An analytical dose-averaged LET calculation algorithm considering the off-axis LET enhancement by secondary protons for spot-scanning proton therapy.

Purpose: To evaluate the biological effects of proton beams as part of daily clinical routine, fast and accurate calculation of dose-averaged linear energy transfer (LET ) is required. In this study, we have developed the analytical LET calculation method based on the pencil-beam algorithm (PBA) considering the off-axis enhancement by secondary protons. This algorithm (PBA-dLET) was then validated using Monte Carlo simulation (MCS) results.

Methods: In PBA-dLET, LET values were assigned separately for each individual dose kernel based on the PBA. For the dose kernel, we employed a triple Gaussian model which consists of the primary component (protons that undergo the multiple Coulomb scattering) and the halo component (protons that undergo inelastic, nonelastic and elastic nuclear reaction); the primary and halo components were represented by a single Gaussian and the sum of two Gaussian distributions, respectively. Although the previous analytical approaches assumed a constant LET value for the lateral distribution of a pencil beam, the actual LET increases away from the beam axis, because there are more scattered and therefore lower energy protons with higher stopping powers. To reflect this LET behavior, we have assumed that the LETs of primary and halo components can take different values (LET and LET ), which vary only along the depth direction. The values of dual-LET kernels were determined such that the PBA-dLET reproduced the MCS-generated LET distribution in both small and large fields. These values were generated at intervals of 1 mm in depth for 96 energies from 70.2 to 220 MeV and collected in the look-up table. Finally, we compared the LET distributions and mean LET (LET ) values of targets and organs at risk between PBA-dLET and MCS. Both homogeneous phantom and patient geometries (prostate, liver, and lung cases) were used to validate the present method.

Results: In the homogeneous phantom, the LET profiles obtained by the dual-LET kernels agree well with the MCS results except for the low-dose region in the lateral penumbra, where the actual dose was below 10% of the maximum dose. In the patient geometry, the LET profiles calculated with the developed method reproduces MCS with the similar accuracy as in the homogeneous phantom. The maximum differences in LET for each structure between the PBA-dLET and the MCS were 0.06 keV/μm in homogeneous phantoms and 0.08 keV/μm in patient geometries under all tested conditions, respectively.

Conclusions: We confirmed that the dual-LET-kernel model well reproduced the MCS, not only in the homogeneous phantom but also in complex patient geometries. The accuracy of the LET was largely improved from the single-LET-kernel model, especially at the lateral penumbra. The model is expected to be useful, especially for proper recognition of the risk of side effects when the target is next to critical organs.