Reporting and analyzing dose distributions: a concept of equivalent uniform dose.

Modern treatment planning systems for three-dimensional treatment planning provide three-dimensionally accurate dose distributions for each individual patient. These data open up new possibilities for more precise reporting and analysis of doses actually delivered to irradiated organs and volumes of interest. A new method of summarizing and reporting inhomogeneous dose distributions is reported here. The concept of equivalent uniform dose (EUD) assumes that any two dose distributions are equivalent if they cause the same radiobiological effect. In this paper the EUD concept for tumors is presented, for which the probability of local control is assumed to be determined by the expected number of surviving clonogens, according to Poisson statistics. The EUD can be calculated directly from the dose calculation points or, from the corresponding dose-volume distributions (histograms). The fraction of clonogens surviving a dose of 2 Gy (SF2) is chosen to be the primary operational parameter characterizing radiosensitivity of clonogens. The application of the EUD concept is demonstrated on a clinical dataset. The causes of flattening of the observed dose-response curves become apparent since the EUD concept reveals the finer structure of the analyzed group of patients in respect to the irradiated volumes and doses actually received. Extensions of the basic EUD concept to include nonuniform density of clonogens, dose per fraction effects, repopulation of clonogens, and inhomogeneity of patient population are discussed and compared with the basic formula.