Mathematical complexities in radionuclide metabolic modeling: A review of ordinary differential equation kinetics solvers in biokinetic modeling.

Biokinetic models have been employed in internal dosimetry to model the human body's time-dependent retention and excretion of radionuclides. Consequently, biokinetic models have become instrumental in modeling the body burden from biological processes from internalized radionuclides for prospective and retrospective dose assessment. Solutions to biokinetic equations have been modelled as a system of coupled ordinary differential equations (ODEs) representing the time-dependent distribution of materials deposited within the body. In parallel, several solving mathematical algorithms were developed for solving general kinetic problems, upon which biokinetic solution tools were constructed. This paper provides a comprehensive review of mathematical solving methods adopted by some known internal dose computer codes for modeling the distribution and dosimetry for internal emitters, highlighting the mathematical frameworks, their capabilities, and their limitations. Further discussion details the mathematical underpinnings of biokinetic solutions in a unique approach paralleling advancements in internal dosimetry with capabilities in available mathematical solvers in computational systems. A survey of ODE forms, methods, and solvers, including state-of-the-art solvers specifically in Python programming language, was conducted to highlight modern capabilities for advancing the utilization of modern toolkits in internal dosimetry. This review is the first of its kind, which provides a comprehensive analysis of biokinetic solving methods and base knowledge for understanding the computational demands, schemes, and implementations for biokinetic modeling, which can be leveraged for an expedited radiation dose assessment.

Evaluating county-level lung cancer incidence from environmental radiation exposure, PM2.5, and other exposures with regression and machine learning models.

Characterizing the interplay between exposures shaping the human exposome is vital for uncovering the etiology of complex diseases. For example, cancer risk is modified by a range of multifactorial external environmental exposures. Environmental, socioeconomic, and lifestyle factors all shape lung cancer risk. However, epidemiological studies of radon aimed at identifying populations at high risk for lung cancer often fail to consider multiple exposures simultaneously. For example, moderating factors, such as PM2.5, may affect the transport of radon progeny to lung tissue. This ecological analysis leveraged a population-level dataset from the National Cancer Institute's Surveillance, Epidemiology, and End-Results data (2013-17) to simultaneously investigate the effect of multiple sources of low-dose radiation (gross [Formula: see text] activity and indoor radon) and PM2.5 on lung cancer incidence rates in the USA. County-level factors (environmental, sociodemographic, lifestyle) were controlled for, and Poisson regression and random forest models were used to assess the association between radon exposure and lung and bronchus cancer incidence rates. Tree-based machine learning (ML) method perform better than traditional regression: Poisson regression: 6.29/7.13 (mean absolute percentage error, MAPE), 12.70/12.77 (root mean square error, RMSE); Poisson random forest regression: 1.22/1.16 (MAPE), 8.01/8.15 (RMSE). The effect of PM2.5 increased with the concentration of environmental radon, thereby confirming findings from previous studies that investigated the possible synergistic effect of radon and PM2.5 on health outcomes. In summary, the results demonstrated (1) a need to consider multiple environmental exposures when assessing radon exposure's association with lung cancer risk, thereby highlighting (1) the importance of an exposomics framework and (2) that employing ML models may capture the complex interplay between environmental exposures and health, as in the case of indoor radon exposure and lung cancer incidence.

Comparison of atmospheric radionuclide dispersion models for a risk-informed consequence-driven advanced reactor licensing framework.

Current nuclear facility emergency planning zones (EPZs) are based on outdated distance-based criteria, predating comprehensive dose and risk-informed frameworks. Recent advancements in simulation tools have permitted the development of site-specific, dose, and risk-based consequence-driven assessment frameworks. This study investigated the computation of advanced reactor (AR) EPZs using two atmospheric dispersion models: a straight-line Gaussian plume model (GPM) and a semi-Lagrangian Particle in Cell (PIC). Two case studies were conducted: (1) benchmarking the NRC SOARCA study for the Peach Bottom Nuclear Generating Station and (2) analyzing an advanced INL Heat Pipe Design A microreactor's end-of-cycle inventory. The dose criteria for both cases were 10 mSv at mean weather conditions and 50 mSv at 95th percentile weather conditions at 96 h post-release. Results demonstrated that GPM and PIC estimated similar mean peak dose levels for large boiling water reactors in the farfield case, placing EPZ limits beyond current regulations. For ARs with source terms remaining in the nearfield, PIC modeling without specific nearfield considerations could result in excessively high doses and inaccurate EPZ designations. PIC dispersion demonstrated an order of magnitude higher estimate of nearfield inhalation dose contribution when compared to GPM results. Both models significantly reduced EPZ sizing within the nearfield. Thus, reductions in the AR source term may eliminate the need for a separate EPZ.

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

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 inhaled60Co (Type M) and131I (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 andexpmare 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.

Shielding Analysis of a Preclinical Bremsstrahlung X-ray FLASH Radiotherapy System within a Clinical Radiation Therapy Vault.

ABSTRACT: A preclinical radiotherapy system producing FLASH dose rates with 12 MV bremsstrahlung x rays is being developed at Stanford University and SLAC National Accelerator Laboratory. Because of the high expected workload of 6,800 Gy w -1 at the isocenter, an efficient shielding methodology is needed to protect operators and the public while the preclinical system is operated in a radiation therapy vault designed for 6 MV x rays. In this study, an analysis is performed to assess the shielding of the local treatment head and radiation vault using the Monte Carlo code FLUKA and the empirical methodology given in the National Council on Radiation Protection and Measurements Report 151. Two different treatment head shielding designs were created to compare single-layer and multilayer shielding methodologies using high-Z and low-Z materials. The multilayered shielding methodology produced designs with a 17% reduction in neutron fluence leaking from the treatment head compared to the single layered design of the same size, resulting in a decreased effective dose to operators and the public. The conservative assumptions used in the empirical methods can lead to over-shielding when treatment heads use polyethylene or multilayered shielding. High-Z/Low-Z multilayered shielding optimized via Monte Carlo is shown to be effective in the case of treatment head shielding and provide more effective shielding design for external beam radiotherapy systems that use 12 MV bremsstrahlung photons. Modifications to empirical methods used in the assessment of MV radiotherapy systems may be warranted to capture the effects of polyethylene in treatment head shielding.

Monte Carlo simulation of shielding designs for a cabinet form factor preclinical MV-energy photon FLASH radiotherapy system.

PURPOSE: A preclinical MV-energy photon FLASH radiotherapy system is being designed at Stanford and SLAC National Accelerator Laboratory. Because of the higher energy and dose rate compared to conventional kV-energy photon laboratory-scale irradiators, adequate shielding in a stand-alone cabinet form factor is more challenging to achieve. We present a Monte Carlo simulation of multilayered shielding for a compact self-shielding system without the need for a radiation therapy vault. METHODS: A multilayered shielding approach using multiple alternating layers of high-Z and low-Z materials is applied to the self-shielded cabinet to effectively mitigate the secondary radiation produced and to allow the device to be housed in a Controlled Radiation Area outside of a radiation vault. The multilayered shielding approach takes advantage of the properties of high-Z and low-Z radiation shielding materials such as density, cross-section, atomic number of the shielding elements, and products of radiation interactions within each layer. The Monte Carlo radiation transport code, FLUKA, is used to simulate the total effective dose produced by the operation. RESULTS: The multilayered shielding designs proposed and simulated produced effective dose rates significantly lower than monolayer designs with the same total material thickness at the regulatory boundary; this is accomplished through the manipulation of the locations where secondary radiation is produced and reactions due to material properties such as neutron back reflection in hydrogen. Borated polyethylene at 5 wt% significantly increased the shielding performance as compared to regular polyethylene, with the magnitude of the reduction depending upon the order of the shielding material. CONCLUSIONS: The multilayered shielding provides a path for shielding preclinical FLASH systems that deliver MV-energy bremsstrahlung photons. This approach promises to be more efficient with respect to the shielding material mass and space claim as compared to shielded vaults typically required for clinical radiation therapy with MV photons.

ESTIMATION OF PROTECTION FACTORS FOR SURROGATE VEHICLE MODELS IN ENVIRONMENTAL CONTAMINATION SCENARIOS.

In the event of a nuclear or radiological incident involving the release of radioactive material, it may be critical to estimate doses to individuals who are transported through contaminated areas by vehicles. The radiation protection factor (RPF) for vehicles can be calculated to determine the level of shielding protection by the vehicle from external radiation sources. Prior studies evaluating RPFs demonstrate a lack of realistic vehicle configurations and the results cannot be extended directly to scenarios where a vehicle is surrounded by a contaminated environmental field. In this work, sex-averaged effective dose-rate coefficients were computed employing International Commission on Radiological Protection Publication 103 recommendations for radionuclides of interest and used to calculate the RPF as the ratio of unshielded to shielded dose for various radionuclides of interest in consequence management scenarios. Comparisons to dose reduction factors calculated using environmental measurement data from the 2011 Fukushima Daiichi nuclear incident were conducted to benchmark to experimental field measurements.

177Lu-PSMA Therapy for Metastatic Castration-Resistant Prostate Cancer: A Mini-Review of State-of-the-Art.

BACKGROUND: Prostate specific membrane antigen (PSMA) ligand labeled with Lutetium-177 (177Lu) is a promising therapeutic option for metastatic castration-resistant prostate cancer (mCRPC). Several prospective and retrospective studies as well as clinical trials are completed or underway. This has ultimately led to the approval of this therapy by the US Food and Drug Administration (FDA) on March 23 2022. Our work aims to present a mini-review of the most recent research performed and the potential future directions of 177Lu-PSMA-radioligand therapy (RLT) for mCRPC patients. MAIN BODY: For patients with mCRPCwho have met the eligibility criteria for 177Lu-PSMA RLT, numerous studies and trials are either ongoing or have been completed. The studies included in this review have reported overall biochemical response, defined as a prostate-specific antigen (PSA) decline of at least 50%, in at least 44% of patients with mCRPC. The median ranges of overall survival (OS) and radiographic progression-free survival (rPFS) were reported within 10.7-56 and 3.6-16 months, respectively. With data from several retrospective and prospective studies published, the safety of 177Lu-PSMA RLT in mCRPC has been confirmed and demonstrated by its low toxicity profile. Various studies have published pharmacokinetic/pharmacodynamic models to better understand the absorption, distribution, metabolism, and excretion of the RLT in this patient population. Findings have been published for 177Lu-PSMA RLT alone and in combination with other agents. We summarize their findings in our review. CONCLUSIONS: The efficacy of 177Lu-PSMA RLT for patients with mCRPC has been proven thus far with promising results: PSA response, OS and rPFS when used alone or in combination with other treatment options, relative to the standard treatment options alone. The low toxicity profile noted also proves the safety of 177Lu-PSMA RLT in these patients.

The enduring legacy of Marie Curie: impacts of radium in 21st century radiological and medical sciences.

PURPOSE: This review is focused on radium and radionuclides in its decay chain in honor of Marie Curie, who discovered this element. MATERIALS AND METHODS: We conglomerated current knowledge regarding radium and its history predating our present understanding of this radionuclide. RESULTS: An overview of the properties of radium and its dose assessment is shown followed by discussions about both the negative detrimental and positive therapeutic applications of radium with this history and its evolution reflecting current innovations in medical science. CONCLUSIONS: We hope to remind all those who are interested in the progress of science about the vagaries of the process of scientific discovery. In addition, we raise the interesting question of whether Marie Curie's initial success was in part possible due to her tight alignment with her husband Pierre Curie who pushed the work along.

Clinical Management of End-Stage Renal Disease Patients on Dialysis Receiving Radioactive Iodine Treatment.

PURPOSE: Radioactive iodine (RAI) is used to treat thyroid cancer patients with a clear paradigm for most patients. End-stage renal disease (ESRD) patients pose several challenges when undergoing RAI treatment, primarily due to the lack of renal clearance. We retrospectively report our experience with RAI treatment in a cohort of patients with ESRD and provide a set of recommendations on aspects such as the need for adjusted dose activity, balancing scheduling between RAI therapy and dialysis, and radiation safety precautions. PATIENTS AND METHODS: In this study, we report on 5 patients (6 cases), with ESRD on dialysis, treated with RAI for thyroid cancer. Retention measurements to determine individual biological clearance of RAI from the patient's body before and after dialysis sessions were assessed using external exposure dose rates measured at 1 m. RESULTS: Delayed biological clearance of RAI, after the first hemodialysis session, resulted in a longer RAI effective half-life as a consequence of longer retention periods, consistent with observations reported in scientific literature. To achieve a much closer radiation exposure compared with a nondialysis patient, one would recommend administering ~20%-30% of the dose activity normally administered to a thyroid cancer patient based on their medical history, histopathology, and uptake with the appropriate dialysis schedule. CONCLUSIONS: Special precautions should be taken with the administration of RAI in ESRD patients by adjusting the prescribed dose activity, dialysis sessions, and paying special attention to wastes. Pooling data from multiple centers may be useful to build a consensus and substantiated recommendations.

Dose Coefficient Calculation for Use in Dosimetry Assessment of a Fission-Based Weapon.

In the event of a fission-based weapon or improvised nuclear device (IND) detonation, dose coefficients can be harnessed to provide dose assessments for defense, emergency preparedness, and consequence management, as well as to prospectively inform the assessment of radiation biomarkers and development of medical prophylaxis countermeasures for defense and homeland security stakeholders and decision-makers. Although dose coefficients have previously been calculated for this group, they would apply specifically to the studied population, the 1945 Japanese cohort, after which their anthropomorphic computational phantoms were modeled. For this reason, applications to other populations may be limited, and instead, an assessment of a more standardized population is desired. We employed a series of computational human phantoms representing international reference individuals: UF/NCI voxel phantom series containing newborn, 1-, 5-, 10-, 15-, and 35-year-old males and females. Irradiation of the phantoms was simulated using the Monte Carlo N-Particle transport code to determine organ dose coefficients under four idealized irradiation geometries at three distances from the detonation hypocenter at Hiroshima and Nagasaki using DS02 free-in-air prompt neutron and photon fluence spectra. Through these simulations, age-specific dose coefficients were determined for individual organs. Various articulated PIMAL stylized phantoms were simulated as well to estimate the effect of body posture on dose coefficients and determine the effect of posture on dosimetric estimation and reconstruction. Results additionally demonstrate that 137Cs and the Watt fission spectra are not ideal general surrogate sources for fission weapons, which may be considered for experimental testing of medical countermeasures. Supplementary data provided tabulates the compilation of organ dose-rate coefficients in this study.

Comparison of Neutron Organ and Effective Dose Coefficients for PIMAL Stylized Phantoms in Bent Postures in Cranial and Caudal Irradiation Geometries.

ABSTRACT: Radiation dose estimations in the human body are performed using computational reference phantoms, which are anatomical representations of the human body. In previous studies, dose reconstructions have been performed focusing primarily on phantoms in an upright posture, which limits the accuracy of the dose estimations for postures observed in realistic work settings. In this work, the International Commission on Radiological Protection (ICRP) Publication 103 recommendations for monoenergetic neutron plane sources directed downward from above the head (cranial) and upward from below the feet (caudal) for adult female and male reference phantoms were used to calculate organ absorbed and effective dose coefficients. The Phantom with Moving Arms and Legs (PIMAL) and the Monte Carlo N-Particle (MCNP) radiation transport code were used to compute organ-absorbed dose and effective dose coefficients for the upright, half-bent (45°), and full-bent (90°) phantom postures. The doses calculated for each of the articulated positions were compared to those calculated for the upright posture by computing the ratios of the coefficients (45°/upright and 90°/upright). These ratios were used to assess the effectiveness of upright phantoms in providing a comparable estimate when conducting dose estimations and dose reconstructions for articulated positions. This work compiling neutron cranial and caudal posture-specific dose coefficients completes the series of dose coefficients computed for posture-specific ICRP Publication 116 irradiation geometries for monoenergetic photons and neutrons, in addition to cranial and caudal monoenergetic photons. Results reported demonstrated that organ-absorbed dose coefficients for most of the organs in the CRA and CAU irradiation geometries were significantly higher for the bent phantoms than for the upright phantom. Since the upright phantom underestimates the organ-absorbed dose, this demonstrates the impact of posture while performing dose calculations. Organ doses reported in past neutron dose coefficient data were found to omit effects from neutron resonances at energies of 0.435, 1.0, and 3.21 MeV from 16O in tissue. Reported data notes as high as 60% underestimation for neutron organ-absorbed doses, specifically at the neutron resonance energy region omitted by smoothing. Ongoing studies are examining the effect of resonances on reported neutron organ-absorbed dose coefficients in ICRP 116 geometries.

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 ([Formula: see text]) and organ cross-dose ([Formula: see text]). 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.

Stylized versus voxel phantoms: a juxtaposition of organ depth distributions.

For external irradiation, the variability in organ dose estimation found between computational phantom generations arises particularly from the differences in organ positioning. This work represents the first effort to quantify the differences in organ depth below the body surface between a stylized and voxel phantom series. Herein, the revised Oak Ridge National Laboratory stylized phantom series and the University of Florida/National Cancer Institute voxel phantom series were compared. Both series include whole-body models of the newborn; the 1-, 5-, 10-, and 15-year-old; and the adult human. Organ depths from eight different directions applicable to external irradiation geometries were computed: antero-posterior, postero-anterior, left and right lateral, rotational, isotropic, cranial and caudal directions. Organ depths in the stylized phantoms were computed using a ray-tracing technique available through Monte Carlo radiation transport simulations in MCNP6. Organ depths in the voxel phantom were found using phantom matrix manipulation. Resultant organ depths for both series were plotted as distributions; available are twenty-four organs and two bone tissue distributions for each of six phantom ages and in each of the eight directional geometries. Quantitative data descriptors (e.g. mean and median depths) were also tabulated. For demonstration purposes, a literature review of relevant stylized versus voxel comparison works was performed to explore where the quantification of organ depth differences can provide further insight or evidence to study conclusions. The entire dataset of organ depth distributions and their data descriptors can be found in online supplementary files.