Summary
When cells are subjected to ionizing radiation the specific energy rate (microscopic analog of dose-rate) varies from cell to cell. Within one cell, this rate fluctuates during the course of time; a crossing of a sensitive cellular site by a high energy charged particle produces many ionizations almost simultaneously, but during the interval between events no ionizations occur. In any cell-survival model one can incorporate the effect of such fluctuations without changing the basic biological assumptions. Using stochastic differential equations and Monte Carlo methods to take into account stochastic effects we calculated the dose-survival relationships in a number of current cell survival models. Some of the models assume quadratic misrepair; others assume saturable repair enzyme systems. It was found that a significant effect of random fluctuations is to decrease the theoretically predicted amount of dose-rate sparing. In the limit of low dose-rates neglecting the stochastic nature of specific energy rates often leads to qualitatively misleading results by overestimating the surviving fraction drastically. In the opposite limit of acute irradiation, analyzing the fluctuations in rates merely amounts to analyzing fluctuations in total specific energyvia the usual microdosimetric specific energy distribution function, and neglecting fluctuations usually underestimates the surviving fraction. The Monte Carlo methods interpolate systematically between the low dose-rate and high dose-rate limits. As in other approaches, the slope of the survival curve at low dose-rates is virtually independent of dose and equals the initial slope of the survival curve for acute radiation.
Similar content being viewed by others
References
Albright N (1989) A Markov formulation of the repair-misrepair model of cell survival. Radiat Res 118:1–20
Braby LA, Roesch WC (1978) Testing of dose rate models withChalmydomonas reinhardi. Radiat Res 76:259–270
Breiman L (1969) Probability and stochastic processes. Houghton Mifflin, Boston Mass, pp 32–38
Brenner DJ (1988) On the probability of interaction between elementary radiation-induced chromosomal injuries. Radiat Environ Biophys 27:189–199
Brenner DJ (1990) Track structure, lesion development and cell survival. Radiat Res (in press)
Charlton DE, Nikjoo H, Humm JL (1989) Calculation of initial yields of single and double strand breaks in cell nuclei from electrons, protons and alpha particles. Int J Radiat Biol 56:1–19
Curtis SB (1989) The lethal and potentially lethal model - a review and recent development. In: Kiefer J (ed) Quantitative mathematical models in radiation biology. Springer, New York Berlin Heidelberg, pp 137–146
Dillehay LE (1990) A model of cell killing by low-dose-rate radiation including repair of sub-lethal damage, G2 block, and cell division. Radiat Res (in press)
Goodhead DT (1985) Saturable repair models of radiation action in mammalian cells. Radiat Res 104:S58-S67
Goodhead DT (1987) Relationship of microdosimetric techniques to applications in biological systems. In: Kase KR, Bengt B, Attix FH (eds) The dosimetry of ionizing radiation, vol II. Academic Press, Orlando FA, pp 1–89
Günther K, Schulz W (1983) Biophysical theory of radiation action. Akademie-Verlag, Berlin
Grimmet GR, Stirzaker DR (1988) Probability and random processes. Oxford Science Publications. Clarendon Press, Oxford, Sect. 6.8
Hagen U (1989) Biochemical aspects of radiation biology. Experientia 45:7–12
Hall E.J, Marchese M, Hei TK, Zaider M (1988) Radiation response characteristics of human cells in vitro. Radiat Res 114:415–424
Harder D (1989) The pairwise lesion interaction model. In: Kiefer J (ed) Quantitative mathematical models in radiation biology. Springer, New York Berlin Heidelberg, pp 159–170
Hug O, Kellerer AM (1966) Stochastik der Strahlenwirkung. Springer, Berlin Heidelberg New York
ICRU (1983) Microdosimetry. Report #36, ICRU, Bethesda, Md
Kelland LR, Steel GG (1989) Recovery of radiation damage in human squamous carcinoma of the cervix. Int J Radiat Biol 55:119–127
Kellerer AM (1985) Fundamentals of microdosimetry. In: Kase KR, Bengt B, Attix FH (eds) The Dosimetry of ionizing radiation, vol I. Academic Press, Orlando Fa, pp 78–162
Kellerer AM, Rossi HH (1972) The theory of dual radiation action. Curr Top Radiat ResQ 8:85–158
Kellerer AM, Rossi HH (1978) A generalized formulation of dual radiation action. Radiat Res 75:471–488
Kiefer J (1989) A repair fixation model based on classical enzyme kinetics. In: Kiefer J (ed) Quantitative mathematical models in radiation biology. Springer, New York Berlin Heidelberg, pp 171–180
King CR, Nath R, Rockwell S (1988) Effects of continuous low dose-rate irradiation: computer simulations. Cell Tissue Kinet 21:339–351
Lea DE, Catcheside DG (1942) The mechanism of the induction by radiation of chromosome aberrations inTranscendentia. J Genet 44:216–245
Marchese MJ, Zaider M, Hall EJ (1987) Dose-rate effects in normal and malignant cells of human origin. Br J Radiol 60:573–576
Mitchell JB, Bedford JS, Bailey SM (1979) Dose-rate effects in mammalian cells in culture. III. comparison of cell killing and cell proliferation during continuous irradiation of six different cell lines. Radiat Res 79:520–536
Ostashevsky JY (1989) A model relating cell survival to DNA fragment loss and unrepaired double-strand breaks. Radiat Res 118:437–466
Payne MG, Garrett WR (1975) Application of microdosimetry to models of cell survival. Radiat Res 63:201–210
Radford IR (1987) Effect of cell-cycle position and dose on the kinetics of DNA double-strand breakage repair in X-irradiated Chinese hamster cells. Int J Radiat Biol 52:555–564
Rossi HH, Zaider M (1989) Saturation in dual radiation action. In: Kiefer J (ed) Quantitative mathematical models in radiation biology. Springer, New York Berlin Heidelberg, pp 111–118
Schulz RJ, Bongiorni P (1989) The dose rate dependence of the relative biological effectiveness of241Am versus226Ra γ rays. Radiat Res 118:420–436
Steel GG, Down JJ, Peacock JH, Stephens TC (1986) Dose-rate effects and repair of radiation damage. Radiother Oncol 5:321–331
Steel GG, Deacon JM, Duchesne GM, Horwich A, Kelland LR, Peacock JH (1987) The dose rate effect in human tumor cells. Radiother Oncol 9:299–310
Thames HD (1985) An “incomplete-repair” model for survival after fractionated continuous irradiations. Int J Radial Biol 47:319–339
Tobias CA (1985) The repair-misrepair model in radiobiology: comparison to other models. Radiat Res [Suppl 8] 104:S77-S95
Ward JF (1988) DNA damage produced by ionizing radiation in mammalian cells: identities, mechanisms of formation, and repairability. Prog Nucleic Acid Res Mol Biol 35. Cohn W, Moldave K (eds). Academic Press, New York, pp 95–125
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Sachs, R.K., Hlatky, L.R. Dose-rate dependent stochastic effects in radiation cell-survival models. Radiat Environ Biophys 29, 169–184 (1990). https://doi.org/10.1007/BF01210521
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF01210521