Accuracy , reproducibility , and uncertainty analysis of thyroid-probe-based activity measurements for determination of dose calibrator settings

Purpose: In the nuclear medicine department, the activity of radiopharmaceuticals is measured using dose calibrators (DCs) prior to patient injection. The DC consists of an ionization chamber that measures current generated by ionizing radiation (emitted from the radiotracer). In order to obtain an activity reading, the current is converted into units of activity by applying an appropriate calibration factor (also referred to as DC dial setting). Accurate determination of DC dial settings is crucial to ensure that patients receive the appropriate dose in diagnostic scans or radionuclide therapies. The goals of this study were (1) to describe a practical method to experimentally determine dose calibrator settings using a thyroid-probe (TP) and (2) to investigate the accuracy, reproducibility, and uncertainties of the method. As an illustration, the TP method was applied to determine 188Re dial settings for two dose calibrator models: Atomlab 100plus and Capintec CRC-55tR. Methods: Using the TP to determine dose calibrator settings involved three measurements. First, the energy-dependent efficiency of the TP was determined from energy spectra measurements of two calibrationsources (152Euand 22Na).Second, thegammaemissions fromthe investigated isotope (188Re) were measured using the TP and its activity was determined using γ-ray spectroscopy methods. Ambient background, scatter, and source-geometry corrections were applied during the efficiency and activity determination steps. Third, the TP-based 188Re activity was used to determine the dose calibrator settings following the calibration curve method [B. E. Zimmerman et al., J. Nucl. Med. 40, 1508–1516 (1999)]. The interobserver reproducibility of TP measurements was determined by the coefficient of variation (COV) and uncertainties associated to each step of the measuring process were estimated. The accuracy of activity measurements using the proposed method was evaluated by comparing the TP activity estimates of 99mTc, 188Re, 131I, and 57Co samples to high purity Ge (HPGe) γ-ray spectroscopy measurements. Results: The experimental 188Re dial settings determined with the TP were 76.5±4.8 and 646±43 for Atomlab 100plus and Capintec CRC-55tR, respectively. In the case of Atomlab 100plus, the TP-based dial settings improved theaccuracyof 188Reactivitymeasurements (confirmedbyHPGemeasurements) as compared to manufacturer-recommended settings. For Capintec CRC-55tR, the TP-based settings were in agreement with previous results [B. E. Zimmerman et al., J. Nucl. Med. 40, 1508–1516 (1999)] which demonstrated that manufacturer-recommended settings overestimate 188Re activity by more than 20%. The largest source of uncertainty in the experimentally determined dial settings was due to the application of a geometry correction factor, followed by the uncertainty of the scatter-corrected photopeak counts and the uncertainty of the TP efficiency calibration experiment. When using the most


INTRODUCTION
In nuclear medicine departments, the activity of radiotracers is measured using dose calibrators (DCs).A dose calibrator (also known as re-entrant ionization chamber) consists of a pressurized gas detector which measures the ionization current generated by radiation (emitted from the radiotracer) crossing its sensitive volume.The intensity of the generated current is proportional to the total energy deposited by radiation in the gas chamber.In order to obtain an activity reading, the current is converted into units of activity by applying an appropriate calibration factor.Calibration factors [also referred to as DC dial settings (DS's)] must be specified for each isotope and source geometry.Instrument manufacturers supply DC dial settings for most isotopes commonly used in nuclear medicine to be measured in standard source geometries.
3][4][5] Since β-emitting isotopes are gaining importance in radionuclide therapies (for example, 188 Re, 90 Y, or 177 Lu), having the correct dial settings to determine activity is critical for ensuring that patients receive effective treatments and are not underdosed or overdosed.Based on multiple studies investigating the geometry dependence of the dose calibrator response to β-emitting isotopes, [5][6][7][8][9] it has been recommended to empirically determine dose calibrator settings for less common isotopes and nonstandard geometries that may be used in clinical procedures. 10ethods to experimentally determine or verify dosecalibrator settings require independent measurements (or prior knowledge) of the activity of a sample of the isotope of interest.There are two main approaches to measure sample activity: liquid scintillation counting and γ-ray spectroscopy techniques.The former method was applied to determine DC settings to a variety of standard and nonstandard isotopes used in nuclear medicine including 117 mSn, 11 188 Re, 1 62 Cu, 12 and 223 Ra. 13 On the other hand, using the γ-ray spectroscopy approach, Cannata et al. 14 determined 99m Tc DC settings with a 4πγ-sodium iodide (NaI) detector.Similarly, Marengo et al. 15 and Beattie et al. 16 used high purity germanium (HPGe) detectors to calibrate their DC for 188 Re and two β + -emitting isotopes ( 89 Zr and 124 I).These methods, however, require the use of sophisticated equipment that is not easily accessible in average nuclear medicine (NM) departments.
A practical approach to determine DC settings is to make use of the equipment that is already available in the NM department.A gamma camera, a well-counter and a thyroid probe (TP) are such widely available NM instruments capable to perform γ-ray spectroscopy measurements.Our decision to use the TP was justified by the following reasons: TP has relatively high counting sensitivity, its configuration and collimation allow for reproducible measurements of sources of different sizes (contrary to well-counter), it offers a fast and flexible user interface to analyze the data, and finally, it is less frequently used for patient studies (thus, more available) than the gamma camera.
Using the TP (or any other γ-ray spectrometer) to determine DC settings for the isotope of interest involves performing three measurements (Fig. 1).First, the energy-dependent efficiency of the thyroid probe (i.e., NaI detector) must be established using standard sources with well known activities.This step is crucial, as the accuracy of the TP-based activity measurements depends on the accuracy of its efficiency determination.At the second stage, the gamma radiation emitted by the sample of the investigated isotope is measured with the TP.Now, this sample activity can be determined using γ-ray spectroscopy methods, given that the information about the TP efficiency, isotope photon yield, and half-life is known.If necessary, background, source-geometry, and deadtime corrections should be applied during the efficiency and the activity determination steps.Finally, in the third step, the TP-based activity is used to determine the DC settings by direct calibration or using the calibration curve method. 1 The details of the latter approach will be discussed in Sec.2.A.4; it is used in cases when the true sample activity cannot be determined prior to the DC measurement.Each one of these steps introduces errors that propagate and impact the accuracy of the DC settings determination.Identification of sources of these errors and estimation of their values are essential if one wants to optimize the accuracy of determination of the TP-based dose calibrator settings and maximize accuracy of future activity measurements.
In this work, we discuss the method which allows us to use TP to measure isotope activity and determine (or verify) dose calibrator settings.Furthermore, we identify and analyse the sources of errors associated with each step of the measurement process in order to determine the accuracy and reproducibility of activity measurements based on the TP method.Although the method used here uses well-established γ-ray spectroscopy techniques, the detailed analysis presented in this study leads to a series of recommendations on how to perform accurate and practical in-house verification of dose calibrator settings F. 1. Diagram showing the steps and measurements involved in the thyroid probe-based method to determine dose calibrator settings.
using equipment easily available in the nuclear medicine department.
In order to illustrate the performance of the TP method and to compare its results with the published data, 1 we applied it to determine DC dial settings for accurate measurement of 188 Re activity.

MATERIALS AND METHODS
The thyroid probe used in this study was an Atomlab 950 Thyroid Uptake System (Biodex Medical Systems, USA).This system contains a 5.08×5.08cm (diameter×height) NaI crystal coupled to a multichannel analyzer (MCA) with 1024 channels which enables acquisition of the energy spectrum of γ-emission.The MCA is connected to a personal computer for system operation, data acquisition, and analysis.A lead collimator placed at the front of the system accepts only photons coming within the probe acceptance angle, thus limiting background counts.In our experiments, a custom designed Styrofoam box was used to support radioactive sources.Source positions were determined using a custommade distance template, as shown in Fig. 2. All sources were placed at the same distance from the detector (d = 20.5 cm) which resulted in the total acceptance angle equal to 14 • .
Following manufacturer recommendation, before every experiment, a daily energy calibration test of the probe was performed using a 137 Cs source.In addition, a blank scan was acquired each day to measure the ambient background radiation.In all our experiments, the multichannel analyzer was set to cover the energy range from 0 to 763.5 keV, which resulted in a 1024 channel spectrum with the energy bin size of 0.746 keV.For analysis, the acquired spectra were saved in ASCII format and processed using  (Mathworks, USA).

2.A. Determination of dose calibrator settings using the thyroid probe
Figure 1 summarizes the steps needed to determine DC settings based on TP measurements of activity.Sections 2.A.1-2.A.4 describe these steps in detail.

2.A.1. Thyroid-probe efficiency curve
Prior to measuring sample activity, the energy-dependent efficiency of the TP must be determined.This should be done using standard sources with well-known activities.We let ε(E) represent this efficiency, defined as where E represents the energy of the photopeak photons, N photopeak (E) is the number of detected photopeak photons, F.The variable f represents any other factors that may affect efficiency determination such as the coincidence sum peaks from cascade emissions (in particular, when using standard sources with multiple γ-emissions) and detector related temperature effects.A detailed analysis on the factors that may affect γ-ray spectroscopy measurements for NaI detectors can be found in the American National Standard Institute (ANSI) report N42.12-1994. 17Based on Eq. ( 1), the TP efficiency will depend on a number of factors, including the characteristics of the NaI crystal, the geometry of the source, and the sourceto-detector distance.
The TP efficiency was measured using two NIST-traceable calibration sources: 152 Eu and 22 Na (Table I).The geometry of 152 Eu (a point source encapsulated in solid 0.6 cm thick acrylic disk and placed parallel to the detector front plane) was used as the reference geometry.Since the 22 Na activity was encapsulated in a thinner (0.3 cm) solid acrylic disk, a correction factor (disk-to-reference) had to be applied to account for its geometry.The geometry correction factor was estimated using an analytical expression that accounts for the differences in photon attenuation between the 152 Eu and the 22 Na disk geometries (Sec.2.A.3).The measured count-rates of 152 Eu and 22 Na sources were 0.5 kcounts/s and 0.7 kcounts/s, respectively, well below the TP maximum count rate of 100 kcounts/s reported by the manufacturer.Therefore, the dead-time losses were assumed to be negligible (i.e., the DT factor was equal to 1).For higher count rates, however, it is essential to measure dead-time of the system so that the factor DT can be estimated.The TP dead-time can be measured by various methods such as the "decayingsource method" 18 or the "two-source method." 17Although coincidence sum peaks may be important for 152 Eu, this factor was assumed to be negligible because of the large source-to-detector distance (20.5 cm) and the small acceptance angle (14 • ) which minimized the probability of detecting such coincidence peaks.The validity of these assumptions was later confirmed by the accuracy of activity estimates obtained with the TP method (Sec.3.C.1) and the agreement between the measured and the simulated TP efficiencies. 19e energy spectra of the calibration sources were measured five times.After each measurement, the source was intentionally removed and repositioned again at the Styrofoam box so that the variability in photopeak counts due to source positioning could be evaluated.In particular, the energy spectra of 152 Eu and 22 Na were measured each time for 68 and 20 min, respectively, which resulted in more than 10 000 counts in their respective photopeaks.For each energy spectrum, the following analysis was performed: • The counts acquired from the daily blank scan (ambient radiation) were removed from the measured energy spectra.The ambient count-rate was approximately 1.5% of the 152 Eu and 22 Na source count-rates.• A wide energy window was selected around the photopeak to count the number of detected photons N detected .They included both photopeak and scattered photons with energies that fell within the photopeak window.• Two additional windows were positioned on both sides of the photopeak and counts were recorded (N L and N U ).The upper and lower windows were selected as indicated in Fig. 3. Details of the energy window settings for the efficiency calibration isotopes can be found in Table II • The total number of photopeak photons, N photopeak , was calculated by subtracting the scatter component (N SC ), from the total number of detected photons, where the scatter component, estimated using the triple energy window method, 22 is equal to where N U and N L represent the number of photons detected in the upper and lower windows, respectively, and W detected , W U and W L represent the width of the corresponding windows.• A geometry correction factor was applied to the TP efficiency value measured at 511 keV ( 22 Na).
For each photopeak E, the number of emitted photons N emitted (E) was calculated as the product of the time-integrated activity (i.e., the total number of decays occurring during acquisition time T) and the photon yield corresponding to the analyzed photopeak E (i.e., the number of photons with energy E emitted per decay; see Table I), where T represents the acquisition time, T 1/2 represents the isotope half-life, A 0 represents the activity of the source at the time of measurement, and Y (E) represents the photon yield for the photopeak of energy E. The factor DF(T 1/2 ,T) represents the solution to the time-integral of the exponential function.
In order to characterize the efficiency of the thyroid-probe as a function of energy, the following 2-parameter function was fit to the experimental data using a weighted least-squares fitting method: The weighting factors for the least-square fit were defined as where ∆ε(E) represents the efficiency uncertainty.Uncertainty analysis is described in the supplementary material. 19

2.A.2. Sample activity determination using the thyroid-probe
Once the efficiency of the thyroid probe is obtained, the unknown activities of additional samples can be determined using the following equation: where ε ′ (E) represents the fitted efficiency at energy E, κ(E) represents the geometry factor that corrects for differences between the geometry of the calibration source (reference) and that of the measured sample, DT Ṅ represents the deadtime correction factor, and f represents additional correction factors, as discussed in Sec.2.A.1.
The method was applied for 99m Tc, 188 Re, 131 I, and 57 Co sources (Table III).In the cases of 99m Tc, 188 Re, and 131 I, the activities were diluted in 20 ml of water and dispensed into 25 ml glass vials.A geometry correction factor (vial-toreference) was applied when estimating the activities of these samples.The 57 Co source was confined at the bottom part of T III.Manufacturer specifications, source geometry, photopeak energy, and photon yield for isotopes used to evaluate accuracy of thyroid-probe activity estimates.The quantities in brackets represent the expanded uncertainties (k = 2) at 95% confidence level.Nuclear data were obtained from the Decay Data Evaluation Project (Ref.23)  a plastic tube (r = 0.6 cm, h = 7.5 cm); therefore, a geometry correction factor (tube-to-reference) was also applied in this case.Since the measured count-rate of all investigated isotopes was lower than 5 kcounts/s, the count losses due to deadtime were assumed to be negligible.The ambient count-rate was 0.1%, 5%, 4%, and 33% of the 99m Tc, 188 Re, 123 I, and 57 Co source count-rates, respectively.While a single 140 keV photopeak was used to measure 99m Tc activity, for 188 Re and 131 I, three photopeaks were identified in each spectrum and these isotopes activities were determined independently using each of these peaks.Estimating the activity of the 57 Co source was challenging due to the overlap between its two γ photopeaks: 122 and 136 keV.For this reason, the 57 Co activity was estimated using two different methods: (1) using a standard photopeak window set around 122 keV and (2) using a wider window covering both the 122 keV and the 136 keV photopeaks and using the sum of the corresponding photon yields.The energy window settings for each of these isotopes are shown in Table IV.

2.A.3. Geometry correction factors
Three types of geometry correction factors were calculated to account for differences between the source and the reference geometries used for calibration of the TP: (1) a vial-to-reference geometry correction factor κ VR (E) for each photopeak energy E of 99m Tc, 188 Re, and 131 I isotopes; (2) a disk-to-reference geometry correction factor κ DR (E) for the 511 keV 22 Na photopeak; and (3) a tube-to-reference geometry correction factor κ TR (E) for the 122 and 136 keV 57 Co photopeaks.
In general, each source-to-reference geometry correction factor was estimated as the ratio of the average photon transmission factor in the 0.6 cm thick solid acrylic disk (reference geometry) to the average photon transmission factor in the geometry of interest.Details of the specific sourcegeometry correction factor calculations used in our study can be found in the supplementary material. 19n order to validate the analytical geometry correction factor model, Monte Carlo simulations of the TP system and the vial and reference source geometries were performed.The details of the Monte Carlo simulations can be found in the supplementary material. 19The accuracy of the analytical geometry factor was evaluated by the percent difference between the analytical (κ(E)) and the Monte Carlo geometry factors (κ MC (E)),

2.A.4. Determination of the dose calibrator dial settings
After measuring the sample activity using the thyroid probe, the dose calibrator dial settings can be determined.There are two possible scenarios: (a) Direct calibration.This method can be applied to the samples which activity was determined using thyroid probe prior to the DC measurements.In this case, the sample is placed inside the dose-calibrator and the dial setting (DS) is adjusted until the DC activity reading (A DC ) agrees with the activity determined by the thyroid-probe (A TP ).(b) Calibration curve method.This method, introduced by Zimmerman et al., 1 is very useful in cases when the sample activity is too high for the thyroid probe (i.e., high dead-time losses) or when the isotope half-life is very short.The method is a four-step procedure.First, the sample is placed inside the DC and the DS's are uniformly changed over a wide range of values.At each dial setting, the apparent activity (A app ) of the sample (i.e., the DC reading) is recorded.Second, a linear fit is applied to the measured data (apparent activity vs dial setting) resulting in a function A ′ app (DS) that describes the response of the DC to the change in dial settings.For Biodex models, the DC response has the form of A ′ app = c× DS +d.For Capintec, the DC response can be described as Third, the sample is left to decay until its activity is low enough (<1 MBq) to prevent dead-time losses in the TP detector.Then, the sample activity is measured with the TP (A TP ) and it is decay corrected to the time of DC measurements.
The correct dial setting is found by solving the equation In our work, the calibration curve method was applied to determine 188 Re DC settings for two commercial dose calibrators: Atomlab 100plus (Biodex Medical Systems, USA) and Capintec CRC55-tR (Capintec, USA).Since the response (A ′ app ) of the Capintec chamber was measured in a small range of DS, its functional form was well approximated by A ′ app = c × DS + d.The empirically determined 188 Re DC dial settings were compared with the manufacturer recommendations and with the experimental settings reported in the literature. 1 Although Zimmerman findings were obtained using a different Capintec model (CRC-12), the 188 Re DC settings for both CRC-12 and CRC-55tR are the same (as reported by the manufacturer 27,28 ).

2.B. Uncertainty of dose calibrator settings determined with the thyroid probe
As discussed in Sec.2.A, the method to determine DC settings for a new isotope (or a new sample geometry) using TP consists of the following three steps: (1) efficiency calibration of TP, (2) determination of activity of the new isotope sample using TP, and (3) determination of the DC dial settings for the new isotope.Based on Eqs. ( 1)-( 7), the uncertainty of the TP-based DC dial settings (∆DS) is affected by the following factors: • Uncertainty of the TP-efficiency ∆ε, which was calculated by applying the standard error propagation formula 29 through Eq. ( 1).This uncertainty depends mainly on the uncertainty of the photopeak counts ∆N photopeak , the uncertainty of the number of emitted photons ∆N emitted (which is dominated by the standard-source activity uncertainty ∆A 0 and the uncertainty of the photon yield ∆Y ), and the uncertainties associated to geometry (∆κ) and dead-time correction factors (∆DT), when applicable.The uncertainty of the fitted efficiency (∆ε ′ (E)) was determined by the uncertainty of the measured efficiency propagated through Eq. ( 5).• Uncertainty of sample activity determination using the TP (∆A), which was calculated by applying the error propagation formula to Eq. ( 7).The main factors affecting the uncertainty of the TP-based activity are the uncertainty of the photopeak counts ∆N photopeak and the uncertainty of the fitted efficiency curve ∆ε ′ (E).
Additionally, uncertainty of the sample's geometry correction factor was also determined.
A detailed mathematical description of uncertainty calculations can be found in the supplementary material. 19

2.C.1. Accuracy of thyroid-probe-based activity
In order to evaluate the accuracy of activity determination using the TP-based gamma spectroscopy method, the true activity of a sample must be known to be compared with that determined using the TP.Thus, for each investigated isotope ( 99m Tc, 188 Re, 131 I, and 57 Co), this information had to be independently acquired.In the case of 57 Co, which is a NIST-traceable source, the true activity was provided by the calibration report.The activities of other isotopes were measured using a HPGe detector (Canberra, USA) available at the BCCA Cyclotron Laboratory.The efficiency of the HPGe detector was independently determined using a NISTtraceable multinuclide source (Eckert & Ziegler Isotopes products, USA) having the same geometry as the 99m Tc, 188 Re, and 131 I sources.In all cases, the activities were in the range of 37-74 kBq (1-2 µCi) which resulted in the HPGe dead-time losses below 6%.
The accuracy of the activity determined with the TP (A TP ) was quantified in terms of the percent difference with respect to the true activity (A TRUE ), where A TRUE represents the activity determined with HPGe for 99m Tc, 188 Re, and 131 I, and the activity provided by the calibration report for 57 Co.

2.C.2. Interobserver reproducibility
The quantity N photopeak in Eq. ( 7) may depend on the window settings that are used for the determination of N detected , N U , and N L and these may change from one user to another.To investigate the interobserver reproducibility, the following experiment was performed.Five different observers (with experience in energy-spectrum analysis) were asked to select the energy window settings for two photopeaks: the 152 Eu 344 and the 662 keV photopeaks from a 137 Cs calibration source.For each photopeak, the interobserver reproducibility of N photopeak was quantified in terms of the coefficient of variation (COV).The error propagation formula was then applied to evaluate the interobserver reproducibility of the TP efficiency for these energies.

3.A.1. Thyroid-probe efficiency curve
The energy spectra of 152 Eu and 22 Na measured using the TP are shown in Fig. 4. The low energy (30-45 keV) peak observed in 152 Eu corresponds to the x-ray emissions from its respective daughter nuclei 21 (for 22 Na, the x-rays have very low energies and are not displayed 20 ).The measured values of the TP efficiencies are shown in Fig. 5.Note that the measured efficiency at 511 keV ( 22 Na) was rescaled using the disk-toreference geometry factor.The TP efficiency curve derived from these measurements is also shown in Fig. 5.While there are many functions that could be used to model the detector efficiency, a simple 2-parameter model [Eq.( 5)] was used as there was a limited number of efficiency points, it was a simple model and provided an adequate fit to the experimental data (p-value < 0.01 and the R 2 = 0.9850).This is likely because the NaI-efficiency decreases smoothly with energy for energies greater than 120 keV. 30If additional data points were measured at energies below 120 keV, a function with more than two parameters might be necessary to accurately describe the efficiency of the thyroid-probe.
The parameters of the fit obtained in our study are specific to the reference source geometry, a combination of the TP lead collimator and source-to-detector distance of 20.5 cm, and the intrinsic efficiency of this particular NaI detector.It is important to note that the efficiency curve determined in this study cannot be directly applied to a different thyroid-probe, even when all the experimental conditions are identical, as the intrinsic efficiency may vary between detectors.F. 4. Energy spectra of 152 Eu and 22 Na measured with the thyroid-probe and used for the efficiency calibration experiment.The photon yields are shown in parenthesis.

3.A.2. Dose calibrator dial settings for 188 Re
The 188 Re activity was extracted from a 188 W/ 188 Re generator (iTG-Isotopen Technologien München, Germany), diluted into 20 ml water, and dispensed into a 25 ml glass vial.Since the sample activity was too high to be measured using the TP prior to DC measurements, the "calibration curve method" (Sec.2.A.4) was applied.The response of both dose calibrators in the measured dial setting range was well modeled by the linear function A ′ app = c × DS + d, with R 2 = 1 and R 2 = 0.9987 for Atomlab 100plus and Capintec CRC-55tR, respectively.
188 Re dose calibrator settings determined with the thyroidprobe are shown in Table V.These results are compared to the manufacturer recommended settings and to other recommended settings found in the literature. 1 For both dose calibrators, the manufacturer-recommended values disagree with those determined in our experiments.
For Atomlab 100plus, using the manufacturer-recommended settings would overestimate the 188 Re activity by approximately 10% relative to the TP-based settings.It is important to note that the manufacturer recommends to use these settings when measuring 188 Re in a rather broad variety of geometries (a plastic syringe, vial, or thin wall glass ampoule) which are all different than our calibration geometry (a 25 ml glass vial).In order to clarify if the difference between the TP-based and the manufacturer settings are caused by variations in response due to source geometry, the Atomlab 100plus activity readings were additionally determined for three different containers: a 10 ml plastic syringe, a 20 ml plastic syringe, and the 25 ml glass vial used for calibration (Fig. 6).The difference in DC response for a plastic syringe and the 25 ml glass vial was less than 4%.These results, in addition to the independent measurement of 188 Re sample activity using HPGe (Sec.3.C.1), suggest that using TP-based dial settings would result in more accurate activity readings than when using manufacturer-recommended settings for the Atomlab 100plus.Figure 6 also shows that, for filling volumes larger than 5-ml, the Atomlab 100plus dose calibrator response remains nearly constant for the 20-ml syringe and the 25-ml glass vial.Similar findings were reported for a 3-ml vial filled with increasing volumes of 186 Re (Ref.6) and for a 10-ml plastic syringe filled with 90 Y. 7 For Capintec CRC-55tR, the manufacturer recommended 188 Re dial setting is 496 × 10. 27 This setting, which is recommended for all the Capintec models, 28 was reported to overestimate 188 Re activity by 30%. 1 The TP-based 188 Re settings for CRC-55tR confirm the results of Zimmerman 1 and illustrate the importance of experimental determination of DC settings, in particular for nonconventional isotopes.

3.A.3. Geometry correction factors
Figure 7 shows a comparison between the vial-to-reference (κ VR ) geometry correction factors and those obtained with Monte Carlo simulations for 99m Tc, 188 Re, and 131 I photopeaks.The analytical model 19 underestimates the Monte Carlo factors by 2.4%, on average.Differences in the calculated factors are likely due to the approximations used in the analytical method which only consider uniform photon attenuation, T V. Comparison between 188 Re dose calibrator settings determined empirically by different methods and recommended by the manufacturer.All reported uncertainties are expanded uncertainties (k = 2) at 95% confidence level.

Atomlab 100plus
Capintec while the Monte Carlo simulation accounts for attenuation, scatter, and also the changes in the energy spectrum of photons reaching the detector.Despite these differences in modeling, the analytical method still provides a good approximation of the geometry correction factors and it is necessary to improve the accuracy of TP-based activity estimates when sources with different geometries are used, as discussed in Sec.3.C.1.The application of the vial-toreference geometry factor is especially important for low energy photons, for which the loss of counts in the photopeak was approximately 10%-14% due to larger photon attenuation within the vial source as compared to the reference disk geometry.

3.B. Factors affecting uncertainty of dose calibrator settings determined with the thyroid-probe
In Secs.3.B.1-3.B.3, all the reported uncertainties represent expanded uncertainties.The expanded uncertainties were calculated by multiplying the standard uncertainties (Sec.2.B and the supplementary material 19 ) by a coverage factor k = 2, which resulted in the uncertainty interval having a 95% confidence interval.

3.B.1. Uncertainties of thyroid-probe efficiency curve
The uncertainties of the TP efficiency values, which are represented by the error bars in Fig. 5, ranged from 3.2% to 4.4% (relative uncertainty).These error bars were F. 6. Atomlab 100plus relative response for three source geometries (10 ml plastic syringe, 20 ml plastic syringe, and 25 ml glass vial) filled with increasing volumes of 188 Re solution.calculated by combining the contributions from the individual uncertainties discussed in Sec.2.B.The most significant contribution was the uncertainty of the number of emitted photopeak photons (∆N emitted ), which accounted for 2.9% at most.This uncertainty is determined by the uncertainty of the isotope half-life, the uncertainty of the photon yield (reported on nuclear data tables), and the uncertainty of the standard source activity (provided by the manufacturer).These individual contributions cannot be minimized and set a limitation on the lowest uncertainty that can be achieved with this method.The application of the disk-to-reference geometry correction factor resulted in an additional contribution of 0.6% to the 511 keV ( 22 Na) efficiency uncertainty, illustrating the importance of using the same geometry for all the calibration sources to maximize accuracy.The uncertainty of the scattercorrected photopeak counts (∆N photopeak ) contributed to 0.6% for the 511 keV 22 Na photopeak and ranged from 1.2% to 1.9% for 152 Eu photopeaks.The increase in ∆N photopeak for 152 Eu is due to the presence of high scatter under the photopeak (Fig. 4).The uncertainty of the scatter-corrected photopeak counts may be minimized by considering the following: (1) long enough acquisition times of the energy spectrum so that the statistical errors in the photopeak counts are minimized; (2)  precisely measuring the source-to-detector distance so that the variability due to positioning of the source is decreased; and (3) when available, measuring efficiency using photopeaks for which the presence of scatter is low compared to the intensity of the peak.F. 7. Comparison of the analytical and the Monte Carlo vial-to-reference geometry correction factors.

3.B.2. Uncertainties of thyroid-probe activity measurements
The uncertainties of the samples' activities measured with the TP (Table VII) ranged from 6.6% to 12.7%.The largest uncertainties were obtained when the activity was estimated using photopeaks with low intensity and/or very high scatter counts (relative to the photopeak counts) such as the 478 and 633 keV 188 Re photopeaks and the 122 keV 57 Co photopeak (Fig. 8).In the case of activities determined with the most intense photopeaks, the uncertainties ranged from 6.6% to 8.1%.
The largest contribution to the TP-based activity uncertainty was the uncertainty of the vial-to-reference geometry factor which ranged from 3.4% to 4.8%.This uncertainty, however, could be minimized if the dimensions of the vial geometry were measured with more precision.The second largest contribution to the uncertainty of the sample's activity was the uncertainty of the scatter-corrected photopeak counts (which ranged from 1% to 5.6%), followed by the uncertainty of the fit efficiency (ranging from 1.8% to 2.9%).Lastly, the uncertainties associated with the photon yields were usually low, with the exception of the uncertainty of the 155 keV 188 Re and 364 keV 131 I photon yields, which represented in the 2.3% and 2% relative uncertainties, respectively.The uncertainty of the decay factors DF, which are related to the uncertainty of the isotope half-life, was negligible in all cases.
The most precise measurements were obtained when the photopeaks with the largest number of counts were used.In addition to our limitation in the knowledge of the nuclear data, there is a lower limit to the activity uncertainty set up by the uncertainty of the TP efficiency.It is therefore crucial to precisely and accurately determine the efficiency of the TP in order to optimize activity measurements, and eventually DC settings.
In the best case scenario, when the source geometry is the same as the reference geometry (i.e., ∆κ would be zero), the lowest uncertainty of the TP based activity would range from 3% to 4% for the isotopes investigated.This uncertainty, however, is still higher than uncertainties obtained by other techniques such as liquid scintillation counting which may yield 1% uncertainty for 188 Re activity measurements. 1herefore, we recommend to use these other techniques that T VI.Top: expanded uncertainty components (k = 2, at 95% confidence interval) of the TP-based 188

3.B.3. Uncertainties of dose calibrator settings
For the case of 188 Re, the relative uncertainties of the DC settings were 6.16% and 6.67% for the Atomlab 100plus and the Capintec CRC-55tR, respectively.These uncertainties were a combination of the uncertainty of the sample activity (6.15%), the uncertainty of the DC response (DC repeatability), and the propagation of the uncertainty through the fit.
Table VI shows the contribution of each individual component to the DC settings uncertainty.The main factor limiting the uncertainty of the DC settings was the uncertainty of the sample activity.
The experimentally determined dial settings not only depend on the sample activity but also on the parameters of the fit used for the calibration curve method.Therefore, the uncertainty of the activity readings using the newly determined settings (∆A DS ) depends on the dial setting uncertainty propagated through the equation of the fit (A ′ app = c × DS + d).For Atomlab 100plus, a 6.16% uncertainty on the DS settings resulted in a 6.26% uncertainty of the activity readings.For Capintec CRC-55tR, a 6.67% uncertainty of the DS settings T VII.Comparison between activity measured with HPGe and activity determined with the thyroid-probe for 99m Tc, 188 Re, 131 I, and 57 Co.All the reported uncertainties are expanded (k = 2) at 95% confidence interval.is translated into 6.94% uncertainty of the activity reading, showing a greater impact of the variability of the calibration curve (i.e., larger uncertainty of the parameters of the fits c and d) on the final uncertainty.

Isotope
Being able to determine uncertainties of the method is essential to understand its limitations.Having 6.2% relative expanded uncertainty (k = 2) of the DC settings (as in the case of 188 Re) means that the TP method is able to provide DC settings sensitive to source geometry in situations where the DC response variations are larger than, at least, 3.1% (i.e., the DC uncertainties partially overlap).If the response of the DC settings is less than 3.1% to changes in source geometry, the TP method would not be sensitive enough to yield two different DC settings.

3.C.1. Accuracy of thyroid-probe activity
The energy spectra measured with TP and corresponding to the 99m Tc, 188 Re, 131 I, and 57 Co sources are shown in Fig. 8.For the 188 Re energy spectrum, two low intensity photopeaks are visible (633 and 478 keV).However, due to poor detector energy resolution and its low efficiency at high energies, the selection of good energy-window settings for these two peaks was difficult.A similar situation was encountered with the 637 keV and the 284 keV photopeaks of 131 I which were lying on top of a very large background.The energy spectrum of 57 Co shows the 122 keV peak.Although not visible, the shape of the 122 keV high-energy tail indicates the presence of the 136 keV peak.
Table VII compares these isotope activities determined using the HPGe-based γ-ray spectroscopy method and with the thyroid-probe.Very good accuracy (errors below 3.8%) was found when the isotope activity was estimated using its most intense photopeak such as the 140 keV 99m Tc photopeak, the 155 keV of 188 Re photopeak, and the 364 keV 131 I photopeak.The accuracy of the 122 keV 57 Co photopeak was lower (7.5% error), reflecting the challenges of determining the proper window settings due to the presence of two overlapping photopeaks.Similar situation occurs for the 637 keV 131 I photopeak, which partially overlaps with a lower intensity photopeak at 721 keV.

3.C.2. Interobserver variability
The COV for the background-corrected photopeak counts calculated from the energy window set by five independent observers was equal to 6.2% for the 152 Eu 344 keV peak and 2.0% for the 137 Cs 662 keV peak.The higher COV value for the 344 keV photopeak is likely due to a larger fraction of scattered photons present in this photopeak relative to the 662 keV photopeak.The interobserver reproducibility of the efficiency was 6.4% for the 152 Eu 344 keV peak and 2.3% for the 137 Cs peak 662 keV.These results indicate that the triple-energy window correction method is more sensitive to energy window settings when the scatter is high.In the case of the 622 keV peak, only 6% of counts in the photopeak were estimated as belonging to scatter; thus, variations in window settings between observers had less impact on the photopeakcorrected counts.
These results indicate that the average variation of the efficiency determination between observers was as high as 6.4% for photopeaks with high-scatter.It is therefore recommended that, when available, photopeaks with highintensity and low scatter are used to minimize the variability in efficiency determination due to energy window settings.

3.D. Limitations and practical considerations in the nuclear medicine department
The presented method can be applied to determine DC settings for a number of γ-emitting isotopes as long as their photopeak energies fall within the energy range of the measured TP efficiency.Accurate determination of the TP efficiency is probably the main challenge of the proposed method as it requires availability of calibration sources with the appropriate energies.Although the efficiency of the TP was determined using NIST-traceable sources, it is important to note that activity measured using the presented method does not guarantee NIST-traceability.This method, however, is shown as an example of a practical in-house protocol that could be used in the nuclear medicine department to optimize or verify dose calibrator settings, in particular for nonstandard isotopes in which manufacturer settings may not be available.
The lack of suitable standard sources for TP calibration can be overcome by performing this TP calibration using radioisotopes typically used in diagnostic NM scans for which DC settings are known to be accurate.Additionally, for some isotopes, the DC dial settings may be determined or verified using a single photopeak.In such cases, performing a full efficiency-calibration experiment might not be necessary if the following conditions are met: (1) the photopeak energy of the isotope of interest is close to the photopeak energy of another isotope available in the department and (2) the DC-settings for the second isotope are known to be accurate.Then the TP efficiency can be calculated using a single energy point corresponding to the isotope with a known DC calibration factor and applied to determine activity of the isotope for which DC settings are unknown.Subsequently, using this newly determined activity, the DC dial settings can be found.This approach is feasible because the TP-efficiency (i.e., NaI efficiency) changes smoothly with photon energy for energies larger than 120 keV.For the case of 188 Re, the TP efficiency at 155 keV could be approximated by the efficiency at 140 keV that can be calculated from TP measurements of a 99m Tc source.By making this approximation, the 188 Re activity (A 140 ) would be underestimated by 2.5% with respect to the activity determined using the efficiency at 155 keV (A 155 ).
Finally, it is also important to point out that any other photon-counting instrument capable of acquiring the energyspectrum of γ-emitting isotopes could be used in place of TP.For instance, Morgat et al. 31 proposed a method to standardize dose calibrators for new β + -emitters using quantitative PET imaging study of a phantom.This approach, however, only applies to β + -emitting isotopes and relies on the assumption that PET camera calibration is correct and accurate.Although not always applied to DC settings determination, it is a common practice in many hospitals to perform secondary measurements of isotope activity using other equipment available in the department.In this matter, Dantas et al. 32 developed a method to monitor 131 I contamination using the gamma camera.Alternatively, Maioli et al. 33 evaluated the accuracy of the well-counter as a tool to measure activities and perform quality control tests of 99m Tc radiopharmaceuticals.

CONCLUSIONS
A practical method, based on γ-ray spectroscopy, to determine DC settings using the thyroid-probe was described.A detailed analysis of the factors that affect the uncertainty of the dose calibrator settings determined with this method was performed.The accuracy and reproducibility of thyroid probe-based activity measurements were investigated.
Our results suggest that the largest source of uncertainty of the thyroid probe-based DC settings is due to the application of geometry correction factor, followed by the uncertainty in the photopeak corrected counts and the uncertainty of the TP efficiency calibration experiment.In order to minimize this uncertainty and improve the accuracy of the TP efficiency determination, we recommend the following: the use of accurately calibrated standard sources, precisely measured source-to-detector distance, acquisition times long enough to minimize statistical errors in photopeak counts, and the use of calibration sources with consistent geometries.
Our analysis shows that the thyroid probe method allows us to determine activities of the samples to within 5% of their true activities using the most intense photopeaks of the sample's emissions.In such situations, the expanded uncertainties of the measurements were as low as 6.6% (at 95% confidence level).The reproducibility of this method when used by different observers (evaluated by COV) was found to range from 2% to 6%, which suggested that a single observer should perform the experiments to minimize variability of the results.
The described protocol was applied to determine the 188 Re dial settings for two commercial dose calibrators (Atomlab 100plus and Capintec CRC-55tR).Dial settings obtained using the TP-method were compared to the manufacturerrecommended settings.For Atomlab 100plus, manufacturerrecommended settings overestimate 188 Re activity by 10% relative to thyroid-probe settings, which were shown to yield more accurate results confirmed by HPGe γ-ray spectroscopy.For Capintec CRC-55tR, differences larger than 20% were found between the manufacturer recommendation and the thyroid probe method, in agreement with previous results. 1n conclusion, this study shows that accurate (within 5% errors) and reproducible (with 6%-8% expanded uncertainties at 95% confidence level) measurements of activity can be performed using a thyroid probe.Additionally, identifying the factors that impact the uncertainties of the dose calibrator settings enabled us to maximize accuracy of this method, and potentially of any similar method that may use alternative instruments available in the nuclear medicine department (such as gamma camera or well-counter).

F. 5 .
Thyroid-probe efficiency curve (solid line) as a function of energy determined by fitting the 2-parameter linear function in log(ε).Dashed lines represent the derived uncertainty from the fit.Error bars represent experimental uncertainties.All uncertainties are expanded uncertainties (k = 2) at 95% confidence level.
Manufacturer specifications, source geometry, activity, photopeak energy, and photon yield for isotopes used in thyroid-probe efficiency calibration experiment.The quantities in brackets represent the expanded uncertainties (k = 2) at 95% confidence level.Nuclear data were obtained from the Nuclear Data Sheets (Refs.20 and 21).
dow.The shaded area represents the scatter estimate using the triple energy window method.Medical Physics, Vol.43, No. 12, December 2016 T II.Energy window settings for isotopes used in thyroid-probe efficiency calibration experiment.The values in brackets indicate the window boundaries.
T IV.Energy window settings for isotopes used to evaluate the accuracy of thyroid-probe activity estimates.The values in brackets indicate the window boundaries.
Re activity.Bottom: resulting uncertainties of 188 Re activity,188Re DC dial settings, and 188 Re DC activity readings using the TP-based dial settings.
Energy spectra of 99m Tc, 188 Re, 131 I, and57Co measured with the thyroid-probe and used to evaluate accuracy of activity estimates.