## 3 Results  
Figure 2 shows the relative distribution of bias across all the 35 regions of the brain. The distribution of bias is smaller in the TOF reconstructed images and majority of the subjects (8/10 in 3-class and 7/10 in 2-class MRAC) show a reduced bias across all the attenuation maps when TOF reconstruction is applied. Overall, the median differences are small (within 1%) between TOF and non-TOF reconstructions. The VOI averages can be seen in Table 11, where TOF showed a maximum error reduction of 3% in the region of the vermis. The reduction of bias was smaller when the accuracy of the attenuation map increased, meaning the PET reconstruction using an attenuation map with the least accuracy gained the most benefit from TOF. Figure 3 shows the regression plots with all attenuation maps with TOF and non-TOF reconstruction. The TOF reconstructions shows only minor changes in correlation to CTAC reconstructed PET across all MRAC methods. Distribution of data points is narrower with TOF reconstruction. Figure 2: Box and whisker plots of the relative difference to CTAC reconstructed PET when using TOF and non\(-\)TOF reconstructed images. (**A**) 3\(-\)class MRAC, (**B**) 2\(-\)class MRAC, (**C**) 2\(-\)class MRAC without air cavities. The box plots show the results of each patient using the set of 35 VOIs’ mean bias as data. For each subject, the red TOF box plot is presented first, followed by blue non-TOF box plot immediately to its right. Outlier values are denoted with red ‘+’ symbol. A value beyond the maximum whisker length of 1.5 times the quartile range is considered an outlier. Table 1 contains the fitting coefficients and R\({}^{2}\) values from the correlation analysis. The R\({}^{2}\) values are similar with 3-class MRAC with and without TOF. The TOF reconstruction with 2-class MRAC shows an improved R\({}^{2}\). All correlations are statistically significant,  
Figure 3: Regression plots of non-TOF (marked as blue ‘o’ symbol) and TOF (marked as red ‘\(\times\)’ symbol) reconstructed activity values with different MRAC methods versus CTAC reconstructed PET. (**A**) 3\(-\)class MRAC, (**B**) 2\(-\)class MRAC, (**C**) 2\(-\)class MRAC without air cavities. and the 95% confidence intervals are close to each other between non-TOF and TOF reconstructions. The regression coefficients all improve, as coefficients \(a\) approach 1 and coefficients \(b\) approach 0 when TOF reconstruction is used. However, the confidence intervals for coefficient \(a\) overlap between TOF and non-TOF reconstructions, albeit very narrowly, meaning that the detected differences are not statistically significant. Two out of three coefficients \(b\) with TOF reconstruction are not significantly different from zero, while all non-TOF coefficients \(b\) are. This indicates improvement, even if all confidence intervals for coefficients \(b\) include their counterpart estimate as well, denoting the differences are not statistically significant. Figure 4 shows the Bland-Altman plots with all the attenuation maps with TOF and non-TOF reconstruction. Limits of agreement and the mean bias are slightly smaller with the TOF reconstruction across all MRAC methods. The results from statistical testing are given in Table 2. For the 2-class MRAC without air and the 3-class MRAC, the changes were statistically significant at 95% significance level with \(p=0.018\) and \(p<0.001\), respectively. Using the Benjamini-Hochberg method with FDR set to 5%, the null hypothesis of equal medians can be rejected for both 2-class MRAC without air and the 3-class MRAC, meaning that these two MRAC methods gained significant improvements when applying TOF reconstruction even after correction for multiple comparisons.