Safety Evaluation and Visualization Technology of Radiation Fields for Small Pressurized Water Reactors

Authors: Wu Jiebo¹³, Shi Jiangwu¹³, Liu Guangkun¹³, Bi Yuepeng¹, Zhao Yanan², Wei Wei⁴, Xia Genglei¹, Zhu Haishan¹*
¹ College of Nuclear Science and Technology, Harbin Engineering University, Harbin, 150000
⁴ CNNC Wuhan Nuclear Power Operations Technology Co., Ltd., Wuhan, 430000

Corresponding author: Zhu Haishan, E-mail: zhuhaishan@hrbeu.edu.cn

Supported by: Key Laboratory of Advanced Nuclear Energy Design and Safety, Ministry of Education

Abstract

The compact structure of small reactors, combined with the complexity of the refueling process and the high radioactivity of spent fuel, makes radiation dose assessment during refueling particularly critical. This study performed burnup and dose calculations for KLT-40S (Korabl–Likhterovoz–Transportnii–40 MW Series, a marine 40 MW improved reactor) spent fuel assemblies after 1278 days of full-power operation. A floating nuclear power platform model was constructed using 3Ds MAX software, and spatial radiation dose field visualization and refueling operation process visualization were implemented using the Unity virtual simulation engine. The results indicate that when lifting spent fuel assemblies within a shielding sleeve, the dose rate inside the assembly geometry reaches a maximum level of 1.36×10⁴ μSv/h. At a distance of 3 meters from the center of the spent fuel assembly, the spatial radiation dose rate is 6.02 μSv/h. In the event of spent fuel assembly breakage, based on the human radiation dose calculation model, the permissible residence time for workers in the reactor compartment is approximately 14.60 to 38.46 hours. The spatial distribution of the radiation dose field becomes more intuitive with the support of visualization technology. This study integrates simulation analysis with visualization technology for dose assessment during the refueling process, providing support for the design and analysis of refueling procedures in small reactors.

Keywords: Floating nuclear power plant; Loading and refueling; Radiation field; Visualization; Dose assessment

1. Introduction

Unlike conventional nuclear power plant reactors installed on stable land, the refueling process for floating nuclear power platforms (small pressurized water reactors) is carried out at sea. Additionally, the power level of floating nuclear power platform reactors differs from traditional nuclear power plants. Therefore, modeling and calculations must be performed based on the actual design parameters of floating nuclear power platforms to complete the visualization of radiation field distribution during their loading and refueling processes. The KLT-40S (Korabl–Likhterovoz–Transportnii–40 MW Series, a marine 40 MW improved reactor) is a small modular reactor developed by Russia's OKBM (Afrikantov Experimental Design Bureau for Mechanical Engineering) based on the KLT-40 reactor [1]. Russia has built the world's first floating nuclear power platform, the "Akademik Lomonosov," equipped with two KLT-40S reactors.

Internationally, Vadim Naumov et al. [2] studied the comparison of spent fuel radioactivity between KLT-40S and RITM-200M small reactors, while Beliavskii et al. [3] simulated the effects of thorium-uranium fuel on fuel lifetime and burnup for the KLT-40S reactor using Monte Carlo methods. Given that few small reactors have been commercially operated to reach their designed burnup lifetime and undergo shutdown for refueling, and considering that marine reactor refueling is performed at sea with factors such as high winds and waves, limited operating space, and increased risk of collision, the refueling process requires particularly careful planning. Overall, the foundation for radiation dose assessment and visualization research on small reactor loading and refueling processes remains relatively weak [4-7].

Concurrently, with the development of virtual reality and augmented reality engines, three-dimensional visualization technology can display more intuitive and comprehensive physical information [8-10] and is playing an increasingly important role in reactor refueling scheme design, optimization, and safety assessment [11-13]. Therefore, this study developed an Intelligent Evaluation and Planning Platform for Radiation Doses of Multi-functional Small Modular Reactors based on virtual simulation engines, burnup activation programs, Monte Carlo programs, and path planning programs. Using this platform, research was conducted on the visualization of the KLT-40S small modular reactor's onboard loading and refueling process and personnel radiation dose assessment.

The research content is illustrated in [FIGURE:1]. After the KLT-40S small reactor with a four-loop fuel assembly design completed 1278 EFPDs (Effective Full Power Days), radiation field dose assessment and process visualization for the reactor loading and refueling process were performed. First, the radiation dose safety assessment and scenario planning platform calls the burnup calculation program ORIGEN2 to perform activity calculations on the KLT-40S spent fuel assemblies, obtaining output files of radiation source intensity for the spent fuel assemblies and shielding materials. It then calls the Monte Carlo program Super MC to perform radiation field calculations, obtaining text files of spatial radiation field distribution results for the material exchange process, which serve as input for radiation field visualization rendering in the virtual scenario. Next, the path generation program generates staff walking path schemes based on spatial coordinate text data provided by the user. Finally, the platform implements dynamic changes in the radiation field during the KLT-40S reactor loading and refueling process based on the Unity 3D engine, as well as dynamic visualization of different radiation doses received by staff during scene switching. For instance, using spent fuel assembly breakage criterion analysis methods and the ICRP human irradiation dose assessment model, the platform analyzes radiation dose levels received by staff working in real-time in nuclear emergency scenarios when radioactive noble gases fill the reactor compartment space due to breakage of spent fuel assemblies during the lifting process.

1.1 Burnup Activation Calculation

ORIGEN2 is a burnup activation calculation program developed by Oak Ridge National Laboratory in the United States. It employs a single-group cross-section approach with short computation time and can simulate various neutron nuclear reaction processes between neutrons and nuclides in nuclear fuel, calculating the accumulation and decay of radioactive materials during nuclear reactions. The program provides source term parameters such as nuclide composition, radioactivity, and neutron and photon yields, making it suitable for calculating burnup, activation, and decay processes in different reactor types. The ORIGEN2 calculation model incorporates several assumptions: first, neutron flux and reaction cross-sections are assumed not to vary with nuclide composition; second, all nuclides are assumed to occupy the same spatial point and undergo equal neutron irradiation, making it unable to handle problems related to system geometry, such as spatial distributions of neutron flux density and dose rates [14-15]. Based on reactor burnup cycle, power density, and nuclear fuel composition information, the ORIGEN2 program can calculate the radioactivity of reactor spent fuel, serving as the input source intensity coefficient for Monte Carlo dose calculations.

Generally, the rate of change of nuclide i's number over time ( ) can be expressed by the following non-homogeneous first-order ordinary differential equation:

In equation (1): = =1 − ( + ∙ + represents the atomic density of nuclide i; is the number of atoms of the nuclide; is the fraction of nuclide j decaying to i; is the decay constant of nuclide i; is the average neutron flux; is the fraction of nuclide k reacting with neutrons to generate i; is the average neutron absorption cross-section of nuclide k; is the continuous removal rate of nuclide i from the system; and is the continuous supply rate of nuclide i to the system.

1.2 Radiation Field Calculation

This study uses the Super MC3.3 program to calculate the spatial radiation dose of spent fuel assemblies during the refueling process. The Institute of Nuclear Energy Safety Technology of the Chinese Academy of Sciences began independent development of the Super Monte Carlo Nuclear Computational Simulation Software System Super MC in 1999 [16]. Super MC3.3 supports transport simulation of various particles including neutrons (1 e-11–150 MeV), photons (1 keV–1 GeV), electrons, and protons. It can calculate and statistically analyze commonly used physical quantities in nuclear design and analysis, as well as new reactor physics parameters such as ks.

The flux estimation based on the track length method is [17]:

where T is the sum of all particle track sequences in the volume of interest, is the length of track i, and is the particle weight sum. Reaction rate calculations are generally based on flux estimation, and the track length estimate of reaction rates can also be obtained by multiplying equation (2) by the microscopic cross-section:

The power per unit volume at any point in the core, i.e., the power density at point , is:

where is the macroscopic fission cross-section of fissile material, is the neutron flux density at point , and is the energy released per fission.

1.3 Voxel Model

When considering spent fuel assembly breakage, external irradiation from environmental sources of radioactive nuclides is an important pathway for radiation exposure to workers engaged in nuclear facility maintenance, originating from routine emissions, major accident releases, or environmental contamination after radioactive material leakage. The International Commission on Radiological Protection (ICRP) comprehensively evaluated age-dependent internal irradiation dose coefficients in Reports No. 56, 67, 69, 71, and 72 (ICRP, 1990, 1993, 1995a,c,d), and published updates to adult reference dose coefficients in the "Occupational Intakes of Radionuclides" series (ICRP, 2015, 2016a,b, 2017a, 2019). ICRP Report No. 144 provides age-dependent external environmental exposure dose rate reference coefficients for the public [18]. When dose rate coefficients are needed to evaluate effective doses from measurements or assessments of environmental radioactive concentrations, air radiation rates, air absorbed dose rates, or ambient dose equivalent rates, calculating dose coefficients requires assessment of the environmental field (e.g., irradiation source geometry, soil density and composition, distribution of radionuclide concentrations in environmental media), radiation information, and human computational models (representing polygon mesh skin models of adult males and females as reference voxel models for the exposed public), as shown in [FIGURE:2], as well as transport simulation of radiation in environmental media and the anatomical structures of exposed individuals.

1.4 Three-Dimensional Modeling and Radiation Field Rendering

In the platform, the visualization process requires simulation of three stages: (1) establishment of the three-dimensional scene, including the floating platform model and marine environment; (2) dynamic processes of KLT-40S reactor refueling and fuel loading; and (3) spatial radiation field visualization and human dose assessment.

Three-dimensional modeling software is used to construct the three-dimensional model of the Akademik Lomonosov floating nuclear power platform. The Lomonosov's hull has numerous components with complex structures, requiring powerful solid design modeling software. 3Ds MAX is a three-dimensional model creation and rendering software developed by Autodesk. Due to its good interactive extensibility, rich plugins, and powerful modeling capabilities, it is widely used in various design and production fields. Spatial radiation field rendering is implemented using volume rendering technology, which converts three-dimensional radiation field volume data into color values and opacity using mapping functions, composes them into three-dimensional textures in a specific order, creates materials using three-dimensional textures, creates solids using slice meshes, binds solids to scene nodes, and finally binds materials to solids for volume rendering.

2. System Composition and Architecture

The computational platform used in this study employs the virtual simulation engine tool Unity 3D to construct virtual reality scenarios of the KLT-40S refueling process. Unity 3D, as an important virtual reality development platform, features data interaction, integrated simulation, visualization, and application programming interfaces. The radiation field rendering process in Unity is shown in [FIGURE:3]. Virtual reality development engines cannot directly use mesh models constructed by mainstream CAD (Computer Aided Design) modeling software, requiring conversion of three-dimensional models into mesh models. This study uses the FBX format file, specifically by exporting three-dimensional models created in 3Ds MAX software (version 3Ds MAX 2022) through the software's export function into the FBX format commonly used by Unity 3D (version 2022.3.17f1c1), where dose radiation field visualization rendering and loading/refueling process visualization are performed.

As shown in [FIGURE:4], the overall visualization process is divided into four parts: floating platform scene construction, real-time radiation dose display, loading/refueling process confirmation, and personnel dose assessment. By integrating these processes into the Unity engine, visualization research on the reactor refueling process is completed. Since the Unity engine can read multiple scene files, this radiation dose safety assessment and scenario planning platform can quickly call actual application scenarios for spatial radiation dose assessment according to different operational requirements. Additionally, due to the compact and complex equipment arrangement within the ship, paths automatically generated using the shortest path method may pass directly through equipment, which is unrealistic. Therefore, based on user-preset three-dimensional spatial paths, personnel radiation dose assessment under specific radiation fields is completed. Physical quantities such as total path length, maximum radiation dose rate along the path, and cumulative dose are displayed in real-time on the platform's UI interactive interface. By comparing final results, rapid generation of personnel minimum radiation dose schemes under different path options is achieved.

3. Numerical Model Calculations

3.1 KLT-40S Reactor Design Parameters

According to literature [19], the Akademik Lomonosov began operation in May 2020, with two KLT-40S reactors installed on board. The first reactor began refueling preparation in November 2023, with refueling completed in December 2023. Therefore, its burnup cycle is 3.5 years, consistent with the original design refueling cycle of 3–4 years. The main design parameters of the reactor on the floating platform are shown in [TABLE:1].

3.2 Radiation Field Calculations

Based on the burnup cycle in Section 3.1, the ideal burnup depth of the first KLT-40S reactor is 150 MW × 1278 days = 1.917×10⁵ MWD. The shutdown decay time is one month.

The activity of major nuclides in the spent fuel of the whole reactor is shown in [TABLE:2]. According to literature [1], the reactor compartment space is a rectangular volume of 12 m × 7.92 m × 12 m. ORIGEN2 calculations show that 30 days after KLT-40S shutdown, the total photon source intensity of the entire core's spent fuel assemblies is 9.18×10¹⁷ photons/second. With 121 assemblies in the reactor, the photon source intensity per spent fuel assembly is 7.59×10¹⁵ photons/second, serving as the source intensity coefficient for Super MC dose calculations.

For the spatial radiation field, the reactor compartment space is divided into 10 cm × 10 cm × 10 cm spatial grids using the mesh tally method, resulting in 120 × 80 × 120 = 1,152,000 calculation points for the spatial radiation field distribution, with 10⁸ particles simulated.

[FIGURE:5] and [FIGURE:6] show the spatial radiation fields at different heights during the lifting process of spent fuel assemblies (along the Y-axis). The left side shows the XZ-plane view of the radiation field at Y = 0 m, and the right side shows the XZ-plane view at Y = 8 m. According to calculations, the spatial radiation dose rate continuously decreases radially outward from the center of the spent fuel. The dose rate inside the spent fuel assembly geometry reaches a maximum level of 1.36×10⁴ μSv/h. At a distance of 3 meters from the center of the spent fuel assembly, the spatial radiation dose rate is 6.02 μSv/h, and at 6 meters from the center, it is 1.16 μSv/h.

3.3 Visualization Implementation

[FIGURE:7] shows the rendering effect of the Lomonosov geometric model by the seaside. By modeling the floating platform main body, internal compartments, and equipment, interaction between the radiation field and refueling scenarios is achieved. During the refueling operation, the crane hook lifts the spent fuel assembly from the core through a 1 cm-thick lead shielding sleeve.

[FIGURE:8] shows the platform's implementation in Unity of opening the reactor core cover after shutdown, with the crane lifting the cover. In this unloading operation, a scheme of lifting individual assemblies one by one is adopted. [FIGURE:9] shows the lifting process, where the radiation field changes dynamically as the spent fuel assembly displaces in space. After unloading from the core, spent fuel assemblies are transported to the spent fuel storage room adjacent to the reactor compartment, which contains empty storage boxes. Spent fuel assemblies are sequentially transported from the reactor compartment into the storage boxes, which are then sealed and left to stand after all assemblies are unloaded. [FIGURE:10] simulates this dynamic process. [FIGURE:11] demonstrates that after all spent fuel assemblies are removed from the core, the crane loads new fuel from the new fuel room adjacent to the reactor compartment into the core vessel. Since new fuel has not undergone fission reactions and does not possess high radioactivity, radiation field changes during the loading process are not simulated.

3.4 Accident Scenario and Personnel Dose Assessment

Noble gases are chemically stable, not easily depleted, and migrate with gas diffusion at a migration speed positively correlated with temperature. Compared with other fission products, when fuel rods in spent fuel assemblies break, fission gases ⁸⁵Kr and ¹³³Xe in the fuel cladding are most likely to be released into the entire reactor compartment space.

As shown in [TABLE:2], the activity of ⁸⁵Kr in the core's spent fuel assemblies after shutdown is =1.78×10¹⁵ Bq, and that of ¹³³Xe is =2.89×10¹⁵ Bq. Therefore, the activity of ⁸⁵Kr in a single fuel rod is A₁=2.13×10¹¹ Bq, and the activity of ¹³³Xe is A₂=3.46×10¹¹ Bq. The reactor compartment volume is approximately V=1140.48 m³.

Breakage criterion analysis employs the minimum probability method with the following assumptions [20]: (1) Among the 121 spent fuel assemblies (totaling 8349 fuel rods) in the container, only one fuel rod is broken, with a breakage probability f₁=1.198×10⁻⁴. (2) Considering that the pressure inside the cladding is higher than in the reactor compartment space, it is further assumed that all noble gases are released, with a release probability f₂=1.

The specific activity of released ⁸⁵Kr and ¹³³Xe can be calculated using the following formula:

where C is specific activity (Bq/m³), N is the total number of fuel rods, and V is the containment volume (m³). Letting K be the specific activity coefficient, equation (5) becomes equation (6):

According to ICRP Report No. 144, the air conversion dose coefficients for adult males in a radiation environment for ⁸⁵Kr and ¹³³Xe are 7.78×10⁻⁴ nSv/h/Bq/m³ and 4.03×10⁻³ nSv/h/Bq/m³, respectively.

The air conversion dose factors are shown in [TABLE:3]. To simulate exposure to environmental radiation fields, ICRP Report No. 144 discusses three typical environmental source cases: (1) soil (ground) contamination, simulated as an infinite planar source at and below the surface; (2) air immersion, simulated as a semi-infinite volume source of radionuclides in air; and (3) water immersion, simulated as an infinite volume source of radionuclides in water. Considering the specific source geometry, for ground contamination the source size is considered infinite while the irradiation geometry space is considered semi-infinite. Therefore, the calculation model can select either an "infinite planar source on the ground" or an "infinite planar source in the horizontal direction." During air immersion, the body is irradiated by an infinite air source from the ground, making the geometry space "semi-infinite."

[FIGURE:12] shows the scenario when inert gas diffuses throughout the reactor compartment due to spent fuel assembly breakage. According to calculations, when radioactive noble gases fill the entire reactor compartment, maintenance personnel must consider the air immersion coefficient when entering. Using adult males as an example, as shown in [FIGURE:12], the radiation source in the reactor compartment is centered on the broken spent fuel assembly, with the maximum radiation dose rate to the human body being 1.37 mSv/h, and the dose rate around the corners of the reactor compartment being approximately 0.52 mSv/h.

[FIGURE:13] displays real-time maximum dose rates along the path and cumulative radiation dose levels received by personnel under different scenarios and path options. According to this assessment model, the annual average individual dose for radiation workers should be less than 20 mSv [21]. When such radiation leakage accidents occur, the permissible residence time for maintenance personnel in the reactor compartment is approximately 14.60 to 38.46 hours.

4. Conclusion

This study evaluated the radioactivity of spent fuel assemblies and calculated the spatial radiation dose field distribution for the KLT-40S reactor loading and refueling process. An intelligent evaluation and planning platform for radiation doses of small modular reactors was developed based on the Unity 3D virtual simulation engine, enabling dynamic visualization of the above processes and completing dynamic interaction between the spatial radiation dose field and the virtual simulation scene of the floating nuclear power platform. Finally, based on fuel rod breakage criterion analysis methods, the impact of radiation doses on maintenance personnel was assessed when collision accidents during spent fuel assembly lifting cause cladding breakage.

Author Contributions Statement

Wu Jiebo was responsible for simulation calculations, data compilation, and drafting the manuscript; Shi Jiangwu and Liu Guangkun conducted literature research and compilation; Bi Yuepeng and Wei Wei performed data processing; Zhao Yanan revised the manuscript; Xia Genglei provided technical guidance; Zhu Haishan secured research funding and finalized the manuscript.

References

1. International Atomic Energy Agency. Small Modular Reactors: Advances in SMR Developments 2024[M]. Vienna, IAEA, 2024. DOI: https://doi.org/10.61092/iaea.3o4h-svum.

2. Naumov V, Gusak S, Naumov A, et al. Small nuclear power plants for power supply in Arctic regions: assessment of spent nuclear fuel radioactivity[J]. Nuclear Energy and Technology, 2018, 4(2): 119-125. DOI: 10.3897/nucet.4.30677.

3. Beliavskii S, Balachkov M, Danilenko V, et al. Fuel lifetime extension for the KLT-40S small modular reactor by means of thorium-uranium fuel cycle[J]. Annals of Nuclear Energy, 2023, 192: 109982. DOI: 10.1016/j.anucene.2023.109982.

4. Liu Yina, Wang Zhiqiang, Li Chunjuan, et al. Establishment of a Neutron Reference Radiation Field for Pressurized Water Reactor Workplace Simulations[J]. Atomic Energy Science and Technology, 2020, 54(12): 2476-2480. DOI: 10.7538/yzk.2020.youxian.0465.

5. Liu Liye, Fan Qing, Li Hua, et al. Reconstruction of gamma radiation field based on inversion of nonuniform source activity distribution[J]. Nuclear Techniques, 2025, 48(04): 83-92. DOI: 10.11889/j.0253-3219.2025.hjs.48.240184.

6. Li Hui, Fan Qing, Li Hua, et al. Study on the fast measurement method of three-dimensional γ dose rate field based on VSLAM[J]. Atomic Energy Science and Technology, 2024, 58(S1): 157-166. DOI: 10.7538/yzk.2024.youxian.0171.

7. Chen Changqi, Xia Xiaobing, Cai Jun, et al. Radiation dose analysis under a failure event of the covering gas cleaning system of a 2 MW thorium-based molten salt reactor[J]. Nuclear Techniques, 2018, 41(05): 93-98. DOI: 10.11889/j.0253-3219.2018.hjs.41.050604.

8. Meng Fanxing, Yang Ming, Wang Hao, et al. Evaluation study of radiation accident emergency response exercise based on AHP-FCE[J]. Nuclear Techniques, 2022, 45(11): 70-79. DOI: 10.11889/j.0253-3219.2022.hjs.45.110501.

9. Liu Wenqian, Han Lifeng, Huang Li, et al. TMSR-SF0 Data Monitoring and Visualization Solution Based on Digital Twins[J]. Nuclear Techniques, 2022, 45(02): 83-90. DOI: 10.11889/j.0253-3219.2022.hjs.45.020604.

10. Cao Pei, Long Pengcheng, Gan Quan, et al. Source visualization analysis methods and applications in Monte Carlo particle transport calculations[J]. Nuclear Techniques, 2019, 42(02): 64-71. DOI: 10.11889/j.0253-3219.2019.hjs.42.020502.

11. Luo X, Qiu R, Wu Z, et al. THUDosePD: a three-dimensional Monte Carlo platform for phantom dose assessment[J]. Nuclear Science and Techniques, 2023, 34(11): 44-54. DOI: 10.1007/s41365-023-01315-y.

12. Bi Y, Luo Z, Guo J, et al. Fast three-dimensional radiation field characterization in large-scale nuclear installations[J]. Nuclear Science and Techniques, 2017, 28(05): 58-64. DOI: CNKI:SUN:HKXJ.0.2017-05-010.

13. Li C, Xia X, Cai J, et al. Radiation dose distribution of liquid fueled thorium molten salt reactor[J]. Nuclear Science and Techniques, 2021, 32(02): 114-124. DOI: 10.1007/s41365-021-00857-3.

14. Croff A G. ORIGEN2: a versatile computer code for calculating the nuclide compositions and characteristics of nuclear materials[J]. Nuclear Technology, 1983, 62(3): 335-352. DOI: https://doi.org/10.13182/NT83-1.

15. Ma Huiqiang, Yuan Xudong, Yu Tao, et al. Development and verification of shutdown dose rate calculation program based on MCNP5 and ORIGEN2.1[J]. Journal of University of South China (Science and Technology), 2020, 34(3): 97–104. DOI: 10.19431/j.cnki.1673-0062.2020.03.015.

16. Wu Yichang, Song Jing, Hu Liqing, et al. Super Monte Carlo Core Computational Simulation Software System SuperMC[J]. Nuclear Science and Engineering, 2016, 36(01): 62-71. DOI: CNKI:SUN:HKXY.0.2016-01-009.

17. Zhang Kuan, Song Jing, Chen Zhenping, et al. Mesh tally method study for Monte Carlo particles transport simulation[J]. Nuclear Science and Engineering, 2016, 36(2): 200–204. DOI: 10.3969/j.issn.0258-0918.2016.02.009.

18. Petoussi-Henss N, Satoh D, Endo A, et al. ICRP publication 144: dose coefficients for external exposures to environmental sources[J]. Annals of the ICRP, 2020, 49(2): 11-145. DOI: 10.1177/0146645320906277.

19. International Atomic Energy Agency. Technology roadmap for small modular reactor deployment[R]. IAEA Nuclear Energy Series No.NR-T-1.18, IAEA, Vienna (2021). DOI: https://re.public.polimi.it/handle/11311/1208283.

20. Ren He, Weng Songfeng, Dong Dailin, et al. Detecting method of failed fuel assemblies in spent fuel transportation container[J]. Nuclear Science and Engineering, 2018, 38(2): 303–306. DOI: 10.3969/j.issn.0258-0918.2018.02.019.

21. ICRP 2007. The 2007 recommendations of the international commission on radiological protection. ICRP publication 103[J]. Annals of the ICRP, 2007, 37(2–4): 1-332. DOI: 10.1016/j.icrp.2007.10.003.