EQUIVALENT UNIFORM DOSE SENSITIVITY TO CHANGES IN ABSORBED DOSE DISTRIBUTION

Abstract

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 Lévy 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.