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H. Fuchs, P. Moser, M. Gröschl, D. Georg:
"Magnetic field effects on particle beams and their implications for dose calculation in MR-guided particle therapy";
Medical Physics, 44 (2017), 3; 1149 - 1156.

Purpose: To investigate and model effects of magnetic fields on proton and carbon ion beams for
dose calculation.
Methods: 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 c-index analysis was utilized, using a criteria of 2%/2 mm of the local maximum.
Results: 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 cmean (mean value of the c distribution) of 0.6, with 14.4% of
the values above 1 and c1% (1% of all points have an equal or higher c 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 ls. The impact of tissue interfaces on the proton dose distributions was
found to be less than 2% for a dose voxel size of 1 9 1 9 1 mm3.
Conclusion: 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 energycorrected
relativistic Lorentz equation was able to describe the beam path, taking into account the
particle energy, magnetic field, and material. © 2017 American Association of Physicists in Medicine
[https://doi.org/10.1002/mp.12105]

carbon ion, characterization, ion beam therapy, magnetic field, MR, proton