal decay at high b-values can 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 all these processes³⁸. Sampling DW-MRS data at high b-values is necessary to derive information on tissue morphology at the microscopic scale^6,39. Although reaching ultra-high b-values > 15,000 s/mm² 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 to capture deviations from mono-exponentiality using the kurtosis approach, with a reasonably high b-value of 7300 s/mm² and a relatively short acquisition protocol. Significantly higher K mean values in GM compared to WM for all metabolites confirmed previous results suggesting greater diffusional heterogeneity in GM⁴⁰. Coefficients of variation for K were much higher than those obtained for the ADCs.

4.3. Inter-subject and intra-subject variability

The inter-subject variability calculated from full data-sets 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). Instead, 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 sub-sampling of the data. The procedure was repeated for different number of averages per diffusion-weighted 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 minutes (Figure 9A, B). With scheme b_[0,1,2], the same variability could be reached with at least 90 averages, indicating that acquiring spectra at low b-value of 850 s/mm² 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. Figure 4S (Supplementary material) shows the behavior of the diffusion metrics’ variabilities as a function of the SNR estimated at b₀. These plots report the non-diffusion-weighted 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 diffusion-weighted signal detected in the region of interest, the SNR at b₀ cannot be directly linked to the robustness of the measurements, and these results should be adapted with caution to different experimental conditions.

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 to healthy subjects^41,42. Wood et al. reported differences of almost 20% in the tNAA diffusivity in the corpus callosum of patients with multiple sclerosis¹³, while differences in tCho and tCr ADCs of more than 15% were observed in systemic lupus erythematosus¹¹. Our results on ADC_exp repeatability (Table 3) suggest that for investigating 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 minutes, 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.

5. Conclusions

We 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 post-processing (peak thresholding in addition to standard phase and frequency corrections) are all 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 white matter diseases, while the diffusion of tCho and tCr represent potential markers of inflammation and glial cells alterations. DW-semi-LASER may allow the exploration of microscopic cellular alterations in different pathological conditions, providing useful insights on 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.

Abbreviations:

ADC

apparent diffusion coefficient

C_R

coefficient of repeatability

CR

corona radiata

CRLB

Cramér-Rao lower bound

C_V

coefficient of variation

δ

diffusion gradient duration

DW

diffusion-weighted

mIns

myo-inositol

PCC

posterior cingulate cortex

SD

standard deviation

SNR

signal-to-noise ratio

tCho

choline containing compounds

tCr

creatine + phosphocreatine

t_d

diffusion time

tNAA

N-acetylaspartate + N-acetylaspartylglutamate

VOI

volume of interest