Abstract
In this paper, we study an interesting geometric partition problem, called optimal field splitting, which arises in Intensity-Modulated Radiation Therapy (IMRT). In current clinical practice, a multi-leaf collimator (MLC) is used to deliver the prescribed intensity maps (IMs). However, the maximum leaf spread of an MLC may require to split a large intensity map into several overlapping sub-IMs. We develop the first optimal linear time algorithm for solving the field splitting problem while minimizing the total complexity of the resulting sub-IMs. Meanwhile, our algorithm strives to minimize the maximum beam-on time of those sub-IMs. Our basic idea is to formulate the field splitting problem as computing a shortest path in a directed acyclic graph, with a special “layered” structure. The edge weights of the graph satisfy the Monge property, which enables us to speed up the algorithm to optimal linear time. To minimize the maximum beam-on time of the resulting sub-IMs, we consider an interesting min-max slope path problem in a monotone polygon which is solvable in linear time. The min-max slope path problem is of its own interest.
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
Aggarwal, A., Klawe, M.M., Moran, S., Shor, P., Wilber, R.: Geometric Applications of a Matrix-Searching Algorithm. Algorithmica 2, 195–208 (1987)
Bortfeld, T., Craft, D., Trofimov, A., Halabi, T., Kufer, K.-H.: Quantifying the Tradeoff between Complexity and Conformality. In: 7th Annual Meeting and Technical Exhibition of the American Association of Physicists in Medicine (AAPM), Seattle, WA. Medical Physics, vol. 32(6) (2005)
Chen, D.Z., Wang, C.: Field Splitting Problems in Intensity-Modulated Radiation Therapy. In: Asano, T. (ed.) ISAAC 2006. LNCS, vol. 4288, pp. 690–700. Springer, Heidelberg (2006)
Chen, D.Z., Healy, M.A., Wang, C., Wu, X.: A New Field Splitting Algorithm for Intensity-Modulated Radiation Therapy. In: 13th Annual Int. Computing and Combinatorics Conference (COCOON) (July 2007)
Engel, K.: A New Algorithm for Optimal Multileaf Collimator Field Segmentation. Discrete Applied Mathematics 152(1-3), 35–51 (2005)
Kamath, S., Sahni, S., Ranka, S., Li, J., Palta, J.: Optimal Field Splitting for Large Intensity-Modulated Fields. Medical Physics 31(12), 3314–3323 (2004)
Kamath, S., Sahni, S., Li, J., Palta, J., Ranka, S., Generalized, A.: Field Splitting Algorithm for Optimal IMRT Delivery Efficiency, The 47th Annual Meeting and Technical Exhibition of the American Association of Physicists in Medicine (AAPM), 2005. Also, Med. Phys. 32(6) 1890 (2005)
Siochi, A.C.: Virtual Micro-Intensity Modulated Radiation Therapy. Medical Physics 27(11), 2480–2493 (2000)
Webb, S.: Intensity-Modulated Radiation Therapy, Institute of Cancer Research and Royal Marsden NHS Trust (2001)
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)
Wu, X., Dou, X.: Optimal Field Splitting with Feathering in Intensity-Modulated Radiation Therapy. In: Kao, M.-Y., Li, X.-Y. (eds.) AAIM 2007. LNCS, vol. 4508, pp. 327–336. Springer, Heidelberg (2007)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Wu, X., Dou, X., Bayouth, J., Buatti, J. (2007). New Algorithm for Field Splitting in Radiation Therapy. In: Tokuyama, T. (eds) Algorithms and Computation. ISAAC 2007. Lecture Notes in Computer Science, vol 4835. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77120-3_60
Download citation
DOI: https://doi.org/10.1007/978-3-540-77120-3_60
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-77118-0
Online ISBN: 978-3-540-77120-3
eBook Packages: Computer ScienceComputer Science (R0)