## 5 Conclusions  
Using TOF reconstruction could be beneficial in reducing the quantitative errors due to imperfections in MRAC also in the head region and needs further investigation and validation with PET systems capable of higher timing resolution. Nevertheless, even when using TOF reconstruction, accurate attenuation correction remains a necessary prerequisite in PET/MR neuroimaging. We have detected an effect where the majority of the regions showed reduced bias when TOF was applied; however, more bias, although small, was introduced in certain regions, confirming that the effect seen is indeed non-local. Overall, the differences seen in our study were small quantitatively and the improvements in average error were statistically significant only in two out of three MRAC methods when applying TOF. Although TOF reconstructions showed improvement in correlation and regression parameters, these differences were non-significant between TOF and non-TOF reconstructions. As a continuation of our preliminary study, we strongly encourage further investigations on this matter to determine how large gains in quantitative and visual accuracy in PET could be achieved with TOF with systems capable of higher timing resolutions. Conceptualization, J.L. and J.T. ; Data Curation, J.T. ; Formal Analysis, J.L. and J.T. ; Funding Acquisition, R.K. and M.T. ; Investigation, J.L. and J.T. ; Methodology, J.L. and J.T. ; Project Administration, R.K. and M.T. ; Software, J.T. ; Supervision, R.K.; Validation, J.L. ; Visualization, J.L. and J.T. ; Writing--Original Draft, J.L. and J.T. ; Writing--Review and Editing, J.L., J.T., R.K. and M.T. All authors have read and agreed to the published version of the manuscript. **Funding:** This study was financially supported by The Finnish Cultural Foundation Grant ID 00150543, Grant from Division of Imaging TUCH, the Alfred Kordelin Foundation, The Paulo Foundation (Paulon Saatio) and the Finnish Cultural Foundation, Varsinais-Suomi Regional Fund. Financial support was also received from State Research Funding (the expert responsibility area of TYKS, Turku University Hospital) (project numbers 13236, 13720), and grants from State funding for university-level health research, Turku University Hospital (11232). **Institutional Review Board Statement:** The study was conducted as a retrospective registry study at Turku PET Centre (study number: T7/2021). The study protocol was approved by Turku University Hospital Research Board and the legislative team. The requirements for ethical review in Finland are stipulated primarily in the Medical Research Act (488/1999, as amended) and the Act of the Medical Use of Human Organs, Tissues and Cells (101/2001 as amended). Ethical review is statutorily required for interventional medical research and some circumstances for studies on human organs, tissues, or cells. According to Finnish legislation, no ethical assessment or approval by an independent review board is mandatory for registry studies. The study was conducted in accordance with the Declaration of Helsinki. **Informed Consent Statement:** The need to acquire an active informed consent from the individuals included in the study was waived as the study was conducted as a retrospective registry study at Turku PET Centre. **Data Availability Statement:** Although all data cannot be shared because of patient confidentiality, some data generated or used during the study are available from the corresponding author by request. The source codes for the methods presented in this paper can be downloaded free of charge from the GitLab account ([[https://gitlab.utu.fi/jllind](https://gitlab.utu.fi/jllind)]([https://gitlab.utu.fi/jllind](https://gitlab.utu.fi/jllind)), accessed on 19 April 2022) of the corresponding author, hosted by the University of Turku, or by contacting the corresponding author directly ([PERSON]). **Acknowledgments:** We want to acknowledge [PERSON] for the assistance in implementing the data analysis pipeline and [PERSON] for helpful discussion and ideas in implementing this study.