Analysis of relative biological effectiveness of high energy heavy ions in comparison to experimental data

We report that the relative biological effectiveness (RBE) of accelerated heavy ions for inactivation of cells can be analyzed by using the quadratic dependence on the linear energy transfer (LET) of the cellular effect. For high-LET radiation in low-dose regions, the inactivation cross section (sigma) can be approximately expressed as sigma max [1-exp[-k.(LET/Li)2]; here, k is the number of heavy-ions traversed in a cell nucleus and Li is a geometrical parameter related to the DNA structure, which depends on cell type. This original expression was first presented by Powers et al [Int. J. Radiat. Biol. 14 (1968)]. Using this expression and the Poisson distribution for the stochastic property of particle hitting, the mortality of cell populations was calculated. The numerical results were compared to the RBE values recently obtained with Chinese hamster V79 cells, and an Lt value of 152 keV/micron was found to give the best fit. At LETs of between 30 and 500 keV/micron, the D10 values (10% survival dose) agreed with the experimental data within an error range of -15%-(+8%).