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At least 19 records

Mathematical solutions in internal dose assessment: A comparison of Python-based differential equation solvers in biokinetic modeling

Abstract In biokinetic modeling systems employed for radiation protection, biological retention and excretion have been modeled as a series of discretized compartments representing the organs and tissues of the human body. Fractional retention and excretion in these organ and tissue systems have been mathematically governed by a series of coupled first-order ordinary differential equations (ODEs). The coupled ODE systems comprising the biokinetic models are usually stiff due to the severe difference between rapid and slow transfers between compartments. In this study, the capabilities of solving a complex coupled system of ODEs for biokinetic modeling were evaluated by comparing different Python programming language solvers and solving methods with the motivation of establishing a framework that enables multi-level analysis. The stability of the solvers was analyzed to select the best performers for solving the biokinetic problems. A Python-based linear algebraic method was also explored to examine how the numerical methods deviated from an analytical or semi-analytical method. Results demonstrated that customized implicit methods resulted in an enhanced stable solution for the inhaled 60 Co (Type M) and 131 I (Type F) exposure scenarios for the inhalation pathway of the International Commission on Radiological Protection (ICRP) Publication 130 Human Respiratory Tract Model (HRTM). The customized implementation of the Python-based implicit solvers resulted in approximately consistent solutions with the Python-based matrix exponential method ( expm ). The differences generally observed between the implicit solvers and expm are attributable to numerical precision and the order of numerical approximation of the numerical solvers. This study provides the first analysis of a list of Python ODE solvers and methods by comparing their usage for solving biokinetic models using the ICRP Publication 130 HRTM and provides a framework for the selection of the most appropriate ODE solvers and methods in Python language to implement for modeling the distribution of internal radioactivity.

61 RADIATION PROTECTION AND DOSIMETRY↗

Biokinetic models for group IVB elements

The International Commission on Radiological Protection (ICRP) is updating its biokinetic models in a series of reports titled Occupational Intakes of Radionuclides (OIR series). This paper provides an overview of biokinetic data for the group IVB elements hafnium (Hf) and titanium (Ti), compares these data with findings for the more extensively studied Group IVB element zirconium (Zr), and proposes biokinetic models for systemic Hf and Ti for use in the OIR series. A biokinetic model for systemic Zr recently adopted by the ICRP is proposed for application to Hf in view of the nearly identical chemical and physical properties of these two elements, their closely similar behavior in the environment, and their nearly identical biokinetic properties suggested by available comparative data. Finaly, the model structure applied to Zr and Hf is also applied to Ti, but a separate set of transfer coefficients is proposed for Ti.

61 RADIATION PROTECTION AND DOSIMETRY↗

Analysis of biokinetic parameters reveals patterns in mercury accumulation across aquatic species

Mercury (Hg) is a potent neurotoxicant and poses a risk to human health through the ingestion of Hg-contaminated fish. Mercury, especially in its organic form methylmercury (MeHg), biomagnifies up food chains such that even small aqueous concentrations of Hg can result in significant concentrations of total Hg in fish. Understanding the ecological and human health risks associated with Hg and MeHg exposure requires an understanding of the factors that affect its bioaccumulation in aquatic species. We compiled estimates of three biokinetic parameters: uptake rate (k u ), assimilation efficiency (AE), and efflux rate (k e ). These parameters describe contaminant uptake from aqueous (k u ) and dietary (AE) exposure and the rate of excretion (k e ). We found parameter values for 38 and 34 different species of fish and aquatic invertebrates, respectively, and collected 502 parameter values in total. Here, we used a machine learning technique to establish the relationships between experimental and physiological variables and these parameter values. We found differences in which variables were associated with biokinetic parameter values for fish and aquatic invertebrates. The form of Hg was the most impactful variable, influencing values of all parameters except k u for invertebrates, for which aqueous exposure time was the only significant predicator variable. The parameter k e were the only values significantly influenced by more than one variable, with water type (freshwater, brackish, or marine), organism weight, and form of Hg significantly impacting parameter values for fish and/or invertebrates. To our knowledge, this study represents the most extensive review of biokinetic parameters of Hg and MeHg accumulation in aquatic organisms. Environmental parameters found to significantly impact Hg and MeHg bioaccumulation in past studies were not identified as important in our analyses across aquatic ecosystems and species. Our dataset and analysis reveal novel patterns that may help us better understand and manage Hg bioaccumulation.

54 ENVIRONMENTAL SCIENCES↗

Basis for the ICRP’s updated biokinetic model for systemic astatine

The International Commission on Radiological Protection (ICRP) recently updated its biokinetic models for workers in a series of reports called the OIR (occupational intakes of radionuclides) series. A new biokinetic model for astatine (At), the heaviest member of the halogen family, was adopted in OIR Part 5 (ICRP in press). Occupational intakes of radionuclides: Part 5). Furthermore, this paper provides an overview of available biokinetic data for At; describes the basis for the ICRP's updated model for At; and tabulates dose coefficients for intravenous injection of each of the two longest lived and most important At isotopes, 211 At and 210 At. At-211 (T 1/2 = 7.214 h) is a promising radionuclide for use in targeted α-particle therapy due to several favourable properties including its half-life and the absence of progeny that could deliver significant radiation doses outside the region of α-particle therapy. At-210 (T 1/2 = 8.1 h) is an impurity generated in the production of 211 At in a cyclotron and represents a potential radiation hazard via its long-lived progeny 210 Po (T 1/2 = 138 days). Tissue dose coefficients for injected 210 At and 211 At based on the updated model are shown to differ considerably from values based on the ICRP's previous model for At, particularly for the thyroid, stomach wall, salivary glands, lungs, spleen, and kidneys.

61 RADIATION PROTECTION AND DOSIMETRY↗

IDAC-Bio, A Software for Internal Dosimetry Based on the New ICRP Biokinetic Models and Specific Absorbed Fractions

Radiation dosimetry is central to virtually all radiation safety applications, optimization, and research. It relates to various individuals and population groups and to miscellaneous exposure situations—including planned, existing, and emergency situations. The International Commission on Radiological Protection (ICRP) has developed a new computational framework for internal dose estimations. Important components are more detailed and improved anatomical models and more realistic biokinetic models than before. The ICRP is currently producing new organ dose and effective dose coefficients for occupational intakes of radionuclides (OIR) and environmental intakes of radionuclides (EIR), which supersede the earlier dose coefficients in Publication 68 and the Publication 72 series, respectively. However, the ICRP only publishes dose coefficients for a single acute intake of a radionuclide and for an integration period of 50 years for intake by adults and to age 70 years for intakes by pre-adults. The new software, IDAC-Bio, performs committed absorbed dose and effective dose calculations for a selectable intake scenario, e.g., for a continuous intake or an intake during x hours per day and y days per week, and for any selected integration time. The software uses the primary data and models of the ICRP biokinetic models and numerically solves the biokinetic model and calculates the absorbed doses to organs and tissues in the ICRP reference human phantoms. The software calculates absorbed dose using the nuclear decay data in ICRP publication 107. IDAC-Bio is a further development and an important addition to the internal dosimetry program IDAC-Dose2.1. Here, the results generated by the software were validated against published ICRP dose coefficients. The potential of the software is illustrated by dose calculations for a nuclear power plant worker who had been exposed to varying levels of 60 Co and who had undergone repeated whole-body measurements, and for a hypothetical member of the public subject to future releases of 148 Gd from neutron spallation in tungsten at the European Spallation Source.

61 RADIATION PROTECTION AND DOSIMETRY↗

An age- and sex-specific biokinetic model for radon *

Publication 137 of the International Commission on Radiological Protection (ICRP) describes a biokinetic model for radon used to derive dose coefficients for occupational intake of radon isotopes. The model depicts transfer of inhaled or ingested radon to blood, exchange of radon between blood and tissues, and gradual loss of radon from the body based on physical laws governing transfer of a non-reactive and soluble gas between materials. Here, this paper describes an age- and sex-specific variation of that model developed for use in an upcoming ICRP series of reports on environmental intake of radionuclides by members of the public titled ‘Dose Coefficients for Intakes of Radionuclides by Members of the Public’. The proposed model modifies the model structure and transfer coefficients presented in Publication 137 to allow more realistic dosimetric treatment of bone marrow and breast and expands the model to address pre-adult ages, based on the physical principles used in the development of the model of Publication 137 together with anatomical and physiological changes occurring during human development.

61 RADIATION PROTECTION AND DOSIMETRY↗

Biokinetic and Dosimetric Models [Slides]

Presentation describes internal dosimetry as an intersection of disciplines involving Physiology, Anatomy, Physics, Mathematics and Computer Science, which some people call "The art of Internal Dosimetry". The basic components for internal dose calculations are: Biokinetic (metabolic) models describing the intake, distribution, retention and excretion of radionuclides in the body, Dosimetric models describing the interaction of radiation within the several body organs and tissues, and System of dose limitation.

61 RADIATION PROTECTION AND DOSIMETRY↗

A biokinetic model for systemic sodium

This paper describes an updated biokinetic model for systemic sodium (Na), developed for use in a series of reports by the International Commission on Radiological Protection (ICRP) on occupational intake of radionuclides. In contrast to the ICRP's previous model for intake of radio-sodium by workers, the updated model depicts realistic directions of movement of Na in the body including recycling of activity between blood and tissues. The updated model structure facilitates extension of the baseline transfer coefficients for adults to different age groups and to special exposure scenarios such as transfer of radio-sodium from the mother to the foetus or the nursing infant. Dose coefficients for 22Na and 24Na based on the updated model generally do not differ greatly from those based on the ICRP's previous Na model when both models are connected to the ICRP's latest dosimetry system. The main exception is that the updated model yields roughly twofold higher dose coefficients for endosteal bone surface than does the previous model due to the dosimetrically cautious assumption in the updated model that exchangeable Na in bone resides on bone surface.

61 RADIATION PROTECTION AND DOSIMETRY↗

Accounting for erroneous model structures in biokinetic process models

In engineering practice, model-based design requires not only a good process-based model, but also a good description of stochastic disturbances and measurement errors to learn credible parameter values from observations. However, typical methods use Gaussian error models, which often cannot describe the complex temporal patterns of residuals. Consequently, this results in overconfidence in the identified parameters and, in turn, optimistic reactor designs. Here, we assess the strengths and weaknesses of a method to statistically describe these patterns with autocorrelated error models. This method produces increased widths of the credible prediction intervals following the inclusion of the bias term, in turn leading to more conservative design choices. However, we also show that the augmented error model is not a universal tool, as its application cannot guarantee the desired reliability of the resulting wastewater reactor design.

42 ENGINEERING↗

Methods of improving brain dose estimates for internally deposited radionuclides *

The US National Council on Radiation Protection and Measurements (NCRP) convened Scientific Committee 6–12 (SC 6–12) to examine methods for improving dose estimates for brain tissue for internally deposited radionuclides, with emphasis on alpha emitters. This Memorandum summarises the main findings of SC 6–12 described in the recently published NCRP Commentary No. 31, ‘Development of Kinetic and Anatomical Models for Brain Dosimetry for Internally Deposited Radionuclides’. The Commentary examines the extent to which dose estimates for the brain could be improved through increased realism in the biokinetic and dosimetric models currently used in radiation protection and epidemiology. A limitation of most of the current element-specific systemic biokinetic models is the absence of brain as an explicitly identified source region with its unique rate(s) of exchange of the element with blood. The brain is usually included in a large source region called Other that contains all tissues not considered major repositories for the element. In effect, all tissues in Other are assigned a common set of exchange rates with blood. A limitation of current dosimetric models for internal emitters is that activity in the brain is treated as a well-mixed pool, although more sophisticated models allowing consideration of different activity concentrations in different regions of the brain have been proposed. Here case studies for 18 internal emitters indicate that brain dose estimates using current dosimetric models may change substantially (by a factor of 5 or more), or may change only modestly, by addition of a sub-model of the brain in the biokinetic model, with transfer rates based on results of published biokinetic studies and autopsy data for the element of interest. As a starting place for improving brain dose estimates, development of biokinetic models with explicit sub-models of the brain (when sufficient biokinetic data are available) is underway for radionuclides frequently encountered in radiation epidemiology. A longer-term goal is development of coordinated biokinetic and dosimetric models that address the distribution of major radioelements among radiosensitive brain tissues.

61 RADIATION PROTECTION AND DOSIMETRY↗

Statistical Uncertainty of Inhalation Dose Coefficients in Consequence Management: Propagated Dose Uncertainty in ICRP 66 Human Respiratory Tract Model

Reference inhalation dose models rely on deterministic biokinetics and reference computational phantoms, limiting their applicability to the variability present in population-specific exposures encountered in emergency response scenarios. Here, this study introduces REDCAL, a Python-based computational framework developed to propagate uncertainty in inhalation dose coefficients using the International Commission on Radiological Protection (ICRP) Publication 66 Human Respiratory Tract Model. REDCAL integrates ICRP deposition and clearance models, systemic biokinetics, and governing physics principles, and leverages Sandia National Laboratories’ Dakota toolkit for uncertainty quantification via Latin Hypercube Sampling. REDCAL was validated against DCAL, with biokinetic retention results differing by less than 1% and effective dose coefficients by less than 2% across all tested radionuclides. Stochastic sampling introduced variability in dose coefficients, with geometric standard deviations (GSD) in committed effective dose coefficients (CEDC) ranging from 1.0 to 1.5, based on lognormal distribution fits. Analysis demonstrated that variations in the activity median aerodynamic diameter (AMAD) notably influenced the computed CEDC values. Smaller particles (<1 µm) increased doses by 20–30% due to deeper lung deposition and prolonged retention for alpha emitting radionuclides, such as 241 Am and 239 Pu. Radionuclides with fast clearance, such as 133 I, demonstrated a dose reduction exceeding 50%, as AMAD increased beyond 5 µm due to upper airway deposition and rapid mucociliary clearance. The greatest GSD among the radionuclides reported in this study was for 241 Am. In most cases, the largest GSDs in the CEDC were associated with larger particle sizes, an expected outcome, as ICRP Publication 66 defines GSD in particle size as a function of AMAD, resulting in an extended tail of the lognormal distribution. The findings support improved inhalation dose assessments and enhance consequence management strategies for the U.S. Federal Radiological Monitoring and Assessment Center by quantifying uncertainty in dose coefficients and strengthening decision-making for emergency response scenarios.

Biokinetic Modeling↗

Modeling Plutonium Decorporation in a Female Nuclear Worker Treated with Ca-DTPA after Inhalation Intake

The present work models plutonium (Pu) biokinetics in a female former nuclear worker. Her bioassay measurements are available at the US Transuranium and Uranium Registries. The worker was internally exposed to a plutonium-americium mixture via acute inhalation at a nuclear weapons facility. She was medically treated with injections of 1 g Ca-DTPA on days 0, 5, and 14 after the intake. Between days 0 and 20, fecal and urine samples were collected and analyzed for 239 Pu and 241 Am. Subsequently, she was followed up for bioassay monitoring over 14 y, with additional post-treatment urine samples collected and analyzed for 239 Pu. The uniqueness of this dataset is due to the availability of: (1) both early and long-term bioassay data from a female with plutonium intake; (2) data on chelation therapy for a female; and (3) fecal measurement results. Chelation therapy with Ca- and/or Zn-salts of DTPA is known to aid in reducing the internal radiation dose by enhancing the excretion of plutonium and americium from the body. Such enhancement affects plutonium biokinetics in the human body, posing a challenge to the internal dose assessment. The current radiation dose assessment practice is to exclude the data affected by Ca-DTPA from the analysis. The present analysis is the first to explicitly model the chelation-affected bioassay data in a female by using a newly developed chelation model. Thus, the bioassay data collected during and after the Ca-DTPA administrations were used for biokinetic modeling and dose assessment. The Markov Chain Monte Carlo method was used to investigate model parameter uncertainty, based on the bioassay data and assumed prior probability distributions. A χ 2 /nData (number of data points) ≈ 1 was observed in this study, which indicates self-consistency of the data with the model. Results of this study show that the worker’s 239 Pu intake was 12 Bq, with a committed effective dose to the whole-body of 1.2 mSv and a committed equivalent dose to the bone surfaces, liver, and lungs of 37.8, 9.1, and 0.8 mSv, respectively. This study also discusses the worker’s dose reduction due to chelation treatment.

61 RADIATION PROTECTION AND DOSIMETRY↗

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. Finally, 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.

61 RADIATION PROTECTION AND DOSIMETRY↗

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

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Chelation Modeling: The Use of Ad Hoc Models and Approaches to Overcome a Dose Assessment Challenge

Here, chelating agents are administered to treat significant intakes of radioactive elements such as plutonium, americium, and curium. These drugs may be used as a medical countermeasure after radiological accidents and terrorist acts. The administration of a chelating agent, such as Ca-DTPA or Zn-DTPA, affects the actinide's normal biokinetics. It enhances the actinide's rate of excretion, posing a dose assessment challenge. Thus, the standard biokinetic models cannot be directly applied to the chelation-affected bioassay data in order to assess the radiation dose. The present study reviews the scientific literature, from the early 1970s until the present, on the different studies that focused on developing new chelation models and/or modeling of bioassay data affected by chelation treatment. Although scientific progress has been achieved, there is currently no consensus chelation model available, even after almost 50 y of research. This review acknowledges the efforts made by different research groups, highlighting the different methodology used in some of these studies. Finally, this study puts into perspective where we were, where we are, and where we are heading in regards to chelation modeling.

61 RADIATION PROTECTION AND DOSIMETRY↗

Development of a New Chelation Model: Bioassay Data Interpretation and Dose Assessment after Plutonium Intake via Wound and Treatment with DTPA

The administration of chelation therapy to treat significant intakes of actinides, such as plutonium, affects the actinide’s normal biokinetics. In particular, it enhances the actinide’s rate of excretion, such that the standard biokinetic models cannot be applied directly to the chelation-affected bioassay data in order to estimate the intake and assess the radiation dose. Here we propose a new chelation model that can be applied to the chelation-affected bioassay data after plutonium intake via wound and treatment with DTPA. In the proposed model, chelation is assumed to occur in the blood, liver, and parts of the skeleton. Ten datasets, consisting of measurements of 14 C-DTPA, 238 Pu, and 239 Pu involving humans given radiolabeled DTPA and humans occupationally exposed to plutonium via wound and treated with chelation therapy, were used for model development. The combined dataset consisted of daily and cumulative excretion (urine and feces), wound counts, measurements of excised tissue, blood, and post-mortem tissue analyses of liver and skeleton. The combined data were simultaneously fit using the chelation model linked with a plutonium systemic model, which was linked to an ad hoc wound model. The proposed chelation model was used for dose assessment of the wound cases used in this study.

60 APPLIED LIFE SCIENCES↗