A quality index for equivalent uniform dose

Equivalent uniform dose (EUD) is the absorbed dose that, when homogeneously given to a tumor, yields the same mean surviving clonogen number as the given non-homogeneous irradiation. EUD is used as an evaluation tool under the assumption that two plans with the same value of EUD are equivalent, and their biological effect on the tumor (clonogen survival) would be the same as the one of a homogeneous irradiation of absorbed dose EUD. In this work, this assumption has been studied, and a figure of merit of its applicability has been obtained. Distributions of surviving clonogen number for homogeneous and non-homogeneous irradiations are found to be different even if their mean values are the same, the figure of merit being greater when there is a wider difference, and the equivalence assumption being less valid. Therefore, EUD can be closer to a uniform dose for some cases than for other ones (high a values, extreme heterogeneity), and the accuracy of the radiobiological indices obtained for evaluation, could be affected. Results show that the equivalence is very sensitive to the choice of radiobiological parameters, and this conclusion has been derived from mathematical properties of EUD.