Database of ICRP Publication 144 for soil contamination

Fig 1 shows a schematic representation of the simulated geometry for computing the dose-rate coefficients for soil contamination presented in ICRP Publication 144, and Table 1 summarizes its specification. Radiation-transport simulations starting from widely distributed radiation sources in the environment require considerable computing time to achieve sufficient statistical accuracy of the radiation field at its center. It is inefficient to repeat the time-consuming simulation for every sex- and age-specific phantom. Therefore, in the methodology adopted for the work of ICRP Publication 144 and other similar studies [1–6], the radiation-transport simulation was divided into two steps. (1) Simulation of the environmental radiation fields for monoenergetic photon and electron sources on and in the soil and (2) simulation of the doses absorbed by organs and tissues in the human body, i.e., reference phantoms exposed to environmental radiation. Therefore, the environmental radiation field obtained in Step 1 was used to the Step 2 simulation for the radiation transport in the phantoms.

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Fig 1. Simulation steps for soil contamination following ICRP Publication 144.

MFP: mean-free path of photons in the air.

https://doi.org/10.1371/journal.pone.0310552.g001

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Table 1. Specifications of ICRP Publication 144 [7] database for soil contamination.

https://doi.org/10.1371/journal.pone.0310552.t001

In Step 1, planar sources of monoenergetic photons, whose energies ranged from 10⁻² to 8 MeV with 25 energy points, were set to depths of 0.0, 0.2, 1.0, 2.5, and 4.0 mean-free path (MFP) of photons in the soil. Electron transport was only performed for a planar source of monoenergetic electrons on the ground surface as electrons in the soil hardly reach the surface. To model the environment that infinitely extends in the horizontal direction, the radius of the cylindrical simulation geometry was set to 5 MFP of photons in the atmosphere. The actual length was varied according to the source energy. The radiations propagating through the environment were recorded in terms of their type, energy, and angle of incidence on the surface of a virtual cylinder (60-cm diameter, 200-cm height; coupling cylinder) on the soil at the center of the geometry.

In Step 2, the radiation-transport simulation was restarted from the surface of the coupling cylinder in which air and the phantom were placed. Equivalent dose rates of organs and tissues, except for the skin, were calculated using the voxel-type ICRP reference pediatric (newborn, 1-, 5-, 10-, and 15-year-old children) [14] and adult [17] male and female phantoms. The skin doses were estimated using the mesh-type ICRP reference phantoms [15, 16, 18] for a 50-μm-thick layer within a depth range of 50–100 μm below the skin surface, which is considered to be the radiosensitive target layer. Effective dose rates were obtained based on the definition of the current ICRP system of radiological protection described in the ICRP 2007 Recommendations [8]. Therefore, the same set of tissue weighting factors was used in their computation for all age groups [7], and the differences in the effective dose rates as a function of age are only due to the anatomical differences in the phantoms. In addition, ambient dose equivalent and air kerma rates were computed at a height of 1 m above the ground. The combined relative uncertainties given as one standard deviation from both Step 1 and Step 2 simulations were less than 1% and 10%, respectively, for the air kerma rates and the equivalent dose rates of most organs and tissues.

The dose-rate coefficients for monoenergetic planar sources at depths in the soil expressed in MFP were evaluated using the aforementioned simulations. The unit of the dose-rate coefficients was nSv h⁻¹ Bq⁻¹ m², except for those of air kerma [nGy h⁻¹ Bq⁻¹ m²]. Based on these data, the dose-rate coefficients for monoenergetic planar sources at specific depths of 0.0, 0.5, 3.0, and 10.0 g cm⁻² were computed and tabulated. Furthermore, the coefficients for volume sources with exponential distributions bearing relaxation masses per unit area of 0.5, 1.0, 2.5, 5.0, 10.0, 20.0, 50.0, and 100.0 g cm⁻² were computed and tabulated [7]. The distribution of the volumetric sources was limited to a depth of 100 g cm⁻² below the ground surface.

Nuclide-specific coefficients were deduced from the data for the monoenergetic sources according to the radioactive decay data of the 1252 nuclides of 97 elements presented in ICRP Publication 107 [13]. X-rays, gamma rays, annihilation photons, beta particles, and internal conversion and Auger electrons within the energy range of 10⁻² to 8 MeV were considered radiations emitted from the radioactive decay. The contribution of bremsstrahlung generated by beta particles and electrons in the soil was considered [1]. In ICRP Publication 144, dose-rate coefficients of a radionuclide only include the contribution of radiations from the decay of that nuclide and not the contributions from progeny nuclides produced in the decay chain.

Dose-rate coefficients for volumetric sources in soil to an effectively infinite depth

First, the coefficients for photons, electrons, and bremsstrahlung were determined separately for monoenergetic volumetric sources in soil to an effectively infinite depth with 25 energy points from 10⁻² to 8 MeV. Thereafter, the coefficients were interpolated and summed, considering the radiations from each nuclide. For photons, the sources were uniformly distributed from the ground surface to the depth of 4 MFP in the soil; this depth can be regarded as an effectively infinite depth because the dose contribution to a person on the ground from deeper sources is negligible. The dose-rate coefficient of the infinite photon source, [nSv h⁻¹ Bq⁻¹ kg], was obtained using the previously developed weighted-integral method [19, 20] as follows: (1) where E [MeV] is the energy of the monoenergetic photon source, and A [Bq m⁻¹] and a(ζ) [Bq m⁻²] are the total activity to the infinite depth and the activity concentration on the planar source at depth ζ [m], respectively. [nSv h⁻¹ Bq⁻¹ m²] is the dose-rate coefficient of photons with energy E from the planar source at depth ζ.L(E) [m] is the physical depth of the volumetric source obtained by converting 4 MFP of the photons in the soil with a density of ρ [kg m⁻³]. a(ζ) is a constant value with respect to ζ owing to its uniform distribution. The integration was numerically solved using a trapezoidal rule with small strips, in which the quantity, , was determined using the piecewise cubic Hermite interpolating polynomial (PCHIP) [21] for the data of ICRP Publication 144.

Only beta particles and electrons emitted from nuclides on the ground surface were considered; therefore, the dose-rate coefficient of beta particles and electrons for the infinite source, [nSv h⁻¹ Bq⁻¹ kg], was expressed as follows: (2) where [nSv h⁻¹ Bq⁻¹ m²] is the dose-rate coefficient of an electron with energy E at ζ = 0 from ICRP Publication 144. a(0) [Bq m⁻²] is the activity concentration of the source in a thin layer of the ground surface, whose thickness Δζ was set to 0.1 μm. A [Bq m⁻¹] is the total activity of the infinite source and has the same value as that in Eq (1). Electrons emitted from an underground source cannot penetrate the soil; however, they produce bremsstrahlung, which is a type of photon. The maximum energy of the bremsstrahlung reaches the energy of the electron and can contribute to the dose rate above the ground. Using the same method as that in ICRP Publication 144, the dose contribution of bremsstrahlung from electron sources deeper than 0.5 g cm⁻² was considered. The dose-rate coefficients for monoenergetic bremsstrahlung, [nSv h⁻¹ Bq⁻¹ kg], were estimated using the data of planar photon sources, , as follows: (3) where B_min is the lower integral limit corresponding to the physical depth of 0.5 g cm⁻² in the soil.

Nuclide-specific dose-rate coefficients for photon and electron sources, and [nSv h⁻¹ Bq⁻¹ kg], respectively, were obtained from the results of the aforementioned monoenergetic photons and electrons using the following equations: (4) where and are the yields of the photon and electron with discrete energy E_i emitted from radionuclide N, respectively. Φ^N,e(E) [MeV⁻¹] in the integration of the second term for electrons denotes the yield of beta particles with a continuous energy spectrum. The data regarding radiation yields from the radioactive decay of nuclides were obtained from ICRP Publication 107 [13]. The dose-rate coefficients were estimated by interpolating the dose coefficients of monoenergetic sources (given for 25 energy points; 10⁻² to 8 MeV) using the PCHIP [21]. For bremsstrahlung, the nuclide-specific dose-rate coefficient, [nSv h⁻¹ Bq⁻¹ kg], was evaluated as follows: (5) where Φ^N,b(E) [MeV⁻¹] is an energy fluence of bremsstrahlung produced by electrons emitted from the decay of nuclide N in the soil. E is the energy in a continuous bremsstrahlung spectrum. The numerical data of Φ^N,b(E) for each nuclide were obtained from a supplemental file of ICRP Publication 144, named “Brems_Spec. TXT”.

Finally, the dose-rate coefficient of radionuclide [nSv h⁻¹ Bq⁻¹ kg], was computed by summing the components of photons, electrons, and bremsstrahlung as follows: (6) where w^γ and w^e are the radiation weighting factors for photons and electrons, respectively, both with values of 1. w^γ was applied for bremsstrahlung because it is a type of photon.

Using the aforementioned procedure, dose-rate coefficients for 1252 nuclides of 97 elements distributed in the soil to an infinite depth were obtained, including organ equivalent dose rates for males and females separately for newborns; 1-, 5-, 10-, and 15-year-olds; and adults. Furthermore, the respective effective dose rates; ambient dose equivalent rates; and air kerma rates at 1 m above the ground were obtained.

The present dose-rate coefficients were calculated for idealized and hypothetical exposure situations, for instance, for an unclothed reference human standing in an upright position on unpaved soil. In real exposure situations, radiations, particularly electrons, could be attenuated by pavement materials. However, similarly to previous studies [3, 4, 7], this effect was not considered in the present study.

Radioactive decay chain in secular equilibrium

Fig 2 illustrates the decay chains of the thorium, uranium, and actinium series, which are in secular radioactive equilibrium, with the branching fractions from the parent nuclide to the daughters. The information on the radioactive decay chains was obtained from ICRP Publication 107 [13]. The thorium series, headed by ²³²Th, is the most abundant of all naturally occurring radionuclides, with a half-life of 1.405 × 10¹⁰ years, and the uranium series, headed by ²³⁸U, has a half-life of 4.468 × 10⁹ years. The actinium series is headed by ²³⁵U with a half-life of 7.04 × 10⁸ years, which is less important compared with the other primordial decay chains owing to its abundance. The dose contribution of alpha particles from alpha decay is negligible because of their short range in the soil and was, therefore, not considered here for the evaluation of the dose-rate coefficients. In addition to the primordial radionuclide decay chains, the decay from ¹³⁷Cs to ^137mBa was considered. Notably, ^137mBa, which emits a gamma ray of 0.662 MeV with a half-life of 2.552 min, is formed by the decay of ¹³⁷Cs, whose half-life is 30.167 years, with a branching fraction of 0.944 and establishes a secular equilibrium.

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Fig 2. Decay chains of the thorium, uranium, and actinium series in secular equilibrium treated.

The numerical values indicate the blanching fraction of the decay from one nuclide to another taken from ICRP Publication 107 [13].

https://doi.org/10.1371/journal.pone.0310552.g002

Based on the Bateman equation [22, 23], the radioactivity of the i-th nuclide in the radioactive decay chain, A_i(t), at time t is as follows: (7) where j and k are the members of the decay chain, A₁(0) is the activity of the 1-st nuclide at t = 0,λ_j is the decay constant for the j-th radionuclide, and f_{j,j + 1} is the branching fraction of the nuclear decay of chain member j forming member (j + 1). Using the activity, A_i(t), the dose, D, during the period of t = 0 to t = T, considering the decay chain of the radionuclide, is as follows: (8) where n is the number of nuclides in the decay chain, and is the dose-rate coefficient of the i-th nuclide evaluated in this study. When secular equilibrium was established, Eq (8) was simplified as follows: (9)

Using Eq (9), the dose-rate coefficient of the radioactive decay chain, C, in secular equilibrium, [nSv h⁻¹ Bq⁻¹ kg], was as follows: (10)

For example, the dose-rate coefficient of the decay from ¹³⁷Cs to ^137mBa, [nSv h⁻¹ Bq⁻¹ kg], was computed as follows: (11) where and are the dose-rate coefficients of ¹³⁷Cs and ^137mBa, respectively, given by Eq (6), and 0.944 is the branching fraction of ¹³⁷Cs forming ^137mBa.

Dose-rate coefficients for monoenergetic radiation sources

Fig 3 shows the effective dose-rate coefficients for monoenergetic photon sources, together with the coefficients of the ambient dose equivalent rate, and air kerma rate, , 1 m above ground. The age-dependent effective dose rates were higher for the younger age groups because children with shorter stature have organs and tissues closer to the soil, i.e., to the source. The operational quantity, representing the equivalent dose rate at a depth of 1 cm from the surface of a tissue-equivalent sphere [8], exhibited larger values than the effective dose rate, which is the protection quantity, for the entire energy range, except at 0.01 MeV. Note that has limited practical application in radiological protection for low-energy photons around 0.01 MeV [24]. was observed to be larger than the effective dose rate for the entire energy range. The results showed that the effective dose rate to the public from photon-emitting radionuclides uniformly distributed to an infinite depth in the soil can be adequately controlled by monitoring the ambient dose equivalent and air kerma rates.

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Fig 3. Effective dose-rate coefficients for monoenergetic photon sources uniformly distributed to an infinite depth in the soil and corresponding ambient dose equivalent rate, , and air kerma rate, , 1 m aboveground.

Numerical data are provided in S12 Table.

https://doi.org/10.1371/journal.pone.0310552.g003

Fig 4 shows the effective dose-rate coefficients for monoenergetic electrons, with the coefficients of the ambient dose equivalent rate, , and air kerma rate, , for monoenergetic photon sources. As mentioned, the total activity of the volumetric electron source was calculated assuming a uniform distribution to a depth equivalent to 4 MFP of photons in the soil, as in the case of photon sources. However, only the electron sources in the 0.1-μm thick top layer of the ground surface contributed to the dose rates above the ground. Consequently, the dose-rate coefficients of electron sources normalized to the total radioactivity were more than one order of magnitude lower than those of the photon sources. The effective dose rates to electron sources were mainly contributed by the skin equivalent dose rates, calculated for the sensitive 50–100 μm layer below the skin surface of the mesh-type ICRP reference phantoms [15, 16, 18]. Electrons with an energy less than 0.06 MeV cannot reach the sensitive layer of the skin and deposit energy by the secondary photons, including bremsstrahlung produced in the body.

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Fig 4. Age-dependent effective dose-rate coefficients for monoenergetic electron sources uniformly distributed to an infinite depth in the soil.

The open circles and solid line with cross marks indicate the coefficients of ambient dose equivalent and air kerma rates, respectively, for the photon sources, which are the same as those shown in Fig 3. Numerical data are provided in S13 Table.

https://doi.org/10.1371/journal.pone.0310552.g004

Nuclide-specific dose-rate coefficients

Table 2 lists the nuclide-specific coefficients of age-dependent effective dose, ambient dose equivalent, and air kerma rates for typical nuclides in NORM exposures. These nuclides have a long half-life of over a billion years and do not form a radioactive decay chain. Notably, ⁴⁰K is one of the main sources of natural radiation on the earth because of its abundance. This nuclide undergoes nuclear transformations into ⁴⁰Ar and ⁴⁰Ca, releasing a gamma ray of 1.46 MeV with a branching fraction of 0.109 and a beta-minus particle, whose maximum energy is 1.31 MeV, with a branching fraction of 0.891. The abundances of the other nuclides were not so significant. However, the dose-rate coefficients of ¹⁷⁶Lu were of the same order of magnitude as those of ⁴⁰K because the average energies of gamma rays and beta particles emitted via a single nuclear transformation are similar. For ⁵⁰V and ¹³⁸La, the average photon energy per nuclear transformation exceeds 1 MeV, and these coefficients were higher than those of the other nuclides. ⁸⁷Rb and ¹¹⁵In are pure beta emitters, and ¹²³Te is an X-ray emitter. Thus, these nuclides exhibit low dose-rate coefficients.

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Table 2. Effective dose-rate [nSv h⁻¹ Bq⁻¹ kg]; ambient dose equivalent rate, [nSv h⁻¹ Bq⁻¹ kg]; and air kerma rate, [nGy h⁻¹ Bq⁻¹ kg], coefficients for nuclides uniformly distributed to an infinite depth in the soil.

and were estimated at 1 m above the ground. Here, 15-y, 10-y, 5-y, and 1-y indicate 15-, 10-, 5-, and 1-year-old children, respectively.

https://doi.org/10.1371/journal.pone.0310552.t002

Table 3 lists the dose-rate coefficients for radionuclides of the thorium, uranium, and actinium series, as well as ¹³⁷Cs/^137mBa in secular radioactive equilibrium. To verify the computational procedure applied in the present study, the results were compared with those of previous studies [3, 4] calculated with similar source and phantom configurations. Table 4 provides a comparison of the effective dose-rate coefficients derived in the present study for adults, 10- and 5-year-old children, and newborns with values of previous studies. The data of the ²³²Th series, ²³⁸U series, and ⁴⁰K were obtained from Petoussi-Henss et al. [4], who evaluated the dose rates for homogeneous distributions up to a depth of 100 cm in the soil using the ICRP voxel adult phantoms [17] and the Helmholtz Zentrum München (HMGU) voxel pediatric phantoms [25] in conjunction with the radiation-transport simulation code, EGSnrc [26]. The dose coefficients for ¹³⁷Cs/^137mBa were derived by Eq (11) from the respective data of ¹³⁷Cs and ^137mBa from Bellamy et al. [3], who employed stylized hermaphrodite phantoms [27] and the simulation code, MCNP6 [28]. Their data were also used for the ⁴⁰K and ⁵⁰V.

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Table 3. Effective dose-rate [nSv h⁻¹ Bq⁻¹ kg]; ambient dose equivalent rate, [nSv h⁻¹ Bq⁻¹ kg]; and air kerma rate, [nGy h⁻¹ Bq⁻¹ kg], coefficients for nuclides of the radioactive decay chain in secular equilibrium uniformly distributed to an infinite depth in the soil.

Decay chains headed by ²³²Th, ²³⁸U, and ²³⁵U are the thorium, uranium, and actinium series shown in Fig 2, respectively. The ¹³⁷Cs chain indicates the secular radioactive equilibrium between ¹³⁷Cs and ^137mBa.

https://doi.org/10.1371/journal.pone.0310552.t003

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Table 4. Ratio of the effective dose-rate coefficients reported by Petoussi-Henss et al. [4] and Bellamy et al. [3] for adults, 10- and 5-year-old children, and newborns to those obtained in the present work.

Here, 10-y and 5-y indicate 10- and 5-year-old children, respectively.

https://doi.org/10.1371/journal.pone.0310552.t004

The relative deviations between the data of the present work and those of Petoussi-Henss et al. [4], who used voxel phantoms, are less than 4%. The deviations to the data of Bellamy et al. [3], who used stylized hermaphrodite phantoms for the calculations, were found to be within 10% for ¹³⁷Cs/^137mBa and ⁵⁰V; note that for these nuclides, photons play a dominant role in the dose contribution. The equivalent dose rates of skin, muscle, and skeleton were slightly higher than those of the other organs and tissues; however, there are no organs or tissues that exhibit markedly higher dose rates than other organs. It was also found that the deviations between the present and previous results do not vary significantly among age groups.

For ⁴⁰K which releases a beta-minus particle per nuclear transformation with a branching fraction of 0.891, the deviations of the present results to the data of Bellamy et al. were up to approximately 30%. Both studies employed the same methodology [1] for the generation of bremsstrahlung by the electrons inside the soil and their contribution to organ equivalent dose rates. However, the methodology for the dose contribution to skin by the primary electrons released near the ground surface was quite different. Bellamy et al. used the point-kernel method [29] for calculating the electron skin dose, while the present work employed the results of radiation-transport simulations for electrons and photons. Since the deviations are less than 10% for nuclides for which photons are the major contributor to the dose rate, it can be concluded that the disagreement is due to the difference in methodology for estimating skin equivalent dose rate from primary electrons.