Investigation of a measurement-based dosimetry approach to beta particle-emitting radiopharmaceutical therapy nuclides across tissue interfaces

Objective. In this work, we present and evaluate a technique for performing interface measurements of beta particle-emitting radiopharmaceutical therapy agents in solution. Approach. Unlaminated EBT3 film was calibrated for absorbed dose to water using a NIST matched x-ray beam. Custom acrylic source phantoms were constructed and placed above interfaces comprised of bone, lung, and water-equivalent materials. The film was placed perpendicular to these interfaces and measurements for absorbed dose to water using solutions of 90Y and 177Lu were performed and compared to Monte Carlo absorbed dose to water estimates simulated with EGSnrc. Surface and depth dose profile measurements were also performed. Main results. Surface absorbed dose to water measurements agreed with predicted results within 3.6% for 177Lu and 2.2% for 90Y. The agreement between predicted and measured absorbed dose to water was better for 90Y than 177Lu for depth dose and interface profiles. In general, agreement within k = 1 uncertainty bounds was observed for both radionuclides and all interfaces. An exception to this was found for the bone-to-water interface for 177Lu due to the increased sensitivity of the measurements to imperfections in the material surfaces. Significance. This work demonstrates the feasibility and limitations of using radiochromic film for performing absorbed dose to water measurements on beta particle-emitting radiopharmaceutical therapy agents across material interfaces.


Introduction
In recent years, radiopharmaceutical therapy (RPT) has become increasingly popular for systemic treatment of various cancers.RPT may employ several mechanisms to 'target' specific tumor sites throughout the body.This approach, in theory, allows for a more conformal and systemic radiation treatment compared to conventional external beam and brachytherapy (Goldsmith 2020).In addition to damage caused by ionizing radiation, synergistic effects created through localized immune-mediated response may increase the efficacy of the treatment (Chen et al 2019).These reasons, in combination with improved imaging techniques, have led to an increased interest in the use of radiopharmaceuticals for therapeutic treatments.
Estimation of absorbed dose from image-based techniques has become common in RPT, but suffers from a large degree of uncertainty stemming from the activity distribution estimate, possible assumed biokinetics, volume delineation of the region of interest, and a lack of validation of current dosimetry estimates with calibrated dosimeters (Pouget et al 2015, Besemer et al 2017, Li et al 2017, James et al 2021).One study by Finocchiaro et al (2020) found that the uncertainty in the absorbed dose estimate increased dramatically with smaller volumes of interest, which is concerning considering the potentially high number of small tumors treated with RPT.Establishing methods for RPT clinics to compare measurements performed using calibrated dosimeters to absorbed dose estimates from imaging-based systems would provide clinicians with a greater level of confidence in their RPT dosimetry.
Increased interest in comparing Monte Carlo (MC)-based dosimetry for RPT agents with absorbed dose to water (D w ) measurements from calibrated dosimeters has led to multiple studies investigating surface measurements and absorbed dose profiles of beta particle-emitting radionuclide solutions through tissue-equivalent materials (Tiwari et al 2020, Van et al 2022).Performing these measurements can be challenging due to the readily attenuated beta emissions from the source and steep dose gradients through tissue-equivalent materials.Therefore, experimental setup and choice of dosimeter remain crucial to accurate dosimetric measurements.

Radiochromic film
There is currently a growing interest in the use of radiochromic film for beta dosimetry.Some early studies investigating beta dosimetry with radiochromic film came from the need to measure absorbed dose to verify MC simulations for radiation synovectomy.A study by Johnson et al (1995) used Gafchromic DM1260 film to measure absorbed dose in a knee phantom from 166 Ho and 165 Dy solutions that were absorbed in filter paper.Film measurements generally agreed with the MC predicted absorbed doses within approximately 15%, however, large uncertainties stemming from the activity quantification of the sources were present (Johnson et al 1995).
A more popular film for radiotherapy applications, due to its useable absorbed dose range, and relative energy (Sipilä et al 2016) and absorbed dose rate independence (Borca et al 2013), is Gafchromic EBT3 (Ashland Global Specialty Chemicals Inc., Wilmington, DE).EBT3 film comes in its standard form of an active layer sandwiched between two polyester protective layers, and an unlaminated version consisting of an exposed active layer, which is half the thickness of the active layer in the standard form of the film, and a single layer of the polyester base (Hansen 2018).The absence of the polyester base on one side provides a means of obtaining surface measurements without attenuation of the incident radiation.This is ideal when performing measurements for low-energy radiation, or heavy charged particles that would otherwise be readily attenuated; however, it comes at the cost of risking more damage to the active layer through exposure to the ambient environment and handling.
One recent study on liquid sources of beta particle-emitting radionuclides was performed by Tiwari et al (2020).In this study, line sources of 90 Y and 177 Lu were contained in micro-capillary tubes that were run through the center of a phantom composed of lung, bone, or water-equivalent material.EBT3 film was used to measure absorbed dose radially outward from the source and compared to MC simulations with mean absorbed dose differences between measurements and simulations of 5.0% and 7.2% for 90 Y and 177 Lu, respectively (Tiwari et al 2020).A similar study by Van et al (2022) validated an in-house dose planning method using absorbed dose measurements from EBT3 film in a custom phantom that could be filled with a source solution of 90 Y or 177 Lu.The sources were composed of either a saline or bone-equivalent solution.Agreement between simulated and measured absorbed doses was observed within 15% (Van et al 2022).
As previous studies show, EBT3 film, with its thin protective and active layers and relative energy independence, has been a popular dosimeter for beta particle-emitting RPT agents.However, the difficulty of performing these measurements in solution has necessitated creative phantom designs.While surface and depth dose measurements may be used for initial validation of MC-based dosimetry, benchmarking predicted D w distributions with these radionuclides across interfaces formed by common tissues such as bone and lung against measurements is important given the wide distribution of RPT treatment sites throughout the body.

EGSnrc Monte Carlo code
The EGSnrc MC code is composed of multiple, application-specific user codes and is a popular and well-researched code for simulations involving the transport of photons, electrons, and positrons (Kawrakow et al 2011).Many MC codes handle particle transport near material interfaces using boundary crossing algorithms (BCAs).The default, and most accurate, BCA available in EGSnrc is EXACT (Kawrakow et al 2011).The EXACT BCA has previously been tested against theoretical and experimental results for a number of applications (Verhaegen 2002, Aarup et al 2009, Kim et al 2012).

Purpose
The development of a method for performing interface measurements for RPT dosimetry may be of interest to RPT clinics.This is especially important for low-energy beta emissions that are characteristic of the radionuclides used in RPT.While material boundaries have been present in previous studies (Tiwari et al 2020, Van et al 2022), the absorbed dose across tissue-equivalent boundaries has yet to be assessed in-part due the difficulty of performing these measurements.
The aim of this work was to perform measurements with liquid sources of 90 Y and 177 Lu using EBT3 radiochromic film to assess the feasibility of the proposed experimental setup that may be used for measurement-based validation of RPT dosimetry estimates.Particularly, the D w distribution across tissue interfaces of lung-to-bone, bone-to-water, and water-to-lung.To investigate this, custom miniature 'check source' phantoms were designed and created out of PMMA acrylic and a Kapton film (DuPont de Nemours Inc., Wilmington, DE).

Features and materials
The phantoms for this work were designed with a few considerations in mind.First, for convenience, the phantoms were designed to be disposable and, therefore, needed to be easy and cost-effective to produce.Second, the phantoms were designed with a window thin enough to negligibly attenuate the beta particles emitted from within the source cavity.Finally, the phantoms were designed to be small (approximate source diameter, height, and volume of 7.5 mm, 3 mm, and 135 µL, respectively) to maximize the source's activity concentration in the vicinity of the interface.
To simplify production, all components of the phantom, except for the polyimide windows, were cut using a BOSS LS1420 laser cutting system (BOSSLASER, Sanford, FL).The bodies of the phantoms are composed of an acrylic ring with etched cross-hairs for source alignment.These rings were sanded on both sides to ensure uniform flatness and thickness of the ring within 10 µm (measured using a micrometer).Compressed air was then used to remove dust and the rings were washed with water.This is important for minimizing any potential air gaps between the window and the film.Any variations in the height of the ring could result in fluctuations in the source volume between phantoms and impact the total contained activity.Once the rings were sanded, they were glued to a sheet of 7.62 µm-thick Kapton using a two-part epoxy, EP21TDC (MasterBond, Hackensack, NJ), to form the source cavity windows.The epoxy was left to cure for at least 48 h before cutting each ring from the Kapton sheet.Following this, a low viscosity super glue was applied to each of the glue barriers to seal the epoxy from the source solution.
The lids of the phantoms are composed of an acrylic disk with two holes that served as fill and vent ports.Rings were etched around the holes in the lids to prevent glue from spilling into the phantom volume during sealing.Disks were also laser cut to serve as caps to the phantoms, which were used to seal the phantoms by gluing them to the lids after filling.The lids were chemically welded to the rings using a solution of ethylene dichloride with dissolved PMMA shavings.The phantoms were then allowed to cure for at least 48 h.After filling, the phantoms were sealed using caps and a rapid curing super glue.Filled and unfilled phantoms are shown in figure 1.

Experimental setup
The experiment was run separately for 90 Y and 177 Lu.Three setups for each type of tissue interface were constructed for a total of nine interface setups for each radionuclide.Each of these setups needed to be shielded from the next using lead blocks.Additionally, three surface D w measurements were performed for each radionuclide with single pieces of film on top of 2-5 cm-thick slabs of Virtual Water TM (VW) (Med-Cal, Inc., Verona, WI) for backscatter, under three separate source phantoms.The surface D w measurements were performed to obtain missing surface D w measurements for the two radionuclides since the interface setups would be unable to provide this.The surface measurements were also used to assess the uniformity of the absorbed dose distribution from the phantom.
To measure the D w distribution across a tissue interface, each setup was composed of four (1.5 cm × 1.5 cm × 2 cm) tissue-equivalent blocks.Half of a piece of film was sandwiched between two blocks of the same material, and this was mirrored on the other half of the film with two blocks of a different material to form a seamless interface running perpendicular to the plane of the film.The water-equivalent material, VW, was used along with the tissue-equivalent materials, medium density lung, (LG3) from CIRS (Sun Nuclear Corporation, Melbourne, FL) and cortical bone-equivalent material (19F2), also from CIRS.Elemental composition and density of the lung and bone-equivalent materials were obtained from Tiwari et al (2020).
Activity measurements were performed with a Capintec CRC-25 R dose calibrator.Per the manufacturer's recommendation for 177 Lu (Capintec Inc 2015) and previous studies for 90 Y (Graves et al 2022), calibration factors were set to 56 × 10 and 450 × 10 for 90 Y and 177 Lu, respectively.The 90 Y solution for the interface measurements was diluted to the desired activity concentration of 2.52 MBq ml −1 using an aqueous solution of HCl with a pH of 2 to prevent the metal ions from clinging to the plastic walls of the phantom (Weltje et al 2004, Park et al 2008).Interface phantoms were then filled and sealed.For 177 Lu, the solution for the interface measurements was prepared by diluting the initial source solution with an aqueous solution of HCl (pH = 2) to the appropriate activity concentration of 19.17 MBq ml −1 .The interface concentrations were estimated from MC simulations to deliver 1 Gy to the sixth row of voxels in the film for 177 Lu after a 24-h exposure, and 3 Gy to the sixth row for 90 Y after a 24-h exposure.
The phantoms for the surface D w measurements were filled with an activity concentration of 0.81 and 1.48 MBq ml −1 for 90 Y and 177 Lu, respectively.The surface experiments were estimated to deliver 2 Gy to the film after approximately 24 h.

Monte Carlo modeling 2.2.1. Absorbed dose to water simulations
The MC simulations were designed to reflect the experimental setup through accurate modeling of the PMMA phantom, film, VW, and tissue-equivalent materials.Elemental fractions by weight for the bone and lung-equivalent materials were obtained from Tiwari et al (2020).The egs_chamber user code was used for all simulations in this work.Due to the need to accurately transport low-energy electrons, electron impact ionizations and Rayleigh scattering were turned on, ESTEPE (the maximum fractional energy loss per step) was set to 25% (the default value), 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 parameters were left to their default values.For radionuclide source modeling, EGSnrc contains a database for radionuclide decay data as ENSDF files located in the EGS_HENHOUSE.The emission spectra for these radionuclides were obtained from the Laboratoire National Henri Becquerel (Townson et al 2017).The source modeled in this work was simulated as a cylindrical isotropic radionuclide source in homogeneous water inside the phantom's source volume.
D w was scored to a grid of voxels within the active region of the film, which itself (in addition to the film's polyester layer) was simulated as water.The exact dimensions of the voxels varied depending on the radionuclide in question as a higher resolution grid was needed for the 177 Lu than for 90 Y. Voxel sizes of  (ti→tf) , to each region between the start time of the measurement, t i , and the end time of the measurement, t f , was calculated using equation (1).
here, D MC is the MC simulated D w per disintegration, A 0 is the activity measured by the dose calibrator at time t 0 , and λ is the decay constant of the radionuclide.A photon cross-section enhancement VRT was used with an enhancement factor of 32.A schematic diagram of the setup is shown in figure 2.

Determination of correction factors
The absorbed dose correction factor was obtained for each voxel by repeating each D w simulation within the film's active region, except the active and protective layers of the film were simulated using their actual material compositions (Tiwari et al 2020).Absorbed dose to the film's active layer was scored using the same voxel method as mentioned in the D w simulations.A script was then used to obtain the absorbed dose ratio at each corresponding voxel location and divide it by the MC simulated D w to absorbed dose to film ratio from the calibration setup using equation ( 2), where D w is the absorbed dose to water, D det is the absorbed dose to the detector material (in this case the active layer of the EBT3 film), Q exp represents the radiation quality in the experimental conditions, and Q cal represents the radiation quality in the calibration conditions.
From this, a voxelized correction factor map could be generated and applied to the measured D w from each piece of film.The corrections increase with depth due to the difference in stopping power and charged particle fluence between water and film.EBT3 film remains largely water-equivalent above 100 keV; however, as the energy of the incident radiation decreases, the film becomes less water-equivalent, and thus larger correction factors are required as the beta particles lose energy as they go through the tissue-equivalent materials.

Film readout and calibration
Readout of EBT3 film was performed using an EPSON Expression 10000XL (EPSON, Suwa, Nagano, Japan) flatbed scanner.The scanner was used in Professional mode with 48-bit color and all corrections turned off.The scan resolution was set to 2400 dpi.The document type was set to Film and the film type was set to Positive Film.A custom mask was created to minimize light penetration around the edges of the film and maintain a consistent position for each film piece on the scanning bed from scan to scan.
Calibrations were performed using the UW-250 M x-ray beam (tube potential of 250 kVp and tube current of 12 mA) in 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 × 7) cm 3 slab.The field size at this location was 10 × 10 cm 2 and with a flatness of approximately 2%, though the irradiated film took up a region of approximately 4 × 4 cm 2 within this field.As the highest energy orthovoltage calibration x-ray beam available for this work with an average photon energy at calibration depth of 135.4 keV, the UW-250 M was the closest available calibration beam energy to the average energy of the emissions from the radionuclides investigated.Exposure times were calculated for the calibrations based on the measured NIST-traceable air kerma rate and an MC calculated air kerma to D w coefficient.The unlaminated film pieces were arranged in vacuum sealed plastic bags in sets of 5 and taped to the center of a 5 cm thick VW stack.Clamps were then used to sandwich the bags between the 5 cm backscatter block and 2 cm of build-up VW.The film was allowed to develop over approximately 72 h between exposure and readout.From this, a 12-point calibration curve was created, spanning doses from 0 to 1000 cGy, using the net change in optical density (OD) evaluated through the red color change.A third order polynomial was fit to the curve to establish the relationship between net ∆OD and absorbed dose to water.

Interface and surface measurements
Measurements were performed by filling and sealing the phantoms with a radionuclide solution and placing them on top of either an interface or surface setup.For the interface measurements, phantoms were centered by aligning cross-hairs that were etched into the rings of the phantoms to the interfaces below.Material blocks were held together using square acrylic rings that fit snuggly around the setup.Each setup was shielded from the next using lead bricks and were divided into separate bays as shown in figure 3. Measurements were performed over approximately 24 h.Unlaminated EBT3 film was cut substrate side up in the center of a RotaTrim Mastercut II (RotaTrim, Bedford, England) sliding paper cutter, which was found to leave a minimal burr (∼5 µm) and a minor amount of fraying along the cutting edge while also maintaining straight cut edges.Unlaminated film was used for all experiments to prevent delamination near the edge of the film and to minimize the size of the burr from the polyester base.An optical microscope was used to analyze the edge of a piece of the cut film to verify the cut's precision.Pre-scans of the film were also performed to account for any variability in the base OD of individual film pieces.
Scanning and analysis of the film was performed at least 72 h after the conclusion of the experiment to allow for consistent development.The post-irradiation OD growth of EBT3 in the dose range up to 6 Gy between 72 and 96 h (the approximate difference in time between the start and end of the experiment for post-irradiation OD growth to occur) is negligible (Liu et al 2023).A mask was arranged to block as much light from being transmitted around the film edges as possible while still allowing for accurate readout along the edge.NIST-traceable reference OD filters were included in each scan and arrangements between pre-irradiation and post-irradiation scans remained the same to minimize inter-scan variability.Because red light is most readily absorbed by the EBT series of film (Soares et al 2009), only the red color channel was used in determination of OD.Scans were analyzed using pixel values from the red color channel to convert to OD and net change in OD was used along with the calibration curve and correction factors to obtain D w .
A custom MATLAB (MathWorks, Natick, MA) script was used to draw ROI grids along the edges of the film to compare to corresponding voxels from the MC simulations.Figure 4(a) shows an ROI grid applied to the edge of a piece of film used in the 90 Y experiment.Accounting for a scanning resolution of 2400 dpi, the dimensions of the ROIs for the 177 Lu experiments were set to correspond to the 50 × 50 µm 2 voxels from the simulations.Preliminary scans of unirradiated film showed evidence of a dark banding effect near the edges of the film.Line profiles of the bands were used to determine the depth at which the bands would no longer be present.This was found to be approximately 150 µm from the edge of the film with a more stable, but slightly darkened area between 100 and 150 µm.An image of one of these bands and a corresponding line profile is shown in figure 4. The bands are likely due to a combination of a scanning artifact from the abrupt change in OD near the edge of the film and damage to the active layer of the film from the cutting process.Because implementing a complete correction for these effects is impossible, and the D w to these voxels were outside of the range of the calibration, data from ROIs at shallow depths (less than approximately 200-500 µm depending on the film cut) were potentially unusable.

Uncertainty analysis
Uncertainty in the measured and predicted D w values 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).Sources of statistical uncertainty included scanner uniformity, OD measurements, and statistical fluctuations in the MC dose estimate, while sources of type B uncertainty included film orientation, film development, film positioning within the experiment, the calibration fit, energy correction, MC geometry, and uncertainty in the measured activity of the source.
Estimates for these uncertainties are provided in table 1. Uncertainties with ranges represent the minimum and maximum values that were individually calculated and applied to individual ROIs.All uncertainties are expressed at the k = 1 level.The uncertainty contribution, σ D fit , from the calibration fit, D fit , was calculated by propagating the associated error, σ x i , for each fit parameter, x i , in equation (3).Cross-correlations between terms were ignored for simplicity and lack of significance.The relative contribution from these uncertainties were then included in the overall uncertainty calculation. (3) In addition to the numeric uncertainties outlined in the example uncertainty budget in table 1, statistical uncertainty from the OD determination and MC simulations in the calculation of the absorbed dose response and D w were applied to each individual ROI.Fit uncertainties in the D w calculation and calibration of the film were also applied to each individual ROI for an accurate determination of the total uncertainty at a local level.Example ranges for the individual uncertainties are included in table 1.

177 Lu
Three D w profile measurements at different depths were compiled for a representative piece of film from each of the different interfaces.Additionally, depth profiles through each material, averaged over a few columns in the D w grid away from the interface (in flattest regions of the lateral profiles), were measured.Uncertainty in both the D w (vertical error) and film location with respect to the tissue interface (horizontal error) are accounted for in the shaded measurement uncertainty regions of the following figures.Surface D w measurements agreed with MC D w estimates with values of 222.0 ± 20.4 cGy and 214.2 ± 15.1 cGy, respectively.No evidence of window bowing was observed, with the OD uniformity in the ROI within 5%.
The results from the lung-to-bone interface are shown in figure 5. Lateral profile distances were made relative to the edge of the MC ROI such that the interfaces occur at a distance of 2 mm from the edge of the film.Measured depth dose profiles within the first few hundred microns from the film edge yielded inaccurate results due to D w values being outside of the calibration range and the edge effect from the cutting and scanning processes.The measured D w in the bone profile could be obtained only at a relatively low signal due to the large linear stopping power compared to the lung and water.Agreement is seen within k = 1 uncertainty values for most of the measured portion of the lung depth dose and some of the bone depth dose.
Interface measurements agree with MC predictions within k = 1 uncertainty for the lung portions of the profiles and along the material boundaries.Fewer points of agreement were found in the bone regions due to the steep dose gradients of the measurement and greater sensitivity to material heights.A spike occurs in the measured D w on the lung side of the 725 µm depth profile.This is believed to be caused by debris or a mark on the film at these points.Large levels of noise exist for all 177 Lu profiles considering the small voxel sizes required to obtain adequate resolution.The results from the lung-to-water interface are shown in figure 6.For the depth dose profiles, better agreement is observed between predicted and measured D w for the lung profile than the water profile due to the increased penetration of the emitted beta particles in the lung-equivalent material.A large discrepancy in dose between measured and predicted values on the water side of the profile was also observed.This may have been due to a small offset in the height of the lung block relative to the water block.Results within the first few hundred microns once again could not be obtained due to the edge effects from the film.Additionally, a peak near the interface is observed in the measurement data where there is a small, conical air gap between the material blocks.This caused the measured shoulder in the dose distribution at the lung interface to take on a different shape than predicted.This same effect is observed again in the bone-to-water interface.For this reason, only one example profile from each of these setups is included.
The results from the bone-to-water interface are shown in figure 7. Depth dose curves for the water-to-bone interface show generally good agreement between measured and predicted D w beyond the initial few hundred microns of the film's edge.Interface measurements showed a relatively large peak occurring at all depths near the interface.This is believed to be due to the slightly rounded corners of the tissue-equivalent blocks that were more significant in the bone-to-water blocks due to the relative density of the materials and lower signal at a given depth compared to the lung-interface measurements.The overall gap created by these corners was measured using a micrometer to be approximately 1 mm wide at the surface and 0.55 mm deep, though this may have varied slightly based on individual blocks in the experiment.An MC simulation was performed to estimate the effect of this air gap on the measurements by simulating a conical gap at the center of the interface with height 0.55 mm and radius 0.5 mm.The results of this simulation are shown in figure 8. Unfortunately, due to the nature of the machining process for the blocks, there was no feasible method for eliminating sub-millimeter defects.

9.
Measured and predicted bone (a) and water (b) depth dose curves for 90 Y. Bone-to-water interface profiles for 90 Y at depths of 1.5 mm (c), 2.3 mm (d), and 3.5 mm (e).

90 Y
The higher energy of the emitted beta particles from 90 Y allowed for deeper penetration through the phantom materials and higher D w away from the edge of the film.This led to more accurate results compared to the 177 Lu measurements.Once again, three depths were investigated for interface profiles as well as depth dose curves through each material for each interface type.Surface D w measurements averaged 272.6 ± 29 cGy and agreed with the MC estimate of 267.3 ± 18.9 cGy.As before, no evidence of window bowing was observed, with OD uniformity in the ROI within 5%.
The results for the bone-to-water interface are shown in figure 9. Lateral profile distances were shown relative to the edge of the MC ROI such that the interfaces occur at a lateral distance of 2.5 mm.Agreement within k = 1 uncertainty was observed between the measured and simulated D w for both the bone and water depth dose curves.A slight under-response was observed in the bone depth dose curve likely due to a small offset in the height of the bone blocks relative to the water blocks, leading to the film edge starting at a slightly deeper depth in the bone material.Overall, the measured and simulated D w agree within k = 1 uncertainty for the profiles at the two shallower depths and most of the points in the deeper profile.
The results for the lung-to-bone interface are shown in figure 10.The measurements for the depth dose curves for the lung and bone-equivalent materials both agree with MC simulated estimates.All measurement profiles for the bone-to-lung interface show agreement within k = 1 uncertainty values of MC simulated predictions.An under-response of approximately 40 cGy in the measured D w was observed in the lung region of the profiles at the start of the interface, primarily at the 2.3 and 3.5 mm depths.While the D w difference seems large, the steep dose gradient transitioning from the region to the bone-equivalent region can create small positioning uncertainties, with respect to the location of the film relative to the interface, resulting in large D w uncertainties.
The results for the lung-to-water interface are shown in figure 11.The depth dose curve for the lung-equivalent material shows a small under-response compared to predicted values near the surface of the phantom.The interface measurements at all depths agree with predicted values for the entirety of their profiles at the k = 1 level.Despite this agreement, there is a small difference in the observed shapes of the curves with the measured curves showing a steeper drop off in dose near the interface.

Uncertainty analysis
The largest uncertainties in the measured data stem from the positional uncertainty of the film within the phantom, pixel value standard deviations within the selected ROIs (which ranged from 2%-10% for 90 Y and 2%-9% for 177 Lu), and the calibration of the film (which could be as large as 6% depending on the ROI's OD).The largest sources of uncertainty in the MC predicted D w estimates were in the activity quantification of the source and modeling of the experimental geometry.To account for the lateral positional uncertainty in the measurements, a horizontal uncertainty was included in the interface measurements equivalent to one ROI in length (50 µm for 177 Lu and 200 µm for 90 Y).

177 Lu
Measurements for 177 Lu in this experimental setup are challenging due to the short range and steep absorbed dose fall-off through material of the emitted beta particles.Small imperfections in the corners or edges of the tissue-equivalent blocks, or slight differences in block height, can create large offsets between measured and predicted D w .Despite this, an effort was made to obtain D w measurements across all tissue interfaces.
Fewer points along the interface curves agree between measured and predicted D w for the lung-to-water interface than the lung-to-bone interface.This is hypothesized to be due to imperfect, rounded corners in the material blocks.This effectively created a conical air gap at the surface of the blocks near the interface leading to an increase in measured D w near the interface.The measured D w was found to be approximately 10 cGy higher than predicted in the water regions of the interface.These results are echoed in the depth dose curve for water and are likely due to a small mismatch between the surface of the film and the surface of the water-equivalent material blocks.
The best agreement between measured and simulated D w values was found in the lung-equivalent material where penetration of the emitted beta particles was highest.Additionally, because of the similarity between air and lung, the effect of an airgap is minimized for measurements involving the lung-equivalent material.Interface measurements with 177 Lu remain difficult due to the low energy, and therefore short range, of the emitted particles.In this experimental setup, analysis of the film needed to be performed as close to the edge as possible, but far enough to avoid damaged regions of the film.To minimize the damage from cutting or scanning artifacts in this region, it was beneficial to use unlaminated film and eliminate any potential delamination effects near the film's cut edges.
Agreement between measured and simulated absorbed dose for the water and lung depth dose measurements were similar to those found in Van et al and Tiwari et al where differences in measured and predicted absorbed dose generally remained below 15% (Tiwari et al 2020, Van et al 2022).However, the average percent difference for the bone depth dose curves was approximately 30%, largely due to the lower D w values in the usable region of the film.The average differences for the water depth dose were approximately 7% for the water-to-bone interface and 40% for the water-to-lung interface.The large discrepancy for the water-to-lung interface is likely due to a small offset in the surfaces between the two phantom materials.The average difference for the lung depth dose curves was approximately 2%-3% for both interfaces, falling well within the uncertainty bounds at k = 1.
The agreement between the measured and simulated D w at the exact interface locations was within k = 1 uncertainty for the lung-to-bone, and water-to-lung interfaces.The large discrepancies between the simulations and measurements at the bone-to-water interfaces highlight the importance of eliminating any defects in the surfaces and corners of the investigated materials.Small air gaps in the form of surface abnormalities on the order of hundreds of microns can contribute to significant spikes in the measured D w due to the steep gradients through denser materials and tissues.

90 Y
For the bone-to-water interface, the increasing offset in the profile measurements with depth is likely due to a small angulation of the film with respect to the interface.The larger voxel sizes and D w led to overall lower noise in the interface measurements compared to the 177 Lu experiments.Reduction in the D w at the edges of the profiles can be observed due to a larger investigated region on the film in the 90 Y measurements relative to the lateral extent of the source volume.
While the measured water-to-lung interface profile curves agree to within k = 1 uncertainty bounds with the predicted D w , the measured shape of the curve in this profile does not match the predicted shape.This could potentially be due to the large lateral gradient of the dose profile in the lung region, or a mismatch in height of the two materials.The measured depth dose profile for the water side of the interface shows better agreement with predicted values and the overall shape of the curve.
In general, measurements in the water and lung-equivalent materials were easier to obtain due to the deeper penetration of the emitted beta-particle radiation relative to the bone-equivalent material.However, for the 90 Y setup, the high dose gradients near the edges of the source made depth profiles more difficult to measure.This is primarily due to the small radius of the source in this experiment relative to the range of the emitted beta particles, which creates the wave-like shape of the interface profiles as the absorbed dose begins to fall off at the lateral extent of the source and the lateral dose distribution never reaches a true plateau.Therefore, assessment of the depth dose profile in this setup was also affected by the uncertainty in the lateral position of the source.Additionally, an under-response in the lung-to-water interface measurements of approximately 12% was observed for all profiles close to the interface on the water side.This may have been due to stress marks on the active layer of the film, or a small offset in the depth of the film on the water side of the interface.
Overall, the D w measurements from the 90 Y experiments agreed with MC D w predictions within the k = 1 uncertainty values.The decrease in lateral D w in the profiles was primarily due to the size of the source relative to the investigated region of interest.While the depth dose curves were not purely representative of true depth dose profiles through homogeneous setups of the different materials, the MC simulations accounted for the averaging effects near the edge of the source for a fairer comparison to the measurements.The uncertainties in measured 90 Y values remained large, like the 177 Lu measurements, due to uncertainty in the location of the film with respect to the measured interface.The average depth dose differences between MC and measured values for bone and water in the bone-to-water interface were 8.5% and 4.3%, respectively; in the bone-to-lung interface, 13.1% and 3.3% for the bone and lung, respectively; and in the lung-to-water interface, 6.1% and 2.5% for the lung and water, respectively.One challenge of performing these measurements is that large dose gradients through different materials create a wide range of absorbed dose levels at varying depths in each material.This narrows the range of depths that may be investigated due to the usable D w limits of the film.Overall, the results show that measurements with high energy beta particle-emitting RPT agents, like 90 Y, across interfaces may be adequately performed using EBT3 film with relatively good agreement to predicted D w values.
In comparing the results from the 177 Lu experiments to the 90 Y experiments, general agreement between measured and MC predicted D w values was observed.The most difficult interface to measure was the lung-to-bone interface for 177 Lu due to increased sensitivity of the measurements to slight imperfections in the surfaces and corners of the phantom materials.As expected from its higher energy emissions and greater penetration, D w measurements of 90 Y were overall in better agreement with predicted values and exhibited less noise than those of 177 Lu.
While EBT3 film has proven relatively energy independent, for institutions using medical linear accelerator beams to calibrate film, future work may focus on the feasibility of using these higher energy beams, especially energy degraded electron beams, for calibration of film to be used in similar experiments involving beta particle-emitting agents.Comparison of measured D w across tissue interfaces in similar experiments with image-based RPT dosimetry systems may be of interest for commissioning or quality assurance purposes in RPT clinics.However, it should be noted that image-based dosimetry comparisons may require micro-CT and SPECT systems to obtain adequate resolution of the proposed experimental setup.Other beta particle-emitting radionuclides, like 153 Sm, and alternative tissue interfaces should also be investigated.

Conclusions
Due to the variety of tissues present in the human body and the systemic nature of RPT, it is necessary to assess the ability of current dosimetry systems to accurately estimate D w at tissue boundaries or in the presence of tissue inhomogeneities.This work has presented and tested a relatively simple and inexpensive method for the validation of MC-based D w estimates of RPT agents in solution across different tissue boundaries using radiochromic film.
While the transport of beta-particle emissions across interfaces has been investigated previously for MC codes like EGS (Kwok et al 1987, Nunes et al 1993), this has primarily been for the investigation of backscatter coefficients near dissimilar boundaries.Those studies specifically obtained relative dosimetry estimates for 32 P (which has higher-energy beta-particle emissions than 177 Lu).Additionally, some of these studies use outdated versions of EGS and BCAs.The results of this work show that it is feasible to obtain film-based measurements of D w for liquid solutions of RPT agents across different tissue interfaces for comparison to MC and may potentially be used for comparison to image-based RPT dosimetry software.
The primary limitation of these experiment is in the machining of the phantom blocks.This is especially true for lower energy beta-particle emitters like 177 Lu where small imperfections in the edges and corners of the blocks can lead to large discrepancies in simulated and measured D w .Furthermore, the edge effect observed along the cut edge of the film prevents accurate dosimetry within the first few hundred microns.This effect may be reduced with different cutting and readout techniques like laser densitometry.For validation of surface D w , source uniformity, and activity concentration, it was useful to perform a separate measurement with a piece of unlaminated film en face with the source window.

Figure 1 .
Figure 1.Photograph of a filled and sealed phantom (left) and unfilled phantom (right) (a).Photograph of the bottom of the filled phantom (b).

Figure 2 .
Figure 2. Schematic diagram of the interface experimental setup: top view (a) and cross-sectional view (b).The location of the cross-section in (b) is represented by the dotted black line in (a).Tissue-equivalent materials are in orange and blue with film in red.The blue and black lines in (b) represent approximate locations of depth and interface profiles, respectively.

Figure 3 .
Figure 3. Photograph of 90 Y experiment interface setups.Pink blocks are lung-equivalent, brown blocks are water-equivalent, and gray blocks are bone-equivalent.The top left three bays were reserved for surface measurements with VW underneath.

Figure 4 .
Figure 4. Image of ROI grid over scanned film irradiated with 90 Y (a).The darkened region of the film towards the left side of the image indicates the surface edge closest to the source.Scanned image of dark banding along edge of film (b).OD line profile corresponding approximately to the red line on the left (c).

Figure 6 .
Figure 6.Measured and predicted lung (a) and water (b) depth dose curves for 177 Lu.Lung-to-water interface profile for 177 Lu at a depth of 725 µm (c).

Figure 7 .
Figure 7. Measured and predicted bone (a) and water (b) depth dose curves for 177 Lu.Bone-to-water interface profile for 177 Lu at a depth of 725 µm (c).

Figure 8 .
Figure 8. Bone-to-water interface profile at a depth of 725 µm with MC simulated conical air gap of radius 0.5 mm and depth 0.55 mm.

Figure 10 .
Figure 10.Measured and predicted lung (a) and bone (b) depth dose curves for 90 Y. Bone-to-lung interface profiles for 90 Y at depths of 1.5 mm (c), 2.3 mm (d), and 3.5 mm (e).

Figure 11 .
Figure 11.Measured and predicted lung (a) and water (b) depth dose curves for 90 Y. Lung-to-water interface profiles for 90 Y at depths of 1.5 mm (c), 2.3 mm (d), and 3.5 mm (e).

Table 1 .
Example uncertainty budget for EBT3 film ( 90 Y) measurements and simulations.Indicates uncertainty applied to the location of the measured absorbed dose point in mm. a