Beam orientation optimization for intensity-modulated radiation therapy using mixed integer programming

Abstract

The purpose of this study is to extend an algorithm proposed for beam orientation optimization in classical conformal radiotherapy to intensity-modulated radiation therapy (IMRT) and to evaluate the algorithm's performance in IMRT scenarios. In addition, the effect of the candidate pool of beam orientations, in terms of beam orientation resolution and starting orientation, on the optimized beam configuration, plan quality and optimization time is also explored. The algorithm is based on the technique of mixed integer linear programming in which binary and positive float variables are employed to represent candidates for beam orientation and beamlet weights in beam intensity maps. Both beam orientations and beam intensity maps are simultaneously optimized in the algorithm with a deterministic method. Several different clinical cases were used to test the algorithm and the results show that both target coverage and critical structures sparing were significantly improved for the plans with optimized beam orientations compared to those with equi-spaced beam orientations. The calculation time was less than an hour for the cases with 36 binary variables on a PC with a Pentium IV 2.66 GHz processor. It is also found that decreasing beam orientation resolution to 10 degrees greatly reduced the size of the candidate pool of beam orientations without significant influence on the optimized beam configuration and plan quality, while selecting different starting orientations had large influence. Our study demonstrates that the algorithm can be applied to IMRT scenarios, and better beam orientation configurations can be obtained using this algorithm. Furthermore, the optimization efficiency can be greatly increased through proper selection of beam orientation resolution and starting beam orientation while guaranteeing the optimized beam configurations and plan quality.

An IMRT/VMAT Technique for Nonsmall Cell Lung Cancer

“…Our previous study demonstrated that some gantry angles benefited plan quality the most from beam modulation for some specific targets and OARs configuration [22]. Li and Xing [23] and Matuszak et al [24] also demonstrated that an additional modulation from “optimal” beam angle improved plan quality compared with VMAT alone.…”

Comparison of beam angle selection strategies for intracranial IMRT

“…Most studies concentrate on the demonstration of the feasibility of a novel BAS algorithm. 4,6,9,10,12,14,16,22,38 Studies covering clinical endpoints in greater detail observe comparable effects regarding improved OAR sparing by BAS. 7,8,39 Secondary plan characteristics, as discussed in this paper, are not quantified.…”

“…9 Hence, the BAS problem is usually formulated as a combinatorial optimization (CO) problem, i.e., the selection of an ensemble with η beams from a discrete set of |B| candidate beams. This combinatorial BAS problem may be solved efficiently with metaheuristics for CO-like simulated annealing, 3,5,10 genetic algorithms, 6,11,12 swarm algorithms, 13,14 and mixed integer programming 15,16 or with iterative strategies. 7,15,17,18 Independent BAS strategies, in contrast, exploit prior knowledge that may be based on geometric 8,19,20 or dosimetric 2,21,22 considerations to select a beam ensemble before the FO.…”

“…5 Both approaches have demonstrated clear benefits in comparison to standard beam configurations applying equispaced coplanar beams. 2,3,[5][6][7][8][10][11][12][13][14][15][16][17][18][19][20][21][22] In the literature, however, there is neither a comprehensive comparison of different BAS strategies nor a detailed analysis of the underlying BAS parameters and their clinical implications.…”

From analytic inversion to contemporary IMRT optimization: Radiation therapy planning revisited from a mathematical perspective

“…Local beam angle refinement has been approached through gradient descent [27], whereas most researchers applied stochastic search methods like genetic algorithms [38] or particle swarm algorithms [39]. Exact approaches that aim at truly finding an optimal subset of beam directions from a larger set of candidate beams are based on Mixed Integer Programming (MIP) methods [61]. See also the mathematically oriented review by Ehrgott et al [28].…”