Frontiers in Oncology (Aug 2015)
A Simpler Energy Transfer Efficiency Model to Predict Relative Biological Effect (RBE) for Protons and Heavier Ions.
Abstract
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 alphaL and betaL 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 in relation to Z, and (b) the ultimate value of alpha at this point (alphaU) being non-linearly related to alphaL. Using the same procedure for beta, on the logical assumption that the changes in beta with LET, although smaller than alpha, are symmetrical with those of alpha, since there is symmetry of the fall off of LET-RBE curves with increasing dose, which also suggests that LETU must be identical for alpha and beta. Then, using iso-effective linear quadratic model equations, the estimated RBE is scaled between alphaU and alphaL and between betaU and betaL from for any input value of z, alphaL, betaL 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 estimation of relevant RBE`s. In clinical practice LET values smaller than LETU are mostly encountered, but the model extends to higher values beyond LETU dedicated international laboratory, using a basket of different models to deter
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