Estimating internal dose coefficients of short-lived radionuclides in accordance with ICRP 2007 recommendations

ABSTRACT

For radiation protection in high-energy accelerator facilities, internal dose coefficients of short-lived radionuclides were estimated using the dosimetric methodology in accordance with the International Commission on Radiological Protection (ICRP) 2007 Recommendations. A computational program was developed for estimating the dose coefficients. The program was verified by confirming whether it could reproduce the dose coefficients provided by ICRP for intakes of representative radionuclides. In addition, the estimated dose coefficients of short-lived radionuclides were compared to the values generated by Dose and risk CALculation software (DCAL), which is based on a dosimetric methodology that is in accordance with the ICRP 1990 Recommendations, to discuss the reasons why the dose coefficients were changed by the revision of the dosimetric methodologies. The comparison revealed a decreasing trend of dose coefficients in the case of inhalation upon revision of the dosimetric methodologies. By contrast, in the case of ingestion, the dose coefficients tended to increase.

KEYWORDS:

• Radiation protection
• internal exposure
• internal dosimetry
• dose coefficients
• committed effective doses
• ingestion
• inhalation
• nuclear decay data
• specific absorbed fractions
• biokinetic models

1. Introduction

At high-energy accelerator facilities, various radionuclides are generated as byproducts of nuclear reactions of primary and secondary particles with a variety of materials such as targets, beam dumps, shields, and ambient air. Because these radionuclides are potential sources of radiation exposure to workers in the event of an accident, it is important to assess exposure doses prospectively for radiation protection. For internal dose estimation, the International Commission on Radiological Protection (ICRP) has developed dose coefficients for radionuclide intake by workers and members of the public [1,2] based on the 1990 Recommendations of ICRP [3]. Two types of dose coefficients, namely, e(τ) (Sv Bq⁻¹) and h_T(τ) (Sv Bq⁻¹), are defined as a committed effective dose E(τ) (Sv) and a committed equivalent dose for tissue T H_T(τ) (Sv) per unit intake of radioactivity, respectively. The symbol ‘τ’ denotes the committed period. For workers, τ is generally set to 50 years. Internal doses can be obtained as the product of the corresponding dose coefficients and estimated radioactivity intake. However, the dose coefficients of short-lived¹ radionuclides with half-lives shorter than 10 min are not provided, even though a few such short-lived radionuclides are expected to be produced [4–6]. At Japan Proton Accelerator Research Complex, for example, the dose coefficients of short-lived radionuclides were estimated [4] by acquiring nuclear decay data of the aforementioned radionuclides [7,8]. ICRP has been developing revised dose coefficients for workers in accordance with the 2007 Recommendations of ICRP as a series of publications called ‘Occupational Intakes of Radionuclides (OIR)’ [9–12]. In addition, ICRP has released a database of the revised dose coefficients and reference bioassay functions as an electronic annex of OIR [11]. However, the latest database (version 3.01.05.18) does not yet include the dose coefficients of short-lived radionuclides. Therefore, it is necessary to estimate the dose coefficients for intake of short-lived radionuclides from the viewpoint of radiation protection planning at the facilities in accordance with the 2007 Recommendations.

The procedures for estimating dose coefficients from basic dosimetric data and models such as nuclear decay data [13], specific absorbed fraction (SAF) data [14] (SAF is the fraction of deposited energy per mass to a target region emitted from a source region), and biokinetic models for radionuclides incorporated into the body are quite complicated [10–12]. Therefore, we developed a program for computing dose coefficients by using a methodology in accordance with 2007 Recommendations [10]. Subsequently, we estimated the dose coefficients for the intake of short-lived radionuclides by using the developed program.

On the other hand, dose coefficients in accordance with the 1990 Recommendations continue to be used widely in actual scenes. When we use the revised dose coefficients, it is important to grasp the reasons why the dose coefficients change with the revision of ICRP Recommendations. There are some studies which analyze the effects of revisions of dosimetric procedure, models, and data. In a previous work, a tendency to decrease colon doses was observed by the revision of the gastro-intestinal model [15]. In another research, e(τ) values for inhalation cases indicated a decreasing tendency by the revision of calculation procedure for h_T of the remainder tissues [16]. Adoption of energy-dependent electron SAFs also decreased self-irradiation doses of organs [11]. However, these studies consider the change of the models and data individually. In this study, we estimated the dose coefficients of short-lived radionuclides in accordance with the 2007 Recommendations with those based on the 1990 Recommendations to discuss the comprehensive effects of the revision of ICRP Recommendations.

2. Materials and methods

2.1 Procedure for calculating e(τ)

In the biological and dosimetric methodology of ICRP Publication 130 for determining internal doses [10], the value of e(τ) is defined as follows:

(1) $\text{eleft(tau right) = mathop {mathop sum nolimits^ }limits\_{rm{T}} {w\_{rm{T}}}{h\_{rm{T}}}left(tau right)}$(1)

where w_T is the tissue weighting factor of a target organ or tissue T. The target organs and tissues to which w_T is applied and the values of w_T are listed in the 2007 Recommendations [9]. The value of h_T(τ) is calculated as follows:

(2) $h_{\mathrm{T}}\left(\tau \right)=\frac{h_{\mathrm{T}}^{\mathrm{M}}\left(\tau \right)+h_{\mathrm{T}}^{\mathrm{F}}\left(\tau \right)}{2}$(2)

where $h_{\mathrm{T}}^{\mathrm{M}}\left(\tau \right)$ (Sv Bq⁻¹) and $h_{\mathrm{T}}^{\mathrm{F}}\left(\tau \right)$ (Sv Bq⁻¹) are the committed equivalent dose coefficients corresponding to T in the Reference Computational Phantom of Adult Male (RCP-AM) and Female (RCP-AF) constructed by ICRP [17], respectively. When T consists of more than one target regions r_T in the SAF data [14], the values of $h_{\mathrm{T}}^{\mathrm{M}}\left(\tau \right)$ and $h_{\mathrm{T}}^{\mathrm{F}}\left(\tau \right)$ are calculated as follows [10]:

(3) $\text{left{ matrix{ {h\_{rm{T}}^{rm{M}}left(tau right) = mathop {mathop sum nolimits^ }limits\_{{{rm{r}}\_{rm{T}}}} fleft({{{rm{r}}\_{rm{T}}},{rm{T}}} right){ }{h^{rm{M}}}left({{{rm{r}}\_{rm{T}}},tau } right)} cr {h\_{rm{T}}^{rm{F}}left(tau right) = mathop {mathop sum nolimits^ }limits\_{{{rm{r}}\_{rm{T}}}} fleft({{{rm{r}}\_{rm{T}}},{rm{T}}} right){ }{h^{rm{F}}}left({{{rm{r}}\_{rm{T}}},tau } right)} cr }right.}$(3)

where f(r_T,T) is the target region fractional weight [10], and h^M(r_T,τ) (Sv Bq⁻¹) and h^F(r_T,τ) (Sv Bq⁻¹) are the committed equivalent dose coefficients in r_T of RCP-AM and RCP-AF, respectively. Then, the values of h^M(r_T,τ) and h^F(r_T,τ) are computed as follows [10]:

(4) $\left\{\begin{array}{c}{h}^{\mathrm{M}}\left({\mathrm{r}}_{\mathrm{T}},\tau \right)=\sum _i\sum _{{\mathrm{r}}_{\mathrm{S}}}{\tilde{A}}_i\left({\mathrm{r}}_{\mathrm{S}},\tau \right)S_{\mathrm{w}}^{\mathrm{M}}{\left({\mathrm{r}}_{\mathrm{T}}\leftarrow {\mathrm{r}}_{\mathrm{S}}\right)}_i\\ h^{\mathrm{F}}\left({\mathrm{r}}_{\mathrm{T}},\tau \right)=\sum _i\sum _{{\mathrm{r}}_{\mathrm{S}}}{\tilde{A}}_i\left({\mathrm{r}}_{\mathrm{S}},\tau \right)S_{\mathrm{w}}^{\mathrm{F}}{\left({\mathrm{r}}_{\mathrm{T}}\leftarrow {\mathrm{r}}_{\mathrm{S}}\right)}_i\end{array}\right.$(4)

where Ã_i(r_S,τ) (Bq s) is the number of disintegrations occurring in the source region r_S of chain member i per activity intake of a parent nuclide, and $S_{\mathrm{w}}^{\mathrm{M}}{\left({\mathrm{r}}_{\mathrm{T}}\leftarrow {\mathrm{r}}_{\mathrm{S}}\right)}_i$ (Sv (Bq s)⁻¹) and $S_{\mathrm{w}}^{\mathrm{F}}{\left({\mathrm{r}}_{\mathrm{T}}\leftarrow {\mathrm{r}}_{\mathrm{S}}\right)}_i$ (Sv (Bq s)⁻¹) are the radiation-weighted S coefficients S_w in r_T per disintegration of the chain member i in r_S for RCP-AM and RCP-AF, respectively. The values of Ã_i(r_S,τ) are evaluated by integrating a series of ordinary differential equations constructed based on biokinetic models provided by ICRP. Kinetics in the alimentary and respiratory tract regions are modeled as the Human Alimentary Tract Model [15] and the revised Human Respiratory Tract Model [10], respectively. Notably, the transfer coefficients of males are used to evaluate Ã_i(r_S,τ) for both males and females, even when sex-specific data are provided [10]. Absorption into the blood via the respiratory tract regions and the small intestine, and radionuclide kinetics after absorption are depicted by systemic kinetic models considering element-specific characteristics [11,12]. The values of $S_{\mathrm{w}}^{\mathrm{M}}{\left({\mathrm{r}}_{\mathrm{T}}\leftarrow {\mathrm{r}}_{\mathrm{S}}\right)}_i$ and $S_{\mathrm{w}}^{\mathrm{F}}{\left({\mathrm{r}}_{\mathrm{T}}\leftarrow {\mathrm{r}}_{\mathrm{S}}\right)}_i$ are calculated as follows [10]:

(5) $\text{left{ matrix{ {S\_{rm{w}}^{rm{M}}{{left({{{rm{r}}\_{rm{T}}} leftarrow {{rm{r}}\_{rm{S}}}} right)}\_i} = c{ }mathop {mathop sum nolimits^ }limits\_{rm{R}} {w\_{rm{R}}}mathop {mathop sum nolimits^ }limits\_j {E\_{i,{rm{R}},j}}{Y\_{i,{rm{R}},j}}{⁋hi ^{rm{M}}}{{left({{{rm{r}}\_{rm{T}}} leftarrow {{rm{r}}\_{rm{S}}},{E\_{i,{rm{R}},j}}} right)}\_i}} cr {S\_{rm{w}}^{rm{F}}{{left({{{rm{r}}\_{rm{T}}} leftarrow {{rm{r}}\_{rm{S}}}} right)}\_i} = c{ }mathop {mathop sum nolimits^ }limits\_{rm{R}} {w\_{rm{R}}}mathop {mathop sum nolimits^ }limits\_j {E\_{i,{rm{R}},j}}{Y\_{i,{rm{R}},j}}{⁋hi ^{rm{F}}}{{left({{{rm{r}}\_{rm{T}}} leftarrow {{rm{r}}\_{rm{S}}},{E\_{i,{rm{R}},j}}} right)}\_i}} cr }}$(5)

where c (J MeV⁻¹) is a constant value (1.602 × 10¹³) to convert units from MeV to J; w_R is the radiation weighting factor for radiation type R [9]; E_i,_R,j (MeV) and Y_i,_R,j are the energy and yield of the jth radiation of type R of chain member i, respectively [13]; and ϕ^M(r_T←r_S,E_i,_R,j)_i (kg⁻¹) and ϕ^F(r_T←r_S,E_i,_R,j)_i (kg⁻¹) are the SAFs from r_S to r_T at the energy of E_i,_R,j, respectively. The SAF values for the given energies are obtained by interpolating the SAF data, which are provided as energy discrete values [14].

2.2 Development of program to calculate e(τ)

Various computational codes have been developed to calculate e(τ), such as Dose and risk CALculation software (DCAL) [18], Integrated Modules for Bioassay Analysis (IMBA) [19], and MONitoring to Dose cALculation (MONDAL) [20]. These codes, however, are designed to calculate e(τ) based on a dosimetric methodology in accordance with the 1990 Recommendations [1] (referred to hereinafter as ‘former methodology’). As of September 2018, there are no published codes to compute e(τ) based on a dosimetric methodology in accordance with the 2007 Recommendations as described in the Section 2.1 (referred to hereinafter as ‘current methodology’). Thus, we constructed a computation algorithm to derive dose coefficients by using the current methodology and developed a Fortran program based on the aforementioned algorithm.

Figure 1 shows a flow of the program to execute the procedure for calculating e(τ) by using the current methodology. The program first reads calculation conditions and subsequently obtains the nuclear decay data of radionuclides including the radioactive progenies of the incorporated radionuclides, and the corresponding biokinetic data. Next, the program constructs a compartment model based on the biokinetic data and calculates the cumulative number of radionuclide disintegrations in the source regions per unit intake Ã(τ) by using Leggett’s algorithm [20] as with DCAL [18]. In the steps for calculating sex-specific h_T(τ), the flow is looped by the two sexes [21]. The program obtains sex-specific SAF data and interpolates the SAF data with radiation energies by using the Piecewise Cubic Hermite Interpolation Package (PCHIP) [22]. The values of sex-specific S_w are calculated using Equation (5)(5) $\text{left{ matrix{ {S\_{rm{w}}^{rm{M}}{{left({{{rm{r}}\_{rm{T}}} leftarrow {{rm{r}}\_{rm{S}}}} right)}\_i} = c{ }mathop {mathop sum nolimits^ }limits\_{rm{R}} {w\_{rm{R}}}mathop {mathop sum nolimits^ }limits\_j {E\_{i,{rm{R}},j}}{Y\_{i,{rm{R}},j}}{⁋hi ^{rm{M}}}{{left({{{rm{r}}\_{rm{T}}} leftarrow {{rm{r}}\_{rm{S}}},{E\_{i,{rm{R}},j}}} right)}\_i}} cr {S\_{rm{w}}^{rm{F}}{{left({{{rm{r}}\_{rm{T}}} leftarrow {{rm{r}}\_{rm{S}}}} right)}\_i} = c{ }mathop {mathop sum nolimits^ }limits\_{rm{R}} {w\_{rm{R}}}mathop {mathop sum nolimits^ }limits\_j {E\_{i,{rm{R}},j}}{Y\_{i,{rm{R}},j}}{⁋hi ^{rm{F}}}{{left({{{rm{r}}\_{rm{T}}} leftarrow {{rm{r}}\_{rm{S}}},{E\_{i,{rm{R}},j}}} right)}\_i}} cr }}$(5) , and thereafter, the values of h_T(τ) are calculated by combining Ã(τ) and S_w, as in Equation (4)(4) $\left\{\begin{array}{c}{h}^{\mathrm{M}}\left({\mathrm{r}}_{\mathrm{T}},\tau \right)=\sum _i\sum _{{\mathrm{r}}_{\mathrm{S}}}{\tilde{A}}_i\left({\mathrm{r}}_{\mathrm{S}},\tau \right)S_{\mathrm{w}}^{\mathrm{M}}{\left({\mathrm{r}}_{\mathrm{T}}\leftarrow {\mathrm{r}}_{\mathrm{S}}\right)}_i\\ h^{\mathrm{F}}\left({\mathrm{r}}_{\mathrm{T}},\tau \right)=\sum _i\sum _{{\mathrm{r}}_{\mathrm{S}}}{\tilde{A}}_i\left({\mathrm{r}}_{\mathrm{S}},\tau \right)S_{\mathrm{w}}^{\mathrm{F}}{\left({\mathrm{r}}_{\mathrm{T}}\leftarrow {\mathrm{r}}_{\mathrm{S}}\right)}_i\end{array}\right.$(4) . Finally, the value of e(τ) is obtained by summing the sex-averaged values of h_T(τ) weighted using the corresponding w_T. Table 1 summarizes the dosimetric data and models used in the program. The data of element-specific systemic models are recorded in files separate from the execution file in plaintext format. Therefore, users can edit the data of systemic models if needed.

Table 1. Dosimetric data and models used in program developed in the present study

Item	Reference
Radiation and tissue weighting factors	ICRP Publication 103 [9]
Nuclear decay data	ICRP Publication 107 [13]
Clearance model in alimentary tract	ICRP Publication 100 [17]
Clearance model in respiratory tract	ICRP Publication 130 [10]
Element specific systemic model	ICRP Publication 134 [11]
Specific absorbed fraction data	ICRP Publication 133 [14]

Figure 1. Calculation flow of program developed in the present study.

2.3 Verification of developed program

Verification of the developed program was performed by confirming whether the program reproduces the e(τ) values recorded in the tables of OIR part 2 [11]. The OIR tables lists e(τ) with two significant figures for 98 classifications of the intake (hereinafter called case) of 19 nuclides of 14 elements. The confirmation was performed for all 98 cases.

2.4 Calculation conditions of dose coefficients of short-lived radionuclides

Table 2 lists the radionuclides whose dose coefficients are evaluated in this study. All of them are not included in the OIR Data Viewer, although they are recorded in the current nuclear decay data [13]. The classifications of intake patterns, which include variations of intake paths and chemical forms, were determined by referring to ICRP Publication 68 [1] to compare the calculation results against the e(τ) values generated using DCAL [18]. The current version of DCAL, version 9.4, can calculate dose coefficients by using the former methodology, except for the nuclear decay data because DCAL version 9.4 uses the latest version of nuclear decay data [13]. In addition, both DCAL and the developed program use Leggett’s algorithm to calculate Ã(τ). Therefore, we can discuss the impact of revision of the dosimetric methodology on the values of e(τ) by means of this comparison.

Table 2. Object radionuclides for calculation of dose coefficients

Element	Nuclides
Carbon	^10C
Phosphorus	^30P
Sulfur	^37S
Calcium	^49Ca
Iron	^53Fe, ^53mFe, ^61Fe, ^62Fe
Cobalt	^54mCo, ^62Co
Zinc	^60Zn, ^61Zn, ^71Zn
Strontium	^79Sr, ^93Sr, ^94Sr
Yttrium	^81Y, ^83Y, ^83mY, ^89mY
Zirconium	^85Zr, ^89mZr
Niobium	^87Nb, ^88mNb, ^94mNb, ^99Nb, ^99mNb
Molybdenum	^89Mo, ^91mMo
Technetium	^91Tc, ^91mTc, ^92Tc, ^102Tc, ^102mTc, ^105Tc

3 Results

3.1 Program verification

The calculated values of e(τ) generated using the developed program were compared with the values tabulated in OIR part 2 (reference values) [11]. For 91 of the total 98 cases, the results generated using the developed program were consistent with the reference values within two digits. Table 3 lists the cases in which the calculation results did not agree with the values given in OIR part 2. The difference between the corresponding values of e(τ), D (%), is defined as follows:

(6) $D=\left(e_{\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{g}}/e_{\mathrm{O}\mathrm{I}\mathrm{R}}-1\right)\times 100$(6)

Table 3. Values of e(τ) generated using developed program and those listed in OIR part 2, and differences in values of e(τ) and D between the two sets of values

Nuclide	Pathway	Material	e(τ) (Sv Bq^−1)		D (%)
			This study	OIR part 2
^35S	Inhalation	Type S	5.0E−10	4.9E−10	2.0
^60Co	Ingestion	Other compounds	3.3E−09	3.2E−09	3.1
^89Sr	Ingestion	Other compounds	9.0E−10	8.9E−10	1.1
^85Sr	Inhalation	Type S	6.8E−10	6.7E−10	1.5
^95Zr	Ingestion	All compounds	3.3E−10	3.2E−10	3.1
^95Nb	Ingestion	All compounds	3.1E−10	3.0E−10	3.3

where e_prog (Sv Bq⁻¹) is the e(τ) calculated using the developed program, and e_OIR (Sv Bq⁻¹) is the reference value. The D values were lower than 5%, as listed in Table 3. Slight discrepancy is unavoidable because of rounding errors over multiple calculation steps. As a result, the program was considered to be verified.

3.2 Calculation of e(τ) for short-lived radionuclides

Tables 4 and 5 summarize the calculation results obtained using the developed program and DCAL for inhalation and ingestion of short-lived radionuclides, respectively. The ratio is the quotient of e(τ) generated using the developed program divided by that obtained using DCAL. Most e(τ) values decreased in the inhalation cases, as shown in Table 4. By contrast, the e(τ) values in the ingestion cases tended to increase.

Table 4. Values of e(τ) generated using developed program and those generated using DCAL, and ratios of e(τ) for inhalation of short-lived radionuclides

Nuclide	Type or chemical form	e(τ) (Sv Bq^−1)		Ratio
		This study	DCAL
^10C	CO2 gas	2.0E−13	9.5E−14	2.1
	CO gas	8.0E−14	3.8E−14	2.1
^30P	F	3.6E−12	5.4E−12	0.67
	M	3.6E−12	6.3E−12	0.57
^37S	F	6.1E−12	1.1E−11	0.55
	M	6.6E−12	1.3E−11	0.51
	Vapor	1.6E−11	1.1E−11	1.5
^49Ca	M	1.9E−11	3.0E−11	0.63
^53Fe	F	8.5E−12	1.4E−11	0.61
	M	1.2E−11	1.9E−11	0.63
^53mFe	F	3.1E−12	6.7E−12	0.46
	M	4.3E−12	8.6E−12	0.50
^61Fe	F	7.5E−12	1.3E−11	0.58
	M	1.1E−11	1.8E−11	0.61
^62Fe	F	2.7E−12	5.0E−12	0.54
	M	3.0E−12	5.6E−12	0.54
^54mCo	M	2.8E−12	5.7E−12	0.49
	S	2.8E−12	5.8E−12	0.48
^62Co	M	2.2E−12	4.1E−12	0.54
	S	2.2E−12	4.2E−12	0.52
^60Zn	S	6.7E−12	1.2E−11	0.56
^61Zn	S	2.8E−12	5.1E−12	0.55
^71Zn	S	2.9E−12	5.2E−12	0.56
^79Sr	F	5.7E−12	8.4E−12	0.68
	S	6.5E−12	1.1E−11	0.59
^93Sr	F	1.2E−11	2.0E−11	0.60
	S	1.4E−11	3.0E−11	0.47
^94Sr	F	3.3E−12	4.8E−12	0.69
	S	3.8E−12	6.2E−12	0.61
^81Y	M	3.7E−12	6.2E−12	0.60
	S	3.7E−12	6.4E−12	0.58
^83Y	M	1.1E−11	1.9E−11	0.58
	S	1.1E−11	1.9E−11	0.58
^83mY	M	4.8E−12	8.4E−12	0.57
	S	4.8E−12	8.6E−12	0.56
^89mY	M	2.4E−14	1.1E−13	0.22
	S	2.4E−14	1.1E−13	0.22
^85Zr	F	1.3E−11	1.9E−11	0.68
	M	1.5E−11	2.6E−11	0.58
	S	1.6E−11	2.7E−11	0.59
^89mZr	F	7.8E−13	1.8E−12	0.43
	M	8.4E−13	2.2E−12	0.38
	S	8.5E−13	2.2E−12	0.39
^87Nb	M	1.1E−11	2.1E−11	0.52
	S	1.1E−11	2.2E−11	0.50
^88mNb	M	1.5E−11	2.8E−11	0.54
	S	1.5E−11	2.8E−11	0.54
^94mNb	M	1.5E−13	4.7E−13	0.32
	S	1.5E−13	4.8E−13	0.31
^99Nb	M	3.8E−13	1.3E−12	0.29
	S	3.8E−13	1.3E−12	0.29
^99mNb	M	4.0E−12	7.2E−12	0.56
	S	4.0E−12	7.3E−12	0.55
^89Mo	F	4.7E−12	6.8E−12	0.69
	S	5.3E−12	9.0E−12	0.59
^91mMo	F	1.4E−12	2.3E−12	0.61
	S	1.6E−12	2.9E−12	0.55
^91Tc	F	7.8E−12	1.4E−11	0.56
	M	1.0E−11	1.6E−11	0.63
^91mTc	F	8.6E−12	1.5E−11	0.57
	M	1.1E−11	1.8E−11	0.61
^92Tc	F	7.6E−12	1.5E−11	0.51
	M	9.0E−12	1.8E−11	0.50
^102Tc	F	1.0E−13	1.9E−13	0.53
	M	1.0E−13	1.9E−13	0.53
^102mTc	F	4.8E−12	1.0E−11	0.48
	M	5.9E−12	1.2E−11	0.49
^105Tc	F	1.0E−11	2.1E−11	0.48
	M	1.5E−11	2.7E−11	0.56

Table 5. Values of e(τ) generated using developed program and those generated using DCAL, and ratios of e(τ) for ingestion of short-lived radionuclides (1/2)

Nuclide	Chemical form	e(τ) (Sv Bq^−1)		Ratio
		This study	DCAL
^10C	All compounds	1.4E−12	1.0E−12	1.4
^30P	All compounds	1.5E−11	1.2E−11	1.3
^37S	Elemental	1.9E−11	1.6E−11	1.2
	Other forms	1.9E−11	1.6E−11	1.2
^49Ca	All compounds	4.5E−11	3.8E−11	1.2
^53Fe	All compounds	3.7E−11	2.9E−11	1.3
^53mFe	All compounds	1.3E−11	1.1E−11	1.2
^61Fe	All compounds	3.0E−11	2.6E−11	1.2
^62Fe	All compounds	1.2E−11	9.5E−12	1.3
^54mCo	Insoluble oxides	1.4E−11	1.2E−11	1.2
	Other forms	1.4E−11	1.2E−11	1.2
^62Co	Insoluble oxides	1.1E−11	8.6E−12	1.3
	Other forms	1.1E−11	8.6E−12	1.3
^60Zn	All compounds	2.1E−11	1.7E−11	1.2
^61Zn	All compounds	1.3E−11	1.0E−11	1.3
^71Zn	All compounds	1.1E−11	8.3E−12	1.3
^79Sr	Titanate	2.3E−11	1.9E−11	1.2
	Other forms	2.3E−11	1.9E−11	1.2
^93Sr	Titanate	3.1E−11	3.6E−11	0.86
	Other forms	3.1E−11	3.4E−11	0.91
^94Sr	Titanate	1.2E−11	9.4E−12	1.3
	Other forms	1.2E−11	9.4E−12	1.3
^81Y	All compounds	1.4E−11	1.1E−11	1.3
^83Y	All compounds	3.8E−11	3.2E−11	1.2
^83mY	All compounds	1.6E−11	1.4E−11	1.1
^89mY	All compounds	8.9E−14	8.4E−14	1.1
^85Zr	All compounds	4.7E−11	4.3E−11	1.1
^89mZr	All compounds	1.8E−12	1.9E−12	0.95
^87Nb	All compounds	3.2E−11	2.9E−11	1.1
^88mNb	All compounds	5.1E−11	4.2E−11	1.2
^94mNb	All compounds	1.2E−13	7.1E−13	0.17
^99Nb	All compounds	1.6E−12	2.1E−12	0.76
^99mNb	All compounds	1.6E−11	1.3E−11	1.2
^89Mo	Sulfide	2.1E−11	1.9E−11	1.1
	Other forms	2.1E−11	1.7E−11	1.2
^91mMo	Sulfide	5.7E−12	4.5E−12	1.3
	Other forms	5.7E−12	4.5E−12	1.3
^91Tc	All compounds	3.8E−11	3.1E−11	1.2
^91mTc	All compounds	4.2E−11	3.4E−11	1.2
^92Tc	All compounds	3.4E−11	2.8E−11	1.2
^102Tc	All compounds	5.5E−13	5.7E−13	0.96
^102mTc	All compounds	1.7E−11	1.4E−11	1.2
^105Tc	All compounds	3.9E−11	3.9E−11	1.0

4. Discussion

4.1 Cause analyses of differences in e(τ) for inhalation cases

In the inhalation cases, the e(τ) values generated using the developed program were lower than those obtained using DCAL, except for the inhalation of ¹⁰C gases and ³⁶S vapor, as shown in Table 4. First, the case of inhalation of ^89mY Type M was analyzed because in this case, the e(τ) ratio was the smallest in Table 4. Table 6 lists the calculation results of h_T(τ) and e(τ) for the inhalation of ^89mY Type M. Here, a proportion index for a tissue P_T is introduced to analyze a key tissue or organ with a changed e(τ) value. The values of P_T obtained using the developed program (P_T,p) and DCAL (P_T,D) are defined as follows:

(7) $\text{left{ matrix{ {{P\_{{rm{T}},{rm{p}}}} = {w\_{{rm{T}},2007}}{h\_{{rm{T}},{rm{p}}}}/{e\_{rm{D}}}} cr {{P\_{{rm{T}},{rm{D}}}} = {w\_{{rm{T}},1990}}{h\_{{rm{T}},{rm{D}}}}/{e\_{rm{D}}}} cr }}$(7)

Table 6. Values of h_T(τ) and P_T, and difference in P_T for inhalation of ^89mY Type M

Organ, tissue	hT(τ) (Sv Bq^−1)		Proportion index, PT^*1		Difference in PT
	This study	DCAL	This study	DCAL
Red marrow	1.5E−14	1.0E−14	0.0165	0.0110	0.0055
Colon	1.0E−15	8.0E−16	0.0011	0.0009	0.0002
Lungs	3.3E−14	2.8E−14	0.0362	0.0307	0.0055
Stomach	5.8E−15	8.5E−15	0.0064	0.0093	−0.0030
Breasts	1.0E−14	7.6E−15	0.0110	0.0035	0.0075
Gonads	1.2E−16	4.4E−16	0.0001	0.0008	−0.0007
Urinary bladder	2.0E−16	2.3E−16	0.0001	0.0001	0.0000
Esophagus	5.6E−14	2.1E−14	0.0205	0.0096	0.0109
Liver	5.6E−15	3.9E−15	0.0020	0.0018	0.0003
Thyroid	5.0E−14	1.7E−14	0.0183	0.0078	0.0105
Bone surface	1.4E−14	1.2E−14	0.0013	0.0011	0.0002
Brain^*2	4.8E−14	–	0.0044	–	0.0044
Salivary glands	8.8E−14	–	0.0081	–	0.0081
Skin	7.2E−15	6.5E−15	0.0007	0.0006	0.0001
Remainder	8.8E−14	2.0E−12	0.0966	0.9149	−0.8183
Adrenals	3.8E−15	4.6E−15
Brain^*2	–	1.6E−14
ET region	7.8E−13	4.0E−12
Gall bladder	3.6E−15	–
Heart	1.6E−14	–
Kidneys	2.3E−15	2.3E−15
Lymphatic nodes	3.8E−14	–
Muscle	5.7E−15	1.4E−14
Oral mucosa	2.6E−13	–
Pancreas	2.9E−15	4.9E−15
Prostate, uterus	1.6E−16	4.0E−16
Small intestine	1.1E−15	7.8E−16
Spleen	6.0E−15	4.2E−15
Thymus	2.6E−14	2.1E−14
e(τ)	2.4E−14	1.1E−13

^*1Ratio of w_T-weighted h_T(τ) to e(τ) generated using DCAL. ^*2Brain is a member of the remainder tissue according to the 1990 Recommendations.

where w_T,2007 and w_T,1990 are the tissue weighting factors given in the 2007 and 1990 Recommendations of ICRP, respectively; h_T,p (Sv Bq⁻¹) and h_T,D (Sv Bq⁻¹) are the h_T values obtained using the developed program and DCAL, respectively; and e_D (Sv Bq⁻¹) is the e(τ) value generated using DCAL. Note that the denominator of Equation (7)(7) $\text{left{ matrix{ {{P\_{{rm{T}},{rm{p}}}} = {w\_{{rm{T}},2007}}{h\_{{rm{T}},{rm{p}}}}/{e\_{rm{D}}}} cr {{P\_{{rm{T}},{rm{D}}}} = {w\_{{rm{T}},1990}}{h\_{{rm{T}},{rm{D}}}}/{e\_{rm{D}}}} cr }}$(7) for P_T,p is e_D to elucidate the contribution of h_T(τ) in the change in e(τ) based on e_D. In addition, Table 6 also lists the values of P_T and the difference between P_T,p and P_T,D. In this case, the dominant cause that led to a decrease in e(τ) was the decrease in h_T(τ) for the remainder tissues (h_rem), as presented in Table 6. The calculation procedures of h_rem in the current and the former methodologies are different [3,9]. In the former methodology, h_rem is defined as the tissue-mass-weighted average of the values of h_T(τ) for the members of the remainder tissues by using the so-called splitting rule [23]. The splitting rule for calculating h_rem is expressed as follows:

(8) $\left\{\begin{array}{c}{h}_{\mathrm{r}\mathrm{e}\mathrm{m}}=\frac{{\sum }_{i=1}^{10}{m}_i{h}_i}{{\sum }_{i=1}^{10}{m}_i},\mathrm{i}\mathrm{f}{h}_{{\mathrm{T}}^{\prime }}\le h_{\mathrm{m}\mathrm{a}\mathrm{x}}\\ h_{\mathrm{r}\mathrm{e}\mathrm{m}}=0.5\frac{{\sum }_{i=1\left(i\ne {\mathrm{T}}^{\prime }\right)}^{10}{m}_i{h}_i}{{\sum }_{i=1\left(i\ne {\mathrm{T}}^{\prime }\right)}^{10}{m}_i}+0.5h_{{\mathrm{T}}^{\prime }},\mathrm{i}\mathrm{f}{\mathrm{h}}_{{\mathrm{T}}^{\prime }}>{\mathrm{h}}_{\mathrm{m}\mathrm{a}\mathrm{x}}\end{array}\right.$(8)

where m_i (kg) is the mass of the ith member of the remainder tissues, h_i (Sv Bq⁻¹) is the committed equivalent dose coefficient of the ith tissue, h_T’ is the maximum h_T(τ) among the tissues included in the remainder tissues, and h_max is the maximum h_T(τ) among the tissues that are assigned specific w_T values. By contrast, in the current methodology, h_rem is defined as the arithmetic mean of the values of h_T(τ) for the members of the remainder tissues, and the splitting rule is abolished [9]. In all inhalation cases with an increase in e(τ), the tissue receiving the highest h_T(τ) was the ET region in the DCAL result. That is, the relatively high value of h_rem was caused by the predominantly large h_T(τ) for the ET region in the DCAL result. Therefore, abolishment of the splitting rule led to a decrease in the value of h_T(τ) for the ET region (h_ET).

The ET region consists of the anterior nasal passage (ET₁), and the posterior nasal passage, pharynx, and larynx (ET₂). The value of h_ET is defined as follows:

(9) $h_{\mathrm{E}\mathrm{T}}=h_{\mathrm{E}\mathrm{T}1}{A}_{\mathrm{E}\mathrm{T}1}+h_{\mathrm{E}\mathrm{T}2}{A}_{\mathrm{E}\mathrm{T}2}+h_{\mathrm{L}\mathrm{N}-\mathrm{E}\mathrm{T}}{A}_{\mathrm{L}\mathrm{N}-\mathrm{E}\mathrm{T}}$(9)

where h_ET1, h_ET2, and h_LN-ET are the h_T(τ) of ET₁, ET₂, and lymphatic nodes in the ET region (LN-ET), respectively; and A_ET1,A_ET2, and A_LN-ET are the apportionment factors considering the differences in radiation sensitivity between the tissues for ET₁, ET₂, and LN-ET, respectively. The values of A_ET1, A_ET2, and A_LN-ET are 0.001, 0.998, and 0.001, respectively, according to the former methodology [24]. In the current methodology, LN-ET is not a member of the ET region, and the values of A_ET1 and A_ET2 are 0.001 and 0.999, respectively [10]. In any case, h_ET2 is generally dominant in h_ET in both methodologies. The decrease in h_ET was caused by a change in the photon SAF data of self-absorption in ET₂. Figure 2 shows the photon SAF data from the surface of ET₂ to the target cells in ET₂ in the current and the former methodologies [14,25]. The current data are averages of the values for males and females. The ratio of the current SAF to the former SAF is 0.41 at the energy of the main photon emitted from ^89mY, which is 0.91 MeV [13]. In the former methodology, the photon SAFs to the thyroid from the source regions were substituted with those to ET₂ [24] because the ET regions were not modeled in the previous human model used to evaluate SAF data [26]. By contrast, the current human models include the ET₁ and ET₂ regions, and the mass of ET₂ is smaller than that of the thyroid [17]. Self-absorption SAF depends on the mass of the tissue or region [27–30]. In addition, the deposition fraction of inhaled aerosol to ET₂ decreased by 35% owing to revision of the Human Respiratory Tract Model (HRTM) based on a review of particle transport in the ET regions after publication of the original HRTM [10]. Therefore, the h_ET values decreased in most inhalation cases. These findings revealed that the decrease in e(τ) in the inhalation cases was caused by three factors. The first was abolition of the splitting rule for calculating h_rem adopted in the former methodology; the second was the change in the photon SAF data; and the third was the change in the deposition fraction of inhaled radioactive aerosols to ET₂ region.

Figure 2. Photon SAFs to target cells in ET₂ from surface of ET₂. The solid curve and the broken curve indicate the current data [14] and the previous data [25], respectively.

The e(τ) values increased for inhalation of ¹⁰C gases and ³⁷S vapor, as listed in Table 4. In these cases, the radionuclides inhaled into the lungs were assumed to be absorbed instantly into the blood [1,11,24], and most radionuclides decayed in the blood owing to their short half-lives. The former blood source SAFs are evaluated with the assumption that blood is distributed throughout the body in proportion to the masses of the tissues and organs [25]. However, the current blood source SAFs are evaluated considering the blood fractions of the tissues and organs [17]. The lungs, colon, and liver, to which relatively large w_T values are assigned, are characterized by relatively high blood fractions. Consequently, the current blood source SAFs to highly weighted organs and tissues are larger than the former SAFs. As a result, the increase in e(τ) was caused by the change in SAF whose source region is the blood.

4.2 Cause analyses of differences in e(τ) for ingestion cases

In most ingestion cases, the e(τ) values obtained using the developed program were larger than those obtained using DCAL, as can be inferred from Table 5. The primary cause of increase in e(τ) was the increase in the h_T(τ) value of the esophagus. In the former methodology, the h_T(τ) value of the esophagus is substituted by that for the thymus [31] because the esophagus is not incorporated in the former human model [26] used for SAF evaluation. By contrast, the esophagus is considered in both the biokinetic models and the human models in the current methodology [10,17]. Therefore, the current methodology can consider that the esophagus tissue receives radiation energy emitted from the radionuclides in the esophagus directly. Consequently, the h_T(τ) of the esophagus tended to increase in most of the ingestion cases.

The ratio of e(τ) for ^94mNb was the smallest in the decrement cases. An analysis using P_T revealed that the decrease in h_T(τ) for the stomach (h_st) caused the change in e(τ). Then, the change in h_st was caused by revision of the electron SAFs to the stomach from its contents [14,32]. In the former methodology, the electron SAFs are constant for the alimentary tract region based on simple assumptions [32]. By contrast, the revised SAFs for the alimentary tract region are evaluated by radiation transport simulations considering the positions of the target stem cells buried in the alimentary tract wall [15]. As a result, the electron SAFs to the stomach from its contents are zero below 80 keV because the electrons are shielded by the wall tissue between the surface of the wall and the target stem cells [14,15]. Such difference in the electron SAFs led to the decrease in h_st, and consequently, a decrease in e(τ) in the case of ^94mNb ingestion. The underlying causes in the cases of ^89mZr and ⁹⁹Nb were the same as that in the case of ^94mNb.

The e(τ) values decreased in the two cases of ⁹³Sr. In these cases, it was found in an analysis using P_T values that the decrease in the e(τ) values was caused by changes in the h_T(τ) values of the colon. The half-life of ⁹³Y, which is the progeny of ⁹³Sr, is 10.2 h, and it is longer than that of ⁹³Sr, 7.42 min [13]. Therefore, the number of decays of ⁹³Y in the colon content, which is the latter part of the alimentary tract, was larger than that in the other ingestion cases because the retention time of colon content is longer than the retention times of the upper parts of the alimentary tract [15,32]. Beta decay electrons are the dominant radiation for exposure dose due to ⁹³Y [13]. The electron SAFs in the colon region decrease when the SAF data are updated [14,32] for the same reason as in the stomach case. Such changes in the SAFs of the colon led to a decrease in the h_T(τ) of the colon, and consequently, e(τ) in the cases of ⁹³Sr.

4.3 Comparison to previous studies

In a previous work, it was noted that abolition of the splitting rule tends to decrease e(τ) in the inhalation cases [16]. This present study revealed that the decreasing tendency of e(τ) in the inhalation cases is enhanced by changes in the deposition fraction to the ET₂ region associated with revision of the clearance model in the respiratory tract region. By contrast, the present study is the first report in which changes in the blood source SAFs tended to increase e(τ) in the inhalation cases.

For the ingestion cases, it was reported that the e(τ) values decreased owing to changes in the electron SAFs to the colon from its content owing to consideration of the target stem cell position in a few cases [15]. This phenomenon has been observed, but it hardly occurred in the present study because of the short half-lives. On the contrary, the tendency of e(τ) to increase was observed in this study because of the increase in the value of h_T(τ) of the esophagus owing to the adoption of human models in which the esophagus is included. If the half-life of the ingested radionuclide is comparatively long, the number of disintegrations in the esophagus will be smaller than those in the colon and the systemic organs and tissues. Consequently, the contribution of h_T(τ) of the esophagus to e(τ) will be small. Therefore, the trend of increase in e(τ) for the ingestion cases seems to be limited to short-lived radionuclides.

5. Conclusions

Committed effective dose coefficients of short-lived radionuclides were estimated using a program developed in the present study that employs the dosimetric methodology that is in accordance with the 2007 Recommendations of ICRP. The program was verified using the data listed in OIR part 2.

The calculated coefficients were compared to the values generated using DCAL, which uses the dosimetric methodology that is in accordance with the 1990 Recommendations of ICRP. The trend of decrease in the e(τ) values was observed in the inhalation cases. This was caused by the abolition of the splitting rule, revision of SAF data, and changes in the deposition fraction of inhaled aerosols to the ET₂ region. On the contrary, the tendency of e(τ) to increase was observed in the ingestion cases owing to consideration of the esophagus in the current human models and biokinetic models. However, this trend seems to be specific to short-lived radionuclides because the contribution of h_T(τ) of the esophagus to e(τ) is small for radionuclides with comparatively long half-lives. By contrast, the influence of revisions in element-specific biokinetic data on dose coefficients was not analyzed because most of the activities disappeared in element-independent regions, such as the respiratory tract and the alimentary tract, because of the short half-lives. Analyses of radionuclides with long half-lives are necessary to discuss the influence of revisions to element-specific systemic kinetics.

The calculated dose coefficients will be available to estimate potential doses resulting from intake of short-lived radionuclides at high-energy accelerator facilities. In addition, knowledge of the influences of revisions to dosimetric methodologies on dose coefficients will be helpful for revision of regulatory standards for radiation protection in accordance with the 2007 Recommendations.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. In this paper, ‘short-lived’ means that the half-life is shorter than 10 min.