  We present a method to include robustness into a multi-criteria optimization
(MCO) framework for intensity-modulated proton therapy (IMPT). The approach
allows one to simultaneously explore the trade-off between different objectives
as well as the trade-off between robustness and nominal plan quality. In MCO, a
database of plans each emphasizing different treatment planning objectives, is
pre-computed to approximate the Pareto surface. An IMPT treatment plan that
strikes the best balance between the different objectives can be selected by
navigating on the Pareto surface. In our approach, robustness is integrated
into MCO by adding robustified objectives and constraints to the MCO problem.
Uncertainties of the robust problem are modeled by pre-calculated
dose-influence matrices for a nominal scenario and a number of pre-defined
error scenarios. A robustified objective represents the worst objective
function value that can be realized for any of the error scenarios. The
optimization method is based on a linear projection solver and is capable of
handling large problem sizes resulting from a fine dose grid resolution, many
scenarios, and a large number of proton pencil beams. A base-of-skull case is
used to demonstrate the robust optimization method. It is demonstrated that the
robust optimizationmethod reduces the sensitivity of the treatment plan to
setup and range errors to a degree that is not achieved by a safety margin
approach. A chordoma case is analyzed in more detail to demonstrate the
involved tradeoffs between target underdose and brainstem sparing as well as
robustness and nominal plan quality. The latter illustrates the advantage of
MCO in the context of robust planning. For all cases examined, the robust
optimization for each Pareto optimal plan takes less than 5 min on a standard
computer, making a computationally friendly interface possible to the planner.
