On the Linear Extrapolation to Low Doses

Abstract

IntroductionThe linear quadratic model is widely used in radiobiology to fit data of limited dynamic range, nominally not greater than two decades in dose, and at doses in the neighborhood of grays as summarized in NCRP report No. 104 [1]. This model has only qualitative and rhetorical support, in the form of statements about one track and two track effects, as justifying the linear and the quadratic components, respectively, and ignores the statistical fluctuation of track intersections with targets, especially important in the limit of low doses. There is no quantitative theoretical base for such a model other than the assertion that electron track ends might act like high LET radiations, a qualified appraisal at best, unsupported by direct experimental evidence, though frequently inferred from energy deposited in small volumes which approximate small sections of DNA at track ends by stopping electrons, or from the number of ionizations therein, both from Monte Carlo calculations. The relation between the linear quadratic formula and the theory of dual radiation action [2] is noted, but it must be pointed out that it is the experimental fit of the linear quadratic formula to data which supports the theory of dual radiation action, rather than the converse. Quoting Kellerer "Concepts of microdosimetry are, of course, essential in any analysis of the action of ionizing radiation on the cell. Their employment has led to important insights but not, as yet, to a quantitative treatment of the primary cellular changes" [3]. It is widely recognized that the linear quadratic formula fails outside its fitted range. Linear Extrapolation to Low Doses of Low LET RadiationsIn NCRP Report 104 [1], observations of biological effects with low LET radiations are extrapolated linearly to doses of 1 mGy and below in order to evaluate the RBE of high LET radiations at low doses. However, a flux of relativistic electrons at which single electrons pass through cells deposits a dose in the neighborhood of 1 mGy. It may be asked, do single electron transits through cells kill, mutate, transform mammalian cells? Do single electron transits induce cancers? It must be kept in mind that the extrapolation involved is substantial, as much as three or four orders of magnitude, frequently from grays to milligrays. But the extrapolation is not only quantitative. It is qualitative as well, pressing on the very validity of the concept of dose. Is there any basic reason why dose, an amorphous concept used to characterise a chaotic distribution of secondary electrons which experience has proven adequate as a plotting parameter when thousands of electrons from orthovoltage X rays or gamma rays traverse cells, should also be valid when single electrons traverse cells, and when the statistical consideration invoked in target theory is ignored? Experimental DataSeveral of the following citations have already been noted [4].Cole et al. [5] have found that some 500 electrons pass into the nucleus of a CHO cell, on average, for inactivation. 52:1-4 (1994...