Quantization of setup uncertainties in 3-D dose calculations

Random setup errors can lead to erroneous prediction of the dose distribution calculated for a patient using a static computed tomography (CT) model. Multiple recomputations of the dose distribution covering the range of expected patient positions provides a way to estimate a course of treatment. However, due to the statistical nature of the setup uncertainties, many courses of treatment must be simulated to calculate a distribution of average dose values delivered to a patient. Thus, direct simulation methods can be time consuming and may be impractical for routine clinical treatment planning applications. Methods have been proposed to efficiently calculate the distribution of average dose values via a convolution of the dose distribution (calculated on a static CT model) with a probability distribution function (generally Gaussian) that describes the nature of the uncertainty. In this paper, we extend the convolution-based calculation to calculate the standard deviation of potential outcomes sigmaD(x,y,z) about the distribution of average dose values, and we characterize the statistical significance of this quantity using the central limit theorem. For an example treatment plan based on a treatment protocol in use at our institution, we found that there is a 68% probability that the actual dose delivered to any point (x,y,z) will be within 3% of the average dose value at that point. The standard deviation also yields confidence limits on the dose distribution, and these may be used to evaluate treatment plan stability.