31P Transversal Relaxation Times and Metabolite Concentrations in the Human Brain at 9.4T

A method to estimate phosphorus (31P) transversal relaxation times (T2) of coupled spin systems is demonstrated. Additionally, intracellular and extracellular pH (pHext, pHint) and relaxation corrected metabolite concentrations are reported. Echo time (TE) series of 31P metabolite spectra were acquired using STEAM localization. Spectra were fitted using LCModel with accurately modeled Vespa basis sets accounting for J-evolution of the coupled spin systems. T2s were estimated by fitting a single exponential two-parameter model across the TE series. Fitted inorganic phosphate frequencies were used to calculate pH, and relaxation times were used to determine the brain metabolite concentrations. The method was demonstrated in the healthy human brain at a field strength of 9.4T. T2 relaxation times of ATP and NAD are the shortest between 8 ms and 20 ms, followed by T2s of inorganic phosphate between 25 ms and 50 ms, and PCr with a T2 of 100 ms. Phosphomonoesters and –diesters have the longest T2s of about 130 ms. Measured T2s are comparable to literature values and fit in a decreasing trend with increasing field strengths. Calculated pHs and metabolite concentrations are also comparable to literature values.


Introduction
In vivo phosphorus MR Spectroscopy ( 31 P-MRS) provides insight into energy and phospholipid membrane metabolism noninvasively 1 . It also offers the possibility for intracellular and extracellular pH measurements, or the determination of intracellular Mg 2+ concentration 1,2 . Thereby, this technique is used for different applications, such as pH mapping in cancer 3,4 , measurement of altered phospholipid and energy-related metabolites in schizophrenia 5 , or measurement of free cytosolic magnesium in neurodegenerative disorders or migraine 6,7 .
So far, 31 P MRS is rarely used for clinical applications due to the low intrinsic sensitivity of 31 P, and therefore its low spatial and temporal resolution. Since 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 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, echo time, and free precession times, knowledge on relaxation times is essential as well. Since relaxation times are field strength dependent, they need to be measured at every field strength 10,11 .
Several studies show an increase in T 1 and decrease in T 2 relaxation times in the human brain for protons with increasing field strengths 1,10,12 . In 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 relaxation times, no coherent trend with magnetic field strength can be extracted from literature 11,[13][14][15][16] . Especially reports on transversal relaxation times of ATP largely vary 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 relaxation times 14,15 . Adjusted acquisition methods using selective refocusing pulses or homonuclear decoupling allow the accurate determination of T 2 relaxation times 11,13,19 .
None of the studies measuring 31 P T 2 relaxation times 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 Vespa or MARSS, are specific for each sequence and timing and fully consider Jevolution 21,22 . Using this approach, no selective refocusing pulses or homonuclear decoupling is needed in the acquisition sequence. Since 31 P T 2 relaxation times are expected to be very short at an ultrahigh field strength (UHF) and are typically estimated by observing the exponential signal decay in echo time (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 SAR-related concerns at UHF 11,13,16,18,19,23 .
The primary goal of this study was to demonstrate a method to measure 31 P T 2 relaxation times of Jcoupled metabolites without frequency-selective refocusing or homonuclear decoupling, as was done 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 relaxation times was demonstrated in the human brain at a field strength of 9.4T. 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 to 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 homebuilt 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 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 (7 females, 5 males, age 27 ± 3 years) and all data were included in the data processing. The total scan time per volunteer was 100 minutes and the measurement was well tolerated by all volunteers.
For spatial localization, a stimulated echo acquisition mode (STEAM 25 ) sequence (TM/TR 5/5000 ms) optimized for phosphorus spectroscopy in the human brain at 9.4T was used, similar as recently described 24 . Hamming-windowed sinc excitation pulses with a flip angle of about 90°, estimated from phantom B 1 + maps, and a pulse duration of 1.5 ms were used for slice selection. The time-bandwidth product was set to 6.0 (corresponding to six zero-crossings of the amplitude modulation) resulting in an excitation bandwidth of 4.3 kHz. Thus, the chemical shift displacement error (CSDE) was 3.8% per ppm in each voxel dimension. Spoiler gradients and phase cycling scheme were optimized using DOTCOPS 24,27 .
Spoiler gradients were arranged as shown in Dorst et al. 24 with a spoiling moment of 18 ms•mT/m after the first and third slice selective pulse, and 36 ms•mT/m during the mixing time. For phase cycling, a fourstep COG(0,1,2;3) 27,28 scheme was implemented, which, together with the spoilers, removed all unwanted coherence pathways. T 2 relaxation time measurements were performed by acquiring a TE series with roughly exponentially spaced TEs of 6,8,11,15,20,30,50,80,150 ms. For all spectra, a voxel of 5x5x5 cm 3 was placed in the occipital lobe. For each TE time, spectra with 120 averages were acquired with 4096 complex sampling points, an acquisition bandwidth of 10 kHz and a measurement time of 10 minutes. The first 4 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 non-filtered 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 ppm and +30 ppm in the real part of the spectrum.

Spectral fitting:
Spectra were fitted with LCModel (version 6.3-1L) 20 using basis sets simulated in Vespa (v1.0.0) 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 the TEs specified. The following metabolites were simulated: phosphoethanolamine and phosphocholine (PE, PC), extracellular and intracellular free inorganic phosphate (P i ext , P i int ), glycerophosphoethanolamine and glycerophosphocholine (GPE, GPC), phosphocreatine (PCr), γ-and α-adenosine triphosphate (γ-ATP, α-ATP), and nicotinamide adenine dinucleotide (NAD+, NADH). 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 metabolite spectrum was adjusted to a Lorentzian linewidth similar to in vivo linewidths (see Table 2), the peaks were phase corrected, and the absolute of the peak integral was normalized. An artificial reference peak needed in the basis spectra for referencing was added at 15 ppm before the creation of LCModel basis sets.
To perform LCModel analyses for 31 P spectra, several adjustments are required, as described in Deelchand et al. 30 In comparison to 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 31 . To display correct x-axis frequencies with PCr set to 0 ppm, control parameters were adjusted to SHIFMX(2) = -4.63 and SHIFMN(2) =-4.77 defining the range about the expected value of the referencing shift 31 . LCModel analyses were then performed over the spectral range from -10 ppm to 10 ppm.

T 2 calculation:
To calculate the apparent T 2 relaxation times, the LCModel-fitted metabolite concentrations were fit to a single exponential two-parameter decay across the TE series according to

exp
with M xy being the transverse magnetization. The goodness of the fit statistics was evaluated by the coefficients of determination R 2 . T 2 estimates with R 2 < 0.5 were discarded from further analyses. pH p log where pK a = 6.73 is the acid dissociation constant, and δ a = 3.275 ppm and δ b = 5.685 ppm the chemical shifts of the protonated and deprotonated forms of free phosphate, respectively 9 . Intracellular as well as extracellular pH values were calculated from LCModel-fitted frequencies of P i int and P i ext . 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 Hz and 9.7 ± 1.6 Hz, respectively. Mean spectra across all volunteers and their standard deviations are shown for the echo time 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 -10 ppm to 8 ppm with low fit residual. Mean spectral linewidths across all volunteers and their standard deviations are reported in Table 2  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 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 relaxation times 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 coefficients of determination R 2 . Mean coefficients of determination 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. The calculated T 2 relaxation times are visualized in boxplots in decreasing order in Figure 4 and span a wide range between ~150 ms and ~7 ms. A literature comparison of T 2 relaxation times in the human brain at different field strengths is presented in Table 4. Table 3. Table 3.  31 P resonances and tNAD acquired from spectra of 12 healthy volunteers with TE 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 relaxation time reported for tNAD was used 38 . Relaxation-corrected, as well as non-corrected concentrations, are also reported in Table 5 calculated from summed as well as individual spectra. ** for NADH, NAD+ and tNAD, the same T 1 relaxation time was assumed.

Spectral quality
Even though 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

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. Since J-evolution was considered in the basis sets, measurement of spectra at any echo time desired is possible.
With this approach, neither frequency-selective refocusing or 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 TE a multiple of 1/J. However, for the three different ATP moieties, this is fulfilled at different echo times since their J-coupling constants are slightly different 17,18 .

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 relaxation times on a single volunteer basis for 10 31 P metabolites. For P i int , PCr, γ-and α-ATP, which are involved in chemical exchange and/or crossrelaxation, the measured dephasing rates reflect the apparent T 2 relaxation times. The T 2 relaxation times of all measured metabolites could be reliably estimated in individual volunteers as well as from spectra summed across all volunteers with coefficients of determination higher than 0.7 except for P i ext .
Leaving the two studies at 2T, 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 relaxation times 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 . While the influence of dipolar relaxation decreases with increasing main magnetic field strength, CSA relaxation increases with the square of the main magnetic field strength 1,23,42 . It is therefore expected that CSA becomes increasingly important for the relaxation mechanisms in 31 P metabolites with increasing B 0 43 . The relative contribution of each mechanism to the relaxation times also depends on the phosphate group present in different metabolites 43 . Since 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 much shorter T 2 relaxation times of ATP in comparison to 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 suggested to possibly originate 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 besides 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 relaxation times of NAD+ and NADH are also very short below 20 ms and in a similar range as estimated ATP T 2 relaxation times. Estimated NAD+ and NADH T 2 relaxation times are similar, which is in accordance with assumptions made in 1 H measurements 35 .
The estimated T 2 relaxation times 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 extend 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 T 2 s of PE, GPE and GPC.
Estimated apparent T 2 s of inorganic phosphate are rather short in comparison to T 2 s of phosphomonoand -diesters. The short apparent P i int could be explained by the exchange of P i int with γ-ATP via glycolysis which has short relaxation times 9,16,39 . However, the T 2 of P i ext measured in our study is lower than of P i int , although the extracellular P i pool was shown to be metabolically inactive 9,16,44 . Yet, it has to be mentioned that P i ext could not be fitted in every volunteer reliably and its SNR is low which results in an uncertainty of the estimated T 2 relaxation time, reflected in the low coefficient of determination R 2 of P i ext in the summed spectra analysis.
The shorter apparent T 2 of PCr in comparison with phosphomonoesters and -diesters can also be explained by the chemical exchange of PCr with γ-ATP 9,39 . Additionally, 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 to the phosphomonoesters and -diesters (P atoms bond to four oxygen atoms) resulting in faster relaxation of PCr 9 .
While the apparent T 2 relaxation times 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 though our results fit in a decreasing trend of T 2 with increasing B 0 , a more detailed comparison to published data at lower field strengths is difficult due to the application of different measurement methods and hardware setups, different data processing and fitting, and different volunteer populations measured.

pH estimation
The estimated intracellular and extracellular pH values were observed to be consistent among the two different fitting types. Compared to earlier studies, our estimated values of intracellular and extracellular pH agree well with pH int 6.98 and pH ext 7.32 measured in the human brain at 7T with a pulse-acquire sequence in combination with 4 outer volume suppression bands 45 . Our pH int and pH ext values also confirm those measured with 3D 31 P MRSI at 7T 4 and 9.4T 46 in mixed grey and white matter tissue.

Metabolite concentrations
The majority of metabolite concentrations obtained in this study are comparable to values reported in Ren et al. 9 measured at 7T 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 one measured in Ren et al. 9 , whereas the PE and P i ext concentrations from this study are much lower. Since 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 34,47 . 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 concentration might result from different measurement techniques. In comparison to the 7T study, localized spectra were acquired in this study. As was shown in a previous study, the extracellular P i peak might originate from blood and CSF in the peripheral region of the brain 45 . This explanation is supported by a previously published 3D MRSI study reporting similar P i ext concentrations to this study 46 . However, it is also possible that the P i ext concentration reported in this study is slightly too low due to too low estimated T 2 relaxation times as a result of possible muscle tissue influence on our data. Although the PCr concentration calculated in this study fits to Ren et al. 9 , it is slightly higher than concentrations calculated in Ruhm at al. 46 , employing 3D MRSI at 9.4T. This also might hint at small contamination of brain spectra by muscle tissue, since the PCr concentration in muscle tissue is much higher than in the brain 40,48 . The metabolite concentrations of all metabolites obtained in this study are about 40% lower than in a recently published ISIS localized study at 9.4T, 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 49 . 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.

31
P transversal relaxation times of human brain metabolites at 9.4T 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