OSLD nanoDot characterization for carbon radiotherapy dosimetry

Objective. This study characterized optically-stimulated luminescent dosimeter (OSLD) nanoDots for use in a therapeutic carbon beam using the Imaging and Radiation Oncology Core (IROC) framework for remote output verification. Approach. The absorbed dose correction factors for OSLD (fading, linearity, beam quality, angularity, and depletion), as defined by AAPM TG 191, were characterized for carbon beams. For the various correction factors, the effect of linear energy transfer (LET) was examined by characterizing in both a low and high LET setting. Main results. Fading was not statistically different between reference photons and carbon, nor between low and high LET beams; thus, the standard IROC-defined exponential function could be used to characterize fading. Dose linearity was characterized with a linear fit; while low and high LET carbon linearity was different, these differences were small and could be rolled into the uncertainty budget if using a single linearity correction. A linear fit between beam quality and dose-averaged LET was determined. The OSLD response at various angles of incidence was not statistically different, thus a correction factor need not be applied. There was a difference in depletion between low and high LET irradiations in a primary carbon beam, but this difference was small over the standard five readings. The largest uncertainty associated with the use of OSLDs in carbon was because of the k Q correction factor, with an uncertainty of 6.0%. The overall uncertainty budget was 6.3% for standard irradiation conditions. Significance. OSLD nanoDot response was characterized in a therapeutic carbon beam. The uncertainty was larger than for traditional photon applications. These findings enable the use of OSLDs for carbon absorbed dose measurements, but with less accuracy than conventional OSLD audit programs.


Introduction
Carbon radiotherapy is a promising technology for treatment of radioresistant tumors.With favorable patient outcomes reported by several carbon therapy centers (Takagi et al 2014, Shirai et al 2017, Hu et al 2020), the United States is currently building carbon therapy facilities.But carbon therapy at present is quite heterogeneous, with different machines, treatment regimens, radiobiological models, and dosimetry protocols used around the world.There is a need for peer review of carbon beams, as well as a framework for intercomparison of absorbed dose between institutions.
The Imaging and Radiation Oncology Core (IROC) provides peer review for radiotherapy clinical trials run by the National Cancer Institute in the United States.Because of the multi-center nature of these trials, international participation by proton and photon clinics is common.With over 2000 institutions monitored by IROC, passive dosimeters play a large role in the ability to audit so many institutions annually.One such dosimeter is the optically-stimulated luminescent dosimeter (OSLD).The OSLDs used by IROC, Al 2 O 3 :C nanoDots (LANDAUER, Glenwood, IL), are small, durable detectors that can be mailed to an institution, irradiated, and sent back to IROC to be analyzed.However, these detectors may be particularly complicated to characterize and use in carbon beams.Data from prior OSLD experiments have shown a detector response that is dependent on linear energy transfer (LET) (Yasuda and Kobayashi 2001, Sawakuchi et al 2008, Reft 2009, de Freitas Nascimento et al 2022, Yukihara et al 2022).Additionally, a more recent study by Parisi et al demonstrated particle type dependence in Al 2 O 3 :C response (Parisi et al 2022).
While IROC has a robust program for OSLD dosimetry in photon and electron beams, the detectors have yet to be fully characterized in carbon.Some research has been done to explore the use of OSLDs in a therapeutic carbon beam (Reft 2009, Sawakuchi and Yukihara 2012, Yukihara et al 2015), but none have characterized OSLD response to carbon using the AAPM Task Group 191 formalism.Furthermore, the IROC framework for remote passive dosimetry is distinct from historical experiments.For example, as IROC monitors a wide range of beams, all corrections must be generalized and applicable to arbitrary situations, while maintaining the tightest possible uncertainty.Therefore, this study explored the detector correction factors required for OSLD nanoDot carbon dosimetry and the associated uncertainties in absorbed dose calculation.

Methods
IROC's OSLD program uses Aluminum Oxide OSLD nanoDots (LANDAUER, Glenwood, IL).The planar crystal sits in a plastic casing.The OSLDs are read using a microStar-ii reader (LANDAUER, Glenwood, IL), which takes five readings per dot.In current programs, OSLDs are typically irradiated to 100 cGy, bleached using fluorescent light (GE F54W/T5/835/ECO), and then reused up to a cumulative absorbed dose of 10 Gy (Alvarez et al 2017) (although this is expected to be extended to higher doses based on recent data) (Scott 2024).
Raw counts from the reader are averaged and converted to dose by an NIST-traceable calibration coefficient determined by IROC.These dots are unscreened, meaning IROC determines the k s,i for each detector through a commissioning process; this detector-specific correction is part of the High Accuracy framework laid out in AAPM TG-191 (Kry et al 2020).Several additional correction factors are used to correct and refine the estimate of absorbed dose.AAPM TG-191 established these factors, which include a fading factor (k F ), nonlinearity factor (k L ), beam quality factor (k Q ), angularity factor (k θ ), and depletion factor (k d ) (Kry et al 2020).We determined these correction factors using therapeutic carbon beams at the Centro Nazionale di Adroterapia Oncologica (CNAO) in Pavia, Italy.Dose-averaged LET calculations were performed using FLUKA Monte Carlo simulations (Kozłowska et al 2019) commissioned for the CNAO carbon beam.The number of primaries was 10 6 , simulated on a water phantom for each simulation.The HADRONTHErapy default option was activated, using delta-ray production and transport cuts of 100 keV.Neutrons were tracked down to thermal energies.The EMF package handled energy loss, straggling and multiple Coulomb scattering of charged particles.The PEANUT model was used for hadron-nucleus interactions, including an intra-nuclear cascade stage followed by a pre-equilibrium stage, and then the equilibrium one.Beam relative momentum spread and water mean excitation energy were set to 77.5 eV and 0.1%, respectively.LET D was calculated with the FLUKA subroutines fluscw (FLUence Scoring Weight), by scoring, on a voxel basis, the fluence of particle species with Z 6 and energy E, weighted by the unrestricted LET for the same kinetic energy.The voxel resolution was 0.5 mm, balancing between accuracy and computational speed.
Fading correction (k F ) While OSLDs store dose information by trapping electrons in the crystal lattice, spurious signal is released prior to actual reading of the detector.This loss of signal decreases rapidly immediately following irradiation, and then stabilizes to a relatively small loss over time.The fading correction (k F ) accounts for this loss of signal in the days since irradiation (Kry et al 2020).Equation (1) is used to characterize OSLD fading for photon and electron beams, with d representing the number of days since irradiation of the dosimeter: We benchmarked the OSLD carbon fading to our established OSLD photon fading correction (Alvarez et al 2017).Standard reference dosimeters were irradiated in a Co-60 beam to a reference absorbed dose of 100 cGy.On the same day, the carbon OSLDs were irradiated to absorbed doses of 100 cGy in a carbon beam at two depths: one in the entrance (2.0 cm, 14.0 keV μm −1 ) and one in the proximal region (14.5 cm, 73.7 keV μm −1 ) of a monoenergetic carbon Bragg peak (range 14.8 cm).The experimental and reference OSLDs were read at increasing time points post-irradiation, up to 100 d after irradiation.Two OSLDs were read as standards and as experimentals for each time point.The ratio of the reference to experimental readings were plotted over time to see if there was an increase or decrease in the OSLD response to carbon relative to the reference standards.

Linearity correction (k L )
The linearity correction, k L , corrects for a linear dose response in the dosimeters.For IROC dosimetry, 100 cGy is the standard reference for OSLD.When the experimental doses deviate from these values, the linearity correction is applied (Kry et al 2020).
To characterize carbon linearity, OSLDs were irradiated to various absorbed dose levels ranging from 45 up to 400 cGy in a low LET position (depth 2 cm in a 6 cm × 6 cm high energy monoenergetic carbon beam, range 24.8 cm, LET D 11.9 keV μm −1 ), and from 50 up to 450 cGy in the center of a spread-out Bragg peak (SOBP) of a uniformly modulated carbon beam (range 9.1 cm, SOBP width 2.8 cm, LET D 67.5 keV μm −1 ).Two to four OSLDs were irradiated at each dose/LET condition.Ion chamber measurements were used to verify absorbed dose under irradiation conditions.

Beam quality correction (k Q )
The beam quality correction accounts for differences in detector response to the type and energy of radiation compared to our reference standards, in this case, various carbon energies compared to Cobalt-60 (Kry et al 2020).Since carbon is a heavy ion, a therapeutic carbon beam has a mix of ion species in the beam path, and the proportions of each species will vary as you get closer to the Bragg peak (Guan et al 2018).The dose-averaged LET is a reasonable descriptor of the beam and good approximation of the energy deposited by the beam and was therefore used as the beam quality metric.
To characterize beam quality, two to four OSLDs for each condition were irradiated to 100 cGy (as determined by ion chamber measurements) at several depths in three monoenergetic and four SOBP beams.Irradiation conditions are shown in table 1.The response was calculated relative to the response expected based on Co-60 reference irradiations.

Angular correction (k Θ )
Because OSLDs are a planar dosimeter, there can be an angular dependence of the dose response, k θ (Kry et al 2020).This variation in response can be caused by the differences in cassette thickness, effective thickness of the active detector, or the air gap that the radiation beam traverses for en face versus edge-on irradiation configurations, as well as angles in between.
For the angularity experiment, the OSLDs were irradiated to 100 cGy (reference absorbed dose level) in the entrance of a 6 cm × 6 cm high energy monoenergetic carbon beam (range 24.8 cm).The irradiation was repeated at different angles ranging from 0°(en face) to 270°, with four to eight OSLDs irradiated at each angle.

Depletion correction (k d )
Typically, OSLDs are read multiple times.With each reading, there is a small loss of signal due to the destructive nature of the readout process.This depletion of signal in subsequent readings can be characterized by a depletion correction factor, k d (Kry et al 2020).To test if there was a difference in depletion between carbon and photon OSLD readings, nanoDots were irradiated to 100 cGy in a Cobalt-60 beam, in the entrance of a 6 cm × 6 cm high energy monoenergetic carbon beam (range 14.8 cm), and proximal to the Bragg peak of the same monoenergetic carbon beam.Two nanoDots per condition were read repeatedly, 60 times each.The relative loss in signal was quantified.To assess whether the relationship between read sequence and relative reading differed by LET D , we fit a linear regression model with relative reading as the response and read sequence and the interaction between read sequence and LET D as predictors.We used low LET D carbon as the reference level for dose and assumed a fixed intercept of 1 so that all dose levels had the same starting point.

Statistical and uncertainty analysis
Statistical analyses for significance and uncertainty were performed in the Statistical Package for the Social Sciences (SPSS) version 26 (IBM) and Office 365 Excel version 1908 (Microsoft).The uncertainty for each correction factor was calculated following TG-191 recommendations (Kry et al 2020).For linearity and beam quality, the uncertainty was calculated using the root mean error of the residuals of the linear regression.For angularity, the uncertainty was calculated using the standard error over the measured angles.For depletion, the uncertainty was based on the difference between depletion-corrected and non-depletion-corrected readings.

Fading correction (k F )
The readings for the reference photon and experimental carbon irradiations are shown in figure 1.When the normalized ratios were compared, the OSLD fading for carbon was not statistically different from the fading for reference photons, regardless of LET D (linear regression, p > 0.05).Thus, IROC's photon-based equation can be used to characterize OSLD fading in a carbon beam (equation (1)).

Linearity correction (k L )
A linear fit was applied to the data for low LET D and high LET D irradiations, with 100 cGy as the reference dose level-see figure 2. The high LET D fit was nearly unity across all dose levels, and there was a small difference between the low (11.8 keV μm −1 ) and high (72.4keV μm −1 ) LET carbon linearity corrections, although this difference was less than 1% over the range of 0-300 cGy.Importantly, the linearity correction factor differed between carbon and the reference Co-60 photon beam, and this difference was pronounced: At a 300 cGy dose level, there was a difference in response of almost 7% between carbon beams and photon beams.

Beam quality correction (k Q )
The beam quality correction factor was characterized by dose-averaged LET of the carbon beams and associated secondaries.The data, shown in figure 3, indicated a linear relationship: as the LET D increased, the k Q factor increased.This effect was very pronounced; the OSLD response varied by almost a factor of 2 as LET D changed.The error bars are included for both LET D and k Q and in some cases are too small to be seen.While error bars were small for low LET D , the uncertainty increased for high LET D measurements due to the sharper increase in LET D over a short distance.

Angular correction (k Θ )
The normalized response of the OSLDs (normalized to the mean of all data points) by incident carbon beam angle are reported in figure 4. The data include initial and repeat measurements.The analysis showed no statistical difference between mean values for the different angles (one-way ANOVA, F(7, 36) = 1.406, p = 0.23).

Depletion correction (k d )
Figure 5 shows the linear fits for each irradiation group.Our results showed that relative reading decreased as read sequence increased for the reference low LET D condition (coefficient = −0.00078,p < 0.0001).We found that relative reading decreased quicker for high LET D (coefficient for interaction effect = −0.00018,p < 0.0001), while relative reading decreased slower for reference photons (coefficient for interaction effect = 0.00027, p < 0.0001).However, the magnitude of the differences was small.For example, the slope-predicted relative reading for low LET D at 5 readings was 0.996 ± 0.005, while for high LET D it was 0.995 ± 0.006 and for photons it was 0.997 ± 0.004.These differences were smaller than the uncertainty of the measurements themselves.However after 60 readings, the predicted relative readings were 0.953 for low LET D , 0.943 for high LET D , and 0.970 for reference photons, showing a larger difference.

Uncertainty analysis
The difference in uncertainty between low and high LET D irradiations were small.The combined uncertainty at the one sigma level is shown in table 2. This uncertainty was calculated with the following parameters: the uncertainty for reference Co-60 standards for a high accuracy system as determined by Alvarez et al (2017), the reference photon fading correction (shown to be not statistically different from carbon), the carbon-specific linearity correction combined between low and high LET D , the calculated uncertainties for beam quality and angularity, and the added uncertainty if no depletion correction is applied.The overall uncertainty budget at the one-sigma level is 6.3%, as compared to 1.6% in reference photon beams (Alvarez et al 2017).

Discussion
In this work we characterized OSLD Al 2 O 3 :C nanoDots in clinical carbon beams.Different characteristics of the detector showed different types of responses relative to photon beams.For example, fading was found to be the same between carbon and photon beams.In contrast, linearity and depletion were both different in carbon than in photons, though the differences for depletion were small under our standard reading conditions.Finally, some characteristics, such as beam quality dependence and depletion, were found to vary by the nature of the carbon beam.As a result, the response of OSLD nanoDots must consider not only the beam type (e.g.carbon) but also the characteristics (LET D ) of that beam.
In photon-based uses of the OSLD nanoDot, nonlinearity in the detector response is typically the largest correction that must be considered and is typically around 7% by 3 Gy.However, this study found that as the LET D of a particle increases, the linearity correction becomes less pronounced (figure 2).For high LET D irradiations (>72 keV μm −1 ) in this experiment, the detector response was virtually independent of the absorbed dose level up to 450 cGy.For low LET D irradiations, the dose linearity corrections were less close to unity, but remained small compared to the overall uncertainty.A 10 cGy deviation from the reference absorbed dose resulted in a 0.08% difference in detector response, while a 50 cGy deviation from the reference absorbed dose results in 0.38% difference in response.Particularly for the IROC program, the desired dose level for each irradiation is tightly controlled; provided the instructions are followed, there may be no need to correct for nonlinear dose response.These results were similar to those observed by Yasuda and Kobayashi, showing a decreasing dose linearity correction with increasing LET D (Yasuda and Kobayashi 2001).
The largest correction factor in this work was found to be k Q , which ranged from 1.2 to 2.1 over the range of 11.9-76.0keV μm −1 .This substantial variability in response is in sharp contrast to the use of this detector in MV photons, where the response varies by less than one percent over the range of nominal MV energies (Reft 2009).This shows a similar trend to data by Reft et al, who examined beam quality in a monoenergetic carbon beam for a prior model of the nanoDot (Reft 2009).Data from Yukihara et al shows a steeper slope for a larger diameter, thicker crystal OSLD configuration (Yukihara et al 2015).Our data set includes a larger variety of beam configurations (e.g.monoenergetic and various SOBPs, each of which spanned a wide range of LET D ), which may further explain the differences observed.The highly varied response in carbon beams is due to a quenching effect of the solid-state detectors with increasing LET D (Gambarini et al 2016).Additionally, the variability of the mix of secondary particles in the experimental beams influences the detector response (Parisi et al 2022).The accuracy of the positioning of detectors in depth is also an important factor to consider.Misalignments of a few tenths of a millimeter could lead to significant variation in LET D values.In this work we described the beam quality using dose-averaged LET, which was found to provide a simple and reasonably accurate fit for k Q .The largest deviations from the linear k Q versus LET D fit were found at ∼25 keV μm −1 where the linear fit was in error by as much as 15%.This generic k Q fit allows us to apply the correction under a variety of irradiation conditions, which are bound to occur in an international audit program of various carbon ion machines.There may be a dosimetric parameter, such as a microdosimetric value, that better fits the data (Parisi et al 2022).This will be examined in future work.Previous studies in photon beams have shown an angular dependence of the nanoDot as electrons scatter out of the high-density detector disc and into the surrounding air gap (a phenomenon which is dependent on the angle of the beam because of the disc shape of the active volume).With these air gaps, it is reasonable to imagine that the carbon beam may experience some streaming or scatter that would also manifest as an angular dependence between an edge on and an en face irradiation setup.However, as seen in figure 4, no such effect was observed.This is also consistent with previous findings for proton beams (Kerns et al 2011) and carbon (Yasuda and Kobayashi 2001).Despite the consistency seen as a function of irradiation angle, for consistency purposes, optimal irradiation conditions are to orient the OSLD dot in the same direction for irradiation of standards and experimental detectors if possible.
While the depletion of OSLDs changed by beam type and LET, these differences were observed over 60 readings.Typically, IROC uses just 5 readings, over which the differences in depletion are small (0.1% for low LET D irradiations and 0.2% for high LET D irradiations).
Overall, the uncertainty associated with using OSLDs in a carbon beam is larger than it is in a photon beam; the combined uncertainty at the one sigma level was 6.3% for carbon compared to 1.6% for photons (Alvarez et al 2017).Therefore, IROC is unable to use a standard ±5% acceptance criteria on absorbed dose measurements with OSLDs in a carbon beam.A wider acceptance criterion could be used (e.g.±10.3% at the 90 percent confidence interval), but this does not fall under the high accuracy framework laid out in AAPM TG-191 (Kry et al 2020).We are currently exploring LiF:Mg,Sn TLD-100 as an alternative to Al 2 O 3 nanoDots for passive dosimetry in a therapeutic carbon beam, using the high accuracy controlled framework of IROC's TLD-100 program (Alvarez et al 2017).

Conclusion
Carbon dosimetry with OSLDs is complex, and the detectors respond differently in carbon than in photons, and differently in different locations in the carbon beam.Nevertheless, the response of OSLD can be characterized with the appropriate information about the carbon beam, such as dose-weighted LET, with a 6.3% uncertainty at the one-sigma level.This characterization could allow IROC to use these detectors for remote dose measurements of carbon therapy beams, but with less accuracy than standard photon remote dosimetry audits.

Figure 1 .
Figure1.The fading of Co-60 photons (grey), low LET carbon (blue), and high LET carbon (orange).The fading between the groups was not statistically different.

Figure 2 .
Figure2.The linearity correction factor for reference Co-60 photons (grey) compared to low-LET carbon (blue) and high LET carbon (orange).The differences between low and high LET carbon linearity corrections are small over ±50 cGy from the reference 100 cGy.

Figure 3 .
Figure 3.The carbon therapy beam quality correction factor (k Q ) plotted at a function of dose-averaged LET (keV/μm) of the primary carbon beam and associated secondaries, including historical carbon Al 2 O 3 :C data from Yasuda and Kobayashi (2001), Reft (2009), and Yukihara et al (2015).

Figure 4 .
Figure 4.The normalized OSLD response is reported for the eight angular positions tested.The error bars represent the coefficient of variation for the measurements.No statistical difference was found between OSLD response at different angles.

Figure 5 .
Figure5.OSLD depletion for reference cobalt-60 (grey), low LET carbon (blue), and high LET carbon (orange).There was a statistical difference between the depletion of each group.

Table 1 .
Beam characteristics for the experimental setup for OSLD beam quality carbon measurements.The field size for all beams was 6 cm × 6 cm square field.WED = water-equivalent depth; LET D = dose-weighted linear energy transfer.

Table 2 .
Overall uncertainty budget calculated at the one standard deviation level for carbon irradiations of OSLD.