Dosimetric Deviations of Bragg-Peak Position Shifts in Uniform Magnetic Fields for Magnetic Resonance Imaging-Guiding Proton Radiotherapy: A Monte Carlo Study

Objective: To investigate dosimetric deviations in scanning protons for Bragg-peak position shifts, which were caused by proton spiral tracks in an ideal uniform field of magnetic resonance (MRI) imaging-guided proton radiotherapy (MRI-IGPRT). Methods: The FLUKA Monte-Carlo (MC) code was used to simulate the spiral tracks of protons penetrating water with initial energies of 70–270 MeV under the influence of field strength of 0.0–3.0 Tesla in commercial MRI systems. Two indexes, lateral shift (marked as WD) perpendicular to the field and a penetration-depth shift (marked as ΔDD) along the beam path, were employed for the Bragg-peak position of spiral proton track analysis. A comparison was performed between MC and classical analytical model to check the simulation results. The shape of the 2D/3D dose distribution of proton spots at the depth of Bragg-Peak was also investigated. The ratio of Gaussian-fit value between longitudinal and transverse major axes was used to indicate the asymmetric index. The skewness of asymmetry was evaluated at various dose levels by the radius ratio of circumscribed and inscribed circles by fitting a semi-ellipse circle of 2D distribution. Results: The maximum of WD deflection is 2.82 cm while the maximum of shortening ΔDD is 0.44 cm for proton at 270 MeV/u under a magnetic field of 3.0 Tesla. The trend of WD and ΔDD from MC simulation was consistent with the analytical model, which means the reverse equation of the analytical model can be applied to determine the proper field strength of the magnet and the initial energy of the proton for the planned dose. The asymmetry of 2D/3D dose distribution under the influence of a magnetic field was increased with higher energy, and the skewness of asymmetry for one proton energy at various dose levels was also increased with a larger radius, i.e., a lower dose level. Conclusions: The trend of the spiral proton track under a uniform magnetic field was obtained in this study using either MC simulation or the analytical model, which can provide an optimized and planned dose of the proton beam in the clinical application of MRI-IGPRT.