Dose-averaged LET calculation for proton track segments using microdosimetric Monte Carlo simulations

Abstract

Purpose: There is an increasing interest in calculating linear energy transfer (LET) distributions for proton therapy treatments in order to assess the influence of this quantity in biological terms. Microdosimetric Monte Carlo (MC) simulations are useful tools to calculate dose-averaged LET, as this has been broadly proposed as the most adequate quantity to characterize these biological effects. However, a straightforward uniform sampling of the scoring site turns out to be computationally unaffordable. In contrast, some issues have been pointed out with the more efficient weighted sampling approach, frequently used in literature. Here, we address the issues associated with the latter method and propose adequate corrections to achieve reliable calculations of dose-averaged LET values from microdosimetry.

Methods and materials: Proton track structures have been simulated with Geant4-DNA considering two different approaches. One version employs a uniform sampling for placing the spherical site and is used as the reference. The other one uses a weighted sampling by considering the spatial distribution of transfer points. Some corrections are proposed for calculating a dose-averaged LET comparable to the reference case. An additional MC approach is proposed to obtain the weighted mean of the energy imparted per electronic collision of the proton within the site, the ${\delta }_2$ function, related to the straggling distribution, as an intermediate step in the LET calculation.

Results: Energy imparted per event distributions are different when employing either sampling methods, due to the different geometrical randomness. We have found an agreement below (0.15 ± 0.05) keV/μm in the worst case for uniform and weighted methods in dose-averaged LET values when the weighted sampling results are corrected according to our proposal. Our analysis is restricted to spherical sites of 1 and 10 μm diameter and monoenergetic beams in the range from 2 to 90 MeV.

Conclusions: This work shows a reliable and computational-efficient method to perform calculations of track segment dose-averaged LET using MC simulations for proton therapy beams, including the necessary considerations for obtaining the straggling distribution characteristics. The validity of this approach remains as long as the stopping power of the proton can be considered as constant along its track within the site.

Keywords: Geant4-DNA; LETd calculation; microdosimetry; proton therapy; sampling method.