Estimation of Errors Associated With Use of Linear-Quadratic Formalism for Evaluation of Biologic Equivalence Between Single and Hypofractionated Radiation Doses: An In Vitro Study

Abstract

To investigate the reliability of the linear-quadratic (LQ) formalism and the magnitude of errors associated with its use in assessing biologic equivalence between single, high radiation doses and hypofractionated radiation doses. V79 and EMT6 single cells received single doses of 2-12 Gy or two or three fractions of 4 or 5 Gy, each at 4-h intervals. Single and fractionated doses to actually reduce the cell survival to the same level were determined by a colony assay. The alpha/beta ratio was obtained from the cell survival curves. Using the alpha/beta ratio and the LQ formalism, equivalent single doses for the hypofractionated doses were calculated. They were then compared with the actually determined equivalent single doses for the hypofractionated doses. The V79 spheroids received single doses of 5-26 Gy or two to five fractions of 5-12 Gy at 2 or 4-h interval, and then were assayed for cell survival. Next, equivalent single doses for the hypofractionated doses were determined, as were done for the single cells. The alpha/beta ratio was 5.1 Gy for the V79 single cells and 0.36 Gy for EMT6. In V79, the equivalent single doses for the hypofractionated doses calculated using the LQ formalism were 12-19% lower than the actually measured biologically equivalent single doses. In the EMT6 cells, this trend was also seen, but the differences were not significant. In the V79 spheroids, the calculated doses were 18-30% lower than the measured doses. Conversion of hypofractionated radiation doses to single doses using the LQ formalism could underestimate the effect of hypofractionated radiation by < or =30%.