Selection of intensity modulated radiation therapy treatment beam directions using radial basis functions within a pattern search methods framework
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The selection of appropriate radiation incidence directions in radiation therapy treatment planning is important for the quality of the treatment plan, both for appropriate tumor coverage and for better organ sparing. The objective of this paper is to discuss the benefits of using radial basis functions within a pattern search methods framework in the optimization of the highly non-convex beam angle optimization (BAO) problem. Pattern search methods are derivative-free optimization methods that require few function value evaluations to converge and have the ability to avoid local entrapment. These two characteristics gathered together make pattern search methods suited to address the BAO problem. The pattern search methods framework is composed by a search step and a poll step at each iteration. The poll step performs a local search in a mesh neighborhood and assures convergence to a local minimizer or stationary point. The search step provides the flexibility for a global search since it allows searches away from the neighborhood of the current iterate. Radial basis functions are used and tested in this step both to influence the quality of the local minimizer found by the method and to obtain a better coverage of the search space in amplitude. A set of retrospective treated cases of head-and-neck tumors at the Portuguese Institute of Oncology of Coimbra is used to discuss the benefits of using this approach in the optimization of the BAO problem.
KeywordsIntensity modulated radiation therapy Beam angle optimization Pattern search methods Radial basis functions
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- 4.Aleman, D.M., Mišić, V.V., Sharpe, M.B.: Computational enhancements to fluence map optimization for total marrow irradiation using IMRT. Comput. Oper. Res. (Forthcoming). doi: 10.1016/j.cor.2011.05.028
- 8.Conn, A.R., Scheinberg, K., Vicente, L.N.: Introduction to derivative-free optimization. SIAM, Philadelphia (2009)Google Scholar
- 30.MATLAB, The MathWorks Inc. http://www.mathworks.com
- 35.Powell M.: Radial basis function methods for interpolation to functions of many variables. HERMIS Int. J. Comput. Maths Appl. 3, 1–23 (2002)Google Scholar
- 40.Rocha, H., Dias, J.M., Ferreira, B.C., Lopes, M.C.: Beam angle optimization using pattern search methods: initial mesh-size considerations. In: Proceedings of the 1st International Conference on Operations Research and Enterprise Systems (2012)Google Scholar
- 51.Stone M.: Cross-validatory choice and assessment of statistical predictions. J. R. Stat. Soc. 36, 111–147 (1974)Google Scholar
- 53.Tu, J.: Cross-validated multivariate metamodeling methods for physics-based computer simulations. In: Proceedings of the IMAC-XXI (2003)Google Scholar
- 54.Tu, J., Jones, D.R.: Variable screening in metamodel design by cross-validated moving least squares method. In: Proceedings of the 44th AIAA (2003)Google Scholar