be a critical factor in the production of chromosomal aberrations (Lea 1946).

Recoil protons with energy of a few hundred kiloelectronvolts appear, in line with the above biophysical considerations, to be the particles that produce maximal cellular damage per unit energy imparted. This is confirmed by various experimental studies that consistently demonstrate the maximal effectiveness of neutrons at a neutron energy of about 0.4 MeV (Kellerer and Rossi 1972b).

The dose-effect relationship, E(D), for photons can in many radiobiological investigations be described as a linear quadratic function of absorbed dose:

(1-1)

In experiments with fast neutrons, the effect is typically proportional to the absorbed dose, Dn, of neutrons over a variable dose range depending on the tissue and effect:

(1-2)

The linear dose coefficient, an, for neutrons is always substantially larger than the linear dose coefficient, a, for photon radiation. The RBE of neutrons is defined as the ratio of a γ-ray dose to the neutron dose that produces the same effect:

(1-3)

In terms of Equations (1-1) and (1-2), RBE can be expressed as a function of the neutron dose or the photon dose. The latter expression is somewhat simpler:

(1-4)

This implies that RBE assumes its maximal value, RBEmax = an/a, at low doses, whereas it decreases with increasing dose and then tends to be inversely proportional to the photon dose.

Experimental Observations

Indeed, numerous experimental investigations of chromosomal aberrations, cellular transformations, and cell killing have confirmed that maximal RBE values of neutrons occur at low doses and that, at somewhat higher doses, RBE varies inversely with increasing reference dose (i.e., the photon dose). The same has been observed for more complex effects such as opacification of the lens and, more important in the context of risk assessment, induction of tumors in animals. A synopsis of such findings was provided in the context of the microdosimetric interpretation of the neutron RBE (Kellerer and Rossi 1972b).

Although the general features of the dependence of neutron RBE on dose are brought out consistently in experimental studies, the numerical values of RBE vary, and the variation appears to be largely a matter of the different magnitude of the linear dose component for photon radiation.

Cell survival curves usually exhibit pronounced initial slopes, and the observed maximal neutron RBE rarely exceeds a factor of about 10. For dicentric chromosomal aberrations in human lymphocytes, values of about 70 are obtained for the maximal RBE of 0.5 MeV neutrons against γ-rays (Dobson and others 1991; Schmid and others 2000). This large maximal value might be seen as an indication of an exceptionally high effectiveness of neutrons at low doses. In fact the dose-effect relationship for neutrons is simply linear, and the high maximal RBE of neutrons is merely a reflection of the very shallow and imprecisely known (standard error, 30–40%) initial slope in the dose-effect relationship for γ-rays. The RBE of neutrons versus a γ-ray dose of 1 Gy is only about 12 (Bauchinger and others 1983; Schmid and others 2000).

In the context of risk estimation, the major interest is in neutron RBEs that have been evaluated in animal experiments with regard to tumor induction. A multitude of results have been reported in the literature for many tumor systems (NCRP 1990). Experiments with rodents show considerable variation, especially in female mice and rats, and this variation reflects the decisive influence of hormonal status. In experiments with female Sprague-Dawley rats, Shellabarger and others (1980) found that 4 mGy of fast neutrons produced as many mammary neoplasms as 0.4 Gy of X-rays, which implied an RBE of 100. Broerse and Gerber (1982) used female Sprague-Dawley rats, which have a much lower spontaneous incidence, and found substantially lower values of neutron RBE. However, considerable differences in neutron RBE at higher doses were observed for different tumor types. As an extreme example, one may refer to lung adenomas in female RFM mice, in which there is a clear reduction in age-adjusted incidence after γ-ray exposures up to about 2 Gy, but neutron doses of 0.2 Gy cause a substantial increase (Ullrich and others 1976). The simple assumptions made in the calculation of RBE do not seem to be applicable in such a case.

In view of this complexity, it appears best to refer to experiments with male mice or rats that determine the overall incidence of solid tumors. In an extensive series of studies of the French Commissariat a l’Energie Atomique using male Sprague-Dawley rats, a fission neutron dose of 20 mGy was consistently found to be equivalent to an acute γ-ray dose of 1 Gy with regard to both nonlethal tumors (Lafuma and others 1989) and lethal tumors (Wolf and others 2000). This comparison corresponds to a neutron RBE of 50 against a reference γ-ray dose of 1 Gy. When the experiments were evaluated in terms of life shortening as a proxy for tumor mortality, the inferred RBE was closer to 30 (Wolf and others 2000). Smaller values of the RBE—around 20 compared to a γ-ray dose of 1 Gy and about 15 compared to X-rays—are suggested by major studies with mice that were evaluated in



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