Pareto navigation: algorithmic foundation of interactive multi-criteria IMRT planning.

Inherently, IMRT treatment planning involves compromising between different planning goals. Multi-criteria IMRT planning directly addresses this compromising and thus makes it more systematic. Usually, several plans are computed from which the planner selects the most promising following a certain procedure. Applying Pareto navigation for this selection step simultaneously increases the variety of planning options and eases the identification of the most promising plan. Pareto navigation is an interactive multi-criteria optimization method that consists of the two navigation mechanisms 'selection' and 'restriction'. The former allows the formulation of wishes whereas the latter allows the exclusion of unwanted plans. They are realized as optimization problems on the so-called plan bundle -- a set constructed from pre-computed plans. They can be approximately reformulated so that their solution time is a small fraction of a second. Thus, the user can be provided with immediate feedback regarding his or her decisions. Pareto navigation was implemented in the MIRA navigator software and allows real-time manipulation of the current plan and the set of considered plans. The changes are triggered by simple mouse operations on the so-called navigation star and lead to real-time updates of the navigation star and the dose visualizations. Since any Pareto-optimal plan in the plan bundle can be found with just a few navigation operations the MIRA navigator allows a fast and directed plan determination. Besides, the concept allows for a refinement of the plan bundle, thus offering a middle course between single plan computation and multi-criteria optimization. Pareto navigation offers so far unmatched real-time interactions, ease of use and plan variety, setting it apart from the multi-criteria IMRT planning methods proposed so far.