摘要
Treatment planning in external beam radiation therapy （EBRT） utilizes dose volume histograms （DVHs） as optimization and evaluation tools. They present the fraction of planning target volume （PTV） receiving more than a given absorbed dose, against the absorbed dose values, and a number of radiobiological indices can be computed with their help. Equivalent uniform dose （EUD） is the absorbed dose that, uniformly imparted, would yield the same biological effect on a tumor as the dose distribution described by the DVH. Uncertainty and missing information can affect the dose distribution, therefore DVHs can be modeled as samples from a set of possible outcomes. This work studies the sensitivity of the EUD index when a small change in absorbed dose distribution takes place. EUD is treated as a functional on the set of DVHs. Defining a Levy distance on this set and using a suitable expansion of the functional, a very simple expression for a bound on the variation of EUD when the dose distribution changes is found. This bound is easily interpreted in terms of standard treatment planning practice.
