Validation of Monte Carlo simulated absorbed-dose-to-water inside a custom SPECT/CT phantom using active and passive dosimeters: a feasibility study using 99mTc

Objective.This project aims to provide a novel method for performing dosimetry measurements on TRT radionuclides using a custom-made SPECT/CT compatible phantom, common active and passive detectors, and Monte Carlo simulations. In this work we present a feasibility study using 99mTc for a novel approach to obtaining reproducible measurements of absorbed-dose-to-water from radionuclide solutions using active and passive detectors in a custom phantom for the purpose of benchmarking Monte Carlo-based absorbed-dose-to-water estimates. Approach. A cylindrical, acrylic SPECT/CT compatible phantom capable of housing an IBA EFD diode, SNC600c Farmer type ion chamber, and TLD-100 microcubes was designed and built for the purpose of assessing internal absorbed-dose-to-water at various points within a solution of 99mTc. The phantom is equipped with removable inserts that allow for numerous detector configurations and is designed to be used for verification of SPECT/CT-based absorbed-dose estimates with traceable detector measurements at multiple locations. Three experiments were conducted with exposure times ranging from 11 to 21 h with starting activities of approximately 10–16 GBq. Measurement data was compared to Monte Carlo simulations using the egs_chamber user code in EGSnrc 2019. Main results. In general, the ionization chamber measurements agreed with the Monte Carlo simulations within k = 1 uncertainty values (±4% and ±7%, respectively). Measurements from the TLDs yielded results within k = 1 agreement of the MC prediction (±6% and ±5%, respectively). Agreement within k = 1 uncertainty (±6% and ±7%, respectively) was obtained for the diode for one of three conducted experiments. Significance. While relatively large uncertainties remain, the agreement between measured and simulated absorbed-doses provides proof of principal that dosimetry of radionuclide solutions with active detectors may be performed using this type of phantom with potential modifications for beta-emitting radionuclides to be introduced in future work.


Introduction
Treatment of advanced metastatic cancers has historically been challenging using radiation therapy due to the potentially numerous microscopic disease sites making conventional external beam and brachytherapy treatments to all sites impractical. Targeted radionuclide therapy (TRT) offers a systemic approach to target wide-spread tumor sites through the delivery of radionuclides conjugated to a drug with an affinity for a certain target or disease. The inception of TRT was over 75 years ago with the use of radioactive iodine for the treatment of thyroid disease (Jadvar 2017). Since then, the application of TRT has expanded to numerous radioisotopes and disease sites. Currently there is growing interest in quantitative radionuclide imaging and personalized dosimetry to increase the treatment efficacy of TRT (Li et al 2017, Gupta et al 2019.
Unlike external beam radiation therapy (EBRT), TRT suffers from a lack of traceable dosimetry. Biokinetic models may be used in conjunction with the MIRD formalism (Stabin et al 2005, Bolch et al 2009 to provide a starting point for generalized absorbed-dose estimates, but issues remain with assumptions of tumor shape and mass, as well as time-dependent activity distribution (Donoghue et al2022). Additionally, the current 'onedose-fits-all' approach to injected activity for patients with the same body weight and disease type has led to under and over-dosing patients (Li et al 2017). Therefore, the current gold-standard for personalized TRT dosimetry is quantitative imaging-based Monte Carlo (MC) simulation that allows for patient specific absorbeddose calculation. There are numerous MC codes specifically tuned for combining imaging, radiation therapy, and dosimetry such as GATE, a user-friendly GEANT4 based code that incorporates patient radionuclide imaging data for calculating 3D voxelized dose simulations (Sarrut et al 2014), MCNP, and EGSnrc, though the latter is limited to the transport of electrons, positrons, and photons. Due to computational and time limitations, the use of MC remains cumbersome for many clinical applications (Flux et al 2018, Tiwari et al 2020. A rapidly expanding body of research is aimed at using Dose Kernel (DK), or more specifically Dose Point Kernel (DPK), convolution for TRT dosimetry. DPK has been used as an efficient and enhanced method for dose calculation entering the realm of TRT dosimetry (Sanchez-Garcia et al 2014). One critical limitation of the DPK method and MC-based codes is their lack of experimental validation with measurements from detectors with traceable calibrations for the dosimetry of TRT radionuclides. To date, few studies have benchmarked common MC based methods with measurements. This is in part due to the difficulty of measuring the short-ranged particles commonly used in TRT applications (Tiwari et al 2020).
Previous work in measuring absorbed dose from radionuclides has primarily employed the use of passive dosimeters such as TLDs, radiochromic film, and polymer gel with varying levels of success (Johnson et al 1995, Villarreal-Barajas et al 1999, Braun et al 2009, Tiwari et al 2020, Van et al 2022. There are several challenges that arise when performing dosimetric measurements of liquid beta-emitting radionuclide sources, including their rapid attenuation through material leading to low signal and volume averaging effects across the active layer of the detector, potential contamination of or damage to the dosimeter, and the change in response of the detector due to the positional variation in energy spectrum. Therefore, it is ideal to use dosimeters that minimally perturb the incident radiation field. This is often achieved using small detectors with thin entrance windows. For example, (Van et al 2022) performed measurements in a 3D printed phantom containing a 25.4 μm thick Kapton window to separate a source solution of either 90 Y or 177 Lu from a piece of radiochromic film with an equally thick active layer. The obtained measurements showed agreement generally within 5% of dose estimates simulated using EGSnrc, MCNP6, and an in-house Dose Planning Method (DPM).
In a first step toward in-phantom active dosimetry measurements of liquid sources of beta-emitting TRT agents, this work aims to validate MC dose calculation methods with measurements made from commonly used active and passive dosimeters within a custom SPECT/CT compatible phantom injected with a radioactive  solution. While not directly included in this work, the phantom was designed with the intent of being used inside a SPECT/CT scanner for comparing absorbed-dose-to-water (ADW) rate estimates calculated using activity obtained from SPECT/CT scans and appropriate absorbed-dose calculation software to measurements from dosimeters and detectors with traceable calibrations. A primarily gamma-emitting radionuclide was chosen for the initial phase of this work to assess the validity of the experimental setup and the efficacy of the selected detectors for this purpose. The availability and half-life (6.007 h) of 99m Tc makes it an excellent choice for this investigation (Stanford Environmental Health and Safety 2020). The results from this work will help facilitate future work investigating ADW measurements from active and passive dosimeters using other radionuclides.

Methods
Phantom design and construction A cylindrical, acrylic phantom of outer diameter 20 cm, internal diameter 18 cm, and length 20 cm was designed using SOLIDWORKS 2019 (Dassault Systemes, Velizy-Villacoublay, France). The phantom consisted of a cylindrical shell, which houses the radioactive solution, chemically welded to a solid acrylic back on one end and an acrylic ring, which served as a flange, on the other. The flange was equipped with screw holes and an O-ring groove for bolting and sealing to an acrylic front face. The front face of the phantom contained 10 sealable ports to accommodate removable detector inserts as shown in figure 1. The phantom was designed for versatility, such that numerous detector configurations could be adopted for different experiments. The detector ports doubled as fill and drain ports and, when not occupied by a detector holder, could be sealed using an acrylic plug. All phantom components were leak tested to an internal pressure of at least 2 psi.
The positions of the ports were selected to both maximize the number of detector positions and allow for each position to have at least one other position at the same radial distance for signal comparisons if necessary. The numerical port configuration is shown in figure 2. Additionally, a port was placed at the center of the phantom to provide reference to the point of maximum dose. A summary of these positions is outlined in table 1 where the given angle is relative to the line connecting ports 5 and 7.
Inserts for an SNC600c™ Farmer type ion chamber (Sun Nuclear Corporation, Melbourne, FL) and an EFD 3G-pSi electron field diode (IBA Dosimetry, Schwarzenbruck, Germany) were designed to fit into the detector ports, such that the effective points of measurement for each detector were aligned in-depth with the mid-plane of the phantom. The inserts were composed entirely of acrylic and manufactured in three parts. First, a flange was constructed which allowed for bolting the insert to the phantom's front face. The second section was composed of cast acrylic tubing. The distal portion of the tubing was welded to an endcap with the appropriate shape of the detector tip. While the inserts for the diode could only accommodate the IBA EFD, the inserts for the ion chamber could also accommodate water-equivalent plastic probes used to hold TLD-100 LiF:Mg, Ti microcubes. The external design was kept constant for simplicity in the calculation of internal fill volume.

Detector calibration and orientation dependence investigation
All detector calibrations were performed at the University of Wisconsin Accredited Dosimetry Calibration Laboratory (UWADCL) using a NIST-traceable x-ray beam line.

Diode and ion chamber calibration
The diode and ion chamber were calibrated using the UW250-M x-ray beam. This beam was chosen for its average photon energy at calibration depth (135.4 keV) which was the closest match to the average MC simulated photon energy in the 99m Tc phantom at the center of the phantom (131 keV). The calibration was conducted in a water tank at 100 cm source to surface distance (SSD) and depth of 2 cm in accordance with Lawless (Lawless 2016). Both the diode and ion chamber were aligned with their effective points of measurement on the central axis of the beam. The diode was oriented with its stem parallel to the beam's axis while the ion chamber was oriented with its stem perpendicular to the beam's axis. Four, 30 s integrated charge readings were obtained with each of the detectors, and ADW calibration coefficients (N D w kV ,

250
) were determined using measured air-kerma rates, the appropriate pressure and temperature correction (ion chamber), and the previously established ADW to air-kerma ratio (Lawless 2016).

TLD calibration
Individual TLD chip factors (CFs) were determined through multiple irradiations and readouts using a Hopewell G10 Cs-137 irradiator (Alpharetta, GA) and a Harshaw Model 5500 TLD reader (Thermo Fisher Scientific, Waltham, MA). Before irradiating, the TLDs were annealed at 420°C for 80 min, cooled to room temperature, annealed for an additional 24 h at 80°C, and left to cool at room temperature for at least 24 h. CFs for each microcube, i, were obtained using equation (1)

CF
Response nC Median Response of Sort nC , 1 The TLDs were calibrated using the 250-M x-ray beam. The setup for the TLD calibrations consisted of a water equivalent plastic stack, Virtual Water TM (Med-Cal Inc, Verona, WI), aligned with the central axis of the beam. Three Virtual Water TM probes, each containing 4 microcubes, were loaded and labeled 1-3. They were then inserted into a slab which allowed for 2 cm of buildup and 5 cm of backscatter. The probes were irradiated to 10, 50, and 100 cGy absorbed-dose-to-water, respectively. The TLDs were readout 24 h after irradiation and corrected for background signal and cf A three-point calibration curve was then determined using ADW (cGy) versus detected thermoluminescent signal (nC) and fitted with a linear trend whose slope was used as the calibration coefficient (N D w kV ,

250
). The resulting intercept from the fit was determined to be less than 0.01 cGy, and therefore, insignificant for the measurements performed in this work. This process was repeated after each experiment to ensure the calibration and chip factors did not shift over time.

Diode orientation investigation
Diodes have been known to exhibit orientation dependence with respect to the direction of the incident radiation, and while the EFD's dependence on orientation in the field has been shown to be minimal relative to other common diodes (Ralston et al 2012), it was necessary to determine what effect, if any, the experiment geometry would have on the EFD. To assess this, the EFD diode and an IBA PFD diode were placed in the water tank in the calibration setup. A protractor was positioned on top of the water tank with markings for 90°, 80°, 70°, 60°, 45°, 22.5°, and 0°with respect to the beam axis. The diodes were aligned at each of these angles by rotating the stem to the appropriate angle and then shifting the effective point of measurement of the diode to the same location in the tank. Four 30 s integrated charge readings were averaged at each angle and normalized to the charge reading for the diode at 0°(inline). The relative responses of the diodes at each angle are shown in figure 3.
As indicated in figure 3, the PFD shows a steep fall off in response beginning at about 70°with respect to the beam axis while the EFD maintains a consistent response for all angles with no significant difference between inline and crossline. Therefore, the EFD was chosen as the preferred diode for this experiment.

Diode energy, dose rate, and temporal stability investigation
To test for changes in the diode's response over long exposure periods at different energies, the diode was irradiated using a 20 kVp and 250 kVp x-ray beam as well as 60 Co, 241 Am, and 137 Cs sources. These irradiations lasted between 1.5 and 15 h.
Additionally, dose rate dependence was tested for using the relative response of the diode compared to the relative response of the SNC600c ion chamber at different exposure rates in both 137 Cs and the 250-M x-ray beam. All collections for the temporal stability and dose rate experiments used repeated 120 s integrated charge readings to obtain a time-averaged current reading.

Solution preparation and measurement
The 99m Tc used for this work was medical grade adhering to the NRC's 10 CFR 35.204 99 Mo breakthrough limit of 5.55 kBq of 99 Mo per 37 MBq of 99m Tc (U.S.NRC 2018). The exact activity of 99m Tc eluted from the generator varied between experiments but always resulted in approximately 10-16 GBq injected into the phantom. This solution was measured using two Capintec CRC-55tW dose calibrators (Florham Park, NJ), diluted in room temperature water, and mixed well to produce an even distribution of source activity. While not specifically for 99m Tc, quality assurance of the dose calibrator's calibration factors is performed annually and was determined using three standard sources ( 133 Ba, 57 Co, and 137 Cs) of known activity with maximum observed variances in measurements of these sources between 4%-5%. The manufacturer recommended calibration number, which is based on an initial calibration by the manufacturer using a master chamber and standard sources, for 99m Tc was used. The times of these measurements were recorded for decay correction. Activity left behind in the mixing bucket and filling syringe was measured and subtracted from the measured activity of the whole solution. After sealing the front plate to the phantom body with the appropriate detector insert configuration, the phantom was slowly filled with the radioactive solution to minimize bubbles and dead space. The filling port was then sealed to be watertight and eliminate the possibility of leaks.

Monte Carlo simulations and energy correction
MC simulations were performed with the egs_chamber user-code in EGSnrc 2019. The egs_chamber user-code is commonly used for electron and photon simulations of various detectors including ion chambers and diodes. The phantom and detector holders were modeled according to the mechanical drawings used to create them and simulated as PMMA acrylic. The TLD probes were modeled as Virtual Water TM using PEGS4 data generated from chemical composition information obtained from Cameron et al (Cameron et al 2017). The ion chamber was modeled according to mechanical drawings provided on the manufacturer's website, and the diode was modeled using a combination of dimensional information from the manufacturer and materials from Eklund et al (Eklund and Ahnesjö 2010). The photon and electron cutoff parameters were each set to 10 keV which satisfy the recommendation that the electron CSDA range be smaller than the mean chord length, l, of the active volume (l = 4 V S −1 ) (Benmakhlouf et al 2014). The internal volume of the phantom was simulated as water and acted as an isotropic, radionuclide volume source of 99m Tc. The total number of histories was adjusted for each simulation to give a statistical uncertainty in the reported ADW per disintegration of <1%.
To relate the absorbed doses from the simulations to the ADW calibrations, the scoring volumes were simulated as water and reflected the same geometries and locations of the active volumes of the detectors. Energy fluence was also scored in regions of the phantom corresponding to the active volumes of the TLDs. The spectra at these locations were used in conjunction with spectra scored in the calibration setup to determine the absorbed-dose energy correction factors for the TLDs. The absorbed-dose energy correction factors in the keV range can be calculated as the ratio of the mass energy-absorption coefficient of the detector to that of the medium as shown in equation (2) where RC E is the relative spectral contribution from photons at energy (E Mobit et al 1996, Bartol and Davis 2009, Lawless 2016. A bin size of 1 keV was used for all energy bins.  (3) and (4). The simulated ADW per disintegration from the experiment (D MC ) was multiplied by the total number of decays using the decay corrected activity (A t i ( )) for each collection's starting time point. The time, t f ,represents the current collection's end time. (4) represents the activity measured by the dose calibrators at time t 0 and l is equal to the decay constant for 99m Tc.

Data collection
The ion chamber was inserted into the center port on the phantom (port 5) while the EFD was placed in the adjacent port 6. TLD probes or solid acrylic plugs were then placed in the remaining ports. Table 2 summarizes the detector configurations for each experiment. Experiment 2 provided a repeat trial of Experiment 1 with similar results expected adjusted for different source activities. The configuration was selected to place the SNC600c at the center of the phantom due to its lower sensitivity than the EFD. The EFD was placed in the adjacent port for proximity to the ion chamber for a rough comparison of ADW rates, though the ADW rate at the location of the EFD will be theoretically less, and to maximize the ADW rate to the EFD for an increased signal to noise ratio. Experiment 3 added two more TLD probes such that measurements could be performed at each location in the phantom simultaneously. Data collection for the ion chamber and diode was performed with either 90 s, or 2 min integrated charge readings which were repeated over the duration of each experiment (10 to 21 h) using two Standard Imaging MAX4000 electrometers (Middleton, WI) automated with custom software. The loaded TLD probes were inserted into their respective ports and the entry and removal times were recorded. Once the TLD probes were inserted into the phantom, they were left for the full duration of the experiment. This typically resulted in an exposure time of approximately 24 h, depending on activity, which was required to deliver the desired cumulative ADW of approximately 40-50 cGy. After removal, they were read out at the UWMRRC using the Harshaw TLD reader. ADW rate measured by the detectors was computed from the measurement data at each collection time point M t t raw, i f ( )  using equation (5) for the ion chamber and diode and equation (7) for the TLDs.
The pressure-temperature correction (P TP t t , i f  ) was calculated using equation 10 from American Association of Physicists in Medicine (AAPM) Task group 51 with pressure and temperature data that was collected at each measurement time point (Almond et al 1999). P elec is the electrometer correction factor determined from the electrometer calibration. Due to the minimal variation in temperature between measurements and calibration conditions, P TP t t , i f  was assumed to be unity for the diode. The absorbed-doseto-water calibration coefficient (N D w kV ,

250
) was determined using the methods outlined in the diode and ion chamber calibration section. The average background (Bkg avg ) was determined through multiple background readings obtained with the ion chamber and diode before the experiment. Beam quality conversion factors, k Q , used for the diode and ion chamber were generated using MC simulations and equation (6) (Muir and Rogers 2010) Both beam quality and absorbed-dose energy correction factors (equation (2)) were less than 5%, with the exception of the EFD which was approximately 15%. Equation (7), used to calculate ADW for the TLDs, is similar to equation (5) with the exception that P TP t t , i f  is replaced by P E (calculated using equation (2)), to account for the absorbed-dose energy response between the experimental measurements and the calibration, and the raw reading is corrected using the CF calculated in equation (1) Cumulative ADW was calculated by fitting functions to the measurement curves and then integrating the curves between the start of the measurement and an elapsed number of half-lives. Simulated ADW was calculated using the measured activity, theoretical absorbed-dose model accounting for decay (the numerator of the right side of equation (3)), and experiment durations. For most curves, an exponential function in the form of y be , at = and associated error statistics, were generated. An exception to this was made for the measured data from the diode in Experiment 3 where the curve does not fit an exponential of this form, so a 5th order polynomial was used to determine area under the curve.

IBA EFD
As shown in figure 4, the experimental ADW rate results for the diode in the first experiment showed generally good agreement (average difference of 6%) with the MC predicted ADW, within k = 1 calculated uncertainty values. A planned break occurs in the second experiment as time was taken to restart and zero the electrometer to ensure no significant background signal accumulation was affecting the detector/electrometer system. This was performed to check for any change in background conditions during the lengthy collection. In addition, data in the second experiment showed an offset between measured and predicted ADW rates with the measured ADW rates falling short of predicted values by approximately 20%, a large difference beyond the estimated k = 1 uncertainty values assigned to the ADW rates. The measured ADW rate data for the third experiment showed a similar offset at the start of the measurements in both magnitude (22%) and direction. The shape of the measurement curve did not align with the known decay rate of the source during the third experiment causing the measured data to exceed the predicted ADW by 27% by the end of the collection despite no known contamination and insignificant generator breakthrough. This is made evident by the cross-over point seen in figure 4(f). While the half-life of Tc-99m is 6.00 h, the measured half-life for the first and second experiments are 6.47 h and 5.77 h, respectively. The measured half-life of the third experiment could not be obtained for the diode due to the inability to fit a mono-exponential curve to the data. Ambient temperature recorded during the experiments varied by no more than 1°C and were within ±1°C of the temperature recorded during calibration. This corresponds to an uncertainty in response of the diode of roughly 0.35% (Ärlebrand 2007).
The cumulative ADW generally follow the same trends for agreement (overlap between MC and measured k = 1 uncertainty ranges) as the dose rates. Cumulative ADW measured in the first experiment was lower than predicted by about 9% on average. In the second experiment, the measured values fell short of predicted by 22% on average. During the third experiment, the cumulative ADW results begin out of agreement with an average difference of 18% but fall back into agreement after 3.5 half-lives due to the crossover of the measured and predicted ADW rate curves towards the end of the measurement collection. The results from the temporal and absorbed-dose rate stability investigations show relatively constant response across the energies and absorbeddose rates investigated, as shown in figure 5.

SNC600c ion chamber
Data from the second and third experiments are shown in figure 6. The experimental ADW rate results agree with simulations within k = 1 calculated uncertainty estimates for both the second and third experiments despite observed offsets (8% and 1%, respectively) with measured values remaining larger than predicted. Differences in the cumulative ADW averaged 7% and 4% for the second and third experiments, respectively.
TLDs TLD data were plotted as a function of radial distance from the center of the phantom. A consistent under response, of 3% on average, was observed in the measured ADW throughout all experiments. Despite this, the results from all three experiments agree with MC predictions within k = 1 uncertainty as shown in figure 7.

Uncertainty analysis
Uncertainty was estimated using a root sum of squares approach on all contributing sources of type A (statistical) and type B (non-statistical) uncertainty from each measurement or simulation (JCGM 100 2008). Larger sources of uncertainty for the MC simulations were the detector modeling and the uncertainty in measured activity from the dose calibrator. Additionally, uncertainty in the modeling of the diode and ion chamber was estimated and taken into consideration in the calculation of the beam quality correction factor. In conjunction with observed variations between measurements as well as the manufacturer estimate, the uncertainty in measured activity is in the range of 2%-6% so an approximated value of 4% was used for this work. One standard uncertainty was 0.1176 ---calculated for each detector in each experiment and then applied to each point in the ADW rate curves (figures 4(b), (d), (f), 6(b), d) as well as the cumulative ADW points from the TLDs ( figure 7). Key sources of uncertainty for the diode measurement included the uncertainty in calibration setup, and energy correction. The largest sources of uncertainty for the ion chamber included the calibration setup, and pressure and temperature measurements. The largest sources of uncertainty for the TLD measurements included chip factor determination, reader stability and linearity, positional uncertainties within the probe, calibration setup, and energy correction factor determination. For cumulative ADW, the uncertainty contribution from the linear least squares fit for the curve used to integrate the ADW rates was calculated by propagating the associated error for each fit parameter, x , i from Excel through the closed form of the integrated fit and assessed using equation (8). Cross-correlations between fitting parameters were ignored for simplicity. The relative contribution from these uncertainties were then included in the overall uncertainty calculation which was calculated separately for each cumulative ADW calculation point.
Total uncertainties in ADW rate for the EFD measurements and its MC simulations were approximately 6% and 7%, respectively. For cumulative ADW, the uncertainty in the fit caused the overall measurement uncertainty to expand to 6%. Total uncertainties for the ion chamber measurements and MC simulations were approximately 4% and 7%, respectively. For cumulative ADW the measurement uncertainty expanded to between 4%-5%. An example budget showing relative uncertainties for the TLDs are provided in table 3.

Discussion
IBA EFD diode Despite their small size and increased sensitivity compared to ion chambers, diodes have a reputation for their dependence on numerous environmental and experimental factors. Measuring absolute ADW with diodes remains challenging due to their temperature, absorbed-dose rate, energy, and orientation dependence (Zhu andSaini 2009, Ralston et al 2012). While the preliminary investigation into the orientation dependence of the EFD showed a relatively uniform response from 0°to 90°, the experimental setup was such that radiation was incident on the detector in 4π geometry. Therefore, a possible contributing factor to the under-response observed in the experimental setup is radiation incident on the detector at angles larger than 90°. Additionally, uncertainties in the diode's MC modeling and unaccounted for intrinsic energy dependence could also have contributed to the observed under-response.
The absorbed-dose rate dependence of the EFD has been shown to be minimal (∼2%) in this absorbed-dose rate range (Wong et al 2012). The absorbed-dose energy dependence in the experimental energy regime can be quite large due to the difference in mass energy-absorption coefficients between silicon and water. The absorbed-dose energy response was corrected for using MC simulations and calculated with equation (6).
Despite these considerations, the ADW calculated from the diode measurements was consistently lower than what was predicted by MC simulation during the second experiment. It is possible that the response of the diode changed slightly in the time between first and second experiments due to handling and storage techniques, or changes in environmental factors. Comparatively, the measurements from the first experiment were more consistent with the MC simulation. Data from the third experiment indicated measured and simulated ADW agreed along one portion of the decay curve, but a significant drift caused the measurements to eventually surpass the predicted values. Upon verifying that no known contaminants existed in the phantom or its surrounding region, elution data was analyzed from the supplier for possible generator breakthrough. The data indicated contamination of 99 Mo at levels of 0.008 kBq MBq −1 , far below those allowed for medical-grade 99m Tc (0.15 kBq MBq −1 ), and were found to have no significant impact on the overall half-life of the source (U.S. NRC 2018).
The cause of the observed drift in response was investigated further through experiments testing for absorbed-dose rate dependence and temporal stability. While the radiation spectrum reaching the detector remains unchanged throughout the experiment, it was hypothesized that a temporal change in response could occur at a given energy or absorbed-dose rate. However, the data indicate good temporal stability of the diode at various beam qualities and absorbed-dose rates. Additionally, the diode was shown to be relatively independent (compared to the magnitude of the drift observed in experiment 3) of absorbed-dose rate at the two beam qualities investigated. Therefore, the cause of the drift is unlikely to be due to an inherent absorbed-dose rate or stability dependence of the diode. One possible cause of the difference in measured and theoretical absorbeddose rate curves is a non-uniform distribution of activity within the source volume. While unlikely, considering the ion chamber data and its proximity to the diode, a preferential absorption or clinging of the radionuclide to one PMMA surface over another could theoretically have also caused the observed drift in response by introducing a time-dependent activity distribution.
One motivation for calculating cumulative ADW was to combine many repeated measurements into a single data point. In this sense, a cumulative ADW estimate from the detectors, after a given number of half-lives, may be compared to cumulative ADW estimates integrated from absorbed-dose rate calculated using appropriate software and activity measurements from a SPECT/CT system. Additionally, presenting the data as a function of the radionuclide's physical half-life allows for a more natural comparison between radionuclides. The observed agreement in the cumulative ADW in the first experiment shows promise for the feasibility of using commercially available therapy diodes for long radionuclide measurements in a phantom. This is important due to the active nature (allowing for real-time readouts) and high sensitivity of diodes, as well as the low signal associated with nuclear medicine applications making useable signal levels difficult to achieve with other commercially available active detectors such as ion chambers.

SNC600c ion chamber
Ion chambers are popular detectors for most radiation therapy applications. Their relative simplicity, minimal energy dependence, and thoroughly investigated behavior make them a good choice for many clinical applications. One drawback of using ion chambers, however, is their relatively large size when compared to diodes. This has notably created issues in maintaining charged particle equilibrium and accounting for volume averaging effects in high gradient and small fields commonly found in intensity modulated radiotherapy (IMRT) and stereotactic radiosurgery (SRS) (Ralston et al 2012). Theoretically, these limitations may also apply to common thimble type Farmer chambers when used for the dosimetry of short-ranged beta-emitting TRT agents, necessitating the use of a different chamber design or correction factors. For this investigation however, these limitations do not apply since the primary measured emissions are photons of significant energy in adequate build-up material.
The agreement between the measured and simulated ADW rates and cumulative ADW are encouraging due to the lack of agreement observed in the diode data for the same experiments. Ideally, the ion chamber could be used as a check for other detectors used in similar experiments with the phantom, however, the large activity required to produce adequate signal may not be feasible. Therefore, when performing low to medium activity experiments, passive dosimeters such as TLDs or film should be used to compare to the measurements from active detectors. A small observed drift in the ADW rate data for the third experiment may have been due to the low signal (<20 fA) encountered towards the end of the collection period.
LiF:Mg, Ti TLD-100 microcubes One primary advantage of using TLDs for radionuclide dosimetry is their lack of any wall material or entrance window which allows for minimal attenuation of incident radiation making them particularly attractive for dosimetry of short-ranged particles like betas. Additionally, TLD-100 has a near water equivalence compared to some other detector types (Oberhofer and Scharmann 1981). TLDs have been used in the past for photon and beta-emitting radionuclide dosimetry, particularly for 90 Y (D'Arienzo et al 2017, Ahmad and Nisar 2018). In one study by D'Arienzo et al an anthropomorphic PET/CT phantom and LiF:Mg,Cu,P TLD chips were used in measuring absorbed dose from 90 Y microspheres and achieved an agreement within 3%-20% of various treatment planning absorbed-dose calculation algorithms and MC simulation (D'Arienzo et al 2017).
Despite their lack of build-up material, TLDs are passive dosimeters making instant, real-time measurements impossible. While this is often not an issue for research purposes, it does make dosimetry with TLDs a less convenient option for performing dosimetry measurements in the clinic for quality assurance purposes where immediate dosimetry of a radionuclide solution may be preferred. Additionally, while TLDs are relatively energy independent in the MeV range, they are known to exhibit significant energy dependence in the lower keV range where the emissions for many medical radionuclides reside (Oberhofer and Scharmann 1981). Therefore, appropriate energy corrections should be applied between calibration and measurement data. Figure 7 shows a slight, but consistent under-response in the TLD measurements throughout all experiments though agreement within calculated k = 1 uncertainty is preserved. This may have been caused by various factors including the calibration setup, simulation geometry, or temperature fluctuations during transit.
Future work will incorporate beta-emitting radionuclides and modified attachments to the current phantom to assess the feasibility of measuring ADW from commonly used TRT agents. Specifically, detector inserts with localized source cavities and thin windows will be utilized to maximize signal and reduce attenuation of shortranged beta-emissions.