Implementation and verification of Monte Carlo particle transport in electromagnetic fields in GATE

Abstract

Magnetic resonance guidance in proton therapy is currently being investigated by several research groups in radiation oncology. The first stage of research includes feasibility studies in silico to evaluate the impact of the magnetic field on the dose calculation, optimization and delivery. Moreover, dosimetric protocols in the presence of a strong magnetic field can be affected and the existing Code of Practices have to be reevaluated. These studies rely on accurate and validated Monte Carlo (MC) simulation frameworks. This project aimed to study particle transport in electromagnetic fields in the MC toolkit GATE. First, the accuracy of GATE for the transport of charged particles in electromagnetic fields was assessed. Afterwards, the accuracy of GATE for dosimetric applications within external magnetic fields was tested. More specifically, the relative deviation from the analytical solution of the Boltzmann transport equation is quantified based on the Fano theorem. In a first step, GATE was extended to simulate particle transport in electromagnetic fields. The correctness of the implementation was benchmarked against an independently calculated numerical solution. Afterwards, a Fano cavity test for electrons and protons was implemented, also in the presence of a magnetic field. Mono-energetic electrons with energies between 0.05-20 MeV and protons with 1.5-250 MeV were spatially uniform and isotropically generated inside a plane parallel ionization chamber. The chamber was modelled as a cylinder with an energy-dependent radius and a 2 mm cavity inside it, ensuring the conditions of charged particle equilibrium and the Fano theorem. Uniform magnetic fields of B = 0.35-3 T were applied along the central axis of the chamber. Different multiple scattering models (MSC) were employed to evaluate the performance in terms of accuracy and calculation time. Electromagnetic physics list option 3 (Urban MSC) and option 4 (Goudsmit-Saunderson for electrons and WentzelVI for protons) were primarily used. The relative difference between the simulated absorbed dose in the cavity and the theoretical calculated dose value (based on the Fano theorem) was determined to assess the accuracy of the MC transport algorithm. Electrons with energies between 0.5-20 MeV showed deviations less than 0.3% (B = 0 T) and 0.6% (B > 0 T) for a maximum step size of 0.1 mm in the cavity (option 4 ). Comparable results with option 3 could only be achieved with a maximum step size of 0.001 mm. The electron transport showed a lack of accuracy and stability in the low energy spectrum (0.05-0.1 MeV), even for different physics lists (e.g., single scattering) and smaller step sizes in the nanometer range. Differences up to 4.9% (option 4 ) and 5.8% (option 3 ) were obtained for B ≥ 0 T. Protons with energies between 60-250 MeV showed relative differences less than 0.2% for B = 0 T and 0.3% for B > 0 T using a maximum step size of 0.1 mm (option 4 ). The relative deviation of protons in the energy range of 3-40 MeV was less than 0.6% for B = 0 T and 0.01 mm. A maximum deviation of 7.7% was obtained for 1.5 MeV and could not be considerably improved by a single scattering model, different electromagnetic physics lists or smaller step sizes. Deviations of up to 8% were observed within the transport algorithm, depending on the physics lists, step size and energy range. The simulation of low energy particles (≤ 1.5 MeV) must be further investigated and improved since the results indicate considerable differences from the theoretical values. The results of this study pave the road towards the simulation of ionization chambers in magnetic fields. Moreover, the implemented extension in GATE, allows particle transport using custom and realistic electro-magnetic field maps, as generated using finite element models from external software.