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One approach to multi-criteria IMRT planning is to automatically calculate a data set of Pareto-optimal plans for a given planning problem in a first phase, and then interactively explore the solution space and decide for the clinically best treatment plan in a second phase. The challenge of computing the plan data set is to assure that all clinically meaningful plans are covered and that as many as possible clinically irrelevant plans are excluded to keep computation times within reasonable limits. In this work, we focus on the approximation of the clinically relevant part of the Pareto surface, the process that consititutes the first phase. It is possible that two plans on the Parteto surface have a very small, clinically insignificant difference in one criterion and a significant difference in one other criterion. For such cases, only the plan that is clinically clearly superior should be included into the data set. To achieve this during the Pareto surface approximation, we propose to introduce bounds that restrict the relative quality between plans, so called tradeoff bounds. We show how to integrate these trade-off bounds into the approximation scheme and study their effects.
Modeling and formulation of optimization problems in IMRT planning comprises the choice of various values such as function-specific parameters or constraint bounds. These values also affect the characteristics of the optimization problem and thus the form of the resulting optimal plans. This publication utilizes concepts of sensitivity analysis and elasticity in convex optimization to analyze the dependence of optimal plans on the modeling parameters. It also derives general rules of thumb how to choose and modify the parameters in order to obtain the desired IMRT plan. These rules are numerically validated for an exemplary IMRT planning problems.