Influence of the external and internal radioactive contamination of the body and the clothes on the results of the thyroidal ¹³¹I measurements conducted in Belarus after the Chernobyl accident—Part 2: Monte Carlo simulation of response of detectors near the thyroid

Abstract

This paper describes the calculation of the response of the most common types of radiation detectors that were used within the first few weeks after the Chernobyl accident to determine the activity of ¹³¹I in the thyroids of Belarusian subjects of an epidemiologic study of thyroid cancer. The radiation detectors, which were placed against the necks of the subjects, measured the exposure rates due to the emission of gamma rays resulting from the radioactive decay of ¹³¹I in their thyroids. Because of the external and internal radioactive contamination of the monitored subjects, gamma radiation from many radionuclides in various locations contributed to the exposure rates recorded by the detectors. To estimate accurately the contribution from gamma rays emitted from various internal and external parts of the body, the calibration factors of the radiation detectors, expressed in kBq per µR h^− 1, were calculated, by means of Monte Carlo simulation, for external irradiation from unit activities of 17 radionuclides located on 19 parts of the body, as well as for internal irradiation from the same 17 radionuclides in the lungs, from caesium radionuclides distributed uniformly in the whole body, and from ¹³¹I in the thyroid. The calculations were performed for six body sizes, representative of the age range of the subjects. In a companion paper, the levels of external and internal contamination of the body were estimated for a variety of exposure conditions. The results presented in the two papers were combined to calculate the ¹³¹I activities in the thyroids of all 11,732 Belarusian study subjects of an epidemiologic study of thyroid cancer and, in turn, their thyroid doses.

Appendix: Technique to accelerate Monte Carlo calculations for a radiation source uniformly distributed on a curved surface

Local weight procedure

To accelerate Monte Carlo calculations for a radiation source uniformly distributed on a body surface, a special procedure was developed that uses the local weight of the particle.

A uniformly contaminated curved surface area can be presented as a sum of elementary surface sources with activity proportional to their area. The weight w of each elementary surface source (weight of the particle) is determined by dividing its area by the total area of all elementary sources of a given area. In the proposed variant, the value of w is not a constant for the particle in the given cell but is proportional to the area of the surface element dσ(x,y,z) in photon position (x,y,z). If the surface is given parametrically r = r (u, v) (u, v are the coordinates given on the surface), then the area element dσ on it can be written as dσ = w_L × du × dv, where w_L can be used as the local weight of the particle at the point u, v on the surface.

Using equations of differential geometry (Korn and Korn 1968), the local weights for each type of body surface were found to be:

$${\text{right circular cylinder }}\left( {{\text{regions }}3 - 6,{\text{ }}u=\varphi ,v=z} \right):\quad {w_L}=r$$

(9)

$$\begin{gathered} {\text{ellipsoid }}\left( {{\text{region }}1,{\text{ }}u=\varphi ,{\text{ }}v=\theta } \right): \hfill \\ {w_L}=\sqrt {{a^2} \times {b^2} \times {\text{co}}{{\text{s}}^2}\theta +{c^2} \times {\text{si}}{{\text{n}}^2}\theta \times \left( {{a^2} \times {\text{si}}{{\text{n}}^2}\varphi +{b^2} \times {\text{co}}{{\text{s}}^2}\varphi } \right)} \hfill \\ \end{gathered} $$

(10)

$${\text{elliptic cylinder }}\left( {{\text{regions }}2,9 - 16,18,19,{\text{ }}u=\varphi ,{\text{ }}v=z} \right):~{w_L}=\sqrt {{a^2}+\left( {{b^2} - {a^2}} \right) \times {\text{co}}{{\text{s}}^2}\theta } $$

(11)

$$~{\text{parabolic cylinder }}\left( {{\text{regions }}7,8,17,{\text{ }}u=y,{\text{ }}v=z} \right):{w_L}=\sqrt {1+4 \times b_{{{\text{sh}}}}^{2} \times {{\left( {y - {y_{0{\text{sh}}}}} \right)}^2}} $$

(12)

where θ and φ are the polar and azimuth angles, respectively. The azimuth angle was uniformly sampled in the interval (0,2π), while for the polar angle the quantity cosθ was uniformly sampled in corresponding sectors.

In Eqs. (10)–(12), a, b, and c are the semi-axes of the relevant ellipsoids or elliptic cylinders, and r is the radius of right circular cylinder, in particular:

$$\begin{gathered} {\text{region }}1\quad a={a_{\text{h}}},\;b={b_{\text{h}}},\;c={c_{{\text{h}}2}} \hfill \\ {\text{regions }}2,18,19\quad a={a_{\text{h}}},\;b={b_{\text{h}}} \hfill \\ {\text{areas }}3 - 6\quad r={r_n} \hfill \\ {\text{areas }}9 - 16\quad a={a_{\text{t}}},\;b={b_{\text{t}}}, \hfill \\ \end{gathered} $$

(13)

where a_t and b_t are the body semi-axes, a_h and b_h are the head semi-axes, c_h2is the height of the elliptic head top, b_sh, y_0sh are parameters in Eq. 12 describing the parabolic shape of the trunk (Ulanovsky and Eckerman 1998), r_n is the radius of the neck. Values of parameters for the family of ORNL human phantoms are given in Table 10. The family of ORNL human phantoms is represented as erect with the position z-axis directed upward toward the head. The x-axis is directed to the phantom’s left, and the y-axis is directed toward the posterior side of the phantom. The origin is taken at the center of the base of the trunk section of the phantom.

Table 10 Age-dependent parameters of body parts for the family of ORNL human phantoms (Cristy and Eckerman 1987)

The result for a surface under consideration (tally in MCNP) was normalized to the sum of local weights for this surface. The validity of this procedure of using local weights was verified for regular surfaces such as sphere and circular cylinder, by comparison with the built-in MCNP values.

Auxiliary means for improvement of calculation efficiency

It should be noted that the variance reduction technique cannot be applied to the spectrum tally F8 usually used for the SRP-68-01 device with a scintillation detector. For the DP-5 it was necessary to use flux tally (F1 in MCNP) instead of the spectrum (F8 in MCNP) and specify the relative cells importance in the sample problem to help particles move more easily to the important regions of the geometry. Such variance reduction technique for the DP-5 is matched with the FORTRAN sub-routine “source.f” which was developed for the implementation of the local weights approach.

To process the information from the MCNP results, a special script, written in Perl language, was developed. This script arranges a cycle by desired energies from the list, inserting the required energy (and the corresponding number of histories) at each step of the cycle into the same input file. As soon as the MCNP code calculated the response function, the Perl script prepared a two-dimensional array (energy, response function) which was ready for use to calculate the calibration factor.