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In this paper, we compare two radiation effect models: the average surviving fraction (ASF) model and the integral biologically effective dose (IBED) model for deriving the optimal irradiation scheme and show the superiority of ASF. Minimizing the effect on an organ at risk (OAR) is important in radiotherapy. The biologically effective dose (BED) model is widely used to estimate the effect on the tumor or on the OAR, for a fixed value of dose. However, this is not always appropriate because the dose is not a single value but is distributed. The IBED and ASF models are proposed under the assumption that the irradiation is distributed. Although the IBED and ASF models are essentially equivalent for deriving the optimal irradiation scheme in the case of uniform distribution, they are not equivalent in the case of non-uniform distribution. We evaluate the differences between them for two types of cancers: high α/β ratio cancer (e.g. lung) and low α/β ratio cancer (e.g. prostate), and for various distributions i.e. various dose-volume histograms. When we adopt the IBED model, the optimal number of fractions for low α/β ratio cancers is reasonable, but for high α/β ratio cancers or for some DVHs it is extremely large. However, for the ASF model, the results keep within the range used in clinical practice for both low and high α/β ratio cancers and for most DVHs. These results indicate that the ASF model is more robust for constructing the optimal irradiation regimen than the IBED model.

Comparison of the average surviving fraction model with the integral biologically effective dose model for an optimal irradiation scheme