Radiobiological model for calculating the probability of death of mammalian cells exposed to ionizing radiation with different linear energy transfer

«Radiation and Risk», 2022, vol. 31, No. 2, pp.97-110

DOI: 10.21870/0131-3878-2022-31-2-97-110

Authors

Dolgikh A.P. – Chief Specialist, C. Sc., Phys.-Math., Rosenergoatom JSC.
Pavlik T.I. – Engineer, GPI RAS. Contacts: 38, Vavilova str., Moscow, Russia, 119991. Tel. +7 (499) 503-87-34; e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it. .
1 Rosenergoatom JSC, Moscow
2 Prokhorov General Physics Institute of the RAS, Moscow

Abstract

One of the fundamental problems of radiobiology is to predict a quantitative relationship between the onset of a specified radiation-induced effect on a biological object and the dose of exposure to ionizing radiation under different conditions (for ionizing radiation of different quality and different time of exposure). The purpose of this article is to solve a particular part of the general problem: the development of a mathematical model for the probability of death of mammalian cells depending on the radiation dose with arbitrarily specified linear energy transfer (LET), with a single irradiation of these cells in vitro. To solve this problem, microdosimetric approaches based on the theory of the dual action of radiation were used. When developing the model, the following assumptions were used: 1) there are sensitive volumes (SVs) in the cell, damage to the volumes can lead to cell death; 2) the probability of cell death depends on the number of damaged SVs; 3) the probability of damage to the SVs depends on the energy absorbed in it; 4) to calculate the energy absorbed in the SVs, a simple model for the interaction of ionizing particles with matter was used: the particles move in a straight line, the LET of the particles coincide with the linear energy absorbed in the matter. The developed mathematical model for estimating relationship of the probability of cell death on the dose explicitly contains LET. Thus, the use of the proposed model makes possible separation of biological parameters responsible for the onset of radiation-induced effect from radiation characteristics of the irradiation conditions., Classical radiobiological data, underlying the IAEA ionizing radiation recommendations for determining the relative biological effectiveness (RBE) of different types present an argument for the model validation. Experimental data on irradiation of human kidney T1 cells present an example. The article demonstrates that the developed model makes it possible to calculate the probability of cell death depending on the dose of ionizing radiation with an arbitrarily set LET for photons, electrons, and -particles with a LET from 0.4 to 200 keV/ μm. It follows from the proposed model that a linear-quadratic dependence can occur not only in DNA damage, but also in other biologically important molecules. The use of this model can be extended to predict other radiation-induced effects, as well as the probability of occurrence of radiation-induced effects under various time exposure regimes.

Key words
theoretical radiobiology, radiobiological model, ionizing radiation, probability of death of mammalian cells, dual action of radiation, microdosimetry, linear energy transfer, relative biological efficiency, human kidney T1 cells, survival prediction, cell irradiation in vitro.

References

1. Hug O., Kellerer A.M. Stokhasticheskaya radiobiologiya [Stochastic radiobiology]. Moscow, Atomizdat, 1969. 184 p.

2. Kellerer A.M., Rossi H.H. A generalized formulation of dual radiation action. Radiat. Res., 1978, vol. 75, no. 3, pp. 471-488.

3. Ivanov V.I., Lystsov V.N., Gubin A.T. Spravochnoye rukovodstvo po mikrodozometrii [Reference manual for microdosimetry]. Moscow, Energoatomizdat, 1986. 184 p.

4. Ivanov V.I. Kurs dozimetrii, 3-e izd. [Course dosimetry, 3rd ed.]. Moscow, Atomizdat, 1978. 392 p.

5. Keirim-Markus I.B., Savinsky A.K., Chernova O.N. Koefficienty kachestva ioniziruyuschikh chastits [Quality coefficients of ionizing particles]. Moscow, Energoatomizdat, 1992. 320 p.

6. Stolbovoy A.V., Zalyalov I.F. Radiobiological models and clinical radiation oncology. Onkologiya. Zhurnal imeni P.A. Gertsena – P.A. Herzen Journal of Oncology, 2016, vol. 5, no. 6, pp. 88-96. (In Russian).

7. Korotovskikh O.I., Vazirov R.A., Agdantseva E.N., Baranova A.A. Mathematical modeling of the factor of dose change in radiation-induced adaptation. ANRI, 2019, no. 4, pp. 57-63. (In Russian).

8. Gubin A.T., Sakovich V.A. Dual theory of action ionizing radiation and spontaneous cancer. Radiatsionnaya Gygiena – Radiation Hygiene, 2015, vol. 8, no. 1, pp. 30-34. (In Russian).

9. Bodgi L., Canet A., Pujo-Menjouet L., Lesne A., Victor J.-M., Foray N. Mathematical models of radiation action on living cells: From the target theory to the modern approaches. A historical and critical review. J. Theor. Biol., 2016, vol. 394, pp. 93-101.

10. Barendsen G.W., Beusker T.L. Effects of different ionizing radiations on human cells in tissue culture. I. Irradiation techniques and dosimetry. Radiat. Res., 1960, vol. 13, pp. 832-840.

11. Barendsen G.W., Koot C.J., Van Kersen G.R., Bewley D.K., Field S.B., Parnell C.J. The effect of oxygen on impairment of the proliferative capacity of human cells in culture by ionizing radiations of different LET. Int. J. Radiat. Biol. Relat. Stud. Phys. Chem. Med., 1966, vol. 10, no. 4, pp. 317-327.

12. Barendsen G.W., Walter H.M.D., Fowler J.F., Bewley D.K. Effects of different ionizing radiation on human cells in tissue culture: III. Experiments with cyclotron-accelerated alpha-particles and deuterons. Radiat. Res., 1963, vol. 18, no. 1, pp. 106-119.

13. Todd P. Fractionated heavy ion irradiation of cultured human cells. Radiat. Res., 1968, vol. 34, no. 2, pp. 378-389.

14. Todd P. Reversible and irreversible effects of ionizing radiations on the reproductive integrity of mammalian cells cultured in vitro. Dissertation for Ph.D. degree. University of California, Radiation Laboratory, Report UCRL-11614. Berkeley, 1964.

15. Scaife J.F. The RBE of 137Cs-, 250 kV and 100 kV X-rays for mitotic delay and survival in human kidney cells. Int. J. Radiat. Biol., 1969, vol. 15, no. 3, pp. 278-283.

16. Broerse J.J., Barendsen G.W. Effects of monoenergetic neutron radiation on human cells in tissue culture. In: Biological effects of neutron and photon irradiations. Vienna, IAEA, 1964, vol. 1, pp. 309-324.

17. Barendsen G.W., Broerse J.J. Measurement of relative biological effectiveness and oxygen enhancement ratio of fast neutrons of different energies. In: Biophysical aspects of radiation quality. Vienna, 1968, vol. 2, pp. 55-63.

18. Broerse J.J., Barendsen G.W. Recovery of cultured cells after fast neutron irradiation. Int. J. Radiat. Biol., 1969, vol. 15, no. 4, pp. 335-339.

19. Todd P., Gerci J.P., Furcinitti P.S., Rossi R.M., Mikage F., Theus R.B., Schroy C.B. Comparison of the effect of various cyclotron-produced fast neutrons on the reproductive capacity of cultured human kidney (T-1) cells. Int. J. Radiat. Oncol. Biol. Phys., 1978, vol. 4, no. 11-12, pp. 1015-1022.

20. Raju M.R., Gnanapurani M., Richman C., Martins B.I., Barendsen G.W. RBE and OER of - mesons for damage in cultured T-1 cells of human kidney origin. Br. J. Radiol., 1972, vol. 45, no. 531, pp. 178-191.

21. Blakely E.A., Tobias C.A., Yang T.C.H., Smith K.C., Lyman J.T. Inactivation of human kidney cells by high-energy monoenergetic heavy-ion beams. Radiat. Res., 1979, vol. 80, pp. 122-160.

Full-text article (in Russian)