Magnetic field effects on particle beams and their implications for dose calculation in MR-guided particle therapy

To investigate and model effects of magnetic fields on proton and carbon ion beams for dose calculation.

In a first step, Monte Carlo simulations using Gate 7.1/Geant4.10.0.p03 were performed for proton and carbon ion beams in magnetic fields ranging from 0 to 3 T. Initial particle energies ranged from 60 to 250 MeV (protons) and 120 to 400 MeV/u (carbon ions), respectively. The resulting dose distributions were analyzed focusing on beam deflection, dose deformation, as well as the impact of material heterogeneities. In a second step, a numerical algorithm was developed to calculate the lateral beam position. Using the Runge-Kutta method, an iterative solution of the relativistic Lorentz equation, corrected for the changing particle energy during penetration, was performed. For comparison, a γ-index analysis was utilized, using a criteria of 2%/2 mm of the local maximum.

A tilt in the dose distribution within the Bragg peak area was observed, leading to non-negligible dose distribution changes. The magnitude was found to depend on the magnetic field strength as well as on the initial beam energy. Comparison of the 3 T dose distribution with non-B field (nominal) dose distributions, resulted in a γ_mean (mean value of the γ distribution) of 0.6, with 14.4% of the values above 1 and γ₁ % (1% of all points have an equal or higher γ value) of 1.8. The presented numerical algorithm calculated the lateral beam offset with maximum errors of less than 2% with calculation times of less than 5 μs. The impact of tissue interfaces on the proton dose distributions was found to be less than 2% for a dose voxel size of 1 × 1 × 1 mm³ .

Non-negligible dose deformations at the Bragg peak area were identified for high initial energies and strong magnetic fields. A fast numerical algorithm based on the solution of the energy-corrected relativistic Lorentz equation was able to describe the beam path, taking into account the particle energy, magnetic field, and material.