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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↗

Site 300 B-851 Permit: Radiological Assumptions and Source Term - Air Dispersion Modeling for Radiological Dose Assessment

The following modeling assumptions and source term that is provided in the attachments to this document are meant to serve as a guide to the presentation delivered on April 23rd, 2020, to the San Joaquin Air District Permit Services slides. This analysis is in response to the District’s “Project Incompleteness Letter” (Facility Number: N-472 and Project Number: N-1173492) regarding the potential for depleted uranium (DU) to be resuspended from areas of contaminated soil at Site 300 as a result of high explosive (HE) experiments increased to a requested permitted maximum of 1,000 pound detonations with an annual HE throughput not to exceed 7,500 pounds per year. LLNL has taken every step in the radiological health risk concerns in the modeling assumptions and final source term to be at a level of maximum conservativeness. As an example, forty soil samples were taken in the B-851 area (LLNL-AR-738708 – 2018) and assayed for uranium-234, uranium-235, and uranium-238 concentrations. The maximum uranium soil concentrations were used in the assumptions (potential for resuspended dust occurring from detonation experiments) and not the use of median uranium soil concentrations – a more realistic outcome. Additionally, these uranium soil concentrations were considered to be at 100% uptake in the vegetation for prescribed burns; vegetation uptake factors were not used as that would lower the final source term. This level of conservativeness was maintained throughout the modeling assumptions.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗

Marshall Islands Dose Assessment and Radioecology Program: Report on the (i) 2018 Visual Study of Exterior Concrete of the Cactus Crater Containment Structure (ii) Periodic Monitoring of Groundwater on Runit Island and (iii) Initial Health Risk Assessment from Contaminants in the Cactus Crater Containment Structure

In 2012, Congress passed P.L. 112-149, Insular Areas Act of 2011, which amended the Compact of Free Association Amendments Act of 2003 by assigning Cactus Crater containment monitoring and reporting requirements to the Secretary of Energy (Secretary). Effective January 1, 2012, the Secretary was required to “periodically (but not less frequently than every 4 years) conduct -- (I) a visual study of the concrete exterior of the Cactus Crater Containment Structure on Runit Island; and (II) a radiochemical analysis of the groundwater surrounding and in the Cactus Crater Containment Structure on Runit Island.” 48 U.S.C. 1921b(f)(1)(B)(i). The Secretary was also directed to submit to Congress a report describing the results of each visual survey and the radiochemical analysis and “a determination on whether the surveys and analyses indicate any significant change in the health risks to the people of Enewetak from the contaminants within the Cactus Crater Containment Structure.” 48 U.S.C. 1921b(f)(1)(B)(ii)(II).

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Assessment of doses in contaminated urban areas: modelling exercise based on Fukushima data

State-of-the-art dose assessment models were applied to estimate doses to the population in urban areas contaminated by the Fukushima Daiichi Nuclear Power Plant accident. Assessment results were compared among five models, and comparisons of model predictions with actual measurements were also made. Assessments were performed using both probabilistic and deterministic approaches. Predicted dose distributions for indoor and outdoor workers from a probabilistic approach were in good agreement with the actual measurements. In addition, when the models were applied to assess the doses to the representative person, based on a concept recommended by the International Commission on Radiological Protection and in the International Atomic Energy Agency Safety Standards, it was evident that doses to the representative person obtained with a deterministic approach were always higher than those obtained with a probabilistic approach using the same model.

dose assessment↗

Revealing low-temperature plasma efficacy through a dose-rate assessment by DNA damage detection combined with machine learning models

Low-temperature plasmas have quickly emerged as alternative and unconventional types of radiation that offer great promise for various clinical modalities. As with other types of radiation, the therapeutic efficacy and safety of low-temperature plasmas are ubiquitous concerns, and assessing their dose rates is crucial in clinical settings. Unfortunately, assessing the dose rates by standard dosimetric techniques has been challenging. To overcome this difficulty, we proposed a dose-rate assessment framework that combined the predictive modeling of plasma-induced damage in DNA by machine learning with existing radiation dose-DNA damage correlations. Our results indicated that low-temperature plasmas have a remarkably high dose rate that can be tuned by various process parameters. This attribute is beneficial for inducing radiobiological effects in a more controllable manner.

59 BASIC BIOLOGICAL SCIENCES↗

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↗

Public Health Response and Medical Management of Internal Contamination in Past Radiological or Nuclear Incidents: A Review

Following a radiological or nuclear emergency, workers, responders and the public may be internally contaminated with radionuclides. Screening, monitoring and assessing any internal contamination and providing necessary medical treatment, especially when a large number of individuals are involved, is challenging. Experience gained and lessons learned from the management of previous incidents would help to identify gaps in knowledge and capabilities on preparedness for and response to radiation emergencies. In this paper, eight largescale and five workplace radiological and nuclear incidents are reviewed cross 14 technical areas, under the broader topics of emergency preparedness, emergency response and recovery processes. The review findings suggest that 1) new strategies, algorithms and technologies are explored for rapid screening of large populations; 2) exposure assessment and dose estimation in emergency response and dose reconstruction in recovery process are supported by complementary sources of information, including ‘citizen science’; 3) surge capacity for monitoring and dose assessment is coordinated through national and international laboratory networks; 4) evidence-based guidelines for medical management and follow-up of internal contamination are urgently needed; 5) mechanisms for international and regional access to medical countermeasures are investigated and implemented; 6) long-term health and medical follow up programs are designed and justified; and 7) capabilities and capacity developed for emergency response are sustained through adequate resource allocation, routine nonemergency use of technical skills in regular exercises, training, and continuous improvement.

61 RADIATION PROTECTION AND DOSIMETRY↗

Validation of Spent Fuel Dose Rate Calculations Using NDA Measurement Campaign Data

The predicted radiation gamma dose rate is a key parameter to determine if a spent nuclear fuel assembly is self-protected from misuse as well as an indicator for worker/inspector safety. Recent studies showed that using state-of-the-art techniques for dose rate calculations, including the one adopted for this study, the numerical calculations of the gamma dose rates are three times lower than those from the most commonly-cited reference values for spent LWR fuel used by domestic and international agencies. With only a few publically available experimental data points worldwide for this type of benchmark study, the gamma flux measurements from the Spent Fuel Non Destructive Assay (NDA) measurement campaign can be used to help validate the physics approach used in calculating gamma dose rates. Specifically, this data would validate the gamma flux calculation from spent fuel, which is a key component of these multi-physics techniques for dose rate assessments; dose rate measurements were not part of the NDA campaign. These data are primarily the passive gamma measurements of the spent nuclear fuel assemblies from the Swedish Nuclear Fuel and Waste Management Company (SKB).

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Risk Informed, Performance-Based, Technology-Inclusive Regulatory Infrastructure: Technology-Inclusive Determination of Mechanistic Source Terms for Offsite Dose-Related Assessments for Advanced Nuclear Reactor Facilities

This report summarizes a risk informed, performance-based and technology-inclusive approach to determine source terms for dose related assessments at advanced nuclear facilities. This approach uses a graded process which allows both the non-mechanistic source terms calculation methods, which adopt conservative approaches and assumptions based on known physical and chemical principles, and more importantly the mechanistic source term calculation methods, which consider design-specific scenarios and use best estimate models with uncertainty quantification for a range of licensing basis events (LBEs), to be used for the design and licensing of advanced nuclear technologies. The source terms developed with this graded approach, and radionuclide inventories elsewhere in the facility that are determined during source term analysis, can be used to address licensing issues to support the application processes of 10 CFR Part 50 for a construction permit and operating license or 10 CFR Part 52 for a Combined Operating License (COL), Standard Design Certification, Early Site Permit, Standard Design Approval or Manufacturing License. They can also be used for other purposes including equipment environmental qualification, control room habitability analyses, and assessments of severe accident risks in environmental impact statements. There are many advanced reactor concepts being developed including high temperature gas-cooled reactor (HGTR), sodium-cooled fast reactor (SFR), lead-cooled fast reactor (LFR), molten salt reactor (MSR), micro-reactor, etc. The graded approach presented in this report for source terms determination is, to the extent possible, generic to any of these reactor designs and to future reactor designs. This report provides information on the review of the regulatory foundation for use of conservative bounding source terms as well as event-specific mechanistic source terms for advanced nuclear reactor designs.

07 ISOTOPE AND RADIATION SOURCES↗

Radioidone Event of March 2023

Internal Dosimetry (RP-SVS) will send each affected employee a dose assessment based on their thyroid measurement results. Affected employees will be kept apprised of their dose assessment with an issued progress report. Included in the progress report is an upper limit on the committed effective dose (total dose incurred before the radioiodine leaves the body). Final dose results are expected to be reported within about two weeks of the initial thyroid measurement. You can contact Deepesh Poudel (505-665-1798), John Klumpp (505-667-0325), or Sara Dumit (505-665-4095) if you have any questions about the status of your dose assessment

63 RADIATION, THERMAL, AND OTHER ENVIRON. POLLUTAN↗

Bioaccumulation Factor for Radium in Rio Grande Biota

The Los Alamos National Laboratory (LANL or Laboratory) Environmental Protection and Compliance Division’s Environmental Stewardship Group (EPC-ES) performs the radiological analysis portion of biota dose assessments using the computer program RESRAD-Biota (DOE 2004, DOE 2020). RESRAD-Biota uses a default bioaccumulation factor, B iv , for radium in aquatic animals. This bioaccumulation factor, also listed in Department of Energy (DOE) Standard, DOE-STD-1153-2019, is the ratio of a radionuclide concentration in fresh weight biota to the environment in which it resides, which for aquatic animals is water. DOE-STD-1153-2019 offers conservative values for these ratios that are specific to the radiological contaminant, the biota, and the environment. The B iv in RESRAD-Biota can be used for general screening (Level 1 screening). If the factor proves to be too conservative, then a site-specific B iv may be used. The biota dose assessment of fish from the northern New Mexico region of the Rio Grande fail the general screen, which indicates that further analysis is necessary. Level 2 analysis is site-specific but still has conservative limitations. Level 3 analysis is a more realistic and representative, sitespecific analysis. The purpose of this paper is to use data specific to the Rio Grande to calculate a new aquatic animal radium B iv . This B iv can then be used for Level 3 analysis of aquatic animals specifically in the northern New Mexico region of the Rio Grande. The calculated radium B iv is a useful value for performing detailed, accurate biota dose assessments and calculating dose to fish using RESRAD-Biota when only sediment data are available.

54 ENVIRONMENTAL SCIENCES↗

Updates to Composite Analysis Base Case and Null Space Monte Carlo Sensitivity Based on New Unit Dose Factors

This environmental calculation file (ECF) presents the results of the exposure route-specific and total radiological dose assessments for the groundwater exposure pathway as a part of the updated Composite Analysis for Low-Level Waste Disposal in the Hanford Site Central Plateau (FY 2022), based on revised unit dose factors (UDFs) published in CA Special Studies: Updates to the Groundwater Pathway Radiological Dose. The reason for these radiological dose assessments is to estimate the cumulative radiological impacts from all screened sources of ionizing radiation and exposure routes that could potentially contribute to the projected dose to a hypothetical member of the public. Sources of ionizing radiation can include existing or future disposal facilities and other sources including past-practice discharge sites. Additionally, the results of the exposure route-specific and total radiological dose assessments have been revised for the groundwater pathway based on the null space Monte Carlo (NSMC) groundwater concentrations and the most recent updates to the UDFs as a part an uncertainty analysis for the updated Hanford Site CA.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗