A New Approach to the Mathematical Theory of the Action of High-Energy Radiation on Single Cells: I. Formulation of the Theory

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Abstract
Theoretical expressions for the probability of survival of an irradiated cell are both complicated and uncertain. A new approach is proposed whereby the survival probability under any kind of high-energy radiation is expressed in terms of survival probability under X-rays. The assumption which makes this possible is that the diffusion lengths of the intermediaries are long compared to nuclear dimensions. The result can be expressed essentially as [image] in which S(y) is the survival probability as a function of the average number, y, of radiation tracks through the nucleus, X(D) is the X-ray survival probability as a function of dose D, and [eta] is an equivalent X-ray dose corresponding to one track. Indications are given as to how this formula can and will be used.