TY - JOUR
T1 - 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)
AU - Li, Shidong
AU - Miyamoto, Curtis
AU - Wang, Bin
AU - Giaddui, Tawfik
AU - Micaily, Bizhan
AU - Hollander, Andrew
AU - Weiss, Stephanie E.
AU - Weaver, Michael
N1 - Publisher Copyright:
© 2021 The Authors. Medical Physics published by Wiley Periodicals LLC on behalf of American Association of Physicists in Medicine.
PY - 2021/4
Y1 - 2021/4
N2 - 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 (Formula presented.) using only the extrapolation number of n and the dose slope of Do 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.
AB - 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 (Formula presented.) using only the extrapolation number of n and the dose slope of Do 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.
KW - EQD2
KW - HDR
KW - Radiobiological Outcome modeling
KW - SBRT
KW - SRS
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UR - https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=purepublist2023&SrcAuth=WosAPI&KeyUT=WOS:000618227400001&DestLinkType=FullRecord&DestApp=WOS
U2 - 10.1002/mp.14690
DO - 10.1002/mp.14690
M3 - Article
C2 - 33590493
SN - 0094-2405
VL - 48
SP - 2038
EP - 2049
JO - Medical Physics
JF - Medical Physics
IS - 4
ER -