Mizuta 2
AbstractPurpose: Hypofractionated irradiation is often used in precise radiotherapy instead of conventional multi-fractionated irradiation. We propose a novel mathematical method for selecting a hypofractionated or multi-fractionated irradiation regime based on physical dose distribution adding to biological consideration.Methods and Materials: The linear quadratic (LQ) model was employed for the radiation effects on tumor and normal tissues, especially OARs. Based on the assumption that the OAR receives a fraction of the dose intended for the tumor, the minimization problem for the damage effect on the OAR was treated under the constraint that the radiation effect on the tumor is fixed.Results: For an N-time fractionated irradiation regime, the constraint of tumor lethality was described by an N-dimensional hypersphere. The total dose of the fractionated irradiations was considered for minimizing the damage effect on the OAR under the hypersphere condition. It was found that the advantage of hypofractionated or multi-fractionated irradiation therapies depends on the magnitude of the ratio of ïĄïŻïą parameters for the OAR and the tumor in the LQ model and the ratio of the dose for the OAR and the tumor.Conclusions: The present mathematical method shows that the multi-fractionated irradiation Mizuta 3 with a constant dose is better if the ratio of ïĄïŻïą for the OAR and the tumor is less than the ratio of the dose for the OAR and the tumor, while hypofractionated irradiation is better otherwise.