Multi-criteria optimization methods in radiation therapy planning: a review of technologies and directions

We review the field of multi-criteria optimization for radiation therapy treatment planning. Special attention is given to the technique known as Pareto surface navigation, which allows physicians and treatment planners to interactively navigate through treatment planning options to get an understanding of the tradeoffs (dose to the target versus over-dosing of important nearby organs) involved in each patient's plan. We also describe goal programming and prioritized optimization, two other methods designed to handle multiple conflicting objectives. Issues related to nonconvexities, both in terms of dosimetric goals and the fact that the mapping from controllable hardware parameters to patient doses is usually nonconvex, are discussed at length since nonconvexities have a large impact on practical solution techniques for Pareto surface construction and navigation. A general planning strategy is recommended which handles the issue of nonconvexity by first finding an ideal Pareto surface with radiation delivered from many preset angles. This can be cast as a convex optimization problem. Once a high quality solution is selected from the Pareto surface, a sparse version (which can mean fewer beams, fewer segments, less leaf travel for arc therapy techniques, etc.) is obtained using an appropriate sparsification heuristic. We end by discussing issues of efficiency regarding the planning and the delivery of radiation therapy.