Investigation of the dose rate and linear-energy-transfer of the signal quenching of radiochromic silicone-based dosimeters for different curing times and compositions

The response of radiochromic dosimeters based on silicone is influenced by the dose-rate quenching and also the linear energy transfer (LET). However, the impact of curing time and composition on quenching has not been fully characterized. We investigated two dosimeter compositions, with 5% and 9% curing agent, which cured for 1, 3 or 5 days and that subsequently were irradiated with an 80 MeV proton beam with three different beam currents. Monte Carlo simulations were utilised for the estimation of dose, dose rate and LET profiles. We found a significant decrease in LET-dependent quenching with curing time, but no significant decrease in dose-rate-dependent quenching.


Introduction
State-of-the-art proton therapy (PT) utilises the technique of spot-scanning, where the target is covered layer-by-layer by moving a thin monoenergetic proton beam [1].Each energy layer is delivered with a dose rate determined by the cyclotron i.e., the machine-set dose rate, to ensure that the beam moves slowly enough to be steered by the magnets [1].Consequently, the local dose rate can vary significantly in a single field.In addition to that, linear energy transfer (LET) increases towards the end of the proton range.
Three-dimensional (3D) dosimetry has the capability of providing high spatial resolution measurements [2-4], which can be valuable in the experimental validation of radiotherapy (RT).However, the demanding beam characteristics of spot-scanning PT challenge the use of 3D dosimeters, since they quench, i.e. under-respond [5][6][7].
In this study, radiochromic silicone-based dosimeters composed of leucomalachite green (LMG) were investigated, a radiosensitive dye and chloroform, which acts as an initiator for the chain process that converts the (colourless) LMG into malachite green (MG), both dispersed in a silicone matrix [8,9].Given the matrix flexibility, this dosimeter garnered interest for the verification of motion and deformation studies [10].However, complex and time-consuming correction models must be used in order to correct proton beam measurements of these dosimeters, since they present significant LET-and dose-rate dependent quenching, which cannot be realistically implemented in a clinical setting [7].Previously, we found that curing time can have an impact on the dosimetric properties of radiochromic dosimeters, but only photons and low-LET protons (<2 keV/μm) were investigated [10].Therefore, the aim of this study was to obtain a more comprehensive LET and dose rate parametrization of the dosimeter response.

Fabrication and curing conditions
Dosimeters were fabricated from an silicone elastomer kit (SYLGARD 184 (DOW, Corning) which is commercially available, LMG and chloroform.Two different formulations were utilised in this study, containing different ratios of curing agent (CA) to silicone elastomer.The first formulation contained (in weight percentage) 5% CA, and the second, 9% CA.All formulations contained 0.26% LMG and 1.5% chloroform and the remaining weight percentage in silicone.The fabrication procedure was described detail by Høye et al. [11].The mixture was transferred with a large syringe into optical polystyrene cuvettes of dimensions 1×1×4.5 cm 3 and of a wall thickness of 1 mm.Whilst left curing at ~20°C, the cuvettes were protected from the light.Batches of dosimeters were cured for 1, 3 and 5 days prior to the irradiation day.

Dosimeter readout
Dosimeters were read out 1 hour before and 1 hour after irradiation with an optical 1D-scanner built inhouse.The scanner uses a 635 nm laser diode with a 4.5mW beam, with width of 0.054±0.01mm and height of 6 mm.Before the pre-irradiation read out, the dosimeters were removed from the cuvettes.The dosimeter was placed on a holder, which was moved in discrete 0.25 mm steps by a linear stage.The attenuation coefficient response of the samples, Δα = αpostαpre, was defined as the difference between the dosimeter's attenuation coefficient measured before and after irradiation.

Proton irradiation
Dosimeters were irradiated at Aarhus University Hospital (Aarhus, Denmark) in the Danish Centre for Particle Therapy with protons using a Varian ProBeam isochronous cyclotron.A monoenergetic beam of 80 MeV that spot-scanned, delivering a 5x7 cm 2 uniform field was used.Varying dose-rate levels were achieved by requesting different cyclotron currents in Varian's beam delivery diagnostic tool.For this experiment, a spot separation of 5 mm was chosen, which was sufficient to achieve a homogeneous field according to the treatment planning systems (Eclipse version 15.6).The dosimeters were placed parallel to the beam direction, with 2 cm of solid water placed directly in front of them.Three dosimeters were irradiated for each curing time and composition for each cyclotron current.

Monte Carlo simulations
The distributions of proton dose and dose-averaged-LET (LETd) were estimated using TOPAS (version 3.2) Monte Carlo (MC) in [12].The silicone base of the dosimeter was defined using information from the manufacturer and using an expected chain length of polydimethylsiloxane (n = 362) [6,11].A phasespace model used to simulate the beam was validated with an ionization chamber array (Giraffe, IBA dosimetry), a scintillator screen (XRV-4000 Beam Profiler, Logos Systems) and integral depth-dose measurements in a water phantom (MP3-PL, PTW) with a parallel plate ionization chamber (ROOS, PTW dosimetry).Local dose rates (  ̇) were estimated from the MC dose distributions and the beamon time, retrieved from irradiation log files.

Dose-rate and LET parametrization
We parametrized the dose-rate and LETd dependent-quenching by the quenching correction factor (QCF) defined by an empirical formula [7]: 12th International Conference on 3D and Advanced Dosimetry Journal of Physics: Conference Series 2630 (2023) 012021 The dimensionless fit parameters were estimated using the Scikit-learn package in Python [13].The change in the parameter-dependent coefficients a and c, which correspond, respectively, to the LET and dose-rate dependency, where used to evaluate the dosimeter quenching.
1. Optical densities (Δα) and calculated MC dose (shown in black for comparison) normalized 1 cm into the beam entrance, for the 5% and 9% CA dosimeter compositions, curing for 1, 3 or 5 days (Left panel).Ratio between (normalized) Δα and MC dose as a function of LETd (Right panel).

Results
The surface fit resulted in R-squared values >0.96 for all datasets.The parameter-dependent coefficients (Table 1) indicated a significant decrease in LET quenching with longer curing times.The decrease in LET quenching is also clearly seen in Fig 1 and was even larger for 9% CA.Dose rate quenching did not decrease significantly between 3 and 5 days of curing for either of the two CA compositions (Fig 2, Table 1).There was a decrease by 13% and 34% in the dosimeter signal from 1 to 5 days for 5% CA and 9% CA dosimeters respectively.

Discussion
The LET and dose-rate-dependent quenching for different curing conditions and compositions and for silicone-based radiochromic dosimeters were investigated.A significant decrease in dose-rate quenching was not found, which is consistent with the findings of Jensen et al [14], but there seemed to be a trend for decreasing dose-rate dependency with curing time for both curing compositions.The LETd dependency decreased significantly with curing time for both curing compositions, although it was more pronounced for 9% CA dosimeters (Fig 1).Although extrapolating the current results could indicate a benefit in increasing the curing time even further, the decrease in dose response and continuous hardening of the silicone base [15] should be taken into consideration.
Although the main source or initiator of radical production of the chain process leading to the conversion of LMG into malachite green (MG) is believed to be chloroform [11,16], other not chemically cross-linked molecules could serve as an additional source of free radicals.This theory is supported by the higher dose response associated with dosimeters with less CA [14].Since the 5% CA dosimeter compositions investigated in this study have a lower ratio of CA as specified by the manufacturer, not-cross-linked molecules are likely present.Additionally, dosimeters that have not been fully cured, as the batch curing for 1 day, were expected to have an even higher number of not-crosslinked molecules present.
Track structure theory could help explain the decrease of LETd-dependent quenching with curing time [17].Consider the dosimeter to be composed of discrete radiosensitive elements that are dispersed in a matrix, and that these elements can be "activated", i.e., have an interaction that leads to a measurable signal, by "hits" from ionizing radiation.Close to the end of the proton range (high LET), interactions alongside the ion track have a very short range, making it harder to reach a radiosensitive element, which lowers the probability of a "hit".In a dosimeter with a high dose response, more of these sensitive elements are quickly activated at lower doses, saturating the elements close to the particle track.Additionally, the large availability of radicals close to the particle track could increase the chance of radical recombination, and consequently, more chain processes would not generate a "hit", leading to an increase in LET-quenching [18].A similar argument could be made to explain the dose-ratedependent quenching; since proton beams with higher dose rate should also generate radicals at a higher rate, increasing the change of recombination.By lowering the concentration of free radicals by either having a higher percentage of CA or longer curing, LET and dose-rate quenching were expected to decrease, which was indeed observed for the LET quenching.Regarding the dose-rate quenching, while this decrease has been observed for photons [14], it was not significant in this study (Figure 2).A potential explanation could be that, since the dose rate levels for protons are so much higher than photons, any potential improvement gained by lowering the availability of radical sources was not large enough to be significant.
In conclusion, it was found that longer curing times had the effect of reducing the LETd-dependent quenching for both curing with a significantly larger effect on the 9% CA dosimeters.However, curing time had a very small impact on the dose-rate-dependent quenching for proton beams.

Acknowledgments
Mateusz Sitarz is kindly acknowledged for his assistance during irradiation.The Novo Nordisk Foundation funded the research.

Figure 2 .
Figure 2. Surface fit to the 9% CA dosimeters cured for 3 days.The black dots represent the mean of the three cuvettes irradiated with each beam current, with the surface fit overlayed on top (left panel).The dosimeter quenching as a function of dose-rate and LETd for different dosimeter compositions (upper panels: 5% CA, lower panels: 9% CA), and curing times (1, 3 or 5 days).Black markers indicate the measurement points, while the colormap was calculated from equation (1) (right panel).