Physical characteristics at the turnover-points of relative biological effect (RBE) with linear energy transfer (LET)

This paper considers the kinematic physical characteristics of ionic beams for maximum relative bio-effectiveness (RBE).

RBE studies, based on heterogenous cell survival studies at different laboratories and linear energy transfer (LET) conditions for proton, helium, carbon, neon and argon ions, have been further analysed to determine the LET_U values where RBE is maximal and the LET-RBE relationship has a turnover point. The SRIM stopping power software and other classical equations are used to determine the particle velocities, kinetic energies and their effective ionic charges at LET_U.

The estimated mean LET_U values increase with atomic number (Z). Each LET_U has a unique relativistic velocity, β  =  v/c, the velocity v expressed as a fraction of the speed of light, (c), and which is non-linearly proportional to Z. For ions helium and heavier ions, these velocities indicate that the effective charge Z ^* is around 0.99 of the full Z value at each LET_U, with remarkably stable velocities of 3–4 nm · fs⁻¹ per nucleon, or around 6–8 nm · fs⁻¹ per unit Z. For Z  =  1, (protons and deuterium) some values fall outside these ranges but the result depends on the mix of proton and deuterium used in experiments. An alternative index of βA/Z ² (A is the atomic mass number), suggests an average velocity of around 15 nm · fs⁻¹ for each particle at LET_U. These distances, traversed in the time of the radiochemical process initiation, are all within the dimensions of the nucleosome. Curve fitting of the data set provides a predictive equation for LET_U for any ion, as LET_U  =  30.4  +   (1  −  Exp[−0.61  √  (Z  −  1)]) when normalised to protons. These data can be extended to heavier ions such as silicon and iron and give values that are consistent with experimental data.

Each ion probably has a unique LET_U value. Kinematic studies show maximum bio-effectiveness occurs at particle velocities where electron stripping remains at around 99% and where the velocity per nucleon is around 3–4 nm · fs⁻¹.

This study enhances the limited prior knowledge about the physical conditions of particle beams that provide maximum bio-effectiveness, with applications in particle radiotherapy, radiation protection and space travel. (paper)