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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.

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  1. Astakhova LN, Anspaugh LR, Beebe GW, Bouville A, Drozdovitch VV, Garber V, Gavrilin YI, Khrouch VT, Kuvshinnikov AV, Kuzmenkov YN, Minenko VP, Moschik KV, Nalivko AS, Robbins J, Shemiakina EV, Shinkarev S, Tochitskaya SI, Waclawiw MA (1998) Chernobyl-related thyroid cancer in children of Belarus: a case-control study. Radiat Res 150:349–356

    ADS  Google Scholar 

  2. Beaumont T, Rimlinger M, Broggio D, Ideias PC, Franck D (2018) A systematic experimental study of parameters influencing 131-iodine in vivo spectroscopic measurements using age-specific thyroid phantoms. J Radiol Prot 38:651–665

    Google Scholar 

  3. Bratilova AA, Zvonova IA, Balonov MI, Shishkanov NG, Trushin VI, Hoshi M (2003) 131I content in the human thyroid estimated from direct measurements of the inhabitants of Russian areas contaminated due to the Chernobyl accident. Radiat Prot Dosim 105:623–626

    Google Scholar 

  4. Brenner AV, Tronko MD, Hatch M, Bogdanova TI, Oliynik VA, Lubin JH, Zablotska LB, Tereschenko VP, McConnell RJ, Zamotaeva GA, O’Kane P, Bouville AC, Chaykovskaya LV, Greenebaum E, Paster IP, Shpak VM, Ron E (2011) I-131 dose response for incident thyroid cancers in Ukraine related to the Chornobyl accident. Environ Health Perspect 119:933–939

    Google Scholar 

  5. Briesmeister JF (1997) MCNP: A General Monte Carlo N-Particle Transport Code, Version 4B. . LA-12625-M: adiation Shielding Information Center, Los Alamos

    Google Scholar 

  6. Cardis E, Kesminiene A, Ivanov V, Malakhova I, Shibata Y, Khrouch V, Drozdovitch V, Maceika E, Zvonova I, Vlasov O, Bouville A, Goulko G, Hoshi M, Abrosimov A, Anoshko J, Astakhova LN, Chekin S, Demidchik E, Galanti R, Ito M, Korobova E, Lushnikov E, Maksioutov M, Masyakin V, Nerovnia A, Parshin V, Parshkov E, Piliptsevich N, Pinchera A, Polyakov S, Shabeka N, Suonio E, Tenet V, Tsyb A, Yamashita S, Williams D (2005) Risk of thyroid cancer after exposure to 131I in childhood. JNCI 97:724–732

    Google Scholar 

  7. Cristy M (1980) Mathematical phantoms representing children of various ages for use in estimates of internal dose. Report No ORNL/NUREG/TM-367. Oak Ridge National Laboratory, Oak Ridge

    Google Scholar 

  8. Cristy M, Eckerman KF (1987) Specific absorbed fractions of energy at various ages from internal photon sources. Report No ORNL/TM-8381/V1. Oak Ridge National Laboratory, Oak Ridge

    Google Scholar 

  9. Drozdovitch V, Minenko V, Golovanov I, Khrutchinsky A, Kukhta T, Kutsen S, Luckyanov N, Ostroumova E, Trofimik S, Voillequé P, Simon SL, Bouville A (2015) Thyroid dose estimates for a cohort of Belarusian children exposed to 131I from the Chernobyl accident: assessment of uncertainties. Radiat Res 184:203–218

    ADS  Google Scholar 

  10. Gavrilin YuI, Gordeev KI, Ivanov VK, Il’in LA, Kondrusev AI, Margulis UI, Stepanenko VF, Khrouch VT, Shinkarev SM (1992) Characteristics and results of the determination of the doses of internal irradiation of the thyroid gland in the population of contaminated districts of the Byelorussian Republic. Vestn Akad Med Nauk SSSR 2:35–43 ((in Russian))

    Google Scholar 

  11. Gómez-Ros JM, Moraleda M, Teles P, Tymińska K, Saizu MA, Gregoratto D, Lombardo P, Berkovsky V, Ratia G, Broggio D (2019) Age-dependent calibration factors for in-vivo monitoring of 131I in thyroid using Monte Carlo simulations. Radiat Meas 125:96–105

    Google Scholar 

  12. Hatch M, Furukawa K, Brenner A, Olinjyk V, Ron E, Zablotska L, Terekhova G, McConnell R, Markov V, Shpak V, Ostroumova E, Bouville A, Tronko M (2010) Prevalence of hyperthyroidism after exposure during childhood or adolescence to radioiodines from the Chornobyl nuclear accident: dose-response results from the Ukrainian-American Cohort Study. Radiat Res 174:763–772

    ADS  Google Scholar 

  13. Hiatt JL, Gartner LP (2010) Textbook of head and neck anatomy, 4th edn. Lippincott Williams & Wilkins, Philadelphia (a Walter Kluwer business)

    Google Scholar 

  14. Kaidanovsky GN, Dolgirev EI (1997) Calibration of radiometers for mass control of incorporated 131I, 134Cs and 137Cs nuclides with the help of volunteers. Radiat Prot Dosim 71:187–194

    Google Scholar 

  15. Khrutchinsky A, Drozdovitch V, Kutsen S, Minenko V, Khrouch V, Luckyanov N, Voilleque P, Bouville A (2012) Mathematical modeling of a survey-meter used to measure radioactivity in human thyroids: Monte Carlo calculations of device response and uncertainties. Appl Radiat Isotopes 70:743–751

    Google Scholar 

  16. Kim E, Yajima K, Hashimoto S, Tani K, Igarashi Y, Iimoto T, Ishigure N, Tatsuzaki H, Akashi M, Kurihara O (2020) Reassessment of internal thyroid doses to 1,080 children examined in a screening survey after the 2011 Fukushima nuclear disaster. Health Phys 118:36–52

    Google Scholar 

  17. Kopecky KJ, Stepanenko V, Rivkind N, Voillequé P, Onstad L, Shakhtarin V, Parshkov E, Kulikov S, Lushnikov E, Abrosimov A, Troshin V, Romanova G, Doroschenko V, Proshin A, Tsyb A, Davis S (2006) Childhood thyroid cancer, radiation dose from Chernobyl, and dose uncertainties in Bryansk Oblast, Russia: a population-based case-control study. Radiat Res 166:367–374

    ADS  Google Scholar 

  18. Kutsen S, Khrutchinsky A, Minenko V, Voillequé P, Bouville A, Drozdovitch V (2019) Influence of the external and internal radioactive contamination of human body on the results of the thyroidal 131I measurements conducted in Belarus after the Chernobyl accident. Part 2: Monte Carlo simulation of response of the detectors near the thyroid. Radiat Environ Biophys 58:215–226

    Google Scholar 

  19. Li C, Tremblay M, Capello K, Kurihara O, Youngman M, Etherington G, Ansari A, López MA, Franck D, Dewji S (2019) Monitoring and dose assessment for children following a radiation emergency–Part II: calibration factors for thyroid monitoring. Health Phys 117:283–290

    Google Scholar 

  20. Likhtarev IA, Shandala NK, Gulko GM, Kairo IA, Chepurny NI (1993) Ukrainian thyroid doses after the Chernobyl accident. Health Phys 64:594–599

    Google Scholar 

  21. Likhtarev IA, Gulko GM, Sobolev BG, Kairo IA, Pröhl G, Roth P, Henrichs K, Grulko GM (1995) Evaluation of the 131I thyroid-monitoring measurements performed in Ukraine during May and June of 1986. Health Phys 69:6–15

    Google Scholar 

  22. Likhtarev I, Bouville A, Kovgan L, Luckyanov N, Voillequé P, Chepurny M (2006) Questionnaire- and measurement-based individual thyroid doses in Ukraine resulting from the Chernobyl nuclear reactor accident. Radiat Res 166:271–286

    ADS  Google Scholar 

  23. Likhtarov I, Kovgan L, Vavilov S, Chepurny M, Bouville A, Luckyanov N, Jacob P, Voilleque P, Voigt G (2005) Post-Chornobyl thyroid cancers in Ukraine. Report 1: estimation of thyroid doses. Radiat Res 163:125–136

    ADS  Google Scholar 

  24. Likhtarov I, Kovgan L, Vavilov S, Chepurny M, Ron E, Lubin J, Bouville A, Tronko N, Bogdanova T, Gulak L, Zablotska L, Howe G (2006) Post-Chornobyl thyroid cancers in Ukraine. Report 2: risk analysis. Radiat Res 166:375–386

    ADS  Google Scholar 

  25. Likhtarov I, Kovgan L, Chepurny M, Ivanova O, Boyko Z, Ratia G, Masiuk S, Gerasymenko V, Drozdovitch V, Berkovski V, Hatch M, Brenner A, Luckyanov N, Voilleque P, Bouville A (2011) Estimation of the thyroid doses for Ukrainian children exposed In Utero after the Chernobyl accident. Health Phys 100:583–593

    Google Scholar 

  26. Likhtarov I, Kovgan L, Masiuk S, Chepurny M, Ivanova O, Gerasymenko V, Boyko Z, Voillequé P, Antipkin Y, Lutsenko S, Oleynik V, Kravchenko V, Tronko M (2013a) Estimating thyroid masses for children, infants, and fetuses in Ukraine exposed to (131)I from the Chernobyl accident. Health Phys 104:78–86

    Google Scholar 

  27. Likhtarov I, Thomas G, Kovgan L, Masiuk S, Chepurny M, Ivanova O, Gerasymenko V, Tronko M, Bogdanova T, Bouville A (2013b) Reconstruction of individual thyroid doses to the Ukrainian subjects enrolled in the Chernobyl Tissue Bank. Radiat Prot Dosim 156:407–423

    Google Scholar 

  28. Likhtarov I, Masiuk S, Chepurny M, Kukush A, Shklyar S, Bouville A, Kovgan L (2013c) Error estimation for direct measurements in May–June 1986 of 131I radioactivity in thyroid gland of children and adolescents and their registration in risk analysis. In: Antoniuk A, Melnik V (eds) Mathematics and life sciences. Publ House De Gruyter, Berlin, pp 231–244

    Google Scholar 

  29. Likhtarov I, Kovgan L, Masiuk S, Talerko M, Chepurny M, Ivanova O, Gerasymenko V, Boyko Z, Voilleque P, Drozdovitch V, Bouville A (2014) Thyroid cancer study among Ukrainian children exposed to radiation after the Chornobyl accident: improved estimates of the thyroid doses to the cohort members. Health Phys 106:370–396

    Google Scholar 

  30. Likhtarov IA, Kovgan LM, Chepurny MI, Masiuk SV (2015) Interpretation of results of radioiodine measurements in thyroid for residents of Ukraine (1986). Probl Radiat Med Radiobiol 20:185–203

    Google Scholar 

  31. Little MP, Kukush AG, Masiuk SV, Shklyar SV, Carroll RJ, Lubin JH, Kwon D, Brenner AV, Tronko MD, Mabuchi K, Bogdanova TI, Hatch M, Zablotska LB, Tereschenko VP, Ostroumova E, Bouville AC, Drozdovitch V, Chepurny MI, Kovgan LN, Simon SL, Shpak VM, Likhtarev IA (2014) Impact of uncertainties in exposure assessment on thyroid cancer risk among Ukrainian children and adolescents exposed from the Chornobyl accident. PLoS ONE 9(1):e85723

    ADS  Google Scholar 

  32. Manual D (1986) Geological scintillation device SRP-68: technical description and user manual. Electron, Zheltye Vody ((in Russian))

    Google Scholar 

  33. Masiuk S, Shklyar S, Kukush A (2013) Berkson errors in radiation dose assessments and their impact on radiation risk estimates. Probl Radiat Med Radiobiol 18:25–29

    Google Scholar 

  34. Masiuk SV, Shklyar SV, Kukush AG, Carroll RJ, Kovgan LN, Likhtarov IA (2016) Estimation of radiation risk in presence of classical additive and Berkson multiplicative errors in exposure doses. Biostatistics 17:422–436

    MathSciNet  Google Scholar 

  35. Masiuk SV, Kukush AG, Shklyar SV, Chepurny MI, Likhtarov IA (2017) Radiation risk estimation: based on measurement error models. De Gruyter Series in Mathematics and Life Sciences, vol 5. Walter de Gruyter GmbH, Berlin

    MATH  Google Scholar 

  36. Masiuk S, Buderatska V, Chepurny M, Ivanova O, Boiko Z, Drozdovitch V (2020) Thyroid doses in Ukraine due to 131I intake after the Chornobyl accident. Report II: Revision of doses for the Ukrainian-American cohort of exposed children and associated uncertainties. Radiat Environ Biophys (in preparation)

  37. MH – Ministry of Health of the USSR (1986) Temporary permissible levels of radionuclides in food and drinking water. Resolution of Chief Medical Officer# 4104–86, 6 May 1986. Ministry of Health of the USSR, Moscow ((in Russian))

    Google Scholar 

  38. Molina EC (1973) Poisson’s exponential binomial limit. Krieger Pub Co, New York

    Google Scholar 

  39. Pitkevich VA, Khvostunov IK, Shishkanov NK (1996) Influence of dynamics of 131I fallout due to the ChNPP accident on value of absorbed doses in thyroid for population of Bryansk and Kaluga regions of Russia. Radiat Risk 7:192–215 ((in Russian))

    Google Scholar 

  40. Powers JG, Klemp JB, Skamarock WC, Davis CA, Dudhia J, Gill DO, Coen JL, Goghis DJ, Ahmadov R, Peckham SE, Grell GA, Michalakes J, Trahan S, Benjamin SG, Alexander CR, Dimego GJ, Wang W, Schwartz CS, Romine GS, Liu Z, Snyder C, Chen F, Barlage MJ, Yu W, Duda MG (2017) The Weather Research and Forecasting model: overview, system efforts, and future directions. Bull Amer Meteor Soc 98:1717–1737

    ADS  Google Scholar 

  41. Simon SL, Hoffman FO, Hofer E (2015) The two-dimensional Monte Carlo: a new methodologic paradigm for dose reconstruction for epidemiological studies. Radiat Res 183:27–41

    ADS  Google Scholar 

  42. Stezhko VA, Buglova EE, Danilova LI, Drozd VM, Krysenko NA, Lesnikova NR, Minenko VF, Ostapenko VA, Petrenko SV, Polyanskaya ON, Rzheutski VA, Tronko MD, Bobylyova OO, Bogdanova TI, Ephstein OV, Kairo IA, Kostin OV, Likhtarev IA, Markov VV, Oliynik VA, Shpak VM, Tereshchenko VP, Zamotayeva GA, Beebe GW, Bouville AC, Brill AB, Burch JD, Fink DJ, Greenebaum E, Howe GR, Luckyanov NK, Masnyk IJ, McConnell RJ, Robbins J, Thomas TL, Voillequé PG, Zablotska LB, Chornobyl Thyroid Diseases Study Group of Belarus, Ukraine, and the USA (2004) A cohort study of thyroid cancer and other thyroid diseases following the Chornobyl accident: objectives, design, and methods. Radiat Res 161:481–492

    ADS  Google Scholar 

  43. Talerko N (2005) Reconstruction of (131)I radioactive contamination in Ukraine caused by the Chernobyl accident using atmospheric transport modelling. J Environ Radioact 84:343–362

    Google Scholar 

  44. Talerko MM, Lev TD, Drozdovitch VV, Masiuk SV (2020) Reconstruction of radioactive contamination of the territory of Ukraine by Iodine-131 in the initial period of the Chornobyl accident using the results from numerical WRF model. Probl Radiac Med Radiobiol (submitted)

  45. Tronko MD, Howe GR, Bogdanova TI, Bouville AC, Epstein OV, Brill AB, Likhtarev IA, Fink DJ, Markov VV, Greenebaum E, Olijnyk VA, Masnyk IJ, Shpak VM, McConnell RJ, Tereshchenko VP, Robbins J, Zvinchuk OV, Zablotska LB, Hatch M, Luckyanov NK, Ron E, Thomas TL, Voilleque PG, Beebe GW (2006) A cohort study of thyroid cancer and other thyroid diseases after the Chornobyl accident: thyroid cancer in Ukraine detected during first screening. JNCI 98:897–903

    Google Scholar 

  46. Tronko M, Brenner A, Bogdanova T, Shpak V, Hatch M, Oliynyk V, Cahoon EK, Drozdovitch V, Little MP, Tereshchenko V, Zamotayeva G, Terekhova G, Zurnadzhi L, Hatch M, Mabuchi K (2017) Thyroid neoplasia risk is increased nearly 30 years after the Chernobyl accident. Int J Cancer 141:1585–1588

    Google Scholar 

  47. Ulanovsky AV, Eckerman KF (1998) Modification of ORNL phantom series in simulation of the responses of thyroid detectors. Radiat Prot Dosim 79:429–432

    Google Scholar 

  48. Ulanovsky A, Drozdovitch V, Bouville A (2004) Influence of radionuclides distributed in the whole body on the thyroid dose estimates obtained from direct thyroid measurements made in Belarus after the Chernobyl accident. Radiat Prot Dosim 112:405–418

    Google Scholar 

  49. United Nations Scientific Committee on the Effects of Atomic Radiation (2011) UNSCEAR 2008 Report. Annex D: Health effects due to radiation from the Chernobyl accident. Sales No. E.11.IX.3. United Nations, New York

    Google Scholar 

  50. Venturini L (2003) Evaluation of systematic errors in thyroid monitoring. Radiat Prot Dosim 103:63–68

    Google Scholar 

  51. Vilardi I, Antonacci G, Battisti P, Bortoluzzi S, Castellani C-M, Contessa GM, Di Marco N, Giardina I, Iurlaro G, La Notte G, Sperandio L, Zicari S (2018) Large-scale individual thyroid monitoring following nuclear accidents by means of non-spectrometric devices. J Radiol Prot 38:1454–1468

    Google Scholar 

  52. Yunoki A (2019) Uncertainty of measurement in the response test of a thyroid monitor. Radiat Prot Dosim 184:531–534

    Google Scholar 

  53. Zvonova IA, Balonov MI, Bratilova AA, Baleva GE, Gridasova SA, Mitrokhin MA, Sazhneva VP (1997) Thyroid absorbed dose estimations for population of the Bryansk, Tula, Orel regions according to results of radiometry in 1986. Radiat Risk 10:96–117 ((in Russian))

    Google Scholar 

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This paper is dedicated to the memory of the late Ilya Likhtarov who created the thyroid dosimetry system for the Ukrainian population based on the measurements of 131I thyroid activity. We would gratefully like to acknowledge the contributions of André Bouville, Lionella Kovgan, and Paul Voillequé at different stages of the 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.


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.

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Correspondence to Vladimir Drozdovitch.

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Appendix. Errors in measured 131I thyroid activities

Appendix. Errors in measured 131I thyroid activities

Estimation of classical measurement errors for 131I 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:

$${I}_{\mathrm{th}}^{\mathrm{meas}}\sim N\left({I}_{\mathrm{th}}^{\mathrm{tr}},{\sigma }_{\mathrm{th}}^{2}\right),{I}_{\mathrm{bg}}^{\mathrm{meas}}\sim N\left({I}_{\mathrm{bg}}^{\mathrm{tr}},{\sigma }_{\mathrm{bg}}^{2}\right),$$

where \(N(m,{\sigma }^{2})\) is a normal distribution with expectation value \(m\) and variance \({\sigma }^{2}\), \({I}_{\mathrm{th}}^{\mathrm{meas}}\) and \({I}_{\mathrm{bg}}^{\mathrm{meas}}\) 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, \({\sigma }_{\mathrm{th}}^{2}=\frac{{I}_{\mathrm{th}}^{\mathrm{tr}}}{{t}_{\mathrm{th}}}\) and \({\sigma }_{\mathrm{bg}}^{2}=\frac{{I}_{\mathrm{bg}}^{\mathrm{tr}}}{{t}_{\mathrm{bg}}}\) are the variances of corresponding measurement errors, \({t}_{\mathrm{th}}\) is the duration of a thyroid measurement, and \({t}_{\mathrm{bg}}\) 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 \({I}_{\mathrm{th}}^{\mathrm{meas}}\) and \({I}_{\mathrm{bg}}^{\mathrm{meas}}\) include an instrumental error, with variance \({\sigma }_{\mathrm{dev}}^{2}\). The full variances of the measurement errors for both thyroid and background are as follows:

$${\widehat{\sigma }}_{\mathrm{th}}^{2}=\frac{{I}_{\mathrm{th}}^{\mathrm{meas}}}{{t}_{\mathrm{th}}}+{\sigma }_{\mathrm{dev}}^{2}\mathrm{ and }{\widehat{ \sigma }}_{\mathrm{bg}}^{2}=\frac{{I}_{\mathrm{bg}}^{\mathrm{meas}}}{{t}_{\mathrm{bg}}}+{\sigma }_{\mathrm{dev}}^{2}.$$

Based on the calibration method used one can write down the approximate relation:

$${C}_{a}^{\mathrm{meas}}\approx {C}_{a}^{\mathrm{tr}}\bullet \left(1+{\delta }_{C}\bullet {\gamma }_{1}\right),\hspace{1em}{\gamma }_{1}\sim N\left(\mathrm{0,1}\right),$$

where \({C}_{a}\) is the conversion coefficient (Eq. 2) and \({\delta }_{C}\) is the relative error of the conversion coefficient, which includes the error of the 131I activity in the bottle source used for the device calibration, the device’s error of the measurement, and the error of the age-dependent factor \(G\).

Using Eqs. (A1)‒(A3), 131I activity in the thyroid estimated from the direct thyroid measurement (see Eq. 1) can be presented as:

$${Q}^{\mathrm{meas}}\approx {C}_{a}^{\mathrm{tr}}\bullet \left(1+{\delta }_{C}\bullet {\gamma }_{1}\right)\bullet \left({I}_{\mathrm{th}}^{\mathrm{tr}}-{f}_{\mathrm{sh}}\bullet {I}_{\mathrm{bg}}^{\mathrm{tr}}+{\sigma }_{n}\bullet {\gamma }_{2}\right),$$

where \({\sigma }_{n}=\sqrt{{\widehat{\sigma }}_{\mathrm{th}}^{2}+{f}_{\mathrm{sh}}^{2}\bullet {\widehat{\sigma }}_{\mathrm{bg}}^{2}}\) and \({\gamma }_{2}\sim N(\mathrm{0,1})\).

Then, Eq. (A4) can be written as:

$${Q}^{\mathrm{meas}}\approx {C}_{a}^{\mathrm{tr}}\left({I}_{\mathrm{th}}^{\mathrm{tr}}-{f}_{\mathrm{sh}}\bullet {I}_{\mathrm{bg}}^{\mathrm{tr}}+\left({I}_{\mathrm{th}}^{\mathrm{tr}}-{f}_{\mathrm{sh}}\bullet {I}_{\mathrm{bg}}^{\mathrm{tr}}\right){\delta }_{C}\bullet {\gamma }_{1}+{\sigma }_{n}{\bullet \gamma }_{2}+{\delta }_{C}\bullet {\sigma }_{n}\bullet {\gamma }_{1}\bullet {\gamma }_{2}\right).$$

Because \({Q}^{\mathrm{tr}}={C}_{a}^{\mathrm{tr}}\bullet ({I}_{\mathrm{th}}^{\mathrm{tr}}-{f}_{\mathrm{sh}}\bullet {I}_{\mathrm{bg}}^{\mathrm{tr}})\), Eq. (A5) can be expressed as:

$${Q}^{\mathrm{meas}}\approx {Q}^{\mathrm{tr}}+{C}_{a}^{\mathrm{tr}}\bullet \left({\sigma }_{n}\bullet {\gamma }_{2}+\left({I}_{\mathrm{th}}^{\mathrm{tr}}-{f}_{\mathrm{sh}}\bullet {I}_{\mathrm{bg}}^{\mathrm{tr}}\right)\bullet {\delta }_{C}{\bullet \gamma }_{1}+{\delta }_{C}\bullet {\sigma }_{n}\bullet {\gamma }_{1}\bullet {\gamma }_{2}\right)\approx {Q}^{\text{tr}}+{\sigma }_{Q}^{\mathrm{tr}}\bullet \gamma ,$$

where \({\sigma }_{Q}^{\mathrm{tr}}={C}_{a}^{\mathrm{tr}}\bullet \sqrt{{\sigma }_{n}^{2}+{\sigma }_{n}^{2}\bullet {\delta }_{C}^{2}+({I}_{\mathrm{th}}^{\mathrm{tr}}-{f}_{\mathrm{sh}}\bullet {I}_{\mathrm{bg}}^{\mathrm{tr}}{)}^{2}\bullet {\delta }_{C}^{2}}\) and \(\gamma \sim N(\mathrm{0,1})\).

As \({I}_{\mathrm{th}}^{\mathrm{tr}}\) and \({I}_{\mathrm{bg}}^{\mathrm{tr}}\) are unknown, \({\sigma }_{Q}^{\mathrm{tr}}\) can be written as:

$${\sigma }_{Q}^{\mathrm{meas}}={C}_{a}^{\mathrm{meas}}\bullet \sqrt{{\sigma }_{n}^{2}+{\sigma }_{n}^{2}\bullet {\delta }_{C}^{2}+({I}_{\mathrm{th}}^{\mathrm{meas}}-{f}_{\mathrm{sh}}\bullet {I}_{\mathrm{bg}}^{\mathrm{meas}}{)}^{2}\bullet {\delta }_{C}^{2}}.$$

The error factor \({\delta }_{C}\) of the age-dependent conversion coefficient \({C}_{a}\), (Eq. 2) can be calculated as:

$${\delta }_{C}=\sqrt{{\delta }_{b}^{2}+{\delta }_{G}^{2}},$$

where \({\delta }_{b}\) is the relative error factor of the device’s calibration using a bottle phantom, and \({\delta }_{G}\) 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 \({I}_{\mathrm{ref}}^{\mathrm{meas}}-{I}_{\mathrm{bg}}^{\mathrm{meas}}\) caused by radioactivity \({Q}_{\mathrm{ref}}\) of a reference radiation source. Therefore, \({\delta }_{b}\) is specified as:

$${\delta }_{b}=\sqrt{{\delta }_{\mathrm{ref}}^{2}+{\left(\frac{{\sigma }_{S}}{{I}_{\mathrm{ref}}-{I}_{\mathrm{bg}}}\right)}^{2}},$$

where \({\delta }_{\mathrm{ref}}\) 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”); \({\sigma }_{S}\) 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 \({\sigma }_{S}\) can be calculated as:

$${\sigma }_{S}=\sqrt{{\widehat{\sigma }}_{\mathrm{ref}}^{2}+{\widehat{\sigma }}_{\mathrm{bg}}^{2}},$$

where \({\widehat{\sigma }}_{\mathrm{ref}}^{2}=\frac{{I}_{\mathrm{ref}}^{\mathrm{meas}}}{{t}_{\mathrm{ref}}}+{\sigma }_{\mathrm{dev}}^{2}\) is the error variance of measuring the intensity of the reference source during the measurement time \({t}_{\mathrm{ref}}\).

For devices with missing information about the calibration, \({\delta }_{b}\) was, based on expert judgement, estimated to be 30%. The value of the relative error factor \({\delta }_{G}\) 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 \({\delta }_{G}\) 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:

$${Q}^{\mathrm{meas}}={Q}^{\mathrm{tr}}+{\sigma }_{Q}^{\mathrm{meas}}\bullet \gamma .$$


Measurements of 131I 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 \({I}_{\mathrm{th}}^{\mathrm{tr}}-{f}_{\mathrm{sh}}{\bullet I}_{\mathrm{bg}}^{\mathrm{tr}}\ge 0.68\bullet {\sigma }_{n}\), where \({\sigma }_{n}\) is defined by Eq. (A4), i.e., the critical limit of 131I in the thyroid was accepted to be \(0.68\bullet {\sigma }_{n}\). The result of a measurement providing less than the critical limit was replaced by half of the critical limit. It was accepted that \({I}_{\mathrm{th}}^{\mathrm{tr}}-{f}_{\mathrm{sh}}\bullet {I}_{\mathrm{bg}}^{\mathrm{tr}}=0.34\bullet {\sigma }_{n}\) under the condition \({I}_{\mathrm{th}}^{\mathrm{tr}}-{f}_{\mathrm{sh}}\bullet {I}_{\mathrm{bg}}^{\mathrm{tr}}<0.68\bullet {\sigma }_{n}\).

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, 2017) arising from deviation of the 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 \(G{F}_{j}\) 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 \(G{F}_{j}\) is equal to unity for the proper measurement geometry, i.e., \({\left.G{F}_{j}\right|}_{S=0}=1.\) Then \(G{F}_{j}\) can be approximated by a function which is quadratic in the shift S:

$$G{F}_{j}={a}_{j}{\bullet S}^{2}+{b}_{j}\bullet S+1.$$

Model of mixed classical and Berkson errors in thyroid measurements

Factors that are characterized by uncertainty of Berkson type are denoted as:

$${F}_{ij}=G{F}_{ij}\bullet {AF}_{j}^{\mathrm{meas}},$$

where \(G{F}_{ij}\) 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; \({AF}_{j}^{\mathrm{meas}}\) 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:

$${A}_{ij}^{\mathrm{meas}}={F}_{ij}^{\mathrm{meas}}{\bullet Q}_{i}^{\mathrm{meas}},$$

where \({Q}_{i}^{\mathrm{meas}}\) is the measured 131I thyroid activity associated with the classical additive error (Eq. (A11)).

The unknown true radioactivity \({A}_{i}^{\mathrm{tr}}\) is expressed as:

$${A}_{ij}^{\mathrm{tr}}={F}_{ij}^{\mathrm{tr}}{\bullet Q}_{i}^{\text{tr}}.$$

The connection between \({F}_{ij}^{\mathrm{tr}}\) and \({F}_{ij}^{\mathrm{meas}}\) is determined by a Berkson multiplicative error:

$${F}_{ij}^{\mathrm{tr}}={F}_{ij}^{\mathrm{meas}}\cdot {\delta }_{F,ij},$$

where error \({\delta }_{F,ij}\) has a log-normal distribution \(\mathrm{log}({\delta }_{F,ij})\sim N(-\frac{{\sigma }_{F,ij}^{2}}{2},{\sigma }_{F,ij}^{2})\) with an expectation value \({\varvec{E}}{\delta }_{F,ij}=1\); \({F}_{ij}^{\mathrm{meas}}\) and \({\delta }_{F,ij}\) are stochastically independent, and \({\sigma }_{F,ij}^{2}\) is the variance of \(\mathrm{log}({\delta }_{F,ij})\). Values of \({F}_{ij}^{\mathrm{meas}}\) and \({\sigma }_{F,ij}^{2}\) can be obtained by the two-dimensional Monte Carlo procedure described in (Simon et al. 2015).

According to Eq. (A11), the measured 131I activity in the thyroid, \({Q}_{i}^{\mathrm{meas}}\), can be expressed as:

$${Q}_{i}^{\mathrm{meas}}={Q}_{i}^{\mathrm{tr}}+{\sigma }_{Q,i}^{\mathrm{meas}}\bullet {\gamma }_{i},\hspace{1em}i=1,...,N,$$

where \({\gamma }_{1},...,{\gamma }_{N}\) are the independent standard normal variables; \({\sigma }_{Q,i}^{\mathrm{meas}}\) are the individual standard deviations of errors of direct thyroid measurements that were estimated according to Eq. (10). The values \({\sigma }_{Q,i}^{\mathrm{meas}}\bullet {\gamma }_{i}\) and \({Q}_{i}^{\text{tr}}\) are independent random variables.

Substituting Eqs. (A17)–(A15) and denoting \({\overline{A}}_{ij}^{\mathrm{tr}}={F}_{ij}^{\mathrm{meas}}{\bullet Q}_{i}^{\mathrm{tr}}\) results in:

$${A}_{ij}^{\mathrm{meas}}={F}_{ij}^{\mathrm{meas}}\bullet {Q}_{i}^{\mathrm{meas}}={F}_{ij}^{\mathrm{meas}}\bullet \left({Q}_{i}^{\mathrm{tr}}+{\sigma }_{Q,i}^{\mathrm{meas}}\bullet {\gamma }_{i}\right)={F}_{ij}^{\mathrm{meas}}\cdot {Q}_{i}^{\mathrm{tr}}+{F}_{ij}^{\mathrm{meas}}\bullet {\sigma }_{Q,i}^{\mathrm{meas}}\bullet {\gamma }_{i}.$$

Random variables \(\{{\delta }_{F,ij},i\ge 1\}\), \(\{{\gamma }_{i},i\ge 1\}\) and random vectors \(\{({F}_{i}^{\mathrm{meas}},{Q}_{i}^{\mathrm{tr}}),i\ge 1\}\) are jointly independent, but \({F}_{i}^{\mathrm{meas}}\) and \({Q}_{i}^{\mathrm{tr}}\) can be correlated. If the notations \({\sigma }_{ij}={F}_{ij}^{\mathrm{meas}}\bullet {\sigma }_{Q,i}^{\mathrm{meas}}\) and \({\overline{A}}_{ij}^{\mathrm{tr}}={F}_{ij}^{\mathrm{meas}}\cdot {Q}_{i}^{\mathrm{tr}}\) are introduced, Eqs. (A14) – (A18) become the following:

$${A}_{ij}^{\mathrm{meas}}={\overline{A}}_{ij}^{\mathrm{tr}}+{\sigma }_{ij}{\bullet \gamma }_{i},$$
$${A}_{ij}^{\mathrm{tr}}={\overline{A}}_{ij}^{\mathrm{tr}}{\bullet \delta }_{F,ij}.$$

Equations (A19) and (A20) compose a dose observations model with a classical additive error and a Berkson multiplicative error (Masiuk et al. 2016, 2017).

Finally, the relationship between expectations of true radioactivity and radioactivity measured with Berkson error can be expressed as:


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Masiuk, S., Chepurny, M., Buderatska, V. et al. Thyroid doses in Ukraine due to 131I intake after the Chornobyl accident. Report I: revision of direct thyroid measurements. Radiat Environ Biophys 60, 267–288 (2021).

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  • Chornobyl
  • Chernobyl
  • Radiation exposure
  • Thyroid dose
  • Iodine-131 measurement
  • Classical error
  • Berkson error