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A practical method for assessment of dose conversion coefficients for aquatic biota

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An Erratum to this article was published on 18 October 2006

An Erratum to this article was published on 18 October 2006

Abstract

Radiological impact assessment for flora and fauna requires adequate dosimetric data. Due to the variability of habitats, shapes, and masses of the non-human biota, assessment of doses is a challenging task. External and internal dose conversion coefficients for photons and electrons have been systematically calculated by Monte Carlo methods for spherical and ellipsoidal shapes in water medium. An interpolation method has been developed to approximate absorbed fractions for elliptical shape organisms from absorbed fractions for spherical shapes with reasonable accuracy. The method allows an evaluation of dose conversion coefficients for arbitrary ellipsoids for photon and electron sources with energies from 10 keV to 5 MeV, and for organism masses in the range from 10−6 to 103 kg. As an example of the application of the method, a set of dose coefficients for aquatic organisms discussed as reference animals and plants in a draft of an up-coming publication of the International Commission on Radiological Protection has been determined.

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Notes

  1. Following the terminology adopted in [11], electrons produced by β-decays with a continuous energy spectrum are termed β-particles, when it is necessary to distinguish them from discrete energy electrons (Auger- and conversion electrons).

  2. Hereafter, the indices E and M will be omitted, because the main interest of the study is focussed on the dependence of the re-scaling factors on the parameter η.

  3. A superellipse is a shape described by the following equation: | x/a |r + | y/b |r = 1, where r takes values in the range of [ 0, + ∞ ].

  4. The authors have numerically checked Thomsen’s approximation and found it valid for values of the scaling parameters that lie at least in the range from 10−3 to 1, which would correspond to values for η between 0.02 and 1. For a more pronounced non-sphericity, this approximation still provides reasonable accuracy. For example, if the scaling parameters vary in the range from 10−5 to 1 (min(η)≈ 10−3), the maximum error is less than 1.3%.

References

  1. ICRP (2003) A framework for assessing the impact of ionizing radiation to non-human species. ICRP publication 91. Ann ICRP 33(3):201–270

  2. Larsson C-M (2004) The FASSET framework for assessment of environmental impact of ionizing radiation in European ecosystems—an overview. J Radiol Prot 24:A1–A12

    Article  Google Scholar 

  3. Polikarpov GG (1964) Radioecology of aquatic organisms. North Holland Publishing Co., Amsterdam

    Google Scholar 

  4. Woodhead DS (1970) The assessment of the radiation dose to developing fish embryos due to accumulation of radioactivity by the egg. Radiat Res 43:582–597

    Article  Google Scholar 

  5. IAEA (1976) Effects of ionizing radiation on aquatic organisms and ecosystems. Technical report series no. 172. International Atomic Energy Agency, Vienna

  6. IAEA (1979) Methodology for assessing impacts of radioactivity on aquatic ecosystems. Technical report series no. 190. International Atomic Energy Agency, Vienna

  7. NCRP (1991) Effects on ionizing radiation on aquatic organisms. NCRP report no. 109. National Council on Radiation Protection and Measurements, Bethesda, MD

  8. Vives I Batlle J, Jones SR, and Gómez-Ros JM (2004) A method for calculation of dose per unit concentration values for aquatic biota. J Radiol Prot 24:A13–A34

    Article  Google Scholar 

  9. Taranenko V, Pröhl G, Gómez-Ros JM (2004) Absorbed dose rate conversion coefficients for reference biota for external photon and internal exposures. J Radiol Prot 24:A35–A62

    Article  Google Scholar 

  10. ICRP (1983) Radionuclide transformations: energy and intensity of emissions. ICRP publication 38. Ann ICRP, 11–13(Parts 1–2):1–1250

  11. Eckerman KF, Westfall RJ, Ryman JC, Cristy M (1994) Availability of nuclear decay data in electronic form, including beta spectra not previously published. Health Phys 67(4):338–345

    Article  Google Scholar 

  12. Loevinger R, Berman M (1976) A revised schema for calculating the absorbed dose from biologically distributed radionuclides NM/MIRD pamphlet no. 1, Rev., March 1976, Society of Nuclear Medicine, NY

  13. Shultis JK, Faw RE (1996) Radiation shielding. Prentice Hall, PTR, NJ

  14. Briesmeister J (ed) (2000) MCNP—a general Monte Carlo N-particle transport code, version 4C. LANL report LA-13709-M. Los Alamos National Laboratory, Los Alamos, NM

  15. ICRU (1980) Radiation quantities and units, ICRU Report 33. Bethesda, MD: International Commission on Radiation Units and Measurements. Superseded by: ICRU(1993) Quantities and Units in Radiation Protection Dosimetry, ICRU Report 51. International Commission on Radiation Units and Measurements, Bethesda, MD

  16. Moré J, Garbow B, Hillstrom K. User guide for MINPACK-1. Technical report ANL-80-74, Argonne National Laboratory, August 1980

  17. Hubbel JH, Seltzer SM (1995) Tables X-ray mass attenuation coefficients and mass energy-absorption coefficients from 1 keV to 20 MeV for elements Z=1–92 and 48 additional substances of dosimetric interest. National Institute of Standards and Technology Report NISTIR 5632. NIST, Gaithersburg, MD, http://www.physics.nist.gov/PhysRefData/XrayMassCoef/cover.html

  18. Berger MJ (1999) ESTAR, PSTAR, and ASTAR: computer programs for calculating stopping-power and range tables for electrons, protons, and helium ions. National Institute of Standards and Technology Report NISTIR 4999. NIST, Gaithersburg, MD. Available on-line: http://www.physics.nist.gov/Star

  19. ICRP (2006) The Concept and Use of Reference Animals and Plants for the purposes of Environmental Protection. Draft of the ICRP Publication. Available on-line: http://www.icrp.org (in press)

  20. Chambers DB, Osborne RV, Garva AL (2006) Choosing an alpha radiation weighting factor for doses to non-human biota. J Env Radiat 87:1–14

    Article  Google Scholar 

  21. Thomsen K (2004) Denmark. 2004-04-26. Available on-line: http://www.home.att.net/∼numericana/answer/ellipsoid.htmor http://www.en.wikipedia.org/wiki/Ellipsoid

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Acknowledgments

This work was performed within the EU-supported project “ERICA—Environmental Risk from Ionizing Contaminants: Assessment and Management” under Contract no. FI6R-CT-2003-508847. The authors express their cordial thanks to Dr. J. Vives-i-Battle from Westlakes Scientific Consulting Ltd (Cumbria, United Kingdom) for valuable and fruitful discussions.

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Authors and Affiliations

  1. GSF—Forschungszentrum für Umwelt und Gesundheit, GmbH, Ingolstädter Landstraße 1, 85764, Neuherberg, Germany

    A. Ulanovsky & G. Pröhl

Authors
  1. A. Ulanovsky
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  2. G. Pröhl
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Correspondence to A. Ulanovsky.

Additional information

An erratum to this article can be found at http://dx.doi.org/10.1007/s00411-006-0069-9

Appendix: definition of the organism shape

Appendix: definition of the organism shape

Organisms are approximated by ellipsoids, i.e., by closed second-order surfaces (18):

$$\frac{x^2}{a^2}+\frac{y^2}{b^2}+\frac{z^2}{c^2}=1,$$
(18)

where a, b, and c are the semi-axes of the ellipsoid.

Let \(R_0 =\sqrt[3]{a\,b\,c}\) be the radius of a sphere of the same mass as the organism’s ellipsoid. Then, the ellipsoid’s semi-axes can be expressed in terms of R 0 (19):

$$a=k_a \,R_0, \quad b=k_b \,R_0, \quad c=k_c \,R_0,$$
(19)

where the parameters k a , k b , and k c are the so-called normalized semi-axes.

From the definitions given in (19), and the equality of masses and volumes of the ellipsoid and the sphere, it follows that (20)

$$k_a \,k_b \,k_c =1.$$
(20)

If the body’s major axis is oriented along the x-axis, i.e., a = max(a, b, c) and k a  = max(k a ,  k b ,  k c ), then the following scaling parameters can be introduced (21):

$$\xi =\frac{k_b }{k_a }\quad\hbox{ and }\quad\chi =\frac{k_c }{k_a },$$
(21)

where ξ and χ are the lengths of the two shorter semi-axes, expressed in terms of the length of the longest semi-axis.

Obviously, the scaling parameters vary between 0 and 1. A value of zero should be excluded from the range of possible values, because this value corresponds to degenerate cases. To be more specific, the cases of ξ  = 0 and χ  = 0 correspond to the degenerate plane figures “circle” and “ellipse”, respectively. If both parameters are equal to 0, the body degenerates to a line. If both parameters are equal to 1, the body has spherical shape.

Thus, any organism of ellipsoidal shape can be fully defined by its mass, M, and the two scaling parameters, ξ and χ. That is, from the mass of the organism one can deduce the radius of the equal-mass sphere, R 0, and from the scaling parameters one gets the following normalized semi-axes (22):

$$k_a =\left({\xi \,\chi } \right)^{-{1}/{3}}, \quad k_b =\xi \,k_a, \quad k_c =\chi \,k_a .$$
(22)

To quantify the deviation of an ellipsoidal shape from a sphere, the ratio of the corresponding surface areas is used (23):

$$\eta =\frac{S_0 }{S}.$$
(23)

The more an ellipsoid deviates from a spherical shape, the higher is its surface area S compared to that of the sphere S 0, provided the ellipsoid has the same mass as the sphere. As a result, the non-sphericity parameter η shows lower values for less spherical ellipsoids.

To compute the value of the non-sphericity parameter one needs to calculate the sphere and ellipsoid surface areas. In contrast to the surface of a sphere, there is no closed analytical expression for the surface area of an ellipsoid. However, there exists an empirical approximation suggested by Knud Thomsen [21]: (24).

$$S \approx 4\pi \left( {\frac{\left({ab} \right)^p+\left({ac} \right)^p+\left({bc} \right)^p}{3}} \right)^{{1}/{p}},$$
(24)

where a value of the parameter p = 1.6075 results in a relative error less than 1.061% Footnote 4.

Using (24), one gets the ratio of the surface areas of an ellipsoid and a sphere in terms of the scaling factors (25):

$$\eta =\frac{S_0 }{S}=\frac{1}{\left({\xi \,\chi } \right)^{{1}/{3}}}\left( {\frac{3}{1+\xi ^{-p}+\chi ^{-p}}} \right)^{{1}/{p}}.$$
(25)

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Ulanovsky, A., Pröhl, G. A practical method for assessment of dose conversion coefficients for aquatic biota. Radiat Environ Biophys 45, 203–214 (2006). https://doi.org/10.1007/s00411-006-0061-4

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