TU-F-CAMPUS-J-02: Developing a Phenomenological Model of the Proton Trajectory Within a Heterogeneous Medium Required for Proton Imaging

Abstract

Purpose: To develop an accurate phenomenological model of the cubic spline trajectory (CST) estimate of the proton path, accounting for the initial proton energy and water equivalent thickness (WET) traversed. Methods: Geant4 Monte Carlo (MC) simulations were used to calculate the path of protons crossing various slabs (5–30 cm WET) of different material (LN300, water and CB2–50% CaCO3) for a range of initial energies (150–330MeV). For each MC trajectory, CST was constructed based on the proton entrance and exit information and compared with the MC using the root mean square (RMS) metric. The CST path is dependent on the direction vector magnitudes (|P0,1|). First, |P0,1| is set to the proton path length. Then, a factor Λ is introduced to modify |P0,1|. The factor is varied to minimize the RMS with MC paths for every configuration. Finally, a set of Λopt factors that minimizes the RMS is presented. These are dependent on the ratio between WET and water equivalent path length (WEPL). The resolution along the path is investigated with a set of slabs. MTF analysis is performed on proton radiographs of a line-pair phantom reconstructed using the CST trajectories (Λopt and Λ1). Results: Λopt was fitted to the ratio of WET/WEPL using a power function (Y=1-AXB where A=0.36, B=4.07). The RMS deviation calculated along the path, between the CST and the MC path, increases with the WET. The increase is larger when using Λ1 than Λopt (difference of 5.0% with WET/WEPL=0.86). For 230(330) MeV protons, the MTF10% was found to increase by 40%(6%) respectively for a thick phantom (30cm) and by 25%(1%) for thinner phantom (25cm) when using the Λopt model compared to the Λ1 model. Conclusion: Based on these results, using CST with the Λopt factor reduces the RMS deviation and increases the spatial resolution when reconstructing proton trajectories.