SU-E-T-712: Study of the Linear-Quadratic-Linear and Universal-Survival- Curve Models for Lung SBRT Using BED and EQD2 Concepts




Linear-quadratic-linear(LQ-L) and Universal-Survival-Curve(USC) models are investigated for the changes in biologically effective dose(BED) and equivalent dose at 2Gy/fraction(EQD2) for SBRT.


Survival data were extracted from published reports for 5 small-cell(SC) and 6 non-small cell(NSC) lung cancer cell lines. The best-fit regression and chi-square fit used to compute α and β of LQ, D0, and n of multitarget(MT) and y of LQ-L models, and used to calculate BED and EQD2 for lung SBRT.


The value of parameters α and β was determined by best-fit regression for low dose survival data(R2≥0.97) and by interactive-inspection and chi-square best-fit to initial curvature points for LQ model, respectively. D0 and n were calculated by best-fit regression to final slope points. Mean value of α, α/β, D0 and n with 95%CI was 0.756±0.152Gy-1, 16.31±7.78Gy, 1.014±0.308Gy and 1.688±0.696, respectively, for SC; and 0.18±0.081Gy-1, 7.74±5.893Gy, 2.90±1.704Gy and 3.69±3.36, for NSC, respectively. Mean value of α, α/β, D0 and n for lung tumors, averaging parameter values for all cell lines, was 0.442±0.194Gy-1, 11.63±5.241Gy, 1.28±1.07Gy and 2.78±1.88, respectively. BED and EQD2 for LQ, LQ-L and USC models calculated for dose levels I-IX of RTOG0813 protocol were 67.52–121.59Gy and 57.61–104.02Gy, 78.25–132.55Gy and 66.77–113.10Gy, 59.14–94.49Gy and 50.46–80.62Gy, respectively. USC curves closely overlap to survival data. For transition dose Dt=2α/β (α/β>6Gy) LQ-L curves have significant difference at higher doses than USC and survival data. When Dt(LQ-L)-Dt(USC), LQ-L curves exceptionally close to USC and experimental data. In SBRT doses, BED and EQD2 calculated by LQ and LQ-L(α/β>6Gy) are higher than that of USC model.


USC curves closely match with experimental data. BED and EQD2 for dose levels of RTOG0813 protocol for LQ and LQ-L(α/β>6Gy) have significant difference than USC values. BED matching for designing SBRT treatment should consider comprehensive calculations to include BED of USC model.