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

Abstract

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. 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 ²⁴¹Am and ²³⁹Pu. Radionuclides with fast clearance, such as ¹³³I, 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 ²⁴¹Am. 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.

INTRODUCTION

Assessing radiation dose from internalized radionuclides is a central goal of radiological protection, specifically in occupational settings, environmental contamination incidents, and emergency response scenarios. Dose estimation models rely on biokinetic and dosimetric frameworks to predict radionuclide deposition, retention, and clearance, which inform health risk assessments and compliance with regulatory limits. Inherent limitations exist in the ability to measure and estimate organ absorbed doses following the internalization of radionuclides by an exposed member of the public during a radiological incident. Inhalation of radioactive material poses a distinct hazard, as inhaled material is transported within the body and incorporated into metabolic and immune processes. Tracking the movement of inhaled radionuclides involves understanding their deposition in the respiratory tract, subsequent absorption into the circulatory system, clearance into the gastrointestinal (GI) tract, and eventual excretion via urine or feces (Eckerman 1994; ICRP 1994).

Inhalation dosimetry models are comprised of two primary calculation components. First, a biokinetic model tracks the metabolic transport, distribution of radioactive material in the body, and excretion from the body. Second, a dosimetric model calculates radiation doses to organs and nearby tissues from source tissues based on radioactive decay. The dosimetric model relies on organ- and tissue-specific source strength data, derived by solving the system of ordinary differential equations (ODEs) defined by the biokinetic model. The International Commission on Radiological Protection (ICRP) incorporates biological data and experimental evidence to predict radionuclide behavior, with limited human data available. Specifically, the Human Respiratory Tract Model (HRTM) given in ICRP Publication 66 (Fig. 1) divides the respiratory tract into compartments to simulate inhaled radionuclide movement through airway regions. This model accounts for deposition, mechanical clearance, dissolution/absorption, and radioactive decay within the lungs (ICRP 1994).

Fig. 1.

The Human Respiratory Tract Model (HRTM) illustrating material transport within the respiratory tract, clearance of material to the gastrointestinal tract, and material transfer to regional lymph nodes (ICRP 1994). The arrows depict the transfer of materials between compartments with an assigned transfer rate. AI₁: relatively short-term retention (half-time about 35 d); AI₂: long-term retention (half-time about 700 d); AI₃: very long-term retention (half-time about 6000 d); BB₁: short-term retention (half-time about 100 min) of particles in the BB region; bb₁: short-term retention (half-time about 8 h) of particles in the bb region; BB₂: intermediate retention (half-time about 20 d) of particles in the BB region; bb₂: intermediate retention (half-time about 20 d) of particles in the bb region; BB_SEQ: long-term retention (half-time about 70 d) in airway walls of a small fraction of the particles deposited in the BB region; bb_SEQ: long-term retention (half-time about 70 d) in airway walls of a small fraction of the particles deposited in the bb region; ET₁: retention of material deposited in the anterior nose (region ET1); ET’₂: short-term retention (half-time about 10 min) of the material deposited in the posterior nasal passage, larynx, pharynx and mouth (region ET2); ET : long-term retention (half-time about 700 d) in airway tissue of a small fraction of particles deposited in the nasal passages; LN_ET: lymphatics and lymph nodes that drain the extrathoracic region; LN_TH: lymphatics and lymph nodes that drain the thoracic regions.

Although individual anatomical and physiological variability is widely recognized, reference biological models have nevertheless been developed for radiation protection and for establishing dose limits across various exposure scenarios. These models are primarily based on data from reference adults, mainly because the human data used to construct these models are often derived from occupational cohorts. A reference person, as defined by the ICRP for radiation protection, represents an idealized person with standardized anatomical and physiological characteristics, for whom the equivalent doses to organs and tissues are calculated by averaging the corresponding doses of a reference male and female (ICRP 2002, 2015). As a result, limited data are available for the broader public demographic regarding the mechanisms, retention, and excretion stemming from the biokinetic behavior of internalized radionuclides. This lack of variability in the dose coefficients commonly used for public protection creates a gap in understanding the certainty of calculated dose values when applied to diverse populations. In ICRP Publication 66 Annex D and Annex E, the impact of variability and uncertainty on respiratory tract model parameters is examined (ICRP 1994). Using data from animal and human studies, the annex examines how to further define model parameters such that measured variables fit into them.

Examples of such measured variables impacting the model parameter are particle dissolution rate as a function of particle surface area, particle mass, diameter, particle density, and dissolution rate constant. This examination of dissolution rate through measurable variables enables a straightforward sensitivity analysis of the respiratory tract model. Another detailed examination of a model parameter involves defining deposition within the regions of the respiratory tract by filter efficiency rather than interpolation of tabulated data from Annex F Tables in ICRP Publication 66 (ICRP 1994).

Prior studies conducted by Bolch et al. (2001) systematically reviewed the human respiratory tract deposition model parameters within the ICRP Publication 66 lung model and used the Lung Dose Uncertainty Code (LUDUC) developed by Huston (1995) to evaluate the uncertainties in particle deposition. However, the source code for LUDUC is no longer available compounded by the limitation that its original computational framework was not compatible with modern programming environments. Subsequently, Bolch et al. (2003) investigated parameter uncertainties within the ICRP Publication 66 respiratory tract model, proposing probability distribution functions for uncertain clearance parameters. While this was a significant contribution to the quantification of uncertainty in internal dose assessment following inhalation, the study focused exclusively on the effects of particle clearance parameters in the context of ²³⁹PuO₂ and ²³⁸UO₂/²³⁸U₃O₈ aerosols. Huston et al. (2003) extended this work by conducting a parameter sensitivity analysis of the ICRP Publication 66 HRTM. Huston et al. (2003) combined the uncertain parameters for the deposition and clearance models as proposed by Bolch et al. (2001 & Bolch et al. 2003). However, the sensitivity studies in the equivalent dose per activity exposure were limited to the inhalation of monodisperse aerosol of ²³⁹PuO₂.

The objective of this study was to develop a Radiological Exposure Dose Calculator (REDCAL), a computational framework for propagating total uncertainty in inhalation dose coefficients, based on the ICRP Publication 66 Human Respiratory Tract Model (HRTM), as a function of uncertain input parameters for a compendium of radionuclides relevant to the U.S. Federal Radiological Monitoring and Assessment Center (FRMAC) for specific lung clearance types (e.g., fast (F), moderate (M) and slow (S) clearance). Notably, the comprehensive set of inhalation dose coefficient probability distributions developed in this study establishes a foundation for incorporating uncertainty analysis capabilities of Derived Response Level (DRL) in the Turbo FRMAC software. Turbo FRMAC is developed by Sandia National Laboratories (SNL) and has served as the FRMAC’s radiological dose assessment tool for 20 years (FRMAC 2023a). It is important to emphasize that the methodology in this study is based primarily on ICRP Publication 66 and associated models because FRMAC currently follows the ICRP Publication 60 series of recommendations.

METHODOLOGY

The overall computational workflow for this study is depicted in Fig. 2. The methodology comprises three main phases: uncertain parameter sampling, dose coefficient calculation using REDCAL, and statistical post-processing. Key input parameters of the HRTM were selected to be treated as uncertain, including particle deposition efficiencies, compartmental fractions and respiratory clearance. These parameters were assigned probability distributions as outlined in Table 1. Latin hypercube sampling (LHS), implemented using Dakota (SN’s statistical software package), was used to generate 10,000 sets of input parameter values that capture the full range of possible variation across the 27 uncertain variables. These sampled inputs were input to REDCAL, which propagated the uncertainty through the HRTM. For a given particle size and geometric standard deviation (GSD), REDCAL computed particle deposition across respiratory regions and utilized those results as initial conditions for biokinetic modeling. With the compartment-specific clearance parameters of the biokinetic models, REDCAL solved the time-dependent retention equations using a matrix exponential approach (Mate-Kole et al. 2023), and computed organ-specific dose contributions over a committed period. The committed effective dose coefficients (CEDCs) were calculated for each parameter set using the ICRP Publication 60 tissue weighting factors and radionuclide-specific energy absorption values. Finally, Dakota was harnessed to perform statistical post-processing on the resulting CEDCs, fitting probability distributions that characterize the variability in dose coefficients for each radionuclide and particle size. These distributions supported downstream applications within Turbo FRMAC, including the study of the impact of uncertainty on DRL.

Fig. 2.

Workflow summarizing the dose coefficient modeling and uncertainty sampling process with Dakota handling the statistical processing via Latin Hypercube Sampling (LHS) (Margot et al. 2021).

Table 1.

Sampled input parameter probability distributions for the ICRP human respiratory tract model (Bolch et al. 2001, Bolch et al. 2003; James et al. 1994).

Parameter	Geometric Mean/ Mean	GSD/SD	Distribution Type
Aerodynamic Deposition Efficiency Error Terms
Cae(ET1)	1	1.82	Lognormal
Cae(ET2)	1	1.82	Lognormal
Cae(BB)	1	1.58	Lognormal
Cae(bb)	1	1.58	Lognormal
Cae(AI)	1	1.3	Lognormal
Thermodynamic Deposition Efficiency Error Terms
Cth(ET1)	1	1.18	Lognormal
Cth(ET2)	1	1.18	Lognormal
Cth(BB)	1	1.23	Lognormal
Cth(bb)	1	1.23	Lognormal
Cth(AI)	1	1.23	Lognormal
Compartmental Sequestration Deposition Fraction Terms
fd(ETseq)	0.0005	1.73	Lognormal
fd(BBseq)	0.007	1.73	Lognormal
fd(bbseq)	0.007	1.73	Lognormal
Slow-Clearing Fraction Error Term
E(Fs)	0	0.1	Normal
Fast Clearing Deposition Fraction for Alveolar Interstitial Term
Fd(AI1)	0.3	1.1	Lognormal
Fractional clearance rate constant for mechanical clearance
AI2 → bb1	0.001	1.41	Lognormal
AI3 → bb1	0.0001	1.73	Lognormal
AI3 → LNTH	0.00002	1.41	Lognormal
bb1 → BB1	2	1.41	Lognormal
bb2 → BB1	0.03	1.73	Lognormal
bbseq → LNTH	0.01	1.73	Lognormal
BB1 → ET2	10	1.22	Lognormal
BB2 → ET2	0.03	1.73	Lognormal
BBseq → LNTH	0.01	1.73	Lognormal
ET2 → GI Tract	100	1.73	Lognormal
ETseq → LNET	0.001	1.73	Lognormal
ET1 → Environment	1	1.73	Lognormal

Particle Deposition

In REDCAL, the deposition of radioactive material within the respiratory tract is represented as a series of filtration processes occurring during both inhalation and exhalation. These filtration mechanisms, described in ICRP Publication 66, correspond to specific regions of the respiratory tract where deposition occurs based on aerodynamic and thermodynamic principles. Aerodynamic processes, such as impaction and gravitational settling, influence deposition alongside thermodynamic mechanisms driven by Brownian motion. The overall deposition efficiency for each region is calculated as the geometric mean (GM) of these competing processes, which are influenced by factors such as particle size, aerodynamic and thermodynamic characteristics, and breathing mode (e.g., nasal or nasal-oral). Further details on the computational methodology are detailed in prior studies (Bolch et al. 2001; ICRP 1994; Klumpp, & Bertelli 2017; Mate-Kole et al. 2024).

Biokinetic and Dosimetric Calculations

Current tools, such as Oak Ridge National Laboratory’s Dose and Risk Calculator (DCAL) (Eckerman et al. 2006), developed by the Center for Radiation Protection Knowledge (CRPK) and sponsored by the U.S. Environmental Protection Agency (EPA), implement the ICRP Publication 66 HRTM and rely on a Windows-based Visual Basic platform with limited extensibility for numerical solving. To address these limitations, a new model was developed in REDCAL using Python programming language modules to reconstruct the ICRP Publication 66 models. This computational toolkit was validated against existing models and expanded to incorporate the enhanced HRTM compartmental model from ICRP Publication 130, as well as the ICRP Occupational Intakes of Radionuclides (OIR) publication series (ICRP 2015). The Python implementation leverages updated libraries for linear algebra and numerical methods, improving the precision of solving the system of ODEs required for biokinetic modeling (incorporating radioactive decay chains) while enabling flexible integration with statistical and machine learning modules. A comprehensive mathematical review, including solution methods and analysis using Python as a computational framework, has been discussed elsewhere (Mate-Kole et al. 2023, 2024).

To estimate the committed effective dose coefficients (CEDCs) based on the ICRP Publication 66 HRTM, the in-house computational tool within REDCAL utilizes specific energy equivalent (SEE) values and total decay events to compute internal radiation doses. SEE represents the average energy deposited per decay of a radionuclide within a target organ. REDCAL accesses a predefined database containing SEE values for all relevant source-target combinations. The total number of decays in a source organ is determined by integrating radionuclide activity over a predefined commitment period, 50 years for most radionuclides and 70 years for bone-seekers like strontium, for an adult (Eckerman et al. 2006). Organ doses are then calculated by multiplying the SEE value for each source-target pair by the corresponding number of decays. The effective dose is obtained by summing the products of organ doses and their respective tissue weighting factors, as defined by ICRP Publication 60 (ICRP, 1991). Contributions from all relevant progeny radionuclides are included in the dose calculation.

Dose Coefficient Uncertainty Propagation

The uncertainty propagation framework employed Monte Carlo analysis to quantify uncertainty in inhalation dose coefficients. This approach involved defining probability distributions for uncertain model input parameters, which were then sampled multiple times. For each sample, the deterministic simulation was executed to propagate uncertainty through the model. The resulting set of simulations was analyzed to assess overall uncertainty and evaluate the contribution of individual variables to the total uncertainty.

Various methods can be used to conduct sampling from distributions. Simple random sampling is the most basic approach, where values are drawn randomly from each input distribution. In contrast, LHS stratifies each input distribution, selects samples from each stratum, and then randomly combines them with stratified samples from other inputs. LHS is particularly useful for achieving result convergence with fewer samples and is well-suited for computationally-intensive models. In this study, LHS was implemented using the Dakota toolkit as the sampling engine. Dakota is a robust mathematical toolkit designed for parametric analysis, enabling sampling from various distribution types for uncertainty quantification (Adams et al. 2012). Developed by SNL, it facilitates the integration of simulation codes with iterative analysis methods. Its uncertainty quantification module supports multiple sampling techniques, including LHS and simple random sampling. The uncertain parameters considered in this study are outlined in Table 1, including those related to the human respiratory tract deposition and clearance models. These parameters were adopted from the ICRP Publication 66 (ICRP 1994), Annexes D and E, based on studies by James et al. (1994) and Bailey & Roy (1994) on the deposition of inhaled particles and their clearance from the respiratory tract.

Notably, ICRP Publication 66 provides empirical equations to evaluate aerodynamic and thermodynamic particle deposition efficiencies in the HRTM, derived from regression analyses of experimental data and theoretical models. These deposition efficiency equations are expressed as functions of a, R, and p where a and p are regression coefficients specific to each region of the respiratory tract, defined separately for aerodynamic and thermodynamic mechanisms during both inhalation and exhalation. The R term represents a region-specific parameter that captures the influence of particle behavior related to the governing deposition mechanism. To account for uncertainty in these equations, a random variable C was introduced for both the aerodynamic and thermodynamic terms. This variable is modeled as a log-normal distribution with a GM of 1 and a corresponding geometric standard deviation (GSD), as shown in Table 1. The C variable acts as a multiplicative factor applied to the a parameter in the deposition model to propagate uncertainty through the calculations.

Furthermore, the regional deposition fraction is partitioned among the compartments of each region of the HRTM to account for varying absorption and clearance rates. The sampled parameters from Table 1 introduce uncertainty into the initial compartmental activity allocation, downstream of the deposition fractions. The sampled compartmental partitioning terms were defined for the sequestered compartments of ET₂, BB, and bb, as well as for the AI₁ compartment. To account for uncertainty in the slow-clearing fractions of the bronchial and bronchiolar (BB and bb) regions, an additional error term was introduced. This term modifies the computed average value of the slow-clearing fraction by acting as an additive term. The mean and standard deviation terms for the lognormal distributions in Table 1 are presented in their geometric form. Moreover, uncertainty propagation through the HRTM via mechanical clearance was implemented by assigning a lognormal distribution to each clearance pathway, with their respective GM and GSD values as specified in Table 1.

Radionuclides and Particle Sizes of Interest

Turbo FRMAC can be used to calculate DRLs for any mixture of the 888 radionuclides with inhalation dose coefficients available in DCFPAK (Eckerman and Leggett 1996), a compendium of dose coefficients developed by ORNL. It was infeasible to address all radionuclides in this study, nor do all radionuclides contribute significantly to inhalation dose. As a result, the uncertainty propagation was performed for 31 priority radionuclides of interest to FRMAC. These radionuclides were selected based on the FRMAC Assessment default mixtures for various accident scenarios, including a nuclear weapon accident, a radiological dispersal device, fallout from a nuclear detonation, a radioisotope thermoelectric generator accident, and a nuclear power plant release, with an emphasis on radionuclides for which inhalation dose dominates the total dose used to calculate a DRL (FRMAC 2023b). Results of a subset of these radionuclides, ²⁴¹Am (type M and S), ⁶⁰Co (type M), ¹³³I (type F), ²³⁹Pu (type M and S), ⁹⁰Sr (type M and S), and ⁹⁰Y (type M and S), are discussed in detail in this study, with the full compendium documented by SNL (Cochran et al. 2025). This subset of radionuclides was selected to provide coverage of results and analyses for scenarios of interest in radiological emergencies.

Additionally, this work considered inhalation dose coefficients for a range of particle sizes. Uncertainty propagation and characterization were performed for 10 particle sizes ranging from 0.003 to 30 μm, with results for the selected particle sizes of interest presented in this study.

Statistical Post-Processing

To support the statistical post-processing of the simulation results, an appropriate probability distribution was identified for the CEDC values. This involved performing separate distribution fits for each combination of radionuclide and particle size. Guided by prior studies, subject-matter expertise, and preliminary assessments of the data, the lognormal distribution was selected as a suitable model for characterizing the variability in CEDC. The fit of the lognormal distribution to the observed CEDC data was assessed visually using quantile-quantile (Q-Q) plots. The Q-Q plot was employed because it provides a better representation of the fit quality, particularly at the tails of the distribution, which can often be difficult to assess from empirical density function (EDF) plots. The GM values obtained from the fitted distributions were subsequently compared to published dose coefficient values (e.g., from DCFPAK) and evaluated.

An additional analysis was conducted to examine how the average CEDC varies as a function of particle sizes (AMAD), with uncertainty bounds represented as ±1 standard deviation (SD). For each AMAD, 10,000 samples were generated by sampling the distributions of the uncertain parameters and the corresponding CEDC values were computed. The arithmetic mean and SD of the CEDC for each AMAD were then calculated.

This analysis was carried out for all radionuclides addressed in this study, considering their respective clearance types. However, for ²⁴¹Am, ²³⁹Pu, ⁹⁰Sr, and ⁹⁰Y, the analysis of average CEDC variability with respect to particle size was limited to clearance type M. Although calculations were performed for both types M and S, type M was selected for discussion because it encompasses the full range of accident scenarios considered for these radionuclides, whereas type S corresponds to a single scenario. For example, ²³⁹Pu with clearance type M is applicable to scenarios such as nuclear weapon (NW), radiological dispersal device (RDD), and radioisotope thermoelectric generator (RTG), whereas type S applies only to the NW and RDD scenario. Thus, focusing on type M provides comprehensive coverage while maintaining concise and interpretable data reporting.

RESULTS

For the purposes of this study, results are presented for ²⁴¹Am, ⁶⁰Co, ¹³³I, ²³⁹Pu, ⁹⁰Sr, and ⁹⁰Y in adults based on the ICRP Publication 66 model.

Benchmark with DCAL

REDCA’s biokinetic solver was benchmarked against activity data from DCA’s.ACT files. The percent differences in retention results between REDCAL and DCAL, based on the ICRP Publication 66 model and ICRP 60 recommendations, were under 1% for a vast majority of the cases and a maximum relative percent difference of approximately 2%. For organ equivalent dose coefficients, the average percent differences were less than 1%, while for effective dose coefficients, the relative percent differences were less than 2% for the majority of the cases with a maximum relative percent difference of 5%. To effectively propagate uncertainty in the respiratory tract model, the ICRP Publication 66 deposition model was reconstructed as a Python module. The relative differences between the total deposition fractions computed with REDCAL and those reported by the ICRP were less than or equal to 1%.

Analyses of Uncertainty Propagation

The dose coefficients were computed using REDCAL with variable input parameters. These parameters were sampled from their respective probability density functions and combined using LHS to represent the full range of possible scenarios. A total of 10,000 realizations were generated for each radionuclide to ensure comprehensive coverage of all potential parameter variations.

The results are illustrated in the plots (Fig. 3-8) showing the average CEDC in Sv/Bq (Sieverts per Becquerel of intake) as a function of the AMAD in microns (μm). The plots also include the standard deviation for each simulation, which reflects the variability introduced by the sampled parameters, detailed in Table 1. This analysis was conducted to understand how the accumulated uncertainty from all parameters propagates when computing the CEDC, thereby demonstrating the sensitivity of the CEDC to different sampling conditions.

Fig. 3.

Committed effective dose coefficient (CEDC), mean ± 1 SD, as a function of particle size for ²⁴¹Am type M, based on 10,000 samples from all uncertain input distributions.

Fig. 8.

Committed effective dose coefficient (CEDC), mean ± 1 SD, as a function of particle size for ⁹⁰Y type M, based on 10,000 samples from all uncertain input distributions.

The uncertainty, or width of the bands, indicates the sensitivity of the model to changes in the uncertain parameters for each specific radionuclide. For instance, it is evident that the CEDC for ⁹⁰Y and ¹³³I is almost entirely determined by the AMAD when the particle diameter is large (within the range studied between 10-30 μm). In contrast, for the same range of particle diameters, radionuclides such as ²⁴¹Am and ²³⁹Pu exhibit significant variability. Additionally, all radionuclides show considerable variability in the intermediate AMAD range (10¹ to 10 μm).

Fig. 9 and Fig. 10 illustrate the probability density plot (comparing the lognormal fit with the empirical distribution) and the Q-Q plot, respectively, for ²⁴¹Am, clearance type M, at 1 μm AMAD. The GM values of the resulting distributions were then compared to the deterministic values reported in DCFPAK. Fig. 11 presents this comparison of the CEDC lognormal fit as a function of particle size for ²⁴¹Am type M. For the lognormal fit and geometric analysis, ²⁴¹Am was chosen for illustrative purposes, as similar trends were observed across the other radionuclide cases. Table 2 provides the complete dataset resulting from the lognormal fits for the radionuclides and clearance types considered in this study.

Fig. 9.

The probability density plot (comparing the lognormal fit with the empirical distribution) for ²⁴¹Am, clearance type M, at 1 μm activity median aerodynamic diameter (AMAD).

Fig. 10.

The Q-Q plot for ²⁴¹Am, clearance type M, at 1 μm activity median aerodynamic diameter (AMAD).

Fig. 11.

Plot of the geometric mean values of Committed effective dose coefficient (CEDC) for ²⁴¹Am type M as a function of particle size.

Table 2.

Lognormal distribution fit parameters for Adult Committed Effective Inhalation Dose Coefficients (Sv/Bq). Geometric mean shown with geometric standard deviation in parentheses.

Radionuclide	LCT*	Particle Size (μm AMAD)
		0.003	0.01	0.03	0.1	0.3	1	3	5	10	30
241Am	M	6.3×10−5 (1.1)	1.5×10−4 (1.1)	1.9e-04 (1.1)	7.7×10−5 (1.1)	4.8×10−5 (1.1)	6.1×10−5 (1.2)	6.5×10−5 (1.2)	5.1×10−5 (1.2)	2.7×10−5 (1.2)	8.4×10−6 (1.1)
241Am	S	3.9×10−5 (1.2)	7.4×10−5 (1.1)	7.4×10−5 (1.1)	3.0×10−5 (1.1)	1.8×10−5 (1.1)	2.2×10−5 (1.2)	2.3×10−5 (1.2)	1.6×10−5 (1.3)	5.9×10−6 (1.3)	6.5×10−7 (1.5)
60Co	M	3.8×10−8 (1.2)	5.7×10−8 (1.1)	6.1×10−8 (1.1)	2.5×10−8 (1.1)	1.6×10−8 (1.1)	2.1×10−8 (1.1)	2.4×10−8 (1.2)	2.0×10−8 (1.2)	1.1×10−8 (1.1)	4.5×10−9 (1.1)
133I	F	2.8×10−9 (1.0)	3.3×10−9 (1.0)	3.0×10−9 (1.0)	1.2×10−9 (1.1)	8.0×10−10 (1.1)	1.4×10−9 (1.1)	2.2×10−9 (1.1)	2.3×10−9 (1.1)	2.0×10−9 (1.1)	N/A
239Pu	M	7.2×10−5 (1.1)	1.9×10−4 (1.1)	2.5×10−4 (1.1)	1.0×10−4 (1.1)	6.4×10−5 (1.1)	8.2×10−5 (1.2)	8.7×10−5 (1.2)	6.9×10−5 (1.2)	3.7×10−5 (1.2)	N/A
239Pu	S	3.5×10−5 (1.2)	7.4×10−5 (1.1)	7.9×10−5 (1.1)	3.2×10−5 (1.1)	2.0×10−5 (1.1)	2.3×10−5 (1.2)	2.4×10−5 (1.2)	1.7×10−5 (1.3)	6.5×10−6 (1.3)	6.8×10−7 (1.4)
90Sr	M	6.8×10−8 (1.2)	1.1×10−7 (1.1)	1.3×10−7 (1.1)	5.2×10−8 (1.1)	3.3×10−8 (1.1)	4.2×10−8 (1.2)	4.7×10−8 (1.2)	3.6×10−8 (1.2)	1.8×10−8 (1.2)	5.3×10−9 (1.1)
90Sr	S	8.5×10−8 (1.2)	3.5×10−7 (1.1)	6.0×10−7 (1.1)	2.5×10−7 (1.2)	1.6×10−7 (1.1)	2.0×10−7 (1.2)	2.0×10−7 (1.2)	1.4×10−7 (1.3)	6.2×10−8 (1.3)	5.9×10−9 (1.4)
90Y	M	5.4×10−9 (1.1)	5.1×10−9 (1.1)	3.7×10−9 (1.0)	1.5×10−9 (1.1)	9.6×10−10 (1.1)	1.5×10−9 (1.1)	2.4×10−9 (1.1)	2.4×10−9 (1.1)	1.9×10−9 (1.1)	1.1×10−9 (1.0)
90Y	S	5.8×10−9 (1.1)	5.5×10−9 (1.1)	4.0×10−9 (1.0)	1.6×10−9 (1.1)	1.0×10−9 (1.1)	1.6×10−9 (1.1)	2.6×10−9 (1.1)	2.5×10−9 (1.1)	1.9×10−9 (1.1)	1.1×10−9 (1.0)

^*F = Fast, M = Moderate, and S = Slow. Note: “N/A” indicates that lognormal distribution fit parameters are not reported due to an inadequate representation of the observed data. This typically occurred at the extreme ends of the particle size spectrum, in this case at 30 μm AMAD for ¹³³I type F and ²³⁹Pu type M.

DISCUSSION

The dose coefficients for ²⁴¹Am, ⁶⁰Co, ¹³³I, ²³⁹Pu, ⁹⁰Sr, and ⁹⁰Y exhibited clear variability across particle sizes, driven by stochastic sampling of key parameters such as particle size, mechanical clearance rates, and nasal deposition efficiencies. For ²⁴¹Am, smaller particles (nanoscale) resulted in high extrathoracic (ET1/ET2) deposition but reduced systemic uptake due to rapid clearance, while mid-sized particles (1–5 μm) yielded maximum alveolar-interstitial (AI) retention, increasing dose contributions from alpha emissions. Larger particles (>10 μm) were deposited primarily in the upper airways, leading to lower effective doses. Uncertainty stemmed from the interplay of particle size variability and sex-averaged breathing parameters, which may obscure sex-specific differences in deposition efficiency (e.g., females’ smaller lung volumes may increase ET1/ET2 deposition).

Iodine-133 demonstrated a decline in average dose coefficient with increasing particle size (10⁻² to 10⁻¹ μm), reflecting reduced thyroid uptake as larger particles are deposited in the upper airways. The fast clearance (type F) of ¹³³I minimized retention in deep lung compartments, though stochastic sampling of lung parameters and mucociliary clearance introduced variance.

Plutonium-239 exhibited elevated average dose coefficients at smaller particle sizes (10⁻² μm) due to prolonged retention in the deep lung and alpha self-irradiation, further compounded by recycling through systemic organs (e.g., liver and bone surfaces). Ingrowth of radioactive progeny introduces minor additional uncertainty. For larger particles, significant deposition occurs in the ET1 and ET2 regions. A substantial fraction is subsequently cleared to the GI tract, where its low absorption fraction (f1) limits systemic uptake.

The modeled results for ⁹⁰Sr, which included progeny ingrowth, highlight its contribution to uncertainty in bone marrow dosimetry; as a bone-seeking radionuclide, its dose coefficients are strongly influenced by particle size and GI absorption (f1 values). Progeny such as ⁹⁰Y (from ⁹⁰Sr decay) introduce beta-emitting sources in bone marrow, amplifying dose uncertainty if retention occurs. For ⁹⁰Y (pure ⁹⁰Y as a parent), the average dose coefficient at 10⁻² μm AMAD reflected its high-energy beta emissions in bone tissues, with variance driven by particle size and systemic recycling rates.

Cobalt-60 results demonstrated average dose coefficients ranging from 10⁻⁹ to 10⁻⁸ Sv/Bq across particle sizes (10⁻² to 10¹ μm AMAD). Smaller particles (0.01–1 μm) demonstrated higher doses due to deeper lung deposition and subsequent systemic circulation, where gamma emissions from ⁶⁰Co irradiated high tissue-weight organs. Larger particles (>5 μm) deposited in upper airway reduced the effective doses but increased nasal deposition uncertainty.

Sex-specific dependencies, though not explicitly analyzed in this study, likely influenced variance across all radionuclides. For instance, sex differences in tidal volume and breathing rates could alter deposition patterns (e.g., higher nasal deposition in females for specific particle sizes), but the use of sex-averaged biokinetic parameters reduced apparent differences between sexes. Age is also a relevant factor influencing inhalation dose coefficients, particularly through its effect on respiratory tract morphology and breathing parameters. The ICRP Publication 66 deposition model incorporates scaling factors that adjust airway dimensions and breathing parameters with respect to age, sex and race. These adjustments reflect the model’s sensitivity to anatomical and physiological differences in the deposition phase, which tend to be more pronounced across different ages. Overall, the dominance of particle size and nasal deposition fraction as uncertainty drivers accentuates the need for scenario-specific parameterization in emergency response models, particularly for alpha emitters (e.g., ²³⁹Pu, ²⁴¹Am), beta/gamma emitters (e.g., ⁶⁰Co, ⁹⁰Y), and radionuclides with complex progeny chains.

The lognormal distribution was generally a suitable fit for the modeled dose coefficients in this investigation. While small deviations were observed at the tails of the particle size range, pronounced deviations were uncommon. Although the sample distributions were predominantly described by a lognormal distribution with minor differences, specific cases may be more appropriately represented by an alternative distribution. In instances where the lognormal distribution did not adequately capture the data, typically at the extreme ends of the particle size spectrum (e.g., near 0.003 μm, or 10 to 30 μm), lognormal distribution parameters were not reported and are marked as “N/A” in Table 2. However, in some cases with moderate or even severe deviations in the distribution tails, the affected regions correspond to extremely low-probability values (e.g., the upper tail), meaning the impact of an inadequate lognormal fit in this region may not have a high impact. Therefore, for a series of analyses based on the updated HRTM, the analyst should explore what distribution (if any) is most suitable for modeling the CEDC. In addition, the empirical results from running REDCAL can also be used to propagate uncertainty in a Monte Carlo framework. This would be a preferred method when there is not a close distributional fit.

The mean stochastic computations from REDCAL closely match the CEDCs reported in DCFPAK for most radionuclides analyzed in this study. Fig. 11 illustrates the comparison of GM of CEDC values from the REDCAL simulation with dose coefficient values from DCFPAK for ²⁴¹Am as an example for illustrative purposes, as similar trends were observed for the other radionuclides considered (Cochran et al. 2025). When comparing the GM of the CEDC from the fitted lognormal distribution and the DCFPAK value, the GM of CEDC from the fitted distribution is generally higher than the DCFPAK value between 0.3 and 10 μm. Additionally, the simulated stochastic mean values tend to exhibit a distinct peak within this range, whereas DCFPAK CEDC values typically follow a flatter trend. This peaking in simulated results is expected due to the stochastic treatment of uncertainty in deposition fractions and integration across particle size. Consequently, stochastic deposition values are slightly higher than the default deposition fractions, with uncertainty bands covering a broader range of possible CEDCs.

CONCLUSIONS

Predictive modeling plays a central role in developing protocols and plans for emergency responses to nuclear and radiological incidents. This necessitates a framework and methodologies that account for the complexities of internal exposure. To address this challenge and enable eventual stochastic analyses for consequence management, the computational toolkit, REDCAL, was developed to compute internal radiation dose coefficients, both deterministic and stochastic, following a specified intake scenario, which in this study focuses on inhalation. REDCAL demonstrated good agreement with DCAL, with retention results, organ equivalent dose coefficients, and effective dose coefficients remaining consistently aligned. This confirms agreement between REDCA’s biokinetic solver and existing benchmark models to reproduce ICRP dose coefficients. Although this study used sex-averaged parameters, future work could explore these effects to improve dose estimation, particularly in emergency response scenarios where population variability must be considered. Overall, REDCAL offers a flexible and extensible platform for modeling inhalation dose variability. These results support the integration of stochastic internal dosimetry into consequence assessment workflows and emergency preparedness planning.

Fig. 4.

Committed effective dose coefficient (CEDC), mean ± 1 SD, as a function of particle size for ¹³³I type F, based on 10,000 samples from all uncertain input distributions

Fig. 5.

Committed effective dose coefficient (CEDC), mean ± 1 SD, as a function of particle size for ⁹⁰Sr type M, based on 10,000 samples from all uncertain input distributions.

Fig. 6.

Committed effective dose coefficient (CEDC), mean ± 1 SD, as a function of particle size for ²³⁹Pu type M, based on 10,000 samples from all uncertain input distributions.

Fig. 7.

Committed effective dose coefficient (CEDC), mean ± 1 SD, as a function of particle size for ⁶⁰Co type M, based on 10,000 samples from all uncertain input distributions.