Effect of daily localization and correction on the setup uncertainty: dependences on the measurement uncertainty, re-positioning uncertainty and action level.

With the advent of commercial image-guided radiotherapy, daily correction of the setup uncertainty is feasible. It is beneficial to understand the dependence of the probability density function (pdf) of the corrected setup variation on the action level, localization uncertainty and re-positioning uncertainty so that an appropriate action level is used. Also, that pdf can be used in treatment planning to incorporate setup variation directly in the planning process to generate treatment plans more robust to setup variations. We have found an analytical expression of the pdf of the corrected setup variation assuming normal distributions for the uncertainties. Using the second moment of that pdf as a metric, we have explored the dependence of the metric on the action level for the following cases: (1) the uncertainties in measurement and re-positioning are less than the initial setup uncertainty, (2) the uncertainties in measurement and re-positioning are on the order of the initial setup uncertainty, (3) the uncertainty in measurement is the least and (4) the uncertainty in re-positioning is the least. An optimal action level exists in case 3. We have also found that an action level of [Formula: see text] works well in practice where micro(p) is the mean of the re-positioning uncertainty, sigma(p) is the standard deviation of the re-positioning uncertainty and sigma(m) is the standard deviation of the localization uncertainty. In typical clinical situations, the distribution of the corrected setup variation can be closely approximated by a normal distribution.