The Katz cell-survival model and beams of heavy charged particles

Abstract

In this paper, we describe how the Katz cell-survival model has been used to predict survival along the central axis of the dose vs depth curve of beams of heavy charged particles. Unmodified beams with sharp Bragg peaks as well as ridge-filter-modulated beams with spread Bragg peaks have been studied. The analysis in terms of this model leads to the definition of twocoefficients, “ion kill” and “gamma kill”, which characterize the radiation quality of the beams. In this way, the relative importance of the primary and secondary (fragmentation) contributions can be assessed easily. Setting the model parameter m equal to 2 yields two interesting results: the survival expression becomes linear-quadratic at low doses and the inactivation cross-section at small values of Z ∗2/β 2 (low-LET) increases as (Z ∗2/κβ 2) 2 in accordance with the Lethal-Potentially Lethal (LPL) model. With this restriction on m and these approximations (low-LET and low dose) and for delayed plating experiments of stationary phase cells (i.e. when repair is complete), the Katz model and the LPL model reduce to the same analytical form (linear-quadratic) with simple expressions linking the constants.