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.

Stopping power accuracy and achievable spatial resolution of helium ion imaging using a prototype particle CT detector system

“…Recently, Collins-Fekete et al [9] revisited and extended the Bayesian approach to work for the estimation of heavier ions trajectories. Additionally, the complex, time-consuming MLP algorithm was linked to the recent, more efficient phenomenological approach [8]. The algorithm uses cubic splines and includes the information of the Water Equivalent Path Length (WEPL) and the Water Equivalent Thickness (WET) to derive an accurate path estimate.…”

“…To overcome the problem of MCS, various path estimation algorithms have been proposed for protons, of which the most likely path (MLP) algorithm is the most widely used [4][5][6][7][8]. Compared to protons, heavier ions suffer less from MCS, due to on average smaller deflection angles per scattering.…”

A proton imaging system using a volumetric liquid scintillator: a preliminary study

“…These systems measure residual energies of individual proton particles along with determining their location and angular direction using position sensitive detectors placed before and after the patients (Pemler et al 1999, Sipala et al 2011, Esposito et al 2018. This information, when complemented with a suitable path estimation model, can correct for proton scattering, leading to better prediction of proton trajectories within the tissues (Williams 2004, Collins-Fekete et al 2015. These systems are known to provide good quantitative and imaging resolution but can also be expensive because they require high-speed single-event detectors and have complex instrumentation (Schneider et al 2004, Amaldi et al 2011, Biegun et al 2016, Johnson et al 2017.…”