In photon external beam radiotherapy (EBRT), unintended doses are inevitably delivered to large volumes of normal tissues outside the therapeutic beam path. Historical investigations have shown that these out-of-field doses mainly result from patient scattering, treatment machine head scattering and leakage (Kase et al 1983, Bordy et al 2013, Benzazon et al 2023). Such doses typically range from cGy to mGy (Bordy et al 2013, Kry et al 2017, Benzazon et al 2023), and must be accurately evaluated through measurements (Bordy et al 2013) and calculations (Schneider et al 2014, Benzazon et al 2024), to properly assess their role as risk factors for late side effects, such as subsequent primary cancers (Goy et al 2022), cardiac side effects (Darby et al 2013), or even hematological side effects De Kermenguy et al (2024)

In EBRT, precise dose measurement is a key step to ensure accurate treatment delivery. Usually, modern treatment planning systems (TPSs) are commissioned for accurate dose computations inside the treatment field and its immediate vicinity, with reported accuracies better than 2.5% (Danckaert et al 2023). However, outside these regions, TPSs have demonstrated significant limitations in dose calculation accuracy (Howell et al 2010a, Schneider et al 2014, Colnot et al 2019, Sánchez-Nieto et al 2020, Colnot et al2021). One possible explanation is that, during TPS commissioning, radiotherapy physics teams have traditionally focused on optimizing in-field dose calculations, while comparatively less attention has been given to precisely modeling out-of-field doses (Auerbach et al 2023).

Ionization chambers calibrated under reference conditions (IAEA 2000) are the most commonly used instruments for experimental measurements during TPS commissioning. Owing to their low energy dependence, these detectors have proven to be suitable for accurate measurements even outside the treatment field (Chofor et al 2012). In contrast, the response of non–water-equivalent solid dosimeters can be strongly affected under conditions that differ from the reference ones, due to the softening of the photon energy spectrum. For instance, authors have reported that in a 6 MV photon beam, the average energy outside the treatment field drops to approximately 200 keV at a 20 cm off axis distance and a field size of 20 × 20 cm2 (Scarboro et al 2011). The need for energy-dependence corrections for non–water-equivalent solid detectors was demonstrated by Scarboro’s work (Scarboro et al 2011), who reported deviations of up to 12% when thermoluminescent dosimeters (TLDs) were used out of field. Subsequently, Chofor et al (2012) further evaluated this energy dependence for TLDs and diodes, reporting deviations reaching 20% in out-of-field measurements.

Over the past decade, technological advancements have sparked growing interest in radiophotoluminescent glass dosimeters (RPLGDs) within the field of medical dosimetry, particularly in radiotherapy. Several studies focusing on RPLGDs calibration have reported excellent reproducibility, with variations as low as 0.42%, and a uniform response within 1.1%. (Mizuno et al 2008, Araki and Ohno 2014, Wesolowska et al 2017). In addition, other studies have demonstrated the suitability of RPLGD dosimeters for in vivo measurement (Chung and Kim 2013)], brachytherapy (Hsu et al 2008, Nose et al 2008), total body irradiations (Rah et al 2011) and out-of-field dose measurement (Bordy et al 2013, Knežević et al 2013). RPLGD offers a detection sensitivity that allows for precise dosimetry at dose levels as low as the μGy range, making them particularly well suited for out-of-field dosimetry applications. However, due to their higher effective atomic number compared to TLDs (12.04 versus 8.3), the need to correct for energy dependence is expected to be even more critical for RPLGDs. This effect was already highlighted by Hashimoto (Hashimoto et al 2019), who reported beam quality correction factors ranging from 0.999 to 0.794, when measurements were performed around a 192Ir brachytherapy source with Chiyoda Technol Corporation RPLGDs GD-302M calibrated using a 4 MV Linac photon beam. However, it remains essential to establish and provide beam-quality correction factor data for out-of-field dosimetry using RPLGDs in EBRT. The availability of such data is crucial for improving our understanding of the dose delivered to distant healthy tissues in patients undergoing radiotherapy. In this context, compiling tabulated beam-quality correction factors for RPLGDs represents a key step toward achieving more accurate out-of-field dose measurements in EBRT.

In this study, the energy dependence of Dose Ace GD-300 series RPLGDs (Dose Ace, Asahi Techno Glass Corporation, Shizuoka, Japan) was investigated in out-of-field conditions considering a 6 MV and 18 MV from a Elekta VERSA HD (Elekta, Stockholm, Sweden) and a 6 MV and 20 MV from a Varian Clinac 2300 CD (Varian Medical Systems, Palo Alto, CA, USA). We also provide data on the variation of the effective energy according to out-of-field distance, depth and field size, for these beams. The beam quality correction factors and effective energies estimate reported here are both empirically derived from experimental data.

2.1. General concepts and formalism

According to the International Atomic Energy Agency (IAEA) technical reports series No. 398 (IAEA 2000), when a dosimeter is used in a beam of quality Q, different from that used at its calibration stage (Q0), the absorbed dose to water is given by:

where:

is the absorbed dose to water in the reference conditions,

is the dosimeter reading corrected to the reference values of influence quantities—other than beam quality—for which the calibration factor is valid,

is the calibration factor of the dosimeter in terms of absorbed dose to water for reference beam quality Q0,

is the beam quality correction factor, which corrects for the effects of the difference between the reference beam quality and the user beam quality.

The reference calibration factor—which calibrates the detector’s reading signal to the absorbed dose to water at the reference position for the reference beam quality—is defined as:

where is the corrected reading of the detector at the reference position for the reference beam quality, and is the absorbed dose to water in the reference conditions for the reference beam quality.

The beam quality correction factor, , corrects the detector reading for differences between the reference beam quality Q0 used for calibration and the beam quality Q used for measurements. Here, Q refers to the beam quality at any out-of-field location and is given by:

where and are the detector readings for beam qualities Q and Q0, respectively, corresponding to an absorbed dose to water for beam quality and for beam quality .

2.2. RPLGD system and operating procedure

General information on the basic principles of radiophotoluminescent dosimetry can be found in (Huang and Hsu 2011, Yanagida et al 2022). In the present work, we focus on the key technical characteristics of the measurement system, specifically the GD-302M and GD-352M detectors (GD-302M and GD-352M, Asahi Techno Glass Corporation, Shizuoka, Japan), and the Dose Ace FGD-1000 readout system (Dose Ace FGD-1000, Asahi Techno Glass Corporation, Shizuoka, Japan).

The GD-302M and GD-352M dosimeters consist of silver-doped phosphate glass, each with a diameter of 1.5 mm and a length of 12.0 mm. Their composition by weight is: 31.6% P, 51.2% O, 6.1% Al, 11.0% Na, and 0.2% Ag. The glass has an effective atomic number of 12.04 and a density of 2.61 g cm−3. Two detector models were used in this study: GD-302M and GD-352M. For the GD-302M detector, the glass rod (radiophotoluminescent element) is housed in a plastic holder, measuring 2.8 mm in diameter and 13.0 mm in length. The GD-352M dosimeter uses the same radiophotoluminescent element but incorporates a 0.75 mm-thick low-energy filter composed of 90% tin and 10% lead within the holder (figure 1). Each glass detector has an ID number. In this study, since the glass rods were never used outside their respective holders, all conclusions apply to the glass rod in combination with its specific holder—the plastic holder for the GD-302M and the plastic holder with the low-energy filter for the GD-352M.

Figure 1. Schematic view of (a) RPLGD-352M (b) and RPLGD-302M (b) derived from Nakatake and Araki (2021).

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The Dose Ace FGD-1000 readout system allows measurement of doses ranging from 10 μGy to 10 Gy and can read up to 20 glass rods within a 5 min session. Before each experiment, RPLGDs were annealed in an oven for 1 h at 400 °C to restore their initial state. A pre-dose reading was then performed to determine the baseline signal. Following irradiation, the dosimeters were preheated for 30 min at 70 °C to enhance the radiophotoluminescent signal before the final readout.

Individual sensitivity correction factors (SCF), as defined in (Knežević et al 2013) were established and applied. SCFs ranged from 0.97 to 1.05 and from 0.97 to 1.03, for the 153 GD-302 and the 135 GD-352M RPLGDs selected for the present investigation.

2.3. Determination of effective energy from low-energy filter attenuation

The glass rods in the GD-302M and GD-352M RPLGDs have identical dosimetric properties. In practice, GD-352M RPLGDs are basically designed to under-respond compared to GD-302M RPLGDs at low energies, due to the attenuation of the low-energy photon component by the filter. We exploited this differential response to pragmatically derive an estimate of the out-of-field photon effective energy by irradiating both detector types at the same measurement points under identical conditions. As defined in the Radiation Oncology Physics booklet, the effective energy of a heterogeneous x-ray beam is defined as that energy of a monoenergetic photon beam that would yield the same half-value layer as does the heterogeneous beam (Agency 2005). In this work, we interpreted the effective energy as the monoenergetic energy that yields the same attenuation through the low-energy filter as the heterogeneous out-of-field spectrum. In this aim, experimental data from the literature (Hsu et al 2007, Silva et al 2016) comparing the signal responses of GD-302M and GD-352M RPLGDs detectors from x-ray beams of quality N-10 to N-300, S-Cs and S-Co (ISO 2019) with mean energies ranging from 8.5 to 1250 keV were used. The two energy curves were digitized using the WebPlotDigitizer (Rohatgi, s.d.) web-based software. A Python script based on the NumPy library was developed to perform linear interpolation of the numerical data over the range 75–2000 keV. However, since the measurements were acquired only up to 1250 keV, energies above this threshold were considered out of range. Nevertheless, energies exceeding 1250 keV were deemed measurable if their uncertainty intervals included 1250 keV. From the interpolated response data, we computed the GD-352M/GD-302M signal ratio as a function of photon energy. This calibration curve was then used to infer effective photon energies from measured reading ratios at each out-of-field location.

2.4. Validation of effective energy attenuation

Our validation determination strategy relies on the assumption that the low-energy filter in the GD-352M detectors behaves similarly to an attenuator in standard linear attenuation measurements. However, our experimental conditions differ in that the filter remains in contact with the glass detector, whereas a conventional attenuation measurement typically requires the attenuator to be placed separately. As a result, deviations from theoretical expectations are anticipated, notably due to additional contributions from secondary electrons generated by Compton scattering within the filter, which, in standard configurations, would not contribute to the signal as they are typically scattered or stopped in air. These processes can influence the detector response, and should therefore be taken into account when interpreting the results. In order to validate our method, we used the Xmudat software (Pronyaev 1998) to plot the mass attenuation coefficient of the filter as a function of the energy. For ratio under 0.95, corresponding to energies ranging from 110 keV to 510 keV, we calculated the mass attenuation coefficient defined as:

where:

is the ratio of the GD-352M and GD-302M RPLGD readings,

is the mass attenuation coefficient corresponding to the experimental ratio,

is the density of the low-energy filter,

is the filter thickness.

For each ratio, we retrieved the associated theoretical mass attenuation coefficient and deduced the corresponding effective energy. We then computed the relative differences between the effective energies obtained from the experimental reading ratios (as per Silva et al) and those from the theoretical evaluation.

2.5. Determination of beam quality correction factors

The experimental set up used for the determination of the beam quality correction factors is shown in figure 2. A solid phantom measuring 30 cm × 60 cm × 20 cm was constructed from commercially available water-equivalent plates (PlasticWater®–TheOriginal, CNMC, Nashville, USA) of 30 cm x 30 cm area each and different thicknesses, along with four custom-made 5 mm plexiglass plates (30 cm × 60 cm) equipped with plugs to position RPLGDs along the beam central axis and at intervals of 10 cm up to 40 cm off-axis. The plexiglass plates were positioned in depth to allow dose measurements at 1 cm, 10 cm and 15 cm depths. Out-of-field dose measurements were performed for 3 different field sizes: 5 cm x 5 cm, 10 cm x 10 cm and 15 cm x 15 cm. The Farmer 30 010 ionization chamber (PTW No. 9856, PTW, Freiburg, Germany) coupled with a UNIDOS electrometer (PTW No. 10 009, PTW, Freiburg, Germany) was used for measurements on the Varian Clinac 2300 CD linac (Varian Medical Systems, Palo Alto, CA, USA). For the Elekta VERSA HD linac (Elekta, Stockholm, Sweden), the same ionization chamber was used with a PTW No. 90 552 electrometer. One GD-302M and one GD-352M RPLGD, randomly selected from the batch, were irradiated at the same position in the phantom in alternation with the ionization chamber.

Figure 2. Experimental set up for the determination of beam quality correction factors and effective energies. (a) sagittal view of the custom-made phantom and (b) upper view of the plexiglass plate designed to hold the RPLGDs. Detectors (Ionization chamber and RPLGDs) were placed at 0, 10, 20, 30 and 40 cm from the beam axis at different depths (1, 10, 15 cm). Different field sizes were considered (5×5, 10×10, 15 × 15 cm2). RPL GD-302 M (pink) and RPL GD-352 M (yellow) were positioned on both sides of the measurement point. The blue square represents the treatment field.

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The beam qualities investigated included photon beams from a Varian Clinac 2300 CD (6 MV and 20 MV) with quality indices of 0.675 and 0.792, respectively, as well as photon beams from an Elekta VERSA HD linac (6 MV and 18 MV) with quality indices of 0.683 and 0.777, respectively. For each measurement, the phantom was irradiated using 500 Monitor Units corresponding respectively to 5.44, 6.51, 4.96 and 4.91 Gy in the reference conditions.

Reference calibration coefficients, ND,W,Q0, one for the GD-302M RPLGDs and one for the GD-352M RPLGDs, were determined according to equation (2), for the reference point measurement, in the beam axis at 10 cm depth for a 10 cm × 10 cm field size with the 6 MV Varian Clinac 2300 CD, with a quality index of 0.675. Beam quality correction factors were derived for both types of RPLGDs using equation (3). RPLGD measurements were repeated three times, resulting in a total of 540 individual measurement points for both types of RPLGDs. Ionization chamber measurements were repeated twice, for the reference point measurement, and one measurement was done for the non-reference point resulting in 181 measurements.

2.6. Statistical handling of sparse measurements using bootstrapping

Due to practical constraints on the availability of clinical linacs for research, only three repeated measurements were performed at each irradiation site. For the reference point, each three RPLGDs measurement was paired with the two ionization measurements yielding in six reference calibration values. Each, non-reference measurement point, was randomly paired with one of six reference calibration values, leading to 18 unique combinations per measurement point. This random association reflects real-world uncertainty in calibration procedures and detector response variability. To overcome the limitations of this small sample size and ensure statistically reliable estimates, we applied a non-parametric bootstrapping method (Henderson 2005, Kazmierczak et al 2022). 100 bootstrap samples were generated by resampling with replacement from the 18 combinations, allowing us to build empirical distributions of the parameters of interest, the beam quality correction factors and the effective energy, and compute reliable confidence intervals. This approach was chosen because it enables robust statistical inference without relying on strong parametric assumptions, which are often inappropriate when dealing with limited data. It is particularly well suited to small-sample experimental designs commonly encountered in experimental dosimetry in clinics, where access to treatment machines for research purposes is constrained, and clinical priorities for patient care take precedence. By incorporating both measurement variability and calibration uncertainty, this method enhances the reliability of our results under realistic clinical research conditions. Bootstrapping was implemented based on the python Scipy 1.14.1.

2.7. Analysis of feature importance for out-of-field beam quality correction factors and effective energies

To assess the relative influence of depth, distance from the beam central axis, field size, and treatment beam quality on variations in out-of-field beam quality correction factors and effective photon energies, we performed a feature importance analysis using a multivariable Decision Tree Regressor. Hyperparameter tuning was performed using the GridSearchCV function from the scikit-learn library in Python. Data splitting within GridSearchCV was carried out using ShuffleSplit with n_splits = 10. The dataset was randomly split into a training set (80%) and a test set (20%), and this procedure was repeated across five random splits. For each split, we recorded the coefficient of determination (R2) and computed the mean and standard deviation of R2 as well as the relative importance of each feature, based on the feature_importances attribute of the model. The analysis was implemented using the Python scikit-learn DecisionTreeRegressor (v1.5.1).

3.1. Photon effective attenuation energies in out-of-field regions

The means and associated standard deviations of the effective energies derived from the GD-302M/GD-352M reading ratios (based on Silva et al) are presented in tables 1 and 2 for the Elekta VERSA HD and Varian Clinac 2300 CD linear accelerators, respectively. Results showed consistent trends across both machines. Considering all configurations, effective energies for the Elekta VERSA HD ranged from 180 keV to 1111 keV, while for the Varian Clinac 2300 CD, they ranged from 199 keV to 1302 keV. For both systems, higher beam quality indices were associated with higher out-of-field effective energies. For example, with the Varian Clinac 2300 CD at 10 cm from the field edge and 15 cm depth with a 15 × 15 cm2 field size, mean effective energies were 505 keV for the 6 MV beam and 799 keV for the 20 MV beam. Under the same conditions, the Elekta VERSA HD showed average photon energies of 656 keV for the 6 MV beam and 932 keV for the 18 MV beam.

Table 1. Effective energies measured outside the treatment field for the Elekta VERSA HD linear accelerator. A dash (–) indicates effective energies considered outside the measurement range. Measurements above 1250 keV were classified as out of range unless their uncertainty interval included 1250 keV.

  Elekta VERSA HD  RX—06 MVRX—18 MV Depth (cm) Distancea (cm)1101511015Field size (cm2)Mean (± standard deviation)Mean (± standard deviation)5 × 510807 (±155)572 (±97)548 (±51)726 (±164)—1111 (±121)20492 (±115)916 (±204)966 (±156)412 (±82)601 (±197)—30666 (±216)292 (±32)304 (±36)299 (±46)403 (±37)438 (±38)40710 (±211)659 (±214)535 (±169)260 (±14)426 (±23)418 (±38)10 × 1010262 (±9)404 (±31)574 (±134)272 (±27)545 (±68)943 (±141)20239 (±3)347 (±39)349 (±28)233 (±2)748 (±237)919 (±87)30276 (±27)235 (±4)229 (±3)201 (±3)291 (±27)356 (±27)40436 (±129)295 (±42)267 (±18)218 (±3)246 (±3)318 (±27)15 × 1510232 (±16)395 (±64)656 (±77)364 (±77)512 (±63)932 (±124)20220 (±3)246 (±19)252 (±11)206 (±6)425 (±102)441 (±51)30213 (±6)225 (±4)227 (±3)180 (±15)226 (±3)262 (±15)40265 (±14)224 (±4)235 (±6)197 (±9)256 (±9)279 (±21)

aDistance from beam central axis.

Table 2. Effective energies measured outside the treatment field for the Varian Clinac 2300 CD linear accelerator. A dash (–) indicates effective energies considered outside the measurement range. Measurements above 1250 keV were classified as out of range unless their uncertainty interval included 1250 keV.

  Varian Clinac 2300 CD  RX—06 MVRX—20 MV Depth (cm) Distancea (cm)1101511015Field size (cm2)Mean (± standard deviation)Mean (± standard deviation)5 × 510318 (±25)453 (±32)497 (±37)655 (±147)—1302 (±106)20691 (±54)696 (±32)592 (±11)802 (±163)——30262 (±12)273 (±18)245 (±1)289 (±24)525 (±19)549 (±22)40387 (±20)304 (±16)314 (±15)429 (±16)700 (±37)636 (±16)10 × 1010248 (±19)286 (±12)285 (±14)1048 (±186)692 (±88)578 (±16)20292 (±22)248 (±1)263 (±7)1044 (±194)750 (±30)675 (±15)30276 (±20)237 (±1)238 (±1)652 (±157)414 (±17)475 (±11)40332 (±29)287 (±11)243 (±1)638 (±59)639 (±30)456 (±10)15 × 1510324 (±56)332 (±27)505 (±54)312 (±36)663 (±69)799 (±124)20224 (±5)234 (±2)241 (±4)199 (±14)431 (±31)481 (±10)30250 (±14)232 (±1)235 (±1)240 (±2)356 (±14)416 (±7)40327 (±21)241 (±2)236 (±1)399 (±16)498 (±21)407 (±5)

aDistance from beam central axis.

Effective energy measurements demonstrated the same curve shapes for both machines for the 6 MV beam energy as a function of distance from the beam axis (figure 3). However, at a distance of 40 cm, for a field size of 10 × 10 cm2 and a depth of 10 cm, the effective energy was found to be three times higher for the Varian Clinac 2300 CD operating at 20 MV compared to the Elekta VERSA HD at 18 MV, with measured values of 639 keV and 246 keV, respectively.

Figure 3. Effective energies measured at different distances from the central beam axis at 10 cm depth for a 10 × 10 cm2 field size for different beam qualities.

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Comparison of the two methodologies yields relative differences between the experimental and theoretical effective energies below 22% with a mean of 8.2%, with a 95% confidence interval of [7.9%–8.6%].

3.3. Beam quality correction factors out-of-field

Tables 3 and 4 summarize the beam quality correction factors obtained for the Elekta VERSA HD device using RPLGD-302M and RPLGD-352M respectively. Tables 5 and 6 summarize the results for the Varian Clinac 2300 CD, for GD-302M and GD-352M detectors, respectively. For all beam qualities, values of beam quality correction factors were ranging from 0.745 to 1.284 for the GD-302M and from 0.568 to 1.649 for the GD-352M detectors. For the 6 MV photons, an average relative difference of 5% was observed between the two machines, with a maximum difference of 25% at 10 cm from the beam axis for a 15 × 15 cm2 field and a depth of 10 cm, using GD-302M detectors. The corresponding measured beam quality correction factors values were 0.952 for the Elekta VERSA HD and 0.758 for the Varian Clinac 2300 CD. Similar results were observed for higher beam qualities, with a maximum difference of 33% at 20 cm from the beam axis for a 5 × 5 cm2 field and a depth of 10 cm, where the measured values were 1.236 for the Elekta VERSA HD and 0.926 for the Varian Clinac 2300 CD for the GD-302M detectors. When using GD-352M detectors, a maximum difference of 73% was observed at a point located 20 cm from the beam axis for a 5 × 5 cm2 field at a depth of 10 cm and for the highest beam quality indices, with values of 1.451 for the Elekta VERSA HD (18 MV) and 0.837 for the Varian Clinac 2300 CD (20 MV).

Table 3. Beam quality correction factors for GD-302M detectors for the Elekta VERSA HD linear accelerator.

  RPL GD-302M  Elekta VERSA HD  RX—06 MVRX—18 MV Depth (cm) Distancea (cm)1101511015Field size (cm2)Mean (± standard deviation)Mean (± standard deviation)5 × 500.990 (± 0.023)1.007 (± 0.028)1.002 (± 0.023)0.872 (± 0.014)1.044 (± 0.007)1.066 (± 0.012)101.021 (± 0.047)0.916 (± 0.019)0.944 (± 0.016)1.087 (± 0.053)0.993 (± 0.006)0.956 (± 0.010)201.030 (± 0.037)0.852 (± 0.025)0.936 (± 0.029)1.103 (± 0.033)1.236 (± 0.078)0.947 (± 0.008)301.030 (± 0.097)0.871 (± 0.026)0.887 (± 0.030)1.082 (± 0.042)0.889 (± 0.019)0.886 (± 0.012)401.022 (± 0.122)0.932 (± 0.079)0.913 (± 0.055)1.053 (± 0.015)0.961 (± 0.010)0.889 (± 0.017)10 × 1000.989 (± 0.018)1.031 (± 0.018)