How many plans are needed in an IMRT multi-objective plan database?

In multi-objective radiotherapy planning, we are interested in Pareto surfaces of dimensions 2 up to about 10 (for head and neck cases, the number of structures to trade off can be this large). A key question that has not been answered yet is: how many plans does it take to sufficiently represent a high-dimensional Pareto surface? In this paper, we present a method to answer this question, and we show that the number of points needed is modest: 75 plans always controlled the error to within 5%, and in all cases but one, N + 1 plans, where N is the number of objectives, was enough for <15% error. We introduce objective correlation matrices and principal component analysis (PCA) of the beamlet solutions as two methods to understand this. PCA reveals that the feasible beamlet solutions of a Pareto database lie in a narrow, small dimensional subregion of the full beamlet space, which helps explain why the number of plans needed to characterize the database is small.