Mathematical complexities in radionuclide metabolic modelling: a review of ordinary differential equation kinetics solvers in biokinetic modelling

Biokinetic models have been employed in internal dosimetry (ID) to model the human body's time-dependent retention and excretion of radionuclides. Consequently, biokinetic models have become instrumental in modelling 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 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 modelling the distribution and dosimetry for internal emitters, highlighting the mathematical frameworks, capabilities, and limitations. Further discussion details the mathematical underpinnings of biokinetic solutions in a unique approach paralleling advancements in ID. The capabilities of available mathematical solvers in computational systems were also emphasized. A survey of ODE forms, methods, and solvers was conducted to highlight capabilities for advancing the utilization of modern toolkits in ID. This review is the first of its kind in framing the development of biokinetic solving methods as the juxtaposition of mathematical solving schemes and computational capabilities, highlighting the evolution in biokinetic solving for radiation dose assessment.

Chelation Modeling of a Plutonium-238 Inhalation Incident Treated with Delayed DTPA

This work describes an analysis, using a previously established chelation model, of the bioassay data collected from a worker who received delayed chelation therapy following a plutonium-238 inhalation. The details of the case have already been described in two publications. The individual was treated with Ca-DTPA via multiple intravenous injections and then nebulizations beginning several months after the intake and continuing for four years. The exact date and circumstances of the intake are unknown. However, interviews with the worker suggested that the intake occurred via inhalation of a soluble plutonium compound. The worker provided daily urine and fecal bioassay samples throughout the chelation treatment protocol, including samples collected before, during, and after the administration of Ca-DTPA. Unlike the previous two publications presenting this case, the current analysis explicitly models the combined biokinetics of the plutonium-DTPA chelate. Using the previously established chelation model, it was possible to fit the data through optimizing only the intake (day and magnitude), solubility, and absorbed fraction of nebulized Ca-DTPA. This work supports the hypothesis that the efficacy of the delayed chelation treatment observed in this case results mainly from chelation of cell-internalized plutonium by Ca-DTPA (intracellular chelation). It also demonstrates the validity of the previously established chelation model. As the bioassay data were modified to ensure data anonymization, the calculation of the "true" committed effective dose was not possible. However, the treatment-induced dose inhibition (in percentage) was calculated.

Modelling DTPA therapy following Am contamination in rats

A major challenge in modelling the decorporation of actinides (An), such as americium (Am), with DTPA (diethylenetriaminepentaacetic acid) is the fact that standard biokinetic models become inadequate for assessing radionuclide intake and estimating the resulting dose, as DTPA perturbs the regular biokinetics of the radionuclide. At present, most attempts existing in the literature are empirical and developed mainly for the interpretation of one or a limited number of specific incorporation cases. Recently, several approaches have been presented with the aim of developing a generic model, one of which reported the unperturbed biokinetics of plutonium (Pu), the chelation process and the behaviour of the chelated compound An-DTPA with a single model structure. The aim of the approach described in this present work is the development of a generic model that is able to describe the biokinetics of Am, DTPA and the chelate Am-DTPA simultaneously. Since accidental intakes in humans present many unknowns and large uncertainties, data from controlled studies in animals were used. In these studies, different amounts of DTPA were administered at different times after contamination with known quantities of Am. To account for the enhancement of faecal excretion and reduction in liver retention, DTPA is assumed to chelate Am not only in extracellular fluids, but also in hepatocytes. A good agreement was found between the predictions of the proposed model and the experimental results for urinary and faecal excretion and accumulation and retention in the liver. However, the decorporation from the skeletal compartment could not be reproduced satisfactorily under these simple assumptions.

Biokinetic model analysis with DTPA administration for a case of accidental inhalation of actinides in Japan

Accidental inhalation intake of plutonium isotopes and 241Am occurred at a Pu research facility in Japan in 2017, and the five workers involved in this accident were treated by the administration of Ca/Zn-diethylenetriaminepentaacetic acid (DTPA). For the worker who was most internally exposed, the therapy was continued over 1 y after the accident. Urinary samples collected before and after each administration were subject to bioassay to evaluate the efficacy of the dose reduction. This study performed numerical analyses using a biokinetic model dealing with 241Am-DTPA with reference to the European Coordinated Network on Radiation Dosimetry approach, which assumes that the complex of actinides and Ca/Zn-DTPA is generated in the designated compartments in the biokinetic model. The results of the model prediction well captured the trend of the observed urinary excretion in the long-term bioassay and would be useful to evaluate the efficacy of the Ca/Zn-DTPA administration for the worker involved in the accident.

Actinide Decorporation: A Review on Chelation Chemistry and Nanocarriers for Pulmonary Administration

Chelation is considered the best method for detoxification by promoting excretion of actinides (Am, Np, Pu, Th, U) from the human body after internal contamination. Chemical agents that possess carboxylic acid or hydroxypyridinonate groups play a vital role in actinide decorporation. In this review article, we provide considerable background details on the chelation chemistry of actinides with an aim to formulate better decorporation agents. Nanocarriers for pulmonary delivery represent an exciting prospect in the development of novel therapies for actinide decorporation that both reduce toxic side effects of the agent and improve its retention in the body. Recent studies have demonstrated the benefits of using a nebulizer or an inhaler to administer chelating agents for the decorporation of actinides. Effective chelation therapy with large groups of internally contaminated people can be a challenge unless both the agent and the nanocarrier are readily available from strategic national stockpiles for radiological or nuclear emergencies. Sunflower lecithin is particularly adept at alleviating the burden of administration when used to form liposomes as a nanocarrier for pulmonary delivery of diethylenetriamine-pentaacetic acid (DTPA) or hydroxypyridinone (HOPO). Better physiologically-based pharmacokinetic models must be developed for each agent in order to minimize the frequency of multiple doses that can overload the emergency response operations.

Four-decade follow-up of a plutonium-contaminated puncture wound treated with Ca-DTPA

Contaminated wounds are a common route of internal deposition of radionuclides for nuclear and radiation workers. They may result in significant doses to radiosensitive organs and tissues in an exposed individual's body. The United States Transuranium and Uranium Registries' whole-body donor (Case 0303) accidentally punctured his finger on equipment contaminated with plutonium nitrate. The wound was surgically excised and medically treated with intravenous injections of Ca-DTPA. A total of 16 g Ca-DTPA was administered in 18 treatments during the 2 months following the accident. Ninety-three urine samples were collected and analysed over 14 years following the accident. An estimated²³⁹Pu activity of 73.7 Bq was excreted during Ca-DTPA treatment. Post-mortem radiochemical analysis of autopsy tissues indicated that 40 years post-accident 21.6 ± 0.2 Bq of²³⁹Pu was retained in the skeleton, 12.2 ± 0.3 Bq in the liver, and 3.7 ± 0.1 Bq in other soft tissues; 1.35 ± 0.02 Bq of²³⁹Pu was measured in tissue samples from the wound site. To estimate the plutonium intake, late urine measurements, which were unaffected by chelation, and post-mortem radiochemical analysis results were evaluated using the IMBA Professional Plus software. The application of the National Council on Radiation Protection and Measurements wound model with an assumption of intake material as a predominantly strongly retained soluble plutonium compound with a small insoluble fraction adequately described the data (p= 0.46). The effective intake was estimated to be 50.2 Bq of plutonium nitrate and 1.5 Bq of the fragment. The prompt medical intervention with contaminated tissue excision and subsequent Ca-DTPA decorporation therapy reduced²³⁹Pu activity available for uptake and long-term retention in this individual's systemic organs by a factor of 38.

Experimental Evaluation of 65Zn Decorporation Kinetics Following Rapid and Delayed Zn-DTPA Interventions in Rats. Biphasic Compartmental and Square-Root Law Mathematical Modeling

The decorporation kinetics of internal radionuclide contamination is a long-term treatment raising modeling, planning, and managing problems, especially in the case of late intervention when the radiotoxic penetrated the deep compartments. The decorporation effectiveness of the highly radiotoxic 65ZnCl2 by Zn-DTPA (dosed at 3.32 mg and 5 mg/0.25 mL/100 g body weight) was investigated in Wistar male rats over a ten-day period under various treatments (i.e., as a single dose before contamination; as a single dose before and 24 h after contamination; and as daily administrations for five consecutive days starting on day 12 after contamination). The radioactivity was measured using the whole-body counting method. Mono- and bi-compartmental decorporation kinetics models proved applicable in the case of a rapid intervention. It was found that a diffusion model of the radionuclide from tissues to blood better describes the decorporation kinetics after more than ten days post treatment, and the process has been mathematically modeled as a diffusion from an infinite reservoir to a semi-finite medium. The mathematical solution led to a square-root law for describing the 65Zn decorporation. This law predicts a slower release than exponential or multiexponential equations, and could better explain the very long persistence of radionuclides in the living body. Splitting data and modeling in two steps allows a better understanding, description and prediction of the evolution of contamination, a separate approach to the treatment schemes of acute and chronic contamination.

Effects of the chelating agent DTPA on naturally accumulating metals in the body

Diethylenetriaminepentaacetate (DTPA) is the most widely used chelating agent for Pu and Am. Volunteers were assigned to receive intravenous injections or aerosol inhalations of 1 g of DTPA on days 1-4; volunteers received once daily injections of CaDTPA or ZnDTPA, CaDTPA inhalation as an aerosol, or CaDTPA injection on day 1 and ZnDTPA on days 2-4. CaDTPA injection or inhalation increased the excretion rates of Zn in urine with concomitantly reduced levels of serum Zn. Injection of CaDTPA reduced activities of serum alkaline phosphatase (AP) in parallel with the kinetics of Zn, whereas CaDTPA and ZnDTPA injection reduced activities of lactate dehydrogenase (LDH), and reduced activities of creatinine kinase (CK) were observed upon CaDTPA injection and its inhalation. Intravenous administration of CaDTPA and ZnDTPA enhanced excretion rates of Mn in urine, whereas transient reduction of Mn levels in serum was detected only via CaDTPA injection. Both CaDTPA and ZnDTPA transiently reduced levels of Mg in serum without affecting the excretion rates. On the other hand, both DTPAs increased excretion rates of toxic metals such as Pb and Cd, and CaDTPA also increased the rates of Hg. These results suggest that DTPA, and especially CaDTPA, removes essential metals and that the activities of these metalloenzymes are good indicators for the imbalance of essential metals during the DTPA administration. Our results also show that CaDTPA injection is more potent for removing these metals than ZnDTPA and inhalation of CaDTPA, and DTPA may be useful for the treatment of acute heavy metal poisoning with Pb, Cd, or Hg.

Development and Characterization of a Novel Hydrogel for the Decontaminating of Radionuclide-Contaminated Skin Wounds

Designing skin decontaminating materials with outstanding therapeutic effects, adhesiveness, and suitable mechanical property has great practical significance in radionuclide-contaminated skin wound healing. Here, a physically crosslinked hydrogel is constructed via hydrogen bonding of poly acrylamide, sodium alginate (SA), and the complexing agent diethylene triamine pentaacetic acid (DTPA). The physical and chemical properties of the poly(AAm-SA-DTPA) hydrogel (PASD) are detected according to established methods. The decontaminating property and skin wound healing of the PASD are investigated to confirm multi-functions of wound dressing. The physical and chemical properties results show that the synthesis of the PASD hydrogel is effective and that DTPA is present in the hydrogel. The hydrogel also shows great mechanical and swelling properties. In vitro tests find that PASD shows significant scavenging abilities for strontium and cerium. In vivo experiments show that the PASD hydrogel can remove radioactive strontium from the skin wounds of mice, and can effectively prevent the absorption of radioactive strontium through the skin wound. Furthermore, the PASD hydrogel can effectively promote the formation of granulation tissue in a radioactive contaminated wound. Taken together, the PASD hydrogels, which has good mechanical properties and radionuclides decontamination, is expected to be used as a dressing for radionuclide-contaminated skin wound healing.

Facile preparation of liposome-encapsulated Zn–DTPA from soy lecithin for decorporation of radioactive actinides

Diethylenetriaminepentaacetic acid (DTPA) is an attractive decorporation agent that can enhance the excretion of radioactive actinides such as plutonium, americium, and curium after a radiological incident. However, DTPA is excreted in a short period of time after administration. Several formulations have been developed to improve DTPA pharmacokinetics properties. In this project, liposomes were prepared facilely from soy lecithin as a nanocarrier for pulmonary delivery of Zn–DTPA. Lipid hydration, reverse phase evaporation, and mechanical sonication were three methods evaluated for the preparation of liposome-encapsulated Zn-DTPA (lipo-Zn-DTPA). Mechanical sonication was the method of choice due to simple apparatus and facile preparation. Lipo-Zn–DTPA exhibited a hydrodynamic diameter of 178 ± 2 nm and a spherical shape. The loading capacity and encapsulation efficiency of Zn–DTPA were 41 ± 5 mg/g and 10% ± 1%, respectively. Lyophilization of lipo-Zn–DTPA for extended storage did not affect the amount of encapsulated drug or damage the structure of liposomes. An in vivo cytotoxicity test confirmed no serious adverse effect of Zn–DTPA encapsulated lecithin liposomes in rats.

Validation of a system of models for plutonium decorporation therapy

A recently proposed system of models for plutonium decorporation (SPD) was developed using data from an individual occupationally exposed to plutonium via a wound [from United States Transuranium and Uranium Registries (USTUR) Case 0212]. The present study evaluated the SPD using chelation treatment data, urine measurements, and post-mortem plutonium activities in the skeleton and liver from USTUR Case 0269. This individual was occupationally exposed to moderately soluble plutonium via inhalation and extensively treated with chelating agents. The SPD was linked to the International Commission on Radiological Protection (ICRP) Publication 66 Human Respiratory Tract Model (HRTM) and the ICRP Publication 30 Gastrointestinal Tract model to evaluate the goodness-of-fit to the urinary excretion data and the predictions of post-mortem plutonium retention in the skeleton and liver. The goodness-of-fit was also evaluated when the SPD was linked to the ICRP Publication 130 HRTM and the ICRP Publication 100 Human Alimentary Tract Model. The present study showed that the proposed SPD was useful for fitting the entire, chelation-affected and non-affected, urine bioassay data, and for predicting the post-mortem plutonium retention in the skeleton and liver at time of death, 38.5 years after the accident. The results of this work are consistent with the conclusion that Ca-EDTA is less effective than Ca-DTPA for enhancing urinary excretion of plutonium.