Abstract
PURPOSE: Application of linear-quadratic (LQ) model to large fractional dose treatments is inconsistent with observed cell survival curves having a straight portion at high doses. We have proposed a unified multi-activation (UMA) model to fit cell survival curves over the entire dose range that allows us to calculate EQD2 for hypofractionated SBRT, SRT, SRS, and HDRB. METHODS: A unified formula of cell survival S = n/(e/ + n - 1) using only the extrapolation number of n and the dose slope of D(o) was derived. Coefficient of determination, R(2) , relative residuals, r, and relative experimental errors, e, normalized to survival fraction at each dose point, were calculated to quantify the goodness in modeling of a survival curve. Analytical solutions for α and β, the coefficients respectively describe the linear and quadratic parts of the survival curve, as well as the α/β ratio for the LQ model and EQD2 at any fractional doses were derived for tumor cells undertaking any fractionated radiation therapy. RESULTS: Our proposed model fits survival curves of in-vivo and in-vitro tumor cells with R(2) > 0.97 and r < e. The predicted α, β, and α/β ratio are significantly different from their values in the LQ model. Average EQD2 of 20-Gy SRS of glioblastomas and melanomas metastatic to the brain, 10-Gy × 5 SBRT of the lung cancer, and 7-Gy × 5 HDRB of endometrial and cervical carcinomas are 36.7 (24.3-48.5), 114.1 (86.6-173.1),, and 45.5 (35-52.6) Gy, different from the LQ model estimates of 50.0, 90.0, and 49.6 Gy, respectively. CONCLUSION: Our UMA model validated through many tumor cell lines can fit cell survival curves over the entire dose range within their experimental errors. The unified formula theoretically indicates a common mechanism of cell inactivation and can estimate EQD2 at all dose levels.