Table 1.

Implementation of correction methods

Method	Correction	Weights	Assumptions
Method 1: Phantom replacement	Equation 10: $\frac{\left[\text{m}\right]}{\left[\text{P}\right]}=\frac{F_{\text{m}}\left(\mathit{r}\right){\sum }_{k=1}^N{w}_k{S}_{\text{m},k}\left(\mathit{r}\right)}{F_{\text{P}}\left(\mathit{r}\right){\sum }_{j=1}^N{w}_j\left(\mathit{r}\right)S_{\text{P},j}\left(\mathit{r}\right)}$ and saturation correction per Equation 14: $F_{\text{m}}\left(\mathit{r}\right)=\frac{1-cos\theta \left(\mathit{r}\right)·e^{-\frac{T_{\text{R}}}{T_{1,\text{m}}}}}{sin\theta \left(\mathit{r}\right)\times \left(1-e^{-\frac{T_{\text{R}}}{T_{1,\text{m}}}}\right)}$	WSVD applied to the phantom. The same weights are applied to the in vivo data.	All parameters except saturation correction are identical in both scans. Rather than scanning multiple phantoms with different T1 values, both phantom and metabolite signals were saturation‐corrected using Equation 14.
Method 2: Explicit normalization	Equation 12: $\left[\text{m}\right]/c=\sum _{k=1}^N{\widehat{w}}_k\left(\mathit{r}\right)\frac{1}{I_{\text{m},k}\left(\mathit{r}\right)}{S}_{\text{m},k}\left(\mathit{r}\right)$	WSVD applied separately to in vivo and phantom data. Weights normalized to sum to 1, according to Equation 4.	Assumes uniform metabolite concentration across the PSF.
Method 3: Simplified normalization	Equation 19: $\left[\text{m}\right]/c=\frac{\eta \left(\mathit{r}\right)F_{\text{m}}\left(\mathit{r}\right)}{V}\sum _{k=1}^N{w}_k^{\text{RUN}}\left(\mathit{r}\right)S_{\text{m},k}\left(\mathit{r}\right)$	WSVD applied separately to in vivo and phantom data.	Assumes the ${\text{B}}_1^{\pm }$ values at the central point of each voxel can be used for normalization (i.e., either PSF is sharply peaked and/or ${\text{B}}_1^{\pm }$ are spatially slowly varying).

Abbreviations: PSF, point spread function; WSVD, whitened singular value decomposition.