Cellular Inactivation by Heavy Ions, Neutrons, and Pions

The delta-ray theory of the inactivation of cells by energetic heavy ions describes cellular survival after heavy ion bombardment through a two-component survival model, in which 4 operational parameters (E0,m0, σ0, and κ) describe the response of a particular cellular variety in a particular ambient condition, for an arbitrary radiation environment. The quantities m and E0 are the extrapolation number and extrapolated D-37 dose of the survival curve after gamma-ray irradiation. The quantities σ0 and κ are found from the initial slope of survival curves after irradiation with ions of different LET, and are the value of the saturation cross-section and the value of z2 / 4β2 at which “saturation” is achieved, or rather, where the grain-count regime terminates. In this regime, the inactivated cells are like beads on the string represented by the ion\u27s path. Cells may be inactivated by the passage of a single ion, with probability P = (1 – exp[-z2/ κβ2])m = σ/σ0, where σ is the cross-section for this inactivation mode, called ion-kill, so that the survival probability after irradiation with a beam of particles with fluence F from this mode is e-σF A second inactivation mode results from the capacity of cells to be bruised by the delta-rays from a single ion in the beam, to be killed by the delta-rays from subsequent ions, much as cells are inactivated by secondary electrons from gamma-rays. In this gamma-kill mode, with gamma-kill dose (1-P)D, where D is the dose deposited by the heavy ion beam, the survival probability is 1-[1-e-(1-P)D/E0]m. The survival probability after irradiation with a beam of ions is the product of these two independent survival probabilities. These expressions are extended to a mixed radiation environment in which the spectrum of secondary charged particles is known, to yield survival, OER, RBE, the Anoxic-Aerobic Ratio, and the equivalent monoenergetic beam for neutron and stopped negative pion and heavy ion beam irradiation, where appropriate