## 4 Discussion
The 2-class method showed non-significant differences between the TOF and non-TOF reconstruction after correction of multiple comparisons, indicating two methods out of three showed significant improvement when applying TOF. In Figure 5, the TOF reconstruction shows lower maximum uptake than the non-TOF reconstruction. This is consistent with the results in Figure 3. This may indicate that image noise is suppressed more in the TOF reconstructed images, resulting in a lower maximum uptake. By using TOF, the local under- and overestimations in the PET data are also slightly reduced, bringing the TOF images closer to the CTAC reference (Figure 5), although this effect is small visually. In Figures 6 and 7, the use of the TOF reconstruction resulted in the reduction of standard deviation and mean of the bias. This can be seen in the bias atlas images across all MRAC methods. These findings are similar to what has been reported previously in two whole-body studies [7; 14]. For non-TOF reconstruction, there is overestimation near the sinus regions (Figure 6) for each of the MRAC methods but using TOF reconstruction corrects majority of it. Thus, TOF is beneficial in removing not just underestimation but overestimation due to attenuation correction errors. Our results are in good agreement with previous studies. [PERSON] et al. compared several state-of-the art MRAC methods and concluded that the errors in the non-TOF reconstructions were significantly higher than with the TOF reconstructions [26], similarly to what was presented here. The paper also showed a lower median bias in TOF regardless of the MRAC method. However, looking closely at the results presented with no-bone CT and atlas-CT, the regional bias in the TOF reconstruction may not always be superior to the non-TOF reconstruction, indicating some regional variation remains in TOF similarly to our study. As the study was performed using a different PET/MR system with higher timing resolution (390 ps), this would indicate the effect exists also across systems and with different timing resolutions. Finally, in this small proof-of-concept study, we have shown that TOF might be beneficial for neuroimaging PET studies performed on the PET/MR. Due to the low timing resolution (525 ps) of our PET/MR system, the detected differences were small in terms of regional bias. Statistically significant differences were seen only with two MRAC methods out of three when comparing the average error. Whereas no significant improvement was seen in correlation of MRAC reconstruction to CTAC reconstruction when applying TOF, although both correlation and fitting coefficients improved with TOF. Although, it would seem the use of TOF implies a smaller bias on average (Figure 6). However, we found implications that some regions might increase in bias compared to non-TOF reconstruction, similarly to [PERSON] et al. [16], although TOF shows reduced variation on a global scale (Figure 7). This effect was smaller when the accuracy of the attenuation map increased, making accurate attenuation correction a necessary prerequisite in neuroimaging, also when applying TOF, as recommended by [PERSON] et al. [16]. As the Ingenuity TF PET/MR is capable of 525 ps timing resolution, more gain in quantitative accuracy could be achieved with a PET/MR system capable of higher timing resolution as suggested in [7]. Recently, several brain-dedicated PET imaging systems have been introduced with a timing resolution even close to 100 ps [27; 28]. Thus, it would be worthwhile to investigate our preliminary findings on how much the accuracy of the PET images is affected by the accuracy of the attenuation maps used in these systems in combination of TOF, in addition to studying the changes in regional variation in accordance with TOF timing resolution. Thus, more gain in quantitative and visual accuracy in PET could be achieved when applying TOF with systems capable of higher timing resolutions and we strongly encourage further investigations on this matter.