Comparison of Mathematical Models for Radiation Fractionation

Radiation fractionation data can be plotted in four planes: log N-log D, dose-reciprocal total dose, dose-response, and dose-recovery dose. Properties of curves in these planes corresponding to five models are developed. One model assumes that total dose is a power function of the number of fractions; the other four models assume that the dose-log surviving fraction curve is described by (1) a multitarget, (2) a two component (product of single-hit and multitarget factors), (3) a quadratic, and (4) a cubic function, respectively. Several nonlinear regression criteria are defined and corresponding computer programs have been developed. Best fits for the five models are found for three specific data sets involving normal tissues in mice. One regression criterion and three models are shown to be unsuitable.