Theory of dose-effect relations

Quantitive dose-effect relations are equally important in the medical application of ionizing radiation and in radiation protection; moreover they are fundamental for an understanding of the mechanisms of radiation action. The practical and theoretical aspect cannot always be clearly separated. Many of the equations and parameters, for example, which are used for the description of dose-effect relations go back to theoretical models which have been used in the past but have now lost relevancy. Stripped of its original meaning the mathematical formalism has often been retained because it permits a suitable representation of typical dose-effect relations, and because it is convenient in many cases to describe a dose-effect relation by a formula or by a few parameters instead of giving it in tabular form or graphical representation. In the following an attempt will be made to distinguish between formal description of dose-effect relations for practical purposes and the mathematical analysis which aims at an understanding of the mechanisms of radiation action. Attention will mainly be given to the dose dependence of cellular radiation actions but the focus will be on general principles which are equally applicable to other levels of radiation action such as molecular systems or multicellular systems. Techniques and arguments applicable to the analysis of dose-response relations are discussed, and no attempt is made to review the experimental techniques, the modifying factors, such as the oxygen effect, or the radiobiological results. Numerical data are used to elucidate the structure of the essential arguments. They are not representative for the great number of dose-effect relations studied in radiation biology and radiology, and neither their experimental accuracy nor their statistical significance will be considered.