Calibration strategies for use of the nanoDot OSLD in CT applications

Abstract Aluminum oxide based optically stimulated luminescent dosimeters (OSLD) have been recognized as a useful dosimeter for measuring CT dose, particularly for patient dose measurements. Despite the increasing use of this dosimeter, appropriate dosimeter calibration techniques have not been established in the literature; while the manufacturer offers a calibration procedure, it is known to have relatively large uncertainties. The purpose of this work was to evaluate two clinical approaches for calibrating these dosimeters for CT applications, and to determine the uncertainty associated with measurements using these techniques. Three unique calibration procedures were used to calculate dose for a range of CT conditions using a commercially available OSLD and reader. The three calibration procedures included calibration (a) using the vendor‐provided method, (b) relative to a 120 kVp CT spectrum in air, and (c) relative to a megavoltage beam (implemented with 60Co). The dose measured using each of these approaches was compared to dose measured using a calibrated farmer‐type ion chamber. Finally, the uncertainty in the dose measured using each approach was determined. For the CT and megavoltage calibration methods, the dose measured using the OSLD nanoDot was within 5% of the dose measured using an ion chamber for a wide range of different CT scan parameters (80–140 kVp, and with measurements at a range of positions). When calibrated using the vendor‐recommended protocol, the OSLD measured doses were on average 15.5% lower than ion chamber doses. Two clinical calibration techniques have been evaluated and are presented in this work as alternatives to the vendor‐provided calibration approach. These techniques provide high precision for OSLD‐based measurements in a CT environment.


| INTRODUCTION
The nanoDot optically stimulated luminescent dosimeter (OSLD) (Landauer Inc, Glenwood, IL, USA), is a common detector for point dosimetry, particularly in therapeutic applications. 1-7 More recently, in conjunction with the increased interest in improved computed tomography (CT) dosimetry, there has been interest in using the nanoDot for this purpose. Several recent studies have used OSLD in this capacity, [8][9][10][11][12][13][14] including a few in-depth evaluations of the dosimeter characteristics in a CT environment. [15][16][17][18] Importantly, no studies to date explore or describe calibration procedures for OSL-based dosimetry in a CT environment. This is not just practically useful information when conducting these measurements, but is particularly relevant in the context of dosimetric uncertainty. While the AAPM TG-191 report 19 details dosimetric uncertainty associated with more common applications, the uncertainty of OSLD measurements in CT dosimetry has not yet been quantified.
The general formalism for calculating dose using this dosimeter is shown in eq. (1), 19 where the absorbed dose, D, at the location of the OSLD is equal to product of the average corrected signal reading (M corr ), the calibration coefficient (N D,W ), and any additional necessary correction factors (k).
The average corrected signal, M corr , accounts for signal depletion (2) Correction factors are typically necessary depending on the application, and include linearity (k L ), fading (k F ), and beam quality (k Q ) which are standard and defined elsewhere. 19 Angular dependence (k θ ) describes the difference in signal in a CT environment as the angle of the detector is changed from lying flat in the bore, and the irradiation geometry correction (k G ) accounts for the difference between a static en-face irradiation and an irradiation based on a source rotating around the face of the detector. 18 The calibration procedure determines the value of N D,W , and thereby establishes the relationship between the OSLD signal and dose. A common calibration procedure used clinically is that offered by the vendor, through pre-irradiated dosimeters which are provided with the OSLD reader. 15,16

2.B | Calibration protocols
Optically stimulated luminescent dosimeter calibration establishes the relationship between dosimeter signal and dose using "standards" (i.e., OSLD irradiated to a known dose). For each of the three calibration procedures investigated, the OSLD calibration coefficient was defined using these "standards" as the ratio of the known dose to the OSLD signal (measured in counts) as shown in eq. (4).
Water was selected as the reference medium for defining dose to the standard dosimeters using both the CT-based calibration and the megavoltage-based calibration. As a result, the absorbed dose calculated using the dosimeters and these protocols is dose to water, regardless of the actual measurement medium.
The process to determine this calibration coefficient for each of the three calibration protocols is described below:

2.B.1 | Vendor calibration protocol
This protocol used pre-irradiated dosimeters provided by the dosimeter vendor. Calibration dosimeters are irradiated by the manufacturer on a PMMA phantom using 80 kVp x rays (2.9 mm Al HVL) to known delivered dose levels of approximately 0, 3, and 20 mGy.
The two-sigma uncertainty on the dose delivered to the dosimeters is reported to be ±5%. 24 In this work, the calibration dosimeters were read three times each, and the average of the depletion-corrected signal was used to establish the calibration factor: N D,Vendor . An adjustment for the difference in sensitivity in the vendor-supplied dosimeters and the experimental dosimeters was also made (as these dots came from different production batches), despite the fact that correcting for this difference is not explicitly advised in the vendor calibration procedures: the calibration dosimeters had a mean inherent sensitivity of 0.85 while the experimental dots had a mean inherent sensitivity of 0.93. A uniform factor of the ratio of these (1.094) was therefore applied to the calibration factor to account for this difference.

2.B.2 | Free-in-air CT calibration protocol
This calibration protocol relates the dose measured using a calibrated ion chamber to the OSLD signal for dosimeters irradiated under identical conditions using a CT scanner as the radiation source.
In this work, the ion chamber and OSLD standards were irradiated free-in-air using a 120kVp CT beam (Discovery CT750 HD, The delivered dose (to water) was defined using the average of the ion chamber measurements [described in eq. (3)]. Per eq. (4), the calibration factor for the CT calibration (N D,CT ) was the ratio of dose to signal.

2.B.3 | Calibration using megavoltage beam
The third calibration protocol used a 60 Co beamline to determine dose (although a 6 MV beam could also be used), and followed the general procedure used for OSLD calibration by IROC Houston and other radiotherapy auditing bodies. 3,5,6 This procedure relies on megavoltage equipment, and would therefore be most applicable to radiotherapy environments. One advantage of this protocol is the very high accuracy of the delivered dose to the calibration (standard)  CTDI phantom. For each measurement location, two OSLD were irradiated, and the irradiation was repeated three times for a total of six dosimeters at each location. The irradiation was then repeated with the farmer-type ion chamber in the same location as the OSLD.

2.D | Test measurements
The OSLD were read three times and the average (depletion and element sensitivity-corrected) value was used as the corrected OSLD signal. This same signal was converted to dose using the three different calibration protocols described above, so any differences in measured dose for a given condition reflect differences in the calibration protocol (including associated correction factors).
The CT-scanning techniques used to compare the calibration protocols were selected to represent a range of energy spectra.
Eleven unique measurement conditions were used for this comparison; the scanning parameters and dosimeter position for these 11 cases are shown in Table 1. All scans used a 40 mm beamwidth and either axial or helical scans, depending on scan extent (as shown in Table 1). All helical scans used a pitch of 0.984. Exposures ranged from 200 to 900 mAs with either 1 or 2 s rotations times, such that the dose delivered to the ion chamber at the same position was between 25 and 40 mGy. Each of these conditions was also simulated using a previously benchmarked Monte Carlo model based on the same x-ray source and geometry 26 ; the mean spectral energy at the position of the dosimeter was determined (Table 1).
The dose to the OSLD was determined using eqs.
(1) and (2). For most uses in a CT environment, k L (linearity correction) is unity. 18 All dosimeters were placed flat relative to the CT bore so that there was no angular dependence, and all times were controlled so there was no relative fading between the standards and experimental detectors. Other possible corrections are described below: For the vendor-recommended calibration procedure, the dose was determined using the manufacturer-provided approach, as shown in eq. (5), and using the energy correction provided by the vendor (k Q, Vendor ), which the vendor states is equal to 1.19 for all CT measurements. Other possible correction factors were ignored as no other corrections are suggested by the vendor.
For CT calibration and dosimetry, the value of k G is unity because there is no difference in irradiation geometry between the standards and experimental OSLD. The dose to the OSLD was therefore calculated using eq. (6).
Values for k Q,CT were previously determined using the simulated photon energy spectra and Burlin cavity theory, 18 and are provided in Table 2.
For the megavoltage calibration technique, k G is necessary to account for the differences in irradiation geometry between the calibration conditions (static en-face irradiation of the dosimeter) and the measurement conditions (rotating irradiation), but has a relatively small value of 1.03. 18 The dose to the OSLD for dosimeters following the 60 Co calibration protocol was determined using eq. (7), where the energy correction factors are shown Table 2.
2.E | Uncertainty analysis  N D was determined from the uncertainty in each of its parameters (i.e., the parameters in eq. (1) rearranged to solve for N D ), including the uncertainty in the reference dose associated with each calibration protocol (±5% for the vendor calibration, 24 ±5% for the CT protocol, 27 and 0.9% for the MV protocol 28 ).
Rather than simply combining these component uncertainties in quadrature, the total uncertainty was determined more robustly using eqs. (8) and (9), where var denotes variance and E denotes the expected value (i.e., the mean).
varðXYÞ ¼ varðXÞvarðYÞ þ varðXÞEðYÞ 2 þ varðYÞEðXÞ 2 (8) In eq. (8), X represented a given factor (e.g., M corr ), and Y represented the product of the remaining factors (N D × k L × k F × k G × k θ × k Q ). The variance of Y was calculated by applying eq. (8) recursively to each individual factor (X' = N D , and Y' = k L × k F × k G × k θ × k Q and so on). Calculation of the variance of M corr also required eq. (9), as M corr is a linear combination of products of correlated variables [eq. (2)]. In this case, CoV is the covariance between X and Y: varðX þ YÞ ¼ varðXÞ þ varðYÞ þ 2CoVðX; YÞ This method is more robust than adding uncertainties in quadrature because it does not rely on the normality assumption of the distribution, or on any type of mathematical approximation, and allowed us to analytically determine the standard deviation of the OSLD measured dose.

3.A | Comparison of calibration methods
For a range of measurement conditions, varying measurement position, phantom size, kVp, and scan extent, the dose to the OSLD was determined using each of three calibration protocols. These values were then compared to the dose measured using the farmer-type CT ion chamber and plotted as a function of the mean photon energy for the scan parameters selected (Fig. 3).
The error bars in Fig. 3 represent the relative uncertainty for each method, as calculated in eqs. (8) and (9). A comparison of the measured doses is provided in Table 3, along with the percent difference from the ion chamber measured dose.
The results of the calibration protocol comparison indicate that similar results can be expected using either the CT-based or megavoltage-based calibration method. On average, the absolute difference between the dose determined using OSLD and one of these two methods versus that determined directly using a CT ion chamber was less than 5%.
The Both the CT-based calibration and the megavoltage-based calibration have been shown to be strong alternatives to the vendorprovided approach for calibrating OSLD nanoDots. Each of these two methods provides a measure of dose well within 10% of a CT ion chamber for a wide range of scan conditions. For the scan conditions examined, a very specific energy correction factor was applied to account for variations in the spectra between the calibration conditions and the experimental conditions. Such precise spectral information is rarely known for a particular measurement condition, and energy correction factors based on more general scan parameters (kVp, phantom size, scan extent, etc.) are more useful for clinical application. The sensitivity of k Q to different scan parameters was previously found to be most sensitive to kVp and measurement location, and to be relatively insensitive to scan extent or phantom/patient size (usually less than a 2% effect). 18 Consequently, values for  (Table 4).
For a calibration relative to a megavoltage beam, the value of k Q is far from unity because of the large difference in energy between calibration and measurement. The values provided in Tables 4 and 5 allow for simple and accurate energy correction using either of the two proposed calibration protocols.
Because the spectra may vary between different scanner manufacturers, these values should be applied with caution. While many CT scanners have similar spectra, Toshiba scanners have been known to have a softer spectrum, and therefore will have a different k Q correction factor relative to a distinct calibration beam (i.e., the vendor's calibration beam or a megavoltage beam; e.g., k Q in Table 5). A strength of the CT calibration procedure is that the calibration and experimental readings can be done on the same CT scanner. If the CT spectrum is inherently softer than evaluated in this study, this will be substantially accounted for in the calibration procedure and thereby mitigate the effect of a different calibration CT spectrum. While this will help mitigate substantial uncertainty in k Q from mapping between, for example, a 60 Co beam and an arbitrary CT calibration beam (e.g., scattering between the calibration and experimental dosimeters as shown in Table 4) will nevertheless persist. The magnitude of these differences may be similar to the values shown here in Table 4, but they will not be identical.

3.B | Uncertainty analysis
There are both random and systematic uncertainties associated with the determination of dose using this OSLD system. The uncertainties arise from measurement imprecision in the OSLD signal as well as uncertainties in the various correction factors applied to the signal.
When averaged over the three readings, and as detailed in Table 6, the relative uncertainty in the corrected OSLD signal was consistent regardless of the calibration protocol: 1.3%. This originated with the relative uncertainty in the depletion-corrected raw OSLD reading (0.8%) and the relative uncertainty in the element specific sensitivity factor (1.0%). The uncertainty in N D was dominated by the uncertainty in the delivered dose to the standard dosimeters, which was lowest for the megavoltage calibration protocol and produced an uncertainty in N D,60Co of 1.6%. In contrast, the uncertainty in the calibration coefficient using the other two protocols had a value of slightly over 5%.
Finally, the total uncertainty in the dose determination using each protocol included the uncertainty in the correction factors. The largest component of uncertainty in this step was from the beam quality correction factors. The relative uncertainty in the corrected OSLD reading, the calibration coefficient, and the overall dose determination for the three calibration protocols is shown in Table 6.
The largest overall uncertainty was associated with the vendor calibration, largely because of the simplistic management of the energy dependence of the detector. When comparing the CT and the 60 Co-based protocols, the 60 Co protocol had better precision in the calibration coefficient, but because it had much larger correction factors, it had a larger uncertainty associated with these correction factors, leading to a slightly larger overall uncertainty.
The calibration protocol with the lowest overall uncertainty was the CT-based calibration, and this is likely the best calibration option for most diagnostic CT clinics. The relative uncertainty in dose measurement using properly calibrated OSLD is ±8.3% (2-sigma), which is reasonable for CT dosimetry applications. Precise dosimetry is also achievable using a megavoltage calibration, and this approach may be of interest to radiotherapy clinics due to their familiarity with megavoltage equipment. The relative uncertainty on the vendor calibration protocol was the highest of the three examined. This is largely due to the uncertainty in dose delivered to standards, as well as uncertainty in the correction factor to account for energy or other effects. However, the vendor calibration is also sensitive to systematic uncertainties; for example, as discussed above, the results will be systematically different for a CT scanner with a different energy spectrum.

| CONCLUSION
In this work, two calibration protocols are presented which are strong alternatives to the vendor-supplied calibration method for performing CT dosimetry using the nanoDot OSLD. The CT freein-air calibration requires a previously calibrated ion chamber, and OSLD standards to be irradiated with a consistent and reproducible scan technique. Energy correction factors are generally necessary using this calibration technique and a simple table of factors is provided that cover a wide range of scan conditions. The megavoltage calibration requires a larger correction factor, but offers comparable accuracy. Using either the CT free-in-air or megavoltage-based calibration approaches, point dosimetry with a relative uncertainty of less than ±10% is readily achievable in a CT environment.