When the metabolite signal $$$S_{m}$$$ detected with MRS is compared to a reference signal measured in a phantom with known concentrations and relaxation rates, it is in principle possible to determine in vivo metabolite concentrations without the need of assumptions about an internal reference. However, the changes in sensitivity, i.e. the relation between the transversal magnetization and the detected signal, between the in vivo and the phantom measurement need to be carefully considered. At low field strength one can estimate the magnitude of the $$$B_1^{+}$$$-field per unit current ($$$\mid{\hat{B_1^{+}}}\mid$$$) obtained in the VOI and use it as measure of the local sensitivity¹. This approach based on the reciprocity principle² uses the assumption that the magnitude of the reception field ($$$\mid{\hat{B_1^{-}}}\mid$$$) at a given position is equal to the magnitude of the transmission field ($$$\mid{\hat{B_1^{+}}}\mid$$$). This is true at lower fields but has been demonstrated to be wrong at higher field strengths^3,4. Hence at 3T $$$\mid{\hat{B_1^{+}}}\mid$$$ is not sufficient to estimate $$$\mid{\hat{B_1^{-}}}\mid$$$ at all positions in the sample and can not be used solely to correct for sensitivity changes. In this work, we present a reciprocity based reference method for quantitative MRS at 3T. We propose to use a volume selective power optimization method⁵ (volPO) to determine automatically a measure of $$$\mid{\hat{B_1^{+}}}\mid$$$. This shall not only simplify the measurement of the sensitivity changes but also guarantee signal detection with an optimal flip angle. To account for the deviations of $$$\mid{\hat{B_1^{+}}}\mid$$$ from $$$\mid{\hat{B_1^{-}}}\mid$$$ we introduce a correction factor C_p using reception sensitivity maps determined from contrast minimized images⁶. The proposed method is extensively validated.

Experiments were performed on a Philips Achieva 3T MRI scanner with a commercial T/R head coil. With the mentioned volPO the scaling factor $$$\frac{1}{DS}$$$, which is proportional to the RF pulse voltage needed to yield a given flip angle, is determined prior to each spectroscopic scan and used as a measure of $$$\mid{\hat{B_1^{+}}}\mid$$$. To investigate the stability of this measure the ratio of the water signal $$$S_{H2O}$$$ and $$$\frac{1}{DS}$$$ was measured several times at the same position in a water containing phantom. The ability to correct for the loading of the coil with $$$\frac{1}{DS}$$$ was tested with a series of measurements in a small spherical water containing phantom, while a plastic bottle containing a NaCl solution was stepwise inserted into the coil.

In 31 healthy volunteers always three PRESS-localized voxels (TE:30ms, TR:1800ms, 256 averages, 5ml) aranged in one plane were measured. One VOI was placed in the longitudinal cerebral fissure just above the corpus callosum (position M) containing mostly gray matter and the other two were shifted by 20 mm respectively to the left (positon L) and to the right (position R) into cerebral white matter. Metabolite concentrations using $$$\frac{1}{DS}$$$ were calculated as follows: $$c_{m}^{DS}=\frac{S_m}{S_{ref,c}}\frac{R_{ref,c}}{R_{m}}\frac{DS}{DS_{c}}\frac{C_{p,c}}{C_{p}}\frac{T}{T_{c}}c_{ref,c}\frac{l_{ref,c}}{l_{m}}\frac{1}{1-f_{CSF}}\qquad\text{[Eq.1]}$$ The subscript $$$c$$$ denotes quantities from the calibration measurement, were the reference compound $$$ref$$$ with a known concentration $$$c_{ref}$$$ was measured. $$$R$$$ are approximated relaxation attenuation factors [Table1], $$$T$$$ the temperature, $$$l$$$ the number of spins per molecule and $$$f_{CSF}$$$ the volume fraction of the CSF. $$$C_p$$$ is the factor to correct deviations of $$$\mid{\hat{B_1^{+}}}\mid$$$ from $$$\mid{\hat{B_1^{-}}}\mid$$$. This factor is calculated in each VOI as the ratio of the achieved $$$\mid{B_1^{+}}\mid$$$ taken from a $$$B_1$$$-map⁷ to the reception sensitivity $$$Rx$$$ calculated using 2D reception sensitivity maps⁶. Both maps were scaled with the value measured at the center of the coil.$$C_{p}=\frac{\mid{B_{1,VOI} ^{+}}\mid}{Rx_{VOI}}\qquad\text{[Eq.2]}$$Metabolite concentrations obtained with Eq.1 are compared to values using tissue water as reference⁸ (IWR). Total internal water concentrations obtained with Eq.1 (omitting the last term) are compared with values predicted based on the individual voxel composition:$$c^{seg}=55.126\cdot(f_{CSF}\cdot\alpha_{CSF}+f_{GM}\cdot\alpha_{GM}+f_{WM}\cdot\alpha_{WM})\qquad\text{[Eq.3]}$$

Changes in the loading of the coil can be precisely corrected with the proposed quantity $$$\frac{1}{DS}$$$ [Figure1]. During a time of 2.5 month $$$S_{H2O}$$$/$$$\frac{1}{DS}$$$ was measured 15 times in vitro with a CV of 0.78 % demonstrating a good stability of the proposed method. The need and the effect of the correction factor $$$C_p$$$ in Eq.1 is demonstrated in vitro [Figure2] and in vivo [Figure3]. The correction with $$$C_p$$$ allows to reproduce the $$$c^{seg}$$$ values at all three measured positions. Metabolite concentrations obtained via Eq.1 and IWR highly agree as demonstrated in [Figure4]. However so far only deviations of $$$\mid{\hat{B_1^{+}}}\mid$$$ from $$$\mid{\hat{B_1^{-}}}\mid$$$ along the RL and AP direction are considered. The use of a 3D reception sensitivity map might further improve the accordance of the obtained values. In conclusion, the proposed calibration strategy allows to obtain reliable metabolite concentrations in vivo without the use of additional hardware nor assumptions about an internal reference at 3T.