## 3 Results
### Quantitative Analysis  
For a single preclinical PET detector module, the radial spatial resolution was estimated using Anger logic and MLP as positioning algorithms (Figure 2). The difference between the two algorithms is substantial for an animal-PET scanner with near sub-millimetric spatial resolution. Figure 3a shows histograms in the XY plane of the estimation error X\({}_{\text{real}}\)-X\({}_{\text{estimate}}\) whereas Figure 3b illustrates histograms of the Z-axis (DOI) estimation error Z\({}_{\text{real}}\)-Z\({}_{\text{estimate}}\) from the validation dataset. On the XY plane, the histograms obtained using the MLP approach are almost similar to those obtained using Anger logic. In contrast, along the Z-axis, the MLP histogram is more symmetric in pick neighborhoods (still asymmetric in tails), different from the Anger histogram, depicting a visible difference between the proposed and conventional method. Figure 3: The normalized histograms of the estimation error along (a) XY plane and (b) \(Z\)-axis (DOI) from the validation dataset. Figure 2: Spatial resolution of one detector module for a point source at six distances from the center of the crystal along the radial direction. The scanner's spatial resolution based on Anger and MLP positioning algorithms should be measured at the center and at one-quarter of the axial transverse distance according to the NEMA NU-4 standard. Supplementary measurements were performed along the axial and radial directions with a step size of 5 mm (Figure 4). The calculated radial spatial resolution based on Anger logic varied between 1.5 mm and 2.4 mm (FWHM) while the MLP algorithm led to a radial spatial resolution that varied between 1.21 mm and 1.75 mm (FWHM). The absolute sensitivity of the preclinical PET scanner is independent of the positioning algorithm (Figure 5). The sensitivity was estimated across the axial FOV using the default energy window (150-650 keV). The estimated DOI's FWHM as a function of the scintillation point at depths of 2, 4, 6, 8, and 10 mm were reported in Table 2. The advantage of the MLP algorithm is more evident, relative to Anger logic, in distinguishing details in the \(Z\)-axis. The predicted depths (Z) of scintillations taking place on a detector module, and their corresponding bias and standard deviation (STD), were summarized in Table 3. A scintillation point source was placed at 10 positions (depths) and then displaced with a 1 mm step size from the surface of the SiPM to the entrance surface of the detector. The results showed that the error and STDs increase by increasing \(Z\) (getting close to the SiPM's surface). When the distance from the SiPMs' surface increases, the change in the optical photon distribution map on the photodetector surface leads to a decline in the model's accuracy for the estimation of DOI  
Figure 4: **(a)** Radial and **(b)** axial spatial resolutions of the PET scanner for a point source at five distances from the center of the \(Z\)-axis calculated using the National Electrical Manufacturers Association (NEMA) NU-4 protocol. Figure 5: Absolute sensitivity measured at different distances from the center of the field-of-view (FOV) along the \(Z\)-axis for the simulated PET scanner. Figure 6 illustrates reconstructed slices of the image quality phantom based on the NEMA NU-4 standard produced by the MLP and Anger logic positioning methods during reconstruction. Figures 7 and 8 illustrate images of the grids along with horizontal intensity profiles drawn on images of the spherical sources for the MLP and Anger logic positioning methods, respectively. \begin{table}
\begin{tabular}{c c c} \hline
**Depth (mm)** & **Anger (mm)** & **MLP (mm)** \\ \hline
2 & 0.66 & 0.42 \\
4 & 0.79 & 0.53 \\
6 & 0.98 & 0.75 \\
8 & 1.2 & 0.91 \\
10 & 1.38 & 1.02 \\ \hline \end{tabular}
\end{table} 
Table 2: Depth of interaction resolution for one detector module based on Anger logic and multilayer perceptron (MLP) positioning algorithms.