Incorporating organ movements in inverse planning: assessing dose uncertainties by Bayesian inference

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Abstract
We present a method to calculate dose uncertainties due to inter-fraction organ movements in fractionated radiotherapy, i.e. in addition to the expectation value of the dose distribution a variance distribution is calculated. To calculate the expectation value of the dose distribution in the presence of organ movements, one estimates a probability distribution of possible patient geometries. The respective variance of the expected dose distribution arises for two reasons: first, the patient is irradiated with a finite number of fractions only and second, the probability distribution of patient geometries has to be estimated from a small number of images and is therefore not exactly known. To quantify the total dose variance, we propose a method that is based on the principle of Bayesian inference. The method is of particular interest when organ motion is incorporated in inverse IMRT planning by means of inverse planning performed on a probability distribution of patient geometries. In order to make this a robust approach, it turns out that the dose variance should be considered (and minimized) in the optimization process. As an application of the presented concept of Bayesian inference, we compare three approaches to inverse planning based on probability distributions that account for an increasing degree of uncertainty. The Bayes theorem further provides a concept to interpolate between patient specific data and population-based knowledge on organ motion which is relevant since the number of CT images of a patient is typically small.