Active and passive dosimetry for beta-emitting radiopharmaceutical therapy agents in a custom SPECT/CT compatible phantom

Objective. This work introduces a novel approach to performing active and passive dosimetry for beta-emitting radionuclides in solution using common dosimeters. The measurements are compared to absorbed dose to water (D w) estimates from Monte Carlo (MC) simulations. We present a method for obtaining absorbed dose to water, measured with dosimeters, from beta-emitting radiopharmaceutical agents using a custom SPECT/CT compatible phantom for validation of Monte Carlo based absorbed dose to water estimates. Approach. A cylindrical, acrylic SPECT/CT compatible phantom capable of housing an IBA EFD diode, Exradin A20-375 parallel plate ion chamber, unlaminated EBT3 film, and thin TLD100 microcubes was constructed for the purpose of measuring absorbed dose to water from solutions of common beta-emitting radiopharmaceutical therapy agents. The phantom is equipped with removable detector inserts that allow for multiple configurations and is designed to be used for validation of image-based absorbed dose estimates with detector measurements. Two experiments with 131I and one experiment with 177Lu were conducted over extended measurement intervals with starting activities of approximately 150–350 MBq. Measurement data was compared to Monte Carlo simulations using the egs_chamber user code in EGSnrc 2019. Main results. Agreement within k = 1 uncertainty between measured and MC predicted D w was observed for all dosimeters, except the A20-375 ion chamber during the second 131I experiment. Despite the agreement, the measured values were generally lower than predicted values by 5%–15%. The uncertainties at k = 1 remain large (5%–30% depending on the dosimeter) relative to other forms of radiation therapy. Significance. Despite high uncertainties, the overall agreement between measured and simulated absorbed doses is promising for the use of dosimeter-based RPT measurements in the validation of MC predicted D w.


Introduction
Radiopharmaceutical therapy (RPT) is a form of radiation therapy that involves the injection of a radiopharmaceutical into a patient.Unlike the radionuclides used in diagnostic nuclear medicine imaging, those in RPT have a significant component of short-ranged particle emissions like beta and alpha particles, or Auger electrons to deliver a localized, therapy-level, absorbed dose to targets.RPT often uses radionuclides conjugated to drugs that have a natural affinity for molecules expressed on a target site.While RPT has a long history in medicine, the number of clinically accepted radionuclides and treatments is growing.Advances in imaging capabilities and computational efficiency have led to improved dosimetry capabilities in the use of radiopharmaceuticals for systemic treatment of metastatic disease (Li et al 2017, Gupta et al 2019).
The current RPT dosimetry workflow relies on measurements performed with dose calibrators and SPECT or PET scanners for activity quantification.Monte Carlo (MC) or MC-based techniques are then used to convert time-integrated activity maps into absorbed dose.Image-based MC simulation is becoming a common approach to RPT dosimetry and offers a starting point towards the determination of patient specific absorbed dose distributions.While this is a logical approach to personalized RPT dosimetry, it neglects measurements from dosimeters specifically calibrated for D w .This is an essential part of the dosimetry process in most other forms of radiation therapy.The wide array of available dose calculation software and imaging devices may lead to potential errors in image-based dose calculation.Having a method to perform RPT measurements with dosimeters calibrated for D w would increase the confidence in the doses calculated by image-based techniques.
A number of MC codes are currently available for combining imaging, and activity distribution such as GATE, a user-friendly, GEANT4-based code that incorporates patient radionuclide imaging data for calculating 3D voxelized absorbed dose simulations (Sarrut et al 2014), MCNP, and EGSnrc, though the latter is limited to the transport of electrons, positrons, and photons.Unfortunately, computational requirements limit the use of full MC simulations for many clinics (Flux et al 2018, Tiwari et al 2020).Alternatives to full simulations generally employ a more efficient kernel-based method, such as Dose Point Kernel (DPK) (O'Donoghue et al 2022).While a few studies have attempted to benchmark common MC-based RPT dosimetry methods with film measurements, these have been done using small phantoms with passive dosimeters, namely radiochromic film (Tiwari et al 2020, Van et al 2022).The development of a method for comparing image-based RPT absorbed dose calculation software against dosimeter-based measurements may be of interest to RPT clinics and vendors.
Performing measurements of liquid sources of beta-emitting radionuclides remains difficult due to the rapid attenuation through material leading to low signal, volume averaging effects across the active region 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 reduce the perturbation of the incident radiation field.The best approaches to beta dosimetry often use dosimeters with thin entrance windows and active regions that minimally attenuate beta particles.For example, Van et al (Van et al 2022).performed measurements in a custom phantom with a 25.4 μm-thick Kapton window to separate a 90 Y or 177 Lu source solution from a piece of radiochromic film with an equally thick active layer.The measurements agreed within 5% of absorbed dose estimates simulated using EGSnrc, MCNP6, and an in-house Dose Planning Method (DPM).
This work aims to validate a method for comparing MC D w estimates with measurements from several commercially available active and passive dosimeters performed on solutions of RPT radionuclides within a custom SPECT/CT compatible phantom.Two beta-emitting radionuclides, 131 I and 177 Lu, were selected based on their extensive use in RPT and low average energy beta-particle emissions, 179 keV and 133 keV, respectively, which present a challenging case for dosimetry with common detectors.The results from this work will help provide a feasible method for comparing image-based RPT dosimetry to D w measurements from active and passive dosimeters calibrated for D w .

Phantom description
A cylindrical, acrylic phantom introduced in previous work (Bertinetti et al 2023) and shown in figure 1, was used for the experiments presented here.The phantom was designed to approximate measurement conditions that may be seen in an RPT dosimetry measurement where the target lesion (source cavity), would be surrounded by tissue (water surrounding the insert in the phantom).While not explicitly covered in this work, the phantom was intended to be used in a SPECT/CT system for comparison of D w between image-based dosimetry calculation software and calibrated active and passive dosimeters.Image-based dosimetry is the ultimate goal of the phantom however, the current work focuses on performing dosimeter-based measurements within the phantom and comparing measured results to MC predicted values.
Detector inserts were designed to accommodate both the source solution and the dosimeters.A thin window was used to separate the dosimeters from the source and minimize attenuation of beta particles, as well as confine the source solution to a small, concentrated volume near the dosimeter.The source cavity has a cylindrical design and volume of approximately 1.4 ml.The cavity was constructed entirely of the phantom material, poly(methyl methacrylate) (PMMA), with the exception of the window, which was made of a 25.4 μm-thick polyimide film (ρ = 1.42 g cm −3 ).
A SOLIDWORKS 2019 (Dassault Systemes, Velizy-Villacoublay, France) rendering of the insert is shown in figure 2. To maintain the integrity of the source window, a small PMMA guard ring was attached to the polyimide film against the detector insert tube using epoxy.A cyanoacrylate seal was applied to the epoxy to prevent the absorption of the cavity solution.The main cylindrical cavity funnels into a small cylindrical fill port.The funnel was designed to eliminate any air bubbles.The cavity can be filled using a syringe and sealed using a rubber stopper attached to a thumb screw.A second seal is used to prevent contamination of the water in the larger phantom fill volume.The source cavities of the inserts were leak tested on both the window and fill port ends using an air compressor, adapted nozzle, and pressure gauge, and determined to be air-tight to an internal, relative pressure of at least 2 PSI.
The detector inserts were designed to house the IBA EFD diode (IBA Dosimetry, Schwarzenbruck, Germany), A20-375 ionization chamber (Standard Imaging, Middleton, WI), and custom PMMA detector probes for TLDs and radiochromic film.The inserts are not, however, limited to these detectors.Any cylindrical detector with end-on design and diameter less than 1.27 cm is compatible with the insert.For centering purposes, it is recommended that if a smaller diameter detector is used, it be fitted with at least two acrylic rings to provide multiple points of contact to hold the detector in position within the insert tube.

IBA EFD diode
The IBA EFD (SN: 10652) is a common therapy electron field diode designed for dosimetry in MeV electron beams.The detector was chosen because it is already commonly used in clinical practice and was readily available for this investigation.Additionally, the detector is unshielded and is a pre-irradiated, p-type, silicon diode that exhibits relatively little angular, dose rate, and energy dependence when compared to some other commercially available diode detectors (Ralston et al 2012, Bertinetti et al 2023).The construction of the diode is an important factor in its overall behavior.The silicon detector chip has dimensions of (2.1 × 2.1 × 0.4) mm with an active volume in the shape of a cylinder (1.6 mm in diameter and 0.08 mm-thick).The chip is encapsulated in an epoxy resin, which is covered in an approximately 0.8-1 mm-thick acrylonitrile butadiene styrene (ABS) plastic coating.The effective point of measurement is located approximately 1.2 mm from the surface of the detector (IBA.2022).Due to the external detector's smaller diameter, two acrylic guard rings were used to center the detector in the insert.
The primary concern for beta detection with the EFD is the increased attenuation due to its relatively thick plastic wall.Unfortunately, this minimizes the overall contribution of absorbed dose from beta particles with lower energy (<200 keV) like those emitted from 177 Lu and 131 I. Despite this, gamma emissions from these isotopes are still readily detected and a MC conversion coefficient can be used to estimate surface D w from beta particles, but the EFD alone cannot be considered a direct detector for the electrons emitted from 177 Lu and 131 I.

TLD100 chips
Historically, the thickness of TLDs has led to potentially significant volume averaging effects for beta dosimetry (Holmes et al 2006).Thin TLD100 chips (Thermo Fisher Scientific, Waltham, MA) were used to reduce this effect.Thin chips also reduce the intrinsic energy dependence that results from energy straggling through the TLD.The chips are square with nominal side dimensions of 0.32 cm and thickness 0.015 cm.For reference, an image of a standard TLD100 chip, unlaminated EBT3 film, and the 0.015 cm-thick TLD100 chip is shown in figure 3.
The same annealing procedure was used for all TLDs and is the same procedure outlined by Cameron et al (Cameron et al 1964).For chip factor (CF) determination irradiations, this procedure was repeated following readout.For experimental irradiations and calibrations, an additional anneal in an aluminum tray at 420 °C for 80 min was included after readout.This additional annealing step is required for higher absorbed doses   (>1 cGy), but it may slightly change CFs due to the redistribution of traps in the crystal lattice, and therefore, was not included between consecutive CF irradiations.
The readout procedure utilized a Harshaw 5500 hot gas TLD reader (Thermo Electron Corporation, Oakwood Village, OH).CFs were determined using a 6 MV photon beam from a TrueBeam (Varian Medical Systems, Palo Alto, CA) linear accelerator.The masses of each TLD chip were measured for reference before and after the experiment in case of any discrepancies in future readouts.All TLDs in the sort were irradiated at the same time, and to the same D w of approximately 1 cGy.Readout was performed at least 24 h post-irradiation and individual CFs for each chip, i, were determined using equation (1).
Here, R i is the response of the i th TLD chip and R median is the median response of the entire TLD sort.
PMMA probes were designed to hold the TLDs within the detector inserts.The probes featured an endcap with a 7 micron-thick polyimide window to hold the TLD chips in place.The endcaps were secured on the probes using dowel pins, as shown in figure 3. A small offset between the polyimide window on the endcap and the end of the PMMA probe allowed enough room for the TLDs while still maintaining contact with the window.The unlaminated version of EBT3 was used for this work to eliminate any additional attenuation caused by the external polyester base.The exposure of the active layer to ambient conditions increases the possibility of damage from humidity (León-Marroquín et al 2018).Therefore, the film was stored indoors in a temperaturecontrolled environment, away from any sources of light.

Unlaminated
Circular pieces of unlaminanted film, 0.76 cm in diameter, from the same lot were cut using a BOSS LS1420 laser cutting system (BOSSLASER, Sanford, FL).Film was cut substrate side down with a laser power of 22% and scan speed of 175 mm s −1 .A notch was cut into the top of each piece of film to mark the orientation from which it was cut from the sheet.Additionally, the film was numbered, on the substrate side, for identification using permanent ink.Maintaining film orientation between scans is important due to the potential changes in pixel values during readout (Lewis and Chan 2016).
An EPSON Expression 10000XL scanner (EPSON, Suwa, Nagano, Japan) was used with 48-bit color and all corrections turned off.The scan resolution was set to 1200 dpi.A custom mask (11 cm × 7 cm), was created to eliminate light penetration around the edges and maintain a consistent position for each film piece on the scanning bed from scan to scan.NIST-traceable OD filters were included in each scan for reference to minimize inter-scan variability.Because red light is most readily absorbed by EBT film (Soares et al 2009) and the expected D w was low (less than 10 Gy) (Niroomand-Rad et al 2020), only the red color channel was used in determination of OD.

Exradin A20-375 ion chamber
The Exradin A20-375 parallel plate ion chamber used in this work (SN: X092641) was designed for low-energy radiation measurements.Its relatively large collecting volume (0.074 cm 3 ) and thin entrance window make it ideal for low-signal measurements in low-energy radiation fields.Additionally, its end-on design makes it compatible with the detector inserts used in this work.The relatively large plate separation of the A20 compared to most other commercial parallel plate chambers, however, does create a larger volume averaging effect.
The body, guard, and collector of the A20-375 are composed of C552 (ρ = 1.76 g cm −3 ) air-equivalent plastic.Entrance window measurements specific to the chamber used in this work were obtained from the manufacturer, as well as active volume dimensions determined using COMSOL (COMSOL Inc., Stockholm, Sweden).Theoretically, for most parallel plate chambers, the electric field lines run parallel and uniform across the collecting volume, and due to the small plate separation, this justifies the assumption that the effective point of measurement (EPOM) is located just behind the entrance window.For the extended collecting volume of the A20-375, however, modeling of the electric field lines approximates the EPOM to be located further from the surface of the entrance window (1.8 mm) (Fulkerson 2012).This EPOM was determined in collaboration with the manufacturer and is the accepted EPOM for the commercially available chamber.A drawing of the A20-375 was provided by the manufacturer for MC modeling.

Calibrations
Calibration of the TLDs for D w was performed using the UW-250M x-ray beam (tube potential of 250 kVp and tube current of 12 mA) in Virtual Water TM (VW) (Med-Cal, Inc., Verona, WI) at a depth of 2 cm and source to surface distance (SSD) of 100 cm in a (30 × 30 x 7) cm 3 slab.The average photon energy of the beam at calibration depth was 135.4 keV.Of the calibration beams available for this investigation, the UW-250M provided the closest radiation quality to the radiation emitted from the radionuclides investigated in this work.Differences in energy spectra between emitted radionuclide electrons and secondary electrons in the calibration were primarily corrected for using an MC generated correction factor discussed later.A three-point calibration curve (10, 50, 100) cGy was generated at the time of each experiment and all TLDs were read out, together, at least 24 h post-irradiation.Exposure times were calculated for the calibrations based on the measured NISTtraceable air kerma rate and the MC calculated air kerma to D w coefficient.
There is not currently a primary standard for absorbed dose to water from unsealed solutions of RPT radionuclides, and while an extrapolation chamber developed at NPL has been proposed as a primary standard (Billas et al 2016), it is still in its infancy and, to our knowledge, has not been tested on a wide array of radionuclides.The correction factors, generated with MC, used to convert the detector response under the calibration conditions to the detector response in the experimental conditions are able to effectively correct for the geometry and difference in absorbed dose energy response arising from the change in radiation quality, but not the intrinsic energy responses of the detector.While the intrinsic energy response is generally low in the MeV range of energies it can become more significant for solid state detectors like TLDs and diodes when changing from MeV energies to low keV energies.We have attempted to handle this by making estimated contributions to our uncertainties arising from this effect.Additionally, to minimize the uncertainty as much as possible, we calibrated the detectors using a source that has an average energy close to the emission energies of the source in the experimental setup.The intrinsic response for TLD100 and EBT3 film has previously been investigated by Nunn et al and Hammer et al respectively, and found the intrinsic energy of these dosimeters to be within 3%-5% between effective energies corresponding to the UW-250M beam and approximately 25 keV (Nunn et al 2008, Hammer et al 2018).For the EFD, the absorbed dose came primarily from the gammas emitted by the sources (average energies of 175 keV and 407 keV for Lu-177 and I-131, respectively) which were relatively close in energy to the photons in the calibration conditions.
Film and TLDs were calibrated using the same setup in front of the x-ray beam.Calibration film was irradiated and read out prior to the measurements.From this, a twelve-point calibration curve was created using the net change in OD evaluated through the red color channel.A third order polynomial was fit to the curve to establish the relationship between net ΔOD and D w in the calibrated range.
The EFD and A20-375 ion chamber were both calibrated in a water tank at a depth of 2 cm and 100 cm SSD.The average of four 30 s charge readings were used in combination with the NIST-traceable measured air-kerma rate and a previously determined air-kerma to D w conversion factor to determine the calibration coefficients for each detector (Lawless 2016).Because the A20-375 chamber is not water-proof, a PMMA water-proofing cap with 1 mm build-up obtained from the manufacturer was used during the calibration.Measurements of the cap were made using calipers and telescoping gauges for modeling in MC.

Monte Carlo modeling
The phantom and detector insert were modeled according to specifications using machine drawings that were verified with measurements from calipers, telescoping gauges, and a micrometer.The solid body of the phantom and insert was modeled as PMMA acrylic, while the source window was modeled as a single layer of 25.4 μmthick polyimide.
The TLD100 thin chips were modeled using the density of TLD100 (ρ = 2.64 g cm −3 ) and its material composition (26.7% Li, 73.2% F, 0.02% Mg, and 0.001% Ti) (Lawless 2016).The nominal dimensions of the chips given by the vendor were used for modeling.The TLD and film probes were modeled as acrylic rods with a 7 μm-thick polyimide window.The EBT3 film was modeled as a disk with separate active and protective layers.The material compositions and densities of these layers were obtained from Van et al (2022).
For the active detectors, an approximate model of the EFD was constructed based on information on the manufacturer's website and materials from Eklund et al, (Eklund andAhnesjö 2010, IBA 2022).The A20-375 ion chamber was modeled according to drawings and material specifications obtained through the manufacturer (Fulkerson 2012).An EGSnrc rendering of the A20-375 is shown in figure 4.

Simulation of absorbed dose to water
The egs_chamber user code was used for all simulations in this work.The source was simulated as a cylindrical isotropic radionuclide source with regions corresponding to the physical geometry of the actual source selected.Decay data for the source was obtained from the ENSDF files located in the EGS_HENHOUSE.The emission spectra provided for these radionuclides was obtained from the Laboratoire National Henri Becquerel (LNHB) (Townson et al 2017).The source medium was simulated as pure water.Due to the need to accurately transport low-energy electrons, electron impact ionizations were turned on, ESTEPE (the maximum fractional energy loss per step) was set to 25%, bremsstrahlung cross sections from the NRC library (Seltzer and Berger 1985, 1986, Tessier and Kawrakow 2008) were used, as well as higher-order Koch-Motz bremsstrahlung angular sampling (Koch and Motz 1959), and photon cross sections from the XCOM library (Berger and Hubble 1987).Values for ECUT and PCUT were both set to 1 keV kinetic energy.Other transportation parameters were left to their default values.The number of histories was selected to reduce the reported statistical uncertainty in the D w per disintegration to less than 1%.
D w for the diode and ion chamber was scored using a 1 mm-radius, 0.1 mm-thick disk centered at the external surface of the source window.Additionally, D w was scored to the active volumes of the detectors in separate simulations.These values, along with simulations of the detector calibrations, were used to determine a correction factor, f , Q rel given by equation (2).
is the ratio of D w to absorbed dose to the detector, Q exp is the experimental radiation quality, and Q cal is the calibration radiation quality.In this sense, the correction is used to determine a relationship between the absorbed dose to water in the disk defined at the window surface and the absorbed dose to the active volume of the detector in the experimental conditions.This ratio is then normalized by the absorbed dose to water at a point in the calibration conditions and the absorbed dose to the detector's active volume.The size of this correction was highly dependent on detector geometry and the magnitude of the beta attenuation from the source surface to the active region of the detector.The largest values for this correction resulted from the 177 Lu experiment and was a factor of approximately 130 for the EFD diode and 2.3 for the A20 ion chamber.For 131 I, the relative increase in dose contribution from photons brought the correction down to a factor of approximately 38 for the EFD and 2.1 for the A20.It should be noted that choosing different points of reference to compare measurements and simulations can significantly change the size of the correction, though this is primarily a correction for the geometry of the measurement and can be accurately assessed with MC simulations.Additionally, while the absorbed dose was calculated to a submillimeter-thick disk at the surface of the source in this work, this was a somewhat arbitrary calculation volume and the measurements could, in theory, be used for comparison to the expected absorbed dose at other locations and volumes.This would be performed through the establishment of an MC determined relationship, as in equation (2), between the absorbed dose to the detector's active volume and the absorbed dose to water in the desired volume.
Similarly, absorbed dose for the TLDs and film were scored to the active volumes in their respective geometries.To obtain D w , the dosimeters were simulated as water, but in determining the absorbed dose response from equation (2), the dosimeters were simulated as their appropriate materials.To improve computational efficiency, simulations were run using both a photon cross section enhancement and a Russian Roulette rejection factor of 32.Using this method, the energy corrected D w could be determined in both simulations and measurements for all detectors and dosimeters.The calculation used to convert the MC D w , D , MC in Gy per disintegration to time averaged D w rate, D , w  between times t i and t f (representing the start and end times of the collection for each individual measurement, respectively), is defined using equation (3). .3


Here, A 0 represents the initial source activity at time t , 0 and l represents the decay constant of the source.Equation (3) is valid in approximating the instantaneous dose rate at any time between t i and t f considering the radionuclide did not decay significantly between these times such that the change in D w  remained relatively small.Additionally, cumulative D w was obtained by integrating the D w rate over a given period.For this work, cumulative D w was calculated after each elapsed time, t k T , 1 2

• D =
/ where k = 0.02 for 177 Lu and 0.08 for 131 I.In addition to D w calculations, the relative contribution to absorbed dose from photons and beta particles to each detector for both radionuclides were determined through MC simulations.This is of interest because a larger absorbed dose contribution from the emitted beta particles is associated with greater sensitivities to positioning, energy changes throughout the active volume of the detector, and volume averaging effects.However, a higher absorbed dose contribution from photons will rely more heavily on MC simulations to infer D w from beta particles, leading to larger correction factors.

Detector and dosimeter measurements Calculation of D w
The measured cumulative D w from TLD responses were determined by dividing the individual TLD responses by their respective CFs and applying the linear fit from the calibration curves.This was then multiplied by the appropriate MC correction factor given by equation (2).Similarly, measured cumulative D w from the net change in film ODs were determined using the calibration curve and multiplying by the appropriate correction factor given by equation (2).Measured D w rates from the ion chamber were calculated using repeated measurements over the course of the experiment and, 250kV is the D w calibration coefficient, and M corr is the background subtracted 120 s integrated charge measurement corrected for the electrometer, collection efficiency, polarity, and air density at the time of the measurement.Measurements were performed with a chamber bias of +300 V for the ion chamber and 0 V for the diode.For the diode, measured D w rate was also determined using equation (4), except no additional corrections, other than f , Q rel to the raw measurements were made.A simplified method of obtaining cumulative D w was used by fitting an exponential function of the form y x be mx ( ) = to the measured D w rate with respect to time.

I
Two experiments were performed for 131 I.The EFD was used in the second experiment, but not the first.In both experiments, the source cavity was filled with 131 I in the form of NaI uniformly dissolved in an aqueous solution.The exposure times for the film and TLDs were chosen to give approximately 2 Gy to the surface piece of film and 50 cGy to the TLD based on MC simulations.For the ion chamber, an overnight measurement was performed.For the diode, a multi-day measurement was started at the end of the second day.
The activity of the source was measured using a Capintec CRC-55tw dose calibrator (Mirion Technologies, Atlanta, GA) with the calibration setting set to 151 per the manufacturer's recommendation (Capintec Inc. 2010).The source activity was determined by first measuring the activity in a standard vial, then removing the radionuclide solution using a syringe and performing an additional activity measurement of the vial.The syringe was then placed in the dose calibrator and measured.The ratio of the difference in the vial readings to the syringe measurement was used to determine a syringe correction factor.The source cavity was then filled with the radioactive solution and sealed such that no visible air bubbles were present.The empty syringe was measured once more with the dose calibrator to obtain the final activity within the source cavity as the product of the difference between the syringe measurements and the vial, and the syringe correction factor.This activity was measured to be 162 MBq and 350 MBq for the first and second experiments, respectively.The differences in activity between the experiments was not deliberate but were due to differences in the amount of time between when the sources were obtained and when the experiments could be performed.Both activities were high enough to provide adequate signal to the detectors.
Polarity and recombination correction factors for the ion chamber were determined by performing four measurements each at the start of the experiment with the bias set to −300 V (to obtain data for the polarity correction) and +150 V (to obtain data for the collection efficiency correction).Each of these measurements were decay corrected back to a single time point before calculation of the final correction factors using Equations (9) and (11) from AAPM TG-51 for polarity and recombination, respectively (Almond et al 1999), though it should be noted that these corrections were less than 0.5% for both radionuclides.

Lu
Activity quantification and ion chamber correction factors were determined for the 177 Lu experiment using the same method as described for the 131 I experiments.In preparation of the source, 240 MBq of 177 Lu was diluted in a 2 mL aqueous solution of 0.05 M HCl (pH ∼ 1.3) to prevent hydrolyzation of metal aqua ions and their subsequent sticking to the plastic walls of the phantom.The total activity in the source cavity after filling was determined to be 159 MBq using a Capintec CRC-25R dose calibrator with a calibration setting of 450 × 10, as recommended by the manufacturer (Capintec Inc. 2010).TLDs were once again exposed to receive approximately 50 cGy but film was irradiated to receive approximately 1 Gy to the surface piece due to the reduced activity of the source.

Uncertainty analysis
An uncertainty analysis was conducted for measurements from each of the detectors and dosimeters in addition to the MC simulations.Some of the estimates for these uncertainties are based on MC simulations of depth dose profiles along the insert tubes for each of the radionuclides investigated.Depending on the detector and radionuclide, these contributions could be relatively large.
Uncertainty was propagated using a root sum of squares approach on all contributing sources of Types A and B uncertainty in accordance with the Guide to the expression of uncertainty in measurement (GUM) (JCGM 100.2008).Equation (5) was used to quantify the uncertainty in the fits used to calculate cumulative D w from the active detectors, and in the determination of the uncertainty in the film's calibration curve.Crosscorrelation between fit parameters was ignored considering the dominant sources of uncertainty were independent.

Results
Results from the MC simulations in the determination of relative beta and photon (not including beta-induced bremsstrahlung radiation) absorbed dose contributions for each detector and radionuclide are summarized in table 1.As predicted, the detectors with the least amount of material between their surface and active volumes received relatively higher contributions to their absorbed dose from beta particles.Uncertainty bars in all figures refer to the estimated uncertainty at the 1σ level.Predicted and measured values are considered to be in agreement with each other when their respective uncertainty ranges overlap.

Uncertainty
Detector specific sources of uncertainty include the calibration setups for each of the detectors, the uncertainties in material compositions or construction of the detectors, any fits used in the calibration curves for the TLDs and film, and various correction factors that were determined for each of the detectors.Specifically, for TLDs, a larger uncertainty was assigned for the 'depth' to account for the deviation in chip thickness.Example uncertainty budgets for each of the detectors are provided in the following tables.Uncertainty on measured values as large as 29% were determined for the film furthest from the probe for the 177 Lu experiment due to the low, measured D w at this location.Total measurement uncertainties at k = 1 for most of the film measurements in both experiments was approximately 10%.Total measurement uncertainties for the TLDs at k = 1 were approximately 8%-9%.Total measurement uncertainties for the EFD and A20-375 at k = 1 were approximately 8% and 6%, respectively.Example uncertainty budgets are presented in tables 2-5.The largest sources of uncertainty for the MC simulations were in the modeling of the experiment and determination of the source activity.An approximated uncertainty in the activity measurement of 5% was used based on a combination of manufacturer recommendations and previous publications using dose calibrators for measurements with 131   Reducing the uncertainties in the measurements is detector specific and highly dependent on positioning.One potential method would be to increase the distance of the detector from the source to a region with a flatter dose gradient, however, this would give lower signal and ratio of beta particle to photon D w contribution.Additionally, choosing detectors with smaller active volumes and energy dependence may help to reduce the uncertainties arising from dose volume averaging and any intrinsic energy response from the detector.Uncertainties in MC predictions may be reduced through high-resolution imaging techniques of the experiment, as well as more accurate methods of measuring source activity, potentially through spectrometry or source specific calibrations of activity measuring devices.

I EBT3 film and TLD100
The surface pieces of EBT3 film from the first experiment showed darkened rings of over exposure on their outer edges.The rings were less evident on the pieces of film from the first day of measurements but were clearly present on the pieces irradiated during the second day.This indicated that the radioactive solution was preferentially absorbed through an area where the cyanoacrylate had not fully covered the epoxy.As a result of this, it was decided to repeat the 131 I measurements.In between the first and second experiments, an additional layer of cyanoacrylate was applied to the epoxy on each insert to seal it from the source solution.
Following the re-sealing, the curing process was observed to cause the source window to be pulled back into the source cavity from the guard ring.An interferometer was used to measure this offset for a sealed cavity filled with water.An offset of approximately 150-250 μm was derived from the measurements between the acrylic guard ring and the center of the Kapton window.This offset creates a small airgap between the window and all the detectors, except for the diode due to its smaller external diameter, as the outside of the detectors or probes contact the guard ring before the window itself.This airgap was corrected for using MC simulations for the most accurate determination of measured D w .For 131 I, the ratio of the absorbed dose to the detector with the 200 μm gap to the absorbed dose to the detector without the gap was found to be smallest for the A20 ion chamber (0.943) and largest for the EBT3 film in the second position from the surface measuring (0.986).While significant, it should be noted that for most detectors, this difference is relatively small, typically less than 5%.Considering the relatively small size of the defect and its impact on the final measurements, a complete redesign of the insert was not deemed necessary.Multiple adhesives and curing techniques were investigated in an attempt to remedy this problem, however none provided better results.Using a thicker window helped mitigate the issue, however it would come at the cost of greater electron attenuation from the source.Because the interferometer measurements require the insert to be destroyed, only inserts not used in the experiments could be tested so minor variations in the size of the gap in the experimental inserts may have been present, leading to a larger uncertainty in the experimental setup and MC modeling.
TLD measurements from both experiments agree with predicted cumulative D w within k = 1 uncertainty, as shown in figures 5(a)-(b).Measurements from the first experiment are greater than predicted values by 0.2%-5% while measurements from the second experiment are below predicted values by approximately 9%-13%.The higher measured D w from the first experiment may be due to the absorption of 131 I in the epoxy layer of the source cavity.
As shown in figures 5(c)-(d), the cumulative D w measurements using EBT3 film from the first experiment are all in agreement with predicted values within k = 1 uncertainty margins.The measured D w values in the second experiment are lower than predicted values at all depths through the film stack by approximately 12%, except for the surface piece of film which was lower than predicted by 2%.

IBA EFD diode and A20-375
The ion chamber measurements agreed with predicted values within k = 1 D w uncertainty levels for both the first and second experiments as shown in figures 6(a)-(d).The D w rate for the measured data begins increasing relative to the predicted data in addition to a small under response at the start of the experiment of 5%.During the second experiment, an offset between the measured and predicted values was observed.This offset is approximately 16% with the measured D w rate being lower than the predicted rate.The measurement results from the second experiment follow the expected decay of 131 I with no observed change in decay rate.EFD measurements from the second 131 I experiment agree with the predicted D w within k = 1 uncertainty values, as shown in figures 6(e)-(f).The measured D w rate followed the predicted decay of the source but was consistently higher than the predicted value by 2%-3%.This contradicts the measured D w rate from the ion chamber being less than the predicted rate by approximately 11%.Despite this discrepancy, both the ion chamber and EFD measurements are within the uncertainty tolerances of the predicted D w rates.
177 Lu For 177 Lu, the ratio of the absorbed dose to the detector with the aforementioned 200 μm gap to the absorbed dose to the detector without the gap was found to be smallest for the A20 ion chamber (0.934) and largest for the EBT3 film in the third position from the surface measuring (0.991).

A20-375 and IBA EFD
The D w rate measured using the ion chamber agreed with predicted values within k = 1 uncertainty values, as shown in figures 7(a)-(b).Once again, the measured rate fell consistently below the predicted values by approximately 7%.Cumulative D w measurements were also in agreement with predicted values for each timepoint investigated.The D w rate measured using the EFD agreed with the predicted D w rate within k = 1 uncertainty values, as shown in figures 7(c)-(d).Similar to the ion chamber measurements, the EFD measurements fell consistently below the predicted D w rate by approximately 11%-14%.Cumulative D w measurements were also in agreement with predicted values.TLD100 and EBT3 film Figure 8(a) shows the cumulative D w measured using TLD100 chips.Measurements agreed with the predicted D w for the six probes investigated.Despite this, measured results fell below predicted values by approximately 7%-13%, similar to the offset observed for both the EFD and ion chamber.The cumulative D w measured by the EBT3 film agrees with predicted values within k = 1 uncertainty bounds, as shown in figure 8(b).Notably, the surface and deepest pieces of film in the stack produced measured D w values that were higher than predicted by 5% and 22%, respectively.The large difference in the deepest piece of film can be explained by the low D w at its location (∼ 4 cGy), which also resulted in a large standard deviation in the pieces of film at this location in each probe.

Discussion
While the uncertainties in the measurements presented here are large (sometimes exceeding 10%) when compared to the well-established dosimetry protocols used in EBRT and brachytherapy where uncertainties in measurements rarely exceed a few percent, they are similar to previous measurements of liquid RPT sources, such as those from Tiwari et al and Van et al which estimated measurement uncertainties to be approximately 9% and 7%, respectively (Tiwari et al 2020, Van et al 2022).While not directly comparable, the uncertainties estimated in these measurements are far less than those estimated in clinical RPT procedures which can be well over 60% (Finocchiaro et al 2020).

I
The EBT3 film results in the second 131 I experiment are consistent with the measured values from the other detectors in this experiment except for the EFD.The measured D w in the first experiment are closer to the predicted values for each piece of film.The decreased D w from the first to second experiment may be due to the observed preferential uptake of 131 I in the epoxy of the source window.The uptake may also explain the abrupt change in measured source decay rate from the ion chamber data.
The cause of the offset and disagreement between measured and predicted D w for the ion chamber may be due to an increased size of the airgap in the source window used in the second experiment.In such a case, it is possible that the uncertainties afforded to modeling the experiment in MC were not large enough for the ion chamber to render an agreement between the measured and predicted D w .Unfortunately, due to contamination and radiation safety concerns, it was impossible to perform a surface interferometer measurement on the window of the insert following the experiment.In any case, the magnitude of the discrepancy is small enough that a relatively small increase in the size of the airgap would provide a feasible explanation for the difference.Alternatively, variations in the thickness of the cyanoacrylate or measurement tolerances for the insert used in this experiment may have also contributed to the discrepancy.Further support of these hypotheses can be found in the measurements from the other detectors.
The results show that the use of the A20-375 ion chamber for performing active dosimetry directly on the beta emissions of solutions of 131 I is feasible.While deviations in the measurements from predicted values, on the order of 15%, may be present, this may be due to errors in the experimental geometry, including gaps between the source and detector, and small deviations in the size of the source cavity compared to the MC simulations.However, accurate modeling of the detector and experimental geometry (possibly through highresolution imaging), as well as tighter tolerances on machining of the source geometry and window might help to reduce these uncertainties.Furthermore, it is necessary to shield any epoxy from liquid sources, as radionuclides can be preferentially absorbed into epoxy, leading to a time-dependent, inhomogeneous distribution of the radioactivity of the source.It should be noted that this was not inferred through imaging, but rather the observation of darkened rings on film pieces in regions where the film should have been better shielded from the source by the epoxy.TLD100 remains a favorable dosimeter choice for beta-emitting radionuclides.The 150 μm-thick chips used in this work aid in reducing absorbed dose volume averaging and energy straggling through the detector, which may increase the effects caused by the intrinsic energy dependence of TLD100 at lower energies.The agreement between the measured and predicted D w obtained in this work confirms that these TLDs may be used for the dosimetry of solutions of 131 I provided adequate assessment of their absorbed dose energy response is performed and accounted for.Uncertainties associated with the geometry of beta experiments would likely be a limiting factor in the accuracy of the measurements.
While the manufacturer recommends the EFD only be used in the energy range between 4 and 20 MeV, calibration of the EFD in an x-ray beam with a spectrum of energies may provide an effective method for measuring D w from 131 I.As shown in table 1, the contribution of absorbed dose from beta-emissions is less than 10% for the EFD when measuring 131 I. Therefore, the diode is less sensitive to geometric differences between the experimental and MC conditions than other detectors.However, this also means that the measured D w is primarily an indirect measurement of the beta D w near the surface of the source and will require larger MC generated corrections to convert this measurement to a surface D w .
177 Lu Despite the D w measurements from the A20 once again being less than predicted values, results were in agreement within uncertainty bounds for the 177 Lu experiment, showing that the A20 may be used for multiple beta-emitting RPT radionuclides in solution.The difference between measured and predicted D w values has approximately the same direction and magnitude as the differences observed in the passive dosimeter measurements.Therefore, it is reasonable to assume that, provided an accurate model for the detector, chamber, experimental geometry, and calibration, the A20 ion chamber may be used to measure D w directly from betaemissions of an RPT radionuclide in solution.The difficulty of obtaining an accurate enough model of the experiment should not be underestimated, given the sensitivity of low-energy beta measurements to the experimental geometry.
The agreement within uncertainty limits between measured and predicted D w values shows promise for the use of the EFD in beta RPT dosimetry.However, like with other diodes, numerous factors like intrinsic energy response, temperature, dose rate, and directional dependence may contribute to the overall response of the detector.For this reason, diodes are not typically calibrated for D w by Accredited Dosimetry Calibration Laboratories (ADCLs) and are used primarily for relative measurements.However, when used in reference to an ion chamber with appropriate MC generated corrections, the EFD could potentially be used for RPT measurements, though the relatively thick build-up filters most of the beta particles and results in primarily detecting signal from photons.The effect would be mitigated if it were possible to alter the diode to remove some of plastic build-up material.This is especially true for radionuclides emitting low-energy beta particles.The use of shielded diodes for RPT may lead to potentially severe effects that can result from directional dependencies and shielding materials in the proximity of the active region of the detector.Additionally, diodes with active regions that are minimally shielded from the incident beta spectrum should be used only if a completely accurate model of the detector can be obtained and modeled in a MC simulation due to the steep D w gradient through the active region of the silicon chip and any material in front of it.
Despite the possible shortcomings of the detector, using the EFD in combination with the A20 ion chamber may allow for the establishment of a radionuclide specific conversion between the two detectors provided the geometry of the experiment and ambient temperature remain the same.In this sense, a site-specific phantom may be used in a controlled environment where an initial measurement with the A20 and EFD may be performed and a ratio between their responses determined for a given radionuclide.Future measurements would only need to rely on a single EFD measurement which would be more convenient considering no additional measurements or corrections would need to be performed or applied to the reading.
The results obtained for the 177 Lu experiment give more evidence to the usefulness of thin TLD100 chips for performing D w measurements of beta-emitting radionuclides.The direction and magnitude of the offset found in the TLD measurements was similar to those observed from the other detectors, indicating that the likely cause of the discrepancy is due to activity quantification, geometry, or both.The agreement between detectors is promising for their use in beta RPT dosimetry.
As previously mentioned, radiochromic film has a long history in the dosimetry of beta-emitting radionuclides.In this work, the small difference in the shapes of the measured and predicted curves may be due to small air gaps between the pieces of film created by ridges formed during the laser cutting process.Overall, unlaminated EBT3 film provides an accurate method of beta dosimetry with its relative water equivalence, energy independence, thin active layer, and absence of an attenuating protective layer.The film has been shown to be an accurate dosimeter of solutions of beta-emitting RPT agents like 177 Lu and 131 I.The major drawback of the film is its relatively low sensitivity, requiring higher D w (greater than approximately 10-25 cGy) for accurate measurements, thus needing either long exposure times, or high source activities.This, combined with the passive readout nature of EBT3 film, makes it a less convenient dosimeter compared to active detectors like ion chambers and diodes.

Future directions
Incorporating measurements with dosimeters and standardized RPT phantoms into the current image-based dosimetry workflow would provide clinicians with an extra layer of redundancy in their absorbed dose determinations.Calibrated dosimeters can be used by clinics as a standardized reference to compare to imagebased absorbed dose estimates when switching to a new imaging system, updating software, or adding a new RPT agent to their program.This is especially important in an era of increasing interest in the use of RPT (Sgouros et al 2020), as well as potential investigations into its use as a curative treatment (Gonias et al 2009, Strosberg et al 2017) where higher doses may be administered and patient safety becomes a greater concern.
Future work may investigate improved phantom designs, specifically in the design of the source cavity to eliminate permeation of the solution into the adhesive barrier.While the effect of radionuclide uptake into the glue barrier is relatively small over the course of a few hours, it can become a significant issue for long-term measurements.A potential remedy to this situation may be to pre-saturate the epoxy with a stable form of the isotope before adding the radionuclide solution.Different sizes of sources may also be of interest to compare the imaging system's absorbed dose estimate to the detectors at large and small source volumes.This may also help identify the spatial limits of the image-based dosimetry system.
Additionally, other dosimeters may be investigated.While passive dosimeters are relatively easy to model in MC, generally have well researched properties, and are typically available without entrance windows, their readouts can be time-consuming, costly, and usually take place at least 24 h after irradiation.Additionally, these dosimeters are only capable of obtaining a time-averaged cumulative dose rather than determining dose rates, which may be useful in troubleshooting discrepancies between the dosimeter and imaging-based system.Overall, the instant readout of active dosimeters is attractive because it allows for real-time troubleshooting of the system, as well as the ability to directly obtain dose-rate measurements.

Conclusions
This work has presented and tested a SPECT/CT compatible dosimetry phantom capable of housing active and passive dosimeters for performing absorbed dose to water measurements of beta-emitting RPT radionuclides in solution.The results from this work show that some active and passive dosimeters may be used for accurate and traceable dosimetry measurements of beta-emitting RPT radionuclides ( 177 Lu and 131 I) in solution.Furthermore, these results agree with MC simulations within k = 1 uncertainty values, with only minor exceptions (figures 6(c)-(d)).Despite more work being required to potentially reduce uncertainties through small redesigns of the phantom inserts, investigation or creation of alternative dosimeters, and high-resolution imaging to resolve any small differences between the physical and simulated experiment geometries, we have presented a feasible option for RPT dosimetry measurements using common therapy detectors.The dosimeters used in this study (EBT3 film, thin TLD-100 chips, the Exradin A20-375 parallel plate ion chamber, and the IBA EFD diode) may successfully be used in the SPECT/CT compatible dosimetry phantom presented in this work, or a similar phantom, for the verification of MC and image-based RPT dosimetry software.Future work may compare absorbed dose measurements from these detectors, calibrated for absorbed dose to water, to calculations from image-based dosimetry software.

Figure 1 .
Figure 1.Photograph of the front face of the phantom.

Figure 2 .
Figure 2. Cross-sectional view of phantom with detector insert (a).Component diagram and cross-sectional view of the detector insert (b).

Figure 3 .
Figure 3. Photograph of TLDs and film dosimeters (a).Photograph of TLD100 thin chip in PMMA probe (b).
EBT3 film EBT3 film (Ashland Global Specialty Chemicals Inc., Wilmington, DE) was chosen for its relative energy independence (>100 keV) (Villarreal-Barajas et al 1999, Brown et al 2012, Massillon-JL et al 2012, Sipilä et al 2016, Hammer et al 2018, Tiwari et al 2020), historical use in beta dosimetry (Tiwari et al 2020, Mulet et al 2022, Van et al 2022), sensitivity, minimal volume averaging effects, and high spatial resolution (which allowed for a partial evaluation of the uniformity of the dose distribution near the source window) (McLaughlin et al 1991).
I and 177 Lu (Capintec Inc. 2010, Zimmerman and Bergeron 2016, Tiwari et al 2020, Staanum et al 2021, Van et al 2022).The type B uncertainty implicit to the EGSnrc code was assumed to be negligible compared to the dominant sources of uncertainty in the experiments.

Figure 5 .
Figure 5. Predicted and measured cumulative D w for the first and second 131 I experiment using TLD100 chips (a) and (b), and EBT3 film (c) and (d).

Figure 6 .
Figure 6.Predicted and measured D w rate and cumulative D w for 131 I experiments using the A20-375 from the first experiment (a) and (b), second experiment (c) and (d), and IBA EFD from the second experiment (e) and (f).

Figure 7 .
Figure 7. Predicted and measured D w rate and cumulative D w for the 177 Lu experiment using the A20-375 (a) and (b), and the EFD (c) and (d).

Figure 8 .
Figure 8. Predicted and measured cumulative D w for the 177 Lu experiment using TLD100 (a) and unlaminated EBT3 film (b).

Table 1 .
Relative beta and photon contributions, determined by MC, to absorbed dose for each detector for 177 Lu and 131 I.

Table 2 .
Example uncertainty budget for TLD100 ( 177 Lu) chips measurements and simulations.

Table 3 .
Example uncertainty budget for the EFD ( 177 Lu) measurements and simulations.

Table 5 .
Example uncertainty budget for EBT3 film ( 177 Lu) measurements and simulations.