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

Abstract

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). Methods: 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 depthdependent asymmetry of the LET d distributions. Results: 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 zeroemittance beam, the differences in LET d between the left and right D 20 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 D 20 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 cm 3 ),whereas the degree of LET d distortion did not vary much with depth for the 10 × 10 × 10-cm 3 SOBP field.