Thyroid doses in Ukraine due to 131I intake after the Chornobyl accident. Report I: revision of direct thyroid measurements

The increased risk of thyroid cancer among individuals exposed during childhood and adolescence to Iodine-131 (131I) is the main statistically significant long-term effect of the Chornobyl accident. Several radiation epidemiological studies have been carried out or are currently in progress in Ukraine, to assess the risk of radiation-related health effects in exposed populations. About 150,000 measurements of 131I thyroid activity, so-called ‘direct thyroid measurements’, performed in May–June 1986 in the Ukrainian population served as the main sources of data used to estimate thyroid doses to the individuals of these studies. However, limitations in the direct thyroid measurements have been recently recognized including improper measurement geometry and unknown true values of calibration coefficients for unchecked thyroid detectors. In the present study, a comparative analysis of 131I thyroid activity measured by calibrated and unchecked devices in residents of the same neighboring settlements was conducted to evaluate the correct measurement geometry and calibration coefficients for measuring devices. As a result, revised values of 131I thyroid activity were obtained. On average, in Vinnytsia, Kyiv, Lviv and Chernihiv Oblasts and in the city of Kyiv, the revised values of the 131I thyroid activities were found to be 10–25% higher than previously reported, while in Zhytomyr Oblast, the values of the revised activities were found to be lower by about 50%. New sources of shared and unshared errors associated with estimates of 131I thyroid activity were identified. The revised estimates of thyroid activity are recommended to be used to develop an updated Thyroid Dosimetry system (TD20) for the entire population of Ukraine as well as to revise the thyroid doses for the individuals included in post-Chornobyl radiation epidemiological studies: the Ukrainian-American cohort of individuals exposed during childhood and adolescence, the Ukrainian in utero cohort and the Chornobyl Tissue Bank.


Introduction
The increase in thyroid cancer incidence among individuals exposed as children and adolescents to Iodine-131 ( 131 I) is the main long-term effect of the Chornobyl (Chernobyl) accident (UNSCEAR 2011). Unsurprisingly, this radiationrelated health effect generated great interest and led to a series of radiation epidemiological studies, to quantify the risk of radiation-related thyroid cancer among the residents of the most contaminated regions of the three most affected countries: Belarus, Ukraine and the Russian Federation (e.g. Astakhova et al. 1998;Cardis et al. 2005;Kopecky et al. 2006;Likhtarov et al. 2006;Tronko et al. 2006Tronko et al. , 2017. One of the most advanced post-Chornobyl studies, the Ukrainian-American cohort study of thyroid cancer and other thyroid diseases includes 13,204 individuals who were exposed between ages 0 and 18 years to 131 I from the Chornobyl fallout and who are followed up for thyroid cancer and other thyroid diseases through a standardized screening protocol (Stezhko et al. 2004). Individual doses due to 131 I intakes were reconstructed two times for all cohort members using dosimetry systems that were revised to take improvements into account Likhtarov et al. 2014).
The 'Thyroid Dosimetry 2010 system', TD10, is currently being used to assess the radiation-related risk of thyroid cancer and other thyroid diseases in the Ukrainian-American cohort Hatch et al. 2010;Little et al. 2014;Tronko et al. 2017). However, the limitations in the dosimetry system regarding direct thyroid measurements have been recently recognized. These limitations include an improper geometry of measurement and unknown true values of calibration coefficients for the measuring devices used at that time. A wide-scale radiation monitoring of 131 I activity in the thyroid, called 'the thyroid dosimetry monitoring', in the affected population was organized within a relatively short period of time immediately after the accident. This has led to an increase in errors for some field measurements as compared to purely laboratory-based measurements. These errors were caused by the involvement of personnel in the thyroid dosimetry monitoring who had no or only minimal experience in radiation measurements, by the use of various types of devices that were not designed to measure radioactivity in the thyroid gland, and by application of simplified methods for express measurements (Likhtarov et al. 2015). It was already suspected that errors associated with the thyroid measurements may have resulted in unexpected differences in the radiation-related risk of thyroid cancer between two oblasts of the Ukrainian-American cohort study, Zhytomir and Chernihiv .
The main sources of data used for estimation of thyroid doses in Ukraine were (1) radiation measurements (called 'direct thyroid measurements') that were conducted against the thyroids of all cohort members within the first two months after the Chornobyl accident (Likhtarev et al. 1993(Likhtarev et al. , 1995(Likhtarev et al. , 2015; (2) estimates of 131 I deposition on the ground at each location where the cohort members resided (Talerko 2005); and (3) estimates of age-and gender-specific thyroid masses for children and adolescents (Likhtarov et al. 2013a).
Recently, recognized limitations in the dosimetry system resulted in the revision of thyroid dosimetry in Ukraine including three parts: (1) a detailed analysis of 146,425 measurements resulting in a revision of the measured 131 I thyroid activity and in the identification of sources of shared and unshared errors associated with the measurements; (2) the creation of an improved 'Thyroid Dosimetry 2020 system' (named TD20 here and below) for the entire population of Ukraine which is described by (Likhtarev et al. 2005);and (3) the recalculation of the thyroid doses for the members of the Ukrainian-American cohort (Likhtarov et al. 2014) that incorporated the revised 131 I thyroid activities and new sources of errors associated with direct thyroid measurements, for the Ukrainian in utero cohort (Likhtarov et al. 2011), and for the subjects included in the Chornobyl Tissue Bank (Likhtarov et al. 2013b). The present paper describes the first part of the revision of the thyroid dosimetry in Ukraine, while the other parts will be considered in separate papers.

Thyroid dosimetry monitoring in Ukraine
The accident at the Chornobyl nuclear power plant led to the environmental release of 1.8 EBq of 131 I (UNSCEAR 2011) and, consequently, to radiation exposure to the local population. Wide-scale measurements of 131 I in the thyroid were organized and conducted in May and June 1986 under the supervision of the Ministry of Health of the Ukrainian Soviet Social Republic. About 150,000 measurements were performed in Ukraine during the thyroid dosimetry monitoring. One-third of these measurements were performed using single-channel gamma-spectrometers, namely the GTRM-01ts, NK, DSU-68, DSU-2 and UR devices, within the energy window of 131 I (364 keV, yield: 81.7%), including detectors equipped with lead collimators that significantly reduced the impact of radioactive background on the results of the measurements. The rest of the measurements were done with the SRP-68-01 device, a NaI(Tl) scintillation survey meter, which was commonly used in the former Soviet Union for geological exploration. Since this device was not equipped with a factory-made collimator, homemade collimators with a typical thickness of 4 mm and a length of 5-15 cm were used whenever possible. Exceptionally, measurements were also performed with a gamma-spectrometer, namely the PRL, and the DP-5 device including a Geiger-Mueller (GM) counter, which was designed for use by military and civil defense organizations. Table 1 provides characteristics of the thyroid monitoring by types and models of the devices used, the number of measurements, and duration of the monitoring.
The device's detector was placed against the neck, which was cleaned with alcohol, of the measured person. For some measurements done shortly after the accident, an additional measurement of the forearm was performed because it was assumed that the contamination of the forearm surface was the same as that of the neck. The results of these measurements, which were given in terms of the number of counted pulses or their intensity for the gamma-spectrometer or in Table 1 Number of thyroid measurements a by Oblast and Kyiv city that were done in Ukraine and among the Ukrainian-American cohort members using various types of devices b a Numbers are given according to place of residence although persons could be measured in other areas of Ukraine b Five measurements done by the DP-5 dose rate meter on 8-19 May 1986 and 7 measurements were done by the gamma-spectrometer PRL on 8-12 May 1986 among the Ukrainian-American cohort members are not shown in the  terms of exposure rate for the SRP-68-01, performed by the same team in the same settlement on the same day using the same device were recorded in a so-called 'measuring list'. Every hour or every day, the background radiation in the measurement room was recorded. A cylindrical bottle with 10 ml of a reference solution of 131 I was used as primitive phantom (so-called 'bottle phantom') for routine checking of the sensitivity (hereinafter referred to as "calibration") of the measuring devices, if it was possible, either hourly or daily. A typical measuring list contained up to 700 individual measurements, although in some cases, the number of measurements performed by the team during the day was more than 1000 (see Section on "Gamma-spectrometers" below). The following information was recorded in the measuring list: identification data of the measured individual (full name or last name and initials, date or year of birth), information on the team conducting the measurements, on type of measuring device, the results of the device's calibration, and the value of radiation background in the room. Figure 1 shows the spatial distribution of the number of direct thyroid measurements done after the Chornobyl accident among people residing in the most contaminated study areas of Zhytomir, Kyiv, and Chernihiv Oblasts. It should be noted that numbers of measured individuals are given in terms of their places of residence at the time of the accident, and not in terms of the locations where the measurements were done. Residents of Zhytomir, Kyiv, and Chernihiv Oblasts were measured in these oblasts in the places of residence as well as in other nine oblasts in Ukraine where they were evacuated or where they moved voluntarily shortly after the accident. In addition, local residents were measured in Vinnytsia and Lviv Oblasts. Table 1 shows the number of measurements by Oblast, raion and city using different devices done in Ukraine and, partially, among the Ukrainian-American cohort members. Most of the measurements of the Ukrainian population and of the cohort members were performed by means of the SRP-68-01 device, 93,717 from 146,425 (64.0% of the total) and 7,703 from 13,204 (58.3% of the total), respectively.
Because measurements were performed during the same time period in 12 oblasts of Ukraine, corresponding to about half of the country, it was impossible to supply all measurement teams with the reference radiation sources for calibration of the devices. As a high priority, 131 I solutions for calibration were provided to the teams working with gammaspectrometers. Table 2 shows that most of the gamma-spectrometers, i.e., 26 from 28 (92.9% of the total), were calibrated during the measurement campaigns at least once. In contrast, only 23 from 64 of the radiometer devices (35.9% of the total) were calibrated. Table 3 gives the number of the cohort members measured using calibrated gammaspectrometers and the radiometers. In total, 51.8% (2844 Fig. 1 Spatial distribution of the number of direct thyroid measurements done in Zhytomir, Kyiv, Chernihiv, and Vinnytsia Oblasts, after the Chornobyl accident from 5496) and 18.1% (1393 from 7708) cohort members were measured using calibrated gamma-spectrometers and SRP-68-01 devices, respectively.

Atmospheric modelling
The 131 I ground deposition densities were used to normalize the activities of 131 I measured in the thyroid (see Section on "Comparative analysis to evaluate correct geometry of measurement and calibration coefficient for unchecked devices"). The 131 I deposition density in Ukraine after the Chornobyl accident ( Fig. 1) was calculated using the mesoscale atmospheric transport model LEDI. In that model, the 131 I atmospheric transport over the territory of Ukraine was simulated for the first 12 days after the accident, from 26 April to 7 May 1986 (period of deposition), with the 131 I source term developed by Talerko (2005) that accounted for variability with time of the release rate and the source effective height during the period of release. The meteorological data used in the model were generated by the Weather Research Forecast model (WRF) (Powers et al. 2017), version 3.9.1, adapted for Ukraine. The area covered a central part of Europe including Ukraine and Belarus (247 × 211 grid cells) with a horizontal resolution of 10 × 10 km and 28 vertical layers. The pressure of the top layer was set to 100 hPa and the minimum vertical grid step near the Earth's surface was about 50 m. Data from the European Center for Medium-Range Weather Forecasts were used as boundary conditions for the WRF simulations. Using meteorological fields with a high resolution in time and space from the WRF model allowed to improve the simulation of radionuclide dispersion and deposition of radionuclides in comparison to that of Talerko (2005). The updated daily values of the 131 I airborne concentration and 131 I ground deposition density for the period from 26 April to 7 May 1986 were calculated for 30,352 settlements in entire Ukraine, including 1263 settlements in Kyiv Oblast, 1717 in Zhytomyr Oblast and 1570 in Chernihiv Oblast (Talerko et al. 2020). 1 3

SRP-68-01 survey meter
Sixty-four percent of the direct thyroid measurements were made in Ukraine using the SRP-68-01 device (Fig. 2). This device included a NaI(TI) crystal (∅30 mm × 25 mm length) that responded to the photons emitted by 131 I in the thyroid in terms of exposure rate expressed in μR h −1 . For the conversion of the recorded exposure rate to the 131 I activity in the thyroid at the time of the measurement, the so-called conversion coefficient, C a , expressed in Bq per μR h −1 was used. The measured exposure rate included not only the signal due to 131 I in the thyroid, but also any signal due to (1) background radiation in the room where the measurements were made, (2) external contamination of the body and clothes of the investigated individual and (3) internal contamination of the body with 134 Cs, 136 Cs and 137 Cs. The contribution to the detector reading from other radionuclides, e.g., 95 Zr, 95 Nb, 103 Ru, 106 Ru, 140 Ba, 140 La, was assumed to be negligible and, therefore, was not considered in the study.
To minimize the background signals, the SRP-68-01 devices used in Ukraine were equipped with a hand-made cylindrical lead collimator, which surrounded the radiation detector while having a clear view of the thyroid. However, using such collimators did not completely eliminate the response of the SRP-68-01 device to sources other than 131 I in the thyroid. Instead, depending on the spectral characteristics of the background, the collimator weakened the background signal by a factor of up to 3.
Thyroid 131 I activity at the time of the direct thyroid measurement was calculated as: and where Q is the activity of 131 I measured in the thyroid (kBq);10 −3 is a unit conversion coefficient (kBq Bq −1 ); C a is the conversion coefficient (Bq per µR h −1 ); C b is the (2) C a = C b • G, calibration coefficient for the device obtained from the measurements of the reference radiation source with known 131 I activity (bottle phantom) (Bq per µR h −1 ); G is the correction factor for C b that accounts for the difference of the measurements geometry between the reference source (the bottle) and a person of different ages (unitless); I meas th , I meas bg and I meas net represent the readings of the device during the measurements of the thyroid gland, background, and net device indication, respectively (µR h −1 ); f sh is the fraction of gamma background radiation attenuated by the body of the measured individual that depends, in particular, on the anthropometric parameters of the body (unitless). The f sh -values can vary between 1 (no attenuation) and 0 (full attenuation). The fractions of gamma background attenuation by the body, f sh , for an adult subject, i.e., for the subject with maximal adsorption of gamma radiation, were experimentally obtained by the authors of this work for the SRP-68-01, NK and GTRM-01ts devices. The resulting values were found to be 0.94-0.95 for the SRP-68-01 device and 0.88-0.96 for gamma-spectrometers for 'standard' geometry of measurements, i.e. for the case when the detector was located against the neck. These experimental values are in good agreement with f sh values in the range of 0.87-1.0 that were estimated by Bratilova et al. (2003), Pitkevich et al. (1996, and Zvonova et al. (1997).
It should be noted that the net reading of the devices (Eq. 1) might include the background signal due to external contamination of the body and clothes of the person and due to internal contamination of the body with 134 Cs, 136 Cs and 137 Cs. However, it was considered here that the background signal due to the external contamination of the body and clothes was negligible, because (1) the neck of a measured individual was cleaned with a cotton wool wet in alcohol, and the contribution to the SRP-68-01 response from other contaminated parts of the body was much lower even for a device without a collimator (Kutsen et al. 2019); and (2) the vast majority of direct thyroid measurements in Ukraine were done three weeks or more after the accident and, therefore, individuals wore clean clothes because they are expected to wash their clothes at least every week. This was especially likely for individuals evacuated shortly after the accident to non-contaminated regions of Ukraine where they were measured ( Table 2). The contribution to the response of the measuring device of 131 I activity distributed in the human body outside the thyroid gland, even for non-collimated NaI(TI) detectors, was estimated to be about 1-3% (Gómez-Ros et al. 2019). Therefore, for devices equipped with collimators, the contribution of extrathyroidal iodine activity was insignificant from a practical point of view.
Contribution of the internal contamination of the body with 134 Cs, 136 Cs and 137 Cs to the device response was accounted as follows (Likhtarov et al. 2014): where B Cs t m is the relative contribution of the cesium radioisotopes to the reading of the device at the time of measurement t m (unitless).
The value of C b was determined by measurement of the reference radiation source with known 131 I activity. From Eq. (1), assuming G =1 and f sh =1 for the bottle phantom, the value of the calibration coefficient was calculated as: where Q ref is the activity of 131 I in the reference radiation source (kBq);10 3 is a unit conversion coefficient (Bq kBq −1 ); (3) I meas ref is the device reading during the measurement of the reference source (µR h −1 ). The response of a device to a radioactive source may vary for different reasons, i.e., the parameters of the electronic components of the device might depend on temperature, due to changes in battery voltage, etc. Therefore, to minimize measurement errors, it was recommended to calibrate the device immediately prior to the measurements of the individuals. This in turn implied that the measured team should have a reference radiation source available.
The SRP-68-01 device, for which the C b -value was estimated from measurements of a bottle phantom that contained a 131 I solution with known activity, is referred to as 'calibrated', in this study. For some devices, for various reasons, C b -values were not measured; these devices are referred to as 'unchecked'. Figure Table 4 provides technical characteristics of five types of gamma-spectrometers and the number of individuals measured during thyroid monitoring in Ukraine in May-June 1986. Only one type of gamma-spectrometer, GTRM-01ts, was designed to measure 131 I activity in the thyroid (Fig. 4). Two types of devices, namely the GTRM-01ts and the DSU-2, allowed for the measurement of activity in the thyroid using the mode 'measured percentage of the activity of 131 I source'. Such measurements were considered in the present study to be the most reliable, since any problems with calibration procedure and errors related to different durations of measurement of the individuals and the calibration source were eliminated. Twelve percent of all gamma-spectrometry  1 3 measurements was done in Ukraine using this mode, including 100% of all gamma-spectrometry measurements done in Zhytomyr Oblast. For the NK (Fig. 5) and DSU-68 devices, as well as for some UR devices, the results of the measurements were recorded as number of counts accumulated during the time of measurement, which was from 15 to 120 s (some of the GTRM-01ts and DSU-2 devices were used in this 'accumulated number of counts' mode too), while for the other UR devices, the results of the measurements were recorded from the needle indicator as counts s −1 . Unfortunately, some gamma-spectrometers were not calibrated during the measurement campaign using the bottle phantom with 131 I solution. Instead, the C b -values were assigned for each of these devices by dosimetrists overseeing the thyroid dosimetry monitoring campaign. In the present study, these devices and measurements were considered to be unchecked.

Age-dependent conversion coefficients for gamma-spectrometers and the SRP-68-01 device
The conversion coefficient, C a , of a device depends on anthropometry of the measured individual, i.e., thyroid size and thickness of tissue overlying the thyroid gland, which both depend on age (e.g., Beaumont et al. 2018;Venturini 2003;Vilardi et al. 2018;Yunoki 2019). Agespecific C a -values for the most commonly used Ukraine gamma-spectrometers (i.e., the GTRM-01ts and the NK which accounted for 70.5% of all spectrometric measurements) were calculated in this study using Monte Carlo simulations of photon and electron transport (Briesmeister 1997). To perform a Monte Carlo simulation, a family of Oak Ridge National Laboratory (ORNL) phantoms (Cristy 1980;Cristy and Eckerman 1987) was used. The phantoms represent the newborn; children aged 1 years, 5 years, 10 years, 15 years; and adults. Ulanovsky and Eckerman (1998) modified the ORLN phantoms to make them anatomically more realistic in the neck area. Response of the GTRM-01ts and the NK gamma-spectrometric devices on 131 I thyroid activity was calculated for different scenarios of collimator position: specifically, in the simulations the collimator was positioned at distances of zero, 0.5 cm and 1 cm from the skin of the neck.
The calibration coefficient, C b , of the devices was also calculated for the reference radiation source, a glass bottle with 10 mL of 131 I solution, which was used for calibration in May-June 1986. Based on these calculations, agedependent values of the correction factor, G , that accounts for the difference of the response of a device to the reference 131 I source and to individuals of different ages (Eq. 2) were obtained. Figures 6 and 7 show the age-dependent values of the correction factor, G , for the GTRM-01ts and NK devices for two measurement geometries: the collimator touching the neck of a measured individual, and the collimator being at a distance of 1.0 cm from the neck surface. The G values obtained for the GTRM-01ts and NK devices can be used for other devices of that type and position of the collimator, independently from duration of measurement, width of energy window, etc.
Monte Carlo calculations of age-specific C a -values were not performed for other types of gamma-spectrometers (i.e., the DSU-2, DSU-68 and UR devices), as such calculations are time-consuming. However, comparison of C a -values for the GTRM-01ts and NK devices obtained in this study with those calculated by Likhtarov et al. (2015) showed reasonable agreement. Therefore, for the DSU-2, DSU-68 and UR devices, the age-dependent C a -values calculated by Likhtarov et al. (2015) were used in the present study.
In contrast to gamma-spectrometers, for which agedependent C a -values had to be calculated, experimental data on age-dependent C a -values were available for the SRP-68-01 device (Gavrilin et al. 1992;Kaidanovsky and Dolgirev 1997). Figure 8 compares the age-dependent C a -values obtained from measurements performed by Gavrilin et al. (1992) for adults and Kaidanovsky and Dolgirev (1997) for individuals of different ages with those obtained using Monte Carlo calculations (Khrutchinsky et al. 2012;Ulanovsky et al. 2004) and using an analytical approach (Likhtarov et al. 2015). The figure demonstrates that there is reasonable agreement between experimentally obtained and calculated age-dependent C a -values.
As was mentioned above, the SRP-68-01 devices used for direct thyroid measurements in Ukraine were equipped with a hand-made cylindrical lead collimator that surrounded the radiation detector. Figure 9 shows a sketch of the SRP-68-01 detector block with a lead collimator surrounding the radiation detector. Measurements at different locations were done by the SRP-68-01 device with different collimator shift, which is defined as distance between the edge of the detector and the edge of the collimator (Fig. 9). The calibration coefficient, C b , of the SRP-68-01 device was calculated in this study using Monte Carlo simulations of photon and electron transport for the reference radiation source, a glass bottle with 10 mL of 131 I solution. Table 5 compares the calibration coefficients, C b , simulated and measured for different shifts of the collimator. The results obtained show a reasonable agreement between the simulated and measured values of the dose rate within the measurement error of the SRP-68-01 device of 13% (DM 1986) and the statistical uncertainty of the Monte Carlo simulations (see Table 5).
Experimental data on age-dependent conversion coefficients, C a , were not available for the SRP-68-01 device with the collimator. Figure 10 shows the age-dependent C a -values for different shifts of the collimator that were calculated by Likhtarov et al. (2015) using an analytical approach. Conversion coefficient for the SRP-68-01 device (Bq per µR h-1) Age (y) Fig. 8 Conversion coefficients, C a , for the SRP-68-01 device without a collimator 1 3

Comparative analysis to evaluate the correct measurement geometry and calibration coefficients for unchecked devices
Comparative analyses were conducted as described below, whenever possible, to evaluate the correct measurement geometry and calibration coefficients for (1) unchecked SRP-68-01 devices and (2) for gamma-spectrometers, for cases in which the correct measurement methodology could not be applied (e.g., when a device was used to measure more than 700 persons per day, see below). The measurement geometry includes the position of the detector with regard to an individual during the thyroid measurement procedure, the anthropometric parameters of the measured individual, the size and shift of the collimator, and other factors.
The following hypothesis was the basis for the analysis: the frequency distributions of 131 I activity in the thyroid measured by different devices in residents of the same or closely located settlements should show a similar pattern. Frequency distribution of 131 I thyroid activity derived from reliable measurements, i.e., done using a calibrated gammaspectrometer or an SRP-68-01 device, was considered in this study to be 'trusted'. The analysis indicated that the distribution of measured 131 I thyroid activity among the residents of the same settlement is approximately log-normal with a geometric standard deviation (GSD) of approximately 2.0. Therefore, if the median of the distribution obtained using Fig. 9 Sketch of the SRP-68-01 detector block with lead collimator surrounding the radiation detector Table 5 Calibration coefficients, C b , of the SRP-68-01 device, for the reference radiation source, a glass bottle with 10 mL of 131 I solution, simulated and measured for different shifts of the collimator a Statistical uncertainty in the Monte Carlo simulations depends on the shift of the collimator b Measurement error is 13%, which is the typical 1-sigma uncertainty in a measurement made by the SRP-68-01 instrument (DM 1986) Shift of collimator ( Fig. 10 The age-dependent calibration coefficients, C a , for the SRP-68-01 device with different shifts of a collimator (Likhtarov et al. 2015): crosses-0 cm, squares-1 cm, diamonds-2 cm, triangles-3 cm 1 3 an 'unchecked' device, e.g., an uncalibrated SRP-68-01 with unknown shift of the collimator, deviated by more than a factor 1.5 from those obtained using a trusted device, this justified the need to adjust the C b -values of an unchecked device, since such a deviation is statistically significant even for a small numbers of measured individuals.
Correction was done using a device-dependent adjustment factor ( AF ) that was calculated in the present study. Frequency distributions of 131 I thyroid activity measured by trusted and unchecked devices were compared for the same 'cluster', i.e., using 131 I activities measured by the same devices in the same settlement or group of settlements.
To decrease dispersion of the distribution of 131 I thyroid activity, measurement results obtained for individuals aged from 8 to 16 years old were included in the analysis, because they were most frequent. To ensure that the results of such a comparative analysis were reliable and the AF -values obtained were correct, the following measurements were included: 1. Measurements performed between 18 May and 5 June 1986 when most direct thyroid measurements were done in Ukraine. Because of the short half-life of 131 I in the thyroid, which is defined by its physical half-life of 8.02 days, 131 I thyroid activities were recalculated to the same date of 31 May 1986 to ensure correct comparison of activities measured within a period of 19 days. Measurements done before 18 May and later than 5 June were not included in the analysis. 2. To increase the number of measurements included in analysis, activities of 131 I in the thyroid measured in residents of neighboring settlements were normalized to the 131 I ground deposition density in the settlement of residence, which was calculated using an improved atmospheric dispersion model (Talerko et al. 2020) (see above).
The device's adjustment factor was calculated as weighted mean of the ratios of 'trusted' to 'unchecked' median of the distribution of 131 I thyroid activity measured at all clusters where the unchecked device was used: where AF j is the adjustment factor for the j-th unchecked device (unitless); Q trust i is the median of the distribution of the trusted 131 I thyroid activity measured in the i-th cluster that was recalculated to 31 May 1986 and normalized to 131 I ground deposition density (Bq per kBq m −2 ); Q uncheck i,j is the median of the distribution of 131 I thyroid activity measured by the j-th unchecked device in the i-th cluster that was (5) recalculated to 31 May 1986 and normalized to 131 I ground deposition density (Bq per kBq m −2 ); N trust i and N uncheck i,j is the number of measurements that were done in i-th cluster by the trusted and j-th unchecked devices, respectively. A cluster was used to calculate the device adjustment factor if more than ten measurements of 131 I thyroid activity had been performed by each trusted and unchecked device.
If AF j was less than 1.5, which corresponds to a shift of the collimator for the SRP-68-01 device of less than 1 cm, calibration coefficients for this device were considered to be correct. Otherwise, the C b -values for the unchecked device was corrected as: where C j, corr b is the corrected calibration coefficient for the j-th unchecked device (Bq per µR h −1 ); C j b is the calibration coefficient used for the j-th unchecked device in TD10 (Bq per µR h −1 ).
The correct geometry of measurement, i.e., the correct shift of the collimator, was evaluated for the SRP-68-01 device by a comparison of the estimated corrected calibration coefficient, C j,corr b , and calibration coefficients obtained for different shifts of a collimator ( Table 5). Values of correction factor, G , which were appropriate for a given measurement geometry, were then used to calculate conversion coefficients, C a , to be used to derive 131 I thyroid activity in individuals of different ages. Figure 11 shows the schema of the comparative analysis and estimation of the AF-values. The revision of direct thyroid measurements and introduction of adjustment factors resulted in new sources of shared and unshared errors related to the estimates of 131 I thyroid activity in the calculation of individual stochastic doses.

Estimation of measurement errors
Errors in the measured 131 I thyroid activity were estimated for each individual measurement. The classical and Berkson components of the errors were evaluated separately using a combination of models, because the influence of these components on estimates of radiation-related risk of thyroid cancer following exposure to 131 I are considerably different (Masiuk et al. 2016(Masiuk et al. , 2017. The following errors in the measurement of the 131 I thyroid activity were identified: 1. Unshared classical errors including those associated with the device response during the measurements of 131 I in the thyroid and in the bottle phantom containing a reference 131 I solution, the device's measurement errors and the errors associated with age-depended individual The Appendix provides a detailed description of the methods used to define and calculate these errors. It also provides the mathematical model of measurement results including classical and Berkson errors that can be used for dose calculations and for further radiation-related thyroid cancer risk analysis.

Measurements among residents of Chernihiv Oblast
Comparative analysis, which was conducted for the unchecked SRP-68-01 devices used for direct thyroid measurements in Chernihiv Oblast, showed that the collimators were used without shift meaning that the edge of the collimator coincided with the edge of the detector. This fact was confirmed by witnesses and participants of the thyroid dosimetry monitoring campaign. There were two more uncalibrated SRP-68-01 devices with unknown shift of the collimator, i.e., unchecked SRP-68-01 devices that were used in Sumy Oblast to measure residents of Chernihiv Oblast (Table 6). An adjustment factor AF=1.55 was obtained for both devices, and the corrected calibration coefficient was

Measurements among residents of Zhytomyr Oblast
Eleven SRP-68-01 devices were used for thyroid dosimetry monitoring among residents of Zhytomyr Oblasts; only three of these devices were calibrated (once on 20 May 1986) and their collimators were shifted by 3 cm (Table 5). Comparative analysis was conducted only for three out of eight unchecked SRP-68-01 devices, because only an insufficient number of measurements were done by means of the trusted devices (gamma-spectrometers GTRM-01ts and calibrated SRP-68-01 devices). As a result, the measurement geometry was evaluated for three devices with a collimator shift of 0, 1 and 3 cm. Corrected calibration coefficients, C j,corr b , and appropriate age-dependent correction factors, G , were assigned to these SRP-68-01 devices. For the other five unchecked SRP-68-01 devices, a zero shift of the collimator was assumed.

Measurements among residents of Kyiv Oblast
It was impossible to conduct a reliable comparative analysis of measurements performed on children and adolescent residents of Kyiv Oblast because they (1) moved shortly after the accident to the non-contaminated Odesa Oblast and Crimea and were measured there, and (2) the dates of relocation from the contaminated settlements were unknown for individuals who were not included in the Ukrainian-American cohort. However, about 96% of the Ukrainian-American cohort members measured on Crimea and in Odesa Oblast were measured by calibrated SRP-68-01 devices. The same geometry of measurement was assigned for the rest of residents of Kyiv Oblast measured by SRP-68-01 devices, i.e., a zero collimator shift was assumed for Crimea and a 1 cm collimator shift was assumed for Odessa Oblast (see Fig. 3; Table 5).

Comparative analysis to evaluate the correct measurement geometry for gamma-spectrometers
To evaluate possibly unreliable results of the gamma-spectrometry measurements, the number of measurements done using the same device at the same day was analyzed. The minimal time required to measure one individual, including the correct positioning of the individuals and detector against the neck, was at least 1 min. Consequently, a maximum of about 700 individuals could be measured during an extended 12-h working day. However, for some days, up to 2000 persons were measured by the same device in Kozeletsky raion in Chernihiv Oblast (Table 7). It is emphasized that it was not possible to complete such a large number of measurements without violation of the requirements for standard measurement procedures, including correct positioning of the individuals and the detector against the thyroid. Improper measurement geometry may have resulted in an inaccurate estimate of 131 I activity in the thyroid as the calibration coefficient used was obtained assuming the standard measurement geometry.  Table 5 1.0 cm 1 3 The comparative analysis showed that calibration coefficients for two gamma-spectrometers GTRM-01ts used in Chernihiv Oblast were underestimated. These devices were characterized by an unrealistically large number of daily measurements done between 30 May and 1 June 1986 (Table 7), and an improper measurement geometry could be the possible reason for the underestimation of the calibration coefficients. Table 8 provides an example of the comparative analysis performed for one of the GTRM-01ts devices with an underestimated calibration coefficient that was used in Kozeletsky raion in Chernihiv Oblast. As a result of the comparative analysis, an adjustment factor AF=4.55 was obtained for the GTRM-01ts device, and the corrected calibration coefficient was calculated using Eq. (6). The same analysis was done for the second GTRM-01ts device with an underestimated calibration coefficient, for which a factor AF=2.0 was obtained. It should be noted that no problems were identified during the comparative analysis for the other gamma-spectrometers used for the thyroid dosimetry monitoring in Ukraine. Table 9 compares the 131 I thyroid activities for all 146,425 measured residents of Ukraine that were estimated in this study with those previously estimated by Likhtarov et al. (2005). The highest 131 I thyroid activity at the time of measurement was found in residents of Zhytomyr, Kyiv, and Chernihiv Oblasts, with arithmetic means among the measured individuals of 18 kBq, 12 kBq, and 10 kBq, respectively. The lowest 131 I thyroid activity (arithmetic mean of 0.29 kBq) was observed among residents of Lviv Oblast, located about 450 km to the west of the Chornobyl nuclear power plant. The revised activity of 131 I in the thyroid among residents of Kyiv city was lower than that for Kyiv Oblast, 2.3 kBq vs. 12 kBq. This observation can be explained by the fact that residents of Kyiv city did not consume fresh cow's milk while milk from trade network was controlled for the permissible level of radioactivity of 3.7 kBq L −1 starting 6 May 1986 (MH 1986). Rather wide frequency distributions of 131 I thyroid activity were observed in different oblasts with GSD values that varied from 2.4 to 5.3. On average, in Vinnytsia, Kyiv, Lviv, and Chernihiv Oblasts, and in the city of Kyiv, the revised values of the 131 I thyroid activities were found to be 10-25% higher than previously estimated by Likhtarov et al. (2005), while in Zhytomyr Oblast, the values of the revised activities were found to be about 50% lower. Figure 12 shows the overall frequency distribution of 131 I thyroid activities at the time of measurement (logarithm of actual value) among 146,425 individuals measured in Ukraine. This distribution is close to a log-normal distribution with a geometric mean (GM) equal to 5.2 kBq and GSD equal to 3.9. The range of 131 I activities in the thyroid measured in the Ukrainian residents is rather wide, and the 90% confidence interval is 0.69-49 kBq. Figure 13 shows the frequency distribution of the ratios of 131 I thyroid activity obtained in the present study to that previously assessed by Likhtarov et al. (2005) for all 146,425 individuals measured in Ukraine. Values of the ratio of less than 1 represent residents of Zhytomyr Oblast, while values of the ratio between 1 and 2 represent individuals from Kiev, Vinnitsa and Chernihiv Oblasts. For some residents of Chernihiv Oblast, this ratio exceeds 2. Activity of 131 I in the thyroid for the members of the Ukrainian-American cohort, which was revised as described above (TD20), was compared with that previously used for TD10 by Likhtarov et al. (2014). Figure 14 compares the 131 I activity in the thyroid, TD20 vs. TD10, by Oblast of residence of the Ukrainian-American cohort members. For about 40% of the cohort members residing in Zhytomir Oblast, the revised values of 131 I thyroid activity (TD20) were found to be 2-3 times lower as compared to those used for previous dose assessment in TD10. For cohort members who resided in Kiev and Chernihiv Oblasts, the revised values of 131 I activity in the thyroid tended to be higher than those from TD10.

Errors in measurements of 131 I thyroid activity
Table 10 provides device-and Oblast-specific classical and Berkson relative errors associated with the measurements of Table 9 Parameters of distribution of 131 I thyroid activity by oblast of residence at the time of the accident (ATA): arithmetic mean (AM), standard deviation (SD), geometric mean (GM) and geometric stand-ard deviation (GSD), obtained in the present study and comparison with those previously estimated by Likhtarov et al. (2005) a Including 420 individuals who resided outside the listed Oblasts  Ratio of 131 I thyroidal activity obtained in this study to that used in (Likhtarov et al. 2005)

Fig. 13
Frequency distribution of the ratios of 131 I thyroid activity obtained in the present study to that previously assessed by Likhtarov et al. (2005) for all 146,425 individuals measured in Ukraine 1 3 131 I activity in the thyroid for the members of the Ukrainian-American cohort. The highest classical errors in measured 131 I thyroid activity were in Chernihiv Oblast, including about 0.5 for the measurements done by the UR and SRP-68-01 devices. For the entire Ukrainian-American cohort, devices ranked highest to lowest in terms of classical errors are: the UR, SRP-68-01, GTRM-01ts, NK, DSU-68 and DSU-2.
The highest relative Berkson errors in 131 I thyroid activity measurements were observed for the Chernihiv Oblast, including 0.86 for the measurements done by the GTRM-01ts device. Such high errors were observed because the calibration coefficients for two gamma-spectrometers GTRM-01ts which were used in Chernihiv Oblast to measure 131 I activities in 930 out of 1546 individuals (60.2% of the total measured by this type of device) were underestimated by a factor of 4.55 (see Section on "Comparative analysis to evaluate the correct measurement geometry for gammaspectrometers" above). For the entire Ukrainian-American cohort, devices ranked highest to lowest in terms of Berkson errors are: the GTRM-01ts, SRP-68-01, NK, UR, DSU-2 and DSU-68.

Discussion
The present paper describes an in-depth analysis and revision of directly measured thyroid 131 I activities done in the Ukrainian population in May-June 1986. The variation of the C b -values for the SRP-68-01 device that was observed in TD10 from one oblast to another (Fig. 3) might be caused, to a large extent, by different positions of the lead collimators that affected the distance between the thyroid gland and the radiation detector. For example, a shift of the collimator from the edge of the detector of up to 3 cm resulted in changes of the C b -values for the SRP-68-01 device of up to factor of 2.5.
A substantial age dependence of a device's conversion coefficients was observed for the SRP-68-01 device, and a ratio of C a -value for an adult individual to that for a 1-year-old child was 1.75 (Fig. 8). It should be noted that the Hitachi-Aloka TCS-161/171/172 survey meter including a NaI(Tl) crystal (∅25.4 mm × 25.4 mm length), similar to the crystal size of the SRP-68-01 device, was used after the Fukushima-Daiichi accident in Japan for measuring the 131 I thyroid activity, has a similar age dependence of C a -values (Kim et al. 2020).
For gamma-spectrometers, the age dependence was less pronounced, and the corresponding ratio was 1.23 and 1.13 for the respectively (Figs. 6,7). Such dependence on age is quite typical for devices including a NaI(TI) crystal with a diameter and thickness of about 2 inches (Li et al. 2019).  The shape, size and position of the lobes and the isthmus of the thyroid gland are variable (e.g., Hiatt and Gartner 2010). Therefore, the position of the thyroid gland relative to the center of the detector could also vary between individuals who underwent direct thyroid measurements. For the SRP-68-01 device without a collimator, shifts of up to 2 cm in position of the thyroid relative to the detector resulted in only small relative error estimates for the 131 I thyroid activity, i.e., up to 0.07 (ratio of standard deviation to central value). However, for the thyroid detectors with collimators, the radiation from 131 I in the thyroid could be shielded by the collimator to different degrees depending on the position of the collimator relative to the thyroid of the measured individual. This leads to increasing measurement uncertainty that is hard to quantify for a particular individual, because of the unknown position and shape of his or her thyroid gland.
Comparative analysis showed a significant variability between individual 131 I thyroid activities that were derived even from calibrated measurements. As a rule, the frequency distribution of 131 I thyroid activities among individuals measured within the same cluster was approximately lognormal and characterized by a GSD value that was typically greater than 2. The observed variability in 131 I thyroid activities is determined by the variability in parameters values of ecological and biokinetic models that define the transfer of 131 I through the chain 'ground deposition' → 'vegetation' → 'milk, milk products' → 'human's thyroid'. The dosimetry model used to calculate thyroid doses in the Ukrainian-American cohort uses more than 50 parameters (Likhtarov et al. 2014). Differences in parameters of the frequency distributions of 131 I thyroid activity measured by trusted and unchecked devices in the same cluster might be caused by statistical uncertainty and variability of values of the parameters considered in the dosimetry model. Therefore, adjustment factors were calculated as a weighted mean of the ratios of 'trusted' to 'unchecked' median of the distribution of 131 I thyroid activity measured among more than ten persons in one cluster (see Eq. 5).

Conclusion
This paper describes an in-depth analysis and revision of 146,425 measurements of 131 I thyroid activity in the Ukrainian population done in May-June 1986. A comparative analysis was conducted, where possible, to evaluate the measurement geometry and calibration coefficients for unchecked SRP-68-01 devices and gamma-spectrometers. New sources of shared and unshared errors associated with 131 I thyroid activity measurements were identified. The revised activities of 131 I in the thyroid and associated classical and Berkson measurement errors were derived from direct thyroid measurements done in Ukraine. The results obtained provide the basis for the assessment of updated thyroid doses in Ukraine due to 131 I intake. The revision of 131 I thyroid activities will result in substantial changes of the thyroid dose estimates for the entire population of Ukraine (Likhtarev et al. 2005) as well as for the subjects of the Ukrainian-American cohort (Likhtarov et al. 2014), the Ukrainian in utero cohort (Likhtarov et al. 2011), and individuals included in the Chornobyl Tissue Bank (Likhtarov et al. 2013b).

Estimation of classical measurement errors for 131 I in the thyroid
It is known that at the fixed intensity of emission for a radioactive source, the probability to register k counts using a measuring device for measuring time t is defined by the Poisson distribution (Molina 1973). For a quite large intensity, the Poisson distribution is close to a normal distribution and can be written as: where N(m, 2 ) is a normal distribution with expectation value m and variance 2 , I meas th and I meas bg are intensities of a radioactive source (providing the reading of a device in terms of pulses per second) registered during the measurement of thyroid and background, respectively, 2 th = I tr th t th and 2 bg = I tr bg t bg are the variances of corresponding measurement errors, t th is the duration of a thyroid measurement, and t bg is the duration of a background measurement. Index 'tr' denotes the true value, while 'meas' denotes the measured value.
In addition to the statistical error of registration, the values I meas th and I meas bg include an instrumental error, with variance 2 dev . The full variances of the measurement errors for both thyroid and background are as follows: Based on the calibration method used one can write down the approximate relation: where C a is the conversion coefficient (Eq. 2) and C is the relative error of the conversion coefficient, which includes the error of the 131 I activity in the bottle source used for the (A3) C meas a ≈ C tr a • 1 + C • 1 , 1 ∼ N(0,1), device calibration, the device's error of the measurement, and the error of the age-dependent factor G. Using Eqs. (A1)-(A3), 131 I activity in the thyroid estimated from the direct thyroid measurement (see Eq. 1) can be presented as: where n = √̂ 2 th + f 2 sh •̂ 2 bg and 2 ∼ N(0,1). Then, Eq. (A4) can be written as: Because Q tr = C tr a • (I tr th − f sh • I tr bg ) , Eq. (A5) can be expressed as: and  ∼ N(0,1). As I tr th and I tr bg are unknown, tr Q can be written as: The error factor C of the age-dependent conversion coefficient C a , (Eq. 2) can be calculated as: where b is the relative error factor of the device's calibration using a bottle phantom, and G is the relative error factor of the age-dependent factor G.
The goal of the calibration of a device using a bottle phantom is to determine its sensitivity, i.e. to find out the values I meas ref − I meas bg caused by radioactivity Q ref of a reference radiation source. Therefore, b is specified as: where ref is the relative error factor of activity for the reference radioactive source, which is known from the technical documentation of the provider (Production Association "Isotope"); S is the error factor in measuring the intensity of the reference source.
Because the process of calibration using a bottle phantom is the same as the process of measurement of radioactivity in the thyroid, the error factor S can be calculated as: dev is the error variance of measuring the intensity of the reference source during the measurement time t ref .
For devices with missing information about the calibration, b was, based on expert judgement, estimated to be 30%. The value of the relative error factor G for the SRP-68-01 device was estimated from empirical data. According to Kaidanovsky and Dolgirev (1997) this factor depends on thyroid mass and is in the range of 15-18%. Since the scintillation crystals of the gamma-spectrometers were located significantly farther from the thyroid than that for the SRP-68-01 device, the influence of measurement geometry was less and G was estimated for spectrometers, again based on expert judgement, to be 5%. This error factor was mainly due to variations in thyroid volume and thyroid position. Based on Likhtarov et al. (2013c), the following observation model of thyroid radioactivity with classical additive error was selected in the present study:

Censoring
Measurements of 131 I thyroid activity were considered reliable if the probability to detect a net signal, which is the difference between thyroid signal and background signal, with the assumption that its true value equals zero, was not more than 25%. This is equivalent to the condition I tr th − f sh •I tr bg ≥ 0.68 • n , where n is defined by Eq. (A4), i.e., the critical limit of 131 I in the thyroid was accepted to be 0.68 • n . The result of a measurement providing less than the critical limit was replaced by half of the critical limit. It was accepted that I tr th − f sh • I tr bg = 0.34 • n under the condition I tr th − f sh • I tr bg < 0.68 • n .

Estimation of Berkson errors due to deviation from the proper measurement geometry
Results of direct thyroid measurements conducted in May-June 1986 were associated with Berkson uncertainties (Masiuk et al. 2013(Masiuk et al. , 2017 arising from deviation of the (A11) Q meas = Q tr + meas Q • .
detector from the proper measurement geometry (where the lower edge of the detector is close to the lower point of the neck). Khrutchinsky et al. (2012) considered deviations from the standard measurement geometry for the SRP-68-01 device without collimator by 0-1 cm shifts in horizontal and vertical direction, and inclinations in horizontal and vertical planes; for such scenarios the relative error was estimated to vary from 0.24 to 0.51 depending on the age of the measured individual.
Following Khrutchinsky et al. (2012), a zero shift of the detector from the neck in horizontal direction was considered to be the proper measurement geometry. It was assumed that with 95% probability the shift of the detector in horizontal direction was in the range 0-2 cm from the neck. It was also assumed to have censored log-normal distributions of the shift with GSD = 2. The impact of a shift in vertical direction along the neck and its inclinations in horizontal and vertical planes were neglected. The uncertainty associated with detector deviation from the proper measurement geometry was considered to be unshared Berkson errors (Drozdovitch et al. 2015;Simon et al. 2015).
Let GF j be the factor due to shift of the j-th device's detector in the horizontal direction away from the neck. For the sake of simplification the detector is calibrated in such way that GF j is equal to unity for the proper measurement geometry, i.e., GF j | | |S=0 = 1. Then GF j can be approximated by a function which is quadratic in the shift S:

Model of mixed classical and Berkson errors in thyroid measurements
Factors that are characterized by uncertainty of Berkson type are denoted as: where GF ij is the factor due to the shift of the j-th device's detector in the horizontal direction away from the neck of the i-th individual; AF meas j is the adjustment factor for the j-th device.
The resulting thyroid radioactivity for the i-th individual measured by j-th device can be represented as: where Q meas i is the measured 131 I thyroid activity associated with the classical additive error (Eq. (A11)).
The unknown true radioactivity A tr i is expressed as: The connection between F tr ij and F meas ij is determined by a Berkson multiplicative error: where error F,ij has a log-normal distribution log( F,ij ) ∼ N(− 2 F,ij 2 , 2 F,ij ) with an expectation value E F,ij = 1 ; F meas ij and F,ij are stochastically independent, and 2 F,ij is the variance of log( F,ij ) . Values of F meas ij and 2 F,ij can be obtained by the two-dimensional Monte Carlo procedure described in .
According to Eq. (A11), the measured 131 I activity in the thyroid, Q meas Equations (A19) and (A20) compose a dose observations model with a classical additive error and a Berkson multiplicative error (Masiuk et al. 2016(Masiuk et al. , 2017.
Finally, the relationship between expectations of true radioactivity and radioactivity measured with Berkson error can be expressed as: study. The authors also would like to thank Drs. Elizabeth K. Cahoon, Mark P. Little and Kiyohiko Mabuchi (NCI) for their thoughtful comments on the paper.
Funding This work was funded by the National Academy of Medical Sciences of Ukraine, state registrations #0111U000757 and #0114U002845, by the Ukrainian research project "Exact formulas, estimates, asymptotic properties and statistical analysis of complex evolutionary systems with many degrees of freedom", state registration #0119U100317, and by the Intramural Research Program of Division of Cancer Epidemiology and Genetics, National Cancer Institute, (NCI, NIH, DHHS) within the framework of the Ukrainian-American Study of Thyroid Cancer and Other Diseases Following the Chernobyl Accident (Protocol #OH95-C-NO20) through Partner Agreement P-004 between the Science and Technology Center in Ukraine and the National Cancer Institute in the US.

Compliance with ethical standards
Conflict of interest The authors declare that this work was carried out in the absence of any personal, professional or financial relationships that could potentially be construed as a conflict of interest.