Radiation and Environmental Biophysics
External dose reconstruction in tooth enamel of Techa riverside residents
Shishkina EA1, Volchkova AYu1, Timofeev Yu.S1,2., Fattibene P3, Wieser A4, Ivanov DV5,6, Krivoschapov VA1, Zalyapin VI2, Della Monaca S3., De Coste V3, Degteva MO1, Anspaugh LR7
1 Urals Research Center for Radiation Medicine, 68A, Vorovsky Str., 454076 Chelyabinsk, Russia
2. Southern Urals State University, 76, Lenin Av., 454080 Chelyabinsk, Russia
3 IstitutoSuperiorediSanità and IstitutoNazionale di FisicaNucleare, Viale Regina Elena 299, 00161 Rome, Italy
4 Helmholtz ZentrumMünchen, German Research Centre for Environmental Health, 85764 Neuherberg, Germany
5 M.N. Mikheev Institute of Metal Physics, Ural Division of the Russian Academy of Sciences, 18 S. Kovalevskaya Street, Ekaterinburg, Russia 620990
6. Urals Federal University, 19 Mira Str, 620002 Yekaterinburg, Russia
7. University of Utah, 201 Presidents circle,Salt Lake City 84112, UT, US
Corresponding author: Shishkina EA
Urals Research Center for Radiation Medicine, 68A, Vorovsky Str., 454076 Chelyabinsk, Russia
Tel. +7351 2327919
Fax. +7351 2327913
Calculation of internal dose of incorporated 90Sr: supplementary justification of the basic assumptions
The basic equation for internal dose calculation in the tooth enamel (Eq in Fig.S1) is based on two sets of assumptions, viz., geometric and biokinetic.
Dose coefficients (DCs) were calculated using Monte Carlo simulation of electron-photon transport, with electron emissions from 90Sr and 90Y decays (assumed to be in secular equilibrium). The calculations were performed in the framework of several studies using the Cascade-5 code (Shved and Shishkina, 2000; Tolstykh et al., 2000; Shishkina et al., 2001), the MCNP code version 4C (Tikunov et al., 2006), the MCNP code version 4C-2 (Volchkova et al., 2009; Shishkina et al, 2010), and the CYLTRAN code from the Integrated Tiger Series (ITS), version 3.0 (Zeltzer et al., 2001). The coupled electron-photon transport physics in these codes takes into account the diffusion and slowing down of all radiation types in the electron-photon cascade whiсh was established in heterogeneous media in a rather accurate way. All results are based on a sample of more than 40 million histories of emitted beta particles.
Fig S1 Basic equation for internal dose calculation in tooth enamel due toincorporated 90Sr, where i is the radionuclide location (enamel, some fraction of crown dentin, or root dentin adjacent to crown); DC is the shape-dependent dose coefficient depending also onthe specific source location (tooth shape may be dependent on time (t), birth year (T) and tooth position (p)); τm is the time of enamel exposure from the beginning of intakes to the year of EPR measurement; is the intake function for a specific radionuclide location; and is the rate of a time dependent decrease in radionuclide activity concentration due to both radioactive decay and biological elimination.
Calculations with different Monte Carlo codes were compared using test simulations of the energy deposition in the tooth enamel due to 90Sr/90Y uniformly distributed in the dentin volume. It turned out that the different MC calculations differed only slightly,due to individual approaches how the chemical composition was described and how many energy bins (consecutive, non-overlapping energy intervals for the description of both 90Sr and 90Y electron spectra) were used. The details of the comparison were presented in Shishkina et al (2002). It has been shown that the differences in the description of the chemical tooth-tissue composition and the bin number describing the decay-energy distribution, introduce uncertaintieswhich do not exceed 4%.
According to the definition,DC is a value of dose rate calculated per unit of activity concentration of both parent and progeny radionuclides. However, the values of radionuclide activity concentrations, , are traditionally expressed in terms of parental radionuclide, 90Sr, only. Therefore, recalculation of to the 90Sr/90Y activity concentration (assumed in secular equilibrium) was done by the use of a factor of 2 (see Eq. in Fig. S1).
FigureS2 presents the evolution of geometrical models of teeth. Initially, the posterior teeth were simply modeled as two concentric cylinders: the inner cylinder composed of dentin, and the outer cylindrical shell composed of enamel.Anterior teeth / Posterior teeth
I. / /
II. / /
III. / /
Fig S2 Evolution of geometrical models of teeth: (I) simple mathematical phantoms (Shved and Shishkina, 2000); (II) refined mathematical phantoms (Tikunov et al., 2006; Krusheva et al., 2008); (III) voxel phantoms (Volchkova et al., 2009; Volchkova, 2014).
Anterior teeth were described as a system of parallel plates: enamel-dentine-enamel (Shved and Shishkina, 2000; Tolstykh et al., 2000; Shishkina et al., 2001). The cylindrical approach was determined due to limitations of the Cascade-5 program (Lappa and Bourmistrov, 1994). However, such an approach allows one to take advantage of the cylindrical symmetry, which makes the calculations much more efficient. The cylindrical approaches were also used for tooth crown modeling in Zeltzer et al (2001). The results were expected to be applicable mainly to teeth, whose shapes are similar to cylinders, such as molars or premolars. The use of the MCNP code allowed to improve the description of the tooth geometry (Tikunov et al., 2006; Volchkova et al., 2009), that was specifically important for incisors.
The sizes of teeth with different positions in the denture were measuredfor rural residents of the Urals (Shved and Shishkina, 2000; Volchkova and Shishkina, 2013). Additionally,a 3 mm layer of the tooth root (about 99% of the decay energy of electrons from 90Sr/90Y decay would be absorbed in the linear approximation of the energy transfer) adjacent to the crown base was taken into consideration.
The individual variability of tooth tissue geometry was preliminarily tested based on the simple cylindrical approach and using a uniform radionuclide distribution in the tooth tissues (Shved and Shishkina, 2000). It was shown that variation in enamel thickness result in dose rate variations, which are not exceeding 6% of the enamel self-exposure and 15% of the enamel exposure tothe dentin. The variability of dentin dimensions can be the cause of a more significant uncertainty. The cylindrical model without the pulp area (phantoms of generation I) can lead to a 20% underestimation of the dose rate in the enamel (Shishkina et al, 2002). The radionuclide activity in the dentin of such models was distributed in a larger volume as compared to the phantoms of the next generation (with pulp cavity). Accordingly, the activity concentration was lower.
The second generation phantoms divided the dentin into two fractions: primary and secondary. The primary dentin is the dentin formed in a tooth before the completion of the apical foramen of the root, while the secondary dentin is formed after the root formation is finished. It should be noted that the volume of the secondary dentin is age-dependent because the dentin grows inwards to fill the pulp cavity. The shapes of the incisors are also age-dependent due to mechanical attrition. Therefore, the third generation phantoms represent a set of phantoms typical of specific tooth position and of different ages.
The first dose calculations (Shved and Shishkina, 2000) used maximum simplification by assuming a uniform radionuclide distribution in enamel, whole dentine, root section adjacent to crown and, additionally, the contribution of the alveolar bone was tested (Fig. S2, generation I).
The possibility to use the approximation of a uniform radionuclide distribution in the tooth tissues was then tested in the experiment with an adult dog (Shishkina, 1998; Shishkina et al., 2001) which was given an injection of 88.8 MBq of 90Sr solution, and then sacrificed at a stage of the maximum 90Sr accumulation in the skeleton (52h after the injection). Then, the enamel of four teeth was measured by means of EPR;tooth tissues were sampled in radial direction to investigate the distribution of 90Sr activity concentration in the tooth body. The distribution of radionuclide concentration in the tooth tissues was also studied with 19 other teeth of the dog.As a result of this experiment it was shown, that the enamel of an adult dog (mature teeth) was contaminated uniformly. In contrast, the 90Sr activity concentration in dentin was decreasingfrom the pulp area tothe dentin-enamel junction by two orders of magnitude. The high concentration of 90Sr in the pulp was due to theshort time that had passed betweeninjection of 90Sr and measurement and, therefore, the radionuclideswere not yet eliminated from the soft tissues and the blood. The dentin layer adjacent to the pulp (secondary dentin) wasalso heavily contaminated (10-15 times higher than the enamel and its neighboring dentin layer).
To analyze the efficacy of different approaches todescribe the radionuclide distribution in the dentin, three assumptions were made inthe enamel dose calculations: (1) realistic distribution of 90Srin the dentin; (2) uniform distribution of 90Sr in the dentin using mean tissue-specific concentrations; (3) uniform 90Sr contamination of only the secondary dentin and the pulp. The third approach was achieved by recalculation of the average activity concentration, , in the whole dentine with dentinemass, md, to adjust for the activity concentration A2 in the dentin fraction with mass, m2, according to Eq. (S1).
The results were then compared with EPR measurement results (Fig.S3). As can be seen from Fig. S3 the assumption of auniform 90Sr distribution in the whole dentine of mature teeth results in a significant dose underestimation. However, both the realistic approach and the approach of theuniform contamination of the secondary dentin and pulp demonstrate a good agreement with the EPR dosimetry results. Therefore it is concluded that the assumption of a uniform 90Sr contamination of the secondary dentin is appropriate for enamel dose calculations, if 90Sr had been incorporated into the mature teeth. It could be expected that the developing teeth incorporate 90Sr mainly into the primary fraction of the dentin.
Fig.S3 Comparison of enamel dose calculated based on three different types of 90Sr distribution in dentin (bars), and EPR-derived doses (horizontal lines crossing points). Dark grey: measured radionuclide distribution; middle grey: uniform 90Sr distribution in whole dentin; light grey: uniform 90Sr distribution in secondary dentin and pulp. Error bars correspond to the dose uncertainty due to error of radionuclide measurements. Plotted based on the Shishkina et al., (2001).
It is important to consider separately the teeth, for which the main intake had been coincided with the period of enamel mineralization (less than three years after beginning of mineralization). Because enamel and a thin dentin layer adjacent to the enamel-dentine junction are formed simultaneously, 90Sr is heavily incorporated in both enamel and theneighboring dentin layer. According to autoradiography data (Rasin, 1970; Romanykha et al., 2002; Shishkina et al., 2002), the activity concentration in the enamel of such teeth is practically equal to that in thedentin layer, whose thickness is comparable to the enamel thickness.Therefore, all teeth could be subdivided into three groups depending on the maturation stage at the time of intakes:
1)Mature teeth; 90Sr is assumed to be uniformly distributed in the secondary dentin;
2)Teeth that were not mature but whose enamel had been completed (≥ three years after the beginning of mineralization); 90Sr is assumed to be uniformly distributed in the primary dentin;
3)Enamel under development (< three years after the beginning of mineralization); 90Sr is assumed to be uniformly distributed in the thin (1 mm) dentin layer adjacent to the enamel-dentine junction; and 90Sr activity concentrations in the enamel and the adjacent dentin are assumed to be equal.
In routine practice, it is impossible to separate different dentin fractions. It is much easier to measure the average 90Sr activity concentration in the whole dentin (Shishkina, 2012) and to recalculate it for the 90Sr activity concentration in the specific dentin fraction which is expected to bethe source of the exposure (Eq.S1).The mass ratios of the whole dentin and its emitting fraction (Eq.S1) were evaluated based on age-dependent tooth phantoms. These mass ratios were used to correct dose coefficients according to Eq. S2.
where is the dose rate in the enamel; is the result of Monte Carlo simulations of the enamel dose rate per unit of 90Sractivity concentration in the dentin fraction i; is the corrected dose coefficient. In this paper, the term “dose coefficient” is assumedto represent the corrected dose coefficient.
The 90Sr intakes were reconstructed for the Techa riverside residents using thousands of measurements of 90Sr content in bones performed with a whole-body counter, thousands of measurements of beta activity of front teeth performed with an "end-window" type Geiger–Müller (G-M) counter, and performed with a variety of other measurements of bioassays (Tolstykh et al., 2011). Figure S4 presents the 90Sr intake function for adult residents of Muslyumovo, which is the reference intakefunction for internal dosimetry in the Techa River Dosimetry System.
Fig.S4 Reference90Srintake function for adult residents of Muslyumovo(according to Tolstykh et al., 2011).
As can be seen in Fig.S4, the time dependence of the 90Srintakes shows a sharp peak at the time of maximum releases. For the riverside residents, the period of maximum intakes was much shorter than the period of subsequent dose accumulation in the enamel (approximately 60 years after the beginning of the intakes). Therefore, it seems reasonable to use the approximation of a single intake.Figure S5 illustrates the comparison of realistic and single intake approaches for calculation of time-dependent enamel contamination (in relative units) for adults taking also into account the radioactive decay of 90Sr.
Fig.S5 Comparisonof the realistic 90Sr intake scenario (gray solid line) and a single intake (black dashed line) approach for calculation of time-dependent enamel contamination.
The time of single intake, TA, was calculated as a weighted average (Eq.S3):
wereωkis the intake fraction correspondingto the time period, andnis the numberof the time periods from T1to T1+ n.
The areas under the two curves, which are proportional to the cumulative doses due to 90Sr intake, differ only by 0.2%. This difference is much smaller than the uncertainty of the EPR measurements. Therefore, the approximation of a single intake is considered to be quite reasonable for the Techa riverside residents.
Rate of 90Sr elimination
The assumption about the rate of biological 90Sr elimination impacts the results of the dose calculation much more than the assumption of a single 90Sr intake discussed above. Figure S6 shows the time dependence of 90Sr enamel contamination after a single intake. One curve (dashed line) takes into account only radioactive decay. The second curve (solid line) predictsa decreasein90Sr contamination due to both radioactive decay and biological elimination (assuming the rate of the eliminationbeing equal to 1.9% per year (Tolstykh et al., 2000)). In this case, the areas under the two curves, which are proportional to the corresponding cumulative doses, differ by 30%. Notethat the value of 1.9% per year was a very preliminary estimate.Thus, the assumption about the rate of biological 90Sr elimination is critical to assess the internal dose to teeth.
Fig.S6 Comparison of 90Sr enamel contamination after a single intake:(1)taking into account radioactive decay of 90Sr/90Y only; (2) assuming both the radioactive decay and metabolic elimination of 90Sr (1.9% per year).
Enamel and dentin are tissues that differ in structure, physicochemical properties and exchange mechanisms. Therefore, enamel and dentin rates of biological 90Sr elimination may also differ. The metabolic processes in enamel are determined by the non-organic ion turnover and ion transport with enamel fluid (Borovsky and Leontyev 1991).It is reasonable to assume that the incorporated90Sr is metabolically inert and its loss is mainly determined by mechanical attrition (Suga and Watabe 1992).A long-term study of beta emission from incisor enamel with an "end-window" G-M counter (Tolstykh et al, 2000) showed a decrease in the counts with time of 1.9% per year, which was more pronounced than what was expected due to the radioactive decay. Note that a study of the age dependence of incisor geometry (Volchkova and Shishkina, 2013; Volchkova,2014) revealed that the loss of enamel (due to caries and mechanical attrition) is equal to 1.8±0.4% per year. In other words, the preliminary estimate (1.9 % per year) might well reflect just the mechanical loss, and no metabolic elimination was observed.Age-dependent changes in the tooth shape were accounted for in the Monte Carlo calculations of dose coefficients (using age-specific phantoms of the 3-d generation). Therefore, the rate of 90Sr elimination from the enamel was assumed to be governed only by the radioactive decay.
The dentin that has developed is isolated from the metabolic processes to a great extent (Hoppenbrouwers et al., 1982).Therefore, the rate of the metabolic loss of 90Sr can be in the range from 0 to 1.9% per year(not exceeding the elimination rate for the compact bone, according to the ICRP (1995) Publication 70).The assumptions about the maximum and minimum possible rate of90Sr elimination from the dentin were tested by comparing EPR dosimetry results and internal dose calculations, using TL (thermoluminescence) passive detection data of 90Sr in the teeth of the Techa riverside residents. Only those teeth whose enamel had mostly been completed (≥ three years after the beginning of mineralization) but whose crowns had not erupted at the time of the intake,weretaken into consideration. The enamel of such teeth was expected to be mainly exposed to radionuclides incorporated in the primary dentin. Only seven teeth were available for the study (Table S1).
As can be seen from Table S1, the average excess of 90Sr activity concentration in the crown dentin when comparedtothe enamel is about a factor of 19 (from 1.2 - 60). It should be noted, that the teeth were exposed to both internal and external radiation. Therefore, the tooth-specific EPR doses have to be higher than, or equal (according to thet-test) to the internal doses.
Table S1 Concentration of 90Sr activity in tooth tissues of Techa riverside residents, whoseteeth were used for testing theassumptionsabout the rates of the metabolic elimination from the dentin.Tooth code / Residence at the distance from the site of releases, km / Crown age at the time of releases, years / 90Sr activity concentration in the tooth tissues, Bq/q
Enamel / Crown dentin / Root dentin
2,608 / 43 / 3 / 8.9 / 16 / 10.9
89 / 54 / 7.2 / 0.24 / 6.1 / 39.7
91 / 54 / 5.4 / 4.66 / 37.6 / 8.6
4714 / 60 / 5.2 / 0.67 / 2.1 / 20.2
116 / 78 / 4 / 0.24 / 7.36 / 62.61
204 / 78 / 4.9 / 0.3 / 18.1 / 1.65
294 / 88 / 4.7 / 1.09 / 1.29 / 35.9
In Table S2 calculated internal and measured cumulative doses in tooth enamel are compared.The uncertainties of the calculated doses include both the uncertainties of 90Sr activity concentrations in the tooth tissues, and the individual variability of the tooth shape (uncertainties of the dose coefficients). The uncertainties of the EPR doses include the measurement error, the error of harmonization, and the error of subtracted background dose (including both the error of the estimate and the individual variability of the background doses).