Discussions

Asc was consistently detected by MRS in more than 93% of the analyzed data sets acquired on a clinical 3T MR scanner. The average concentrations ranged between 0.4 and 0.6 (1/Cre) with relative SDs of about 25% within the collected spectra. These inter individual SDs are comparable to those of other metabolites (Fig. 11). However, this does not necessarily mean that the estimated concentrations of Asc are reliable, as the calculation accuracy of MR spectroscopy is strongly related to the spectral linewidth and SNR [75-77]. If the resonance peaks of various metabolites are close to each other or their spectral linewidths widen, the uncertainty of the concentration estimation increases. This can be evaluated by the CR-SD values.

The main resonance of Asc (C6H2) at 3.73 ppm is close to the multiplet of the Glx compounds. The overlapping between these two metabolites increases the instability of the concentration estimation during the analysis, through which the concentration of Glx and Asc might be over- or under-estimated. The LCModel analyses of the in

vivo spectral data “with” and “without” Asc basis spectrum demonstrate that the

concentration differences of Glx are related to the estimated Asc concentrations. The concentration differences of Glx rose with the increase of the estimated Asc

concentrations, shown in Fig. 12(a). If the overestimated concentration of Glx only originated from Asc, the fitted curve of Glx difference vs. Asc concentration should ideally be a straight line with a y-axis intercept of zero and a slope of 1. However, the result shows the fitted curve with an intercept close to zero (about 0.05) but a slope smaller than 1. This is evidence that in the “without” Asc case not all of the Asc concentration is assigned to Glx but partly to some other metabolites. Glucose is a possible candidate. However, we could not reliably identify it to be this missing metabolite as it was not always detected by LCModel. If then, Asc is included into the basis set, both quantities will add to the concentration of Asc. Therefore, it is advantageous to include the Asc basis into the analysis basis set to lower the overestimation effects of Glx.

In addition, we take CR-SD into consideration. Contrary to the relative inter individual SDs (Fig.11) with values of around 25% of Asc and Glx, the estimated concentrations of Asc show reasonable CR-SD values between 5% and 15% (Fig. 13).

The CR-SD values for Glx change from 6% to 7% when switching analysis from the

“without” to the “with” Asc case. This insignificant change shows that the estimation of Glx remains stable.

In cerebellum, these spectra with some cases of linewidth larger than 0.1 ppm have the poorest quality (Table 4). This fact would potentially affect the results of quantification because of more serious spectra overlapping between metabolites.

Besides, the concentration difference of NAA in frontal lobe is dependent on the increase of estimated ascorbate concentration. Nevertheless, if we compare with the results analyzed from all subjects, it can be observed that the concentration difference of NAA does not show statistical meanings related to the estimated ascorbate concentration (p > 0.2). Therefore, we can conclude that no significant changes to NAA were observed in our study after adding Asc basis into the analysis basis-set and the quantifications of other metabolites are not affected as well.

The above leads to the conclusion that including Asc does not cause instabilities within the estimation of other metabolites and that it is possible to detect Asc using a conventional PRESS pulse sequence for data acquisition in combination with LCModel data analysis.

In order to investigate the reliability of the Asc estimation, we performed a

“virtual titration” with varying SNR and spectral linewidths, as these are the main limitations in spectral quantification. Before applying “virtual titration” to in vivo

spectra, simulated in vitro spectra were created from analysis basis-set in LCModel.

The estimated concentrations are consistent with the real values of in vitro spectra and their CR-SD values of 0% show strong reliability in quantification (Table 3). Even though some of the inexistent metabolites are detected, their estimated concentrations are four to five orders smaller than other metabolites and the CR-SD values are much larger than those existent metabolites. Therefore, they can be viewed as noise.

Furthermore, we put ascorbate into the simulated in vitro spectra and find that its concentration can be precisely detected in every level we added in spite of the resonance peaks of Asc very close to other metabolites (Fig. 14). It proves that the concentration of ascorbate of in vitro spectra can be detected and quantified using LCModel. Hence, the following step of our experiment is to apply virtual titration to

in vivo spectra and to discuss the quantification affected by SNR and linewidths.

SNR affects the SD of the average estimated concentration. Naturally, the SD values of different metabolite concentrations increase with the decreasing SNR in the simulation. Furthermore, the SD values of each metabolite concentration also increase as the added Asc concentration rises due to its increased noise level. The SNR of the examined in vivo spectra is between 15 and 20. For these cases of SNR~ 10 and SNR~20 in our simulation, the SD of the estimated concentration is very low,

especially if the added Asc concentration is below 1.0 mM. Since estimated Asc concentrations have larger SDs for SNR~5 than in other cases, it is advisable to run such an extended analysis including Asc only with datasets with higher SNR.

Therefore, a general SNR level in the range of 15 to 20 for in vivo spectra represents a lower-bound requirement for such an analysis. On the other hand, this implies that it is not necessary to acquire spectra with exceptionally high SNR to detect Asc. SNR for in vivo spectra at 3T [78] is typically sufficient for an analysis, as described in this study.

The spectral linewidth is the second quality criterion that has to be carefully monitored for such an analysis. Therefore, we chose three cases with different FWHM values to examine the relationship between the added Asc concentration and the estimated concentration of some metabolites. The linear correlation coefficients (R²) of the added Asc concentration vs. the estimated Asc concentration are larger than 0.985 in all three cases of different FWHM values (Fig. 16(a)). The different slopes of the three fitted curves might originate from different FWHM values, concentration differences of creatine between subjects, or initial Asc concentrations, which originally existed in the in vivo spectra. However, even though the three slopes vary, the added Asc concentration shows good linearity with the estimated Asc

concentration. This leads to the conclusion that the Asc can be stably and reliably detected.

The NAA concentration change shows a reasonable result when the added Asc concentration less than 1.0mM. The estimated concentration variation of NAA is getting smaller as the spectral linewidth becomes narrower. However, even though the main resonance peak of NAA is located at around 2.05 ppm, which is far from that of Asc, it shows an instant increase of about 0.15 (1/Cre) when the added Asc concentration larger than 1.0 mM at the case of linewidth 0.033 ppm (Fig. 16(b)).

Apparently, it does not result from the partial effects from spectral line overlapping between these two metabolites. Thus, we checked the analysis results from the same subjects adding different levels of vitamin C concentrations and found that the baseline estimation was changed between different analyses (Fig. 16). Although the modified parameters for ascorbate spectra are all the same as the analysis results from the in vivo spectrum during virtual titration, we could not ensure the results of parameter estimation (baseline, lineshape coefficients, etc) before and after the virtual titration identical. These parameters are determined by LCModel automatically using a Marquardt modification of a constrained Gauss-Newton least squares analysis [74].

Up to now, the studies show that the concentrations of Asc in human brains increase

less than 50% after intravenous injection of vitamin C. Thus, this phenomenon, which occurs under the highly-amount added Asc concentration condition, would cause a minor impact on ascorbate quantification for clinical use.

The concentration of other metabolites should not be changed with the virtual titration, but the concentrations of Glx and mI vary with the added Asc concentrations in dissimilar manners (Fig. 16(c)). First we focus on mI. The resonance peaks of mI are at 3.52 ppm, and therefore only 0.21 ppm away from the main Asc resonance.

Even though the distance between the main resonant peaks of these two metabolites is larger than the maximum FWHM value of 0.076 ppm, the concentration of mI is still influenced by the added Asc concentration. Additionally, both metabolites possess minor peaks at around 4.0 ppm (Fig. 9). The trend of this concentration change is strongly related to the FWHM values. The largest concentration increment of mI with about 80% for the maximum added Asc concentration appears at the case of FWHM 0.076 ppm but is much less in the other cases (Table 5). The phenomenon indicates that a spectrum with a wider linewidth would cause more serious overlapping effects to other metabolites. Therefore, the estimated concentration of mI will vary depending on the spectral linewidth.

The increment of Glx vs. added Asc concentration shows different behavior. The largest concentration change of Glx occurs in the case of FWHM 0.076 ppm with an increment of about 0.85 (1/Cre), but the least concentration change occurs at the case of FWHM 0.043 ppm, being only 0.07 (1/Cre) (Table 5). This might be due to the very close proximity of the main resonance peaks from Asc and Glx [79]. This fact is reflected in the CR-SD values of Asc and Glx, which are larger in the other metabolites. It also indicated that the evaluated concentrations of Asc and Glx hold higher relative inter individual SDs (Fig. 11). This influence on the Glx concentrations is below 15 % when 1.0 mM Asc is added and below 10 % for 0.5 mM in all three linewidth cases. For the two lower linewidths the influence decreases to less than 5%

in the 1.0 mM cases (Fig. 16(c)). As the CR-SD values of Asc and Glx are on the order of 10%, an error of below 5% does not introduce severe deviations.

Hence, even if the Asc concentration of the brain is twice as high as usual, the estimated concentration of Asc could still be reliably detected and the concentrations of other metabolites are not significantly influenced. Our results indicate that the limiting FWHM value for reliable Asc detection is between 0.043 ppm and 0.076 ppm.

Therefore, we assume that the linewidth of 0.05 ppm is sufficient for the detection of Asc under the normal Asc concentration level on a 3T system scanner [78].

(a)

(b)

Figure 17. The estimated baselines are varied under different levels of added Asc concentrations. (a) The analysis result of adding 0.1 mM ascorbate into the in vivo spectrum. (b) The analysis result of adding 2.0 mM ascorbate into the same one.