Positron emission tomography (PET) is a nuclear medicine imaging techniquethat uses radiotracers to visualize processes like metabolism and perfusion. Theradiotracer emits positrons, which collide with shell electrons of the atomsthat make up the surrounding tissue. Such a collision produces two gammarayphotons, emitted roughly 180 degrees apart [1]. PET captures thesephotons using a cylindrical arrangement of detectors. When two photons aredetected simultaneously by different detectors, it registers as a line of response(LOR). These LORs are then pre-processed into a sinogram. A mathematicalreconstruction method is used to computationally recover the 3D distribution ofthe radiotracer (activity map) from the sinogram. However, genuine LORs can becorrupted by false LORs that come from scattering, random events, and spuriousevents. Mitigating these in reconstruction algorithms is essential for improvingPET imaging accuracy and reliability.This paper explores the theoretical foundation of the Time of Flight (TOF) SingleScatter Simulation (SSS) model by Watson (2007) [2]. It also includes a Pythonimplementation of the MATLAB code associated with [2]. The model modelsCompton scattering to accurately estimate scattered photons in PET.Incorporating TOF data into the SSS model improves estimation accuracy, albeitat the cost of increased computational time. To expedite computations, thealgorithm was simplified by restricting operations to a subset of rings anddetectors and by pre-processing images through cropping and downscaling.Interpolation fills in missing data, ensuring complete estimation.The outcome of this project is a Python implementation that exhibited a strongcorrelation with the estimates obtained using the MATLAB implementation. Anotable issue arose during the comparison between the main components ofthe SSS algorithm in Python and MATLAB. The Euclidean norm between theresults from these two implementations was significant, indicating that they wereon different scales. Nevertheless, both implementations accurately predictedthe scatter in the same locations and relative magnitudes, despite the scalediscrepancy. Investigation into the discrepancy’s cause is ongoing, but theproject demonstrates the feasibility of implementing the TOF SSS algorithm inPython.