Random sampling for evaluating treatment plans.

We analyze the influence of sampling technique on the accuracy of estimating irradiated volumes, dose-volume histograms and tumor control and normal tissue complication probabilities. The sampling techniques we consider are uniform distribution of points on a regular Cartesian grid and random selection of points. For three-dimensional treatment planning, random sampling leads to a significant reduction in estimation error and/or in the number of calculation points necessary to achieve a required accuracy. We discuss advantages and drawbacks of random sampling, as compared to sampling on a regular grid. It is suggested that, in practical situations, at least 50 times fewer randomly sampled points per organ/volume of interest are needed for fast estimation of complication probability with the same accuracy, i.e., not exceeding 5% (within 95% confidence limits) in the worst case.