On the biophysical interpretation of the mathematical product of dose and relative biological effectiveness.

The mathematical product of dose and relative biological effectiveness (DR) is commonly used empirically as the 'effective' dose of radiations. It is often interpreted as the equivalent dose of a reference radiation, such that the individual DRs of the radiation components are summed like physical doses in a mixture of radiations with different RBE values. It is shown that such a physical interpretation of DR would be both mathematically and logically inconsistent unless the action of each radiation has a constant RBE value for all end-effects. This is contrary to general experimental findings. Based on the isoeffect biological connotation in the definition of RBE, a biophysical interpretation is being introduced in this paper in which DR is always interpreted with respect to a particular end-effect on which the RBE value is evaluated, somewhat similar to having an extra biological dimension. Hence, only DRs evaluated for the same end-effect can be meaningfully computed together in a mixture. From the empirical results of radiobiological experiments using mixtures of radiations of different qualities, DRs of radiation components are shown to be additive in a mixture just like physical doses. A convenient linear computation framework is, therefore, available for the use of DRs in the empirical calculation of effect of mixtures of radiations of different qualities. The bearing of this biophysical interpretation of DR on radiation protection and treatment planning is discussed.