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A Methodology for Calculation of Internal Dose Following Exposure to Radioactive Fallout from the Detonation of a Nuclear Fission Device

Anspaugh, Lynn R.1; Bouville, André2; Thiessen, Kathleen M.3; Hoffman, F. Owen4; Beck, Harold L.5; Gordeev, Konstantin I.6; Simon, Steven L.7

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doi: 10.1097/HP.0000000000001503
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Abstract

INTRODUCTION

The purpose of this paper is to provide a method of calculating internal doses resulting from the ingestion of foods contaminated by radioactive fallout and the inhalation of fallout-contaminated air following the detonation of a nuclear fission device. The method is applicable to exposures to fallout from detonation of fission devices for any purpose, including the postulated detonation of an improvised nuclear device (IND). This paper is one of six in this issue of Health Physics that address the overall topic of dose assessment following a nuclear detonation. Simon et al. (2022) provide an overall introduction and historical review of the development of methods of calculating both external and internal doses. Although as many as 177 radionuclides can be created following a nuclear detonation (Hicks 1981, 1982), Simon et al. (2022) also consider how many and which radionuclides would typically contribute at least >90% of the dose. Beck et al. (2022) develop methods of estimating the deposition density (Bq m−2) of radionuclides on soil and vegetation, which is a necessary step for the methods of calculating internal dose described here. Bouville et al. (2022) consider how external dose can be calculated as a complement to this paper. Thiessen et al. (2022) compile a list of radioecological transfer factors for pathways of food contamination, many of which are essential input data for calculations of internal dose. Melo et al. (2022) provide calculated values of dose coefficients (DC) to assess the conversion of intakes via ingestion and inhalation to dose; these values of DC have been adjusted from the nominal values promulgated by the ICRP (2004, 2011) in order to consider that nuclides in particulate form from a nuclear detonation are expected to be less soluble. This paper develops methods of calculating internal dose with input of critical data from Beck et al. (2022), Thiessen et al. (2022), and Melo et al. (2022).

The methods discussed here have been developed over decades by the authors and other investigators. As explained in Simon et al. (2022), the methods have been used in many studies of dose reconstruction following nuclear detonations; however, the methods are sufficiently general that they have been adapted, for example, to calculate the doses to the northern hemisphere from the Chernobyl accident (Anspaugh et al. 1988).

Other than the data contained in the six papers, the only required input data specific to the detonation are an estimate of the external gamma-exposure rate, X˙t, at locations of interest at a known time and an estimate of the initial time of arrival of the fallout, TOA, at each location of interest. The value of X˙tcan be determined by a measurement with a survey meter or by airborne measurements following the event or, as necessary, by values interpolated from a larger dataset. The value of TOA can be determined by observation of exposure rates or by estimation from data on wind velocity. For exposures that might have occurred decades ago, the value of X˙as it existed at the time of deposition can sometimes be inferred from contemporary analyses of soil samples for 137Cs and 239 + 240Pu and the ratio of 240Pu-to-239Pu (Beck and Krey 1983).

There are two methods that can be used for the calculation of internal dose from the ingestion of contaminated foodstuffs. The first was used in the US Department of Energy’s (DOE) Off-Site Radiation Exposure Review Project (ORERP) (Whicker and Kirchner 1987; Church et al. 1990) and later used in a summary form for the Department of Health and Human Services’ report to Congress on the feasibility of a study of the health consequences of nuclear weapons tests (DHHS 2005). The second method is more traditional and depends upon consideration of individual food pathways, and it uses analytical solutions of time-dependent exposure-assessment models. It also accounts for a more sophisticated analysis of radionuclide mix in the total deposition density as a debris cloud travels downwind.

The summarized version of the ORERP calculations, in terms of Bq intake per Bq m−2 on the ground, as presented here, is by far the simpler of the two to implement, so it is presented as an approach when a simple strategy, or one that can be more rapidly applied, is appropriate. The ORERP method was developed with attention to distances of several hundred kilometers from the site of detonation. In contrast, the traditional approach is useful for moderately close-in distances downwind, particularly for locations close to the axis of the fallout pattern, with corrections for fractionation of radionuclides as specified in Beck et al. (2022).

METHODS: DOSE FROM THE INGESTION OF CONTAMINATED FOODS—ORERP METHOD (SYNTHESIS OF COMPLEX PROCESSES)

Basic equation for the calculation of dose from ingestion

The most basic and simple equation (Ng et al. 1990; Whicker et al. 1996) for the calculation of dose from the ingestion of foodstuffs following a nuclear explosion is

Di=X˙12×DDiTOA×Ii×DCi

where

Di = absorbed organ dose or effective dose from radionuclide i for the age group considered (Gy or Sv);

X˙12 = exposure rate at 12 h post detonation (H + 12) (mR h−1);8

DDi(TOA) = deposition density of radionuclide i at time of arrival (TOA) per unit exposure rate normalized to 1.0 mR h−1 at H + 12 (Bq m−2 per mR h−1);

Ii = time integrated intake of radionuclide i per unit deposition (Bq per Bq m−2);9 and

DCi = absorbed organ or effective dose coefficient for radionuclide i for ingestion for the age group considered (Gy Bq−1 or Sv Bq−1).

Exposure rate at H + 12, (12)

As mentioned in Simon et al. (2022), a key contribution of Knapp (1963) was the normalization of the content of radioiodine in milk (or infant thyroids) to external gamma-exposure rate. A major step in the ORERP study was to develop a normalization to external gamma-exposure rate of deposition density for up to 177 radionuclides. Because the exposure rate following a nuclear detonation changes rapidly with time, it is more convenient to produce these normalized values of exposure rate referenced to a single point in time. The time chosen for this normalization point has traditionally been 12 h post detonation (H + 12), and the exposure rate at H + 12 is referred to as X˙ (12). If the exposure rate is measured at some other time, the first step is to calculate what the exposure rate would have been at H + 12. It has been shown (Hicks 1982; Henderson 1991) that the rapidly changing X˙ (t) can be approximated by a summation of 11 (Hicks) or 10 (Henderson) exponential functions. For this general methodology, we use data from shot Tesla, a 7-kt device detonated on 1 March 1955 on a 91-m tower at the Nevada Test Site. The method of calculating X˙ (12) from the value of X˙(t) measured at some other time is given in Beck et al. (2022), wherein are given in their table 310 the parameters of Henderson’s 10 exponential functions as fit to calculated exposure-rate data for shot Tesla. The parameters of the 10 exponential functions have been normalized so that the summation of the 10 functions returns the value of 1.00 mR h−1 for time equal to 12 h. If, for example, there is a measured value of X˙(30) = 5 mR h−1, the first step to infer the value of X˙ (12) is to calculate the sum of the 10 exponentials at time equal to 30 h. That value is 0.342 mR h−1. The value of X˙ (12) at that location is then calculated as follows:

X˙12=50.342×1mRh=14.6mRh.

Deposition density per unit exposure rate normalized to 1 mR h−1 at H + 12, DDi(TOA)'

As explained in Simon et al. (2022) and Beck et al. (2022), tables of deposition density normalized to 1 mR h−1 at H + 12 have been produced for up to 177 radionuclides by Hicks (1981, 1982) for every atmospheric test at the Nevada Test Site (NTS); values have also been calculated for the Trinity event (Hicks 1985) and selected detonations conducted in the Pacific (Hicks 1984). The data from NTS are discussed here because of their inherent value to estimations of internal dose that might need to be made in the future.

Excerpts of the Hicks tables for shot Tesla are shown in Tables 1a–c11 for 19 selected radionuclides;12 values in Table 1a are for time periods from 0 h to 21 h post detonation, from 0 d to 300 d in Table 1b, and for 0 y to 50 y in Table 1c. Values shown in the tables derived by Hicks for shot Tesla were calculated with consideration of fractionation. An important goal of the ORERP was the calculations of dose to persons living at downwind distances of >150 km from the Nevada Test Site. Experimental data had shown that at such distances, the presence of volatile radionuclides was enhanced. Hicks (1982) compensated for this process by dropping out half of the activity of the refractory elements at these distances, thus leading to an activity ratio of R/V = 0.5, where R indicates the activity of refractory elements and V the activity of volatile elements. This concept of fractionation of nuclear debris is discussed extensively in appendix A of Beck et al. (2022) and will be considered later in this paper.

Table 1a - Excerpted values from Hicks (1981 Part 5) of normalized deposition density, DDi', for important dose-producing radionuclides from shot Tesla. Original values are in units of μCi m−2. Values are for 0 to 21 h post detonation and are in units of Bq m−2 normalized to 1 mR h−1 at H+12. The designation “+P” indicates that one or more progeny radionuclides are included in the dose calculation.
Nuclide 0 1 h 2 h 3 h 4 h 6 h 9 h 12 h 15 h 18 h 21 h
89Sr 8.14×10−2 2.86×103 3.05×103 3.05×103 3.05×103 3.05×103 3.05×103 3.04×103 3.04×103 3.03×103 3.03×103
90Sr+P 1.59×10−1 1.64×101 1.64×101 1.64×101 1.64×101 1.64×101 1.64×101 1.64×101 1.64×101 1.64×101 1.64×101
91Sr+P 2.06×104 3.85×105 3.57×105 3.33×105 3.10×105 2.68×105 2.16×105 1.75×105 1.41×105 1.13×105 9.14×104
97Zr+P 5.33×104 2.32×105 2.22×105 2.14×105 2.05×105 1.89×105 1.67×105 1.48×105 1.31×105 1.16×105 1.03×105
99Mo+P 1.82×102 7.51×104 7.40×104 7.33×104 7.25×104 7.10×104 6.92×104 6.70×104 6.48×104 6.29×104 6.11×104
103Ru+P 5.03 1.17×104 1.17×104 1.17×104 1.17×104 1.16×104 1.16×104 1.16×104 1.16×104 1.15×104 1.15×104
106Ru+P 4.51×101 8.58×102 8.58×102 8.58×102 8.58×102 8.58×102 8.58×102 8.58×102 8.58×102 8.58×102 8.58×102
105Rh 5.14×10−4 3.36×104 6.25×104 8.62×104 1.05×105 1.36×105 1.62×105 1.74×105 1.78×105 1.76×105 1.72×105
132Te+P 4.14×104 1.01×105 9.99×104 9.92×104 9.81×104 9.66×104 9.40×104 9.14×104 8.92×104 8.66×104 8.44×104
131I 6.03×102 2.09×104 3.07×104 3.37×104 3.43×104 3.46×104 3.46×104 3.43×104 3.43×104 3.40×104 3.40×104
133I 4.22×104 4.55×105 4.92×105 4.92×105 4.81×105 4.59×105 4.14×105 3.77×105 3.39×105 3.09×105 2.79×105
135I 7.14×105 1.26×106 1.14×106 1.02×106 9.25×105 7.51×105 5.51×105 4.03×105 2.96×105 2.18×105 1.59×105
136Cs 7.66×102 7.66×102 7.62×102 7.62×102 7.59×102 7.55×102 7.51×102 7.47×102 7.40×102 7.36×102 7.33×102
137Cs+P 3.69 3.96×101 3.96×101 3.96×101 3.96×101 3.96×101 3.96×101 3.96×101 3.96×101 3.96×101 3.96×101
140Ba+P 3.77×103 3.96×104 2.35×104 2.33×104 2.33×104 2.32×104 2.32×104 2.30×104 2.28×104 2.26×104 2.25×104
143Ce+P 1.58×103 1.00×105 1.04×105 1.01×105 9.95×104 9.58×104 8.99×104 8.44×104 7.92×104 7.44×104 6.99×104
144Ce+P 5.96×101 4.26×102 4.26×102 4.26×102 4.26×102 4.26×102 4.26×102 4.26×102 4.26×102 4.26×102 4.26×102
147Nd+P 3.57×10−1 6.73×103 6.92×103 6.88×103 6.88×103 6.85×103 6.81×103 6.73×103 6.70×103 6.62×103 6.59×103
239Np+P 2.37×102 3.96×105 4.59×105 4.66×105 4.63×105 4.51×105 4.33×105 4.18×105 4.03×105 3.89×105 3.74×105

Table 1b - Excerpted values from Hicks (1981 Part 5) of normalized deposition density, DDi', for important dose-producing radionuclides from shot Tesla. Original values are in units of μCi m−2. Values are for 0 to 300 d post detonation and are in units of Bq m−2 normalized to 1 mR h−1 at H+12. The designation “+P” indicates that one or more progeny radionuclides are included in the dose calculation.
Nuclide 0 1 d 2 d 5 d 10 d 20 d 30 d 50 d 100 d 200 d 300 d
89Sr 8.14×10−2 2.44×103 2.41×103 2.31×103 2.17×103 1.89×103 1.66×103 1.28×103 6.51×102 1.72×102 4.51×101
90Sr+P 1.59×10−1 1.64×101 1.64×101 1.64×101 1.64×101 1.64×101 1.64×101 1.64×101 1.62×101 1.62×101 1.61×101
91Sr+P 2.06×104 7.36×104 1.39×104 7.59×101 1.39×10−2 4.59×10−10 1.59×10−17 1.81×10−32 0 0 0
97Zr+P 5.33×104 9.10×104 3.42×104 1.81×103 1.36×101 7.66×10−4 4.29×10-8 1.36×10−16 7.66×10−38 0 0
99Mo+P 1.85×102 5.92×104 4.63×104 2.19×104 6.33×103 5.29×102 4.40×101 3.07×10−1 1.25×10−6 2.06×10−17 3.39×10−28
103Ru 5.03 1.15×104 1.13×104 1.07×104 9.81×103 8.25×103 6.92×103 4.88×103 2.03×103 3.52×102 6.14×101
106Ru+P 4.51×101 8.58×102 8.55×102 8.51×102 8.44×102 8.29×102 8.10×102 7.81×102 7.10×102 5.88×102 4.88×102
105Rh 5.14×10−4 1.65×105 1.08×105 2.68×104 2.65×103 2.57×101 2.50×10−1 2.36×10−5 2.05×10−15 1.54×10−35 1.15×10−55
132Te+P 4.14×104 8.21×104 6.66×104 3.50×104 1.21×104 1.43×103 1.69×102 2.38 5.55×10−5 3.05×10−14 1.66×10−23
131I 6.03×102 3.25×104 3.07×104 2.47×104 1.62×104 6.85×103 2.90×103 5.18×102 6.99 1.28×10−3 2.32×10−7
133I 4.22×104 2.35×105 1.06×105 9.84×103 1.88×102 6.81×10−2 2.47×10−5 3.26×10−12 2.05×10−29 0 0
135I 7.14×105 3.7×104 9.73×103 5.66 2.30×10−5 3.81×10−16 6.25×10−27 1.70×10−48 0 0 0
136Cs 7.66×102 7.25×102 6.88×102 5.88×102 4.51×102 2.64×102 1.55×102 5.33×101 3.70 1.79×10−2 8.66×10−5
137Cs+P 3.69 3.96×101 3.96×101 3.96×101 3.96×101 3.96×101 3.96×101 3.96×101 3.96×101 3.92×101 3.92×101
140Ba+P 3.77×103 2.23×104 2.12×104 1.79×104 1.37×104 7.96×103 4.63×103 1.57×103 1.05×102 4.66×10−1 2.06×10−3
143Ce+P 1.58×103 6.48×104 3.92×104 8.62×103 6.96×102 4.48 2.90×10−2 1.22×10−6 1.37×10−17 0 0
144Ce+P 5.96×101 4.26×102 4.26×102 4.22×102 4.14×102 4.07×102 3.96×102 3.77×102 3.34×102 2.61×102 2.05×102
147Nd+P 3.57×10−1 5.99×103 5.62×103 4.66×102 3.42×103 1.84×103 9.81×102 2.82×102 1.24×101 2.41×10−2 4.66×10−5
239Np+P 2.37×102 3.61×105 2.69×105 1.11×105 2.55×104 1.33×103 6.96×101 1.91×10−1 7.51×10−8 1.79×10−17 1.79×10−17

Table 1c - Excerpted values from Hicks (1981 Part 5) of normalized deposition density, DDi', for important dose-producing radionuclides from shot Tesla. Original values are in units of μCi m−2. Values are for 0 to 50 y post detonation and are in units of Bq m−2 normalized to 1 mR h−1 at H+12. The designation “+P” indicates that one or more progeny radionuclides that are included in the dose calculation.
Nuclide 0 1 y 1.5 y 2 y 3.5 y 5 y 7 y 10 y 20 y 35 y 50 y
89Sr 8.14×10−2 1.91×101 1.67 1.47×10−1 9.88×10−5 6.66×10−8 3.92×10−12 1.79×10−18 1.30×10−39 0 0
90Sr+P 1.59×10−1 1.59×101 1.58×101 1.56×101 1.51×101 1.45×101 1.38×101 3.46×101 9.99 6.92 4.77
103Ru 5.03 1.96 8.03×10−1 3.30×10−2 2.25×10−6 1.54×10−10 4.33×10−16 4.76×10−25 0 0 0
106Ru+P 4.51×101 4.29×102 3.05×102 2.16×102 7.70×101 2.73×101 6.88 8.70×10−1 8.77×10−4 2.82×10−8 9.06×10−13
137Cs+P 3.69 3.88×101 3.85×101 3.81×101 3.66×101 35.3×101 3.38×101 3.16×101 2.49×101 1.77×101 1.25×101
144Ce+P 5.96×101 1.75×102 1.12×102 7.18×101 1.88×101 4.96 8.33×10−1 5.74×10−2 9.22×10−6 1.21×10−11 1.89×10−17

Many of the radionuclides produced in a nuclear detonation do not contribute substantially to internal dose from ingestion. Some have very short half-lives; others, like the isotopes of noble gases, do not deposit on the ground. Thus, while the original tables of Hicks contain up to 177 radionuclides, only 19 are shown in Tables 1a and 1b. This shortened list has resulted from attempts to analyze all radionuclides and determine which are significant contributors to internal dose via ingestion. The 19 radionuclides in Table 1a are those chosen by Ng et al. (1990) based on various screening models including that of NCRP (1984); those 19 radionuclides were found to account for >90% of the internal dose to organs of the gastrointestinal tract, >99% of the internal dose to the thyroid, and > 90% of the internal dose to other organs. Once the TOA of the cloud and a measurement of external gamma-exposure rate at some time and location are known, the main part of the Hicks tables can be used to determine the deposition density of each of 177 radionuclides. From the previous example, a hypothetical exposure rate of 5 mR h−1 at H + 30 and an exposure rate at H + 12 of 14.6 mR h−1 was inferred. A further assumption is made that the TOA was H + 18 h. Then, the values of the deposition density at TOA are found by multiplying the results in Table 1a under “18 h” by the value of external gamma-exposure rate at H + 12. which was determined to be 14.6 mR h−1. For example, the deposition density of 131I is equal to the product of 14.6 mR h−1 at H + 12 and 3.40 × 104 Bq m−2 per mR h−1 at H + 12 or 4.96 × 105 Bq m−2. A similar value for 137Cs is 14.6 mR h−1 at H + 12 times 39.6 Bq m−2 per mR h−1 at H + 12 = 578 Bq m−2. Values for other radionuclides can be similarly computed.

Some of the radionuclides shown in Tables 1a and 1b have half-lives of a few days or less, so with time, the relative importance of the various radionuclides changes; values of the half-lives of the 19 radionuclides and for 239Pu are shown in Table 2.

Table 2 - Values of integrated intake by adult males of 20 radionuclides from all foods per unit fallout deposition according to various fallout dates. Units are Bq per Bq m−2. From Whicker and Kirchner (1987). Dates were chosen to correspond to the events indicated in parentheses. Annie, Simon, and Harry took place in 1953; Tesla occurred in 1955; and Priscilla, Kepler, Smoky, and Morgan took place in 1957.
Radio-nuclide Half-life 1 March (Tesla) 17 March (Annie) 25 April (Simon) 19 May (Harry) 24 June (Priscilla) 24 July (Kepler) 31 August (Smoky) 7 October (Morgan)
89Sr 50.6 d 5.8×10−2 6.6×10−2 1.1×10−1 1.3×10−1 2.4×10−1 1.0×10−1 6.5×10−2 6.1×10−2
90Sr 28.9 y 2.5×10−1 2.4×10−1 6.0×10−1 6.0×10−1 1.1 2.0×10−1 1.6×10−1 1.8×10−1
91Sr 9.65 h 4.5×10−5 1.6×10−5 4.0×10−5 6.9×10−5 1.1×10−4 1.2×10−4 6.0×10−5 3.0×10−5
97Zr 16.7 h 2.6×10−4 9.1×10−5 2.3×10−4 3.7×10−4 5.8×10−4 6.0×10−4 3.0×10−4 1.5×10−4
99Mo 66.0 h 3.7×10−3 1.9×10−3 3.9×10−3 5.5×10−3 9.2×10−3 1.0×10−2 5.3×10−3 3.0×10−3
103Ru 39.2 d 6.1×10−2 7.4×10−2 8.2×10−2 9.0×10−2 1.6×10−1 5.9×10−2 5.2×10−2 6.9×10−2
106Ru 372 d 1.5×10−1 1.8×10−1 2.6×10−1 3.1×10−1 6.8×10−1 1.4×10−1 1.6×10−1 2.3×10−1
105Rh 35.4 h 1.3×10−3 4.8×10−4 1.2×10−3 1.7×10−3 2.7×10−3 2.8×10−3 1.4×10−3 7.2×10−4
132Te 3.20 d 4.5×10−3 2.4×10−3 4.6×10−3 5.7×10−3 9.0×10−3 8.4×10−3 4.5×10−3 2.6×10−3
131I 8.03 d 2.1×10−2 2.0×10−2 3.3×10−2 4.9×10−2 9.1×10−2 1.0×10−1 5.5×10−2 3.7×10−2
133I 20.8 h 4.2×10−4 1.5×10−4 3.7×10−4 1.1×10−3 2.0×10−3 2.9×10−3 1.5×10−3 7.5×10−4
135I 6.58 h 7.8×10−6 2.6×10−6 6.9×10−6 1.5×10−5 2.6×10−5 3.4×10−5 1.8×10−5 8.7×10−6
136Cs 13.0 d 1.0×10−1 1.1×10−1 1.2×10−1 1.4×10−1 1.9×10−1 1.6×10−1 1.1×10−1 1.2×10−1
137Cs 30.1 y 2.0 2.0 3.0 2.6 3.3 1.4 1.6 2.4
140Ba 12.8 d 1.6×10−2 1.6×10−2 2.2×10−2 2.6×10−2 4.5×10−2 2.7×10−2 1.5×10−2 1.0×10−2
143Ce 33.0 h 1.1×10−3 4.2×10−4 1.0×10−3 1.5×10−3 2.4×10−3 2.4×10−3 1.2×10−3 6.2×10−4
144Ce 285 d 3.7×10−2 5.5×10−2 1.5×10−1 2.0×10−1 5.3×10-1 5.5×10−2 4.2×10−2 4.3×10−2
147Nd 11.0 d 1.3×10−2 1.3×10−2 1.8×10−2 2.0×10−2 3.4×10−2 2.0×10−2 1.2×10−2 7.3×10−3
239Np 2.36 d 2.7×10−3 1.1×10−3 2.6×10−3 3.4×10−3 5.4×10−3 5.2×10−3 2.7×10−2 1.4×10−3
239Pu 24,100 y 4.0×10−2 6.0×10−2 2.1×10−1 2.9×10−1 8.1×10−1 6.0×10−2 4.7×10−2 4.9×10−2

Time integrated intake per unit deposition, Ii

This aggregated parameter has been defined and tabulated by Whicker and Kirchner (1987); their calculated values for adult males for 20 radionuclides are shown in Table 2.13 Results are given for eight different fallout dates that correspond to specific nuclear detonations. Values for other fallout dates can be interpolated between the dates of the tests presented in Table 2 or averaged within a season of the year. Doses during the coldest months of the year would be overestimated by use of the values in Table 2, as many pathways would not be present; also, current diets differ from those in the 1950s in the sense that there is less reliance on locally-produced foods. Variation of the time-integrated intake with fallout date depends on, among other things, whether milk cows are on pasture and whether leafy green vegetables are available for harvest.14 Other parameters, such as weather and the productivity of pasture grasses, are important. The integration period for a given radionuclide is the same for all fallout dates and corresponds to a time that accounts for >95% of infinite time-integrated values (Whicker and Kirchner 1987).15

Given a unit value of deposition density of a radionuclide on the ground, the value of Ii is the total intake of that radionuclide from all pathways of ingestion. The pathways considered for the local area of the fallout include:

  • Consumption of leafy vegetables contaminated directly by fallout and by foliar absorption;
  • Consumption of milk and milk products produced by animals grazing on forage directly contaminated by fallout;
  • Consumption of milk and milk products produced by the grazing animal’s incidental ingestion of soil directly contaminated by fallout;
  • Consumption of meat from animals grazing on forage directly contaminated by fallout;
  • Consumption of leafy vegetables, milk, and meat due to recontamination by the processes of resuspension and rain-splash on leafy vegetables or animal forage;
  • Consumption of food products contaminated for long time periods by the movement of radionuclides from soil to vegetation by soil-to-root transfer; and
  • Consumption of eggs contaminated by chickens consuming contaminated food.

Discrete pathways modeled include soil tillage, crop harvest, and livestock-diet changes due to the availability of pasture grass. Continuous processes modeled include resuspension and rain splash, weathering of radionuclides from plants, percolation and leaching of radionuclides into the soil, uptake of radionuclides by roots, absorption of surficial radionuclides by plant tissues, dilution of activity in plants by plant growth, and radioactive decay (Whicker and Kirchner 1987).

These simulations were performed with the use of the PATHWAY model. The details of the model are described in Whicker and Kirchner (1987), Whicker et al. (1990, 1996), and Kirchner et al. (1996). The goal of this present paper is not to describe the complex details of the PATHWAY model but to offer its results as part of a rapid method for forecasting internal radiation dose in the event of an unexpected detonation of a nuclear fission device. One important caveat to using these values is, of course, that the environment of interest should be similar to the environment considered by PATHWAY, that being the temperate zone, and that food-production and preparation customs are similar to those described by Whicker and Kircher for the purposes of the ORERP study. These requirements could limit the applicability of the PATHWAY values in tropical or arctic zones and in some countries, e.g., in Asia, Eastern Europe, Africa, etc., with considerably different food-production methods.

With use of the previous example of 14.6 mR h−1 at H + 12 and the deposition density for 131I of 3.40 × 104 Bq m−2 per mR h−1 at H + 12, the integrated intake from shot Tesla (as an example) would be 0.021 Bq per Bq m−2, and the total intake would be 1.04 × 104 Bq. This example and the use of Table 2 specify results for adult males.16

It has been shown in many investigations, e.g., Pendleton et al. (1963), Ng et al. (1990), and Simon et al. (2010, 2020), that the organs receiving the larger doses from the ingestion of nuclear debris are the thyroid and the colon. The reason for potentially higher doses to the thyroid is due to the natural affinity of the thyroid gland for iodine. Large doses for the colon reflect the time required for the passage of ingested materials through the human gut and the fact that many fallout radionuclides have low solubility.

The dose to the thyroid is greatly enhanced for infants and young children. Whicker and Kirchner (1987) have considered the relative intakes of 131I, 137Cs, and 90Sr for infants <1 y-old drinking cows’ milk, children aged 1–11 y, children aged 12–18 y, and adults as a function of month of intake. At least for these three radionuclides, the integrated intakes for all four age groups are about the same over most of the season when fresh milk is available from animals consuming fresh pasture. For example, for shot Harry (19 May 1953), the time-integrated intakes of 131I were calculated to be 0.061, 0.054, 0.062, and 0.049 Bq per Bq m−2 for the respective age groups. For 137Cs for the same shot, the integrated intakes were estimated as 2.9, 2.4, 3.7, and 2.6 Bq per Bq m−2, respectively. For 90Sr, the calculated integrated intakes were 0.54, 0.45, 0.81, and 0.60 Bq per Bq m−2, respectively. Based on these results, it is recommended that the values of integrated intakes from Table 2 be used for all age groups.

Absorbed organ or effective dose coefficient for ingestion, DCi

Dose coefficients have been derived by the ICRP (2011) from careful consideration of uptake and metabolism of radionuclides in the human body. The companion paper by Melo et al. (2022) considers how the ICRP values for DCs can be altered to reflect the decreased biological availability expected due to radionuclides being vaporized and becoming volume distributed in larger particles. The ORERP methodology was developed for use in situations far from the detonation site. At such distances, particles larger than 50 μm would be expected to have fallen out, and the more volatile radionuclides would be expected to be on the surfaces of smaller particles. This process is explained in detail in Beck et al. (2022). For application of the ORERP methodology, we propose use of the ICRP (2011) dose coefficients without modification.

Example dose coefficients via ingestion are provided in Tables 3a, 3b, and 3c for a 3-mo-old infant, a 1-y-old child, and an adult.17 In all three cases, dose coefficients are given for effective dose and for absorbed organ dose for the bone surface, colon, kidneys, liver, red bone marrow, stomach wall, and thyroid. These organs, except for stomach wall, were chosen for inclusion because the dose coefficients for absorbed organ doses are at least twice the dose coefficient for effective dose for one or more radionuclides. Dose coefficients for the stomach wall were added to be consistent with other studies.

Table 3a - Committed dose coefficients for a 3-mo-old infant via ingestion (ICRP 2011). The ICRP considers a 3-mo-old infant to represent infants aged 0 to 1 y. Values are in Gy Bq−1 for organs and Sv Bq−1 for effective dose.
Radio-nuclide Bone surface Colon Kidneys Liver Red bone marrow Stomach wall Thyroid Effective
89Sr 1.6×10−7 9.8×10−8 2.9×10−9 2.9×10−9 1.6×10−7 1.1×10−8 2.9×10−9 3.6×10−8
90Sr+P 2.3×10−6 1.2×10−7 1.2×10−8 1.2×10−8 1.5×10−6 1.5×10−8 1.2×10−8 2.3×10−7
91Sr+P 3.2×10−9 2.6×10−8 4.3×10−10 4.4×10−10 3.6×10−9 9.9×10−9 2.5×10−10 5.2×10−9
97Zr+P 5.4×10−10 1.6×10−7 6.7×10−10 7.9×10−10 6.9×10−10 1.4×10−8 9.0×10-11 2.2×10−8
99Mo+P 6.9×10−9 5.1×10−9 2.4×10−8 2.4×10−8 8.4×10−9 8.5×10−9 2.6×10−9 5.5×10-9
103Ru 1.3×10−9 4.3×10−8 1.4×10−9 1.5×10−9 1.2×10−9 3.3×10−9 1.1×10−9 7.1×10−9
106Ru+P 2.3×10−8 5.1×10−7 2.3×10−8 2.3×10−8 2.3×10−8 4.4×10−8 2.3×10−8 8.4×10−8
105Rh 9.3×10−11 3.0×10−8 1.1×10−10 1.1×10−10 8.7×10−11 2.4×10−9 6.6×10−11 4.0×10−9
132Te+P 1.3×10−8 8.4×10−8 5.5×10−9 3.9×10−9 5.7×10−9 7.7×10−9 6.5×10−7 4.8×10−8
131I 6.1×10−10 2.6×10−9 4.3×10−10 4.8×10−10 5.2×10−10 3.5×10−9 3.7×10−6 1.8×10−7
133I 4.0×10−10 1.2×10−9 3.8×10−10 4.0×10−10 3.7×10−10 6.5×10−9 9.6×10−7 4.9×10−8
135I 3.0×10−10 6.2×10−10 3.1×10−10 3.4×10−10 2.7×10−10 5.8×10−9 1.9×10−7 1.0×10−8
136Cs 1.4×10−8 2.0×10−8 1.4×10−8 1.4×10−8 1.2×10−8 1.6×10−8 1.5×10−8 1.5×10−8
137Cs+P 1.9×10−8 3.8×10−8 1.9×10−8 1.9×10−8 1.7×10−8 2.2×10−8 1.9×10−8 2.1×10−8
140Ba+P 1.0×10−7 1.4×10−7 6.8×10−9 4.9×10−9 7.8×10−8 9.5×10−9 3.7×10−9 3.2×10−8
143Ce+P 2.7×10−10 9.4×10−8 1.8×10−10 2.6×10−10 2.9×10−10 6.7×10−9 1.8×10−11 1.2×10−8
144Ce+P 3.5×10−8 4.8×10−7 9.1×10−10 1.2×10−8 4.4×10−8 1.5×10−8 8.5×10−10 6.6×10−8
147Nd+P 7.9×10−10 9.3×10−8 1.4×10−10 8.9×10−10 4.8×10−10 4.3×10−9 1.2×10−11 1.2×10−8
239Np+P 4.7×10−10 6.8×10−8 1.4×10−10 1.6×10−10 1.4×10−10 4.1×10−9 1.3×10−11 8.9×10−9

Table 3b - Committed dose coefficients via ingestion for a 1-y-old infant, from ICRP (2011). The ICRP considers a 1-y-old infant to represent infants aged >1 to 2 y. Values are in Gy Bq−1 for organs and Sv Bq−1 for effective dose.
Radio-nuclide Bone surface Colon Kidneys Liver Red bone marrow Stomach wall Thyroid Effective
89Sr 4.9×10−8 9.2×10−8 1.7×10−9 1.7×10−9 3.7×10−8 6.3×10−9 1.7×10−9 1.8×10−8
90Sr+P 7.3×10−7 8.9×10−8 5.5×10−9 5.5×10−9 4.2×10−7 7.1×10−9 5.5×10−9 7.3×10−8
91Sr+P 1.1×10−9 2.4×10−8 3.0×10−10 3.2×10−10 9.8×10−10 5.5×10−9 1.5×10−10 4.0×10−9
97Zr+P 3.3×10−10 1.1×10−7 4.9×10−10 5.5×10−10 3.8×10−10 7.9×10−9 4.6×10−11 1.4×10−8
99Mo+P 5.1×10−9 3.3×10−9 1.5×10−8 1.6×10−8 5.0×10−9 4.9×10−9 1.7×10−9 3.5×10−9
103Ru 5.8×10−10 2.9×10−8 6.6×10−10 7.0×10−10 5.6×10−10 1.7×10−9 4.1×10−10 4.6×10−9
106Ru+P 8.8×10−9 3.3×10−7 8.8×10−9 8.8×10−9 8.7×10−9 2.0×10−8 8.7×10−9 4.9×10−8
105Rh 4.3×10−11 2.0×10−8 5.3×10−11 5.9×10−11 4.2×10−11 1.3×10−9 2.2×10−11 2.7×10−9
132Te+P 5.5×10−9 8.5×10−8 2.4×10−9 2.0×10−9 2.3×10−9 4.4×10−9 3.2×10−7 3.0×10−8
131I 4.4×10−10 1.5×10−9 2.9×10−10 3.3×10−10 3.7×10−10 2.0×10−9 3.6×10−6 1.8×10−7
133I 2.6×10−10 7.8×10−10 2.5×10−10 2.6×10−10 2.5×10−10 3.6×10−9 8.6×10−7 4.4×10−8
135I 2.0×10−10 4.1×10−10 2.1×10−10 2.3×10−10 1.8×10−10 3.3×10−9 1.7×10−7 8.9×10−9
136Cs 9.2×10−9 1.3×10−8 9.2×10−9 9.3×10−9 7.7×10−9 9.9×10−9 9.6×10−9 9.5×10−9
137Cs+P 1.1×10−8 2.3×10−8 1.1×10−8 1.1×10−8 9.9×10−9 1.2×10−8 1.1×10−8 1.2×10−8
140Ba+P 2.0×10−8 1.2×10−7 1.7×10−9 1.4×10−9 1.2×10−8 4.3×10−9 8.3×10−10 1.8×10−8
143Ce+P 1.3×10−10 6.1×10−8 1.3×10−10 1.6×10−10 9.2×10−11 3.7×10−9 8.3×10−12 8.0×10−9
144Ce+P 2.3×10−9 3.1×10−7 1.0×10−10 2.9×10−9 2.4×10−9 7.6×10−9 6.8×10−11 3.9×10−8
147Nd+P 1.8×10−10 6.0×10−8 9.6×10−11 1.6×10−10 9.4×10−11 2.4×10−9 5.7×10−12 7.8×10−9
239Np+P 1.3×10−10 4.4×10−8 9.3×10−11 1.0×10−10 6.6×10−11 2.3×10−9 5.4×10−12 5.7×10−9

Table 3c - Committed dose coefficients via ingestion for an adult. From ICRP (2011). The ICRP considers adults to include individuals >17 y old. Values are in Gy Bq−1 for organs and Sv Bq−1 for effective dose.
Radio-nuclide Bone surface Colon Kidneys Liver Red bone marrow Stomach wall Thyroid Effective
89Sr 5.9×10−9 1.4×10−8 2.0×10−10 2.0×10−10 4.8×10−9 8.7×10−10 2.0×10−10 2.6×10−9
90Sr+P 4.1×10−7 1.3×10−8 6.6×10−10 6.6×10−10 1.8×10−7 9.0×10−10 6.6×10−10 2.8×10−8
91Sr+P 1.4×10−10 3.8×10−9 6.1×10−11 4.9×10−11 1.6×10−10 8.5×10−10 2.0×10−11 6.5×10−10
97Zr+P 6.3×10−11 1.5×10−8 1.1×10−10 7.9×10−11 1.3×10−10 1.2×10−9 3.9×10−12 2.1×10−9
99Mo+P 1.0×10−9 4.9×10−10 3.1×10−9 2.8×10−9 6.1×10−10 7.4×10−10 2.5×10−10 6.0×10−10
103Ru 1.1×10−10 4.3×10−9 1.4×10−10 1.1×10−10 1.6×10−10 3.1×10−10 6.7×10−11 7.3×10−10
106Ru+P 1.5×10−9 4.5×10−8 1.5×10−9 1.5×10−9 1.5×10−9 3.1×10−9 1.4×10−9 7.0×10−9
105Rh 7.7×10−12 2.7×10−9 1.1×10−11 8.2×10−12 1.2×10−11 1.9×10−10 3.0×10−12 3.7×10−10
132Te+P 1.1×10−9 1.3×10−8 4.9×10−10 3.2×10−10 5.3×10−10 7.6×10−10 3.1×10−8 3.8×10−9
131I 1.3×10−10 1.2×10−10 4.6×10−11 4.9×10−11 1.0×10−10 3.0×10−10 4.3×10−7 2.2×10−8
133I 4.9×10−11 1.1×10−10 4.1×10−11 4.0×10−11 4.7×10−11 5.5×10−10 8.2×10−8 4.3×10−9
135I 4.1×10−11 7.3×10−11 4.2×10−11 3.9×10−11 4.0×10−11 5.4×10−10 1.6×10−8 9.3×10−10
136Cs 3.2×10−9 3.4×10−9 3.0×10−9 3.1×10−9 2.8×10−9 3.2×10−9 2.9×10−9 3.0×10−9
137Cs+P 1.4×10−8 1.5×10−8 1.3×10−8 1.3×10−8 1.3×10−8 1.3×10−8 1.3×10−8 1.3×10−8
140Ba+P 1.6×10−9 1.7×10−8 2.3×10−10 1.5×10−10 1.2×10−9 6.3×10−10 8.7×10−11 2.6×10−9
143Ce+P 2.1×10−11 8.3×10−9 2.8×10−11 2.2×10−11 3.5×10−11 5.6×10−10 3.6×10−13 1.1×10−9
144Ce+P 3.3×10−10 4.2×10−8 2.0×10−11 9.6×10-10 1.9×10−10 1.1×10−9 1.2×10−11 5.2×10−9
147Nd+P 3.3×10−11 8.2×10−9 2.0×10−11 2.2×10−11 3.1×10−11 3.6×10−10 2.2×10−13 1.1×10−9
239Np+P 2.5×10−11 6.0×10−9 2.1×10−11 1.4×10−11 2.6×10−11 3.4×10−10 1.5×10−13 8.0×10−10

The coefficients for effective dose shown in Tables 3a, 3b, 3c were based on the tissue-weighting factors specified in ICRP (1991). Modified tissue-weighting factors have been published by the ICRP (2007), and correspondingly modified and updated dose coefficients for ingestion are under revision (ICRP 2015)18 but are not yet available.

As an example of the method, the implementation of Eqn (1) for the absorbed dose to the thyroid from intake of 131I from all ingestion pathways for an adult male for shot Tesla detonated on 1 March 1955 and for the hypothetical measurement of 5 mR h−1 at H + 30 and TOA at H + 18 h is

D131=50.342×1.0mRh1@H+12×3.40×104Bqm2mRh1@H+12×0.021BqBqm2×4.3×107GyBq=0.0045Gy=4.5mGy.

A similar calculation for a 3-mo-old infant yields a value of 38 mGy. As discussed later in this document, the current tendency in the US is to avoid feeding infants cows’ milk.

Uncertainty

The uncertainty in the individual parameters of Eqn (1) were considered by Ng et al. (1990) and have been subsequently considered in similar dose-reconstruction studies (Simon et al. 2006, 2020). Ng et al. estimated the total uncertainty by assuming a multiplicative dose model with each individual parameter having a unique lognormal distribution to describe its uncertainty. The defining parameters of a lognormal distribution are estimates of the geometric mean (GM) and geometric standard deviation (GSD). Ng et al. estimated that the GSD associated with X˙ (12) was ≥1.4; with DDi(TOA)' 1.25; with Ii 1.7–2.7; and with DCi 1.3–2.2. Later refinements of the ORERP calculations (Kirchner et al. 1996; Whicker et al. 1996) led to estimates of GSD of 1.8 for the dose coefficients for most elements (estimates for cesium and strontium were lower—1.3 to 1.6). Thus, an overall estimate of the geometric standard deviation of the product is

GSD=expln1.42+ln1.252+ln2.22+ln1.82=2.9.

Whicker et al. (1996) estimated the uncertainty in median thyroid doses for unspecified persons living in two downwind communities. Their estimates of geometric standard deviations varied from 1.9 to 2.6. Whicker et al. also considered uncertainty in “total body” doses, which were calculated with the assumption that radionuclides were distributed throughout the entire body and eliminated with an inventory-weighted composite-elimination rate. The geometric standard deviations for that “organ” varied from 1.7 to 2.6. These are similar to estimates found in other studies that have used Monte Carlo error propagation (Simon et al. 2006, 2020).

It is reasonable to assume that the values of X˙ (12), DDi(TOA)', and Ii represent geometric means, but it should be noted that the values of DCi are derived from calculations based on a hypothetical hermaphrodite whose anatomy, physiology, and metabolism are known perfectly. In a previous document (Anspaugh 2005), the values of DCs from ICRP (2011) were considered to be arithmetic means, and values of GMs were calculated based upon GSDs of 1.8 for most elements but 1.3 or 1.4 for 137Cs and 90Sr. Given the uncertainty surrounding whether the ICRP values of DCs are actually arithmetic or geometric means, the election for the ORERP method for this paper is to use the values of DCs as taken directly from the ICRP and to assume that they can be represented as geometric means, GM.

With the assumption that the resulting calculations of dose, D, represent unbiased (not overestimated) geometric means with geometric standard deviations of 2.9, the arithmetic mean, x¯, can be calculated as [Eqns (5) and (6) are taken from Ng et al. (1990)].

lnx¯=lnGM+0.5lnGSD2.

If a hypothetical value of GM is taken to be 10 mGy along with a value of 2.9 for GSD, then the value of x¯ is 18 mGy. The arithmetic standard deviation, σ, is calculated by

σ2=exp2lnGM+lnGSD2×explnGSD21,

and σ for this example is equal to 26 mGy. These values can be scaled according to actual values of geometric means. That σ is larger than x¯ is another indication that the uncertainty in the calculation is large, as evidenced initially by the large value of the GSD.

METHODS: DOSE FROM THE INGESTION OF CONTAMINATED FOODS—TRADITIONAL METHOD OF EXAMINATION OF INDIVIDUAL PROCESSES

The application of this method is more complex but more flexible. Eqn (1) is still valid for the traditional approach, but a modified method is used to calculate DDi', and Ii is no longer treated as an aggregate value. Rather, time-integrated intake values for separate pathways are considered; suggested values for individual parameters for radioecological processes are provided in Thiessen et al. (2022).

Radionuclides of interest

The tabulations of radionuclides presented by Hicks (1981) contain up to 177 radionuclides. There have been several examinations to identify those radionuclides that are significant to dose formation. Those considered by the ORERP have been presented in Tables 1a and 2; those radionuclides were selected primarily because of their contribution to dose via ingestion. The ORERP calculations and the more recent calculations of dose to the residents of New Mexico from the Trinity event (Simon et al. 2020) have been reviewed for the importance of radionuclides via pathways of both ingestion and inhalation. The radionuclides selected for inclusion in this study for the traditional method are listed in table 1 of Simon et al. (2022). There are 23 primary radionuclides and 11 progeny radionuclides of 17 chemical elements.

Deposition on the ground and on vegetation

After the ORERP had been completed in the late 1980s, additional work was conducted to create a joint US–Russian semi-empirical method to calculate doses from the fallout from nuclear weapons tests; this US-Russian methodology is discussed extensively in Beck et al. (2022). Key features of the later methodology are improved consideration of fractionation and of deposition on soil and vegetation as a function of particle size. The ORERP procedure discussed above overemphasized the influence of volatile elements at close-in distances and underemphasized the influence of refractory elements at close-in locations.

According to the later US–Russian methodology, DDi(TOA)' is no longer given as a simple look-up value from Hicks, and the fractional deposition on vegetation becomes a more complex function of R/V and other considerations. According to Beck et al. (2022), the total dry or wet deposition at a location is given by

DDiTOAR/V=Ẋ12×DDi12Ẋ12R/V×expλi×TOA12,

where DDi12X˙12R/V×expλi×TOA12 takes the place of DDi(TOA) in Eqn (1). The Equation for the estimate of the deposition on vegetation is substantially more complicated (from Beck et al. [2022]):

DDiTOAR/Vveg=X˙12×β12X˙12R/V×N50×DDi12β12R/V=0.5×expλi×TOA12×fv,

where β(12) is the deposition density of all beta-emitting radionuclides,

N50=N01.3×N0×lnX˙X˙max

and

N0=11a×expd×tr3=N50axis.

Eqns (7)–(10) and the newly inserted parameters are explained in detail in Beck et al. (2022); the value of fv is discussed extensively below and in Thiessen et al. (2022). In Eqn (10), (1-a) and d are fit parameters; tr is the reduced time of arrival and is equal to TOA tmax−1, where tmax is the estimated time for all particles >50 μm physical diameter to be deposited. Beck et al. (2022) provide an 11-step set of instructions on how to implement this model (Eqns 8−10) and provide an example implementation in their appendix E.

Deposition and retention of small particle fallout on vegetation

A major starting point for the calculation of disaggregated values of intake by consumption of contaminated food is the estimation of the fraction of fallout that is retained on vegetation. The implementation of Eqn (8) provides that initial value in terms of deposition of particles of <50 μm physical diameter per unit area. The parameter fv describes the fraction that is retained on vegetation. An important observation by Chamberlain (1970) was of an empirical relationship between the fractional interception, fv, of particles, solutions, or vapors by vegetation and the dry biomass of the vegetation, B (kg m−2):

1fv=eμB,

where μ is an interception parameter with units of m2kg−1. Eqn (11) is based on four experiments analyzed by Chamberlain:

  1. Carrier free 89Sr in solution was applied to eight plots of grassland in a fine spray (Milbourn and Taylor 1965); the overall value of fv was 0.23, and the observed value of μ was 3.33 ± 0.56 m2kg−1.
  2. Solutions of 85Sr, 51Cr, and 210Pb and 51Cr as a suspension of 1-μm particles were applied to old grassland during two experiments in summer and two in winter (Chadwick and Chamberlain 1970); the observed value of μ was 2.30 ± 0.08 m2kg−1.
  3. Lycopodium spores (approximately 30 μm in diameter) tagged with 131I were dispersed upwind of permanent grass (Chamberlain 1967); according to fig. 1 of Chamberlain (1970), about 40 measurements were performed; μ was determined to be 3.08 ± 0.15 m2kg−1.
  4. Elemental 131I vapor was dispersed over grassland (Chamberlain and Chadwick 1966); about 30 measurements were reported with μ = 2.78 ± 0.14 m2kg−1.

These important observations of Chamberlain (1970) are frequently cited as applying only to the process of dry deposition of particles, although as noted above there was only one experiment with dry particles. Two experiments were with droplets, and one experiment was with iodine vapor.

Values of μ in the range of 2.30 to 3.33 m2kg−1 were not found to be applicable to dry fallout from nuclear weapons tests at the Nevada Test Site (NTS) for native desert vegetation or for pasture-type vegetation (Lindberg et al. 1954, 1959; Miller 1963; Romney et al. 1963). Based on data derived from measurements on pasture-type vegetation by Lindberg et al. (1959) and Romney et al. (1963), 19 a more appropriate value of 0.39 m2kg−1 was derived by Whicker and Kirchner (1987) for dry fallout. The smaller value of μ observed following the tests of nuclear weapons is most likely due to larger sizes of particles in NTS fallout (Cederwall et al. 1990) as compared to the small droplets and particles or vapors examined by Chamberlain. Almost all measurements of the retention of fallout downwind of the NTS discussed in this paragraph were separated according to total fallout and fallout associated with particles of physical diameter < 44 μm. The data are unequivocal in demonstrating that particles with physical diameters <44 μm were more readily retained by vegetation—often by a factor of 10 or even more at distances up to 77 km. This is consistent with the assumption in Beck et al. (2022) that only particles with physical diameter < 50 μm are retained by vegetation.

The actual values measured by Lindberg et al. and Romney et al. were of concentration, Cv, (Bq kg−1) in vegetation and of deposition density, DD (Bq m−2). As shown in Anspaugh et al. (2002), fv = Cv × B × DD−1, if DD is measured in such a way that it reflects total deposition.

Equation (11) above can be approximated by expanding the exponential function:

1fv=1μB+μB22!μB33!+μB44!.

If μB is <1, then μ is approximately fv B−1 or Cv DD−1. Values of (fv B−1) have frequently been referred to as the “mass interception factor.” The values of fv and B are not independent; if B increases, then fv will also increase. The combined value of (fv B−1) is more stable, as is the value of μ.

Simon (1990) examined the data on Cv DD−1 for pasture type vegetation and derived the following empirical relationships for Cv DD−1 as functions of distance, x in km, and TOA in h:

μfv,dryB=CvDD=7.02×104×x1.127r2=0.63

and

μfv,dryB=CvDD=0.0417×TOA1.063r2=0.61

The notation fv,dry indicates that the deposition of fallout on vegetation of interest in Eqns (13) and (14) is occurring during dry conditions as opposed to rainfall. A reasonable default value of μ is 3.0 m2kg−1, which is the approximate value for very small particles and gases. Simon (1990) stated a preference for Eqn (14) because x had been determined as a straight-line distance without consideration of plume meandering.

Thiessen et al. (2022) have provided an extensive discussion of the fraction of fallout retained by vegetation under wet conditions of rainout (radioactive materials swept up into a cloud and absorbed into future rain) and washout (rain falling through a cloud of radioactive materials). The approach discussed by Thiessen et al. and shown in their eqn (9) is complicated and depends upon five factors: leaf-area index, water-storage capacity of vegetation, total amount of rainfall, a constant dependent upon the type of radionuclide, and a constant depending upon the type of vegetation and ambient conditions. It is not likely that these factors will be known for the intended use of the model proposed here.

Whicker and Kirchner (1987) simply assumed that the retention by vegetation would be the same under dry and wet conditions:

fv,dryB=fv,wetB=0.39m2kg.

However, retention may be higher for wet deposition or for deposition onto wet surfaces (Thiessen et al. 2022). Anspaugh (1987) examined 20 sets of experimental data on measurements of fv,wet for grass and alfalfa; 11 sets included data on values of B that ranged from 0.02 to 0.34 kg m−2. Some values were reported as negative. An average value of fv,wet for acute exposures (one set of data with strongly negative values was excluded) was 0.47.

Recommendation for fractional retention of fallout by vegetation

It is important to acknowledge that values of (fv,dry B−1) vary substantially with distance from the point of detonation, especially if concern is directed to close-in distances or small values of TOA. Implementation of the method proposed by Beck et al. (2022) is designed to deal with this variation. Their major assumption, which is consistent with experimental data, is that only particles of physical diameter < 50 μm are retained by vegetation. The remaining question is what value to use for the mass-interception factor for submicron up to 50-μm particles. Data on the interception of particles over this broad range are limited and variable (Pröhl and Hoffman 1996; Pinder et al. 1988; Pröhl 2009), but a value for (fv,dry B−1) = 3 m2kg−1 is consistent with much of the data and is recommended as a default value. This value may also be used as a default value for (fv,wet B−1) for an initial assessment; however, (fv,wet B−1) could in some cases exceed 3 m2kg−1, especially for low rainfall amounts.

Weathering of fallout from vegetation

Once fallout radionuclides have been deposited upon vegetation, their concentration in vegetation decreases with time due to physical loss from the vegetation and to dilution resulting from plant growth. A detailed discussion of the involved processes is included in Thiessen et al. (2022). A generic value of 14 d for the half-life of loss of radionuclides from growing vegetation and 30 d for dormant vegetation are typical values. Thiessen et al. (2022) recommend that the values be considered as modes of log-triangular distributions with minimums of 3 and 5 d, respectively, and maximums of 60 and 100 d, respectively. The half-times of 14 d and 30 d correspond to loss rates, λp, of 0.050 d−1 and 0.023 d−1.

Delay time between collection of food and consumption

Foods are not typically consumed immediately after fallout and/or harvesting. Typical minimum and maximum delay times have been tabulated in table 27 of Thiessen et al. (2022). Such delay times are not shown in the analysis of individual pathways in the material in the Methods Section. If it is desirable to consider delay times for the shorter-lived radionuclides, the final result can be multiplied by exp(−λi × t), where λi is the radiological decay rate (day−1) and t is the delay time (day). For the calculations shown in the Results section, a nominal delay time of 1 day has been applied to all pathways explicitly considered, except for the consumption of beef. For the meat pathway, a delay time of 14 day is applied.

Dose from consumption of vegetation contaminated directly by fallout

The dose, Di, from the consumption of fresh fruits and vegetables contaminated directly by dry or wet fallout is given by

Di=DDiTOAR/Vveg×DCi×İidt,

where I˙i (m2day−1) is the intake rate of radionuclide i and is given by20

I˙i=10.57×fvB×R˙ex×1K1×fdry/wet×flocal×fprep×eλp+λit

and R˙ex = consumption rate of exposed fruits and vegetables expressed on a wet weight basis (g day−1);

K1 = unit-conversion constant (1,000 g kg−1);

fdry/wet = ratio of dry weight of food to wet weight of food (unitless);

flocal = fraction of exposed fruits and vegetables produced locally (unitless);

fprep = fraction of radionuclides remaining after food preparation (unitless);

λp = loss rate due to weathering from vegetation (day−1); and

λi = loss rate due to radioactive decay (day−1).

The factor fdry/wet is necessary because the values of B are expressed in terms of dry weight, but values of R˙ex are expressed in terms of wet weight per day. Because the value of fv is imbedded in the value of DDi(TOA, R/V)veg from Beck et al. (2022) and the value of (fv B−1) is more stable than the value of fv alone, Eqn (17) shows the division by 0.57, which is the value of fv assumed by Beck et al. (2022).

Values of consumption rates of exposed21 vegetables and fruits for selected age groups are shown in Table 4, as evaluated and reported by the US EPA (2018a). The listed values are in terms of wet weight consumed per unit body weight (g kg−1day−1). Nominal values for body weight are also shown in Table 4 (US EPA 2011). More than 19,000 measurements of food consumption were evaluated during the study relied upon by the EPA. Mean values and standard error (SE) values are shown in Table 4 as taken from table 9-8 (US EPA 2018a). A wide range of intake values would be expected, and values of the standard deviation (SD) were calculated by the current authors according to SD = SE×N, where N is the number of observations (not shown here). Based upon the values of means and standard deviations, values of geometric means (GDs) and geometric standard deviations (GSDs) were calculated and are presented in the lower half of Table 4.

Table 4 - Food-intake rates for fruits and vegetables as a function of age group. Food-intake values are in g day−1 per kg body weight, edible portion, uncooked weight. Food intake rates are from US EPA (2018a); body weights are from US EPA (2011). Geometric means (GM) and geometric standard deviations (GSD) were calculated by the authors according to formulae in Ng et al. (1990).
Exposed fruits Exposed vegetables Protected fruits Protected vegetables
Age group Weight, kg Mean SE/SD a Mean SE/SD a Mean SE/SD a Mean SE/SD a
Whole population 1.42 0.04/5.5 1.29 0.02/3.1 0.93 0.03/4.0 0.59 0.02/3.1
Birth to <1 year 6.8 7.45 0.35/8.6 1.16 0.12/2.8 3.97 0.29/6.9 3.17 0.20/5.4
1 to <2 year 11.4 6.28 0.39/9.9 2.06 0.11/2.9 4.20 0.42/10 2.10 0.24/6.4
21 to <50 years 0.85 0.02/1.4 1.25 0.03/2.5 0.66 0.03/2.0 0.42 0.02/1.6
50+ years 1.04 0.03/2.2 1.19 0.02/1.6 0.74 0.02/1.4 0.54 0.02/1.6
Estimated for adults 80 0.95 0.01/1.4 1.22 0.01/1.5 0.70 0.01/1.2 0.48 0.01/1.2
GM GSD GM GSD GM GSD GM GSD
Whole population 0.353 5.3 0.497 4.0 0.21 5.6 0.11 6.2
Birth to <1 year 6.8 4.87 2.5 0.448 4.0 1.98 3.2 1.60 3.2
1 to <2 year 11.4 3.36 3.1 1.18 2.9 1.56 4.1 0.651 4.6
21 to <50 years 0.445 3.1 0.567 3.5 0.204 4.6 0.10 5.3
50+ years 0.441 3.7 0.697 2.8 0.341 3.5 0.17 4.6
Estimated for adults 80 0.55 2.9 0.777 2.6 0.350 3.3 0.184 4.0
aStandard error (SE) values as reported in US EPA (2018a); standard deviation (SD) values calculated as SE×
N
, where N is the number of observations (not shown here).

The value of fdry/wet has often been assumed to be 0.2 (e.g., Staven et al. 2003); however, more recent data (US EPA 2018a) indicate that a value of 0.1 may be more appropriate. For this assessment, it is suggested that a uniform distribution be used with a minimum of 0.1 and a maximum of 0.2; a value of 0.15 is recommended if a point estimate is to be used. The value of flocal has also frequently been assumed to be 0.2; for this assessment, it is suggested that a local estimate be provided. In the case of an improvised nuclear detonation, it seems likely that an urban area would be targeted, so the value of flocal might well be zero. Otherwise, a default value of 0.2 can be used. Values of fprep are listed in table 26 of Thiessen et al. (2022); for washing of freshly contaminated vegetables, berries, and fruits, reported values vary from 0.1 to 0.9. A default value of 0.5 is suggested here.

The integral of Eqn (17) from time 0 to time t1 is

Ii=10.57×fvB×R˙ex×1K1×fdry/wet×flocal×fprep×1λp+λi1eλp+λit1,

and with the value of Ii from Eqn (18), Eqn (16) is then applied to calculate the integrated dose.22 Because the value of λp is large (direct fallout is retained on vegetation for only a short time), the exponential function can often be considered to have the value of zero.

Values of DCi at close-in distances should be those provided by Melo et al. (2022), which, as noted, have been modified from those of the ICRP (2011) to account for the lower solubility of particles derived from a nuclear detonation. A method of determining the meaning of “close-in distances” is provided in Beck et al. (2022) and is also discussed below in an example calculation. In general, close-in distances are those where values of tr are <1.0. At far distances, the values of DCi from ICRP (2011) should be used.

Dose from consumption of vegetation chronically recontaminated by rain splash and resuspension

After the original contaminating event has come and gone, there are two longer term pathways for the contamination of plant foodstuffs. One is the recurrent contamination of exposed vegetables and fruits by splash from rain (or spray irrigation) (Dreicer et al. 1984) and resuspension (Maxwell and Anspaugh 2011). These processes result in the physical movement of soil particles onto exposed plant surfaces. For this pathway, the deposition density from Eqn (7) can be used even though it includes the activity initially intercepted and retained on vegetation, because the latter is generally retained on vegetation for only a short time. The time-integrated intake is thus given by

Ii=1ρ×L×R˙ex×fdry/wet×flocal×fprep×1λi1ds1eλit2eλit3+fgrowds2eλit4eλit5,

where

ρ = dry bulk density of soil (g m−3);

L = mass loading of soil on dry weight of plants (g kg−1);

ds1 = initial depth of soil within which contamination is mixed (m);

ds2 = equilibrium depth of soil within which contamination is mixed (m);

fgrow = fraction of season where vegetation is exposed and harvested;

t2 = time from fallout to the beginning of the first growing season (day);

t3 = time from fallout to the end of the first growing season (day);

t4 = beginning of second growing season (day); and

t5 = end of second growing season or time of concern (day).

A typical value for the dry bulk density of soil, ρ, is 1.6 × 106 g m−3. Values of the mass loading of soil on vegetation, L, have been measured by Pinder and McLeod (1989), and those authors have also summarized the then-available literature. Measurement results varied from 1.1 g kg−1 dry weight for cabbage to 260 g kg−1 dry weight for lettuce. The geometric mean for six types of vegetation was 8.9 g kg−1 dry weight with a large geometric standard deviation of 7.8. Hinton et al. (1995) also reviewed the literature and made their own measurements of titanium, scandium, and plutonium in soil and grass; they similarly reported a large spread of measured values. Their own measurements were reported as 9.6 ± 1.3 g kg−1 based on titanium, 21.5 ± 8.0 g kg−1 based on scandium, and 1.3 ± 0.1 g kg−1 based on plutonium. A point estimate of 10 g kg−1 is suggested with the understanding that this value is uncertain and may vary greatly among different types of vegetation.

Observations of the concentration of radioactive materials with depth of soil (Beck 1966, 1980; Gibson et al. 1969; UNSCEAR 2000) have indicated that the immediate effect of surface roughness is equivalent to a depth of about 1 mm of soil and that radionuclides move quickly to an average depth in soil of 1 cm. To account for uncertainty and variability, the value of ds1 can be described as a triangular distribution with a mode of 0.005 m, a minimum of 0.001 m, and a maximum of 0.01 m. Over the longer term it can be assumed that soil has been tilled to an average depth of 0.2 m, which is taken to be the value of ds2. The value of fgrow depends upon local conditions and is the fraction of a year that local vegetation is in a condition where it can be exposed to fallout; a nominal value of 0.3 is suggested. The value of t2 depends strongly on the time of a detonation; a nominal value of 30 d is suggested. The value of t3 can be the time to the end of the first growing season; a default value of 90 d is suggested. The values of t4 and t5 relate to the beginning and end of the second growing season; rather arbitrary values of 365 d and 730 d are suggested—the calculation is rather insensitive to those two latter values.

As for the previous pathway, the values of DCi should be those from Melo et al. (2022) if the value of tr is <1.0; otherwise, values from ICRP (2011) are recommended.

Dose from consumption of vegetation contaminated via the soil-root pathway

Vegetation can also be contaminated over longer-term periods by the uptake of radionuclides present in soil through plant roots. Again, the total deposition (Eqn 7) can be used even though it includes the deposition initially retained by vegetation; thus, the dose for this pathway is

Di=DDiTOAR/V×DCi×I˙idt.

As usual, Ii must be evaluated for this situation. The pathways as previously discussed depended upon the movement of radionuclides by physical processes, but the long-term movement of radionuclides through the soil-root process depends upon the chemical characteristics of each element as well as on the type of soil. Fortunately, for this analysis, the shorter-lived radionuclides would have decayed, so the number of radionuclides of concern is appreciably smaller. The six radionuclides of four elements shown in Table 1c are those with half-lives long enough to be considered via this pathway. Another complication is that the uptake, which is defined as a transfer factor, Fv, can be different for each food type and each chemical element. The equation for the integrated intake of fruits and vegetables is

Ii=1ρ×1ds2×R˙total×Fv×fdry/wet×flocal×fgrow×fprep×1λieλit4eλit5,

where R˙total is the consumption rate of exposed and protected fruits and vegetables as shown in Table 4, Fv is a composite transfer factor for all plants consumed and has units of Bq kg−1dry weight per Bq kg−1 of dry soil, t4 is the beginning of the time of concern typically 1 y after deposition, and t5 is the end of the time of concern. The value of t5 could be infinity or it could be a shorter time when food crops are no longer available from the contaminated site or when the site has been decontaminated; a default value of 730 d is again suggested. Thiessen et al. (2022) have tabulated transfer factors for 17 elements for several different food crops in their table 10. In this methodology, we do not intend to consider each type of food in detail but to use a composite transfer factor.

Table 10 - Parameters and suggested default values for calculating dose from the inhalation of 131I in an airborne cloud (an example is provided in Appendix B). Default values not specifically indicated as for 131I are suggested for any radionuclide.
Symbol Parameter Units Source or relationship Default
TOA Time of arrival h Measured or inferred
Exposure rate at time of arrival mR h−1 at TOA Measured or inferred
Ratio of exposure rate at location of interest to exposure rate at center of path on the same arc unitless Measured
HOB Hight of burst m Inferred 70
wg Settling velocity of 50-μm particle km h−1 Known 0.75
Y Explosive yield kt Inferred 10
CT Top of cloud km = 1.85 × ln(Y)+4.7 9.0
tmax Time for 50-μm particles to reach ground h = CT wg −1 12.0
Exposure rate at H+12 h mR h−1 at H+12 Beck et al. (2022) table 3
tr Reduced TOA unitless = TOA tmax −1
1-a Fit parameter unitless = 1X–[0.1×e−(HOB/70)] 0.95
d Fit parameter unitless Beck et al. (2022) app. B 1.6
N 50 Fraction of fallout on particles <50 μm unitless Eqns (9 and 10)
R/V Ratio of refractory to volatile; depends on N 50 unitless Beck et al. (2022)Table 4
DD I-131 Deposition density of 131I vs. R/V per mR h−1 Bq m−2 Beck et al. (2022)Table 6
∫(1/vd ) Activity weighted integral of (1/vd ) s m−1 Fig. B4
fin/out Reduction factor for average time indoors unitless Eqn (B4) 0.5
BR Ventilation rate, adult male m3 day−1 Table 11 22.18
fcorr Correction factor for in-growth and decay, 6 h unitless Beck et al. (2022) table 1
DD I-131(TOA,R/V) Deposition density of 131I, corrected, per 100 mR h−1 at H+12; R/V=1.0 Bq m−2 Beck et al. (2022) tables 5,6
DC I-131 Inhalation dose coefficient, 20 μm, thyroid Gy Bq−1 Melo et al. (2022) table 24 1.6×10−7
DC I-131 Ingestion dose coefficient, thyroid Gy Bq−1 Melo et al. (2022) table 24 4.3×10−7

For example, for strontium, the mode of the distribution of transfer factors for types of foods consumed by humans, as reported by Thiessen et al. (2022), varies from 0.11 to 0.76 with an average value of 0.4 ± 0.3 for the mode and 0.5 ± 0.3 for the arithmetic mean. Another example is for cesium; its isotope of 137Cs is an important source of dose via this pathway. A similar analysis shows that the mode varies from 0.021 to 0.060 with an average of 0.04 ± 0.02; the arithmetic average has a mean of 0.07 ± 0.02. The lowest minimum value (the minimum value suggested for a log-triangular distribution) for cesium is 0.00020, and the highest maximum value is 0.98.

It is possible that the high maximum values shown in table 10 of Thiessen et al. could have been biased high by the presence of radionuclides that did not arise via this pathway. If the measurements were performed on field crops (as opposed to greenhouse crops), the measured radionuclides could have arisen partially from the pathway previously considered, i.e., from surficial contamination via rain splash and resuspension.

A summary of suggested default values for the transfer via the soil-root pathway for the four elements is presented in Table 5.

Table 5 - Default values of composite transfer factors from soil to vegetation for foods consumed by humans and for feed consumed by grazing animals. Values have units of Bq per kg dry weight of food per Bq per kg dry weight of soil. These values have been extracted from the more detailed values shown in Thiessen et al. (2022) for additional elements and for many different types of food.
Food consumed by humans Feed consumed by grazing animals
Element Mode Mean Mode Mean
Sr 0.4 ± 0.3 0.5 ± 0.3 2.6 ± 1.8 3.6 ± 2.9
Ru 0.03 ± 0.04 0.03 ± 0.03 a a
Cs 0.04 ± 0.02 0.07 ± 0.02 0.13 ± 0.089 0.27 ± 0.16
Ce 0.005 ± 0.001 0.007 ± 0.003 0.13 ± 0.21 0.18 ± 0.27
aNo data given in Thiessen et al. (2022).

Because this pathway involves the processing of radionuclides by biological processes, the DCi values should be those from ICRP (2011).

Dose from the consumption of milk

Dose coefficients for the consumption of milk from cows or goats

Because milk has gone through biological processing by the cow or goat, the recommended dose coefficients are those of the ICRP (2011). It is presumed that the cow’s or goat’s stomach has dissolved even those radionuclides that are volume-distributed throughout larger particles.

Contamination of milk by short-lived radionuclides

During the 1950s, when many of the nuclear tests were performed at the NTS, it was common for rural families to have a single-family milk cow grazing on pasture. It was also common for small communities to be supplied with milk from small dairies where cows were fed “green chop.” These practices are not common in recent times, and it is more likely that milk consumed by most persons would be derived from large dairy operations feeding cows hay or silage that may have been transported from locations at some distance, possibly quite far from the dairy itself. Historically, the cow-milk pathway has received major attention because relatively large doses can be received by the thyroid of an infant consuming fresh milk due to a combination of several factors: (1) a dairy cow on pasture can consume the fallout contained on an area of up to 45 m2 day − 1 (Koranda 1965); (2) a dairy cow can secrete a significant fraction of its iodine intake into milk; (3) an infant, after breast feeding has been discontinued, can be fed almost entirely fresh milk23; and (4) an infant’s thyroid can take up an appreciable amount of ingested radioiodine and concentrate that activity into a small gland. Because the movement of radionuclides from pasture through milk can be rapid and important for short-lived radionuclides, the radionuclide concentration in milk does not remain constant, and thus it cannot be considered as being an equilibrium situation.

There are two traditional ways that the intake of fallout by a dairy cow can be computed. One is by considering either the ground area grazed by a cow or the ground area from which fresh forage is cut to feed to the cow. The second is to consider the cow’s intake of feed that has been contaminated by the processes considered above, even though that contamination might have occurred at locations far removed from the cow’s location. The following material on the concentration of short-lived radionuclides in milk follows Bunch (1966), Garner (1967), and Koranda et al. (1971). The cow’s rate of intake of radionuclide i, I˙cow,i, is given by

I˙cow,i=DDiTOAR/Vveg×UAF=DDiTOAR/Vveg×10.57×fvB×MPD,

where

UAF = dairy cow’s utilized area factor (m2day−1);

MPD = dairy cow’s dry matter intake (kg day−1); and

fv B−1 = a single valued function (m2kg−1) and 0.57 is the value of fv embedded in DDi(TOA,R/V)veg.

Because DDi(TOA,R/V)veg comes into the calculations elsewhere, a normalized function for the intake by the cow is defined as

I˙cow,i=UAF=10.57×fvB×MPD.

The value of I˙cow,i as a function of time is given by

I˙cow,it=I˙cow,i0×eλi+λpt.

The differential equation describing the normalized concentration of radionuclide i in milk is

dCmk,itdt=fmk,i×I˙cow,i0×eλi+λptλi+λmk,iCmk,it,

where

Cmk,i(t) = normalized time-dependent concentration of radionuclide i in milk (m2 L−1);

fmk,i = fraction of intake of radionuclide i secreted per liter of milk (L−1);

I˙cow,i0 = dairy cow’s initial intake of radionuclide i (m2 day −1);

λi = decay constant for radionuclide i (day−1);

λp, = rate of weathering loss from pasture (day−1); and

λmk,i = rate of loss from milk for radionuclide i (day−1).

The solution of Eqn (25) is

Cmk,it=fmk,i×I˙cow,i0λmk,iλp×eλi+λpteλi+λmk,it.

Values for the parameters introduced in Eqns (22)–(26) are shown in Table 6. Fig. 1 is a plot of the relative concentrations of 131I, 133I, and 135I in milk as based on the parameters in Table 6 and the deposition amounts at H + 3 shown in Table 1a. The non-equilibrium situation for all three radioiodines is evident.

F1
Fig. 1:
The concentration in milk of 131I, 133I, and 135I as a function of time following an acute deposition of fallout on pasture. The relative amounts of the radioiodines are as defined in Table 1a for a deposition at H + 3 h.
Table 6 - Values of new parameters introduced in Eqns (22) through (26) for the calculations of non-equilibrium concentrations of radioiodines in cows’ milk.a
Parameter Value
UAF (m2 day−1)
 Continuous grazing 38
 Green chop 19
MPD (kg day−1) 14
λmk,i (day−1) 0.64
fmk,i (L−1) 0.005
aValues are taken from Koranda et al. (1971)

Intake of radionuclides in cows’ milk from the cows’ consumption of pasture

The human-intake rate of radionuclide i in milk is

I˙mk,it=R˙mk×Cmk,it,

where R˙mk is the rate of consumption of milk (L day−1). The integrated intake from time 0 to time τ in the usual formulation is

Imk,i=R˙mk×fmk,i×I˙cow,i0λmk,iλp1eλi+λpτλi+λp1eλi+λmk,iτλi+λmk,i.

If τ is long enough for the exponential functions to approach zero, Eqn (28) simplifies to

Imk,i=R˙mk×fmk,i×I˙cow,i0λi+λpλi+λmk,i.

Values of R˙mk are shown in Table 724 in terms of g day−1 per kg body weight. To convert to L day−1, it is necessary to multiply intake values in Table 7 by the body weight (also shown in the table) and then to divide by 1,000 g kg−1. Further, it is assumed that the density of milk is 1 kg L−1. For example, the estimated intake of dairy products for adults is

Table 7 - Consumer only (as opposed to per capita) intake rates for total dairy products and total meat as a function of age group. Intake values are in g day−1 per kg body weight, edible portion, uncooked weight. Intake rates are from Table 11-4 of US EPA (2018b); body weights are from US EPA (2011). The number of significant digits is as shown in the reference document.
Total dairy products Total meat
Age group Body weight, kg Mean SE/SD a 50th percentile Mean SE/SD a 50th percentile
Whole population 6.28 0.1/16 3.0 1.99 0.02/3.1 1.6
Birth to <1 year 6.8 13.06 1.06/34 6.7 3.02 0.25/5.6 2.2
1 to <2 year 11.4 48.78 1.67/45 47.1 4.05 0.13/3.5 3.6
21 to <50 years 3.24 0.10/8.2 2.3 1.82 0.02/1.6 1.6
50+ years 3.22 0.06/4.9 2.3 1.46 0.02/1.6 1.3
Estimated for adults 80 3.23 0.04/4.8 1.8 b 1.64 0.01/1.2 1.3 b
aStandard error (SE) and 50th percentile values as reported in US EPA (2018b). Standard deviation values calculated as SE ×
N
where N is the number of observations (not shown here).
bEstimated as the geometric mean.

R˙mk=3.23gdaykg×80kg×kg1000g×1Lkg=0.26Lday.

The values of fmk,i shown in Eqns (25)–(29) are not the same as the values of Fm given in table 11 of Thiessen et al. (2022). Their Fm is defined as “either the equilibrium ratio of the fresh weight activity concentration in milk or meat to the daily dietary radionuclide intake of the animal…or the ratio of infinite time-integrated concentrations to the ingested activity….” If equilibrium had occurred, the rate of change of concentration in milk (Eqn 25) would be zero, and the following relationships would apply:

Table 11 - Ventilation rates for different ages and occupations.a
Age Ventilation rate (m3 day−1) Adult occupation Ventilation rate (m3 day−1)
3 months 2.86 Housewife 17.64
1 year 5.20 Sedentary worker, male 22.18
5 year 8.76 Sedentary worker, female 17.68
10 year 15.28 Outdoor worker 25.23
15 year, male 20.10
15 year, female 15.72
aData are from tables B.16A and B.16B of ICRP (1994). The number of significant digits is as in the reference document.

dCmk,itdt=fmk,i×I˙cow,i0×eλi+λptλi+λmk,iCmk,i=0Cmk,it=fmk,i×I˙cow,i0×eλi+λptλi+λmk,i=Fm×I˙cow,i0×eλi+λpt.

The equality Fm = fmk,i (λi + λmk,i)−1 is consistent with the findings of Bunch (1966). It is much more common to find tabulated values of Fm rather than fmk,i; such values for Fm are provided in table 11 of Thiessen et al. (2022), whose values are for chemical elements rather than for specific radionuclides. The values of Fm should be corrected when calculating doses for radionuclides of short half-lives or when applying them to biological pools of fast turnover rates. A method for such correction is provided in eqn (13) of Thiessen et al. (2022).

Intake of short-lived radionuclides in goat’s milk from goats’ consumption of pasture

The same equations apply for goat’s milk as for cow’s milk, but some key parameter values are different, those being the dry matter intake, MPD (kg day−1), and the rate of secretion of the radionuclide into milk, Fm (day L−1). The value of λmk,i for iodine is essentially the same for goats (Lengemann and Wentworth 1966) as it is for cows. Dry matter intake for goats is often given as a percentage of live weight; average values for dairy goats are 4.6% for 50 kg goats, or 2.3 kg day−1 (Jolly 2013). As indicated in table 12 of Thiessen et al. (2022), values of Fm for goats are much higher than for cows. For iodine, a point estimate of 0.20 day L−1 for goats is provided vs. a value for cows of 0.0072 day L−1.

Table 12 - Committed absorbed organ doses and effective doses via ingestion for an adult calculated with the ORERP method. Example is for shot Tesla detonated on 1 March with TOA at 6 h and
X˙6=240
mR h−1 on the center line of the trace. Organ doses are in units of Gy; effective doses are in units of Sv. The value for the highest dose for the indicated organ is shaded. Calculations are made with use of Eqn (1);
X˙12
calculated to be 100 mR h−1; values of DDi(6)' from Table 1a; values of Ii from Table 2; and values of DCi from Table 3c.
Radio-nuclide Bone surface Colon Kidneys Liver Red bone marrow Stomach wall Thyroid Effective
89Sr 1.0E-04 2.5E-04 3.5E-06 3.5E-06 8.5E-05 1.5E-05 3.5E-06 4.6E-05
90Sr+P 1.7E-04 5.3E-06 2.7E-07 2.7E-07 7.4E-05 3.7E-07 2.7E-07 1.1E-05
91Sr+P 1.7E-07 4.6E-06 7.4E-08 5.9E-08 1.9E-07 1.0E-06 2.4E-08 7.8E-07
97Zr+P 3.1E-07 7.4E-05 5.4E-07 3.9E-07 6.4E-07 5.9E-06 1.9E-08 1.0E-05
99Mo+P 2.6E-05 1.3E-05 8.1E-05 7.4E-05 1.6E-05 1.9E-05 6.6E-06 1.6E-05
103Ru 7.8E-06 3.0E-04 9.9E-06 7.8E-06 1.1E-05 2.2E-05 4.7E-06 5.2E-05
106Ru+P 1.9E-05 5.8E-04 1.9E-05 1.9E-05 1.9E-05 4.0E-05 1.8E-05 9.0E-05
105Rh 1.4E-07 4.8E-05 1.9E-07 1.4E-07 2.1E-07 3.4E-06 5.3E-08 6.5E-06
132Te+P 4.8E-05 5.7E-04 2.1E-05 1.4E-05 2.3E-05 3.3E-05 1.3E-03 1.7E-04
131I 9.4E-06 8.7E-06 3.3E-06 3.6E-06 7.3E-06 2.2E-05 3.1E-02 1.6E-03
133I 9.4E-07 2.1E-06 7.9E-07 7.7E-07 9.1E-07 1.1E-05 1.6E-03 8.3E-05
135I 2.4E-08 4.3E-08 2.5E-08 2.3E-08 2.3E-08 3.2E-07 9.4E-06 5.4E-07
136Cs 2.4E-05 2.6E-05 2.3E-05 2.3E-05 2.1E-05 2.4E-05 2.2E-05 2.3E-05
137Cs+P 1.1E-04 1.2E-04 1.0E-04 1.0E-04 1.0E-04 1.0E-04 1.0E-04 1.0E-04
140Ba+P 5.9E-05 6.3E-04 8.5E-06 5.6E-06 4.5E-05 2.3E-05 3.2E-06 9.7E-05
143Ce+P 2.2E-07 8.7E-05 3.0E-07 2.3E-07 3.7E-07 5.9E-06 3.8E-09 1.2E-05
144Ce+P 5.2E-07 6.6E-05 3.2E-08 1.5E-06 3.0E-07 1.7E-06 1.9E-08 8.2E-06
147Nd+P 2.9E-07 7.3E-05 1.8E-07 2.0E-07 2.8E-07 3.2E-06 2.0E-09 9.8E-06
239Np+P 3.0E-06 7.3E-04 2.6E-06 1.7E-06 3.2E-06 4.1E-05 1.8E-08 9.7E-05
Sum 5.8E-04 3.6E-03 2.8E-04 2.6E-04 4.1E-04 3.8E-04 3.4E-02 2.4E-03

Long-term intake of radionuclides in cow’s and goat’s milk

Equations (22)–(31) also apply to calculating the intake of long-lived radionuclides as they appear in the milk of cows and goats. For acute deposition on pasture, the accumulation of long-lived radionuclides is controlled by the rate of loss of nuclides from pasture grass. This “acute” pathway can be described by a modification of Eqn (29):

Imk,i=R˙mk×fmk,i×I˙cow,i0λi+λpλi+λmk,i=R˙mk×Fm×I˙cow,i0λi+λpR˙mk×Fm×I˙cow,i0λp.

Because values such as Fm represent equilibrium values, it is reasonable to assume that λmk,i> > λi and λp> > λi. Eqn (32) is written specifically for cow’s milk, but the equation is valid for goat’s milk as well with an appropriate value of I˙goat,i0, which depends on MPD and Fm.

Another pathway for the intake of long-lived radionuclides in milk is the contamination of pasture through the soil-root pathway. The concentration in milk via this pathway is given by

Cmk,it=1ρ×1ds2×MPD×K1×Fv×Fm×eλit,

and the time-integrated intake by humans is

Imk,i=R˙mk×t4t5Cmk,it=R˙mk×1ρ×1ds2×MPD×K1×Fv×Fm×fgrow×flocal×1λi×eλit4eλit5.

For the above transfer through the soil-root pathway, the associated value of deposition density should be for the total deposition per unit area on the ground and vegetation, i.e., Eqn (7) rather than Eqn (8).

Another long-term pathway is the dose from milk that is contaminated through the cows’ or goats’ consumption of forage or feed that has been contaminated by rain splash and resuspension. This pathway is also associated with the deposition density as given by Eqn (7).

The concentration in milk is

Cmk,it=1ρ×L×MPD×Fm×1ds1+fgrowds2eλit,

and the integrated intake is

Imk,i=R˙mk×1ρ×L×MPD×flocal×Fm×1λi×1ds11eλit1+fgrowds2eλit2eλit3.

A final pathway to be considered is the intake by grazing animals of presumed inadvertent ingestion of soil (Zack and Mayoh 1984; Whicker and Kirchner 1987; Simon et al. 2006). This pathway is more complex, as it is necessary to consider the deposition directly onto soil and the additional amount that comes from the soil originally deposited on plants and subsequently weathered off the leaves onto the ground. This phenomenon is discussed in appendix D of Beck et al. (2022). The direct deposition on soil is equal to the total deposition minus the deposition on vegetation:

DDiTOAR/Vsoil=DDiTOAR/VDDiTOAR/Vveg,

and the amount of activity on vegetation will be lost to soil according to the weathering decay constant, λp. As shown in Beck et al. (2022), the time integrated concentration of radionuclide i in soil, IDDi, (Bq day m−2) is

IDDiTOAR/V=DDiTOAR/Vsoil×1λi+DDiTOAR/Vveg×λpλiλi+λp.

The integrated intake via this pathway is then given by

Imk,i=R˙mk×IDDiTOAR/V×1ρ×1ds3×Fm×S×K1.

For convenience, Eqn (39) already includes the needed information on deposition density, so another value for DDi(TOA,R/V) is not needed in fundamental Eqn (1). Two new variables are introduced in Eqn (39): S is the rate of ingestion of soil by cows or goats and ds3 is the average depth of soil from which ingestion occurs.

The rate of ingestion of soil by cows has been reviewed by Zack and Mayoh (1984); one pertinent paper is Fries et al. (1982), who measured titanium in soils and feces for nine dairy herds. Their results are shown in Table 8; an approximate average value for soil ingestion by dairy cows is 0.5% of dry matter intake. For the dry matter intake for dairy cows assumed here (14 kg day−1), the calculated rate of soil ingestion is 0.07 kg day−1. This is substantially less than the value of 0.5 kg day−1 used in the models of Whicker and Kirchner (1987) and Simon et al. (1990). We have not found data on the rate of ingestion of soil by goats; a default value equal to 0.07 kg day−1, the same as for cows, is recommended.

Table 8 - Soil ingestion by cows as measured by Fries et al. (1982).a
Lactating cows Yearling heifers and dry cows
Condition Value, % Condition Value, %
Confined to concrete 0.14 to 0.53 Confined to concrete 0.52 to 0.81
Freestall barns with soil bedding 0.35 to 0.64 Unpaved lots with no vegetation 0.25 to 2.41
Unpaved lots with no vegetation 0.60 to 0.96 Unpaved lots with sparse vegetation 1.56 to 3.77
Pasture with supplements 1.38 to 2.43
aValues shown are in percentage of dry matter intake.

The value of ds3 is greatly uncertain; for their study of thyroid dose due to ingestion of radioiodine, Simon et al. (2006) assumed a geometric mean of 3 mm with a GSD of 1.6. Another way of looking at the value of ds3 is to consider it as the depth of soil through which the contamination is mixed. This value changes with time, and deposited activity rapidly moves down to an average depth of 1 cm in about 1 mo and, as discussed in Bouville et al. (2022), further descends to about 3 cm by 1 y and eventually to as deep as 10 cm for locations with higher annual precipitation. The depth profile at any site will thus depend on the time since deposition and average annual precipitation. Our recommendation is for default values of 3 mm for short-lived radionuclides, 1 cm for intermediate-lived radionuclides, and 3 cm for long-lived radionuclides.

Intake of radionuclides by infants from consumption of mother’s milk

Another pathway of possible importance is the consumption of mother’s breast milk by infants; this is particularly true for the radioiodines. In terms of minimizing radionuclide intake, an infant is better protected by consuming mother’s milk rather than consuming cow’s or goat’s milk, because the mother will filter out a significant fraction through excretion and, in the case of radioiodines, by concentration in her own thyroid. The fraction of 131I secreted into mother’s milk has been described at length by Simon et al. (2002).

Eqn (1) is still relevant, but now the intake is that of the mother while the value of the dose coefficient is that of the nursing infant and is given as dose per unit intake of radionuclide by the mother. Values of integrated intakes via various pathways have been estimated above. The ICRP (2004) provides values of such dose coefficients, and those values should be applied at distant locations and for elements that have been organically bound. At close-in locations and where elements have not been organically bound, the modified dose coefficients given in Melo et al. (2022) should be applied.

Dose from the consumption of meat

Dose coefficients for the consumption of meat

As for the consumption of milk, it is recommended that the dose coefficients from ICRP (2011) be used for the consumption of meat.

Contamination of meat

The following material is intended to apply primarily to beef, but the equations can be applied to pork, mutton, or chicken with appropriate change in values as given in Thiessen et al. (2022). A general assumption is that the consumption of meat is not the same short-term dynamic process as is the consumption of milk and that there is typically some passage of time between a contaminating event and the harvesting of meat. The normalized function for the intake of radionuclide i by the cow as a function of time is the above Eqn (24), and the differential equation describing the normalized concentration of radionuclide i in meat, Cmt,i(t) (m2 kg − 1) is

dCmt,itdt=fmt,i×I˙cow,i0×eλi+λptλi+λmt,iCmt,it,

where fmt,i is the fraction of intake of radionuclide i that occurs in a kg of meat and λmt,i is the rate of elimination of radionuclide i from meat. If the assumption is made that the process is in a state of equilibrium and that the value of Eqn (40) is 0, then,

Cmt,it=fmt,i×I˙cow,i0×eλi+λptλi+λmt,i=Ff×I˙cow,i0×eλi+λpt,

where Ff equals fmt,i (λi + λmt,i)−1. Values for Ff (day kg−1) are given for elements in table 14 of Thiessen et al. (2022) for beef. Similar values for pork, mutton, goat meat, poultry, and egg contents are given in Thiessen’s table 15. Values for λmt,i can be inferred from the values for biological half-life given in table 23 of Thiessen et al. (2022). For example, the arithmetic mean half-life for the concentration of radionuclides in meat is given as 46 day; thus λmt,i is equal to 0.015 day−1. The values of biological half-life given in table 25 of Thiessen et al. (2022) are intended for use for all forms of meat mentioned above and for egg contents. As was stated for the values of Fm, the values of Ff should be corrected when applying them to radionuclides of short half-life; such a correction method is given in eqn (13) of Thiessen et al. (2022).

Table 14 - Committed absorbed organ doses (Gy) and effective doses (Sv) for an adult calculated with the traditional method for the pathway of direct deposition on exposed vegetables and fruits. DDi(6,1)veg has units of Bq m−2 and Ii has units of Bq per Bq m−2.
DDi (6,1)veg Ii Bone surf Colon Kidneys Liver RBM St wall Thyroid Effective
89Sr 9.9E+02 1.8E-01 5.4E-05 2.9E-04 1.8E-06 1.8E-06 4.3E-05 1.4E-05 1.8E-06 4.3E-05
90Sr 5.3E+00 2.1E-01 2.3E-05 1.6E-06 3.7E-08 3.7E-08 1.0E-05 6.4E-08 3.7E-08 1.7E-06
90Y 5.3E+00 2.1E-01 4.2E-12 2.4E-06 1.5E-13 4.2E-12 4.2E-12 1.2E-07 1.5E-13 3.1E-07
91Sr 8.7E+04 1.4E-03 9.9E-07 5.4E-05 7.0E-07 5.3E-07 1.3E-06 1.0E-05 1.2E-07 8.7E-06
91Y 2.9E+03 1.8E-01 4.5E-08 1.0E-03 2.3E-08 4.6E-08 6.4E-08 3.7E-05 1.1E-09 1.3E-04
92Sr 6.8E+04 4.2E-06 1.1E-09 8.6E-08 9.1E-10 6.6E-10 1.2E-09 1.5E-08 1.5E-10 1.3E-08
92Y 1.0E+06 2.6E-05 5.6E-09 6.9E-06 1.6E-08 1.1E-08 1.3E-08 3.7E-06 3.2E-10 1.3E-06
93Y 7.0E+04 1.6E-03 2.5E-08 9.3E-05 5.7E-08 4.0E-08 5.4E-08 1.5E-05 1.1E-09 1.3E-05
97Zr 6.2E+04 4.9E-03 1.6E-06 4.5E-04 3.3E-06 2.4E-06 3.6E-06 3.6E-05 6.3E-08 6.3E-05
97Nb 6.4E+04 4.9E-03 5.9E-08 4.3E-06 2.0E-07 1.3E-07 1.3E-07 1.2E-05 4.3E-09 2.1E-06
99Mo 2.3E+04 3.5E-02 1.8E-05 6.5E-04 5.1E-05 4.6E-05 1.2E-05 4.5E-05 4.1E-06 9.0E-05
99mTc 8.6E+03 3.5E-02 1.6E-07 2.0E-06 1.7E-07 1.3E-07 1.3E-07 1.7E-06 1.4E-06 6.7E-07
103Ru 3.8E+03 1.7E-01 2.9E-06 2.7E-04 4.9E-06 3.2E-06 7.2E-06 1.6E-05 1.5E-07 4.4E-05
103mRh 3.7E+03 1.7E-01 3.9E-10 3.7E-07 2.8E-10 2.8E-10 3.1E-10 1.7E-06 2.1E-10 2.4E-07
105Ru 2.5E+05 8.5E-05 1.9E-08 3.3E-06 5.0E-08 3.5E-08 4.2E-08 1.1E-06 7.5E-10 6.0E-07
105Rh 4.4E+04 1.6E-02 5.9E-07 2.0E-04 8.0E-07 6.0E-07 8.7E-07 1.4E-05 2.2E-07 2.7E-05
106Ru 5.6E+02 2.1E-01 5.5E-07 5.3E-04 7.0E-07 5.7E-07 8.4E-07 2.0E-05 3.5E-07 6.7E-05
132Te 3.1E+04 4.2E-02 1.6E-04 1.3E-03 1.1E-04 3.9E-05 1.0E-04 9.3E-05 4.6E-03 4.6E-04
132I 3.2E+04 4.2E-02 3.3E-06 6.2E-06 4.4E-06 3.7E-06 3.5E-06 8.4E-05 4.6E-04 3.7E-05
131I 1.1E+04 9.1E-02 1.3E-05 1.2E-05 4.7E-06 5.0E-06 1.0E-05 3.2E-05 4.4E-02 2.2E-03
133I 1.5E+05 7.3E-03 5.3E-06 1.2E-05 4.5E-06 4.4E-06 5.2E-06 6.1E-05 9.0E-03 4.7E-04
135I 2.5E+05 4.2E-04 4.2E-07 7.5E-07 4.4E-07 4.1E-07 4.1E-07 5.4E-06 1.6E-04 9.3E-06
137Cs 1.3E+01 2.1E-01 1.5E-06 3.3E-06 1.5E-06 1.5E-06 1.5E-06 1.6E-06 1.4E-06 1.7E-06
140Ba 7.6E+03 1.2E-01 1.2E-04 1.5E-03 1.8E-05 1.2E-05 8.9E-05 5.6E-05 5.9E-06 2.3E-04
140La 7.5E+02 1.2E-01 1.1E-06 1.2E-04 2.0E-06 1.4E-06 2.3E-06 9.8E-06 4.4E-08 1.8E-05
141La 1.7E+05 4.6E-05 2.3E-10 1.6E-06 5.7E-10 3.9E-10 4.6E-10 7.4E-07 1.2E-11 2.8E-07
142La 6.8E+04 2.1E-08 1.1E-12 6.5E-11 3.5E-12 2.3E-12 2.3E-12 1.2E-10 1.0E-13 2.4E-11
143Ce 3.1E+04 1.5E-02 9.8E-07 3.9E-04 1.3E-06 8.8E-07 1.6E-06 2.6E-05 1.3E-08 5.1E-05
143Pr 3.9E+02 1.2E-01 1.7E-10 4.5E-05 2.7E-10 1.3E-09 1.7E-10 1.7E-06 1.1E-12 5.8E-06
144Ce 1.4E+02 2.1E-01 3.7E-08 1.2E-04 2.0E-08 3.7E-08 6.8E-08 3.1E-06 9.4E-10 1.5E-05
144Pr 1.4E+02 2.1E-01 4.6E-11 3.1E-08 1.8E-10 1.1E-10 8.8E-11 1.2E-06 6.5E-12 1.5E-07
145Pr 7.1E+04 3.0E-04 6.0E-10 5.6E-06 1.5E-09 1.1E-09 1.3E-09 1.5E-06 2.6E-11 8.3E-07
239Np 1.5E+05 3.0E-02 9.6E-06 2.7E-03 9.6E-06 6.1E-06 1.2E-05 1.5E-04 4.8E-08 3.6E-04
239Pu 1.5E+00 2.1E-01 2.7E-07 5.6E-08 1.1E-09 5.6E-08 1.3E-08 2.4E-09 4.9E-10 3.0E-07
Sum 4.1E-04 9.7E-03 2.2E-04 1.3E-04 3.1E-04 7.6E-04 5.8E-02 4.4E-03

Table 15 - Committed absorbed organ doses (Gy) and effective doses (Sv) for an adult calculated with the traditional method for the pathway of indirect contamination of exposed vegetables and fruits. DDi(6,1) has units of Bq m−2 and Ii has units of Bq per Bq m−2.
DDi (6,1) Ii Bone surf Colon Kidneys Liver RBM St wall Thyroid Effective
89Sr 2.5E+03 8.8E-02 6.5E-05 3.5E-04 2.1E-06 2.1E-06 5.2E-05 1.7E-05 2.1E-06 5.2E-05
90Sr 1.3E+01 2.1E-01 5.6E-05 3.9E-06 9.3E-08 9.3E-08 2.5E-05 1.6E-07 9.3E-08 4.2E-06
90Y 1.3E+01 2.1E-01 1.0E-11 5.9E-06 3.7E-13 1.0E-11 1.0E-11 3.1E-07 3.7E-13 7.6E-07
91Sr 2.6E+05 1.3E-26 2.8E-29 1.5E-27 2.0E-29 1.5E-29 3.8E-29 2.9E-28 3.4E-30 2.5E-28
91Y 8.6E+02 9.8E-02 7.0E-09 1.6E-04 3.7E-09 7.3E-09 1.0E-08 5.9E-06 1.8E-10 2.0E-05
92Sr 3.4E+05 3.7E-88 4.7E-91 3.8E-89 4.1E-91 2.9E-91 5.2E-91 6.7E-90 6.7E-92 5.9E-90
92Y 4.7E+05 3.7E-67 3.6E-71 4.5E-68 1.1E-70 7.4E-71 8.3E-71 2.4E-68 2.1E-72 8.6E-69
93Y 3.5E+05 2.3E-25 1.7E-29 6.6E-26 4.0E-29 2.9E-29 3.8E-29 1.0E-26 7.9E-31 9.5E-27
97Zr 3.1E+05 1.4E-16 2.3E-19 6.5E-17 4.8E-19 3.4E-19 5.2E-19 5.2E-18 9.1E-21 9.1E-18
97Nb 3.2E+05 1.4E-16 8.5E-21 6.3E-19 3.0E-20 1.8E-20 1.9E-20 1.7E-18 6.3E-22 3.1E-19
99Mo 1.2E+05 5.2E-06 1.3E-08 4.8E-07 3.8E-08 3.4E-08 9.1E-09 3.3E-08 3.0E-09 6.7E-08
99mTc 5.2E+04 5.2E-06 1.4E-10 1.8E-09 1.5E-10 1.2E-10 1.2E-10 1.5E-09 1.3E-09 6.0E-10
103Ru 9.5E+03 7.0E-02 3.0E-06 2.8E-04 5.0E-06 3.2E-06 7.3E-06 1.7E-05 1.5E-07 4.5E-05
103mRh 9.4E+03 7.0E-02 4.0E-10 3.7E-07 2.9E-10 2.9E-10 3.1E-10 1.7E-06 2.2E-10 2.5E-07
105Ru 6.2E+05 2.8E-54 1.6E-57 2.8E-55 4.2E-57 3.0E-57 3.5E-57 9.4E-56 6.3E-59 5.1E-56
105Rh 1.1E+05 3.3E-09 2.9E-13 9.7E-11 4.0E-13 3.0E-13 4.3E-13 6.9E-12 1.1E-13 1.3E-11
106Ru 1.4E+03 1.8E-01 1.2E-06 1.2E-03 1.5E-06 1.3E-06 1.8E-06 4.3E-05 7.7E-07 1.5E-04
132Te 7.9E+04 1.9E-05 1.8E-07 1.4E-06 1.2E-07 4.4E-08 1.1E-07 1.0E-07 5.1E-06 5.1E-07
132I 8.1E+04 1.9E-05 3.8E-09 6.9E-09 5.0E-09 4.2E-09 3.9E-09 9.5E-08 5.1E-07 4.2E-08
131I 2.8E+04 2.6E-03 9.5E-07 8.7E-07 3.3E-07 3.6E-07 7.3E-07 2.3E-06 3.1E-03 1.6E-04
133I 3.8E+05 7.1E-14 1.3E-16 2.9E-16 1.1E-16 1.1E-16 1.3E-16 1.5E-15 2.2E-13 1.2E-14
135I 6.2E+05 1.1E-37 2.8E-40 5.0E-40 2.9E-40 2.7E-40 2.7E-40 3.6E-39 1.0E-37 6.2E-39
137Cs 3.2E+01 2.1E-01 3.8E-06 8.1E-06 3.7E-06 3.7E-06 3.7E-06 3.9E-06 3.6E-06 4.3E-06
140Ba 2.3E+04 1.1E-02 3.1E-05 4.1E-04 4.8E-06 3.1E-06 2.4E-05 1.5E-05 1.6E-06 6.2E-05
140La 2.2E+03 1.1E-02 2.8E-07 3.1E-05 5.2E-07 3.8E-07 6.1E-07 2.6E-06 1.2E-08 4.7E-06
141La 6.3E+05 6.3E-61 1.2E-65 8.4E-62 2.9E-65 2.0E-65 2.4E-65 3.9E-62 6.4E-67 1.5E-62
142La 3.4E+05 2.4E-152 6.1E-156 3.8E-154 2.0E-155 1.3E-155 1.3E-155 6.9E-154 6.0E-157 1.4E-154
143Ce 1.6E+05 1.1E-09 3.5E-13 1.4E-10 4.6E-13 3.1E-13 5.6E-13 9.4E-12 4.6E-15 1.8E-11
143Pr 2.0E+04 1.2E-02 8.6E-10 2.3E-04 1.4E-09 6.9E-09 8.6E-10 8.9E-06 5.4E-12 3.0E-05
144Ce 7.0E+02 1.7E-01 1.6E-07 5.1E-04 8.5E-08 2.9E-07 1.6E-07 1.3E-05 4.0E-09 6.3E-05
144Pr 7.0E+02 1.7E-01 1.9E-10 1.3E-07 7.9E-10 4.6E-10 3.8E-10 5.0E-06 2.8E-11 6.2E-07
145Pr 3.6E+05 4.4E-41 4.4E-46 4.1E-42 1.1E-45 8.0E-46 9.7E-46 1.1E-42 1.9E-47 6.1E-43
239Np 7.4E+05 1.2E-06 2.0E-09 5.5E-07 2.0E-09 1.3E-09 2.4E-09 3.1E-08 9.9E-12 7.3E-08
239Pu 2.7E+00 2.1E-01 4.7E-07 9.7E-08 1.9E-09 9.7E-08 2.2E-08 4.2E-09 8.5E-10 5.2E-07
Sum 1.6E-04 3.2E-03 1.8E-05 1.5E-05 1.2E-04 1.4E-04 3.1E-03 6.0E-04

Intake of radionuclides in meat

As is the case for milk, there are several pathways that can lead to the intake of radionuclides with the consumption of meat. In general, the rate of intake of radionuclide i in meat is

I˙mt,it=R˙mt×Cmt,it,

where R˙mt is the rate of consumption of meat (kg day−1). For acute deposition on pasture, the concentration in meat is controlled by processes similar to those for milk, but the equation describing the relevant concentration in meat is more complicated. Whereas milk can be consumed within a day or two of the cows’ consumption of forage, such is not presumed to be the case for meat. Thus, a more complicated version of Eqn (28) is shown in Eqn (43) where the integration has been from τ1 to τ2, rather than from 0 to τ:

Imt,i=Ṙmt×fmt,i×İcow,iλmt,iλpeλi+λpτ1eλi+λpτ2λi+λpeλi+λmt,iτ1eλi+λmt,iτ2λi+λmt,i.

In order to use the tabulated values of Ff, the substitution is made that fmt,i = Ff × (λi + λmt,i). Because the values of Ff represent equilibrium values, the usual correction factor is used. A default value of 30 d is used for τ1 and a value of 60 d for τ2; a delay time of 14 d between slaughter and consumption is also used according to table 27 of Thiessen et al. (2022). Values of Ṙmt are shown in Table 7 in terms of g day−1 per kg body weight. For example, the estimated intake of meat by adults is

R˙mt=1.64gdaykg×80kg×kg1000g=0.13kgday.

A second pathway for the contamination of meat is through the animal’s consumption of pasture or stored feed that has been contaminated through the soil-root pathway. The concentration in meat via this pathway is

Cmt,it=1ρ×1ds2×MPD×K1×Fv×Ff×eλit,

and the integrated intake is

Imt,i=R˙mt×fprep×t4t5Cmt,it=R˙mt×fprep×1ρ×1ds2×MPD×K1×Fv×Ff×fgrow×flocal×1λi×eλit4eλit5.

To calculate the dose via this soil-root pathway, the associated value of deposition density should be for the total deposition, i.e., Eqn (7) rather than Eqn (8).

A third pathway is the dose from meat that is contaminated through the animal’s consumption of forage or feed that has been contaminated by rain splash or irrigation splash and by resuspension. This pathway is also associated with the deposition density as given by Eqn (7). The concentration in meat is

Cmt,it=1ρ×L×MPD×Ff×1ds1+fgrowds2eλit,

and the integrated intake is

Imt,i=R˙mt×fprep×1ρ×L×MPD×flocal×Ff×1λi×1ds11eλit2+fgrowds2eλit2eλit3..

A fourth and final pathway for the contamination of meat is the inadvertent consumption of soil by grazing animals. As indicated in the discussion about the contamination of milk via this pathway, the deposition density on soil and the subsequent loss to soil of the deposition on plants to soil should both be considered. This situation has been discussed in appendix D of Beck et al. (2022). Eqn (38) above gives the time-integrated concentration of radionuclide i in soil, IDDi(TOA,R/V). Then the integrated intake of radionuclide i in meat is given by

Imt,i=R˙mt×fprep×IDDiTOAR/V×1ρ×1ds3×Ff×S×K1.

The reader is referred to the discussion on the values of S and ds3 related to the discussion on the intake of milk contaminated via this pathway and is reminded that an additional value of deposition density is not needed in fundamental Eqn (1).

METHODS: DOSE FROM THE INHALATION OF CONTAMINATED AIR

The ORERP did not develop a general methodology of calculating dose from inhalation, except where measurements of airborne radionuclides had been made (Cederwall et al. 1990; Ng et al. 1990). ORERP investigators tried to find a general relationship between airborne concentrations and ground deposition but were not successful. Following the development of the US–Russian joint methodology (Beck et al. 2022), there is understanding that fallout even moderately far downwind can contain large particles that may not be recorded by typical air samplers. Simon et al. (1990) did develop a method to estimate dose from inhalation of fallout, and some modifications were introduced by Bouville et al. (2022). The following material relies partially on those methods.

A general problem is the concern of what particle sizes are respirable or inhalable.25 The ICRP (1994) has published a human respiratory tract model (HRTM) and provided dose coefficients (ICRP 2011) based on that model for occupational workers and for members of the public. In the 2011 publication, dose coefficients have been provided for submicron sizes up through 10−μm activity median aerodynamic diameter (AMAD). Recently, the ICRP (2015, 2016, 2017, 2019a) has been reassessing the models and has released an electronic system that provides dose coefficients for occupational workers for particles sizes from submicron up through 20 μm AMAD (ICRP 2019b), but values for 20-μm particles are available at this time only for effective doses.

As part of this current study, Melo et al. (2022) have provided dose coefficients (DC) with two departures from the ICRP (2011): (1) consideration is given to alteration of the traditional ICRP f1 values for radionuclides that, in fallout particles, were formed at extremely high temperatures and are consequently presumed to have less biological availability, and (2) extension of the inhalation dose coefficients to particles of 20-μm AMAD for each of the traditional organs and for effective dose. Fig. 2 shows examples of the inhalation dose coefficients from Melo et al. for two radionuclides of primary interest for infants and for adults. The values of the dose coefficients do not indicate a major change in going from 10 to 20 μm AMAD. This suggests that particles of larger sizes might also be contributing to dose, but dose coefficients for larger sizes are not available.

F2
Fig. 2:
Dose coefficients as a function of particle size for two radionuclides of major importance for infants and adults. Values of dose coefficients are from Melo et al. (2022).

We thus propose an inhalation-dose model that is dependent on particle size and accounts for inhalation of particles >20 μm AMAD. Because of the paucity and uncertainty of available data on activity on particles >20 μm and the lack of dose coefficients for particles >20 μm AMAD, we propose that only three particle size ranges need to be considered. Following this short description of the model are sections on the technical justification of the assumptions.

Basic parameterization of the inhalation-dose model

  1. Particles 1–20 μm AD: The doses to all organs are directly proportional to the inhalation DC for 20-μm particles (or the mean DC for particles from 1 to 20 μm, which is about the same value) provided in Melo et al.(2022);
  2. Particles >20–100 μm AD: The doses to organs in the respiratory tract are insignificant (less than 3%) and can be ignored. The doses to organs in the GI tract are proportional to 0.34 × DC (ingestion) for infant to 10-y-old mouth breather (assuming light exercise level) and 0.4 × DC (ingestion) for 10-y-old, 15-y-old, and adults (assuming moderate exercise level for both a nose and a mouth breather); and
  3. Particles >100 μm AD: The dose to organs in the respiratory tract are insignificant (less than 1%) and can be ignored. The dose to organs in the GI tract is proportional to 1.0 × DC (ingestion). We do not set a limit on the size of particles that can enter the mouth, but such a limit is likely <800 μm AD.

Justification

There are three possible ways for respiratory air to reach the lungs of a normal healthy subject: through the nose, mouth, or a combination of both routes. Most people breathe through the nose at rest but switch to oro-nasal breathing at higher respiratory minute volumes. The mouth and throat filter particles less efficiently than does the nose. Mouth breathing occurs not only during heavy physical activity but even during low physical activity; for example, during reading and conversation (ICRP 1994).

Because the filtration efficiencies of the nose and mouth are different, a subject’s breathing habit affects the amount of inhaled material that deposits within the respiratory tree. There is also a strong dependence upon particle size with larger particles preferentially being deposited in the extra-thoracic (ET) regions.

Particle sizes <20 μm AD

The deposition in the respiratory tract of particles in the range of 20 μm or less are relatively well understood. The HRTM as discussed in ICRP (1994) was designed to account for the deposition, clearance, and absorption of those size particles in the body. The dose coefficients provided to this study in Melo et al. (2022) adequately account for doses to the organs following inhalation of radioactive fallout for particles ≤20 μm AD.

Particle sizes >20–100 μm AD

Because of lack of data on deposition of particles larger than 20 μm in the different sub-regions of the human respiratory tract (HRT), the ICRP model (ICRP 1994, 2002) can only be applied to calculate the committed doses for particle sizes up to 20 μm AMAD. The ICRP (1994, 2002) has estimated fractional deposition in different regions of the HRT for both mouth and nose breathers. The fractional deposition values for ET2 for all age groups for AMAD values ranging from 1 to 20 μm are summarized in Table 9. Particles inhaled through the nose and deposited in the nasopharynx or particles inhaled through the mouth and deposited there or in the oropharynx are generally swallowed. Particles inhaled by either route may also deposit on the larynx and be carried rapidly to the esophagus in or on the mucus coming up from the trachea.

Table 9 - Fractional deposition in the ET2 region of the human respiratory tract as a function of particle size and according to age group.
AMAD (μm) Light exercise, nose breather/mouth breather Moderate to heavy exercise, nose breather/mouth breather
Infanta 1-y old a 5-y old a 10-y old b 15-y old b Adult c
1 0.31 0.32 0.26 0.17 0.15 0.087
2 0.41 0.41 0.37 0.28 0.26 0.18
3 0.44 0.44 0.41 0.35 0.33 0.25
5 0.44 0.44 0.43 0.42 0.40 0.34
7 0.42 0.42 0.42 0.45 0.44 0.39
10 0.40 0.40 0.39 0.47 0.45 0.43
15 0.36 0.36 0.36 0.47 0.46 0.45
20 0.34 0.34 0.34 0.46 0.45 0.45
Mean 0.39 0.39 0.37 0.38 0.37 0.32
atable A.9 ICRP (2002).
btable A.10 ICRP (2002).
ctable A.6 ICRP (2002).

Our proposal for dose assessment for inhalation of particle sizes in the range > 20 μm to 100 μm is to assume that the deposition of the particles in the ET2 region is responsible for the committed dose and that one can use the fractional deposition in the ET2 region of the HRT for particles to estimate the inhalation dose in the range > 20–100 μm AMAD. This assumption is based on figs. 10 and 11 of ICRP (1994); those figures show that the fractional deposition of particles in the range > 20–100 μm does not change with an increase of particle size. For adults, assuming mouth breathing, the total deposition for 20-μm AMAD particles in the HRT (ICRP 1994, 2002) is 66% of the exposed particles, where 12% is deposited in the ET1 region, 45% in the ET2 region, and 9% in the BB, bb, and AI regions. For nose breathing, the corresponding values are 67%, 29%, 36%, and 2%. The insoluble particles deposited in the ET2 region are swallowed and transferred to the GI tract. Basically, the committed dose is due to the ingestion of the 35X–45% of the inhaled particles that are deposited in the ET2 region. Hence, the committed dose can be calculated by multiplying the fractional deposition in the ET2 region by the dose coefficient for ingestion. We propose using the average deposition for nose and mouth breathers, ~0.4, because most people are likely both.

Particles >100 μm AD

Figures D.7 and D.8 in ICRP Publication 66 (1994) show that there is high variability in the amount of deposition of large particles in the ET region. According to ICRP (1964), “…the characteristic dimension of the ET region during mouth breathing increases with increasing flow rate and with increasing tidal volume. Thus, the oropharyngeal-laryngeal passageway appears to behave like a ‘dynamic’ impactor. The glottis is known to exhibit this type of behavior by opening further with increasing flow rate and tidal volume.” Based on this, and also considering the possibility of fallout deposition on the lips and normal habits to lick the lips, we assume that the deposition of particles >100 μm will be completely deposited in the ET2 region. Hence, the committed dose should be calculated assuming that the pathway of intake is ingestion. For the following calculations, a limit on particle size is set at 500 μm AMAD.

Calculation of dose from inhalation

The general equation for the calculation of dose from inhalation is

Di=j=13DDiTOAR/V×Nj×fin/out×BRage×1K2×DCi×1vddPS,

where the integral is over the range of activity-weighted particles (PS) in each of the three ranges of sizes of interest, 1–20 μm, >20–100 μm, and > 100–500 μm, and Nj is the fraction of total activity of radionuclide i on the particles in that range. The other parameters in Eqn (50) are

Di = absorbed organ dose or effective dose from radionuclide i for the age group considered (Gy or Sv);

DDi(TOA,R/V) = deposition density of radionuclide i (Bq m−2)

TOA = time of arrival of fallout at the location of interest (h);

R/V = average ratio of refractory radionuclide activity to volatile radionuclide activity for the particle sizes in the inhaled air in size range j;

vd = deposition velocity for a given particle size (m s−1);

fin/out = fraction of reduction due to time spent indoors where air concentration is reduced by a suggested factor of 2;

BRage = age-dependent average ventilation rates (m3 day−1);

K2 = constant equal to 86,400 s day−1; and

DCi = age-dependent dose coefficient (Gy Bq−1 or Sv Bq−1) for inhalation of particles in the range of 1–20 μm AMAD or ingestion dose coefficient for particles in the range > 20 μm AMAD.

As discussed in Beck et al. (2022), DDi depends on fractionation (R/V). The closer to the explosion site and to the fallout axis, the more activity is on larger particles enriched in refractory nuclides, while at larger distances, the heavier particles have mostly deposited and the activity is distributed on smaller particles enriched in more volatile nuclides. Furthermore, 1vddPS also depends on the activity-particle size distributions. Thus, to apply Eqn (50), we need to estimate the activity-particle-size distribution at the location of interest within each particle size range j. As discussed in Beck et al. (2022), the degree of fractionation can be estimated by R/V, the average ratio of refractory to volatile beta activity in the fallout deposited at a given location. R/V can be estimated from N50, which in turn can be estimated using a semi-empirical model that depends on the fallout time of arrival as well as the location of the site relative to the center line (axis) of the fallout pattern. A default particle-size distribution as a function of N50 has been estimated from NTS post-detonation measurements of the fraction of beta activity on particles of various physical sizes and the distributions for each size range of interest have been interpolated as a function of N50. Examples of the available NTS data and the interpolated activity-particle-size distributions inferred from the NTS data are given in Appendix B. Because the available NTS data are sparse and are provided only in fairly wide bins, the inferred distributions in the regions of interest, particularly for sizes <20 μm AMAD, are fairly crude. However, the distributions for a given value of N50 do not appear to vary significantly with explosive yield or fissile fuel and thus can be used as a default for any event. If actual data become available from post-detonation measurements to estimate the size distribution for the actual event, they can of course be used in place of the default to lower the uncertainty in calculated dose.

The DDi for the three particle size intervals of interest can be calculated for a given N50 using the methodology presented in Beck et al. (2022). However, because Beck et al. (2022) considered only two particle-size intervals, <50 μm and the entire particle size range, Eqn (8) must be slightly modified as follows:

DDiTOA=X˙12×β12X˙12R/V×Nj×DDi12β12R/V×expλi×TOA12,

where N50 has been replaced by Nj and DDi12β12R/V=0.5 by DDi12β12R/V where R/V’ depends on R/V and j. The R/V’ inferred from a calculated N50 using the model proposed in Beck et al. (2022) represents an average over the entire fallout-particle-distribution deposited. However, Beck et al. (2022) assume an R/V = 0.5 for all particles of physical size <50 μm. Thus, since all particles are <50 μm for j = 1 (1–20 μm AMAD) R/V’ = 0.5. For particles in the range 20–100 μm (~13–89 μm physical diameter), the actual R/V will be slightly higher due to the inclusion of particles >50 μm, and we suggest assuming R/V’ = one bin up in the values of R/V vs. N50 shown in Beck et al. (2022)table 4 (i.e., R/V = 1 → R/V = 1.5, etc., up to a maximum R/V = 3, the highest tabulated in Beck et al. 2022, table 4). Similarly, for particles >100 μm, the actual R/V will be higher than the R/V for the entire fallout distribution and even higher than that for the 20–100 μm range. However, as can be seen from the example calculations in Appendix B, the contribution to the dose from particles in this region is very small. Thus, using the same adjusted R/V as for the range 20–100 μm will not result in a significant impact on the estimated total inhalation dose. Note that although Beck et al. (2022) do not tabulateDDi12β12 separately for R/V > 0.5, the tabulated data in table 6 of Beck et al. for DDi12Ẋ12 represent the products of β12X˙12 and DDi12β12 for the same R/V, so the required DDi12β12 for R/V’ can easily be calculated using both table 5 and table 6 of Beck et al. (2022).

In summary, the general procedure to estimate an inhalation dose at a given site is as follows:

  1. Determine the exposure rate and TOA from either measurements or interpolation;
  2. Calculate N50 using Eqns (9) and (10);
  3. Estimate R/V and R/V’ from N50 (Beck et al. 2022, table 4);
  4. Calculate 1vddPS for each of the three particle-size ranges of interest;
  5. Estimate Nj for each particle size range using the default activity-particle-size distributions inferred from NTS data or actual event-specific measurements;
  6. Calculate DDi (TOA) with Eqn (51) with appropriate values for Nj, R/V, R/V’, and Ẋ12; and
  7. Calculate Di using Eqn (50) using the ingestion DCs for the 20–100 μm and > 100 μm particle sizes and assuming only 0.4 of the activity in the 20–100-μm range is ingested, but all the activities on particles >100 μm are ingested.

Specific examples of how to calculate the dose for both a volatile radionuclide and a refractory radionuclide are given in Appendix B.

Default values for parameters needed to make calculations of inhalation dose are presented in Table 10; values of age-dependent ventilation rates are given in Table 11.

Uncertainties

The greater uncertainties in Eqn (50) are likely the values of Nj, 1vddPS and DCi. Uncertainties in the values of N50 have been discussed in Beck et al. (2022), and the corresponding uncertainties in Nj will be even larger. Uncertainties in the values of DCi are discussed in Melo et al. (2022).

The authors do not know of a method of estimating the uncertainty in the mean value of 1vddPS, which is an integrated value for the activity particle sizes in the three size intervals of interest. Unfortunately, we have only limited data to describe the activity of fallout according to particle size, particularly for <20 μm. The NTS data for <5 μm (physical PS) are very scattered and suspect, particularly for values of small N50. Thus, our interpolations to estimate the distribution of activity between 1 μm and 20 μm are more uncertain than for the other size ranges. Furthermore, the available data from weapons tests are for beta activity, not volatile nuclides such as 131I that may be more preferentially distributed on smaller particles than the measured beta-activity distribution, which would result in a lower mean 1vddPS and higher estimated inhalation dose. Due to these limitations of data, 1vddPS for the size range 1–20 μm is judged to be uncertain by about a factor 2–3 at low values of N50 but less at higher values of N50. As discussed in Beck et al. (2022), N50 is very uncertain at low values of N50 and particularly for sites off-axis, less so as N50 → 1.0. In association with the calculation made in Eqn (4), we estimate that the doses calculated with Eqn (50) are geometric means with a maximum geometric standard deviation of about 2–3 with the higher value for the smaller values of N50.

Figs. 3a and 3b show the results of examples for adult thyroid doses from 131I and colon dose from 239Np as a function of N50 calculated as per the examples in Appendix B. Note that the dose from the ingestion fractions of inhaled particles 20–100 μm is much less than the dose from the inhaled <20 μm particles for all values of N50, and particles >100 μm contribute little to the dose. This suggests that the choice of an assumed maximum inhalable size makes little difference, because even though most of the activity at very low values of N50 is on very large particles, the very large vd results in a negligible air concentration compared to the air concentration of particles <20 μm. With respect to the finding that particles >100 μm do not contribute significantly to dose, there is evidence that the deposition of fallout on the faces and hands of exposed persons perhaps resulting in direct ingestion of large particles led to additional intake of radioiodine following the Bravo test detonated in 1954 in the Marshall Islands (Simon et al. 2010). However, there is not enough information to estimate the possible intake from this pathway in a reliable manner.

F3a
Fig. 3a:
Thyroid dose for adults from inhalation of particles in the indicated size range per mR h−1 as a function of N 50 using default activity-particle-size distribution.dose to adult per mR h−1 as a function of N 50 using default activity particle size distribution.
F3b
Fig. 3b:
Colon dose for adults from inhalation of particles in the indicated size range per mR h−1 as a function of N 50 using default activity-particle-size distributions.

METHODS: SPECIAL CASE OF DOSE TO THE FETAL THYROID

The dose to the fetus has been considered by the ICRP (2001), and they have provided a downloadable system that can be used to calculate doses to the organs of the embryo or fetus as a function of age of the embryo or fetus. Dose coefficients are provided in terms of dose per unit intake by the mother. In general, we have adopted the dose coefficients provided by the ICRP with the exception of those for the radioiodines; the reasons for this exception have been explained in the companion paper by Melo et al. (2022). A modified model is developed there for 131I, 133I, and 135I, and dose coefficients are provided for each day of gestational age.

RESULTS

Example results for the pathways considered have been calculated with the radionuclide mix from the Tesla detonation that occurred on 1 March 1955. A hypothetical location is assumed where the fallout cloud arrived at H + 6 hours, and the exposure rate at that location and time was 240 mR h−1 on the center line of the axis. X˙12 is calculated to be 100 mR h−1 based on the values in table 3 of Beck et al. (2022).

ORERP method

For the situation above, Eqn (1) is used with values of DDi(TOA)' as given in Table 1a, values of Ii from Table 2 for the column headed by 1 March (Tesla), and values of DCi from Table 3c for adults. The results of the calculations of committed dose are presented in Table 12. The highest organ dose is to the thyroid at 34 mGy, and the effective dose is 2.4 mSv; most of these doses are due to 131I. The next higher organ dose is to the colon at 3.6 mGy with significant contributions from 239Np, 140Ba, 106Ru, 132Te, and 103Ru. The calculations with the ORERP method are simple because the intakes from the pathways considered have been rolled up into an integrated value of intake, Ii. An advantage is that the values of integrated intakes have been presented in a seasonally dependent form.

Because the results shown in Table 12 were calculated based upon an event occurring early in the year, it can be expected that the doses would be relatively low, as fresh produce would be minimally available at most locations and cows would not likely be consuming fresh pasture. A second calculation was made with the ORERP method with values of integrated intake from the column headed by 24 June (Priscilla) in Table 1a but still using the radionuclide mix for the Tesla detonation. These results are shown in Table 13 and are significantly higher than those shown in Table 12. Again, the highest dose is to the thyroid at 150 mGy with 140 mGy due to 131I. The second higher dose is still to the colon at 11 mGy with significant contributions by 106Ru, 140Ba, 239Np, 132Te, and 89Sr. The more important radionuclides in Table 13 vs. Table 12 have shifted more toward shorter lived radionuclides, like 99Mo.

Table 13 - Committed absorbed organ doses and effective doses via ingestion for an adult calculated with the ORERP method. Example is for shot Priscilla detonated on 24 June with TOA at 6 h and
X˙6=240
mR h−1 on the center line of the trace. Organ doses are in units of Gy; effective doses are in units of Sv. The value for the highest dose for the indicated organ is shaded. Calculations are made with use of Eqn (1);
X˙12
calculated to be 100 mR h−1; values of DDi(6)' from Table 1a; values of Ii from Table 2; and values of DCi from Table 3c.
Radio-nuclide Bone surface Colon Kidneys Liver Red bone marrow Stomach wall Thyroid Effective
89Sr 4.3E-04 1.0E-03 1.5E-05 1.5E-05 3.5E-04 6.4E-05 1.5E-05 1.9E-04
90Sr+P 7.4E-04 2.3E-05 1.2E-06 1.2E-06 3.2E-04 1.6E-06 1.2E-06 5.1E-05
91Sr+P 4.1E-07 1.1E-05 1.8E-07 1.4E-07 4.7E-07 2.5E-06 5.9E-08 1.9E-06
97Zr+P 6.9E-07 1.6E-04 1.2E-06 8.7E-07 1.4E-06 1.3E-05 4.3E-08 2.3E-05
99Mo+P 6.5E-05 3.2E-05 2.0E-04 1.8E-04 4.0E-05 4.8E-05 1.6E-05 3.9E-05
103Ru 2.0E-05 8.0E-04 2.6E-05 2.0E-05 3.0E-05 5.8E-05 1.2E-05 1.4E-04
106Ru+P 8.8E-05 2.6E-03 8.8E-05 8.8E-05 8.8E-05 1.8E-04 8.2E-05 4.1E-04
105Rh 2.8E-07 9.9E-05 4.0E-07 3.0E-07 4.4E-07 7.0E-06 1.1E-07 1.4E-05
132Te+P 9.6E-05 1.1E-03 4.3E-05 2.8E-05 4.6E-05 6.6E-05 2.7E-03 3.3E-04
131I 4.1E-05 3.8E-05 1.4E-05 1.5E-05 3.1E-05 9.4E-05 1.4E-01 6.9E-03
133I 4.5E-06 1.0E-05 3.8E-06 3.7E-06 4.3E-06 5.0E-05 7.5E-03 3.9E-04
135I 8.0E-08 1.4E-07 8.2E-08 7.6E-08 7.8E-08 1.1E-06 3.1E-05 1.8E-06
136Cs 4.6E-05 4.9E-05 4.3E-05 4.4E-05 4.0E-05 4.6E-05 4.2E-05 4.3E-05
137Cs+P 1.8E-04 2.0E-04 1.7E-04 1.7E-04 1.7E-04 1.7E-04 1.7E-04 1.7E-04
140Ba+P 1.7E-04 1.8E-03 2.4E-05 1.6E-05 1.3E-04 6.6E-05 9.1E-06 2.7E-04
143Ce+P 4.8E-07 1.9E-04 6.4E-07 5.1E-07 8.0E-07 1.3E-05 8.3E-09 2.5E-05
144Ce+P 7.5E-06 9.5E-04 4.5E-07 2.2E-05 4.3E-06 2.5E-05 2.7E-07 1.2E-04
147Nd+P 7.7E-07 1.9E-04 4.7E-07 5.1E-07 7.2E-07 8.4E-06 5.1E-09 2.6E-05
239Np+P 6.1E-06 1.5E-03 5.1E-06 3.4E-06 6.3E-06 8.3E-05 3.7E-08 1.9E-04
Sum 1.9E-03 1.1E-02 6.4E-04 6.1E-04 1.3E-03 1.0E-03 1.5E-01 9.4E-03

Traditional method

These calculations are complex but flexible and can consider the impact of measures of food diversion or other types of remediation. Not all traditional pathways considered above are presented, but detailed results follow for the pathways of direct deposition on exposed vegetables and fruits, indirect deposition on exposed vegetables and fruits via rain-splash and resuspension, contamination of cows’ and goats’ milk from the animal’s consumption of exposed forage, and contamination of beef meat from the animal’s consumption of forage. The defining parameters for the following calculations are as shown in Appendix A and partially in Table 10.

Direct deposition on exposed fruits and vegetables

The results of calculations for this pathway are shown in Table 14 for a period of 30 d following the detonation and with a lag period of 1 d between harvest and consumption. For this calculation, it is assumed that fresh vegetables and fruits are available. Values of deposition on vegetation are calculated from Eqn (8) with values of β12Ẋ12R/V=1.0 and DDi12β12R/V=0.5 from tables 5 and 6 in Beck et al. (2022). The value of N50 calculated from Eqn (9) is 0.49. The TOA was estimated as H + 6 h and is needed for the time correction as shown in the exponential part of Eqn (8); this value of time correction is overridden as necessary according to table 1 of Beck et al. (2022). Further, Beck et al. (2022) have used a default value of 0.57 for fv. The computed values of DDi(6,1)veg are provided in the second column of Table 14. Values of integrated intake, Ii, are shown in the third column of Table 14 and were calculated according to Eqn (18).

The first column of Table 14 shows the radionuclides considered with indications that some radionuclides are progeny of other radionuclides. This is an important consideration, as some of these pairs are in secular equilibrium. If a pair is in secular equilibrium, then the progeny radionuclide will disappear according to the decay rate of the parent rather than that of the progeny itself. For example, 90Y has a half-life of 64.1 h but is the progeny of 90Sr, which has a half-life of 28.9 y. Thus, within a few days, the activity of 90Y will always be equal to that of 90Sr. If a pair of parent-progeny radionuclides is not in secular equilibrium and the progeny half-life is about the same or even much longer than that of the parent, the activity of the progeny, A2, on vegetation in relation to that of the parent, A1, will be

A2t=λ2A10λ2λ1eλ1+λpteλ2+λpt+A20eλ2+λpt,

where λp as before is the rate of loss of radionuclides from vegetation. A few detailed considerations were made with Eqn (52), but it was found that only a small error is made by simply assuming that the two radionuclides each behave according to its own half-life.

The remaining columns in Table 14 present the committed absorbed dose in Gy to the bone surface, colon, kidneys, liver, red bone marrow, stomach wall, and thyroid and the committed effective dose in Sv. The thyroid receives the largest dose of 58 mGy with 44 mGy due to 131I. The colon receives the second higher dose of 9.7 mGy with 2.7 mGy due to 239Np and with appreciable contributions from 140Ba, 132Te, and 91Y. Calculations of dose from 239Pu are included but must be considered only as crude estimates based on findings related to the Trinity event (Beck et al. 2020, 2022).

Indirect deposition on exposed vegetables and fruits via rain-splash and resuspension

The results of dose calculations for this pathway are shown in Table 15. In this case, the deposition on the soil is used in the calculation according to Eqn (7); values of DDi12Ẋ12R/V=1.0 are taken from Beck et al. (2022). Values of the integrated intake are calculated according to Eqn (19). Intake via this pathway was assumed to begin 30 d after the event and to continue for 60 d; it was then presumed that plowing occurred, and intake was assumed to begin again at 365 d and to continue until 720 d.

The thyroid receives the largest committed dose of 3.1 mGy due almost entirely to 131I. The next higher dose is to the colon at 3.2 mGy with 1.2 mGy due to 106Ru and 0.51 mGy due to 144Ce. Because this pathway was assumed to begin only at 30 d post detonation, the dose calculated for very short-lived radionuclides is extremely small. Some of these short-lived radionuclides were included for consideration only because of their contribution to dose from inhalation rather than ingestion.

Contamination of cows’ milk from the cows’ consumption of exposed forage

This pathway has traditionally received the most attention for reasons discussed above. Table 16 presents example results of calculations of dose via this pathway; the assumption has been made that cows are consuming only fresh pasture. Calculations were made according to Eqn (29) remembering that Fm = fmk,i (λi + λmk,i)−1. Values of Fm,i were taken from table 11 of Thiessen et al. (2022). Those values are for equilibrium situations, so correction factors were calculated according to eqn (13) in that reference. To make that correction, a value is needed for λmk,i. Thiessen et al.’s table 25 gives an estimate of the arithmetic mean biological half-life for all elements in milk as 1.9 d, which is longer than the value of 1.1 d as derived from Table 6; nevertheless, the value of 1.9 d was applied for all results reported in Table 16.

Table 16 - Committed absorbed organ doses (Gy) and effective doses (Sv) for an adult calculated with the traditional method for the pathway of cows’ milk with cows’ consumption of fresh pasture. DDi(6,1)veg has units of Bq m−2 and Ii has units of Bq per Bq m−2.
DDi (6,1) veg Ii Bone surf Colon Kidneys Liver RBM St wall Thyroid Effective
89Sr 9.9E+02 2.3E-01 1.3E-04 3.2E-04 4.5E-06 4.5E-06 1.1E-04 2.0E-05 4.5E-06 5.9E-05
90Sr 5.3E+00 3.0E-01 6.6E-05 2.1E-06 1.1E-07 1.1E-07 2.9E-05 1.4E-07 1.1E-07 4.5E-06
90Y 5.3E+00 5.7E-02 1.0E-11 6.4E-07 4.0E-13 1.1E-11 1.1E-11 3.4E-08 4.0E-13 8.2E-08
91Sr 8.7E+04 4.2E-04 5.1E-07 1.4E-05 2.2E-07 1.8E-07 5.8E-07 3.1E-06 7.2E-08 2.4E-06
91Y 2.9E+03 4.5E-02 8.0E-08 2.5E-04 7.9E-09 8.0E-08 8.6E-08 9.0E-06 1.7E-09 3.1E-05
92Sr 6.8E+04 4.3E-07 2.0E-10 7.9E-09 1.1E-10 7.9E-11 1.9E-10 1.5E-09 3.2E-11 1.3E-09
92Y 1.0E+06 6.6E-07 1.4E-10 1.7E-07 4.1E-10 2.9E-10 3.2E-10 9.3E-08 8.0E-12 3.3E-08
93Y 7.0E+04 9.4E-05 1.3E-09 5.5E-06 3.1E-09 2.2E-09 2.9E-09 8.6E-07 6.5E-11 7.9E-07
97Zr 6.2E+04 1.1E-05 4.2E-09 1.0E-06 7.4E-09 5.3E-09 8.8E-09 8.1E-08 2.6E-10 1.4E-07
97Nb 6.4E+04 1.7E-06 2.0E-11 1.5E-09 6.8E-11 4.3E-11 4.6E-11 4.2E-09 1.5E-12 7.3E-10
99Mo 2.3E+04 5.3E-02 1.2E-04 6.0E-05 3.8E-04 3.4E-04 7.5E-05 9.1E-05 3.1E-05 7.4E-05
99mTc 8.6E+03 8.8E-03 3.7E-08 5.1E-07 4.1E-08 3.3E-08 3.3E-08 4.2E-07 3.6E-07 1.7E-07
103Ru 3.8E+03 4.6E-03 1.9E-07 7.5E-06 2.4E-07 1.9E-07 2.8E-07 5.4E-07 1.2E-07 1.3E-06
103mRh 3.7E+03 4.1E-02 9.8E-11 8.6E-08 7.1E-11 7.0E-11 7.6E-11 3.9E-07 5.0E-11 5.7E-08
105Ru 2.5E+05 2.9E-07 7.2E-11 1.1E-08 1.9E-10 1.3E-10 1.6E-10 3.6E-09 1.2E-11 1.9E-09
105Rh 4.4E+04 2.0E-03 6.8E-08 2.4E-05 9.7E-08 7.2E-08 1.1E-07 1.7E-06 2.6E-08 3.3E-06
106Ru 5.6E+02 6.3E-03 5.2E-07 1.6E-05 5.2E-07 5.2E-07 5.2E-07 1.1E-06 4.9E-07 2.4E-06
132Te 3.1E+04 1.4E-02 4.9E-05 5.8E-04 2.2E-05 1.4E-05 2.4E-05 3.4E-05 1.4E-03 1.7E-04
132I 3.2E+04 3.1E-01 2.5E-05 4.6E-05 3.3E-05 2.8E-05 2.6E-05 6.4E-04 3.4E-03 2.9E-04
131I 1.1E+04 8.2E-01 1.2E-04 1.1E-04 4.2E-05 4.5E-05 9.2E-05 2.8E-04 4.0E-01 2.0E-02
133I 1.5E+05 3.3E-02 2.4E-05 5.3E-05 2.0E-05 1.9E-05 2.3E-05 2.7E-04 4.0E-02 2.1E-03
135I 2.5E+05 8.6E-04 8.7E-07 1.5E-06 8.9E-07 8.2E-07 8.4E-07 1.1E-05 3.4E-04 2.0E-05
137Cs 1.3E+01 3.2E+00 5.8E-05 6.2E-05 5.4E-05 5.4E-05 5.4E-05 5.4E-05 5.4E-05 5.4E-05
140Ba 7.6E+03 3.2E-02 3.9E-05 4.1E-04 5.6E-06 3.6E-06 2.9E-05 1.5E-05 2.1E-06 6.3E-05
140La 7.5E+02 2.4E-02 2.0E-07 2.3E-05 4.0E-07 2.9E-07 4.7E-07 2.0E-06 9.3E-09 3.6E-06
141La 1.7E+05 1.3E-06 1.2E-11 4.2E-08 2.5E-11 2.1E-11 2.0E-11 2.0E-08 7.4E-13 7.6E-09
142La 6.8E+04 2.4E-10 1.4E-14 7.7E-13 4.7E-14 3.1E-14 3.1E-14 1.4E-12 1.5E-15 2.9E-13
143Ce 3.1E+04 2.3E-04 1.5E-08 6.0E-06 2.0E-08 1.6E-08 2.5E-08 4.1E-07 2.6E-10 8.0E-07
143Pr 3.9E+02 2.5E-02 1.7E-09 9.1E-06 2.7E-09 1.4E-08 1.7E-09 3.5E-07 1.1E-11 1.2E-06
144Ce 2.8E+02 7.3E-03 6.6E-08 8.4E-06 4.0E-09 1.9E-07 3.8E-08 2.2E-07 2.4E-09 1.0E-06
144Pr 2.8E+02 5.4E-02 2.7E-11 1.5E-08 1.1E-10 6.3E-11 5.1E-11 6.2E-07 4.1E-12 7.5E-08
145Pr 7.1E+04 1.2E-05 1.9E-11 2.2E-07 4.9E-11 4.4E-11 3.9E-11 5.9E-08 1.3E-12 3.3E-08
239Np 1.5E+05 4.3E-03 1.6E-06 3.8E-04 1.3E-06 8.8E-07 1.6E-06 2.1E-05 9.4E-09 5.0E-05
239Pu 1.5E+00 2.9E-02 3.6E-05 2.1E-07 1.5E-07 7.5E-06 1.7E-06 7.1E-08 6.2E-08 1.1E-06
Sum 6.8E-04 2.4E-03 5.7E-04 5.2E-04 4.7E-04 1.4E-03 4.4E-01 2.3E-02

As expected, the highest committed absorbed dose for the adult is to the thyroid at 440 mGy with 400 mGy due to 131I and 40 mGy due to 133I. The second higher dose is to the colon at 2.4 mGy with significant contributions from 132Te, 140Ba, 239Np, 89Sr, and 91Y.

Contamination of goats’ milk from the goats’ consumption of exposed forage

As previously mentioned, the value of Fm for goats is substantially higher than that for cows. On the other hand, goats are smaller and consume a smaller amount of feed. The results of dose calculations for this pathway are shown in Table 17. Values of Fm are taken from table 12 in Thiessen et al. (2022). Values shown as “n/a” (not available) in Table 17 result because no values of Fm have been provided in Thiessen et al.’s table 12. This pathway is well known as providing high concentrations of iodine in milk, so the emphasis for this pathway has always been on radioiodines.

Table 17 - Committed absorbed organ doses (Gy) and effective doses (Sv) for an adult calculated with the traditional method for the pathway of goats’ milk with goats’ consumption of fresh pasture. DDi(6,1)veg has units of Bq m−2 and Ii has units of Bq per Bq m−2.
DDi (6,1) veg Ii Bone surf Colon Kidneys Liver RBM St wall Thyroid Effective
89Sr 9.9E+02 1.0E+00 6.0E-04 1.4E-03 2.0E-05 2.0E-05 4.9E-04 8.9E-05 2.0E-05 2.7E-04
90Sr 5.3E+00 1.4E+00 3.0E-04 9.6E-06 4.9E-07 4.9E-07 1.3E-04 6.6E-07 4.9E-07 2.1E-05
90Y 5.3E+00 1.9E-03 3.5E-13 2.2E-08 1.3E-14 3.8E-13 3.8E-13 1.1E-09 1.3E-14 2.8E-09
91Sr 8.7E+04 1.2E-03 1.5E-06 4.1E-05 6.5E-07 5.2E-07 1.7E-06 9.1E-06 2.1E-07 6.9E-06
91Y 2.9E+03 1.5E-03 2.7E-09 8.3E-06 2.7E-10 2.7E-09 2.9E-09 3.0E-07 5.6E-11 1.0E-06
92Sr 6.8E+04 1.2E-06 5.6E-10 2.1E-08 2.9E-10 2.1E-10 5.1E-10 4.2E-09 8.7E-11 3.4E-09
92Y 1.0E+06 1.3E-08 2.9E-12 3.5E-09 8.4E-12 5.8E-12 6.5E-12 1.9E-09 1.6E-13 6.7E-10
93Y 7.0E+04 2.1E-06 2.9E-11 1.2E-07 6.8E-11 4.8E-11 6.4E-11 1.9E-08 1.4E-12 1.7E-08
97Zr 6.2E+04 2.5E-06 9.8E-10 2.3E-07 1.7E-09 1.2E-09 2.0E-09 1.9E-08 6.1E-11 3.3E-08
97Nb 6.4E+04 2.9E-06 3.6E-11 2.6E-09 1.2E-10 7.5E-11 8.1E-11 7.3E-09 2.6E-12 1.3E-09
99Mo 2.3E+04 5.7E-02 1.3E-04 6.5E-05 4.1E-04 3.7E-04 8.1E-05 9.9E-05 3.3E-05 8.0E-05
99mTc 8.6E+03 n/a n/a n/a n/a n/a n/a n/a n/a n/a
103Ru 3.8E+03 n/a n/a n/a n/a n/a n/a n/a n/a n/a
103mRh 3.7E+03 n/a n/a n/a n/a n/a n/a n/a n/a n/a
105Ru 2.5E+05 n/a n/a n/a n/a n/a n/a n/a n/a n/a
105Rh 4.4E+04 n/a n/a n/a n/a n/a n/a n/a n/a n/a
106Ru 5.6E+02 n/a n/a n/a n/a n/a n/a n/a n/a n/a
132Te 3.1E+04 4.0E-02 1.4E-04 1.6E-03 6.2E-05 4.0E-05 6.7E-05 9.6E-05 3.9E-03 4.8E-04
132I 3.2E+04 1.2E+00 9.7E-05 1.8E-04 1.3E-04 1.1E-04 1.0E-04 2.4E-03 1.3E-02 1.1E-03
131I 1.1E+04 3.4E+00 5.0E-04 4.6E-04 1.8E-04 1.9E-04 3.9E-04 1.2E-03 1.7E+00 8.5E-02
133I 1.5E+05 1.0E-01 7.6E-05 1.7E-04 6.4E-05 6.2E-05 7.3E-05 8.6E-04 1.3E-01 6.7E-03
135I 2.5E+05 2.4E-03 2.5E-06 4.4E-06 2.5E-06 2.3E-06 2.4E-06 3.2E-05 9.6E-04 5.6E-05
137Cs 1.3E+01 5.6E+00 1.0E-04 1.1E-04 9.3E-05 9.3E-05 9.3E-05 9.3E-05 9.3E-05 9.3E-05
140Ba 7.6E+03 1.2E-01 1.5E-04 1.6E-03 2.2E-05 1.4E-05 1.1E-04 5.9E-05 8.2E-06 2.4E-04
140La 7.5E+02 n/a n/a n/a n/a n/a n/a n/a n/a n/a
141La 1.7E+05 n/a n/a n/a n/a n/a n/a n/a n/a n/a
142La 6.8E+04 n/a n/a n/a n/a n/a n/a n/a n/a n/a
143Ce 3.1E+04 8.8E-05 5.7E-09 2.3E-06 7.6E-09 6.0E-09 9.6E-09 1.5E-07 9.8E-11 3.0E-07
143Pr 3.9E+02 n/a n/a n/a n/a n/a n/a n/a n/a n/a
144Ce 2.8E+02 3.6E-03 3.3E-08 4.2E-06 2.0E-09 9.6E-08 1.9E-08 1.1E-07 1.2E-09 5.2E-07
144Pr 2.8E+02 n/a n/a n/a n/a n/a n/a n/a n/a n/a
145Pr 7.1E+04 n/a n/a n/a n/a n/a n/a n/a n/a n/a
239Np 1.5E+05 3.1E-04 1.1E-07 2.7E-05 9.4E-08 6.3E-08 1.2E-07 1.5E-06 6.7E-10 3.6E-06
239Pu 1.5E+00 n/a n/a n/a n/a n/a n/a n/a n/a n/a
Sum 2.1E-03 5.7E-03 9.8E-04 9.0E-04 1.5E-03 4.9E-03 1.8E+00 9.4E-02

The committed dose from consumption of goat’s milk is highest for the thyroid with a calculated dose of 1.8 Gy with 1.7 of that contributed by 131I and 0.13 Gy by 133I. The next higher dose is 5.7 mGy to the colon with 1.6 mGy from 140Ba and significant contributions from 132Te and 89Sr. Fortunately, the consumption of goat’s milk is not common.

Contamination of meat from cattle’s consumption of fresh forage

Committed dose via this pathway was calculated according to Eqn (43); values of Ff were taken from table 15 of Thiessen et al. (2022). Because of time lags, the doses are rather small. The results are shown in Table 18. The thyroid receives the largest dose at 6.3 mGy almost entirely due to 131I. As is the usual case, the colon receives the next higher dose of 1 mGy with significant contributions from 106Ru, 91Y, 144Ce, and 103Ru.

Table 18 - Committed absorbed organ doses (Gy) and effective doses (Sv) for an adult calculated with the traditional method for the consumption of beef meat with cattle’s consumption of fresh pasture. DDi(6,1)veg has units of Bq m−2 and Ii has units of Bq per Bq m−2.
DDi (6,1) veg Ii Bone surf Colon Kidneys Liver RBM St wall Thyroid Effective
89Sr 9.9E+02 4.0E-02 2.3E-05 5.5E-05 7.9E-07 7.9E-07 1.9E-05 3.4E-06 7.9E-07 1.0E-05
90Sr 5.3E+00 8.8E-02 1.9E-05 6.1E-07 3.1E-08 3.1E-08 8.4E-06 4.2E-08 3.1E-08 1.3E-06
90Y 5.3E+00 5.9E-02 1.1E-11 6.5E-07 4.1E-13 1.2E-11 1.2E-11 3.4E-08 4.1E-13 8.4E-08
91Sr 8.7E+04 6.9E-26 8.5E-29 2.3E-27 3.7E-29 3.0E-29 9.7E-29 5.1E-28 1.2E-29 3.9E-28
91Y 2.9E+03 3.5E-02 6.2E-08 1.9E-04 6.1E-09 6.2E-08 6.6E-08 6.9E-06 1.3E-09 2.4E-05
92Sr 6.8E+04 1.8E-85 8.7E-89 3.3E-87 4.4E-89 3.3E-89 7.9E-89 6.6E-88 1.4E-89 5.3E-88
92Y 1.0E+06 2.5E-65 5.4E-69 6.6E-66 1.6E-68 1.1E-68 1.2E-68 3.6E-66 3.1E-70 1.3E-66
93Y 7.0E+04 7.3E-25 1.0E-29 4.2E-26 2.4E-29 1.7E-29 2.2E-29 6.6E-27 5.0E-31 6.1E-27
97Zr 6.2E+04 3.6E-19 1.4E-22 3.3E-20 2.4E-22 1.7E-22 2.9E-22 2.6E-21 8.6E-24 4.6E-21
97Nb 6.4E+04 7.9E-20 9.6E-25 7.1E-23 3.2E-24 2.0E-24 2.2E-24 2.0E-22 7.1E-26 3.4E-23
99Mo 2.3E+04 5.3E-06 1.2E-08 6.0E-09 3.8E-08 3.4E-08 7.5E-09 9.1E-09 3.1E-09 7.4E-09
99mTc 8.6E+03 5.3E-05 2.2E-10 3.0E-09 2.5E-10 2.0E-10 2.0E-10 2.5E-09 2.1E-09 1.0E-09
103Ru 3.8E+03 8.3E-02 3.5E-06 1.4E-04 4.4E-06 3.5E-06 5.0E-06 9.8E-06 2.1E-06 2.3E-05
103mRh 3.7E+03 3.4E-01 8.2E-10 7.2E-07 5.9E-10 5.8E-10 6.3E-10 3.3E-06 4.2E-10 4.8E-07
105Ru 2.5E+05 2.3E-52 5.7E-56 8.6E-54 1.5E-55 1.0E-55 1.3E-55 2.9E-54 9.7E-57 1.5E-54
105Rh 4.4E+04 4.1E-08 1.4E-12 4.9E-10 2.0E-12 1.5E-12 2.2E-12 3.4E-11 5.4E-13 6.7E-11
106Ru 5.6E+02 1.7E-01 1.4E-05 4.2E-04 1.4E-05 1.4E-05 1.4E-05 2.9E-05 1.3E-05 6.5E-05
132Te 3.1E+04 1.3E-04 4.6E-07 5.4E-06 2.0E-07 1.3E-07 2.2E-07 3.2E-07 1.3E-05 1.6E-06
132I 3.2E+04 1.2E-04 9.4E-09 1.7E-08 1.2E-08 1.0E-08 9.7E-09 2.4E-07 1.3E-06 1.1E-07
131I 1.1E+04 1.3E-02 1.9E-06 1.7E-06 6.7E-07 7.1E-07 1.5E-06 4.4E-06 6.3E-03 3.2E-04
133I 1.5E+05 8.0E-13 5.8E-16 1.3E-15 4.9E-16 4.8E-16 5.6E-16 6.5E-15 9.8E-13 5.1E-14
135I 2.5E+05 7.0E-36 7.1E-39 1.3E-38 7.3E-39 6.7E-39 6.9E-39 9.3E-38 2.8E-36 1.6E-37
137Cs 1.3E+01 1.3E+00 2.3E-05 2.4E-05 2.1E-05 2.1E-05 2.1E-05 2.1E-05 2.1E-05 2.1E-05
140Ba 7.6E+03 1.0E-03 1.2E-06 1.3E-05 1.8E-07 1.1E-07 9.2E-07 4.8E-07 6.7E-08 2.0E-06
140La 7.5E+02 9.6E-04 7.9E-09 9.4E-07 1.6E-08 1.2E-08 1.9E-08 7.9E-08 3.7E-10 1.4E-07
141La 1.7E+05 4.6E-60 4.4E-65 1.5E-61 9.2E-65 7.7E-65 7.2E-65 7.1E-62 2.7E-66 2.8E-62
142La 6.8E+04 1.5E-148 8.7E-153 4.8E-151 3.0E-152 1.9E-152 1.9E-152 8.6E-151 9.1E-154 1.8E-151
143Ce 3.1E+04 2.9E-09 1.9E-13 7.4E-11 2.5E-13 1.9E-13 3.1E-13 5.0E-12 3.2E-15 9.7E-12
143Pr 3.9E+02 8.3E-03 5.5E-10 3.0E-06 9.1E-10 4.5E-09 5.5E-10 1.2E-07 3.6E-12 3.9E-07
144Ce 2.8E+02 1.4E-01 1.2E-06 1.6E-04 7.5E-08 3.6E-06 7.2E-07 4.1E-06 4.5E-08 2.0E-05
144Pr 2.8E+02 6.6E-02 3.3E-11 1.8E-08 1.3E-10 7.7E-11 6.2E-11 7.5E-07 4.9E-12 9.1E-08
145Pr 7.1E+04 5.5E-40 9.1E-46 1.0E-41 2.3E-45 2.1E-45 1.8E-45 2.8E-42 6.3E-47 1.5E-42
239Np 1.5E+05 1.3E-06 4.7E-10 1.1E-07 4.0E-10 2.6E-10 4.9E-10 6.4E-09 2.8E-12 1.5E-08
239Pu 1.5E+00 6.4E-04 8.0E-07 4.7E-09 3.3E-09 1.7E-07 3.8E-08 1.6E-09 1.4E-09 2.5E-08
Sum 8.8E-05 1.0E-03 4.2E-05 4.4E-05 7.1E-05 8.4E-05 6.3E-03 4.9E-04

Results for this pathway are sensitive to input assumptions regarding times on pasture and delay between slaughter and consumption. For the calculations shown here, it was assumed that cattle began consuming fresh pasture 30 d after the event and were slaughtered 60 d after the event. The holdup time was assumed to be 14 d.

DISCUSSION AND CONCLUDING REMARKS

This paper is one of six companion papers that present methods for calculating radiation doses following exposure to radioactive fallout from the detonation of a fission device, regardless of whether the event was in the past or is contemporary and whether it is a prospective or retrospective assessment. As discussed in Simon et al. (2022), the main difference might be in the selection of estimates of parameter values and the choice of the simpler or more complex assessment method.

We have presented two alternative methods in this paper for estimating internal doses. The first method is based upon the results of the Offsite Radiation Exposure Review Project (ORERP), which was conducted during the 1980s and whose results have been summarized here to provide estimates of intake by humans, by time of year, or normalized to ground deposition, i.e., Bq intake per Bq m−2 deposition. This numerical summary, derived from detailed pathway analysis (Whicker and Kirchner 1987), provides a quick means of estimation but requires an understanding of the associated limitations, which is the applicability of the original pathway calculations to the location and environmental characteristics of concern for the assessment of interest. The second method provided is composed of analytical solutions to individual models and allows the assessor to tailor the assessments more to the situation of interest. While both methods are endorsed, their choice should be scrutinized for the application. A possible strategy well after any emergency of a nuclear detonation has passed would be to conduct calculations both ways for comparison.

To estimate dose at any location using these methods, it is essential to know or have available a measured or well-estimated value of the exposure rate at that location at a defined time and to know the approximate time of arrival of the fallout at that location. Other necessary information and data are provided in the six companion papers, and the authors have attempted to make the overall calculational system as simple as possible, albeit even those can become relatively complex when using the disaggregated method. To expedite this process, the authors have suggested default values for the various model parameters. Such default values have been presented in Beck et al. (2022) and in Appendix A to this paper.

Several types of input data are difficult to obtain and are difficult and uncertain to estimate. In terms of environmental transport, the most uncertain component of the process is estimating the retention of fallout on vegetation, which is strongly dependent upon the particle size of the fallout. This problem is discussed extensively in Beck et al. (2022). The data from Beck et al. (2022), Thiessen et al. (2022), and Melo et al. (2022) are essential for the goal of this paper, which is to present methods for the calculation of internal dose. External dose, which will generally be larger than internal dose (with the possible exception of dose to the thyroid or colon), is treated in the companion paper by Bouville et al. (2022).

In terms of estimating individual or population exposures, the assumptions about time spent outdoors, building construction and the associated degree of shielding, the origin of food products and the degree of contamination, as well as dietary practices, are all important and their proper evaluations represent difficult challenges. If even a surprise detonation should occur at the present time, it should be possible to avoid most internal dose from the ingestion pathway. Because the pathways to man have been studied by many investigators over the past 70 y and are well understood, it should be possible to interdict and/or divert contaminated foods, and in particular the consumption of fresh milk, so that internal dose can be largely eliminated. A great deal of information on how to suppress internal dose has become available following the Chernobyl accident. These and other countermeasures are summarized in Simon et al. (2022).

Prevention of internal dose from inhalation, however, is more difficult because protective actions would probably be limited to requesting or requiring nearby residents to shelter in place and to turn off ventilation systems that move outdoor air within buildings, at least until the debris cloud has passed. In this paper, we have more completely discussed methods for assessing inhalation dose from particulate fallout than have been previously available.

The radionuclides selected for inclusion in this study include 34 radionuclides composed of 23 primary and 11 progeny radionuclides. If a primary radionuclide itself is ingested, it is not necessary to be concerned about progeny that might arise inside the human body as their contributions to dose are included in the calculated dose coefficient for the primary radionuclide. However, in several cases the progeny radionuclide itself can be ingested and it must therefore be treated separately. Issues concerned with primary and progeny radionuclides have been treated by Beck et al. (2022) and within this paper.

The uncertainty in the calculated values of internal dose is quite large; some estimates of uncertainty have been treated specifically. The overall conclusion regarding uncertainty is that if estimates of the values of model parameters are considered to be geometric means, the associated values of geometric standard deviations are at least a factor of 3 at the one-standard-deviation confidence level. A valuable examination of uncertainty in dose according to time of year has been published by Breshears et al. (1989), and there are numerous examples of uncertainties on ingestion doses published in previous assessments, as discussed earlier in this paper. More detailed calculations of dosimetric uncertainty by Monte Carlo methods might be considered to be carried out in future assessments using the estimated parameter uncertainties provided in the companion papers.

The complete set of fallout dose-assessment methods, of which this is a single component, provides a well conceptualized and internally consistent strategy for estimating radiation doses from exposure to fallout from nuclear detonations. While not every possible means of internal contamination are presented with analytical models, we have focused on those routes of exposure that we believe to be most important for most assessments in the US and western countries. Assessments for specific populations and/or specific exposure scenarios that might vary from the circumstances that we have discussed can adopt easily the methodologic strategies that we have presented. In summary, the methods provided here should be usable and applicable to most fallout contamination situations that can be envisioned and should be valuable to national initiatives in the US to prepare either for expected or unexpected detonations and the resulting contamination.

Acknowledgments

This research was primarily supported by the Intra-Agency Agreement between the National Institute of Allergy and Infectious Diseases and the National Cancer Institute, NIAID agreement #Y2-Al-5077 and NCI agreement #Y3-CO-5117 with additional support from the Intramural Research Program of the NCI, NIH. The results presented here also reflect past long-term funding by the Department of Energy and its predecessor agencies and the National Cancer Institute. The authors acknowledge the extensive work of many investigators who preceded them and contributed to our present-day understanding of exposure to radioactive fallout. Authors of this paper on internal dose express their appreciation for the work of the late Harold Knapp, a former employee of the Atomic Energy Commission; to the late Harry Hicks and Yook Ng, who worked until retirement at the Lawrence Livermore National Laboratory and provided important tools for our analyses; and to Ward Whicker and Thomas Kirchner, who pioneered work at the Colorado State University on understanding and modeling radioecological processes. We thank Dunstana Melo of Melohill Technology and Luiz Bertelli of Los Alamos National Laboratory for their helpful input on evaluating dose from inhalation.

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      APPENDIX A - PARAMETERS, SYMBOLS, AND ACRONYMS LISTED ALPHABETICALLY
      Symbol Parameter or symbol Source or relationship Default value Units
      0.57 Value of fv assumed by Beck et al. (2022) unitless
      (1-a) Fit parameter = 1X–[0.1 × eX–(HOB/70)] 0.95 unitless
      AD Aerodynamic diameter = PD μm
      A 1 Activity of parent nuclide Eqn (52) Bq
      A 2 Activity of progeny nuclide Eqn (52) Bq
      AMAD Activity median aerodynamic diameter μm
      B Dry biomass per unit area Not an independent variable; part of a complex parameter See (fv B −1) kg(dry) m−2
      BRage Breathing (ventilation) rate as a function of age Table 11 m3day−1
      β(12) Deposition density of beta-emitting radionuclides at H + 12 Bq m−2
      Total beta activity per unit area at H + 12 normalized to exposure rate at H + 12; depends on R/V Inferred from measurements Beck et al. (2022)Table 5 Bq m−2 (mR h−1)−1
      Cv Concentration of fallout in vegetation Measurement Bq kg(dry)−1
      Cmk,i Normalized concentration of nuclide i in milk Numerous eqns m2 L−1
      Cmt,i Normalized concentration of nuclide i in meat Numerous eqns m2 kg−1
      CT Top of cloud = 1.85 × ln(Y) +4.7 9.0 km
      d Fit parameter Beck et al. (2022) appendix B 1.6 unitless
      d s1 Initial depth of soil within which radionuclides are mixed 0.005 m
      d s2 Depth of soil tillage 0.2 m
      d s3 Depth of soil consumed by grazing animals Varies with time, see text. m
      Di Dose due to nuclide i, absorbed or effective Numerous Eqns Gy or Sv
      DCi Dose coefficient ICRP (2011); Melo et al. (2022) Gy Bq−1 or Sv Bq−1
      DD Deposition density Bq m−2
      DDi (TOA)' Normalized total deposition density of nuclide i at TOA Bq m−2 (mR h−1)−1
      DDi (TOA,R/V) Deposition density of nuclide i at TOA, depends on R/V Bq m−2
      DDi (TOA,R/V) veg Deposition density of nuclide i on vegetation at TOA, depends on R/V Bq m−2
      Activity fraction of nuclide i to total beta activity intercepted by vegetation at H + 12 for R/V = 0.5 Beck et al. (2022) table C5 unitless
      Deposition density of nuclide i normalized to exposure rate at H + 12. Depends on R/V. Beck et al. (2022)
      Table 6
      Bq m−2 (mR h−1)−1
      ET Extrathoracic region of the HRT ICRP (1994)
      ET2 Posterior nasal passages, larynx, pharynx and mouth ICRP (1994)
      f 1 Fractional absorption in the GI ICRP (2011); Melo et al. (2022) unitless
      fdry,wet Ratio of dry weight to wet weight of food 0.15 unitless
      flocal Fraction of food produced locally 0.2 unitless
      fgrow Fraction of season where vegetation is exposed and harvested 0.3 unitless
      fin,out Factor of reduction in air concentration due to time indoors 0.5 unitless
      fprep Fraction of nuclides remaining after food preparation 0.5 unitless
      fmk,i Fraction of nuclide i secreted in milk L−1
      fmt,i Fraction of nuclide i found in meat kg−1
      fv Fraction of fallout deposited on vegetation Not an independent variable, part of a complex parameter See (fv B −1) unitless
      (fv B −1) Vegetation (dry) mass interception factor Composite variable 3.0 m2 kg−1
      Ff Equilibrium ratio of concentration in meat or eggs to the daily intake Thiessen et al. (2022)Table 14 and Table 15 day kg−1
      Fm Equilibrium ratio of concentration in milk to the daily intake Thiessen et al. (2022)Table 11 (cows) and Table 12 (goats) day L−1
      Fv Soil-to-vegetation transfer coefficient Thiessen et al. (2022)Table 10 Table 5 Bq kg−1 dry plant tissue per Bq kg−1 dry soil
      GI Gastrointestinal tract
      GM Geometric mean
      GSD Geometric standard deviation
      HOB Height of burst of detonation 70 m
      HRT Human respiratory tract
      HRTM Human respiratory tract model ICRP (1994; 2015)
      i Index for radionuclide
      Ii Integrated intake of nuclide i Table 2 Bq (Bq m−2)−1 or m2
      Rate of intake of nuclide i m2 day −1
      Imt,i Integrated intake of nuclide i with meat Bq (Bq m−2)−1 or m2
      Rate of intake of nuclide i with meat m2 day−1
      Cows’ rate of intake of nuclide i Bq day−1
      Cows’ rate of intake of nuclide i normalized to deposition density m2 day−1
      Goats’ rate of intake of nuclide i normalized to deposition density m2 day−1
      IDDi Time integrated concentration of nuclide i in soil Eqn (38) Bq day m−2
      IND Improvised nuclear device
      j Index for particle size range
      K1 Unit conversion constant 1000 g kg−1
      K2 Unit conversion constant 86,400 s day−1
      λ 1 Decay constant for parent nuclide Eqn (52) day−1
      λ 2 Decay constant for progeny nuclide Eqn (52) day−1
      λi Decay constant for nuclide i Thiessen et al. (2022) table 1 day−1
      λmk,i Elimination constant for nuclide i in milk day−1
      λmt,i Elimination constant for nuclide i in meat day−1
      λp Loss constant for nuclide i deposited on vegetation 0.050 growing
      0.023 dormant
      day−1
      L Mass loading of soil on dry vegetation 10 g kg−1
      MPD Rate of dry matter intake for dairy animals 14 for cows
      2.3 for goats
      kg day−1
      μ Chamberlain’s fit parameter Eqn (11) 3.0 m2 kg−1
      N Number of observations unitless
      N 0 Fraction of total beta activity on <50-μm particles deposited on soil+vegetation on the axis of the trace at the same TOA as at the location under consideration. Eqn (10) unitless
      N 50 Fraction of total beta activity on <50-μm particles deposited on soil+vegetation at the location under consideration Eqn (9) unitless
      Nj Fraction of total beta activity in particle-size range j Fig. B3 unitless
      PD Physical diameter of particles μm
      PS Particle size μm
      R Refractory elements
      R/V Ratio of refractory elements-to-volatile elements Beck et al. (2022)Table 4 0.5
      R/V’ Adjusted R/V for inhalation of larger particles Appendix B
      Rate of intake of exposed fruits and vegetables Table 4 gwet day−1
      (kgbody weight)−1
      Rate of intake of all fruits and vegetables Table 4 gwet day−1
      (kgbody weight)−1
      Rate of intake of milk Table 7 gwet day−1
      (kgbody weight)−1
      Rate of intake of meat Table 7 gwet day−1
      (kgbody weight)−1
      ρ Dry bulk density of soil 1.6 × 106 g m−3
      S Rate of ingestion of soil by dairy animals Table 8 0.07 kg day−1
      SD Standard deviation
      SE Standard error
      σ Standard deviation of a distribution
      TOA Time of arrival of fallout Must be measured or inferred
      t 1 Time from fallout to end of consumption of exposed vegetation and fruit Eqn (18) 30 day
      t 2 Time from fallout to the beginning of the first growing season 30 day
      t 3 Time from fallout to the end of the first growing season 90 day
      t 4 Beginning of second growing season 365 day
      t 5 End of second growing season 720
      tmax Time for 50-μm particles to reach the ground = CT wg −1 12.0 h
      tr Reduced TOA TOA tmax −1 unitless
      τ Time consuming fresh milk Eqn (28) day
      τ 1 Time from fallout to the beginning of consumption of meat 30 day
      τ 2 Time to the end of consumption of meat 60 day
      UAF Utilized area factor for dairy cow 38 m2 day−1
      V Volatile radionuclides
      vd Deposition velocity Depends on AD m s−1
      wg Settling velocity of 50-μm particle 0.75 km h−1
      Exposure rate at time t Must be measured or inferred mR h−1
      Exposure rate at TOA Must be measured or inferred mR h−1
      Ratio of exposure rate at location of interest-to-exposure rate on trace center at same arc Must be measured or inferred unitless
      x Straight-line distance from detonation to point of interest km
      Mean value of a distribution
      Y Explosive yield Inferred 10 kt

      APPENDIX B: DETAILS AND EXAMPLES OF CALCULATION OF DOSE FROM THE INHALATION OF FALLOUT

      Method

      Baurmash et al. (1958) reported the fractional activity as a function of physical particle size (<5, <20, <44, <88, etc., up to <2,000 μm) and distance from ground zero for four events (Tesla, Apple-1, Met, and Apple-2) of Operation Teapot that took place in 1955; Miller (1963) has reported values of deposition velocity for fallout particles as a function of physical particle size. Together the two sources provide information from which a numerical integration of Eqn (50) can be performed to estimate the integral activity-weighted average value of (1/vd) as a function of N50 for each size interval of interest.

      Fig. B1 shows an example of using these NTS distributions to estimate the particle-size distributions as a function of N50. The NTS data in each size group (<20, <88, etc.) were plotted vs. N50. Fits to the plots followed by interpolation provided a reasonable estimate of the activity-particle-size distribution vs N50 for each size interval of interest. The scatter of points for a given N50 reflect the fact, as discussed in Beck et al. (2022), that N50 will increase with distance from the axis. Thus, the lowest points at each N50 represent near axis points (N50-axis) while the higher values actually represent the N50 values for off axis sites for the same tr. Thus, we fit to the lower boundary (near axis points) to estimate the actual dependence on N50. Although the NTS data are from a variety of tests with different yield and fuel (Beck et al. 2022, appendix B) there does not appear to be a significant dependence on explosive yield or fuel, consistent with the model for N50 discussed in Beck et al. (2022).

      FB1
      Fig. B1:
      Fraction of total beta activity on particles <88-μm particles (physical diameter) as a function of N 50. The dashed line is our estimate of the values on the trace axis that represent the actual fraction of activity for that value of N 50.

      The inferred particle-size distributions as a function of N50 are shown in Fig. B2. Using these inferred particle-size distributions, we interpolated between the calculated curves to obtain a finer matrix of fraction of beta activity vs. particle size. Fig. B3 shows the estimated particle-size distribution for each of the three relevant size ranges for selected values of N50. We then numerically integrated (1/vd) over the three size ranges of interest. The calculated values of the integral of (1/vd) as a function of N50 for the size ranges of interest are shown in Fig. B4. Note that ∫(1/vd) is relatively independent of N50 reflecting the fact that the increasing fraction of total activity on larger particles for all N50 is offset by the ~r2 increase of vd with increasing particle size. Suggested default values for all other parameters in Eqn (50) are given in Table 10.

      FB2
      Fig. B2:
      Fraction of total beta activity on particles of various physical diameter (μm) as a function of N 50.
      FB3
      Fig. B3:
      Estimated fraction of total deposited beta activity in the indicated aerodynamic particle-size range (N j) as a function of N 50.
      FB4
      Fig. B4:
      Activity-weighted average of (1/v d) over indicated aerodynamic particle size range vs. N 50.
      Example of calculation of dose using Eqns (50) and (51)
      Example 1

      For this example, it is assumed that an individual is at a hypothetical location downwind of a shot similar to NTS test Tesla. The fallout arrived at H + 6 h (TOA), and an exposure rate of 240 mR h−1 was measured at the site and 265 mR h−1 on the center of the trace, so (/max) = 0.9. It is known that Tesla had an explosive yield (Y) of 7 kt and the height of the burst (HOB) was 92 m. (Of course, in a future situation neither of these parameters might be immediately known, so default values are suggested in Table 10.) The settling velocity, wg, of particles of a given size is known from physics considerations. For a 50-μm PD (2.5 g cm−3) particle, wg is taken to be a constant equal to 0.75 km h−1. The top of the resulting cloud (CT) is calculated as shown in Table 10 and is equal to 8.3 km. The time for a 50-μm PD particle to reach the ground, tmax, is calculated as shown to be 11.1 h. The reduced time of arrival (tr) is equal to the TOA divided by tmax, which is 0.54 for the example.

      As discussed in Beck et al. (2022), the fit parameter (1-a) depends on the HOB. With use of the default parameters for d and (1-a) from Table 10, N50 is then calculated to be 0.59. The value of 0.59 then defines the value of R/V for the entire particle size range to be equal to 1.0 as shown in table 5 of Beck et al. (2022). As discussed in the main text, R/V’ for the 1 to 20-μm interval is taken to be 0.5; 1.5 for the >20 to 100-μm region; and 2.0 for the >100-μm region based on the inferred R/V for the entire particle-size distribution.

      The fraction of activity on particles <20 μm, (Nj = 1), >20–100 μm (Nj = 2) and > 100 μm (Nj = 3) from Fig. B3 are 0.22, 0.42, and 0.35, respectively, for N50 = 0.59.

      In order to derive the amount of deposition on the ground, the exposure rate at H + 12 h, X˙ (12), must be estimated from the measured exposure rate at TOA. This is derived through use of the exposure-rate time dependence given in table 3 of Beck et al. (2022) and is calculated to be 100 mR h−1. The correction factor for the in-growth and decay of 131I between H + 6 h and H + 12 h is equal to 1.01 from table 1 in Beck et al. (2022).

      The respective values of DDI-131(TOA = 6 h, N50 = 0.59, X˙12 = 100 mR h−1) for 131I calculated using Eqn (51) for the three particle size intervals for R/V = 1.0, R/V’ = 1.5 are:

      DDI131=0.22×4.19×106×9.48×103×1.01×100=882kBqm2 for 1–20 μm (B1)

      DDI131=0.42×4.19×106×5.15×103×1.01×100=915kBqm2 for >20–100 μm (B2)

      DDI131=0.35×4.19×106×5.15×103×1.01×100=763kBqm2 for >100–800 μm. (B3)

      The integrals of the activity-weighted ratio of (1/vd) (Fig. B4) for 1–20 μm, >20–100 μm, and > 100 μm for N50 = 0.59 are 248, 15, and 1.15 s m−1, respectively.

      A suggested value of fin/out is 0.5. The simple basis is that people spend about 90% of the time at their home where air concentrations are assumed to be about a factor of 2 lower. Thus,

      fin/out=1×0.1+0.920.5.

      Suggested values of ventilation rates for different ages and occupations are shown in Table 11; the data are taken from ICRP (1994).

      The final parameter is the dose coefficient, DCi. The values tabulated in Melo et al. (2022) should be used for inhalation of fallout rather than those of the ICRP (2011). For 131I for an adult male, the values of dose coefficients for the thyroid are shown in their table 24 as 1.5 × 10−7, 2.1 × 10−7, 1.9 × 10−7, and 1.6 × 10−7 Gy Bq−1 for the AMAD particle sizes of 1, 5, 10, and 20 μm, respectively. These values are also shown in Fig. 2. The value of 1.6 × 10−7 Gy Bq−1 for an AMAD particle size of 20 μm is that chosen to be used in Eqn (50). It is about 10% lower than the average value of the dose coefficients for the AMAD particle sizes of 1, 5, 10, and 20 μm, which is 1.8 × 10−7 Gy Bq−1. The ingestion DC for an adult thyroid from table 24 of Melo et al. (2022) is 4.7 × 10−7 Gy Bq−1.

      Then, the solutions of Eqn (50) are:

      DI131120μm=8.82×105×248×0.5×22.18×1.6×107×100086,000=4.5mGy.
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