Title:
Proton beam behavior in a parallel configured MRI-proton therapy hybrid: Effects of time-varying gradient magnetic fields.

Abstract:
Real-time magnetic resonance (MR) guidance is of interest to various groups globally because the superior soft tissue contrast MR images offer over other x-ray-based imaging modalities. Because of the precision required in proton therapy, proton therapy treatments rely heavily on image guidance. Integrating a magnetic resonance imaging (MRI) into a proton therapy treatment is a challenge. The charged particles (protons) used in proton therapy experience magnetic forces when travelling through the MRI magnetic fields. Given that it is desired that proton beams can be delivered with submillimeter accuracy, it is important that all potential sources of beam displacement are well modeled and understood. This study investigated the behavior of monoenergetic proton beams in the presence of a simulated set of realistic three-dimensional (3D) vector magnetic gradient fields required for spatial localization during imaging. This deflecting source has not been previously investigated.
Three-dimensional magnetic vector fields from a superconducting 0.5 T open bore MRI magnet model (previously developed in-house) and 3D magnetic fields from an in-house gradient coil model were applied to two types of computer simulations. In all simulations, monoenergetic proton pencil beams (from 80 to 250 MeV) were used. The initial directions of proton beams were varied. In all simulations, the orientation of the B field coincided with the positive z-axis in the simulation geometry. The first type of simulation is based on an analytic magnetic force equation (analytic simulations) while the second type is a full Monte Carlo (MC) simulation. The analytic simulations were limited to propagating the proton beams in vacuum but could be rapidly calculated in a desktop computer while the MC simulations were calculated in a cluster computer. The proton beam locations and dose profiles at the central plane (z = 0 cm) with or without magnetic fields were extracted and used to quantify the effect of the presence of the different magnetic fields on the proton beam.
The analytic simulations agree with MC results within 0.025 mm, thus acting as the verification of MC calculations. The presence of the B field caused the beam to follow a helical trajectory which resulted in angular offsets of 4.9 , 3.6 , and 2.8 for the 80, 150, and 250 MeV, respectively. Magnetic field deflections caused by a rapid MRI sequence (bSSFP, with maximum gradient strength of 40 mT/m) show a pattern of distortion which remained spatially invariant in the MR's field of view. For the 80 MeV beam, this pattern shows a maximum ranged in the y direction of 1.5 mm. The presence of the B field during the bSSFP simulations adds the same beam rotation to the observed during the B only simulations.
This investigation reveals that time-varying gradient magnetic fields required for image generation can cause a small spread in the proton beams used in the study which are independent of the effects arising from the B field. Further, studies where clinical beam kernels were convolved with this spread show that these magnetic fields are expected to have an insignificant impact on the beam's entrance dose.