The physical separation between the LET associated with the ultimate relative biological effect (RBE) and the maximum LET in a proton or ion beam

Purpose: To identify the relative positions of the ultimate RBE, at a LET value of LET U (where the LET-RBE turnover point occurs independently of dose), and of the maximum LET (LET M ) for a range of ions from protons to Iron ions. Methods: For a range of relativistic velocities ( β ), the kinetic energies, LET values and ranges for each ion are obtained using SRIM software. For protons and helium ions, the LET changes with β are plotted and LET M is compared with LET U. For all the ions studied the residual ranges of particles at LET U and LET M are subtracted to provide the physical separation (S) between LET U and LET M . Results: Graphical methods are used to show the above parameters for protons and helium ions. For all the ions studied, LET U occurs at kinetic energies which are higher than those at LET M , so the ultimate maximal RBE occurs proximal to the Bragg peak for individual particles and not beyond it, as is commonly supposed. The distance S, between LET U and LET M , appears to increase linearly with the atomic charge value Z. Conclusions: For the lighter elements, from protons to carbon ions, S is sufficiently small (less than the tolerance/accuracy of radiation treatments) and so will probably not influence therapeutic decisions or outcomes. For higher Z numbers such as Argon and Iron, larger S values of several centimetres occur, which may have implications not only in any proposed therapeutic beams but also at very low doses encountered in radiation protection where the few cells that are irradiated will typically be traversed by a single particle.