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. Author manuscript; available in PMC: 2013 Apr 1.
Published in final edited form as: Magn Reson Med. 2011 Jul 11;67(4):891–897. doi: 10.1002/mrm.23080

Measurement of transverse relaxation times of J-coupled metabolites in the human visual cortex at 4 T

Dinesh Kumar Deelchand 1, Pierre-Gilles Henry 1, Kâmil Uğurbil 1, Małgorzata Marjańska 1
PMCID: PMC3214249  NIHMSID: NIHMS303956  PMID: 21748799

Abstract

Accurate quantification of 1H NMR spectra often requires knowledge of the relaxation times in order to correct for signal losses due to relaxation and saturation. In human brain, T2 values for singlets such as N-acetylaspartate (NAA), creatine, and choline have been reported, but few T2 values are available for J-coupled spin systems. The purpose of the present study was to measure the T2 relaxation times of J-coupled metabolites in the human occipital lobe using the LASER sequence. Spectra were acquired at multiple echo times and were analyzed with an LCModel using basis sets simulated at each echo time. Separate basis spectra were used for resonances of protons belonging to the same molecule but having very different T2 values (e.g. two separate basis spectra were used for the singlet and multiplet signal in NAA). The T2 values for the NAA multiplet (149 ± 12 ms), glutamate (125 ± 10 ms), myo-inositol (139 ± 20 ms) and taurine (196 ± 28 ms) were successfully measured in the human visual cortex at 4 T. These measured T2 relaxation times have enabled the accurate and absolute quantification of cerebral metabolites at longer echo times.

Keywords: T2, LASER, LCModel, separated basis set, glutamate, myo-inositol, taurine

Introduction

The single shot fully adiabatic spin-echo localization by adiabatic selective refocusing (LASER) (1) sequence has been used for in vivo 1H NMR spectroscopy (2–4) due to its favorable characteristics. In LASER, 3D localization is performed using three pairs of adiabatic full-passage (AFP) pulses that produce sharp edges for the volume-of-interest (VOI), thereby maximizing the signal within the VOI without necessitating the use of additional outer volume suppression. Furthermore, AFP pulses are robust with respect to RF field inhomogeneity, making them useful for applications requiring surface coils. Furthermore, the available peak RF power, which should be large enough in order to minimize the displacement of the voxel for different chemical shifts, does not limit the bandwidth of AFP pulses.

One of the drawbacks of LASER when compared to other pulse sequences, such as stimulated echo acquisition mode (STEAM) and point resolved spectroscopy (PRESS), is the typically longer echo time (TE) that is required due to the presence of six AFP pulses. In LASER, often TE ≥ 50 ms in human studies. In human brain studies at high magnetic fields such as 4 T, longer RF pulses are required due to the lower available γB1 thereby necessitating longer TE. At long TE, the contribution from the macromolecule (MM) baseline is smaller while information from J-coupled compounds is still retained, although the transverse relaxation time (T2) becomes shorter with increasing magnetic field strength (5,6).

To obtain absolute concentrations of metabolites using 1H LASER spectra measured in human brain with moderately long TE, two pieces of information are required: the T2 relaxation times (in order to correct for signal losses due to relaxation) and knowledge of the J-modulation for the multiplet resonances. So far, values for the T2 relaxation times of metabolites have been reported in human brain mostly for the singlet resonances of N-acetylaspartate (NAA), creatine + phosphocreatine (Cr + PCr = tCr) and total choline compounds (tCho) since these metabolites are readily measured for all TE (5,7–12). On the other hand, measurements of T2 for J-coupled resonances are more difficult since their signal intensity decreases with increasing TE (similar to the singlet resonances) in addition to undergoing changes in their spectral pattern due to J-modulation. In addition, these J-coupled metabolites overlap with other resonances thus making their analysis more complex compared to singlet resonances. . Furthermore, using the peak integral as a way to analyze the multiplets is not sufficient in this case. For reliable T2 measurements, the signal changes due to J-modulation need to be taken into account by simulating the spectral patterns at each TE. Recently, a few T2 relaxation time values have become available for J-coupled spin systems, such as the myo-inositol and aspartate multiplet of NAA at 1.5 T (13) and glutamate at 3 T (14,15) in the human brain. Using CP-PRESS and a simulated basis set (13), one group has reported that T2 can be different for non-similar protons within the same molecule: the T2 of the aspartate multiplet of NAA was shorter than its methyl singlet resonance in the human parieto-occipital lobe at 1.5 T.

Recently, T2 relaxation times of many J-coupled cerebral metabolites in the rat at 9.4 T were obtained using simulated echo time (TE) specific basis sets and LCModel analysis (16). The reported T2 values ranged from 89 ms for glutamate to 202 ms for NAA singlet. Myo-inositol was found to have the longest T2 value of 148 ms for coupled spin systems.The aim of the present study was to measure the T2 relaxation times of J-coupled metabolites in the human visual cortex at 4 T. To account for changes in the spectral pattern of J-coupled metabolites with increasing TE, the basis spectra were simulated using a density matrix formalism. Spectra were fitted and quantified using LCModel and the T2 values were estimated based on the decay curves of the fitted signals using a mono-exponential regression. The absolute quantification of the 1H spectra at longer TE with LCModel incorporating the measured T2 values was also performed.

Materials and Methods

Phantom

The agreement of density-matrix simulated basis set with in vitro measurement was tested using a myo-inositol solution (200 mM, pH = 7.2). 1H LASER NMR spectra were measured at several echo times (similar to those used in the in vivo study) as described below.

Subjects and MRS Measurements

Six healthy subjects (37 ± 17 years old) participated in this study after giving informed consent according to procedures approved by the Institutional Review Board at the University of Minnesota. All experiments were performed using a 4-T/90-cm magnet (Oxford Magnet Technology, Oxford, UK) interfaced to a UNITY INOVA console (Varian, Palo Alto, CA, USA) and equipped with an actively-shielded Siemens Sonata gradient system (Siemens, Erlangen, Germany) that is capable of reaching 40 mT/m in 400 µs. The subjects were placed in a supine position with their head above a 1H quadrature transceiver surface coil (7 cm diameter) (17). Transverse and sagittal gradient-echo images (repetition time, TR = 70 ms, TE = 4 ms, slice thickness = 5 mm, FOV = 40×40 cm2 and matrix size = 256×128) were acquired to select a VOI of 27 ml (3×3×3 cm3) in the visual cortex. Shimming was performed using an adiabatic version of FAST(EST)MAP (18) that resulted in a water linewidth at half height of 8 to 11 Hz.

1H NMR spectra were acquired with a LASER sequence (1) using a 4 ms nonselective adiabatic half-passage (AHP) pulse followed by three pairs of AFP pulses (4 ms duration, HS1 modulation, R = 20) for 3D-localization. In the LASER sequence, TE was defined as the delay from the end of the AHP pulse to the start of signal acquisition and was evenly distributed in the delays around the six AFP pulses. Water suppression was achieved with VAPOR (19) using eight RF pulses with variable pulse power and optimized timing. Spectra were acquired with a repetition time of 4 s and with 3 k of acquisition points. Each free induction decay (FID) was individually saved for B0 frequency correction before summation. A non-suppressed water spectrum was acquired for eddy current correction and scaling.

For the T2 measurements, spectra were collected using the following seven TE times: 53, 75, 100, 150, 200, 300 and 400 ms. For TE ≥ 150 ms, 128 averages were recorded in order to increase the signal-to-noise for the J-coupled multiplets, while 64 averages were obtained for the first three echo times. MM spectra (64 averages, TR = 2 s, inversion time, TI = 0.67 s, VOI = 27 ml, 5 ms duration HS1 (R = 10) inversion pulse) were also acquired using the inversion-recovery technique (metabolite-nulled) for all TE’s except for TE = 300 and 400 ms where the MM signal was too weak to be observed.

Spectral Processing and Fitting

In vivo spectra were analyzed using LCModel version 6.1-4A (Stephen Provencher Inc., Oakville, ON, Canada). The basis spectra for each detectable brain metabolite were simulated using home-written programs based on the density matrix formalism (20) in Matlab (The MathWorks Inc., Natick, MA, USA) using the measured and published chemical shifts and J-coupling values (21). The spin evolution during the adiabatic RF pulses, as used in vivo, was also taken into account in the simulation. The model basis set consisted of 19 brain metabolites: alanine (Ala), ascorbate (Asc), aspartate (Asp), Cr, γ-aminobutyric acid (GABA), glucose (Glc), glutamate (Glu), glutamine (Gln), glycerophosphorylcholine (GPC), glutathione (GSH), lactate (Lac), myo-inositol (Ins), NAA, N-acetylaspartylglutamate (NAAG), PCr, phosphorylcholine (PCho), phosphorylethanolamine (PE), scyllo-inositol (sIns), and taurine (Tau). No baseline correction, zero-filling or apodization functions were applied to the in vivo data prior to analysis.

The measured MM spectrum at each TE was included in the LASER basis set, except for TE = 300 and 400 ms where the MM contribution was minimal. Due to the shorter T1 relaxation time of the methylene protons of the tCr peak at 3.93 ppm (22), this resonance was present in the measured metabolite-nulled MM spectra and was removed in the time domain using the HSVD Lanczos algorithm from MRUI 99.2b (23). In addition, unsuppressed water signal obtained at different TE’s (i.e. 53, 75, 100, 150, 200, 300 and 400 ms) was used to determine the tissue and cerebrospinal fluid (CSF) contributions in the defined voxel, as previously described (24). The average CSF tissue fraction for all subjects in the studied VOI was 15 ± 4% (N = 6).

T2 Analysis

The T2 relaxation times of metabolites were determined by fitting the relative concentrations obtained from the LCModel analysis as a function of TE using a two parameter, mono-exponential decay function with a non-linear least square algorithm. For the water T2 in brain tissue, a bi-exponential fit was utilized to account for the contribution of CSF and brain tissue. The standard deviation (SD) was calculated based on the goodness of the non-linear fit.

Results and Discussion

1H LASER Spectral Pattern

An excellent agreement was observed between measured and simulated spectral patterns for myo-inositol at different echo times (Figure 1) suggesting that appropriate prior knowledge was used to generate the basis set.

Figure 1.

Figure 1

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Measured in vitro NMR spectra with LASER sequence [TR = 10 s and number of scans (ns) = 4] and density-matrix simulated NMR spectra for myo-inositol at different echo times. Due to the broader bandwidth of the water suppression pulse used in the phantom measurement, the intensity of multiplet at 4.06 ppm was slightly lower compared to the simulated spectra.

Representative LASER proton spectra acquired from one of the volunteers demonstrated the change in peak intensities and patterns as a function of TE (Figure 2A). The singlet resonances became smaller with increasing echo time whereas the multiplet resonances not only became smaller but also underwent J-modulation. The latter was particularly noticeable for the NAA multiplet (CH2 group, denoted as mNAA) resonating in the 2.49 to 2.67 ppm region in the measured in vivo spectra. The change in spectral pattern of the J-coupled mNAA with different echo times was consistent with the NAA multiplet pattern obtained from simulations (Figure 2B).

Figure 2.

Figure 2

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(A) Series of 1H LASER spectra [TR = 4 s, VOI = 27 ml with ns = 64 for TE < 150 ms and ns = 128 for TE ≥ 150 ms] acquired in vivo at seven echo times from the human brain at 4 T. The grey box focuses on the CH2 group of NAA. (B) The simulated spectra for the CH2 group of the NAA multiplet which are line-broadened to the linewidth observed in the in vivo data (the simulated spectra are not to scale to the in vivo data). (C) The 1H LASER MM spectra measured in vivo using inversion-recovery [scaled by a factor of 10, TR = 2 s, inversion time, TI = 0.67 s, VOI = 27 ml, ns = 256] from all subjects at different echo times.

The summed MM spectra acquired using the metabolite-nulled technique from all subjects at five echo times (Figure 2C) show the existence of major MM resonances at short echo times, although their peak amplitudes were small compared to the normal spectrum. Doubling the TE from 53 ms to 100 ms resulted in a decrease of signal intensity for most of the peaks while the resonances at 0.91 ppm and 1.39 ppm were inverted due to J-modulation. It has previously been reported that the 0.91 ppm and 1.39 ppm resonances are coupled to the 2.05 ppm and 4.32 ppm resonances respectively with a J coupling constant of 7.3 Hz (25). At a long TE of 200 ms, the MM contribution was negligible in comparison with the metabolite signals.

Spectral Fitting using LCModel

The LCModel fit using a simulated standard basis set (one model spectrum per metabolite) for an in vivo spectrum acquired at TE = 75 ms (Figure 3A) showed a large residue in the region of the spectrum where the NAA multiplet resonates. This was due to an overestimation of the NAA concentration based on the singlet resonance observed in the fitted spectrum. The simulated spectrum of NAA assumes that all proton groups have similar T2 relaxation times. However the high residual of the mNAA resonance suggests that in order to obtain a good fit without any residual, the mNAA resonance needed to have a smaller intensity because the T2 of mNAA is shorter than the T2 of the CH3 group (denoted as sNAA). Similar arguments can be made for the tCr resonances since small residuals from the methyl and methylene protons were also visible at 3.03 ppm and 3.93 ppm respectively.

Figure 3.

Figure 3

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LCModel fit of a representative in vivo LASER spectrum obtained from a 27 mL voxel positioned in the occipital lobe of a single subject [TR = 4 s, TE = 75 ms, ns = 128] using (A) the standard basis set and (B) the separated basis set. From top to bottom: the in vivo spectrum, the fit, the residual left after subtracting the reconstructed spectrum from the original spectrum, and the decomposition of the spectrum into NAA, Cr, PCr, NAAG, glutamate and myo-inositol using the standard basis set and with sNAA, mNAA, NAAG, Cr-CH3, Cr-CH2, PCr-CH3, PCr-CH2, glutamate and myo-inositol using the separated basis set. The multiplet of NAA was overestimated when using the standard basis set as shown by the residual. With the separated basis set, the residual shows a nearly flat spectrum with minimal signal present.

Higher residuals from the LCModel analysis were observed with increasing echo time due to the larger T2 discrepancy between the different moieties (data not shown). Increasing TE from 53 to 400 ms, the residual became progressively higher, and four resonances could be easily assigned to sNAA at 2.01 ppm, mNAA between 2.3 and 2.6 ppm, methyl protons of tCr at 3.03 ppm and to the methylene protons of tCr at 3.93 ppm. These results indicated that fitting the spectrum in the usual way would affect the quantification at TE > 53 ms. On the other hand, no major resonances were observed at TE = 53 ms in this study. This was consistent with a previous study that did not report any residual issues when quantifying the LASER spectra (26) using a linear component (LC) modeling with one basis spectrum for each metabolite at TE = 46 ms and at 4 T. At the shorter T2 relaxation times found at higher magnetic fields, the above observations imply that even spectra obtained using a relatively short TE of 40 ms may not be perfectly fitted using the standard basis sets due to differences in relaxation of the different moieties.

One way to obtain reliable quantification using LC modeling without unexpected and erroneous results is to separate the moieties that have different relaxation values either by comparison with simulation or by splitting the spectrum measured from a phantom. Although phantom data will exhibit the same J-evolution as found under in vivo conditions, the relaxation times between different moieties will be very different from in vivo due to differences in environmental conditions of the metabolites. Hence the spectral quantification of the in vivo data might be unreliable if T2 relaxation times measured on phantoms are utilized in the fitting procedure.

Resonances in the residual at TE > 53 ms (data not shown) suggest that only three metabolites NAA, Cr and PCr, need to be separated into different moieties at 4 T, which was done in this study when simulating the basis spectra. Previously, the separation of NAA into sNAA and mNAA has been reported in human at 1.5 T (13) and in rat at 9.4 T (16) studies. In addition, tCr resonances at 3.03 ppm and 3.93 ppm were separated in the rat study at 9.4 T (16). Therefore in the present study, a new basis set was created (the separated basis set) that consisted of the separated and independent spectra for the singlet (CH3 group) and multiplet (CH2 group) of NAA and the singlet CH3 and CH2 groups of tCr. All other brain metabolites were taken into account using one spectrum. This was done in order to minimize the Cramér-Rao Lower bounds (CRLBs) uncertainty, which would inevitably increase if all metabolites were separated to provide the most flexibility and also to minimize bias in the quantification of the low concentration metabolites, such as the multiplets of tCho and NAAG.

Fitting the same spectrum (TE = 75 ms) used in Figure 3A with the separated basis set resulted in a smaller residual (Figure 3B). In addition, the root mean square (RMS) of the residuals was found to decrease by nearly 50% compared to the RMS obtained with the standard basis set except at TE = 53 ms where there was no significant observed difference (P = 0.6). Furthermore, the mean RMS of the residuals obtained from all the subjects with the separated basis set was lower and less than 5% compared to the RMS of the residuals found using the standard basis set at all TE (data not shown). For the standard basis set, higher residuals were obtained using the separated basis set for all spectra with TE ≥ 75 ms (P < 0.002).

It should be noted that another possible method in analyzing the LASER results is to include prior knowledge of the measured T2 values in the basis spectra. While there only is a single basis spectrum for each metabolite, the amplitudes of the resonances change as a function of TE. As such, a new T2-weighted basis set could be formed that consists of 19 basis spectra where each metabolite is taken account using only one basis spectrum.

Measured T2 Relaxation Times

Arbitrary concentrations obtained from fitting the spectra with the separated basis set were used to determine the T2 values (Table 1). T2 exponential fits for various resonances are illustrated in Figure 4. A T2 relaxation time of 264 ± 9 ms (R2 correlation of 0.99) was determined for the NAA singlet. This T2 value was similar to that reported with PRESS [T2 = 239 ± 22 ms, (5)] while being slightly longer than those reported with STEAM [T2 = 185 ms, (10)] or with spin-echo spectroscopic imaging [T2 = 230 ms, (11)] at a similar field strength.

Table 1.

Measured intrinsic T2 values (mean ± SD) of metabolites from six healthy subjects in the visual cortex at 4 T using the LASER sequence. For all singlet resonances, fits with R2 ≥ 0.97 were obtained whereas R2 ≥ 0.91 for the multiplet resonances.

Compound Group T2 (ms)
Singlets NAA 2CH3 264 ± 9
tCr N(CH3) 176 ± 11
tCr 2CH2 124 ± 9
tCho entire molecule 273 ± 54
J-coupled NAA multiplet 3CH2 149 ± 12
Glu entire molecule 125 ± 10
Ins entire molecule 139 ± 20
Tau entire molecule 196 ± 28
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Figure 4.

Figure 4

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Individual exponential fits (represented by the solid decaying lines) of the experimentally measured data for (A) the NAA singlet and multiplet, (B) the methyl and methylene protons of tCr and (C) glutamate and myo-inositol. The amplitude of all data sets (obtained using the separated basis set) was normalized by setting the first echo time point to unity, except for the multiplets of NAA and glutamate where the first point was set to 0.5. Error bars represent the SD between subjects.

T2 for the CH2 protons of NAA was nearly 75% shorter than the T2 found for the NAA singlet (Table 1). It was possible to measure this value since the multiplet was clearly observed even at long TE using LASER (Figure 2A). Using the STEAM sequence, on the other hand, it has been previously demonstrated that the signal of mNAA can only be observed at short echo times (< 100 ms) in the human brain at either 4 T (10) or 7 T (27), which is consistent with these resonances undergoing rapid J-modulation. The difference in relaxation times between the CH2 and CH3 protons within the NAA molecule was previously reported in the parieto-occipital lobe in humans at 1.5 T (13). In the latter case, the T2 of the NAA multiplet was similar [147 ± 32 ms] to that measured in this current study.

Separating the CH3 and CH2 groups of the tCr singlets enabled the accurate measurement of their respective relaxation times using the LCModel (Figure 3). The T2 of the tCr peak at 3.93 ppm was found to be shorter than the 3.03 ppm singlet: 124 ± 9 ms versus 176 ± 11 ms respectively (Table 1); both values were consistent with previous human and animal studies (12,22,28). The T2 value of tCr-CH3 measured in the current study was within the range of T2 values reported at 4 T (i.e. 130 – 150 ms) using PRESS (5), STEAM (10,29) and spin-echo spectroscopic imaging sequences (30).

LASER also allowed for the measurement of the T2 values for other strongly J-coupled metabolites. For example, the T2 value for all protons in glutamate was 125 ± 10 ms. For strongly coupled metabolites such as glutamate or myo-inositol, it can be argued, based on their metabolite levels obtained at TE = 53 ms and on their minimal residuals observed at all TE, that the different proton groups within these molecules have identical or very similar T2 values. This is indeed consistent with two previous studies performed at 3 T that showed that the T2’s for all protons in glutamate are the same (14,15). The T2 values of taurine and myo-inositol resonances were also determined (Table 1).

The relaxation mechanisms of coupled spin systems in vivo have not been extensively studied but they are potentially similar to relaxation mechanisms in non-viscous liquids which have been widely studied (31).

Absolute Quantification of Long TE LASER Spectrum

Knowledge of the T2 relaxation times in turn allowed for the absolute quantification of the metabolites as shown for the 1H LASER spectra acquired at TE = 53 ms (Table 2). These absolute concentrations were determined using the separated basis set after correcting for T2 relaxation, water tissue and CSF contributions in the selected voxel and using the unsuppressed water signal as an internal concentration reference. The measured concentrations were in agreement with previously published data (32). The CRLBs obtained for the dominant metabolites in the LASER spectrum (e.g. NAA, tCr, tCho, Ins and Glu) were found to be below 5% and were comparable to the CRLBs obtained with a STEAM sequence in a similar region of the brain at the same field strength (32–34). The CRLBs for the other metabolites were less than 20% except for lactate and PE.

Table 2.

Comparison of cerebral metabolite absolute concentrations measured using the LASER sequence at echo times of 53 ms and 75 ms (with the separated basis set) at 4 T. The T2 relaxation times for GABA, GSH, sIns, Lac, Asp and PE were assumed to be similar to the T2 value of Ins. The T2 of NAAG and NAA and the T2 of glutamate and glutamine were assumed to be similar respectively. The data is reported as the mean ± standard deviation. The absolute metabolite concentration is not reported for metabolites with a CRLB > 50%.

LASER (TE = 53 ms) LASER (TE = 75 ms)
Metabolites Conc.
(µmol/g) 		CRLB
(%) 		Conc.
(µmol/g) 		CRLB
(%)
Asp 3.2 ± 0.3 14 1.9 ± 0.3 17
GABA - - 0.8 ± 0.1 24
Glu 11.3 ± 1.1 2 11.5 ± 0.8 4
Gln 2.4 ± 0.9 12 2.3 ± 0.3 17
GSH 0.9 ± 0.1 12 - -
Glx 13.7 ± 1.1 2 13.8 ± 0.7 5
Lac 0.6 ± 0.3 29 0.7 ± 0.1 15
Ins 6.6 ± 0.6 2 6.6 ± 0.6 3
NAA 12.5 ± 1.7 2 11.2 ± 1.3 2
NAAG 0.9 ± 0.1 15 0.3 ± 0.2 47
PE 2.9 ± 0.7 23 1.4 ± 0.4 29
sIns 0.4 ± 0.2 12 0.3 ± 0.2 16
Tau 1.2 ± 0.4 14 1.1 ± 0.4 17
tCho 1.5 ± 0.3 2 1.6 ± 0.4 3
tCr 8.7 ± 0.3 1 8.6 ± 0.3 1
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Absolute metabolite concentrations obtained with LASER at TE = 75 ms demonstrated that it is possible to obtain reliable concentrations at long TE (Table 2) although the CRLBs were larger, particularly for the J-coupled metabolites due to loss of signal.

Analysis of the LASER spectra at TE = 75 ms using the T2-weighted basis set resulted in similar CRLBs values for all metabolites measured with the separated basis set (Table 2), with the exception of Asp, GSH and NAAG, where lower CRLBs were obtained (data not shown).

The impact of the uncertainty in T2 values on the measured metabolite concentrations was investigated by varying the T2 values obtained in this study by either ±10% or ±25%. The changes to the calculated absolute metabolite concentrations were within 8% of the measured concentrations (Table 2) when a maximum deviation of ±25% was applied to the T2 values (data not shown). This finding might explain why the metabolite concentrations reported in a previous study using LASER quantification at 4 T (26) were in agreement with the literature values. In that study, in vitro measured basis sets that were corrected for T1 and T2 using the published values (averaged from different pulse sequences) were used to fit the data.

Conclusion

The T2 relaxation times of multiple J-coupled metabolites were measured in the human occipital lobe using the LASER sequence at 4 T. The data was analyzed by using simulated basis sets at each echo time and using separate basis spectra for protons belonging to the same molecule but having different T2 relaxation times. Knowledge of the T2 relaxation times in turn allowed for the absolute quantification of cerebral metabolites from the LASER 1H spectra even at relatively long echo times (> 50 ms).

Acknowledgements

This work was supported by funding from BTRC P41 RR008079 and NCC P30 NS057091. We thank Dr. Jamie Walls for reading the manuscript.

Abbreviations

AFP

adiabatic full-passage

AHP

adiabatic half-passage

CRLBs

Cramér-Rao Lower bounds

LC

linear component

mNAA

NAA multiplet

NAA

N-acetylaspartate

MM

macromolecule

tCr

creatine + phosphocreatine

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