Proton beam electron return effect: Monte Carlo simulations and experimental verification

Proton therapy (PT) is expected to benefit from integration with magnetic resonance (MR) imaging. However, the magnetic field distorts the dose distribution and enhances the dose at tissue-air interfaces by the electron return effect (ERE). The objectives were (a) to provide experimental evidence for the ERE in proton beams and (b) to systematically characterise the dependence of the dose enhancement ratio (DER) on magnetic field strength, orientation, proton energy and voxel size by computer simulations.

EBT3 films were irradiated with 200 MeV protons with and without a 0.92 T transverse field of a permanent magnet to determine the DER at effective measurement depths of 0.156 and 0.467 mm from an air interface. High-resolution Monte Carlo simulations were performed to reproduce the irradiation experiments and to calculate the DER for proton energies between 50–200 MeV and magnetic field strengths between 0.35–3 T as function of distance from the air interface. Voxel sizes of 0.05, 0.5 and 1 mm were analysed.

DERs of (2.2  ±  0.4)% and (0.5  ±  0.6)% were measured at 0.156 and 0.467 mm from the air interface, respectively. Measurements and simulations agreed within 0.15%. For a 200 MeV proton beam, the maximum DER in 0.05 mm voxels increased with magnetic field strength from 2.6% to 8.2% between 0.35 and 1.5 T, respectively. For a 1.0 T magnetic field, maximum DER increased from 3.2% to 7.6% between 50 and 200 MeV, respectively. Voxel sizes of 0.5 and 1 mm resulted in maximum DER values of 2.6% and 1.4%, respectively.

The ERE for proton beams in transverse magnetic fields is measurable. The local dose enhancement is significant, well predictable, decreases rapidly with distance from the air interface, and is negligible beyond 1 mm depth. Its impact on air-filled ionisation chambers and porous tissues (e.g. lung) needs to be considered.