## 2 Materials and Methods
### Study of Optimal Conditions for Awake Acquisition with Point Sources  
In this study, we aimed to investigate the detectability of point sources in PET imaging using a rat numerical phantom with four point sources and to investigate how these sources affect brain uptake estimation. The phantom was designed with two point sources positioned at the snout and two under the ear.  
To evaluate the detectability of point sources and their impact on brain uptake estimation, we explored the effect of different parameters, including the activity of the numerical rat phantom and the activity of the point sources. Specifically, we varied the activity of the rat brain phantom in steps of 20 uCi, ranging from 10 to 210 uCi, and the activity of the point sources in steps of 0.5 uCi, ranging from 1 to 10 uCi. This resulted in a total of 220 combinations of brain and point source activities.  
It is important to note that the brain activity simulated in our experiments corresponds to approximately 15% of the total activity in the rat body. This percentage represents the median activity level observed in the brain across the four rat acquisitions explained in Section 2.4. Since the process involves stochastic elements, each combination was simulated 100 times, randomly moving the rat within the FOV to obtain a detectability value for each case.  
For each simulation, we used a time step of 12.5 ms (corresponding to a frequency of 80 Hz). This choice of time step strikes a balance between precise motion tracking and good detectability of the sources in the image. The execution time of each simulation was not lengthy due to the short time step. Additionally, to address the introduction of more random coincidences with increasing acquisition activity, we investigated how well the delayed window (DW) method, as proposed by [PERSON] et al. [24], can mitigate this issue by subtracting the contribution of random coincidences from the image.  
Apart from detectability, we also studied how the activity of the point sources affects image quality. Our primary goal is to study the brain of the animal accurately, which requires avoiding halo artifacts induced by the point sources attached to the animal's head. Halo artifacts are circular regions around high-activity areas, such as the point sources, where nearby regions underestimate the uptake [25]. In addition, we considered the impact of random coincidences introduced by the sources, and we assessed how the DW method can help reduce their impact.  
To investigate the effects of point source activity on brain quantification, we conducted simulations with different activities injected into the animal, both with and without point sources. We used the image without point sources as the reference and computed the Root Mean Square Error (\(RMS_{e}\)) for the images with different point source activities. The \(RMS_{e}\) values are defined as  
\[RMS_{e}=\sqrt{\frac{\sum_{j\in BR}(I_{j}^{o}-I_{j}^{ps})^{2}}{N}} \tag{3}\]  
where the sum is performed over the voxels \(j\) inside the brain region \(BR\). \(I^{o}\) represents the image without point sources, and \(I^{ps}\) represents the image with point sources. \(N\) is the total number of voxels inside the brain region. To ensure fair comparison, both images are in relative standardized uptake value (\(SUV_{r}\)).  
All simulations took into account scatter and random events to accurately model real-world conditions.  
The results of this study enable us to establish the optimal conditions for detecting point sources while avoiding compromising the quality of the reconstructed brain image by adding too much activity.