Doses from external irradiation and ingestion of ¹³⁴Cs, ¹³⁷Cs and ⁹⁰Sr of the population of Belarus accumulated over 35 years after the Chernobyl accident

Abstract

This study considers the exposure of the population of the most contaminated Gomel and Mogilev Oblasts in Belarus to prolonged sources of irradiation resulting from the Chernobyl accident. Dose reconstruction methods were developed and applied in this study to estimate the red bone-marrow doses (RBMs) from (i) external irradiation from gamma-emitting radionuclides deposited on the ground and (ii) ¹³⁴Cs, ¹³⁷Cs and ⁹⁰Sr ingestion with locally produced foodstuffs. The mean population-weighted RBM doses accumulated during 35 years after the Chernobyl accident were 12 and 5.7 mGy for adult residents in Gomel and Mogilev Oblasts, respectively, while doses for youngest age groups were 20–40% lower. The highest mean area-specific RBM doses for adults accumulated in 1986–2021 were 63, 56 and 46 mGy in Narovlya, Vetka and Korma raions in Gomel Oblast, respectively. For most areas, external irradiation was the predominant pathway of exposure (60–70% from the total dose), except for areas with an extremely high aggregated ¹³⁷Cs soil to cow’s milk transfer coefficient (≥ 5.0 Bq L⁻¹ per kBq m⁻²), where the contribution of ¹³⁴Cs and ¹³⁷Cs ingestion to the total RBM dose was more than 70%. The contribution of ⁹⁰Sr intake to the total RBM dose did not exceed 4% for adults and 10% for newborns in most raion in Gomel and Mogilev Oblasts. The validity of the doses estimated in this study was assessed by comparison with doses obtained from measurements by thermoluminescence dosimeters and whole-body counters done in 1987–2015. The methodology developed in this study can be used to calculate doses to target organs other than RBM such as thyroid and breast doses. The age-dependent and population-weighted doses estimated in this study are useful for ecological epidemiological studies, for projection of radiation risk, and for justification of analytical epidemiological studies in populations exposed to Chernobyl fallout.

Introduction

After the accident on the Chernobyl nuclear power plant (NPP), radiation doses to the population of Belarus resulted from (i) exposure to the thyroid gland from intake of ¹³¹I and short-lived ¹³²I, ¹³³I, ¹³⁵I, ^131mTe and ¹³²Te, and prolonged sources of exposure from (ii) external irradiation from gamma-emitting radionuclides deposited on the ground, and (iii) internal irradiation from ¹³⁴Cs, ¹³⁷Cs and ⁹⁰Sr intake with locally produced foodstuffs. The increase in the incidence of thyroid cancer among individuals exposed to the radioiodine isotopes at childhood and adolescence was the main health effect of the accident (UNSCEAR 2011). However, there is a need for post-Chernobyl radiation epidemiology studies to estimate doses from prolonged sources of exposure to organs other than the thyroid gland, e.g., red bone marrow (RBM) (Davis et al. 2006; Ivanov et al. 1996; Liubarets et al. 2019) or female breast (Cahoon et al. 2021; Rivkind et al. 2020; Zupunski et al. 2021).

Dose reconstruction models have been developed to assess the radiation doses from prolonged exposure pathways to the population living in Ukraine and the Russian Federation in the territories contaminated after the Chernobyl accident (e.g., Bruk et al. 1998; Golikov et al. 2002; Likhtarev et al. 2000, 2002; Travnikova et al. 2001). Similar work has been done in Belarus. This paper describes the corresponding methodology and provides dose estimates from prolonged sources of exposure accumulated over 35 years after the Chernobyl accident by the population of the most contaminated Gomel and Mogilev Oblasts¹ in Belarus.

Materials and methods

Since ⁹⁰Sr intake was considered a prolonged exposure pathway, radiation RBM doses from ⁹⁰Sr intake were estimated in this study and combined with RBM doses from external irradiation and ingestion of radiocaesium isotopes to assess the overall doses to the exposed population resulting from all exposure pathways. The RBM doses from external irradiation and ingestion of radiocaesium isotopes correlate with doses absorbed in other radiation-sensitive organs, i.e., the thyroid gland and the female breast. Within the range of photon energy of major gamma-emitting radionuclides from Chernobyl fallout (0.2–2.3 MeV), the difference between external RBM doses and thyroid doses does not exceed 10%, while for female breast doses this difference does not exceed 15% (ICRP 2010). For internal doses from ¹³⁴Cs ingestion, the difference between the RBM doses and thyroid doses is 0% and 20% for adults and newborns, respectively, while for breast doses this difference is 36% and 17% for the same age groups. The difference for doses from ¹³⁷Cs ingestion is even smaller (ICRP 1993).

In the present study, mean values of the parameters of the dose reconstruction models were used to estimate mean doses to representative individuals of different ages for the settlement under consideration. From these values, the raion- and oblast-averaged population-weighted doses to representative individuals were calculated.

The following information was used to reconstruct the radiation doses from prolonged sources of exposure in Gomel and Mogilev Oblasts:

• Gamma-spectrometric measurements of radionuclide activity concentrations, mainly of ⁹⁵Zr, ⁹⁵Nb, ¹⁰³Ru, ¹⁰⁶Ru, ¹³¹I, ¹³⁴Cs, ¹³⁶Cs, ¹³⁷Cs, ¹⁴⁰Ba, ¹⁴⁰La, ¹⁴¹Ce, and ¹⁴⁴Ce, in 5,652 soil samples performed from 6 May to 31 July 1986, and of ⁹⁵Zr, ⁹⁵Nb, ¹⁰³Ru, ¹⁰⁶Ru, ¹³⁴Cs, ¹³⁷Cs, ¹⁴¹Ce, and ¹⁴⁴Ce in 4,526 soil samples performed from 1 August to 31 December 1986 (Drozdovitch et al. 2013);

• ¹³⁷Cs ground deposition density measured in each settlement (SCHRB 2001);

• ⁹⁰Sr ground deposition density measured in almost every settlement (SCHRB 1998);

• ¹³⁴Cs, ¹³⁷Cs and ⁹⁰Sr activity concentrations derived from measurements of total beta-activity in 10,631 cow’s milk samples done between 29 April and 31 May 1986 (Minenko et al. 2020);

• ¹³⁷Cs activity concentration measured in 60,247 samples of cow’s milk, potato, and other foodstuffs in 1986–1994 (MHRB 1992, 1994);

• ⁹⁰Sr activity concentration measured in 3728 samples of cow’s milk and potato in 1987–1994 (MHRB 1992, 1994);

• More than 650,000 whole-body counter (WBC) measurements of radiocaesium body-burden done in 1986–1996 (e.g., Drozdovitch et al. 1996; Drozdovitch and Minenko 1996; Minenko et al. 2006).

Table 1 summarizes the number of measurements done in Gomel and Mogilev Oblasts, which were used to derive the parameters of the dose reconstruction models, and the number of settlements in which the measurements were made. Although the measurements available in this study were performed in 1986–1996, around 75–85% of the doses received in 1986–2021 were realized during the first 10 years after the accident (Bouville et al. 2007).

Table 1.

Number of measurements done in Gomel and Mogilev Oblasts that were used in the present study to derive the parameters of the dose reconstruction models

Type of measurements	Time period	Number of measurements			Number of settlements where measurements were done
		Gomel Oblast	Mogilev Oblast	Total	Gomel Oblast	Mogilev Oblast	Total
Gamma-spectrometry of soila	28 Apr 1986–31 July 1986	4025	1627	5652	560	315	875
Gamma-spectrometry of soilb	1 Aug 1986–28 Nov 1986	2628	1898	4526	467	250	717
137Cs deposition density	–c	–	–	–	2707	3415	6122
90Sr deposition density	–c	–	–	–	2450	2602	5052
Total beta-activity in cow’s milkd	29 Apr 1986–31 May 1986	9735	896	10,631	892	167	1059
137Cs activity in cow’s milk	25 June 1986–06 Dec 1994	32,241	7540	39,781	1690	840	2530
137Cs activity in potato	2 Sep 1986–06 Dec 1994	10,249	2034	12,283	1110	424	1534
137Cs activity in other foodstuffs	25 June 1986–12 Apr 1993	8183	–	8183	412	–	412
90Sr activity in cow’s milk	8 May 1987–9 Dec 1994	1666	1110	2776	1343	591	1934
90Sr activity in potato	14 Sep 1987–9 Dec 1994	872	80	952	725	80	805
WBCe of caesium body-burden	8 June 1986–28 Aug 1986	636	177	813	49	21	70
WBC of caesium body-burden	28 Sep 1986–12 Dec 1996	484,763	173,163	657,926	1645	1161	2806

^aMeasurements included activity concentrations of ⁹⁵Zr, ⁹⁵Nb, ¹⁰³Ru, ¹⁰⁶Ru, ¹³¹I, ¹³⁴Cs, ¹³⁶Cs, ¹³⁷Cs, ¹⁴⁰Ba, ¹⁴⁰La, ¹⁴¹Ce, and ¹⁴⁴Ce

^bMeasurements included activity concentrations of ⁹⁵Zr, ⁹⁵Nb, ¹⁰³Ru, ¹⁰⁶Ru, ¹³⁴Cs, ¹³⁷Cs, ¹⁴¹Ce, and ¹⁴⁴Ce

^cMeasurements were done during the entire post-accident period

^dActivity concentrations of ¹³⁴Cs, ¹³⁷Cs and ⁹⁰Sr in cow’s milk were derived from these measurements

^eWBC whole-body counter

Study population

This study aimed to assess age-dependent RBM doses for members of the general population in Gomel and Mogilev Oblasts for the following age groups considered by the International Commission on Radiological Protection (ICRP): newborns, children of 1, 5, 10, 15 years old, and adults. These age groups correspond to the time of the accident (ATA), and the aging of the study population over time since the accident was considered in dose calculations. Therefore, the present study did not account for individuals born after the Chernobyl accident. Figure 1 shows the ¹³⁷Cs ground deposition density (SCHRB 2001) and the administrative centers of selected raions in Gomel and Mogilev Oblasts, which are mentioned in this paper.

Fig. 1.

¹³⁷Cs ground deposition density in Belarus (SCHRB 2001) and administrative centers of selected raions in Gomel and Mogilev Oblasts that are mentioned in this paper

Red bone-marrow doses from external irradiation

The RBM dose due to external irradiation from gamma-emitting radionuclides deposited on the ground was calculated as:

$$D_k^{\text{ext}}={10}^{-3}\cdot B{F}_k\cdot {\sum }_{i}D{F}_{i,k}\cdot {\int }_{t_1}^{t_2}{\sigma }_i\left(t\right)\cdot p\left(t\right)dt,$$ (1)

where $D_k^{\text{ext}}$ is the annual RBM dose from external irradiation for an individual from age group k (mGy); 10⁻³ is a unit conversion factor (mGy ${\text{μGy}}^{-1}$); $B{F}_k$ is the behavioral factor that takes into account occupancy factors, describing the fraction of time spent by individual at locations of different types in the settlement (living house, working building, outdoors, etc.), and location factors, which are defined as the ratio of the dose rate at locations of different types in the settlement and the dose rate at an undisturbed lawn far from any buildings, for age group k given in Table 2 (unitless); $D{F}_{i,k}$ is the initial absorbed dose rate in RBM per unit activity of i-th radionuclide in soil for age group k ($\text{μGy}{\text{d}}^{-1}$ per kBq m⁻²); ${\sigma }_i\left(t\right)$ is the ground deposition density of i-th radionuclide at time t in given settlement (kBq m⁻²); $p\left(t\right)$ is the attenuation function that reflects the decreasing dose rate due to radionuclides migration in soil; t₁,t₂ are times corresponding to the beginning and end of each calendar year between 1986 and 2021, counting from the date of the Chernobyl accident (26 April 1986) (d).

Table 2.

Age-dependent behavior factor, BF_k (unitless), for an individual from different age groups resided in settlements of different types

Type of settlement and year of exposure	Newborn	1 year	5 year	10 year	15 year	Adult
Rural settlement
Evacuated settlement	0.22	0.22	0.23	0.34	0.34	0.34
1986	0.19	0.19	0.21	0.28	0.28	0.28
1987+	0.18	0.18	0.19	0.25	0.25	0.25
Semirural settlement
1986	0.15	0.15	0.17	0.21	0.21	0.21
1987+	0.13	0.13	0.15	0.18	0.18	0.19
City
1986	0.11	0.11	0.13	0.15	0.15	0.13
1987+	0.10	0.10	0.11	0.13	0.13	0.12

The initial absorbed dose rates in RBM per unit deposition density of i-th radionuclide on the ground for adults from an effective plane source located at an initial depth of 0.5 g cm⁻², which accounted for soil roughness and initial radionuclide migration, are given in Table 3 based on (Eckerman and Ryman 1993). The age-dependence of the absorbed dose rate in RBM was derived from ICRP Publication 144 (ICRP 2020) assuming that it is of the same pattern as for the effective dose rate.

Table 3.

Age-depended initial red bone marrow (RBM) external dose rate, DF_i,k, per unit activity of i-th radionuclide in soil (Eckerman and Ryman 1993; ICRP 2020)

Radio-nuclide	Half-lifea	Decay product (yield)	Emitted photon energy per disintegration (MeV)a	Initial RBM external dose rate per unit ground deposition of radionuclide (μGy d−1 per kBq m−2) for age group
				Newborn	1 year	5 year	10 year	15 year	Adult
95Zr	64.032 d	95Nb (0.993)	0.732	6.51 × 10−2	5.83 × 10−2	5.37 × 10−2	4.93 × 10−2	4.63 × 10−2	4.47 × 10−2
95Nb	34.991 d		0.765	6.81 × 10−2	6.08 × 10−2	5.61 × 10−2	5.15 × 10−2	4.85 × 10−2	4.66 × 10−2
99Mob	65.94 h		0.148	2.15 × 10−2	1.93 × 10−2	1.77 × 10−2	1.63 × 10−2	1.52 × 10−2	1.47 × 10−2
103Rub	39.26 d		0.496	4.07 × 10−2	3.67 × 10−2	3.39 × 10−2	3.08 × 10−2	2.88 × 10−2	2.80 × 10−2
106Rub	373.59 d		0.206	1.77 × 10−2	1.59 × 10−2	1.46 × 10−2	1.33 × 10−2	1.23 × 10−2	1.19 × 10−2
132Te	3.204 d	132I (1.0)	0.234	1.80 × 10−2	1.62 × 10−2	1.49 × 10−2	1.34 × 10−2	1.25 × 10−2	1.17 × 10−2
131I	8.02 d		0.383	3.32 × 10−2	2.97 × 10−2	2.76 × 10−2	2.50 × 10−2	2.33 × 10−2	2.23 × 10−2
132I	2.295 h		2.265	2.00 × 10−1	1.79 × 10−1	1.65 × 10−1	1.52 × 10−1	1.42 × 10−1	1.38 × 10−1
133I	20.8 h		0.612	5.30 × 10−2	4.76 × 10−2	4.38 × 10−2	4.01 × 10−2	3.74 × 10−2	3.63 × 10−2
135I	6.57 h		1.582	1.34 × 10−1	1.21 × 10−1	1.12 × 10−1	1.04 × 10−1	9.80 × 10−2	9.50 × 10−2
134Cs	2.065 y		1.555	1.36 × 10−1	1.21 × 10−1	1.12 × 10−1	1.03 × 10−1	9.63 × 10−2	9.33 × 10−2
136Cs	13.16 d		2.128	1.89 × 10−1	1.70 × 10−1	1.57 × 10−1	1.45 × 10−1	1.36 × 10−1	1.31 × 10−1
137Csb	30.167 y		0.596	4.94 × 10−2	4.41 × 10−2	4.08 × 10−2	3.72 × 10−2	3.49 × 10−2	3.39 × 10−2
140Ba	12.752 d	140La (1.0)	0.183	1.54 × 10−2	1.39 × 10−2	1.28 × 10−2	1.16 × 10−2	1.08 × 10−2	1.05 × 10−2
140La	1.678 d		2.308	2.00 × 10−1	1.80 × 10−1	1.67 × 10−1	1.55 × 10−1	1.45 × 10−1	1.41 × 10−1
141Ce	32.508 d		0.0768	5.66 × 10−3	5.17 × 10−3	4.73 × 10−3	4.27 × 10−3	3.99 × 10−3	3.78 × 10−3
144Ceb	284.9 d		0.0194	4.26 × 10−3	3.87 × 10−3	3.56 × 10−3	3.19 × 10−3	2.95 × 10−3	2.80 × 10−3
239Np	2.3565 d		0.185	1.29 × 10−2	1.18 × 10−2	1.09 × 10−2	9.86 × 10−3	9.23 × 10−3	8.70 × 10−3

^a ICRP (2008)

^bDose rate includes contribution from the short-lived progeny ^99mTc, ^103mRh, ¹⁰⁶Rh, ^137mBa, and ¹⁴⁴Pr of ⁹⁹Mo, ¹⁰³Ru, ¹⁰⁶Ru, ¹³⁷Cs, and ¹⁴⁴Ce, respectively, assuming that they are in radioactive equilibrium

The deposition density of i-th radionuclide at time t was calculated as (Eq. (2)):

$${\sigma }_i\left(t\right)={\sigma }_i\left(0\right)\cdot e^{-{\lambda }_{r,i}\cdot t},$$ (2)

where ${\sigma }_i\left(0\right)$ is the deposition density of i-th radionuclide at the time of deposition (kBq m⁻²), and ${\lambda }_{r,i}$ is the radioactive decay rate of i-th radionuclide (d⁻¹).

It should be noted that Eq. (2) does not consider the horizontal migration of radionuclides on paved urban territories. According to Jacob et al. (1987) and Roed et al. (1996), during the first few days after the deposition about 60% of the caesium was removed from asphalt, concrete and granite pavements due to traffic and surface run-off water, and the lowest residual levels of radioactivity were found on asphalt, which are the main type of pavement in urban settlements in Belarus. However, residents of urban settlements spent only 4–8% of the day on paved urban areas (Golikov et al. 2002).

For radionuclides ⁹⁵Nb, ¹³²I, and ¹⁴⁰La, that are decay products of ⁹⁵Zr, ¹³²Te, and ¹⁴⁰Ba, the deposition density was calculated under the condition of radioactive equilibrium of parent and daughter radionuclides:

$${\sigma }_i(t)={\sigma }_i(0)\cdot e^{-{\lambda }_{r,i}\cdot t}+{\sigma }_{i,p}(0)\cdot f_i\cdot \frac{{\lambda }_{r,i}}{{\lambda }_{r,i}-{\lambda }_{r,i}^p}\cdot \left(e^{-{\lambda }_{r,i}^p\cdot t}-e^{-{\lambda }_{r,i}\cdot t}\right),$$ (3)

where ${\sigma }_{i,p}(0)$ is the deposition density of parent to i-th radionuclide at the time of deposition (kBq m⁻²); f_i is the daughter radionuclide production yield (unitless); ${\lambda }_{r,i}^p$ is the radioactive decay rate of parent to i-th radionuclide (d⁻¹).

The deposition density of i-th radionuclide at the time of deposition was calculated as (Eq. (4)):

$${\sigma }_i(0)={\sigma }_{Cs137}(0)\cdot R_{i/Cs137},$$ (4)

where ${\sigma }_{Cs137}(0)$ is the deposition density of ¹³⁷Cs on 1 May 1986 (kBq m⁻²); $R_{i/Cs137}$ is the ratio of activity of i-th radionuclide in deposition to that of ¹³⁷Cs at the time of deposition given in Table 4 (unitless) (Minenko et al. 2006).

Table 4.

Ratios of activity of i-th radionuclide in ground deposition to that of ¹³⁷Cs, R_i/Cs137, at the time of deposition (Minenko et al. 2006)

Radionuclide	Region
	1a	2b	3c	4d	5e	6f
	0.5 g	1.8	1.8	2.8	2.4	2.4
95Zr	2.4	3.6	0.17	1.3	4.0	0.34
95Nb	2.4	3.6	0.17	1.3	4	0.34
99Mo	9.3	7.7	2.0	4.4	4.4	2.4
103Ru	3.3	3.7	1.6	2.8	2.4	1.9
106Ru	0.71	0.93	0.42	1.0	0.85	0.34
132Te	10	8	11	2.6	4.2	4.2
131I	13	16	8.3	17	21	21
132I	10	8	11	2.6	4.2	4.2
133I	14	7.5	3.4	3.4	5	5
135I	5.2	1	0.12	0.017	0.13	0.13
134Cs	0.5	0.5	0.5	0.5	0.5	0.5
136Cs	0.3	0.27	0.27	0.26	0.26	0.26
137Cs	1	1	1	1	1	1
140Ba	5	4.7	0.76	6.0	7.6	1.3
140La	5	4.7	0.76	6.0	7.6	1.3
141Ce	3.1	3.9	0.14	2.4	3.8	0.33
144Ce	2	2.8	0.12	1.1	3	0.27
239Np	3	4	0.2	2.4	4	0.3

^aChernobyl 30 km zone

^bBragin, Khoiniki, Elsk, Kalinkovichi, Lelchitsy, Loev Mozyr, Narovlya, and Rechitsa raions

^cGomel-Mogilev caesium spot (see Fig. 1): Buda-Koshelevo, Chechersk, Dobrush, Korma, and Vetka raions in Gomel Oblast and Bykhov, Klimovichi, Kostyukovichi, Krasnopolie, Slavgorod, and Cherikov raions in Mogilev Oblast

^dGomel-City

^eThe remainder of Gomel and Mogilev Oblasts (except for Mogilev-City)

^fMogilev-City

^gTime of main deposition in given zone, given in days after the accident

The attenuation function, p(t), which reflects the decreasing dose rate due to radionuclides migration in soil, was applied only for ¹³⁴Cs and ¹³⁷Cs (Eq. (5)):

$$p(t)=\{\begin{array}{cc}{p}_1\cdot e^{-{\lambda }_1\cdot t}+p_2\cdot e^{-{\lambda }_2\cdot t}\hfill & \hfill {\text{for}}^{134}\text{Cs}{\text{and}}^{137}\text{Cs}\\ 1\hfill & \hfill \text{for}\text{other}\text{radionuclides}\end{array},$$ (5)

where $p_1=0.4$, $p_2=0.6$, ${\lambda }_1=1.27\times {10}^{-3}({\text{d}}^{-1})$, ${\lambda }_2=3.8\times {10}^{-5}({\text{d}}^{-1})$ are the parameters of the attenuation function (Likhtarev et al. 2002).

Red bone-marrow doses from ¹³⁴Cs and ¹³⁷Cs ingestion

The RBM dose from ¹³⁴ and ¹³⁷Cs ingestion was calculated as (Eq. (6)):

$$D_k^{Cs}={\sum }_{r}D{F}_{r,k}\cdot {\sigma }_{Cs137}\cdot {\int }_{t_1}^{t_2}{I}_{r,k}(t)dt,$$ (6)

where $D_k^{Cs}$ is the annual RBM dose due ingestion of radiocaesium isotopes (mGy); $D{F}_{r,k}$ is the RBM ingestion dose coefficient of r-th Cs isotope for an individual from age group k (ICRP 1993) (mGy Bq⁻¹); $I_{r,k}(t)$ is the intake function of r-th Cs isotope with foodstuffs for an individual of age k normalized to ¹³⁷Cs deposition density (Bq d⁻¹ per kBq m⁻²); ${\sigma }_{Cs137}$ is the ¹³⁷Cs deposition density in the settlement of residence (kBq m⁻²).

An initial activity ratio of ¹³⁴Cs to ¹³⁷Cs of 0.5 (Minenko et al. 2006) was used to estimate the normalized ¹³⁴Cs intake function:

$$I_{Cs134,k}(t)=0.5\cdot I_{Cs137,k}(t)\cdot e^{-({\lambda }_{r,Cs134}-{\lambda }_{r,Cs137})\cdot t},$$ (7)

where $I_{Cs134,k}(t)$ and $I_{Cs137,k}(t)$ are the intake functions of ¹³⁴Cs and ¹³⁷Cs, respectively, with diet for an individual of age k at time t after the accident (Bq); ${\lambda }_{r,Cs134}=9.21\times {10}^{-4}({\text{d}}^{-1})$ and ${\lambda }_{r,Cs137}=6.33\times {10}^{-5}({\text{d}}^{-1})$ are the radioactive decay rates of ¹³⁴Cs and ¹³⁷Cs, respectively.

The following sections describe the calculation of doses only from ¹³⁷Cs ingestion. The doses from ¹³⁴Cs ingestion were calculated by analogy with ¹³⁷Cs using the ¹³⁴Cs intake function given by Eq. (7).

Ingestion dose for rural and semirural populations

Two time periods of contamination of food products consumed by residents of rural and semirural² settlements were considered: (i) the first period included April–mid July 1986 when the contamination of vegetation and hence cow’s milk was caused by direct deposition of radionuclides on the grassland surface; and (ii) the second period, which began from around mid-July 1986 and has continued until now, when the intake of caesium with foodstuffs by residents of contaminated areas was defined by the root uptake of radionuclides by vegetation, the processes of sorption of radionuclides in the soil and the transfer of radionuclides to food.

Dose from ¹³⁷Cs intake for rural and semirural populations from April to 15 July 1986

During the first few months after the accident, the time-dependent ¹³⁷Cs activity concentration in cow’s milk, which was the main source of ¹³⁷Cs intake, can be described reasonably well using a modified Garner model (Savkin et al. 1996):

$$C_m(t)=C_0\cdot \sqrt{{\sigma }_{Cs137,nv}}\cdot e^{-{\lambda }_{Cs,w}\cdot \text{Δ}{t}_p}\cdot {\sum }_{j=1}^6{a}_j\cdot e^{-{\lambda }_j\cdot t},$$ (8)

where $C_m(t)$ is the time-dependent ¹³⁷Cs activity concentration in cow’s milk (Bq L⁻¹); C₀ is an empirical coefficient (Bq L⁻¹); ${\sigma }_{Cs137,nv}$ is the numerical value of ${\sigma }_{Cs137}$, the ¹³⁷Cs deposition density in the settlement where milk was produced; ${\lambda }_{Cs,w}=0.047({\text{d}}^{-1})$ is the rate of loss of ¹³⁷Cs activity by pasture grass due to weathering and growth dilution (Ulanovsky et al. 2004); $\mathrm{\Delta }{t}_p$ is the time between the dates of deposition and the beginning of the pasture grazing season (d), which varied from 0 for Gomel Oblast, except Chechersk and Korma raions (see Fig. 1), up to 7 for pastures in the northern part of Mogilev Oblast; a_j equal to 2.9, −5.6, −12.5, 13.5, 1.5 and 1.34 (unitless), and ${\lambda }_j$ equal to 1.84, 0.69, 0.17, 0.05, 0.023 and 0.0072 (d⁻¹) are parameters of the modified Garner model for index j equal to 1, 2, 3, 4, 5 and 6, respectively (Eq. (8)).

According to Minenko et al. (2006), the ¹³⁷Cs intake function with diet normalized to ¹³⁷Cs deposition density,$I_{Cs137,k}(t)$ (see Eq. (6)), was similar to Eq. (8) describing the ¹³⁷Cs activity concentration in cow’s milk:

$$I_{Cs137,k}(t)=I_{Cs137,k}^0\cdot C_m(t)=\frac{I_{Cs137,k}^0\cdot C_0}{\sqrt{{\sigma }_{Cs137,nv}}}\cdot e^{-{\lambda }_{Cs,w}\cdot \text{Δ}{t}_p}\cdot {\sum }_{j=1}^6{a}_j\cdot e^{-{\lambda }_j\cdot t},$$ (9)

where $I_{Cs137,k}^0$ is a scaling factor that reflects the difference between ¹³⁷Cs intake with the entire diet and intake with cow’s milk (L d⁻¹). It should be noted that there was no substantial difference (only around 25–30%) in radioactivity measured in milk samples from privately owned cows and from collective farm produced in the same settlement (Savkin et al. 2004).

The scaling factor for adults, $I_{\text{Cs}137,adults}^0$, was derived from WBC measurements done from 8 June to 28 August 1986 among 813 adults living in 70 settlements in Bragin, Kalinkovichi, Narovlya, and Khoiniki raions in Gomel Oblast and Krasnopolye raion in Mogilev Oblast, as (Eq. (10)):

$$Q_{\text{meas},Cs137}(T)=\frac{I_{Cs137,\mathit{adults}}^0\cdot C_0}{\sqrt{{\sigma }_{Cs137,nv}}}\cdot e^{-{\lambda }_{Cs,w}\cdot \text{Δ}{t}_p}\cdot {\int }_0^T\sum _{j=1}^6{a}_j\cdot e^{-{\lambda }_j\cdot t}\cdot R_{\mathit{adults}}(T-t)dt,$$ (10)

where $Q_{\text{meas},Cs137}(T)$ is the average ¹³⁷Cs body burden measured in given settlement at time T normalized to ¹³⁷Cs deposition density $({\text{Bq per kBq m}}^{-2});I_{Cs137,\mathit{adult}}^0\cdot C_0$=25.9 ± 25.8 (Bq d⁻¹); and R_adults (T – t) is the ¹³⁷Cs retention function for adults (ICRP 1993).

The age-dependent values of $I_{Cs137,k}^0\cdot C_0$ were calculated from $I_{Cs137,\mathit{adult}}^0\cdot C_0$ for adults as (Eq. (11)):

$$I_{Cs137,k}^0\cdot C_0=I_{Cs137,\text{adult}}^0\cdot C_0\cdot S{F}_{Cs137,k},$$ (11)

where ${\mathit{SF}}_{Cs137,k}$ is a scaling factor that was defined as the ratio of ¹³⁷Cs intake by an individual from age group k to that for an adult individual. The ${\mathit{SF}}_{Cs137,k}$-values were obtained from WBC measurements performed from September to December 1986 among population of different ages and were 0.15, 0.35, 0.45, 0.50, and 0.80 for newborns and children aged 1, 5, 10, and 15 y, respectively.

Dose from ¹³⁷Cs intake after 16 July 1986

At later times, the ¹³⁷Cs intake and the ¹³⁷Cs body burden depended on the agricultural and radioecological conditions of the region, on the processes of migration and sorption of radionuclides in soil, as well as on the transfer of radionuclides to food. The radioecological situation in the region was characterized in this study by an aggregated ¹³⁷Cs soil to cow’s milk transfer coefficient, defined as the ratio of the ¹³⁷Cs activity concentration (Bq L⁻¹) in cow’s milk produced in the given settlement to the ¹³⁷Cs deposition density (kBq m⁻²) in that settlement. Four areas were defined based on wide-scale monitoring of ¹³⁷Cs activity concentration in cow’s milk done in 1991–1992: low aggregated ¹³⁷Cs soil to cow’s milk transfer coefficient (<0.3 Bq L⁻¹ per kBq m⁻²), intermediate (0.3–1.0 Bq L⁻¹ per kBq m⁻²), high (1.0–5.0 Bq L⁻¹ per kBq m⁻²), and extremely high (≥ 5.0 Bq L⁻¹ per kBq m⁻²). Figure 2 shows the geographical pattern of the aggregated ¹³⁷Cs soil to cow’s milk transfer coefficient in Gomel and Mogilev Oblasts (MHRB 1992).

Fig. 2.

Geographical pattern of the aggregated ¹³⁷Cs soil to cow’s milk transfer coefficient in 1991–1992 (MHRB 1992)

The aggregated ¹³⁷Cs soil to cow’s milk transfer coefficient was determined by the ¹³⁷Cs transfer from soil to grass and depends on the bioavailability of caesium, soil type, potassium content in the soil, irrigation, and other factors (e.g., IAEA 1994; Rigol et al. 2008; Smith et al. 1993). An extremely high aggregated ¹³⁷Cs soil to cow’s milk transfer was observed in Zhitkovichi and Lelchitsy raions with a predominant peat-boggy soil of varying degrees of water-logging. Such high ¹³⁷Cs soil-to-plant transfer in this area called ‘Belarusian Polesye’ was found in the 1960s after atmospheric nuclear weapons testing (Marey et al. 1974).

The ¹³⁷Cs intake also depended on the origin of the consumed foodstuffs: a private farm (the main source for residents of rural settlements and for a fraction of semi-rural population) or a commercial trade network (for a part of semirural population and for residents of cities³). Therefore, the ¹³⁷Cs intake was considered accounting to (i) residence in a rural or semirural settlement or city; and (ii) different aggregated ¹³⁷Cs soil to cow’s milk transfer coefficient in the rural settlements.

Because first-order differential equation adequately describes the retention function of the ¹³⁷Cs body-burden in individuals of different ages, Eq. (12) was used to calculate the ¹³⁷Cs activity in the body:

$$\frac{d{q}_{Cs137,k}}{dt}=I_{Cs137,k}(t)-{\lambda }_{Cs,k}\cdot q_{Cs137,k},$$ (12)

where q_Cs137,k is the ¹³⁷Cs activity in the body of an individual of age k (Bq); I_Cs137,k(t) is the ¹³⁷Cs intake function (Bq d⁻¹); and λ_Cs,k is the rate constant (d⁻¹) corresponding to the biological half-time of Cs in the body of an individual of age k.

The ¹³⁷Cs intake function was described as (Minenko et al. 2006):

$$I_{Cs137,k}(t)=a_{1,k}^{\prime }\cdot e^{-{\lambda }_{1,k}\cdot t}+a_{2,k}^{\prime }\cdot e^{-{\lambda }_{2,k}\cdot t},$$ (13)

where $a_{1,k}^{\prime }$, $a_{2,k}^{\prime }$ (Bq d⁻¹) and λ_1,k, λ_2,k are the parameters of the ¹³⁷Cs intake function.

Solution of Eq. (12) for the initial condition of q_Cs137,k(0) = 0 is (Eq. (14)):

$$q_{Cs137,k}(t)=\frac{a_{1,k}^{\prime }}{{\lambda }_{Cs,k}-{\lambda }_{1,k}}\cdot e^{-{\lambda }_{1,k}\cdot t}+\frac{a_{2,k}^{\prime }}{{\lambda }_{Cs,k}-{\lambda }_{2,k}}\cdot e^{-{\lambda }_{2,k}\cdot t}-(\frac{a_{1,k}^{\prime }}{{\lambda }_{Cs,k}-{\lambda }_{1,k}}+\frac{a_{2,k}^{\prime }}{{\lambda }_{Cs,k}-{\lambda }_{2,k}})\cdot e^{-{\lambda }_{Cs,k}\cdot t}).$$ (14)

To combine WBC measurements performed in 1986–1996 in different settlements, the results of caesium body-burden measurements in residents were normalized to the ¹³⁷Cs deposition density in the settlement of residence. Normalized WBC measurements were fitted by the following function:

$$q_{Cs137,k}(t)=a_{1,k}\cdot e^{-{\lambda }_{1,k}\cdot t}+a_{2,k}\cdot e^{-{\lambda }_{2,k}\cdot t}-\left(a_{1,k}+a_{2,k}\right)\cdot e^{-{\lambda }_{Cs,k}\cdot t},$$ (15)

where a_1,k, a_2,k are the best fit parameters (Bq per kBq m⁻²) and λ_1,k, λ_2,k are the best fit rate constants (d⁻¹) derived by fitting the function to the data using the technique of least square deviations.

From Eqs. (14) and (15), the ¹³⁷Cs intake function for an individual of age k, I_Cs137,k (Bq d⁻¹ per kBq m⁻²), can be written as (Eq. (16)):

$$I_{Cs137,k}(t)=a_{1,k}\cdot \left({\lambda }_{Cs,k}-{\lambda }_{1,k}\right)\cdot e^{-{\lambda }_{1,k}\cdot t}+a_{2,k}\cdot \left({\lambda }_{Cs,k}-{\lambda }_{2,k}\right)\cdot e^{-{\lambda }_{2,k}\cdot t}.$$ (16)

Table 5 gives the parameters of the ¹³⁷Cs intake function (Eq. (16)) obtained in this study for residents of rural and semirural settlements with different aggregated ¹³⁷Cs soil to cow’s milk transfer coefficients.

Table 5.

Age-dependent parameters of the ¹³⁷Cs intake function (Eq. 16) for residents of rural and semirural settlements

Parameter	Age group
	Newborn	1 year	5 year	10 year	15 year	Adult
${\lambda }_{Cs,k},{\text{d}}^{-1}$	0.043	0.053	0.028	0.017	0.0075	0.0063
Rural settlements
Aggregated 137Cs soil to cow’s milk transfer coefficient less than 0.3 Bq L−1 per kBq m−2
$a_{1,k}$, Bq per kBq m−2	9	15	40	80	440	740
$a_{2,k}$, Bq per kBq m−2	0.6	1	2.5	4.5	13	20
${\lambda }_{1,k},d^{-1}$	3.18 × 10−3
${\lambda }_{2,k},d^{-1}$	1.1 × 10−4
Aggregated 137Cs soil to cow’s milk transfer coefficient of 0.3 – 1.0 Bq L−1 per kBq m−2
$a_{1,k}$, Bq per kBq m−2	8	14	36	70	400	700
$a_{2,k}$, Bq per kBq m−2	0.6	1	2.5	5	15	23
${\lambda }_{1,k},d^{-1}$	2.53 × 10−3
${\lambda }_{2,k},d^{-1}$	1.1 × 10−4
Aggregated 137Cs soil to cow’s milk transfer coefficient of 1.0 – 5.0 Bq L−1 per kBq m−2
$a_{1,k}$, Bq per kBq m−2	34	80	220	420	1650	2400
$a_{2,k}$, Bq per kBq m−2	6	8	20	38	114	190
${\lambda }_{1,k},d^{-1}$	2.53 × 10−3
${\lambda }_{2,k},d^{-1}$	7.0 × 10−5
Aggregated 137Cs soil to cow’s milk transfer coefficient more than 5.0 Bq L−1 per kBq m−2
$a_{1,k}$, Bq per kBq m−2	180	400	1320	2500	9500	14,400
$a_{2,k}$, Bq per kBq m−2	30	50	120	228	600	900
${\lambda }_{1,k},d^{-1}$	2.53 × 10−3
${\lambda }_{2,k},d^{-1}$	7.0 × 10−5
Semirural settlement
$a_{1,k}$, Bq per kBq m−2	4	7	21	41	180	280
$a_{2,k}$, Bq per kBq m−2	0.3	0.5	1.2	3	7	11
${\lambda }_{1,k},d^{-1}$	3.18 × 10−3
${\lambda }_{2,k},d^{-1}$	1.1 × 10−4

Ingestion dose for population of cities

The ¹³⁷Cs activity concentration measured in foodstuffs from the commercial trade network in the cities in Gomel and Mogilev Oblasts was practically the same and did not correlate with the ¹³⁷Cs deposition density in the vicinity of the city (Drozdovitch and Minenko 1996). These foodstuffs were produced outside cities and were monitored for compliance with permissible levels of radioactivity concentration. Therefore, in the present study the RBM doses from ¹³⁴ and ¹³⁷Cs ingestion were obtained from WBC measurements of residents of the cities in Gomel and Mogilev Oblasts, and these doses did not depend on the ¹³⁷Cs deposition density in the cities (Table 6).

Table 6.

Annual red bone-marrow (RBM) doses from ¹³⁴ and ¹³⁷Cs ingestion to residents of cities in Gomel and Mogilev Oblasts

Year	Annual doses from 134 and 137Cs ingestion (mGy) for age group
	Newborn	1 year	5 year	10 year	15 year	Adult
1986	0.130	0.166	0.205	0.249	0.445	0.496
1987	–a	0.098	0.119	0.150	0.259	0.294
1988	–	–	0.047	0.064	0.102	0.122
1989	–	–	0.025	0.037	0.055	0.069
1990	–	–	0.018	0.028	0.039	0.051
1991	–	–	0.015	0.024	0.033	0.043
1992	–	–	0.013	0.022	0.030	0.039
1993	–	–	–	0.020	0.028	0.036
1994	–	–	–	0.019	0.026	0.034
1995	–	–	–	0.018	0.024	0.032
1996	–	–	–	0.017	0.023	0.031
1997	–	–	–	0.016	0.022	0.029
1998	–	–	–	–	0.021	0.028
1999	–	–	–	–	0.020	0.027
2000	–	–	–	–	0.019	0.025
2001	–	–	–	–	0.018	0.024
2002	–	–	–	–	0.018	0.023
2003	–	–	–	–	–	0.022
2004	–	–	–	–	–	0.022
2005	–	–	–	–	–	0.021
2006	–	–	–	–	–	0.020
2007	–	–	–	–	–	0.020
2008	–	–	–	–	–	0.019
2009	–	–	–	–	–	0.019
2010	–	–	–	–	–	0.018
2011	–	–	–	–	–	0.018
2012	–	–	–	–	–	0.017
2013	–	–	–	–	–	0.017
2014	–	–	–	–	–	0.017
2015	–	–	–	–	–	0.016
2016	–	–	–	–	–	0.016
2017	–	–	–	–	–	0.016
2018	–	–	–	–	–	0.015
2019	–	–	–	–	–	0.015
2020	–	–	–	–	–	0.015
2021	–	–	–	–		0.015

^aDoses take into account the aging of the study population over time after the accident, i.e., dose for newborns is not shown for 1987 as newborns moved to the next 1 year age group in 1987

Red bone-marrow doses from ⁹⁰Sr ingestion

The RBM dose from ⁹⁰Sr ingestion for an individual of age k was calculated as (Eq. (17)):

$$D_k^{Sr90}=\sum _{n=1}^{N}D{F}_{sr90,k}^n\cdot {\sigma }_{Sr90}\cdot {\int }_{t_{1,n}}^{t_{2,n}}{I}_{sr90,k}(t)dt,$$ (17)

where $D_k^{Sr90}$ is the annual RBM dose due ⁹⁰Sr ingestion in a given year for an individual of age k (mGy); $D{F}_{sr90,k}^n$ is the RBM dose coefficient per ingestion of ⁹⁰Sr activity realized in a given year after the ⁹⁰Sr intake occurred in year n for an individual of age k (mGy Bq⁻¹); N is the number of years counted from the year of ⁹⁰Sr intake until the given year; ${\sigma }_{Sr90}$ is the ⁹⁰Sr deposition density in the settlement of residence (kBq m⁻²); I_sr90,k(t) is the ⁹⁰Sr intake function with foodstuffs for an individual of age k normalized to the ⁹⁰Sr deposition density (Bq d⁻¹ per kBq m⁻²);t_1,n,t_2,n are times corresponding to the beginning and end of year n(d).

Unlike radiocaesium isotopes with their relatively short biological half-life in the human body (half-time varies from 13 d for 1y child to about 100 d for adults (ICRP 1993)), ⁹⁰Sr is accumulated in the human body, specifically in the bones and, consequently, RBM exposure lasted for a long time. Therefore, the annual age-dependent RBM committed dose coefficients from ingestion of ⁹⁰ Sr given by ICRP (1993) until age of 70 y were derived for each year after ⁹⁰Sr intake. Table 7 gives the RBM committed dose coefficient per unit of ⁹⁰Sr ingestion for each year after intake in representatives of different age groups, ${\mathit{DF}}_{sr90,k}^n$. These values were calculated using the DCAL software (DCAL 2018).

Table 7.

Annual dose coefficient for red bone marrow (RBM) after a single intake due to ingestion of ⁹⁰Sr for an individual of age k, ${\mathit{DF}}_{sr90,k}^n$

Year after intake of 90Sr	90Sr annual ingestion dose coefficient for RBM (mGy Bq −1) for age group
	Newborn	1 year	5 year	10 year	15 year	Adult
1a	9.7 × 10−4	2.4 × 10−4	1.2 × 10−4	1.1 × 10−4	1.1 × 10−4	3.5 × 10−5
2	3.0 × 10−4	8.9 × 10−5	5.8 × 10−5	6.8 × 10−5	7.8 × 10−5	2.4 × 10−5
3	1.2 × 10−4	3.9 × 10−5	3.3 × 10−5	4.5 × 10−5	5.7 × 10−5	2.0 × 10−5
4	5.4 × 10−5	1.9 × 10−5	1.9 × 10−5	3.2 × 10−5	4.2 × 10−5	1.6 × 10−5
5	2.7 × 10−5	1.0 × 10−5	1.2 × 10−5	2.3 × 10−5	3.2 × 10−5	1.4 × 10−5
6	1.5 × 10−5	5.7 × 10−6	7.6 × 10−6	1.7 × 10−5	2.5 × 10−5	1.1 × 10−5
7	8.4 × 10−6	3.4 × 10−6	5.3 × 10−6	1.3 × 10−5	2.0 × 10−5	9.3 × 10−6
8	5.0 × 10−6	2.1 × 10−6	3.9 × 10−6	1.0 × 10−5	1.7 × 10−5	7.8 × 10−6
9	3.1 × 10−6	1.3 × 10−6	2.8 × 10−6	7.9 × 10−6	1.4 × 10−5	6.5 × 10−6
10	1.9 × 10−6	8.6 × 10−7	2.1 × 10−6	6.1 × 10−6	1.1 × 10−5	5.4 × 10−6
11	1.3 × 10−6	6.1 × 10−7	1.7 × 10−6	4.9 × 10−6	9.6 × 10−6	4.5 × 10−6
12	9.6 × 10−7	4.5 × 10−7	1.3 × 10−6	4.1 × 10−6	8.1 × 10−6	3.7 × 10−6
13	7.1 × 10−7	3.4 × 10−7	1.1 × 10−6	3.4 × 10−6	6.9 × 10−6	3.1 × 10−6
14	5.3 × 10−7	2.6 × 10−7	8.3 × 10−7	2.9 × 10−6	5.8 × 10−6	2.6 × 10−6
15	4.2 × 10−7	2.0 × 10−7	6.7 × 10−7	2.4 × 10−6	5.0 × 10−6	2.2 × 10−6
16	3.3 × 10−7	1.7 × 10−7	5.4 × 10−7	2.0 × 10−6	4.2 × 10−6	1.8 × 10−6
17	2.6 × 10−7	1.3 × 10−7	4.4 × 10−7	1.7 × 10−6	3.6 × 10−6	1.5 × 10−6
18	2.1 × 10−7	1.1 × 10−7	3.7 × 10−7	1.5 × 10−6	3.1 × 10−6	1.3 × 10−6
19	1.6 × 10−7	8.3 × 10−8	3.1 × 10−7	1.3 × 10−6	2.7 × 10−6	1.1 × 10−6
20	1.3 × 10−7	6.7 × 10−8	2.7 × 10−7	1.1 × 10−6	2.3 × 10−6	9.3 × 10−7
21	1.1 × 10−7	5.6 × 10−8	2.3 × 10−7	9.4 × 10−7	2.0 × 10−6	7.9 × 10−7
22	9.1 × 10−8	4.8 × 10−8	1.9 × 10−7	8.1 × 10−7	1.8 × 10−6	6.7 × 10−7
23	7.7 × 10−8	4.1 × 10−8	1.6 × 10−7	7.1 × 10−7	1.6 × 10−6	5.8 × 10−7
24	6.5 × 10−8	3.5 × 10−8	1.4 × 10−7	6.2 × 10−7	1.4 × 10−6	4.9 × 10−7
25	5.6 × 10−8	3.0 × 10−8	1.2 × 10−7	5.4 × 10−7	1.2 × 10−6	4.2 × 10−7
26	4.7 × 10−8	2.5 × 10−8	1.1 × 10−7	4.8 × 10−7	1.1 × 10−6	3.7 × 10−7
27	4.0 × 10−8	2.2 × 10−8	9.1 × 10−8	4.2 × 10−7	9.7 × 10−7	3.2 × 10−7
28	3.5 × 10−8	1.9 × 10−8	7.9 × 10−8	3.7 × 10−7	8.7 × 10−7	2.7 × 10−7
29	3.0 × 10−8	1.6 × 10−8	7.0 × 10−8	3.3 × 10−7	7.9 × 10−7	2.4 × 10−7
30	2.6 × 10−8	1.4 × 10−8	6.2 × 10−8	3.0 × 10−7	7.2 × 10−7	2.1 × 10−7
31	2.2 × 10−8	1.2 × 10−8	5.5 × 10−8	2.7 × 10−7	6.6 × 10−7	1.9 × 10−7
32	2.0 × 10−8	1.1 × 10−8	4.9 × 10−8	2.5 × 10−7	6.0 × 10−7	1.7 × 10−7
33	1.7 × 10−8	9.3 × 10−9	4.3 × 10−8	2.2 × 10−7	5.6 × 10−7	1.5 × 10−7
34	1.5 × 10−8	8.3 × 10−9	3.9 × 10−8	2.1 × 10−7	5.1 × 10−7	1.3 × 10−7
35	1.3 × 10−8	7.3 × 10−9	3.5 × 10−8	1.9 × 10−7	4.7 × 10−7	1.2 × 10−7
Sumb	1.5 × 10−3	4.2 × 10−4	2.7 × 10−4	3.7 × 10−4	4.8 × 10−4	1.8 × 10−4

^aFirst year after intake of ⁹⁰Sr occurred

^bEqual to ingestion dose coefficient for RBM per unit activity intake of ⁹⁰Sr given by ICRP (1993)

The ⁹⁰Sr intake function for an individual of age k normalized to the ⁹⁰Sr deposition density was described by Pogodin et al. (2002) as:

$$I_{sr90,k}(t)=4.5\times {10}^4\cdot K_k\cdot \left(0.0014+0.02\cdot e^{-0.22\cdot {\sigma }_{Sr90}}\right)\cdot e^{-0.117\cdot t_{acc}},$$ (18)

where 4.5 × 10⁴ is an empirical coefficient (Bq per kBq m⁻²); K_k is a factor to calculate ⁹⁰Sr intake for an individual from age group k relatively to the intake of an adult (unitless); t_acc is the time since 1986 (y); 365 is the number of days in a year (d).

The ⁹⁰Sr intake function for adults was obtained from the ⁹⁰Sr activity measured in 1991–1995 in ribs bone ash from adult residents of Gomel Oblast (Khramchenkova 1996; Pogodin et al. 1996). The K_k values were 0.40, 0.75, 0.88, 1.0, and 1.0, for newborns and children aged 1, 5, 10, and 15 y, respectively (Pogodin et al. 2002).

Ratios of ¹³⁷Cs and ⁹⁰Sr intake with the diet for adults calculated using Eqs. (16) and (18) were compared with the ratios of ¹³⁷Cs and ⁹⁰Sr activity concentration measured in the same cow’s milk sample from 1398 settlements in Gomel and Mogilev Oblasts in 1991–1992. The use of cow’s milk is reasonable because: (i) cow’s milk was one of the main sources of radionuclides intake with diet for the population of Belarus (Minenko et al. 1996a), and (ii) a similar relative dynamic of ¹³⁷Cs and ⁹⁰Sr activity concentration in cow’s milk measured in 1987–1994 (Khramchenkova 1996). This comparison showed that the ⁹⁰Sr intake function (Eq. (18)) overestimated the ⁹⁰Sr intake (Fig. 3), and, therefore, it was adjusted as (Eq. (19)):

$$I_{Sr90,k}^{\mathit{real}}(t)=I_{sr90,k}(t)\cdot A{F}_{SR90},$$ (19)

where $I_{Sr90,k}^{\mathit{real}}(t)$ is the realistic ⁹⁰Sr intake function (Bq d⁻¹ per kBq m⁻²); AF_SR90 is the adjustment factor for ⁹⁰Sr intake function that was calculated using Eq. (18) (unitless).

Fig. 3.

Comparison of settlement-specific ratio of ¹³⁷Cs intake calculated using Eq. (16) and ⁹⁰Sr intake calculated using Eq. (18) with diet for adults, with ratio of ¹³⁷Cs and ⁹⁰Sr activity concentrations measured in cow’s milk in 1991–1992 (MHRB 1992). Solid line shows the agreement between ratios while dashed lines show a factor of 3 difference between ratios

Table 8 gives the AF _SR90-values obtained in this study depending on the geographical area and the aggregated ¹³⁷Cs soil to cow’s milk transfer coefficient. It should be noted that ¹³⁷Cs and ⁹⁰Sr intake with the diet did not correlate with each other for residents of different settlements. Therefore, an adjustment factor for ⁹⁰Sr intake function was derived using the measurements of ¹³⁷Cs and ⁹⁰Sr activity concentration in cow’s milk produced in different geographical areas with different aggregated ¹³⁷Cs soil to cow’s milk transfer coefficients.

Table 8.

Adjustment factor for ⁹⁰Sr intake function, AF _SR90, (Eq. (19))

Oblast	Raion	Adjustment factor for 90Sr intake function (unitless) for residents of the settlements with aggregated 137Cs soil to cow’s milk transfer coefficient (Bq L−1 per kBq m−2) of
		<0.3	0.3–1.0	1.0–5.0	≥5.0
Gomel	Bragin	0.19	0.16	0.33	–
Gomel	Vetka, Dobrush, Korma, Chechersk	0.35	0.11	0.56	–
Gomel	Elsk, Narovlya	0.67	0.26	0.47	–
Gomel	Zhitkovichi, Lelchitsy, Petrikov	0.30	0.11	0.34	0.92
Gomel	Loev	0.21	0.081	–	–
Gomel	Mozyr	0.28	0.12	0.79	–
Gomel	Khoiniki	0.080	0.28	–	–
Gomel	Other raions	0.21	0.10	0.27	1.0
Mogilev	Bobruisk, Glusk, Kirov, Osipovichi	0.064	0.011	–	–
Mogilev	Klimovichi, Klichev, Kostyukovichi, Krichev, Slavgorod, Khotimsk	0.13	0.035	0.057	–
Mogilev	Other raions	0.064	0.034	0.13	–

Population-weighted raion-averaged annual doses

This study assessed the settlement-specific mean RBM doses received during each calendar year in 1986–2021 by individuals of different ages ATA. In addition, cumulative raion-averaged population-weighted doses were calculated for 42 raions within Gomel and Mogilev Oblasts and for three cities (Gomel, Mogilev, and Bobruisk) using Eq. (20):

$$D_{k,r}^P(T)=\sum _{s=1}^S{D}_{j,s}^P(T)\cdot {\omega }_{r,s}(T),$$ (20)

where $D_{\mathit{raion},k}^p(T)$ is the cumulative mean RBM dose for exposure pathway p (external irradiation, ingestion of radiocaesium isotopes or ⁹⁰Sr ingestion) for an individual of age k ATA in raion r at year T after the Chernobyl accident (mGy); S is the number of settlements in raion r; $D_{j,s}^P(T)$ is the annual mean RBM dose for the pathway p for an individual of age j, which accounts for aging of an individual since the accident, in settlement s at year T after the Chernobyl accident (mGy); ω_R,s is the fraction of population in a settlement s in raion r at year T after the accident.

The population in each settlement in each calendar year in 1986–2021 was estimated by interpolating the population recorded during 1979, 1989, 1999, 2009 and 2019 censuses (e.g., SCAS 1990; MSARB 2000). For settlements relocated in 1990–1999 from the zone of ‘mandatory relocation’ (zones with a ¹³⁷Cs deposition density of more than 1480 kBq m⁻²) and the zone ‘with the right to relocation’ (zones with a ¹³⁷Cs deposition density of 555–1480 kBq m⁻²) interpolation between the 1989 and 1999 census did not provide adequate population data. Therefore, the population size of these settlements was taken from annual statistical reports issued in 1990–1999 (e.g., SCASRB 1992, 1993). The total annual (or cumulative) RBM dose from all exposure pathways was calculated as the sum of the annual (or cumulative) RBM from each exposure pathway.

Results

Table 9 gives the distribution of total RBM doses from all exposure pathways received in 1986–2021 by age of individuals ATA for selected raions in Gomel and Mogilev Oblasts. The highest RBM doses were estimated for adults, while doses for younger age groups were 20–40% lower, depending on predominant exposure pathway: external irradiation or ingestion of radiocaesium isotopes. Figure 4 compares the contribution of exposure pathways to the total RBM dose received in 1986–2021 by individuals of different ages ATA who resided in Korma raion in Gomel Oblast. The contribution of external irradiation to the total dose was highest (more than 75%) among young children and decreased with age, while the contribution of ingestion of radiocaesium isotopes increased with age. The highest contribution of ⁹⁰Sr intake to the total RBM dose was for newborns (2.2% of the total dose), while for adults it was 0.9%.

Table 9.

Distribution of the total mean population-weighted red bone-marrow (RBM) doses received in 1986–2021 by age groups of individuals in 1986 for selected raions in Gomel and Mogilev Oblasts

Raion	137Cs deposition density (kBq m−2)	90Sr deposition density (kBq m−2)	Total mean population-weighted RBM doses (mGy) received in 1986–2021 by age group as of 1986
			Newborn	1 year	5 year	10 year	15 year	Adult
Gomel Oblast
– Bragina	840	65	30	29	30	34	36	37
– Vetka	755	24	43	42	44	48	54	56
– Korma	510	9.9	35	35	36	40	44	46
– Lelchitsy	120	6.2	18	18	20	23	27	28
– Narovlyaa	815	52	51	49	51	57	61	63
– Rechitsa	75	13	5.7	5.4	5.7	6.5	7.3	7.5
– Khoinikia	1,060	125	26	25	26	30	32	33
– Chechersk	595	14	32	31	33	37	42	45
Mogilev Oblast
– Bykhov	190	4.0	13	13	13	15	17	18
– Krasnopolie	700	10	28	27	28	32	37	39
– Krichev	92	1.8	2.7	2.5	2.6	3.0	3.3	3.4
– Slavgorod	480	7.5	28	27	28	31	35	37
– Cherikov	540	8.7	24	24	25	28	31	33

^aIncluding settlements evacuated in 1986 from the 30 km zone around the Chernobyl nuclear power plant (NPP)

Fig. 4.

Comparison of the contribution of exposure pathways to total red bone-marrow (RBM) dose received in 1986–2021 by individuals of different ages resided in Korma raion in Gomel Oblast

Table 10 gives the distribution of the number of settlements and the population according to the settlement-averaged RBM doses from all exposure pathways for adults received in 1986–2021. For 78.8% of residents of Gomel and Mogilev Oblasts, the RBM dose was less than 10 mGy, while 0.5% of residents received doses more than 100 mGy.

Table 10.

Distribution of number of settlements according to mean-settlement total red bone-marrow (RBM) dose for adults in 1986–2021 in Gomel and Mogilev Oblasts

Dose interval (mGy)	Gomel Oblasta		Mogilev Oblast		Both oblasts
	Number of settlements	Populationb (individuals)	Number of settlements	Population (individuals)	Number of settlements	Population (individuals)
< 3	321	87,795	1952	1,009,613	2,273	1,097,408
3–9.99	879	1,130,078	534	107,550	1413	1,237,628
10–19.9	562	200,626	375	74,308	937	274,934
20–29.9	312	89,346	215	45,133	527	134,479
30–39.9	231	58,368	118	13,929	349	72,297
40–49.9	115	33,114	70	8656	185	41,770
50–59.9	68	20,973	41	5235	109	26,208
60–69.9	83	25,133	29	4015	112	29,148
70–79.9	50	17,467	18	2206	68	19,673
80–89.9	25	6535	10	1310	35	7845
90–99.9	26	4691	18	2475	44	7166
100+	35	9745	35	5760	70	15,505
Total	2707	1,683,871	3415	1,280,190	6122	2,964,061

^aIncluding settelements evacuated in 1986 from the 30 km zone

^bThe entire oblast population is given as of 1 January 1986

Figure 5 shows the geographical pattern of total RBM doses for adults accumulated in 1986–2021. In general, the RBM doses follow the pattern of the ¹³⁷Cs deposition density (see Fig. 1). Residents of settlements evacuated from the 30-km zone around the Chernobyl NPP, in the Southern radiocaesium spot (e.g., Bragin, Narovlya, Khoiniki raions), and in high contaminated settlements located in the North-eastern radiocaesium spot in Gomel and Mogilev Oblasts (e.g., Vetka, Korma, Chechersk, Krasnopolie, Slavgorod, Cherikov raions) received the highest doses. However, in some settlements in Elsk, Lelchitsy and Zhitkovichi raions with a low ¹³⁷Cs deposition density (< 185 kBq m⁻²), relatively high doses were realized because of high aggregated ¹³⁷Cs soil to cow’s milk transfer coefficients.

Fig. 5.

Geographical pattern of red bone-marrow (RBM) doses for adults from all exposure pathways accumulated in 1986–2021 in Gomel and Mogilev Oblasts

Table 11 shows the distribution of RBM doses for adults in 1986 and 1986–2021 from different exposure pathways depending on the ¹³⁷Cs deposition density. The oblast-averaged RBM dose received by adults in 1986–2021 was 12 mGy and 5.7 mGy in Gomel and Mogilev Oblasts, respectively. External irradiation accounted for more than 60% of the total dose in areas with ¹³⁷Cs deposition densities of more than 185 kBq m⁻². The dose received in 1986 was around 1/3 of the dose accumulated over 35 years after the accident. Doses from external irradiation and ¹³⁴Cs and ¹³⁷Cs ingesiton received in settlements with different levels of ¹³⁷Cs deposition density were consistent between Gomel and Mogilev Oblasts, with the exception of the areas with a deposition density of more than 1480 kBq m⁻², where the total dose was almost twice higher in Mogilev Obalsts (112 mGy) than in Gomel Oblats (65 mGy). This can be explained by the fact that 30 out of 71 settlements (42.3% of the total) with a ¹³⁷Cs deposition density of more than 1480 kBq m⁻² in Gomel Oblasts were evacuated in 1986, while all high contaminated settlements in Mogilev Oblast were relocated later, in 1990–1992.

Table 11.

Red bone-marrow (RBM) doses for adults in 1986 and 1986–2021 from different exposure pathways depending on ¹³⁷Cs deposition density in Gomel and Mogilev Oblasts

137Cs deposition density (kBq m−2)	Number of settlements	Populationa (individuals)	RBM doses (mGy) for adults from
			External irradiation		134Cs, 137Cs ingestion		90Sr ingestion		Total dose
			1986	1986–2021	1986	1986–2021	1986	1986–2021	1986	1986–2021
Gomel Oblast
< 37	740	223,037	0.55	1.5	1.1	2.1	5.1 × 10−3	0.17	1.6	3.8
37–185	1022	1,203,542	1.1	3.5	1.2	3.3	8.2 × 10−3	0.28	2.3	7.0
185–555	603	156,063	5.1	18	5.3	14	9.5 × 10−3	0.31	10	32
555–1480	271	88,523	13	38	9.3	22	0.017	0.50	22	61
> 1480	71	12,706	30	46	10	19	0.011	0.14	40	65
Entire Oblast	2707	1,683,871	2.2	6.7	2.1	5.2	8.4 × 10−3	0.28	4.3	12
Mogilev Oblast
< 37	2262	1,077,569	0.20	0.66	0.58	1.35	1.6 × 10−3	0.053	0.78	2.1
37–185	579	104,073	1.9	6.5	2.5	4.9	2.2 × 10−3	0.075	4.4	11
185–555	386	74,315	3.5	16	4.9	11	3.0 × 10−3	0.10	8.4	27
555–1480	135	16,760	11	41	10	23	3.6 × 10−3	0.10	21	64
> 1480	53	7,473	24	69	20	43	3.3 × 10−3	0.064	44	112
Entire Oblast	3415	1,280,190	0.80	2.9	1.2	2.7	1.7 × 10−3	0.058	2.0	5.7

^aThe entire population is given as of 1 January 1986

Figure 6 compares the contributions of each exposure pathway to the total RBM dose for adult residents of selected raions. External irradiation was the predominant (60–70% from the total dose) pathway for the residents of highly contaminated Bragin, Khoiniki, Vetka and Cherikov raions with a low or intermediate aggregated ¹³¹Cs soil to cow’s milk transfer coefficients. On the contrary, the intake of radiocaesium isotopes was the main pathway (more than 70% of the total dose) for the residents of Zhitkovichi and Lelchitsy raions that are characterized by a high or extremely high aggregated ¹³¹Cs soil to cow’s milk transfer coefficient. The contribution of ⁹⁰Sr ingestion to the total RBM dose for adults typically did not exceed 3–4%. Figure 7 shows, as example, the time variation of the annual RBM doses from different exposure pathways for adult residents of Narovlya raion in Gomel Oblast.

Fig. 6.

Contribution (%) of exposure pathways to total red bone-marrow (RBM) dose for adult residents of selected raions

Fig. 7.

Variation with time of annual red bone-marrow (RBM) doses from different exposure pathways for adult residents of Narovlya raion in Gomel Oblast

Discussion

Figure 8 compares the model-based settlement-specific annual doses from external irradiation estimated in the present study with the measurement-based doses obtained from the measurements done in 1987–1995 among residents of 63 settlements in 11 raions in Gomel and Mogilev Oblasts using individual thermoluminescence dosimeters (TLDs) (Drozdovitch et al. 2002; Minenko et al. 1996b). A reasonable agreement was observed between the two approaches: 73 out of 82 dose-values (89.0%) are consistent within a factor of 2. The distribution of ratios of the model- to measurement-based doses has an arithmetic mean ± SD of 0.95 ± 0.44 and a median of 0.81; Spearman’s rank correlation coefficient between these doses is ρ = 0.92 (p < 0.001).

Fig. 8.

Comparison of the annual settlement-specific doses from external irradiation in 1987–1995 estimated in this study with the doses derived from TLD measurements (Drozdovitch et al. 2002; Minenko et al. 1996b). Solid line shows the agreement between doses while dashed lines show a factor of 2 difference between doses

Figure 9 compares the settlement- and raion-specific annual model-based doses from ¹³⁴ and ¹³⁷Cs ingestion estimated in the present study with measurement-based doses derived from WBC measurements done in 1990–2015 among residents in 57 settlements and 22 raions in Gomel and Mogilev Oblasts (Averin et al. 2017; Drozd 2017; Eventova et al. 2016; Minenko et al. 1996b; Pogodin et al. 2001; Vlasova et al. 2009; Vlasova 2014). The distribution of ratios of the model- to measurement-based doses has an arithmetic mean ± SD of 1.0 ± 0.47 and a median of 0.90; Spearman’s rank correlation coefficient between these doses is ρ = 0.85 (p < 0.001). There is no difference in agreement between model-based and measurement-based doses for 1990–1996 (the period for which individual dose-related measurements were available for the present study to develop a dose reconstruction model), the arithmetic mean ± SD of the ratios of two types of doses is 1.0 ± 0.35 (median = 0.93) and for 1997–2015 (period for which the model was interpolated) the ratio is 1.0 ± 0.51 (median = 0.90).

Fig. 9.

Comparison of the annual settlement- and raion-specific doses from ingestion of radiocaesium isotopes in 1990–2015 estimated in this study with the doses derived from WBC measurements (Averin et al. 2017; Drozd 2017; Eventova et al. 2016; Minenko et al. 1996b; Pogodin et al. 2001; Vlasova et al. 2009; Vlasova 2014). Solid line shows the agreement between doses while dashed lines show a factor of 2 difference between doses

Table 12 compares the annual RBM doses from ⁹⁰Sr intake in 1994 and 1996 calculated on the basis of ⁹⁰Sr activity in ribs bone ash of adults measured in 11 raions in Gomel Oblast (Khramchenkova 1996; Minenko et al. 1996b) with the model-based doses estimated in the present study. There is reasonable agreement between the two types of dose-values: the arithmetic mean ± SD of the ratios of model-based to measurement-based doses is 0.94 ± 0.27 and the median is 0.88; Spearman’s rank correlation coefficient between these doses is ρ = 0.56 (p = 0.070).

Table 12.

Comparison of raion-averaged annual red bone-marrow (RBM) doses from ⁹⁰Sr intake for adults calculated in this study with those estimated using measurements of ⁹⁰Sr in ribs bone ash of adults

Raion in Gomel Oblast	Raion-averaged annual RBMa (μGy) from 90Sr intake for adults		Ratio of doses estimated in this study to be derived from measured 90Sr activity
	Derived from 90Sr activity measured in ribs bone ash	Estimated in the present study
Bragin	24.5	21.4	0.87
Buda-Koshelevo	11.2	14.3	1.3
Vetkab	26.4	19.5	0.74
Gomel	12.0	10.6	0.88
Gomel-City	12.0	16.0	1.3
Dobrushb	25.1	17.4	0.69
Zhlobinb	22.1	10.8	0.49
Kormab	24.3	24.1	1.0
Loev	15.8	12.8	0.81
Rechitsa	14.4	14.5	1.0
Checherskb	11.6	14.6	1.3

^aAnnual dose in 1994 according to (Khramchenkova 1996) unless otherwise indicated

^bAnnual dose in 1996 according to (Minenko et al. 1996b)

The present study assessed the average dose for each raion of interest. There are obviously uncertainties associated with the assessed doses. Individual doses show significant variability within the settlement, and their distributions are characterized by a geometric standard deviation (GSD) of 1.3–1.7 (Drozdovitch et al. 2002; Minenko et al. 1996a). However, the uncertainty of raion-averaged doses is lower because of the raion size that typically includes 100–160 settlements, except for Bragin, Narovlya and Khoiniki raions where some settlements were evacuated in 1986. In the present study, the GSD of the raion-averaged annual RBM dose was estimated to be in the range 1.2–1.3.

The present study did not consider the intake of long-lived radionuclides such as ²³⁸Pu (half-life T_1/2=87.7 y), ²³⁹Pu (T_1/2=2.41 × 10⁴ y), ²⁴⁰Pu (T_1/2=6564 y), and ²⁴¹Am (T_1/2=432.2 y). The RBM dose per unit activity ingestion due to ingestion of these radioisotopes is higher for some age groups than that for ⁹⁰Sr: for example, it is higher by a factor 2 for adults and by about a factor 8 for newborns (ICRP 1993). Furthermore, the ratio of ^239,240,240Pu to ⁹⁰Sr activity deposited in close vicinity to the Chernobyl NPP was about 0.01–0.03, and much lower at large distances from the Chernobyl NPP areas (SCHRB 2004; UNSCEAR 2011). The contribution of transuranium isotopes to the total RBM dose was small because (i) the transfer coefficient from feed to cow’s milk, TF_m, for transuranium isotopes (1.0 × 10⁻⁵ d L⁻¹ for Pu and 6.9 × 10⁻⁶ d L⁻¹ for ²⁴¹Am) is two to three orders of magnitude lower than that for ⁹⁰Sr (1.5 × 10⁻³ d L⁻¹ (IAEA 2009)); this is consistent with TF_m-values of 2.8 × 10⁻⁶ d L⁻¹ for Pu and 2.0 × 10⁻⁶ d L⁻¹ for ²⁴¹Am measured in Belarus (Averin et al. 2011); and (ii) a ^239,240,240Pu deposition density of more than 3.7 kBq m⁻² occurred only in the 30 km zone around the Chernobyl NPP (SCHRB 2004) where all residents were evacuated within 10 days after the accident; consequently, their annual doses in the following years due to inhalation of transuranium isotopes before evacuation was of the order of several μGy (Minenko et al. 1996b).

The strength of the present study is the use of the results of numerous measurements of radioactivity in the environment and food samples as well as in humans. Comparison with doses derived from TLD and WBC measurements showed that the doses estimated in the present study show a high degree of reliability.

However, this study has also some limitations:

1. The RMB doses from ¹³⁴ and ¹³⁷Cs ingestion realized in a given year were calculated in this study based on the intake of radiocaesium isotopes during this year and the dose coefficient from ICRP Publication 67 (ICRP 1993). Although the ICRP dose coefficient represents the committed dose expected to be realized up to age 70 years, the difference between the committed dose and the dose received during the year of intake is around 10% for adults and less than 6% for younger age groups.

2. The present study considered the accumulation of doses from ⁹⁰Sr ingestion with time according to the model of ICRP Publication 67 (ICRP 1993). However, this model does not consider the significant increase in the rate of strontium elimination from the human body after age of 45–55 year (Shagina et al. 2003). Nevertheless, this has a minor effect on the total dose estimated in the present study since the RBM doses from ⁹⁰Sr intake for adults accumulated during 1986–2021 even by residents of the most contaminated settlements were very low, typically, less than 1 mGy.

Conclusion

In summary, this paper presents the results of assessment of RBM doses from external irradiation and ¹³⁴Cs, ¹³⁷Cs and ⁹⁰Sr ingestion to the population of Gomel and Mogilev Oblasts in Belarus accumulated over 35 years after the Chernobyl accident. The results of measurements of radionuclides in environmental samples and humans were used to determine the parameters of dose reconstruction models as well as to assess the reliability of dose estimates. The mean population-weighted RBM doses accumulated during 35 years after the Chernobyl accident were estimated to be 12 and 5.7 mGy for adult residents in Gomel and Mogilev Oblasts, respectively. RBM doses for younger age groups were about 20–40% lower than those for adults. For most regions, external exposure from radionuclides deposited on the ground was the predominant pathway of exposure (60–70% of the total dose), except for regions with an abnormally high aggregated ¹³⁷Cs soil to cow’s milk transfer coefficient (≥ 5.0 Bq L⁻¹ per kBq m⁻²), where the contribution of the intake of radiocaesium isotopes to the total RBM dose was more than 70%. The contribution of ⁹⁰Sr intake to the total RBM dose did not exceed 4% for adults and 10% for newborns in most of the raions in Gomel and Mogilev Oblasts. The RBM doses from external irradiation and ¹³⁴Cs and ¹³⁷Cs ingestion are representative of whole-body exposure.

The methodology developed in this study can be used to estimate doses from prolonged sources of post-Chernobyl exposure to target organs other than RBM such as thyroid and breast doses. The age-dependent and population-weighted doses estimated in this study are useful for ecological epidemiological studies, for projection of radiation risk, and for justification of analytical epidemiological studies in populations exposed to Chernobyl fallout.