Phosphorus transversal relaxation times and metabolite concentrations in the human brain at 9.4 T

A method to estimate phosphorus ( 31 P) transversal relaxation times (T 2 s) of coupled spin systems is demonstrated. Additionally, intracellular and extracellular pH and relaxation-corrected metabolite concentrations are reported. Echo time (TE) series of 31 P metabolite spectra were acquired using stimulated echo acquisition mode (STEAM) localization. Spectra were fitted using LCModel with accurately modeled Versatile Simulation, Pulses and Analysis (VeSPA) basis sets accounting for J-evolution of the coupled spin systems. T 2 s were estimated by fitting a single exponential two-parameter model across the TE series. Fitted inorganic phosphate frequencies were used to calculate pH, and estimated relaxation times were used to determine the relaxation-corrected brain metabolite concentrations on an assumption of 3 mM γ -ATP. The method was demonstrated in healthy human brain at a field strength of 9.4 T. T 2 times of ATP and nicotinamide adenine dinucleotide (NAD) were shortest between 8 and 20 ms, followed by T 2 s of inorganic phosphate between 25 and 50 ms, and phosphocreatine with a T 2 of 100 ms. Phosphomonoesters and phosphodiesters had the longest T 2 s of about 130 ms. The measured T 2 s are comparable with literature values and fit in a decreasing trend with increasing field strengths. Calculated pHs and metabolite concentrations are also comparable with literature values. are approximated as a linear combination of model spectra. 20 Spectral simulation of the model performed with Versatile Simulation, Pulses and Analysis (VeSPA) 21 or Magnetic Resonance Spectrum Simulator (MARSS), for each and J-evolution. approach, selective pulses or homonuclear decoupling needed in the acquisition 31 T expected be very at an ultrahigh field (UHF) and are typ-ically by observing the exponential signal decay in TE series a localization sequence that allows short TEs or in lead to specific rate (SAR)-related at

To date, 31 P-MRS is rarely used for clinical applications because of the low intrinsic sensitivity of 31 P, and therefore its low spatial and temporal resolution. Because the signal-to-noise ratio (SNR) is dependent on the static magnetic field B 0 , a sensitivity gain and spectral improvement can be obtained at higher field strengths allowing shorter acquisition times and higher spatial resolution. 8 In addition to clinically acceptable measurement times, the comparison of MRS results between patients, different scanners, or acquisition methods is mandatory for the diagnosis of diseases. Such a comparison requires a reliable quantitative evaluation of metabolite concentrations and accurate knowledge about relaxation times is a prerequisite to achieving this. Relaxation times may also be of interest for characterizing molecular dynamics. 9 For setting up measurement protocols and for optimizing respective pulse sequences concerning repetition time (TR), echo time (TE), and free precession times, knowledge of relaxation times is essential as well. Because relaxation times are field strength dependent, they need to be measured at every field strength. 10,11 Several studies show an increase in longitudinal relaxation time (T 1 ) and decrease in transversal relaxation time (T 2 ) in the human brain for protons with increasing field strengths. 1,10,12 By contrast, a decrease in T 1 with increasing field strength was observed for 31 P metabolites in the human brain. 8,9 For human in vivo T 2 s, no coherent trend with magnetic field strength can be extracted from the literature. 11,[13][14][15][16] In particular, reports on T 2 s of adenosine triphosphate (ATP) vary largely. 11,[13][14][15] These discrepancies originate from different acquisition and processing techniques. In some of the studies, the homonuclear scalar coupling of the ATP molecule, which leads to TE-dependent phase and amplitude modulations of the signals, was not considered. 13,17,18 Therefore, these studies report underestimated T 2 s. 14,15 Adjusted acquisition methods using selective refocusing pulses or homonuclear decoupling allow the accurate determination of T 2 s. 11,13,19 None of the studies measuring 31 P T 2 s in the human brain used the approach to consider scalar coupling in the fit procedure. In a frequency domain-fitting approach like LCModel, spectra are approximated as a linear combination of model spectra. 20 Spectral simulation of the model spectra, for instance, performed with Versatile Simulation, Pulses and Analysis (VeSPA) 21 or Magnetic Resonance Spectrum Simulator (MARSS), 22 are specific for each sequence and timing and fully consider J-evolution. Using this approach, no selective refocusing pulses or homonuclear decoupling are needed in the acquisition sequence. Because 31 P T 2 s are expected to be very short at an ultrahigh field (UHF) strength and are typically estimated by observing the exponential signal decay in TE series spectra, a localization sequence that allows short TEs should be used.
Frequency-selective refocusing or homonuclear decoupling used in previous studies lead to specific absorption rate (SAR)-related concerns at UHF strength. 11,13,16,18,19,23 The primary goal of this study was to demonstrate a method to measure 31 P T 2 s of J-coupled metabolites without frequency-selective refocusing or homonuclear decoupling, as was performed in previous studies. 24,25 Therefore, TE series spectra over a broad frequency range were acquired with a stimulated echo acquisition mode (STEAM) localization sequence optimized in a previous study 24 entailing a high SNR per unit of time, which is a critical factor for T 2 measurements. J-modulation of the 31 P metabolites was then considered in the fitting routine using VeSPA in combination with LCModel. 20,21 This approach to estimate 31 P T 2 s was demonstrated in the human brain at a field strength of 9.4 T. Additionally, pH values as well as estimated tissue concentrations of 31 P metabolites after applying relaxation corrections are reported. T 2 values and metabolite concentrations are compared with literature data, and factors affecting their accuracy and comparability are discussed.

| Study design
All data were acquired at a 9.4-T whole-body MRI scanner (Siemens, Erlangen, Germany) using a home-built double-tuned 20-loop 31 P/ 1 H head array. 26 To increase B 1 + for 31 P single-voxel spectroscopy in the occipital lobe, the entire RF power was applied only to the three bottom surface coil transceiver elements using an unbalanced three-way Wilkinson power splitter, as described recently. 24 All measurements with volunteers were in accordance with the local research ethics guidelines, and written informed consent was obtained from all volunteers before the examination. Twelve healthy volunteers participated in the study (seven females, five males, age 27 ± 3 years) and all data were included in the data processing. The total scan time per volunteer was 100 min and the measurement was well tolerated by all volunteers.

| Data acquisition
High-resolution 2D fast low angle shot (FLASH) images (field of view: 192 x 192 mm 2 , in-plane resolution: 0.6 x 0.6 mm 2 , slice thickness: 3 mm, 25 slices, TE/TR 9/378 ms, flip angle: 25 , acquisition time: 2.33 min) were acquired in the sagittal and transversal directions to guide voxel placement in the occipital cortex. Before the spectroscopy measurements, static magnetic B 0 shimming was performed using the Siemens second-order shimming method.
For spatial localization, a STEAM 25 sequence (TM/TR 5/5000 ms) optimized for phosphorus spectroscopy in the human brain at 9.4 T was used, similar as recently described. 24 Hamming-windowed sinc excitation pulses with a flip angle of about 90 , and a pulse duration of 1.5 ms, were used for slice selection. The transmit field was estimated from phantom B 1 + maps, as described in Avdievich et al. 26  For all spectra, a voxel of 5 x 5 x 5 cm 3 was placed in the occipital lobe. For each TE, spectra with 120 averages were acquired with 4096 complex sampling points, an acquisition bandwidth of 10 kHz, and a measurement time of 10 min. The first four averages were taken as preparation scans and omitted from the analysis. The remaining scans were assumed to be at steady-state magnetization.

| Data preprocessing
Raw data were reconstructed with an in-house written MATLAB software. The processing steps comprise averaging, singular value decomposition coil combination based on PCr 29 (weights were calculated from filtered data and applied to nonfiltered data), zero-order phase correction, and aligning PCr to 0 ppm. The zero-order phase was calculated by maximizing the amplitude as well as the integral of the real part of PCr in the frequency domain and calculating its mean. No first-order phase correction was needed.
The full width at half maximum (FWHM) was calculated by increasing the sampling rate by a factor of 20 and finding the maximum peak height of each metabolite in a search area of 0.2 ppm around literature values for each metabolite peak frequency as well as the FWHM using an in-house written MATLAB function.
The SNR was calculated as the ratio between the metabolite peak heights and the spectral noise between +15 and +30 ppm in the real part of the spectrum.

| Spectral fitting
Spectra were fitted with LCModel (version 6.3-1 L) 20 using basis sets simulated in VeSPA (v. 1.0.0). 21 In VeSPA, a density matrix-based spectral simulation employing RF pulse waveforms in agreement with experimentally used realistic shapes and timings was performed for each metabolite and all of the TEs specified. The following metabolites were simulated: phosphoethanolamine (PE) and phosphocholine (PC), extracellular and intracellular free inorganic phosphate (P i ext and P i int , respectively), glycerophosphoethanolamine (GPE) and glycerophosphocholine (GPC), phosphocreatine (PCr), γand α-adenosine triphosphate (γ-ATP and α-ATP, respectively), and nicotinamide adenine dinucleotide (NADH) and its oxidized form (NAD + ). For the simulation, published chemical shifts relative to PCr at 0 ppm and homonuclear and heteronuclear J-coupling constants were used, as summarized in Table 1. γ-ATP and α-ATP moieties were simulated separately to account for possible different relaxation times of the moieties. The VeSPA-simulated metabolite spectra were then imported into MATLAB, where the linewidth of each simulated metabolite basis spectrum was adjusted to a Lorentzian linewidth similar to in vivo linewidths (Table 2). Also in MATLAB, the simulated spectra were phase corrected, and the absolute of the peak integral was normalized against a constant value. An artificial reference peak needed in LCmodel basis spectra for referencing was added at 15 ppm before the creation of LCModel basis sets. 30 To perform LCModel analyses for 31 P spectra, several adjustments are required, as described in Deelchand et al. 30 In comparison with adjustments reported in his publication, we set the standard deviation of the first-order phases (SDDEGP) = 0 to not allow first-order phase correction.
In addition, SDSH control parameters, which specify the standard deviation of the chemical shift, were adjusted for P i int , P i ext , γ-ATP, and α-ATP to account for pH-dependent frequency shifts. 36 To display correct x-axis frequencies with PCr set to 0 ppm, control parameters were adjusted to SHIFMX(2) = À4.63 and SHIFMN(2) = À 4.77 defining the range about the expected value of the referencing shift. 36 LCModel analyses were then performed over the spectral range from À10 to 10 ppm.

| T 2 calculation
To calculate the apparent T 2 s, the LCModel-fitted metabolite concentrations were fit to a single exponential two-parameter decay across the TE series according to with M xy being the transverse magnetization. The goodness of the fit statistics was evaluated by the coefficient of determination (R 2 ). T 2 estimates with R 2 less than 0.5 were discarded from further analyses.

| pH estimation
The chemical shift difference between PCr (0 ppm) and free phosphate (δ in ppm) was used to calculate pH values from the modified Henderson-Hasselbalch equation 9 pH ¼ pK a þ log 10 δ À δ a δ b À δ where pK a = 6.73 is the acid dissociation constant, and δ a = 3.275 ppm and δ b = 5.685 ppm are the chemical shifts of dihydrogen and hydrogen phosphate, respectively. 9 Intracellular as well as extracellular pH values were calculated from LCModel-fitted frequencies of P i int and P i ext .
T A B L E 2 Mean spectral linewidths (LWs) and their standard deviations (std) extracted from processed raw data and LCModel fits at echo time of 6 ms, as well as LWs used for the basis sets in LCModel. The simulated metabolite basis sets were line broadened to compensate for large differences in T 2 * relaxation times and pH effects to best fit the spectra across the TE series

| Metabolite quantification
For metabolite quantification, peak areas S RD, TE, TM ð Þobtained from LCModel fits were corrected for relaxation losses according to with RD ¼ TR À TM À TE=2: 37 TM is the mixing time of the STEAM sequence, TE is the echo time, T 1 are the metabolite specific longitudinal relaxation times taken from Pohmann et al., 38 and T 2 are the metabolite specific transversal relaxation times calculated from summed spectra in this paper ( Table 3). The relaxation-corrected peak areas were converted to 31 P metabolite concentrations using an assumed γ-ATP concentration of 3 mM as an internal reference. 9,39,40

| RESULTS
High-quality spectra were obtained for all volunteers and all acquired TEs with a mean PCr SNR of 36.1 ± 5.9 at TE 6 ms, and of 9.1 ± 2.7 at TE 150 ms, and similar spectral quality at TE 6 ms and TE 150 ms of 10.0 ± 1.1 and 9.7 ± 1.6 Hz, respectively. Mean spectra across all volunteers and their standard deviations are shown for the TE series in Figure 1. The shaded areas represent standard deviations across all volunteers indicating high reproducibility. Figure 2 shows the LCModel fit result for the summed spectrum at TE 6 ms from À10 to 8 ppm with low fit residual. Mean spectral linewidths across all volunteers and their standard deviations are reported in Table 2 for TE 6 ms for preprocessed raw data and LCModel fits. In preprocessed raw data, linewidths of NADH and NAD + cannot be measured separately. In addition, the linewidth P i ext could not be measured reliably on a single volunteer basis. In the last column, linewidths used in LCModel basis sets are reported. The simulated metabolite basis sets were line broadened, following the observation of Deelchand et al. 30 Deelchand et al. applied line broadenings based on the measured in vivo linewidths, to compensate for large differences in T 2 * relaxation times and pH effects. The Lorentzian line broadening factor in this study had to be somewhat larger than the measured linewidths to best fit the spectra across the TE series.
Mean estimated T 2 decay curves are presented in Figure 3 for all fitted metabolites as well as for total NAD (tNAD; summed NADH and NAD + fits). Data points and error bars represent mean fitted peak integrals over all volunteers and their standard deviations in arbitrary units. The calculated apparent T 2 s of summed spectra as well as the mean over all volunteers (after exclusion of R 2 < 0.5) are reported in Table 3 together with the corresponding R 2 s. Mean R 2 s of individual spectra are higher than 0.71, and of summed spectra higher than 0.83, except for P i ext , showing the goodness of the T 2 fits to individual datasets. No mean value of P i ext T 2 is given because P i ext could not be reliably estimated on an T A B L E 3 Apparent phosphorus ( 31 P) transversal relaxation times (T 2 s) in the human brain and coefficients of determination (R 2 s) across volunteers' summed spectra (n = 12), as well as mean values and standard deviations (stds) derived from the individual spectra. P i ext could not be reliably estimated on an individual volunteer basis individual volunteer basis. The calculated T 2 s are visualized in boxplots in decreasing order in Figure 4 and span a wide range between $150 and $7 ms. A literature comparison of T 2 s in the human brain at different field strengths is presented in Table 4.
Relaxation-corrected LCModel quantification results for 11 31 P resonances and tNAD acquired from the spectra of 12 healthy volunteers with TE of 6 ms are presented in Figure 5. Concentration values are given in mM with reference to γ-ATP as an internal reference. For P i ext , no T 1 correction could be applied; for NADH, NAD + , and tNAD, the T 1 reported for tNAD was used. 38 Relaxation-corrected, as well as noncorrected concentrations, are also reported in Table 5, calculated from summed as well as individual spectra.

| DISCUSSION
This study presents in vivo localized T 2 s of singlets as well as J-coupled spin resonances of human cerebral metabolites detectable with 31 P-MRS at 9.4 T. The high spectral resolution in combination with accurately simulated basis sets allowed the estimation of 10 metabolites' T 2 s acquired in one TE spectra series, including for the first time T 2 s of NAD + and NADH measured with 31 P-MRS and P i ext . Also, metabolite concentrations, as well as intracellular pH (pH int ) and extracellular pH (pH ext ), were calculated.

| Spectral quality
Even although the localization efficiency of STEAM is lower than for adiabatic sequences, the single-shot STEAM sequence offers higher SNR per unit time and allows for very short TEs, which are both critical factors for the acquisition of metabolite signals with short relaxation times. 24 The spectra obtained in this study with a STEAM sequence allowing a minimum TE of 6 ms show good SNR for a measurement time of 10 min. The transmit frequency was set to that of PCr to cover most 31

| T 2 estimation methods
The high spectral quality allowed spectral fitting on a single volunteer basis. Based on the quality of the LCModel fit and residual, as shown in Figure 2, the basis sets generated in VeSPA using chemical shifts and J-coupling constants given in Table 1 appear suitable for analyzing 31 P-MRS data. Because J-evolution was considered in the basis sets, measurement of spectra at any TE desired is possible. With this approach, neither frequency-selective refocusing nor homonuclear decoupling, 11,13,16,18,19,23 nor assumptions of signal loss at specific TE of phase-modulated metabolites, 41 nor measurement at specific TEs to exactly match multiples of 1/J to completely refocus the metabolite of interest, 17,18 are necessary. In a frequency-selective spin-echo method, the frequency-selective pulse only affects one of the coupling nuclei (γ-and α-ATP or β-ATP), while the other peaks are presented without distortions. 18 Therefore, no assumptions about J-coupling constants are necessary and spectra at any TE can be acquired for T 2 measurements. However, when using frequency selection, two series of acquisitions are necessary to obtain spectra of all three ATP nuclei, resulting in double the measurement time. When using selective spin decoupling, the effects of phase modulation are suppressed by selectively irradiating one of the coupling nuclei during the period of signal acquisition. The difficulty is to selectively irradiate a single resonance to avoid saturation spillover onto neighboring resonances. To ensure complete decoupling, the decoupler power needs to be sufficiently high. This results in higher frequency spread and might disturb resonances close in frequency to the target. 19 Another option to measure T 2 without sequence modifications is to measure undistorted signals by choosing the TE as a multiple of 1/J. However, for the three different ATP moieties, this is fulfilled at different TEs because their J-coupling constants are slightly different. 17,18 F I G U R E 3 Mean estimated transversal relaxation time (T 2 ) decay curves of all 11 fitted metabolite peaks and summed total NAD (tNAD) (dashed lines). The error bars show the standard deviations of the fitted metabolite peak integrals across all 12 volunteers in arbitrary units. Apparent T 2 s and coefficients of determination (R 2 s) are listed in Table 3. ATP, adenosine triphosphate; GPC, glycerophosphocholine; GPE, glycerophosphoethanolamine; NADH, nicotinamide adenine dinucleotide; NAD + , NAD oxidized; PC, phosphocholine; PCr, phosphocreatine; PE, phosphoethanolamine; P i ext , extracellular inorganic phosphate; P i int , intracellular inorganic phosphate; TE, echo time

| T 2 relaxation
The method chosen in this study to acquire and fit data with accurately simulated spectral basis sets comprising J-evolution resulted in reliable estimation of T 2 s on a single volunteer basis for 10 31 P metabolites. For P i int , PCr, γand α-ATP, which are involved in chemical exchange and/or cross-relaxation, the measured dephasing rates reflect the apparent T 2 s. The T 2 s of all measured metabolites could be reliably estimated in individual volunteers, as well as from spectra summed across all volunteers, with R 2 s higher than 0.7, except for P i ext .
Leaving the two studies at 2 T, where the influence of the homonuclear J-coupling of ATP on the behavior of spin echoes was not completely accounted for, aside, 14,15 our results fit into a decreasing trend of T 2 s with increasing field strength B 0. 11,13,16 This is in line with the theory of the two competing mechanisms of dipolar proton-phosphorus interactions and chemical shift anisotropy (CSA) considered to determine 31 P relaxation times. 1,23 The transversal relaxation time because of the CSA in the extreme narrowing regime (ω 2 τ 2 C ( 1; ω: Larmor frequency, τ C : molecular correlation time) is given by  Table 3. ATP, adenosine triphosphate; GPC, glycerophosphocholine; GPE, glycerophosphoethanolamine; NADH, nicotinamide adenine dinucleotide; NAD + , NAD oxidized; PC, phosphocholine; PCr, phosphocreatine; PE, phosphoethanolamine; P i ext , extracellular inorganic phosphate; P i int , intracellular inorganic phosphate; tNAD, total NAD T A B L E 4 Literature transversal relaxation times (T 2 s) in the human brain at various field strengths. At lower field strength, phosphomonoesters and phosphodiesters (PMEs and PDEs, respectively) could not be fitted separately and are reported as one T 2 value with γ the gyromagnetic ratio, B 0 the main magnetic field strength, σ k and σ ⊥ the shielding parallel and perpendicular to the symmetry axis, and τ C the molecular correlation time. 1 Because dipolar interaction is independent of the main magnetic field strength, the influence of dipolar relaxation on T 2 decreases with increasing main magnetic field strength, while CSA relaxation increases. 1,23,42,43 It is therefore expected that CSA  becomes increasingly important for the relaxation mechanisms in 31 P-containing metabolites with increasing B 0. 44 The relative contribution of each mechanism to the relaxation times also depends on the exact phosphate group present in different metabolites. 44 Because relaxation as a result of CSA correlates with the symmetry of the magnetic shielding, a stronger decrease in T 2 with increasing B 0 is expected for less symmetric molecules. 1,23 The increasing influence of CSA with increasing field strength was shown in several in vitro NMR studies. 42,45 The much shorter T 2 s of ATP in comparison with the other 31 P-MRS-detectable metabolites are in accordance with literature values where J-evolution was taken into account. 11,13,16 This has been proposed as possibly originating partly from the exchange between bound and free states of ATP, its interaction with creatine kinase and ATPase enzymes, and its strong interaction with the unpaired electron of complexed paramagnetic ions, as well as CSA. 1 A further possible explanation for the short relaxation times is that there might be a strong 31 P dipole-dipole interaction through the bond -P-O-P-, which is also true for NAD + and NADH. 9 Measured T 2 s of NAD + and NADH are also very short below 20 ms and in a similar range as estimated ATP T 2 s. Estimated NAD + and NADH T 2 s are similar, which is in accordance with assumptions made in 1 H measurements. 34 Furthermore, the slow rotational motion of ATP, measured to be in the range of 10 À8 -10 À7 s at 7 T, additionally contributes to very short T 2 s. 1,[46][47][48] The estimated T 2 s of PE, GPE, and GPC are the longest and similar at approximately 130 ms. The estimated T 2 of PC is lower at approximately 95 ms. This was also seen in a 7T study 16 and attributed to a contribution of 2,3-diphosphoglycerate (2,3-DPG) from blood to the signal of PC, but to a lesser extent to PE. It was shown that when accounting for 2,3-DPG, which has a shorter apparent T 2 than PC, the estimated T 2 of PC becomes similar to the T 2 s of PE, GPE, and GPC.
Estimated apparent T 2 s of inorganic phosphate are rather short in comparison with T 2 s of phosphomonoesters and phosphodiesters. However, the T 2 of P i ext measured in our study is lower than that of P i int . Yet, it has to be mentioned that P i ext could not be fitted reliably in every volunteer and its SNR is low, which results in a higher uncertainty of the estimated T 2 , reflected in the low R 2 of P i ext in the summed spectra analysis. In addition, a shorter apparent T 2 of PCr in comparison with phosphomonoesters and phosphodiesters was observed.
While chemical exchange involved in the chemical exchange kinetic network PCr $ ATP $ P i influences T 1 s, it has little influence on T 2 s. The measured chemical exchange rates k are slow with k less than 0.6 s À1 at 7 T. 39,49,50 According to equations given in Woessner et al., 51 chemical exchange in the slow exchange regime leads only to a very minor decrease in apparent T 2 . A more severe influence on T 2 occurs from chelation with divalent ions, such as Mg 2+ and Ca 2+ , which affect the chemical shifts of α-, β-, and γ-ATP, as well as of PCr and P i. 52,53 It was shown that a decrease in the concentration of Mg 2+ and Ca 2+ , as associated with a number of chronic diseases, 54 increases the T 2 s of the binding phosphates. 53,55 Additionally, for PCr, the chemical surrounding of the phosphorus atom (bond to three oxygen and one nitrogen atom) might attribute to a relatively large contribution of CSA to relaxation in comparison with the phosphomonoesters and phosphodiesters (P atoms bond to four oxygen atoms), resulting in faster relaxation of PCr. 9 While the apparent T 2 s of metabolites with high SNR could be estimated reliably, the signal intensity tends to be overestimated with increasing TE and, therefore, decreasing SNR. 41 This might induce a systematic error in T 2 estimation, which could be compensated by acquiring more averages for longer TEs. However, acquiring more averages results in longer scan durations not feasible in this study. Also, the assumption about J-modulation used in this study to model basis sets could influence the reliability of estimated T 2 in coupled spin systems. Even although our results fit in a decreasing trend of T 2 with increasing B 0 , a more detailed comparison with published data at lower field strengths is difficult because of the application of different measurement methods and hardware setups, different data processing and fitting, and different volunteer populations measured.

| pH estimation
Compared with earlier studies, our estimated values of pH int and pH ext agree well with pH int 6.98 and pH ext 7.32 measured in the human brain at 7 T with a pulse-acquire sequence in combination with four outer volume suppression bands. 56 Our pH int and pH ext values also confirm those measured with 3D 31 P-MRSI at 7 T 4 and 9.4 T 57 in mixed gray and white matter tissue.

| Metabolite concentrations
The majority of metabolite concentrations obtained in this study are comparable with values reported in Ren et al. 9 measured at 7 T using a pulse-acquire sequence and a long TR of 25 s to guarantee full T 1 recovery. The tNAD concentration measured in this study is higher than the ones measured in previous 7 T studies, 9,34,58 whereas the PE and P i ext concentrations from this study are much lower than the ones reported in Ren et al. 9 Because uridine diphosphoglucose (UDPG), which has overlapping resonance frequencies with NAD + and NADH, was not fitted in this study, the obtained tNAD concentration might be influenced by UDPG. 33,59 Furthermore, the low abundance of NADH and NAD + and the resulting low SNR might have induced fit errors and errors in their T 2 estimation. The much lower P i ext and PE concentrations in comparison with Ren et al. 9 might result from different measurement techniques. In comparison with the 7 T study, localized spectra were acquired in this study.
Because of the CSDE resulting from the single-voxel localization technique, P i ext and PE signals have a higher contribution from cerebellum in comparison with the PCr signal. At this location, B 1 + as well as the receive sensitivity of the coil is lower than at the periphery of the brain. This results in reduced peak intensity, and, therefore, in estimated metabolite concentrations that are too low. In addition, as was shown in a previous study, 56 the P i ext peak might originate from blood and cerebrospinal fluid in the peripheral region of the brain, which was not touched by the P i ext measurement voxel of this study. This explanation is supported by a previously published 3D MRSI study at 9.4 T from Ruhm et al. 57 reporting similar P i ext concentrations to this study. Although the PCr concentration calculated in this study is in accordance with Ren et al., 9 it is slightly higher than concentrations calculated in Ruhm et al. 57 and Du et al. 39 This might hint at small contamination of brain spectra by muscle tissue, because the PCr voxel was placed close to the skull to exploit optimum B 1 + and the PCr concentration in muscle tissue is much higher than in the brain. 40,60 A further aspect influencing absolute metabolite concentrations when normalized to γ-ATP is the fact that because of CSDE, metabolite concentrations were measured from different tissue fractions but normalized based on one specific localization.
The metabolite concentrations of all metabolites obtained in this study are about 40% lower than in a recently published Image-Selected In vivo Spectroscopy (ISIS) localized study at 9.4 T measured with the same hardware setup, except for ATP, tNAD, and PCr. 24 Although ISIS localization implies a short TE, fitting simple peak integrals to analyze multiplets that undergo J-evolution is not sufficient to determine metabolite concentrations. 61 Therefore, a possibly too low γ-ATP concentration was determined in the ISIS study, which results in too high concentrations of the other metabolites when normalized to γ-ATP. A further reason for the discrepancies in metabolite concentrations might be that the CSDE of ISIS was only 0.8% per ppm. As a consequence, the measurement regions of different metabolites were closer together than in the present study, comprised of similar tissue fractions and exposed to similar B 1 + and SNR conditions, as illustrated in fig. 5 in our previous paper. 24 5 | CONCLUSIONS 31 P T 2 s of human brain metabolites at 9.4 T are reported, including values for P i ext , NAD + , and NADH. To the best of our knowledge, T 2 s of 31 P metabolites that undergo J-evolution were estimated for the first time by considering J-evolution in an accurately modeled basis set for each TE used in the fitting routine. A decreasing trend of T 2 with increasing field strength adding to previous literature confirms the limited usability of echo-based acquisition methods for 31 P-MRS at UHF strength. The estimated relaxation times were used for absolute quantification resulting in metabolite concentrations comparable with literature values measured from free induction decay.