A Simpler Energy Transfer Efficiency Model to Predict Relative Biological Effect for Protons and Heavier Ions

Bleddyn Jones

The aim of this work is to predict relative biological effectiveness (RBE) for protons and clinically relevant heavier ions, by using a simplified semi-empirical process based on rational expectations and published experimental results using different ion species. The model input parameters are: Z (effective nuclear charge) and radiosensitivity parameters αL and βL of the control low linear energy transfer (LET) radiation. Sequential saturation processes are assumed for: (a) the position of the turnover point (LETU) for the LET-RBE relationship with Z, and (b) the ultimate value of α at this point (αU) being non-linearly related to αL. Using the same procedure for β, on the logical assumption that the changes in β with LET, although smaller than α, are symmetrical with those of α, since there is symmetry of the fall off of LET-RBE curves with increasing dose, which suggests that LETU must be identical for α and β. Then, using iso-effective linear quadratic model equations, the estimated RBE is scaled between αU and αL and between βU and βL from for any input value of Z, αL, βL, and dose. The model described is fitted to the data of Barendsen (alpha particles), Weyrather et al. (carbon ions), and Todd for nine different ions (deuterons to Argon), which include variations in cell surviving fraction and dose. In principle, this new system can be used to complement the more complex methods to predict RBE with LET such as the local effect and MKM models which already have been incorporated into treatment planning systems in various countries. It would be useful to have a secondary check to such systems, especially to alert clinicians of potential risks by relatively easy estimation of relevant RBEs. In clinical practice, LET values smaller than LETU are mostly encountered, but the model extends to higher values beyond LETU for other purposes such as radiation, protection, and astrobiology. Considerable further research is required, perhaps in a dedicated international laboratory, using a basket of different models to determine what the best system or combination of systems will be to make proton and ion beam radiotherapy as safe as possible and to produce the best possible clinical results.