Abstract.Dose volume histograms are a useful tool in state-of-the-art radiotherapy planning, and it is essential to be aware of their limitations. Dose distributions computed by treatment planning systems are affected by several sources of uncertainty such as algorithm limitations, measurement uncertainty in the data used to model the beam and residual differences between measured and computed dose, once the model is optimized. In order to take into account the effect of uncertainty, a probabilistic approach is proposed and a new kind of histogram, a dose-expected volume histogram, is introduced. The expected value of the volume in the region of interest receiving an absorbed dose equal or greater than a certain value is found using the probability distribution of the dose at each point. A rectangular probability distribution is assumed for this point dose, and a relationship is given for practical computations. This method is applied to a set of dose volume histograms for different regions of interest for 6 brain patients, 8 lung patients, 8 pelvis patients and 6 prostate patients planned for IMRT. These results show how dose computation uncertainty has effects on PTV coverage and, to a lesser extent, in dose to organs at risk. This method allows to quantify these effects.
alpha-DVHs provide bounds for DVH values while dose expected volume histograms can be used as central estimates for DVH when uncertainty is taken into account. They are particularly useful when an optimization approach is necessary.
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 α 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.
Dose expected volume histograms are a useful alternative to dose volume histograms in order to take into account computation uncertainty when prescribing, planning and reporting external beam radiation therapy. Due to the type B nature of computation uncertainties, a rectangular probability distribution was assumed in its definition. In the present work, the changes of dose expected volume histograms when using other recommended point dose uncertainty models are investigated. Results show that the choice of probability distribution, among the ones recommended for uncertainty modelling, has a small effect on the result. Thus, the standard uncertainty of point dose computations is the main parameter affecting dose expected volume histograms.
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