To establish a model for the calculation of biologically effective dose (BED) and EQD2 (Equivalent dose in 2 Gy fractions) in radioactive seed implantation brachytherapy.

The BED formula for EBRT(external beam radiotherapy) and for continuous low dose-rate irradiation established under the L-Q model were introduced. The EDQ2 formula for the continuous low dose-rate irradiation (radioactive seed implantation) was established according to the definition of EQD2 and the formula of BED. The α/β values of common tissues and the T_{r 1/2} values reported in the literature were summarized. The EDQ2 formula were further simplified by using the actual values. The empirical formula of EDQ2 for early reaction tissues and late reaction tissues were proposed, named as Wang-Peng empirical formula. EDQ2≈(10/12) D (Wang-Peng Formula 1) was fit for early response tissue, and EDQ2≈D/2 (Wang-Peng Formula 2) for late reaction tissues. Further examples on the clinical applications of the proposed formula were given, including primary lung cancer, supraclavicular lymph node metastasis of esophageal cancer and celic lymph node metastasis of cervical carcinoma.

According to the Wang-Peng empirical formula, the EDQ2 of the late reaction tissue adjacent to the tumor was only about half that of the tumor tissue, so the radioactive seed implantation brachytherapy "naturally" protected the late reaction tissue by the biological equivalent dose. The actual calculation, showed that the empirical formula of early reaction tissue was more accurate, but the empirical formula of late reaction orgtissue was less inaccurate and could only be roughly estimated.

The BED calculation formula introduced here and the set of EQD2 calculation formula and Wang-Peng empirical formula established here were theoretically feasible and could be used for the conversion and superposition between the physical dose of radioactive seed implantation brachytherapy and the external irradiation dose. But it should be careful to apply the formula, pay attention to the default conditions, and carefully interpret the calculated results.

Biologically effective dose; Radioactive seeds; Implantion brachytherapy; Carcinoma