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A practical neutron energy dependent RBE model has been developed, based on the relationship between a mono-energetic neutron energy and its likely recoil proton energy. Essentially, the linear energy transfer (LET) values of the most appropriate recoil proton energies are then used to modify the linear quadratic model radiosensitivities ( α  and  β ) from their reference LET radiation values to provide the RBE estimates. Experimental neutron studies published by Hall (including some mono-energetic beams ranging from 0.2 to 15 MeV), Broerse, Berry, and data from the Clatterbridge and Detroit clinical neutron beams, which all contain some data from a spectrum of neutron energies, are used to derive single effective neutron energies (NE eff ) for each spectral beam. These energies yield a recoil proton spectrum, but with an effective mean proton energy (being around 50% of NE eff ). The fractional increase in LET is given by the recoil proton LET divided by the proton (LET U ) value which provides the highest RBE. This ratio is then used to determine the change in the linear-quadratic model  α  and  β  parameters, from those of the reference radiation, to estimate the RBE. The predicted proton recoil RBE is then reasonably close to the experimental neutron RBE values found when taking into account the variation inherent in biological experiments. The work has some important consequences. The data of Hall  et al  (1975  Radiat. Res.  64  245–55) shows that the highest RBE values are found with neutron energies around 0.3–0.4 MeV, but this energy cannot possibly generate recoil proton energies which are higher, as necessary for a 0.68 MeV proton with a 30.5 keV  μ m −1  LET U  (the LET value which provides the maximum obtainable RBE for a specified ion). For 0.4 MeV neutrons with proton recoil energies of around 0.2 MeV, the latter have a LET of around 62.88 keV  μ m −1 . This could have an impact on proton beam RBE modelling. However, this is compensated by finding that the maximum radiosensitivity for mono-energetic neutrons was around 1.7 times larger than previously suggested from experimental ion beam studies, probably due to the necessary spreading out of Bragg peaks for ion beam experimental purposes, sampling errors and particle range considerations. This semi-empirical model can be used with minimal computer support and could have applications in ionic beams and in radioprotection.

Fast neutron energy based modelling of biological effectiveness with implications for proton and ion beams