Numerical prediction based on sub-beam decomposition for magnetic deflection in MRI-guided proton therapy

Magnetic resonance image (MRI) guidance for proton therapy is an advantageous choice to improve the targeted dose accuracy, while the MRI magnetic field causes the Bragg peak lateral deflection and longitudinal retraction, eventually leading to dose deviation. Considering the energy spread of the proton beam, this deflection effect is more pronounced, which was demonstrated using Monte Carlo (MC) method in this study. We proposed a Ray-tracing-based numerical equivalent method to rapidly predicate the beam trajectory, by decomposing the beam with a certain energy spread into multiple sub-beams and characterizing it by a mono-energetic proton beam with appropriate energy. The equivalent relation was determined for the numerical algorithm and verified by MC simulations. The results show that the numerical prediction of the deflection trajectory is consistent with the MC simulations in sub-millimetric accuracy and each prediction was performed within 0.1s.