## 4 Discussion  
The effect of TOF imaging in reducing the errors due to imperfect MRAC in the head region was investigated. The results show that TOF reconstruction reduced the visual and quantitative errors in the head region of MRAC, although the overall effect was small. The effect was seen in the majority of the head regions independent of the accuracy of the attenuation map. The gains in quantitative accuracy were in part dependent on the anatomical location and the accuracy of the attenuation map, as TOF resulted in reduction of both over- and underestimations compared to the non-TOF reconstruction. Overall, a better concordance, although slight as well, to CTAC reconstructed PET was achieved when TOF information was applied in the image reconstruction and was statistically significant for two out of three MRAC methods. In Figure 2, a reduction of bias can be seen when applying TOF with all the methods, although there is some variation by patient and the overall gain is small, within 1% of the methods. In some cases, the distribution of bias is also smaller with TOF, although the effect becomes less visible when the accuracy of the attenuation map decreases. Tables A1 and A2 show the mean and SD values for all brain regions separately. When using 3-class and 2-class (air included and excluded) attenuation maps, 26, 23, and 23 regions out of 35 showed lower absolute bias with TOF. Absolute bias increased in 9, 12, and 12 regions with TOF, respectively. The maximum gain due to TOF was 3% at maximum in one region and the gain reduced when the 3-class attenuation map was used (Table A1). In Figure 3, the 2-class MRAC methods show that using TOF reduces the variance when compared to the non-TOF reconstruction. This can also be seen in Table 1, where R\({}^{2}\) values improve with TOF reconstruction for the 2-class methods; however, the differences were small, similarly to the VOI analysis. For the 3-class MRAC method, there are no  
Figure 7: Bias standard deviation images with all the methods. Small local improvements can be seen with the TOF reconstruction with a systematic reduction of standard deviation throughout the brain. (**A**) 3\(-\)class MRAC, (**B**) 2\(-\)class MRAC, (**C**) 2\(-\)class MRAC without air cavities using non\(-\)TOF reconstruction. (**D**) 3\(-\)class MRAC, (**E**) 2\(-\)class MRAC, (**F**) 2\(-\)class MRAC without air cavities using TOF reconstruction. improvements in the R\({}^{2}\) value, as the more accurate attenuation map results in less variance to begin with. The TOF reconstruction also improves the linear regression fitting parameters by bringing slope \(a\) closer to the ideal value of 1 and lowering the intersect \(b\) towards the ideal value of zero for all methods. Two methods out of three showed non-significant differences with parameter \(b\) with TOF, indicating improvement. However, the changes between TOF and non-TOF reconstructions were not statistically significant for coefficients \(a\) and \(b\) as the 95% confidence intervals overlap (Table 1). These would indicate that despite TOF resulting in an improved correlation of MRAC reconstructed PET to CTAC reconstructed PET, the changes were altogether small and statistically non-significant. The Bland-Altman graphs in Figure 4 show a similar reduction of error when TOF reconstruction is used. The non-TOF data points have wider distribution. The 2-class MRAC methods do not have clear differences between each other, but the 3-class MRAC has a tight error distribution in both non-TOF and TOF reconstruction, with TOF reconstruction having even less variance than the non-TOF reconstruction. The statistical testing of the VOI differences from Table A1, presented in Table 2, confirmed that two out of the three MRAC methods (2-class method without air, and the 3-class method) showed statistically significant improvements in the average error when TOF reconstruction was used. The median differences in the average VOI errors were small in accordance with VOI analysis.