Some remarks on non-monotonic effects at low radiation intensities, on the problem of extrapolating doses between high and low intensities and on the problem of thresholds

On the basis of a general descriptive framework which takes into account the intensity factor and the time distribution of radiation, a detailed justification for which is to be found in earlier publications, the three fundamental problems mentioned in the title of this paper can be approached in a new way. If the biological effect e for a given dose D delivered at different radiation intensities phi is studied, we find that the curve e=f(phi) can exhibit non-monotonic shapes. This type of phenomenon is known in pharmacology and toxicology and may well exist also for low- or medium-intensity radiation effects. Extrapolation of the effects of a given dose between high and low radiation intensities phi is usually carried out by means of an empirical linear or linear-quadratic formulation. This procedure is insufficiently justified from a theoretical point of view. It is shown here that the effects can be written in the form e=k(phi)D and that the factor of proportionality k(phi) is a generally very complicated function of phi. Hence, the usual extrapolation procedures cannot deal with certain ranges of values of phi within which the effects observed at a given dose may be greater than when the dose is delivered at higher intensity. The problem of thresholds is actually far more difficult than the current literature on the subject would suggest. It is shown here, on the basis of considerations of qualitative dynamics, that several types of threshold must be defined, starting with a threshold for the radiation intensity phi. All these thresholds are interrelated hierarchically in fairly complex ways which must be studied case by case. These results show that it is illusory to attempt to define a universal notion of threshold in terms of dose. The conceptual framework used in the proposed approach proves also to be very illuminating for other studies in progress, particularly in the investigation of phenomena associated with ageing and carcinogenesis. (author)