## 1 Introduction  
Since the introduction of the first time-of-flight (TOF)-capable positron emission tomography (PET) systems, several advances have been made in terms of PET detector technology and achieving even higher timing resolutions. Recent developments in positron emission tomography/magnetic resonance (PET/MR) instrumentation have paved the way to TOF-capable PET/MR systems by using digital PET detectors [1, 2]. From the PET/MR systems available in the clinical market, the GE Signa PET/MR, the United Imaging uPMR 790 HD TOF PET/MR, and the Philips Ingenuity TF PET/MR are capable of TOF imaging [1, 2, 3]. The timing resolution of the systems are reported as 390 ps for the Signa, 480 ps for uPMR 790, and 525 ps for the Ingenuity TF [1]. Recently, an even higher timing resolution has been reported with a clinical PET/CT system, up to 210 ps [4]. These developments could result in several advantages especially in PET/MR imaging which are highlighted below. The inclusion of TOF in combined PET/MR systems can be considered beneficial due to a multitude of reasons. The visual quality of PET images can be improved by the higher contrast and signal-to-noise ratio (SNR) which TOF offers [5]. The use of TOF also offers additional advantages in robustness. The TOF reconstruction converges faster, especially with higher time resolution, and is more resilient to errors in normalization, scatter, and attenuation correction, due to the addition of additional constraints and reduced cross-dependencies between image voxels [6; 7; 8]. By including TOF information, only the image voxels along the segments of the line of response defined by the TOF resolution can be updated at each iteration, instead of all the voxels along the line of response [7]. The error propagation in TOF imaging can be considered to be proportional to TOF timing resolution, whereas in non-TOF reconstruction the errors are proportional to object size [9]. Therefore, using TOF in combined PET/MR has potential in producing PET images with higher visual and quantitative accuracy due to a reduced sensitivity to errors, especially when inconsistencies in attenuation correction occur. Previous studies have also highlighted several visual and quantitative benefits when applying TOF reconstruction. It has been shown that TOF decreases quantitative and visual errors due to MR-based attenuation correction (MRAC) in whole-body PET imaging, such as in cases of metal artifacts [10], susceptibility artifacts [11], defective PET detectors [12], a variety of PET artifacts [13] including implants [14], and MRAC in general [7]. Studies have shown that TOF reduces PET quantification errors when using MRAC, reducing the error propagation from attenuation maps to PET images [15]. Future systems with increased TOF timing resolution could enable the reduction of artifacts and quantification to an even larger degree [7]. Thus, applying TOF in combination of MRAC could be considered highly beneficial. However, these studies have been mainly performed and shown benefits for whole-body PET only. While these benefits are evident for whole-body imaging, the effect of TOF should be investigated for other body regions as well. Recently, it was shown that increasing the TOF resolution might increase error propagation to neighboring regions, and the effect of this error propagation can no longer be considered local [16]. In a simulation study performed in the lung region with different timing resolutions, it was shown that the errors in TOF-reconstructed regions increased or decreased in accordance with the non-TOF reconstruction [16]. This factor has important implications for neuroimaging, where it is desirable not just to reduce the global bias but to minimize regional variation as well. Thus, the error propagation in TOF reconstruction using imperfect attenuation maps should be further investigated for brain PET/MR imaging.