A Generalized Linear-Quadratic Model for Radiosurgery, Stereotactic Body Radiation Therapy, and High-Dose Rate Brachytherapy

Conventional radiation therapy for cancer usually consists of multiple treatments (called fractions) with low doses of radiation. These dose schemes are planned with the guidance of the linear-quadratic (LQ) model, which has been the most prevalent model for designing dose schemes in radiation therapy. The high-dose fractions used in newer advanced radiosurgery, stereotactic radiation therapy, and high-dose rate brachytherapy techniques, however, cannot be accurately calculated with the traditional LQ model. To address this problem, we developed a generalized LQ (gLQ) model that encompasses the entire range of possible dose delivery patterns and derived formulas for special radiotherapy schemes. We show that the gLQ model can naturally derive the traditional LQ model for low-dose and low-dose rate irradiation and the target model for high-dose irradiation as two special cases of gLQ. LQ and gLQ models were compared with published data obtained in vitro from Chinese hamster ovary cells across a wide dose range [0 to similar to 11.5 gray (Gy)] and from animals with dose fractions up to 13.5 Gy. The gLQ model provided consistent interpretation across the full dose range, whereas the LQ model generated parameters that depended on dose range, fitted only data with doses of 3.25 Gy or less, and failed to predict high-dose responses. Therefore, the gLQ model is useful for analyzing experimental radiation response data across wide dose ranges and translating common low-dose clinical experience into high-dose radiotherapy schemes for advanced radiation treatments.