On the three-objective static unconstrained leaf sequencing in IMRT

Algorithms are an essential part of radiation therapy planning, which includes three optimizations problems: beam angle configuration, fluence map, and realization. This study addresses the third one, also called the leaf sequencing problem, which arises for each chosen irradiation angle, given the optimized fluence map. It consists in defining a sequence of configurations of a device (called multileaf collimator) that correctly delivers radiation to the patient. A usual model for this problem is the decomposition of a matrix into a weighted sum of (0,1)-matrices, called segments, in which the ones in each row appear consecutively. Each (0,1)-matrix corresponds to a configuration of the device. The realization problem has three objectives. The first one is to minimize the sum of weights assigned to the (0,1)-matrices. The second is to minimize the number of segments. Finally, the third one is to find the best order to apply those configurations. This study presents a greedy and randomized algorithm to this problem and compares it with other algorithms presented previously in the literature. Statistical tests show that our algorithm outperformed the previous ones regarding the quality indicators investigated. Graphical Abstract a Illustrates how the IMRT realization is modelled to a mathematical problem. b Shows a decomposition example of the IMRT realization. c The scheme of the algorithm that is proposed on this work, called GRA-SRA.