Constrained segment shapes in direct-aperture optimization for step-and-shoot IMRT

Previous studies have shown that, by optimizing segment shapes and weights directly, without explicitly optimizing fluence profiles, effective IMRT plans can be generated with fewer segments. This study proposes a method of direct-aperture optimization with aperture shape constraints, which is designed to provide segmental IMRT plans using a minimum of simple, regular segments. The method uses a cubic function to create smoothly curving multileaf collimator shapes. Constraints on segment dimension and equivalent square are applied, and each segment can be constrained to lie within the previous one, for easy generation of fluence profiles with a single maximum. To simply optimize the segment shapes and reject any shapes which violate the constraints is too inefficient, so an innovative method of feedback optimization is used to ensure in advance that viable aperture shapes are generated. The algorithm is demonstrated using a simple cylindrical phantom consisting of a hemi-annular planning target volume and a central cylindrical organ-at-risk. A simple IMRT rectum case is presented, where segments are used to replace a wedge. More complex cases of prostate and seminal vesicles and prostate and pelvic nodes are also shown. The algorithm produces effective plans in each case with three to five segments per beam. For the simple plans, the constraint that each segment should be contained within the previous one adds additional simplicity to the plan, for a small reduction in plan quality. This study confirms that direct-aperture optimization gives efficient solutions to the segmental IMRT inverse problem and provides a method for generating simple apertures. By using such a method, the workload of IMRT verification may be reduced and simplified, as verification of fluence profiles from individual beams may be eliminated.