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 (LETd) is required. In this study, we have developed the analytical LETd 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 LETd value for the lateral distribution of a pencil beam, the actual LETd increases away from the beam axis, because there are more scattered and therefore lower energy protons with higher stopping powers. To reflect this LETd behavior, we have assumed that the LETs of primary and halo components can take different values (LETp and LEThalo), which vary only along the depth direction. The values of dual‐LET kernels were determined such that the PBA‐dLET reproduced the MCS‐generated LETd 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 LETd distributions and mean LETd (LETd,mean) 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 LETd 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 LETd profiles calculated with the developed method reproduces MCS with the similar accuracy as in the homogeneous phantom. The maximum differences in LETd,mean 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, res