A semi-empirical approach to the evaluation of the relative biological effectiveness of therapeutic proton beams: the methodological framework.

We address the problem of the evaluation of the relative biological effectiveness (RBE) of therapeutic proton beams for cell inactivation. We consider a general approach to the evaluation of the lethal effect of protons which is applicable to different situations, including those in which an extended Bragg peak is obtained via a modulated beam. Our approach combines two kinds of information: (1) the experimental results available in the literature for the response of Chinese hamster V79 cells to monoenergetic beams and (2) the energy spectrum of the beam in the target volume, computed through a Monte Carlo algorithm. We have applied this method to a simple Bragg peak produced by a broad-field proton beam of about 70 MeV initial energy, such as those that, after attenuation, are typically used for treatment of ocular tumors. We have found that the RBE increases with depth, even beyond the Bragg peak, up to a value close to 2, when evaluated at the same surviving fraction as that resulting after exposure to 2 Gy of X rays.