Implications of Radiation Induced Apoptosis on Calculated Radial Cell Inactivation for a Linear ¹⁹²Ir Source

Abstract

The cell inactivation probability as a function of the radial distance from a 4 cm linear, low dose rate (LDR) ¹⁹²Ir source was calculated using a modified linear-quadratic (LQ) equation, taking into account the effect of radiation induced apoptosis. As a measure of the therapeutic range of the source, the radial distance from the midpoint of the central axis of the source to the point of 50% inactivation probability was calculated. It was found that the therapeutic range increased with increasing values of the maximal radiation induced apoptotic fraction, F_a; but only as long as the ratio between the apoptotic cell kill susceptibility, γ, and the α value is larger than unity. If the ratio was smaller than unity, a decrease in therapeutic range was found. The slope of the radial cell inactivation probability curve was measured as the distance between the point of 10% and 90% inactivation probability. The slope was found to be fairly independent of the repair half-time, T_1/2, but became steeper with decreasing values of F_a.