A Universal Radiobiological Formula For All Cell Survival Curves Over The Entire Radiation-Dose Range Useful For Quantification Of Equivalent Doses In Hypo-Fractioned SBRT, HDR, And SRS

A unified multi-activation (UMA) model of cell survival curves over the entire dose range for calculating equivalent doses in stereotactic body radiation therapy (SBRT), high dose rate brachytherapy (HDRB), and stereotactic radiosurgery (SRS)

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 D D o + n - 1 using only the extrapolation number of n and the dose slope of D_o was derived. Coefficient of determination, R² , 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 R²  > 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.