A critical study of different Monte Carlo scoring methods of dose average linear-energy-transfer maps calculated in voxelized geometries irradiated with clinical proton beams

We compare unrestricted dose average linear energy transfer (LET) maps calculated with three different Monte Carlo scoring methods in voxelized geometries irradiated with proton therapy beams with three different Monte Carlo scoring methods. Simulations were done with the Geant4 (Geometry ANd Tracking) toolkit. The first method corresponds to a step-by-step computation of LET which has been reported previously in the literature. We found that this scoring strategy is influenced by spurious high LET components, which relative contribution in the dose average LET calculations significantly increases as the voxel size becomes smaller. Dose average LET values calculated for primary protons in water with voxel size of 0.2 mm were a factor similar to 1.8 higher than those obtained with a size of 2.0 mm at the plateau region for a 160 MeV beam. Such high LET components are a consequence of proton steps in which the condensed-history algorithm determines an energy transfer to an electron of the material close to the maximum value, while the step length remains limited due to voxel boundary crossing. Two alternative methods were derived to overcome this problem. The second scores LET along the entire path described by each proton within the voxel. The third followed the same approach of the first method, but the LET was evaluated at each step from stopping power tables according to the proton kinetic energy value. We carried out microdosimetry calculations with the aim of deriving reference dose average LET values from microdosimetric quantities. Significant differences between the methods were reported either with pristine or spread-out Bragg peaks (SOBPs). The first method reported values systematically higher than the other two at depths proximal to SOBP by about 15% for a 5.9 cm wide SOBP and about 30% for a 11.0 cm one. At distal SOBP, the second method gave values about 15% lower than the others. Overall, we found that the third method gave the most consistent performance since it returned stable dose average LET values against simulation parameter changes and gave the best agreement with dose average LET estimations from microdosimetry calculations.