An initial systematic study of the linear energy transfer distributions of a proton beam under a transverse magnetic...

To evaluate the biological effectiveness of magnetic resonance (MR)-guided proton beam therapy, comprehensively characterizing the dose and dose-averaged linear energy transfer (LET_d ) distributions under a magnetic field is necessary. Although detailed analysis has characterized curved beam paths and distorted dose distributions, the impact of a magnetic field on LET_d should also be explored to determine the proton relative biological effectiveness (RBE). Hence, this initial study aims to present a basic analysis of LET_d distributions in the presence of a magnetic field using Monte Carlo simulation (MCS).

Geant4 MCS (version 10.1.p01) was performed to calculate the LET_d distribution of proton beams. The incident beam energies were set to 70.2, 140.8, and 220 MeV, and both zero- and finite-emittance pencil beams as well as scanned field were simulated. A transverse magnetic field of 0-3 T was applied within a water phantom placed at the isocenter, and the three-dimensional dose and LET_d distributions in the phantom were calculated. Then, the depth profiles of LET_d along the curved trajectory and the lateral LET_d profile at the Bragg peak (BP) depth were analyzed under changing energies and magnetic fields. In addition, for zero- and finite-emittance beams, the correlation of the lateral asymmetries between the dose and LET_d distributions were analyzed. Finally, spread-out Bragg peak (SOBP) fields were simulated to assess the depth-dependent asymmetry of the LET_d distributions.

A transverse magnetic field distorted the lateral LET_d distribution of a pencil beam at close to the BP, and the magnitude of the distortion at the BP increased for higher energy beams and larger magnetic fields. For a zero-emittance beam, the differences in LET_d between the left and right D₂₀ positions were relatively large; the difference in LET_d was 1.5 and 2.3 keV/μm at 140.8 and 220 MeV, respectively, at a magnetic field of 1.5 T. These asymmetries were pronounced at positions where the dose asymmetries were large. The size of the asymmetry was less substantial for a finite-emittance beam and even less for a scanned field. However, a 1.5-keV/μm difference still remained between the left and right D₂₀ positions of a scanned field penumbra for a 220 MeV beam under the same magnetic field. For the SOBP field, it was found that the distal region of SOBP had the highest LET_d distortions, followed by the central and proximal regions for the middle-sized SOBP (5 × 5 × 5 cm³ ), whereas the degree of LET_d distortion did not vary much with depth for the 10 × 10 × 10-cm³ SOBP field.

Our results indicate that not only the dose but also LET_d distortions should be considered to accurately evaluate the biological effectiveness of MR-guided proton beam therapy.