The general relation between tissue response to x-radiation (α/β-values) and the relative biological effectiveness (RBE) of protons: Prediction by the Katz track-structure model

Abstract

Purpose : Experimental data suggest that the relative biological effectiveness (RBE) of protons compared to x-rays may be determined by the α / β -ratio of the x-ray survival curve. The data are referring to the centre of a spread-out Bragg peak (SOBP) formed to deliver a homogeneous dose to the tumour by modulating the proton energy. In an effort to explore the basis for this observation, calculations were performed to investigate the response of different biological targets through a range of proton energies and doses. Materials and methods : To describe the x-ray survival curve, the parameters of the linear-quadratic equation, α and β, as well as those of the multi-target/single-hit equation, n and D 0, were considered. These parameters were varied to investigate the RBE using the Katz track-structure model. Known cell line characterizations, as well as different hypothetical cells assuming different α / β -ratios but similar target size parameters in the framework of the track-structure theory, were considered. Results : The RBE was found to increase with increasing α / β when the parameter n was varied, but to decrease with increasing α / β when D 0 was varied. This held when all other radiosensitivity parameters were assumed to stay constant. Thus, the RBE cannot be predicted by the α / β -ratio alone. Conclusions : Although there is no direct correlation between the proton RBE and the parameters describing the x-ray survival curve, the track-structure model predicts a tendency for late-responding tissues (low α / β) to have higher RBE values than early-responding tissues (high α / β) . These calculations reinforce the experimental findings, but also strongly suggest that there are circumstances in which the tendency for RBE to increase with increasing α / β does not occur, or even could be reversed.