Abstract
Intensity-modulated radiation therapy (IMRT) is a modern cancer treatment technique that delivers prescribed radiation dose distributions, called intensity maps (IMs), to target tumors via the help of a device called the multileaf collimator (MLC). Due to the maximum leaf spread constraint of the MLCs, IMs whose widths exceed a given threshold cannot be delivered as a whole, and thus must be split into multiple subfields. Field splitting problems in IMRTnormally aim to minimize the total beam-on time (i.e., the total time when a patient is exposed to actual radiation during the delivery) of the resulting subfields. In this paper, we present efficient polynomial time algorithms for two general field splitting problems with guaranteed output optimality. Our algorithms are based on interesting observations and analysis, as well as new techniques and modelings. We formulate the first field splitting problem as a special integer linear programming (ILP) problem that can be solved optimally by linear programming due to its geometry; from an optimal integer solution for the ILP, we compute an optimal field splitting by solving a set of shortest path problems on graphs. We tackle the second field splitting problem by using a novel path-sweeping technique on IMs.
This research was supported in part by the Faculty Research Program of the University of Notre Dame, the National Science Foundation under Grant CCF-0515203, and NIH NIBIB Grant R01-EB004640-01A2.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Ahuja, R.K., Hamacher, H.W.: A Network Flow Algorithm to Minimize Beam-on Time for Unconstrained Multileaf Collimator Problems in Cancer Radiation Therapy. Networks 45, 36–41 (2005)
Boland, N., Hamacher, H.W., Lenzen, F.: Minimizing Beam-on Time in Cancer Radiation Treatment Using Multileaf Collimators. Networks 43(4), 226–240 (2004)
Bortfeld, T.R., Boyer, A.L., Schlegel, W., Kahler, D.L., Waldron, T.L.: Realization and Verification of Three-Dimensional Conformal Radiotherapy with Modulated Fields. Int. J. Radiat. Oncol. Biol. Phys. 30, 899–908 (1994)
Chen, D.Z., Hu, X.S., Luan, S., Naqvi, S.A., Wang, C., Yu, C.: Generalized Geometric Approaches for Leaf Sequencing Problems in Radiation Therapy. Int. Journal of Computational Geometry and Applications 16(2-3), 175–204 (2006)
Chen, D.Z., Hu, X.S., Luan, S., Wang, C., Wu, X.: Geometric Algorithms for Static Leaf Sequencing Problems in Radiation Therapy. In: Proc. of 19th ACM Symposium on Computational Geometry, pp. 88–97 (2003)
Chen, D.Z., Hu, X.S., Luan, S., Wang, C., Wu, X.: Mountain Reduction, Block Matching, and Applications in Intensity-Modulated Radiation Therapy. In: Proc. of 21th ACM Symposium on Computational Geometry, pp. 35–44 (2005)
Engel, K.: A New Algorithm for Optimal Multileaf Collimator Field Segmentation. Discrete Applied Mathematics 152(1-3), 35–51 (2005)
Hong, L., Kaled, A., Chui, C., Losasso, T., Hunt, M., Spirou, S., Yang, J., Amols, H., Ling, C., Fuks, Z., Leibel, S.: IMRT of Large Fields: Whole-Abdomen Irradiation. Int. J. Radiat. Oncol. Biol. Phys. 54, 278–289 (2002)
Kamath, S., Sahni, S., Li, J., Palta, J., Ranka, S.: A Generalized Field Splitting Algorithm for Optimal IMRT Delivery Efficiency. In: The 47th Annual Meeting and Technical Exhibition of the American Association of Physicists in Medicine (AAPM) (2005), Also Med. Phys. 32(6), 1890 (2005)
Kamath, S., Sahni, S., Palta, J., Ranka, S.: Algorithms for Optimal Sequencing of Dynamic Multileaf Collimators. Phys. Med. Biol. 49(1), 33–54 (2004)
Kamath, S., Sahni, S., Ranka, S., Li, J., Palta, J.: Optimal Field Splitting for Large Intensity-Modulated Fields. Med. Phys. 31(12), 3314–3323 (2004)
Nemhauser, G.L., Wolsey, L.A.: Integer and Combinatorial Optimization. John Wiley, Chichester (1988)
Papadimitriou, C.H., Steiglitz, K.: Combinatorial Optimization: Algorithms and Complexity. Prentice-Hall, New Jersey (1982)
Siochi, R.A.C.: Minimizing Static Intensity Modulation Delivery Time Using an Intensity Solid Paradigm. Int J. Radiation Oncology Biol. Phys. 43(3), 671–680 (1999)
Webb, S.: The Physics of Three-Dimensional Radiation Therapy. Institute of Physics Publishing, Bristol (1993)
Webb, S.: The Physics of Conformal Radiotherapy — Advances in Technology. Institute of Physics Publishing, Bristol (1997)
Wu, Q., Arnfield, M., Tong, S., Wu, Y., Mohan, R.: Dynamic Splitting of Large Intensity-Modulated Fields. Phys. Med. Biol. 45, 1731–1740 (2000)
Wu, X.: Efficient Algorithms for Intensity Map Splitting Problems in Radiation Therapy. In: Wang, L. (ed.) COCOON 2005. LNCS, vol. 3595, pp. 504–513. Springer, Heidelberg (2005)
Xia, P., Verhey, L.J.: MLC Leaf Sequencing Algorithm for Intensity Modulated Beams with Multiple Static Segments. Med. Phys. 25, 1424–1434 (1998)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Chen, D.Z., Wang, C. (2006). Field Splitting Problems in Intensity-Modulated Radiation Therapy. In: Asano, T. (eds) Algorithms and Computation. ISAAC 2006. Lecture Notes in Computer Science, vol 4288. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11940128_69
Download citation
DOI: https://doi.org/10.1007/11940128_69
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-49694-6
Online ISBN: 978-3-540-49696-0
eBook Packages: Computer ScienceComputer Science (R0)