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1 Introduction

Body shape has been recognized as a crucial factor in dosimetry, especially in radiology and radiotherapy, where accurate organ dose estimates are essential both within and outside the primary beam (Geyer et al., 2014; Johnson et al., 2009; Li et al., 2014). Therefore, the body shape and weigh percentiles should be closely specified. Most of these studies have focused on photon beams and the impact of body shape on neutron irradiation is not well known for external exposures. In the case of large-scale radiation incidents, such as reactor accidents and weapons detonations, there is a pressing need to estimate organ absorbed doses for a diverse range of individuals. There are various uncertainties in complex situation of nuclear accidents. However, according to the emphasis of the ICRP (ICRP, 2020), every effort should be made to reduce these uncertainties. The weight percentiles can be regarded as one of the factors to consider in this regard.

Monte Carlo simulations and computational human phantoms have been utilized to estimate organ absorbed doses (Xu and Eckerman, 2010; Miri-Hakimabad et al., 2009). However, constructing individual-specific phantoms for each exposed person belonging to various weight percentiles is impractical and time-consuming. In such situations, there is a demand for a quick a straightforward method to estimate organ absorbed doses or whole-body doses. Developing an efficient and rapid dosimetry approach is crucial to effectively assess the radiation doses received by individuals in a timely manner. This can aid in the prompt implementation of appropriate medical interventions and support the overall management of radiation accidents.

So far, researchers have made efforts to develop a simple method for constructing anthropomorphic phantoms representing different weight percentiles from existing phantoms. First, Kim et al. (2003) demonstrated that the effective dose decreased when adding a layer of soft tissue around the torso of a phantom. Their study focused on photon sources with energies of 0.08, 0.3, and 1 MeV. Building upon this idea, Fisher et al. (2014) constructed a 90^th percentile physical phantom based on the existing 50^th percentile model. They add an adipose tissue equivalent substitute material to slices of the 50^th physical phantom to investigate the impact of patient size on organ dose and CT scan image quality. In our previous work, the difference of the torso adipose and muscle layers’ thickness between ORNL with VIPMAN, NORMAN05, Mash-3, and ICRP voxel phantoms was determined. We then added extra layers to the ORNL torso based on these differences (Karimi-Shahri et al., 2013). The Results showed that incorporating appropriate layers of muscle or adipose into different phantoms resulted in similar effective dose values (Karimi-Shahri et al., 2013). This finding provided us a clue to explore the feasibility of constructing different weight percentiles using this approach for specific situations. One of the major concerns in nuclear accidents is the presence of neutron sources, which can cause lethal biological effects (Jamsranjav, 2019).

In the present study, absorbed and effective dose conversion coefficients were calculated using the revised ORNL hermaphrodite phantom (Han et al., 2006). Layers of adipose and muscle added to the existing 50^th percentile torso to create the 65^th, 75^th, 85^th, and 95^th weight percentiles. Simulations were carried out for neutrons in the range of energy 10⁻⁹–20 MeV, focusing on six irradiation geometries: AP, PA, RLAT, LLAT, ROT, and ISO. According to the definitions provided by ICRP and ICRU, various radiation geometries are considered. These include the AP, PA, RLAT, and LLAT geometries. In contrast, the ROT geometry represents environmental contamination when a person moves randomly in a contaminated environment. The ISO geometry is approximated by a body suspended in a large cloud of radioactive gas (like atmospheric contamination) (ICRP,1996; ICRPU, 1998). These different orientations help in accurately assessing the radiation dose. Furthermore, organ absorbed dose and effective dose conversion coefficients of the 95^th percentile were also compared with those of VIPMAN.

2 Material and methods

The revised ORNL hermaphrodite adult phantom (50^th percentile) (Han et al., 2006) with a specific weight and height (75.5 kg and 168.2 cm, respectively) was used. To create weight percentiles above 50, we focused on altering the shape of the torso while keeping all other internal organs constant. Additional layers of muscle and adipose tissue were added to the torso, respectively with adjustments made to the positions of the skin and breasts to accommodate the varying weight percentiles. The phantom’s torso resembles a cylinder with an elliptical cross-section, the minor and major radius underwent changes. To ensure consistency, a constant ratio between the ellipsoid minor and major radius (r_major = 2r_minor) was maintained when incorporating the additional layers. Further information on obtaining weight values for different percentiles can be found in our previous study (Karimi-Shahri, 2020). Table 1 provides details on the thickness of the adipose and muscle layers, as well as the total body weight, for each weight percentile examined in this study.

The MCNPX Monte Carlo code (Denise, 2008) and the revised ORNL phantom (hermaphrodite phantom) were applied for the simulations. The external source emits neutron with energies10⁻⁹, 10⁻⁸, 10⁻⁷, 10⁻⁶, 10⁻⁵, 10⁻⁴, 10⁻³, 0.01, 0.1, 0.5, 1, 3, 5, 8, 10, 12, 15, 18 and 20 MeV. The surface source was emitted neutrons in six different directions: AP, PA, RLAT, LLAT, ISO, and ROT. Neutron cross-sections were obtained from the ENDF/B-VI libraries. Molecular effects known as S (α, β) were taken into account for thermal neutrons. Additionally, transport of both neutrons and neutron-induced photons was considered. To calculate organ absorbed doses, the F6 tally was employed. the red bone marrow dose was computed using the F4 tally with flux to dose conversion coefficients. The radiation weighting factor was derived from equations (1) (ICRP, 2007) to calculate the equivalent dose (H_T).

(1)

The effective dose was computed by the summation of weighted equivalent dose as:

(2)

where, the tissue weighting factor (w_T) was derived from ICRP103 (ICRP, 2007). These data have been utilized in the calculation of the effective dose for all weight percentiles.

The effective dose of the present study was compared with the data reported by Bozkurt et al. (2000) for VIPMAN phantom. To this end, Bozkurt et al’s data was recalculated because the w_T in that study were based on ICRP 60 (1991) and significantly differ from the updated weighting factors from ICRP 103 (2007) used in the present work. The influence of changing radiation and tissue weighting factors (w_R and w_T) on effective dose values has been previously discussed in studies such as Endo et al. (2013) and Miri et al. (2012).

3 Results

The calculated fluence-to-absorbed and effective dose conversion coefficients are expressed in units of pGycm² and pSvcm², respectively. The statistical error of the result is less than 1%. The run time of programs depends on the irradiation geometries, the incident neutron energy, and the phantom weight percentile. To obtain these errors, about 2 × 10⁷ particles were tracked (especially for 10⁻⁹ MeV) for AP, PA, RLAT, and LLAT irradiation geometries, 4×10⁷ particles for ISO, and 2 × 10⁸ particles for ROT on the 50^th weight percentile phantom. As the weight percentile increases, the mean time-consuming also increases so that it reaches approximately tripled for the 95^th weight percentile.

Figures 1a and 1b display the effective dose for all weight percentiles in AP and ROT irradiation geometries, respectively. For AP geometry, the maximum relative differences (RD) between the 50^th and 95^th percentiles are about 18%. These differences arrive to 28%, 22%, 24%, 26%, and 27% for PA, RLAT, LLAT, ISO, and ROT irradiation geometries.

The 95^th percentile effective dose conversion coefficients for ORNL phantom were compared with those obtained from the VIPMAN for AP, PA, LLAT, RLAT, ISO, and ROT geometries. The relative difference between two data sets was calculated and tabulated in Table 2. The first column of Table 2 shows the range of relative differences. The value in each cell is the percentage of cases within the specified relative difference in each row. For example, the first number in Table 2 means that 58% of results between the 95^th percentile and VIPMAN differ by less than 5% in AP geometry.

In addition to the neutron effective dose, the organ absorbed dose conversion coefficients were also studied for various tissues. Figures 2a and 2b show examples of comparisons between absorbed dose values of the 95^th percentile and VIPMAN for the AP adrenals and LLAT stomach, respectively. Figures 3a to 3d present the relative differences in absorbed doses of various organs between the 95^th percentile and corresponding data in the VIPMAN phantom. These organs include the spleen, liver, heart, lungs, and stomach in PA, RLAT, ROT, and ISO irradiation geometries. The lungs, liver, and spleen agree with the results of VIPMAN in all geometries except for the ISO heart at energies 1, 3, and 5MeV and the RLAT lungs. The stomach of the 95^th percentile receives significantly lower dose when irradiated from the right side due to the longer travel distance of neutrons. Conversely, the liver showed this trend when irradiated from the left side. Generally, there is a better agreement between the data of the two phantoms at energies above 1 MeV compared to energies below 1 MeV in all geometries for most organs.

In this study, the absorbed dose data reported by Bozkurt et al. (2000) were used for comparisons. In Bozkurt et al’s study, all organs absorbed doses necessary to calculate the effective dose were available. The effective dose was obtained based on the same w_T, w_R, and calculation method in this study. It is worth noting that Bozkurt et al. used the MCNP4B Monte Carlo code for their calculations, while in this study, MCNPX2.6 was used. Differences in MCNP versions may introduce variations in the data. To investigate the impact of MCNP version differences, the 95^th percentile data were also compared with the new organ absorbed dose of VIPMAN recently reported by McHale et al. using MCNP6.2 (McHale and Walker, 2021). In McHale’s study, a limited number of organs absorbed doses were tabulated, so it was impossible to calculate the effective dose based on this data. Figures 4a to 4d illustrate the relative difference between the 95^th percentile data with the data from Bozkurt et al and McHale et al. for AP lungs, PA thyroid, ISO stomach, and ROT liver, respectively. Similarities between the data, especially in the AP geometry, are observed in these figures. However, for ISO and ROT geometries, the difference is significant, with deviations of about 20% or more.

Fig. 1 Fluence to effective dose conversion coefficients for the different weight percentiles in a: AP, b: ROT irradiation geometries.

Fig. 2 Neutron absorbed doses per unit fluence for Adrenals in AP (a) and Stomach in LLAT (b) irradiation geometry. Comparison between 95th percentile ORNL and VIPMAN phantoms were performed.

4 Discussion

In external dosimetry, the effective dose depends on the distance between the organ boundaries and the irradiated body surface. Thus, the thickness of the outer layers of the body can be favored over the distance between internal organs. Results indicated that the effective dose was decreased by increasing the weight percentile. AP and RLAT show the highest and lowest effective dose for the investigated neutron energy range at all weight percentiles among the six irradiation geometries. It was expected, whereas radiosensitive organs such as breasts are directly exposed to radiation in AP geometry.

The comparison between the 95^th percentile effective dose conversion coefficients and VIPMAN data shows varying degrees of agreement depending on the irradiation geometry. There is a good agreement between results for AP, ISO, and ROT geometries. The VIPMAN’s back is thinner than the 95^th percentile, resulting in higher absorbed dose in abdominal organs when VIPMAN is irradiated from PA geometry. Thus, a relative difference of about 47% of data falls within the range of 15–25%. In lateral geometries (RLAT and LLAT), there are larger discrepancies due to thicker external layers on the sides of the 95^th percentile phantom acting as a shield against neutrons. Generally, the relative difference between the 95^th percentile effective dose and VIPMAN was less than 15% for about 57% of the data and only 33% of data fell within the range of 25–50% across all neutron energies and irradiation geometries used in this study.

The observed differences in absorbed dose values between VIPMAN and the 95^th percentile can be attributed to various factors. Differences in organ topology between individuals can affect the distribution of absorbed dose. Variation in organ depth or the average distance between organs and the radiation source can also contribute to variations in absorbed dose. Also, the choice of Monte Carlo code used for calculations can introduce differences in the calculated absorbed dose values. Despite these discrepancies, a majority of the data (more than 58%) showed a relative difference below 15% between VIPMAN and the 95^th percentile. However, it is important to note that in some cases (23% of the data), the difference exceeded 25% in all studied irradiation geometries and energies.

The similarities between the data from Bozkurt et al. and McHale et al. in the AP geometry suggest that the differences in MCNP versions may have a smaller impact in this particular irradiation geometry. However, large discrepancies are observed in the ISO and ROT geometries, indicating that the choice of MCNP version can significantly affect the calculated absorbed dose values. Interestingly, if the trend of changes is examined for the stomach in Figures 3c and 4c (green symbols), as well as for the liver in Figures 3d and 4d, it is observed that the trend is completely same. This indicates that a significant part of the differences in the absorbed dose data compared to VIPMAN data may originate from differences in the two code versions (MCNP4B versus MCNPX2.6). When versions change can indeed be accompanied by changes in the data cross sections or sampling from different data files. In MCNP6.2, which was used by McHale et al., neutron interaction cross sections are obtained from the endf71x library based on ENDF/B-VII.1 nuclear data, whereas in MCNP4B, the data is get from the endf60 library and ENDF/B-VI data files. These finding highlight the importance of using consistent Monte Carlo code versions when comparing absorbed dose data between studies. It is essential to consider these discrepancies when interpreting and comparing absorbed dose values obtained from different studies, as they can affect the accuracy and reliability of the results.

Fig. 3 Comparison of relative differences in organ absorbed dose between the 95th percentile and VIPMAN phantoms in PA(a), RLAT(b), ISO(c), and ROT(d) irradiation geometries. Organs analyzed include spleen, liver, heart, lung, and stomach.

Fig. 4 Relative difference of the absorbed dose data between the 95th percentile and the reported results for VIPMAN by Bozkurt et al (MCNP4B) and McHale et al. (MCNP6.2) in AP lungs(a), PA thyroid (b), ISO stomach(c), and ROT liver(d).

5 Conclusion

For radiation protection aims, the use of a reference phantom is usually recommended by ICRP. As the results of this study show, there is a difference between the data of the 50^th and other weight percentiles. These differences reach about 30% between the 50^th and 95^th weight percentiles. Therefore, in critical situations where medical interventions are needed and considering that these interventions depended on the level of radiation received, it is suggested that an individual-specific phantom be used instead of a reference phantom. However, constructing a phantom for each individual can be time-consuming and may not be feasible in critical times. In this study, a solution has been examined in these conditions and an attempt to answer the question: “Are data extracted from phantoms with a weight percentile heavier than the 50^th percentile, obtained by adding only layers of muscle and adipose to the torso, reliable in critical situations”? To this end, effective and absorbed dose conversion coefficients were calculated for 19 monoenergetic neutrons spanning 10⁻⁹ to 20 MeV for six irradiation geometries by MCNPX2.6 Monte Carlo code. The 95^th weight percentile results were compared to VIPMAN. Results showed that about 57% and 58% of the effective dose and organ’s absorbed dose data, respectively have a relative difference of less than 15%. Furthermore, the most organs have a good agreement in ISO and ROT irradiation geometries, which are closer to the actual conditions of radiation exposure in accidents compared to other irradiation geometries. A detailed analysis identified that the difference of data cross section used in different versions of MCNP code can be the main factor causing the differences. According to the results, it can be concluded that this method is very reliable when especially the whole body is exposed to radiation especially in the energies above 1 MeV. It should be noted that the value of w_T reported by ICRP 103 are based on population of both sexes and all ages, Therefore, it should be investigated the dependency of tissue weight factors on weight percentiles in future.

Conflict of interest

The authors declare that they have no conflicts of interest in relation to this article.

Funding

This research did not receive any specific funding.

Ethical Approval

Ethical approval was not required.

Informed consent

This article does not contain any studies involving human subjects.

Authors contributions

All authors contributed to various stages of simulations, data analysis, interpretation of results, and manuscript preparation.

Acknowledgments

The author would like to thank the support of the High-Performance Computing Center of the University of Birjand. The results of this study were extracted from the data of a research project under the grant number 1939, which was financially supported by Semnan University of Medical Sciences (SEMUMS).

References

All Tables

All Figures

	Fig. 1 Fluence to effective dose conversion coefficients for the different weight percentiles in a: AP, b: ROT irradiation geometries.
In the text

	Fig. 2 Neutron absorbed doses per unit fluence for Adrenals in AP (a) and Stomach in LLAT (b) irradiation geometry. Comparison between 95th percentile ORNL and VIPMAN phantoms were performed.
In the text

	Fig. 3 Comparison of relative differences in organ absorbed dose between the 95th percentile and VIPMAN phantoms in PA(a), RLAT(b), ISO(c), and ROT(d) irradiation geometries. Organs analyzed include spleen, liver, heart, lung, and stomach.
In the text

	Fig. 4 Relative difference of the absorbed dose data between the 95th percentile and the reported results for VIPMAN by Bozkurt et al (MCNP4B) and McHale et al. (MCNP6.2) in AP lungs(a), PA thyroid (b), ISO stomach(c), and ROT liver(d).
In the text