Fading correction for calibration of a novel 2D OSL-film dosimeter

A new film dosimeter based on optically stimulated luminescence (OSL) was calibrated for high-resolution 2D dosimetry in the context of radiotherapy patient-specific quality assurance (PSQA). The OSL-film signal is linear with the dose and decays with time, in a process called fading. Two models were proposed to characterize the fading: (1) a linear model independent from the delivery and of practical use thanks to the straightforward signal-to-dose conversion, and (2) a delivery-dependent model, to investigate whether a more simplified model may be sufficient to accurately determine the fading independently from the specific-irradiation conditions. The models were used in a nonlinear regression over an experimental dataset acquired with a 6MV photon beam in standard calibration settings. Both models were accurate and showed an adjusted-R 2 of 0.98 (1) and 0.99 (2). The residual analysis on both models allowed to define the minimum scanning time to have a discrepancies between the models <1%. Under this condition the OSL fading can be assumed independent on the irradiation parameters. As a consequence, within these boundary conditions, the linear model can be used for the OSL-film calibration.


Introduction
Advanced radiation therapy (RT) treatments provide highly modulated dose distributions with rapid dose falloff outside the target volumes.The increased complexity of treatment plan ballistics and delivery, stresses the importance of PSQA.The role of dosimetry in PSQA is to verify with multidimensional and high-resolution dose measurements the degree of agreement with respect to the calculated dose distribution.New OSL dosimeters are investigated by the QUARTEL-project (Quality Assurance in RadioTherapy by Stimulated and Excited Luminescence Dosimetry) as an alternative to standard dosimeters (e.g., radiochromic films).These novel devices are capable of performing 2D dose measurements down to low doses with sub-mm spatial resolution defined by the readout system.Moreover, the same OSL-film is reusable after a complete signal erasure and can be applied for multiple dose measurements.The characterization of the new film will allow investigation of the OSL signal for 2.5D dose measurements.This application will require the use of a stack of the same OSL-film.The OSL-film has a linear dose-to-signal [1], [2] measured as luminescence produced after an external light stimulation that induced electron-hole pairs recombination.Luminescent materials suffer from a time-dependent response caused by spontaneous electron-hole pairs recombination and resulting in a reduction of the measured signal intensity.This process is also called fading.A power law physical model was developed to describe the fading according to the probability of spontaneous recombination of excited shallow traps via quantum-mechanical tunneling effect [3].This is the case of some luminescent material such as BaFBr:Eu² + , or Zn2SiO4:Mn, while Jursinic et al. [4] justified the exponential decay for an Al2O3:C phosphor material on the basis of room-temperature instability of the shallow traps [4].
When used for radiotherapy applications, fading affects the signal-to-dose conversion resulting in an error in the evaluation of the delivered dose.Moreover, the degree of signal fading depends on treatment-specific irradiation conditions such as dose rates, and irradiation times.The current work characterized the dose response specific for a BaFBr:Eu² + -based film suitable for PSQA.The signal-todose conversion used a calibration function, modeling both the dose dependence and the time-dependent signal loss caused by fading.This function can be represented as a 2D calibration surface as a function of two variables: delivered dose (D) and the waiting time from the start of the exposure and the film scanning (t scan ).Two models were proposed.The first is characterized by a linear signal build-up followed by a power-law fading independent of the specific irradiation conditions, irradiation time (t  ), and dose rate( ̇).This linear model allows a simple signal-to-dose conversion independently on the point-to-point difference in the effective delivery time.The second, instead, has a signal loss that depends on t  .A residuals error analysis was executed to evaluate the possible error arising when the fading is assumed to be independent of the irradiation parameters.The residual error analysis was used to define the best t  for three radiotherapy schemes, i.e., VMAT, IMRT, and Helicoidal Tomotherapy (HT), with different beam-on times, 3min 10.5min, 20min [5], [6].

Methods and Material
Two different power-law fading models were used to characterize the signal of a novel BaFBr:Eu 2+based OSL-film.First, a linear model was considered.It consists of a linear signal-to-dose relation lowered by a power law factor dependent on the moment at which the film was scanned (tscan) In Eq.1, the delivered dose is given as the product of constant dose rate, Ḋ  , and the duration of the irradiation tirr.The proportionality depends on the film's sensitivity A, while the fading is characterized by material-specific parameters; τ and n.The second model is delivery-dependent.Here each infinitesimal signal contribution has a different degree of fading depending on when it was formed during irradiation.The signal contribution at the beginning of the exposure is higher than the one formed at the end of irradiation The linear model can be derived as a Taylor first-order approximation of the delivery-dependent model in Eq.2.
An experimental dataset of 86 measurements was acquired by irradiating the OSL-film on a TrueBeam TM STx using a 6MV 10x10cm² open field in reference conditions; i.e., 0° gantry angle, 90cm SSD and at 10cm depth.The measurements consisted of three constant dose-rates (D ̇) combined for six irradiation times (t irr ) of 0.2,1, 2, 4.5min at 600MU/min, 12min at 300 MU/min and 23min at 200MU/min, and various readout times (t scan ) between 4 min and 1440 min.The dose-rates were varied to keep the resulting dose levels in the range from classic fractionation to single-fraction SRS doses.The irradiations were executed in dimmed light condition to prevent external stimulation and signal loss due to excessive light exposure.Next, the film was scanned with a computed radiography (CR15-X, Agfa Healthcare) reading system.The reader produced the typical OSL luminescence by exciting the trapped electrons with a solid-state laser of 80mW with a light spectrum centred at 665nm.The net signals, obtained as the mean raw value of a 1x1 cm² ROI minus the correspondent background, were fitted via a robust nonlinear regression method according to the models in Eq.1 and2 and with respect to the variables Ḋ, t irr , t scan .The residual error analysis was performed by considering the relative difference map between the regression models.

Results
The linear and delivery-dependent models fitted the experimental data with an adjusted- 2 respectively of 0.98 and 0.99.Coherently, the logarithm of the root-mean-square error expressed as ln (�∑ ((Ḋ,t irr ,t scan )− S(Ḋ,t irr ,t scan )   =1 ) and relative to the difference between the measured and the estimated signal, decreased from 0.016 for the linear model to 0.013 for the delivery-dependent one.
The estimated models` coefficients obtained via robust nonlinear regression are reported in Tab.1 together with the upper and lower 95% confidence intervals.With the exception of an outlier that has a 5% discrepancy with respect to the fitted values, a regression analysis on the residuals confirmed the accuracy of the models.The model's residual error map (%), depicted in Fig. 1b, is always lower than 3.05 and for longer irradiation, the difference between the models increases at shorter   .

Discussion
The results in Fig. 2 (right) showed that the error when assuming the fading as independent from the specific irradiation conditions increases with the irradiation times (Fig. 2) up to 3.04% for t  =23 min.This error arises by neglecting the fading contribution that occurs during the exposure.However, longer waiting times, t  , decrease the error <1% and allows the use of the approximated linear model for the signal-to-dose conversion in RT application.The characteristic t  for different classes of SRS and SBRT treatments were considered according to their different beam on time: 16 patients treated with (1)  2)sliding window IMRT.In addition (3) one peripheral lung SBRT treatment with Helicoidal Tomotherapy was also considered [5], [6].These treatments have different average beam-on times, respectively 3min to 10.5min and 20min.The minimum readout time to have a model difference <1% is 4min for the multi-arcs VMAT plan, 25min for the IMRT, and 63 min for the longest HT treatment.
The linear model is preferred to a more complex delivery-dependent model because the signalto-dose conversion function does not require to know a priori the time of exposure for point within the treated region,   (, ).This information is not easily accessible in clinical practice.Additionally, the linear model can be inverted to obtain an analytical expression for the signal-to-dose conversion, when D= Ḋ • t irr .

Conclusion
The calibration of a novel OSL-film for RT application was corrected for fading with two different models.If t  > 63min than the fading can be considered approximately independent on the specific RT treatment irradiation conditions as the signal intensity decreases by a fading factor solely dependent on t  .

Acknowledgement
The research is financed in the QUARTEL-project (Quality Assurance in RadioTherapy by Stimulated and Excited Luminescence Dosimetry VLAIO [VLAIO HBC.2020.3003]), a joint financing of the Flemish government and AGFA N.V.

Figure 1 .
Figure 1.(Left) Different fading curves obtained for six irradiation times with a robust nonlinear regression.The regression was performed according to a linear (solid line) and the delivery-dependent model (dashed line).(Right) Relative difference map (%) between the linear and delivery-dependent fading models.The minimum   with a difference < 1% for three IMRT, VMAT, and SBRT treatment modalities is reported.

Figure 2 .
Figure 2. Dose calibration surface for a BAF-based OSL dosimeter affected by signal time decay.