Photon Specific Absorbed Fractions Research Articles

Monte Carlo calculation of photon specific absorbed fractions in digimouse voxelized phantom using InterDosi code

Development of new radiopharmaceuticals is carried out on a small animal such as a mouse. With the aim to well-assess internal absorbed dose reaching various organs of a mouse, physical quantities defined by MIRD methodology known as specific absorbed fractions (SAFs) were evaluated using a voxelized mouse phantom. In our study, in order to provide more accurate photon SAFs, we used recent chemical compositions and densities of human organs taken from ICRP publication number 110. A new computational Geant4-based code called InterDosi has been developed to calculate SAFs for source-target organ pairs in Digimouse phantom irradiated by discrete monoenergetic photons of energies ranging from 0.015 to 4 MeV. Results show that, photon self-irradiation SAFs decrease with increasing energy or mass. For a cross-irradiation case, the photon SAFs were found to depend on distance source-to-target and organs close to the source have the most important photon SAFs. A comparison between our results and those reported in an earlier study with similar values of voxel sizes, masses, densities and chemical compositions, generally shows a significant agreement between them. Therefore, for a given configuration (energy, source), a smooth variation was found in the case of a self-irradiation. Contrariwise, medium discrepancy (less than 24%) was found in the case of a cross-irradiation, which can be attributed to the strong impact of the implementation of physics of the simulation in the two different codes and also the large statistical uncertainties associated to the calculation of SAFs in distant organs.

Specific absorbed fractions for a revised series of the UF/NCI pediatric reference phantoms: internal electron sources

In both the International Commission on Radiological Protection (ICRP) and Medical Internal Radiation Dose (MIRD) schemata of internal dosimetry, the S-value is defined as the absorbed dose to a target organ per nuclear decay of the radionuclide in a source organ. Its computation requires data on the energies and yields of all radiation emissions from radionuclide decay, the mass of the target organ, and the value of the absorbed fraction—the fraction of particle energy emitted in the source organ that is deposited in the target organ. The specific absorbed fraction (SAF) is given as the ratio of the absorbed fraction and the target mass. Historically, in the early development of both schemata, computational simplifications were made to the absorbed fraction in considering both organ self-dose () and organ cross-dose (). In particular, the value of the absorbed fraction was set to unity for all ‘non-penetrating’ particle emissions (electrons and alpha particles) such that they contributed only to organ self-dose. As radiation transport codes for charged particles became more widely available, it became increasingly possible to abandon this distinction and to explicitly consider the transport of internally emitted electrons in a manner analogous to that for photons. In this present study, we report on an extensive series of electron SAFs computed in a revised series of the UF/NCI pediatric phantoms. A total of 28 electron energies—0–10 MeV—along a logarithmic energy grid are provided in electronic annexes, where 0 keV is associated with limiting values of the SAF. Electron SAFs were computed independently for collisional energy losses (SAFCEL) and radiation energy losses (SAFREL) to the target organ. A methodology was employed in which values of SAFREL were compiled by first assembling organ-specific and electron energy-specific bremsstrahlung x-ray spectra, and then using these x-ray spectra to re-weight a previously established monoenergetic database of photon SAFs for all phantoms and source–target combinations. Age-dependent trends in the electron SAF were demonstrated for the majority of the source–target organ pairs, and were consistent to values given for the ICRP adult phantoms. In selected cases, however, anticipated age-dependent trends were not seen, and were attributed to anatomical differences in relative organ positioning at specific phantom ages. Both the electron SAFs of this study, and the photon SAFs from our companion study, are presently being used by ICRP Committee 2 in its upcoming pediatric extension to ICRP Publication 133.

Specific absorbed fractions for a revised series of the UF/NCI pediatric reference phantoms: internal photon sources

Assessment of radiation absorbed dose to internal organs of the body from the intake of radionuclides, or in the medical setting through the injection of radiopharmaceuticals, is generally performed based upon reference biokinetic models or patient imaging data, respectively. Biokinetic models estimate the time course of activity localized to source organs. The time-integration of these organ activity profiles are then scaled by the radionuclide S-value, which defines the absorbed dose to a target tissue per nuclear transformation in various source tissues. S-values are computed using established nuclear decay information (particle energies and yields), and a parameter termed the specific absorbed fraction (SAF). The SAF is the ratio of the absorbed fraction—fraction of particle energy emitted in the source tissue that is deposited in the target tissue—and the target organ mass. While values of the SAF may be computed using patient-specific or individual-specific anatomic models, they have been more widely available through the use of computational reference phantoms. In this study, we report on an extensive series of photon SAFs computed in a revised series of the University of Florida and the National Cancer Institute pediatric reference phantoms which have been modified to conform to the specifications embodied in the ICRP reference adult phantoms of Publication 110 (e.g. organs modeled, organ ID numbers, blood contribution to elemental compositions). Following phantom anatomical revisions, photon radiation transport simulations were performed using MCNPX v2.7 in each of the ten phantoms of the series—male and female newborn, 1 year old, 5 year old, 10 year old, and 15 year old—for 60 different tissues serving as source and/or target regions. A total of 25 photon energies were considered from 10 keV to 10 MeV along a logarithm energy grid. Detailed analyses were conducted of the relative statistical errors in the Monte Carlo target tissue energy deposition tallies at low photon energies and over all energies for source–target combinations at large intra-organ separation distances. Based on these analyses, various data smoothing algorithms were employed, including multi-point weighted data smoothing, and log–log interpolation at low energies (1 keV and 5 keV) using limiting SAF values based upon target organ mass to bound the interpolation interval. The final dataset is provided in a series of ten electronic supplemental files in MS Excel format. The results of this study were further used as the basis for assessing the radiative component of internal electron source SAFs as described in our companion paper (Schwarz et al 2021) for this same pediatric phantom series.

S VALUES FOR NEUROIMAGING PROCEDURES ON KOREAN PEDIATRIC AND ADULT HEAD COMPUTATIONAL PHANTOMS.

Over the past decades, the application of single-photon emission computed tomography and positron emission tomography in neuroimaging has markedly increased. In the current study, we used a series of Korean computational head phantoms with detailed cranial structures for 6-, 9-, 12-, 15-y-old children and adult and a Monte Carlo transport code, MCNPX, to calculate age-dependent specific absorbed fraction (SAF) for mono-energetic electrons ranging from 0.01 to 4 MeV and S values for seven radionuclides widely used in nuclear medicine neuroimaging for the combination of ten source and target regions. Compared to the adult phantom, the 6-y phantom showed up to 1.7-fold greater SAF (cerebellum < cerebellum) and up to 1.4-fold greater S values (vitreous body < lens) for 123I. The electron SAF data, combined with our previous photon SAF data, will facilitate absorbed dose calculations for various cranial structures in patients undergoing neuroimaging procedures.

Development and Validation of RAPID: A Patient-Specific Monte Carlo Three-Dimensional Internal Dosimetry Platform.

This work describes the development and validation of a patient-specific Monte Carlo internal dosimetry platform called RAPID (Radiopharmaceutical Assessment Platform for Internal Dosimetry). RAPID utilizes serial PET/CT or SPECT/CT images to calculate voxelized three-dimensional (3D) internal dose distributions with the Monte Carlo code Geant4. RAPID's dosimetry calculations were benchmarked against previously published S-values and specific absorbed fractions (SAFs) calculated for monoenergetic photon and electron sources within the Zubal phantom and for S-values calculated for a variety of radionuclides within spherical tumor phantoms with sizes ranging from 1 to 1000 g. The majority of the S-values and SAFs calculated in the Zubal Phantom were within 5% of the previously published values with the exception of a few 10 keV photon SAFs that agreed within 10%, and one value within 16%. The S-values calculated in the spherical tumor phantoms agreed within 2% for 177Lu, 131I, 125I, 18F, and 64Cu, within 3.5% for 211At and 213Bi, within 6.5% for 153Sm, 111In, 89Zr, and 223Ra, and within 9% for 90Y, 68Ga, and 124I. In conclusion, RAPID is capable of calculating accurate internal dosimetry at the voxel-level for a wide variety of radionuclides and could be a useful tool for calculating patient-specific 3D dose distributions.

KOREAN PEDIATRIC AND ADULT HEAD COMPUTATIONAL PHANTOMS AND APPLICATION TO PHOTON SPECIFIC ABSORBED FRACTIONS CALCULATIONS.

In recent decades, applications of single photon emission computed tomography and positron emission tomography in clinical neuroimaging have markedly increased. In this study, we developed a series of Korean computational head phantoms with detailed cranial substructures for 6-, 9-, 12- and 15-year-old children and adult by non-uniformly adjusting a template head phantom to match the Korean standard head dimensions. The Korean head phantoms were coupled with a Monte Carlo transport code to calculate age-dependent specific absorbed fraction (SAF) for the combination of 10 source and target regions and mono-energetic photons ranging from 0.01 to 4 MeV. Compared to the adult phantom, the 6-y phantom showed up to 1.4-fold greater self-absorption SAF (cerebellum) and up to 1.8-fold greater cross-irradiation SAF (cerebellum < eye balls). With addition of electron SAFs in the future, our photon SAF data will facilitate dose calculations for various cranial substructures in patients undergoing cranial neuroimaging procedures.

Two Realistic Beagle Models for Dose Assessment.

Previously, the authors developed a series of eight realistic digital mouse and rat whole body phantoms based on NURBS technology to facilitate internal and external dose calculations in various species of rodents. In this paper, two body phantoms of adult beagles are described based on voxel images converted to NURBS models. Specific absorbed fractions for activity in 24 organs are presented in these models. CT images were acquired of an adult male and female beagle. The images were segmented, and the organs and structures were modeled using NURBS surfaces and polygon meshes. Each model was voxelized at a resolution of 0.75 × 0.75 × 2 mm. The voxel versions were implemented in GEANT4 radiation transport codes to calculate specific absorbed fractions (SAFs) using internal photon and electron sources. Photon and electron SAFs were then calculated for relevant organs in both models. The SAFs for photons and electrons were compatible with results observed by others. Absorbed fractions for electrons for organ self-irradiation were significantly less than 1.0 at energies above 0.5 MeV, as expected for many of these small-sized organs, and measurable cross irradiation was observed for many organ pairs for high-energy electrons (as would be emitted by nuclides like 32P, 90Y, or 188Re). The SAFs were used with standardized decay data to develop dose factors (DFs) for radiation dose calculations using the RADAR Method. These two new realistic models of male and female beagle dogs will be useful in radiation dosimetry calculations for external or internal simulated sources.

SU‐E‐T‐345: Validation of a Patient‐Specific Monte Carlo Targeted Radionuclide Therapy Dosimetry Platform

Purpose:There is a compelling need for personalized dosimetry in targeted radionuclide therapy given that conventional dose calculation methods fail to accurately predict dose response relationships. To address this need, we have developed a Geant4‐based Monte Carlo patient‐specific 3D dosimetry platform for TRT. This platform calculates patient‐specific dose distributions based on serial CT/PET or CT/SPECT images acquired after injection of the TRT agent. In this work, S‐values and specific absorbed fractions (SAFs) were calculated using this platform and benchmarked against reference values.Methods:S‐values for 1, 10, 100, and 1000g spherical tumors with uniform activity distributions of I‐124, I‐125, I‐131, F‐18, and Ra‐223 were calculated and compared to OLINDA/EXM reference values. SAFs for monoenergetic photons of 0.01, 0.1, and 1 MeV and S factors for monoenergetic electrons of 0.935 MeV were calculated for the liver, kidneys, lungs, pancreas, spleen, and adrenals in the Zubal Phantom and compared with previously published values. Sufficient particles were simulated to keep the voxel statistical uncertainty below 5%.Results:The calculated spherical S‐values agreed within a few percent of reference data from OLINDA/EXM for each radionuclide and sphere size. The comparison of photon SAFs and electron S‐values with previously published values showed good agreement with the previously published values. The S‐values and SAFs of the source organs agreed within 1%.Conclusion:Our platform has been benchmarked against reference values for a variety of radionuclides and over a wide range of energies and tumor sizes. Therefore, this platform could be used to provide accurate patientspecific dosimetry for use in radiopharmaceutical clinical trials.

Monte Carlo Simulations of Photon Specific Absorbed Fractions in a Mouse Voxel Phantom

For preclinical assessments of several radiopharmaceuticals, photon specific absorbed fractions (SAFs) were evaluated using the voxel-based mouse phantom. The sources were assumed to be mono-energetic in the photon energy range from 10 keV to 4 MeV. The radiation transport was simulated using the Monte Carlo method. Consequently, it was confirmed that the photon SAFs for organ self-absorption are dependent on the masses of the source/target organs. It would appear that the photons SAFs for organ self-irradiation are expressed by a continuous function of photon energy emitted by the source. The photon SAFs for organ cross-irradiation might be subject to the geometry effect such as size and shape of source/target and distance between the source and target.

A comparison between GATE4 results and MCNP4B published data for internal radiation dosimetry

GATE, has been designed as upper layer of the GEANT4 toolkit for nuclear medicine application including internal dosimetry. However, its results have not been fully compared to the well-developed codes and anthropomorphic voxel phantoms have never been used with GATE/GEANT for internal dosimetry. The aim of present study was to compare the internal dose calculated by GATE/GEANT with the MCNP4B published data. The Zubal phantom was used to model a typical adult male. Activity was assumed uniformly distributed in liver, kidneys, lungs, spleen, pancreas and adrenals. GATE/GEANT Monte Carlo package was used for estimation of doses in the phantom. Simulations were performed for photon energy of 0.01-1 MeV and mono-energetic electrons of 935 keV. Specific absorbed fractions for photons and S-factors for electrons were calculated. On average, GATE/GEANT produces higher photon SAF (Specific Absorbed Fraction) values (+2.7%) for self-absorption and lower values (-2.9%) for cross-absorption. The difference was higher for paired organs particularly lungs. Moreover the photon SAF values for lungs as source organ at the energy of 200 and 500 keV was considerably higher with MCNP4B compared to GATE. Despite of differences between the GATE4 and MCNP4B, the results can be considered ensuring. This may be considered as validation of GATE/GEANT as a proprietary code in nuclear medicine for radionuclide dosimetry applications.

IMPACT ON 141Ce, 144Ce, 95Zr, AND 90Sr BETA EMITTER DOSE COEFFICIENTS OF PHOTON AND ELECTRON SAFS CALCULATED WITH ICRP/ICRU REFERENCE ADULT VOXEL COMPUTATIONAL PHANTOMS

The current dose coefficients for internal dose assessment of occupationally exposed persons and the general public were derived using the methodology of the International Commission on Radiological Protection (ICRP), which is similar to the Medical Internal Radiation Dose (MIRD)-type methodology. One component of this methodology is the mathematical representation of the human body (so-called MIRD-type phantoms) developed at the Oak Ridge National Laboratory for calculations of photon specific absorbed fractions (SAFs). Concerning the beta emissions, it is assumed in general that they irradiate only the organ where the radionuclide resides, whereas for walled organs, a fixed fraction of the emitted energy is absorbed within the wall. For the active marrow and bone surface targets, absorbed fractions were explicitly provided in ICRP Publication 30. The ICRP Publications 66 and 100 contain further detailed energy-dependent absorbed fraction data for the airways and the segments of the alimentary tract. In the present work, the voxel phantoms representing the reference male and female adults, recently developed at the Helmholtz Zentrum München-German Research Center for Environmental Health (HMGU) in collaboration with the Task Group DOCAL of ICRP Committee 2, were used for the Monte Carlo computation of photon as well as electron SAFs. These voxel phantoms, being constructed from computed tomography (CT) scans of individuals, are more realistic in shape and location of organs in the body than the mathematical phantoms; therefore, they provide photon SAFs that are more precise than those stemming from mathematical phantoms. In addition, electron SAFs for solid and walled organs as well as tissues in the alimentary tract, the respiratory tract, and the skeleton were calculated with Monte Carlo methods using these phantoms to complement the data of ICRP Publications 66 and 100 that are confined to self-irradiation. The SAFs derived for photons and electrons are then used to calculate the dose coefficients of the beta emitters 141Ce, 144Ce, 95Zr, and 90Sr. It is found that the differences of the dose coefficients due to the revised SAFs are much larger for injection and ingestion than for inhalation. The equivalent doses for colon and ingestion with the new voxel-based SAFs are significantly smaller than the values with the MIRD-type photon SAFs and simplifying assumptions for electrons. For lungs and inhalation, no significant difference was observed for the equivalent doses, whereas for injection and ingestion, an increase of the new values is observed.

Application of the ICRP/ICRU reference computational phantoms to internal dosimetry: calculation of specific absorbed fractions of energy for photons and electrons

The emission of radiation from a contaminated body region is connected with the dose received by radiosensitive tissue through the specific absorbed fractions (SAFs) of emitted energy, which is therefore an essential quantity for internal dose assessment. A set of SAFs were calculated using the new adult reference computational phantoms, released by the International Commission on Radiological Protection (ICRP) together with the International Commission on Radiation Units and Measurements (ICRU). Part of these results has been recently published in ICRP Publication 110 (2009 Adult reference computational phantoms (Oxford: Elsevier)). In this paper, we mainly discuss the results and also present them in numeric form. The emission of monoenergetic photons and electrons with energies ranging from 10 keV to 10 MeV was simulated for three source organs: lungs, thyroid and liver. SAFs were calculated for four target regions in the body: lungs, colon wall, breasts and stomach wall. For quality assurance purposes, the simulations were performed simultaneously at the Helmholtz Zentrum München (HMGU, Germany) and at the Institute for Radiological Protection and Nuclear Safety (IRSN, France), using the Monte Carlo transport codes EGSnrc and MCNPX, respectively. The comparison of results shows overall agreement for photons and high-energy electrons with differences lower than 8%. Nevertheless, significant differences were found for electrons at lower energy for distant source/target organ pairs. Finally, the results for photons were compared to the SAF values derived using mathematical phantoms. Significant variations that can amount to 200% were found. The main reason for these differences is the change of geometry in the more realistic voxel body models. For electrons, no SAFs have been computed with the mathematical phantoms; instead, approximate formulae have been used by both the Medical Internal Radiation Dose committee (MIRD) and the ICRP due to the limitations imposed by the computing power available at this time. These approximations are mainly based on the assumption that electrons are absorbed locally in the source organ itself. When electron SAFs are calculated explicitly, discrepancies with this simplifying assumption are notable, especially at high energies and for neighboring organs where the differences can reach the same order of magnitude as for photon SAFs.

Changes in Radiation Dose with Variations in Human Anatomy: Moderately and Severely Obese Adults

The phantoms used in standardized dose assessment are based on a median (i.e., 50th percentile) individual of a large population, for example, adult males or females or children of a particular age. Here we describe phantoms that model instead the influence of obesity on specific absorbed fractions (SAFs) and dose factors in adults. The literature was reviewed to evaluate how individual organ sizes change with variations in body weight in mildly and severely obese adult men and women. On the basis of the literature evaluation, changes were made to our deformable reference adult male and female total-body models. Monte Carlo simulations of radiation transport were performed. SAFs for photons were generated for mildly and severely obese adults, and comparisons were made to the reference (50th) percentile SAF values. SAFs studied between the obese phantoms and the 50th percentile reference phantoms were not significantly different from the reference 50th percentile individual, with the exception of intestines irradiating some abdominal organs, because of an increase in separation between folds caused by an increase in mesenteric adipose deposits. Some low-energy values for certain organ pairs were different, possibly due only to the statistical variability of the data at these low energies. The effect of obesity on dose calculations for internal emitters is minor and may be neglected in the routine use of standardized dose estimates.

Skeletal dosimetry in a voxel‐based rat phantom for internal exposures to photons and electrons

The skeleton makes a significant contribution to the whole body absorbed dose evaluation of rats, since the bone marrow and bone surface in the skeleton express high radiosensitivity and are considered to be important dose-limiting tissues. The bone marrow can be categorized as red bone marrow (RBM) and yellow bone marrow (YBM). It is important to investigate the bone marrow in skeletal dosimetry. Cryosectional color images of the skeleton of a 156 g rat were segmented into mineral bone (including cortical bone and trabecular bone), RBM, and YBM. These three tissue types were identified at 40 different bone sites and integrated into a previously developed voxel-based rat computational phantom. Photon and electron skeletal absorbed fractions were then calculated using the MCNPX Monte Carlo code. Absorbed fraction (AF) and specific absorbed fraction (SAF) for mineral bone, RBM, and YBM at the 40 different bone sites were established for monoenergetic photon and electron sources placed in 18 organs and seven bone sites. Discrete photon energy was varied from 0.01 to 5.0 MeV in 21 discrete steps, while 21 discrete electron energies were studied, from 0.1 to 10.0 MeV. The trends and values found were consistent with the results of other researchers [M. G. Stabin, T. E. Peterson, G. E. Holburn, and M. A. Emmons, "Voxel-based mouse and rat models for internal dose calculations," J. Nucl. Med. 47, 655-659 (2006)]. S-factors for the radionuclides 169Er, 143Pr, 89Sr, 32P, and 90Y, located in 18 organs and seven bone sites for the skeleton, were calculated and are provided in detail. For internal dose calculations, the AF data reveal that the mineral bone in the rat skeletal system is responsible for significant attenuation of gamma rays, especially at low energies. The photon SAF curves of RBM show that, for photon energies greater than 0.6 MeV, there is an increase in secondary photons emitted from the mineral bone as photon energy increases. The SAF values calculated in this study can also be used to determine the absorbed dose to the skeletal system of rats. The S-factors generated here will be useful in preclinical targeted radiotherapy experiments.

Changes in radiation dose with variations in human anatomy: larger and smaller normal-stature adults.

A systematic evaluation has been performed to study how specific absorbed fractions (SAFs) vary with changes in adult body size, for persons of different size but normal body stature. A review of the literature was performed to evaluate how individual organ sizes vary with changes in total body weight of normal-stature individuals. On the basis of this literature review, changes were made to our easily deformable reference adult male and female total-body models. Monte Carlo simulations of radiation transport were performed; SAFs for photons were generated for 10th, 25th, 75th, and 90th percentile adults; and comparisons were made to the reference (50th) percentile SAF values. Differences in SAFs for organs irradiating themselves were between 0.5% and 1.0%/kg difference in body weight, from 15% to 30% overall, for organs within the trunk. Differences in SAFs for organs outside the trunk were not greater than the uncertainties in the data and will not be important enough to change calculated doses. For organs irradiating other organs within the trunk, differences were significant, between 0.3% and 1.1%/kg, or about 8%-33% overall. The differences are interesting and can be used to estimate how different patients' dosimetry might vary from values reported in standard dose tables.

SEECAL utilizing voxel-based SAFs

The computer program SEECAL, written by Cristy and Eckerman from the Oak Ridge National Laboratory, USA, calculates specific effective energies (also known as S factors in the MIRD terminology) for an adult male, an adult female and five paediatric ages. Its dosimetric methodology is that of the ICRP. Among other parameters, SEECAL requires input data on specific absorbed fractions (SAF) and utilises those derived from the MIRD-type stylised anthropomorphic phantoms. SEECAL has been used worldwide for dose estimations concerning occupational or public exposures due to radionuclides incorporated into the body and has formed the basis for programs developed by other laboratories to calculate, for example, dose to the patients undergoing nuclear medicine procedures. The revised version of SEECAL is at the moment limited to adults and utilises the photon SAFs derived with Monte Carlo methods for the new reference male and female voxel-based phantoms to be adopted by the ICRP.

SU‐FF‐I‐77: Photon and Electron Specific Absorbed Fractions From the UF Pediatric Tomographic Phantoms

Purpose: To calculate photon and electron specific absorbed fractions (SAF) by utilizing series of realistic tomographic phantoms of pediatric patients. Method and Material: The series of UF tomographic phantoms, 9‐month male, 4‐year female, 8‐year female, 11‐year male, and 14‐year male, developed at University of Florida, were imported into the EGSnrc Monte Carlo code for this study. Monoenergetic photons and electrons were simulated as homogeneously distributed in various source organs. All possible source‐target organ pairs were considered to calculate absorbed fractions at the target organs from both internal electron and photon emitters localized in source organs. Results: The new sets of photon and electron SAFs were tabulated for the particle energies from 0.01 MeV to 4 MeV. The photon SAFs were compared with those from the ORNL phantoms. It was shown that ORNL phantoms failed to correctly represent the proximities of certain organ pairs and caused significant discrepancies from the UF phantom in terms of photon SAF values. The electron self‐absorbed fractions calculated from the UF phantoms were compared to that given in the ICRP Publication 30 assumptions. For higher electron energies, the assumption of 100% self‐absorption in the ICRP schema was shown to be incorrect, especially for the smaller phantoms and smaller organs with large surface‐to‐volume ratios. For example, the thyroid self absorption was only 21% for 4 MeV electrons in the UF 9‐month phantom. Conclusion: Photon and electron SAFs were calculated for various ages of pediatric patients by utilizing realistic tomographic computational phantoms. It was shown that the tomographic phantoms accurately represent the shapes of various internal organs and their proximities to surrounding organs. The explicit consideration of electron transport demonstrates that the traditional assumption of full energy deposition by energetic beta‐particles can be in error, especially for the younger and smaller patients of this age series.