On the visualization of universal degeneracy in the IMRT problem

BACKGROUND: In general, the IMRT optimisation problem possesses many equivalent solutions. This makes it difficult to decide whether a result produced by an IMRT planning algorithm can be further improved, e.g. by adding more beams, or whether it is close to the globally best solution. RESULTS: It is conjectured that the curvature properties of the objective function around any globally optimum dose distribution are universal. This allows an assessment of optimality of dose distributions that are generated by different beam arrangements in a complementary manner to the objective function value alone. A tool to visualize the curvature structure of the objective function is devised. CONCLUSION: In an example case, it is demonstrated how the assessment of the curvature space can indicate the equivalence of rival beam configurations and their proximity to the global optimum.