IMRT Beam Angle Optimization Using Non-descent Pattern Search Methods

Abstract

The intensity-modulated radiation therapy (IMRT) treatment planning is usually a sequential process where initially a given number of beam directions are selected followed by the fluence map optimization (FMO) considering those beam directions. The beam angle optimization (BAO) problem consists on the selection of appropriate radiation incidence directions in radiation therapy treatment planning and may be decisive for the quality of the treatment plan, both for appropriate tumor coverage and for enhancement of better organs sparing. This selection must be based on the optimal value of the FMO problem otherwise the resulting beam angle set has no guarantee of optimality and has questionable reliability. Pattern search methods (PSM) have been used successfully to address the BAO problem driven by the optimal fluence value of the FMO problem. PSM are iterative methods generating a sequence of non-increasing iterates such that iterate progression is solely based on a finite number of function evaluations in each iteration, without explicit or implicit use of derivatives. Typically, in IMRT optimization, the quality of the solutions obtained is not simply related to the final value of an objective function but rather judged by dose-volume histograms or considering a set of physical dose metrics. These dose metrics can be simply described as obtaining a minimum prescribed dose for the target volumes (the regions that have to be irradiated) and a maximum or mean tolerance dose values for the remaining surrounding structures (the regions that should be spared). The goal of this paper is to present a non-descent PSM that can be guided both by an objective function formulation of the FMO problem and by physical dose metrics. Four retrospective treated cases of head-and-neck tumors at the Portuguese Institute of Oncology of Coimbra are used to discuss the benefits of non-descent PSM for the optimization of the BAO problem.