Dose- rather than fluence-averaged LET should be used as a single-parameter descriptor of proton beam quality for radiochromic film dosimetry

Purpose: The dose response of Gafchromic EBT3 films exposed to proton beams depends on the dose, and additionally on the beam quality, which is often quantified with the linear energy transfer (LET) and, hence, also referred to as LET quenching. Fundamentally different methods to determine correction factors for this LET quenching effect have been reported in literature and a new method using the local proton fluence distribution differential in LET is presented. This method was exploited to investigate whether a more practical correction based on the dose- or fluence-averaged LET is feasible in a variety of clinically possible beam arrangements.

Methods: The relative effectiveness (RE) was characterized within a high LET spread-out Bragg peak (SOBP) in water made up by the six lowest available energies (62.4-67.5 MeV, configuration " $b_1$ ") resulting in one of the highest clinically feasible dose-averaged LET distributions. Additionally, two beams were measured where a low LET proton beam (252.7 MeV) was superimposed on " $b_1$ ", which contributed either 50% of the initial particle fluence or 50% of the dose in the SOBP, referred to as configuration " $b_2$ " and " $b_3$ ," respectively. The proton LET spectrum was simulated with GATE/Geant4 at all measurement positions. The net optical density change differential in LET was integrated over the local proton spectrum to calculate the net optical density and therefrom the beam quality correction factor. The LET dependence of the film response was accounted for by an LET dependence of one of the three parameters in the calibration function and was determined from inverse optimization using measurement " $b_1$ ." This method was then validated on the measurements of " $b_2$ " and " $b_3$ " and subsequently used to calculate the RE at 900 positions in nine clinically relevant beams. The extrapolated RE set was used to derive a simple linear correction function based on dose-averaged LET ( $L_d$ ) and verify the validity in all points of the comprehensive RE set.

Results: The uncorrected film dose deviated up to 26% from the reference dose, whereas the corrected film dose agreed within 3% in all three beams in water (" $b_1$ ", " $b_2$ " and " $b_3$ "). The LET dependence of the calibration function started to strongly increase around 5 keV/μm and flatten out around 30 keV/μm. All REs calculated from the proton fluence in the nine simulated beams could be approximated with a linear function of dose-averaged LET (RE = 1.0258-0.0211 μm/keV $L_d$ ). However, no functional relationship of RE- and fluence-averaged LET could be found encompassing all beam energies and modulations.

Conclusions: The film quenching was found to be nonlinear as a function of proton LET as well as of the dose-averaged LET. However, the linear relation of RE on dose-averaged LET was a good approximation in all cases. In contrast to dose-averaged LET, fluence-averaged LET could not describe the RE when multiple beams were applied.