Spherical cluster analysis for beam angle optimization in intensity-modulated radiation therapy treatment planning.

An intuitive heuristic to establish beam configurations for intensity-modulated radiation therapy is introduced as an extension of beam ensemble selection strategies applying scalar scoring functions. It is validated by treatment plan comparisons for three intra-cranial, pancreas, and prostate cases each. Based on a patient specific matrix listing the radiological quality of candidate beam directions individually for every target voxel, a set of locally ideal beam angles is generated. The spherical distribution of locally ideal beam angles is characteristic for every treatment site and patient: ideal beam angles typically cluster around distinct orientations. We interpret the cluster centroids, which are identified with a spherical K-means algorithm, as irradiation angles of an intensity-modulated radiation therapy treatment plan. The fluence profiles are subsequently optimized during a conventional inverse planning process. The average computation time for the pre-optimization of a beam ensemble is six minutes on a state-of-the-art work station. The treatment planning study demonstrates the potential benefit of the proposed beam angle optimization strategy. For the three prostate cases under investigation, the standard treatment plans applying nine coplanar equi-spaced beams and treatment plans applying an optimized non-coplanar nine-beam ensemble yield clinically comparable dose distributions. For symmetric patient geometries, the dose distribution formed by nine equi-spaced coplanar beams cannot be improved significantly. For the three pancreas and intra-cranial cases under investigation, the optimized non-coplanar beam ensembles enable better sparing of organs at risk while guaranteeing equivalent target coverage. Beam angle optimization by spherical cluster analysis shows the biggest impact for target volumes located asymmetrically within the patient and close to organs at risk.