Compatibility of the Linear-Quadratic Formalism and Biologically Effective Dose Concept to High-Dose-Per-Fraction Irradiation in a Murine Tumor

Abstract

To evaluate the compliance of linear-quadratic (LQ) model calculations in the high-dose range as used in stereotactic irradiation in a murine tumor model. Female 10-week-old Balb/c mice bearing 1-cm-diameter EMT6 tumors in the hind legs were used. Single doses of 10-25 Gy were compared with 2-5 fractions of 4-13 Gy given at 4-hour intervals. Cell survival after irradiation was determined by an invivo-invitro assay. Using an α/β ratio determined for invitro EMT6 cells and the LQ formalism, equivalent single doses for the hypofractionated doses were calculated. They were then compared with actually measured equivalent single doses for the hypofractionated doses. These fractionation schedules were also compared simultaneously to investigate the concordance/divergence of dose-survival curves plotted against actual radiation doses and biologically effective doses (BED). Equivalent single doses for hypofractionated doses calculated from LQ formalism were lower than actually measured doses by 21%-31% in the 2- or 3-fraction experiments and by 27%-42% in the 4- or 5-fraction experiments. The differences were all significant. When a higher α/β ratio was assumed, the discrepancy became smaller. In direct comparison of the 2- to 5-fraction schedules, respective dose-response curves almost overlapped when cell survival was plotted against actual radiation doses. However, the curves tended to shift downward by increasing the fraction number when cell survival was plotted against BED calculated using an α/β ratio of 3.5 Gy for invitro EMT6 cells. Conversion of hypofractionated radiation doses to single doses using the LQ formalism underestimated the invivo effect of hypofractionated radiation by approximately 20%-40%. The discrepancy appeared to be larger than that seen in the previous invitro study and tended to increase with the fraction number. BED appeared to be an unreliable measure of tumor response.