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)

Abstract

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 ¼ n= e D Do þ n À 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.

Theoretical derivation and clinical dose-response quantification of a unified multi-activation (UMA) model of cell survival from a logistic equation

“…The fitting of other 33 CSCs of human cancer cell lines for typical sites of hypofractionated radiotherapy results γ from 0.1 to 2 Gy −1 and n from 0.2 to 60, respectively. 19 The dose-independent γ and n as well as δ have confirmed the correct assumption in the derivation of Eq. (2).…”

“…Skin intrinsic RS at zero dose defined by γ/ n of the skin cell lines are from 0.34 to 1.14 Gy −1 that are even higher than the initial RS of 0.075/Gy to the squamous cell carcinoma. 19 More importantly, skin RS increases with dose in diagnostic imaging (<0.1 Gy) as predicted by for any skin cell lines with n > 1 to X-rays. Different γ values of 0.67, 1.08 and 2.27 Gy −1 to the fibroblasts from a normal person, a patient with D-deletion retinoblastoma and a patient with ataxia telangiectasia, with the same of n = 2, indicate that the first-order reaction activation constant not the reaction ratio varies significantly among patients with genetic alterations.…”

Linear-quadratic model in the description of the mechanisms of high-dose radiation therapy

“…9. Унифицированная мультиактивационная модель (unified multi-activation model -UMA), S. Li и соавт., 2021 г. работает во всем диапазоне доз, на основе формулы выживаемости клеток S=n/(eD/D0+n-1), использующая только экстраполяционное число n и наклон дозы D0, коэффициент детерминации, относительные остатки и относительные экспериментальные ошибки, нормированные на долю выживаемости в каждой точке дозы [13].…”