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

Abstract

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.

Keywords: LET quenching; Monte Carlo simulations; beam quality correction; linear energy transfer; proton beam therapy; radiochromic film dosimetry.

Figure 1

Schematic overview of the measurement setup in water. The custom film holder fits into the same Trufix Holder (PTW) as the Roos IC. IC and film measurements were carried out sequentially. [Color figure can be viewed at wileyonlinelibrary.com]

Figure 2

Uncorrected film dose (dashed lines) and Monte Carlo simulated dose (solid lines) of three spread‐out Bragg peak (SOBP) beams in water. The 50% and 87% initial fluence contribution of the high‐energy beam to the SOBP of “${\mathrm{b}}_1$” appears as a 0.1 and 0.5 Gy dose tail in “${\mathrm{b}}_2$” and “${\mathrm{b}}_3$,” respectively. The error bars represent the 1σ standard deviation of the three film measurements. [Color figure can be viewed at wileyonlinelibrary.com]

Figure 3

Monte Carlo simulated ${\mathrm{L}}_{\mathrm{d}}$ (solid lines) and ${\mathrm{L}}_{\mathrm{t}}$ (dashed lines) of “${\mathrm{b}}_1$,” “${\mathrm{b}}_2$” and “${\mathrm{b}}_3$” in water. [Color figure can be viewed at wileyonlinelibrary.com]

Figure 4

Relative effectiveness as a function of dose‐ (a) and fluence‐ (b) averaged linear energy transfer. relative effectiveness (RE) measured at a constant dose equal to 1Gy are represented with open markers and error bars. The dose and ${\mathrm{L}}_{\mathrm{d}}$/${\mathrm{L}}_{\mathrm{t}}$ confidence interval is derived from the positioning uncertainty. The former inherits in addition the standard deviation of the three repeated irradiations. The RE at varying dose levels measured in the distal part of “${\mathrm{b}}_1$” are illustrated with filled symbols (a). [Color figure can be viewed at wileyonlinelibrary.com]

Figure 5

Simulated energy spectra of “${\mathrm{b}}_1$” (solid line), “${\mathrm{b}}_2$” (dashed line) and “${\mathrm{b}}_3$” (dotted line) in water at a constant position. The energy deposition is plotted against the left vertical axis in blue, while the fluence is plotted against the right axis in red. All curves are normalized to the integral over the entire spectrum for better visualization. [Color figure can be viewed at wileyonlinelibrary.com]

Figure 6

${\mathrm{D}}_{1/2}$ as a function of linear energy transfer resulting from minimizing the squared differences of the measured and calculated $g_{Q,Q_0}$. [Color figure can be viewed at wileyonlinelibrary.com]

Figure 7

Relative deviation of the calculated to the measured $g_{Q,Q_0}$ correction factors over depth. [Color figure can be viewed at wileyonlinelibrary.com]

Figure 8

Simulated dose deposition spectra of protons differential in linear energy transfer yielding an iso‐${\mathrm{L}}_{\mathrm{d}}$ equal to 6.4 keV/μm. Single energy beams are illustrated in (a). Box shaped spread‐out Bragg peaks with a side length of 5 cm centered at 6 and 30 cm are plotted together with beams “${\mathrm{b}}_1$,” “${\mathrm{b}}_2$” and “${\mathrm{b}}_3$” in (b). [Color figure can be viewed at wileyonlinelibrary.com]

Figure 9

Calculated relative effectiveness as a function of dose‐averaged linear energy transfer for four single energy layers, the beams “${\mathrm{b}}_1$”–“${\mathrm{b}}_3$“ and two cases obtained from a commercial TPS centered at 6 and 30 cm depth. Relative effectiveness (REs) of all cases (at constant ${\mathrm{L}}_{\mathrm{d}}$) are almost overlaying, indicating that RE correlates with ${\mathrm{L}}_{\mathrm{d}}$ in all nine beam configurations. The first and fourth order polynomial fits are represented with solid and dashed lines, respectively. [Color figure can be viewed at wileyonlinelibrary.com]