Abstract
In this paper, we present an almost linear time algorithm for the problem of splitting an intensity map of radiation (represented as an integer matrix) into multiple subfields (submatrices), subject to a given maximum allowable subfield width, to minimize the total delivery error caused by the splitting. This problem arises in intensity-modulated radiation therapy (IMRT) for cancer treatments. This is the first field splitting result on minimizing the total delivery error of the splitting. Our solution models the problem as a shortest path problem on a directed layered graph, which satisfies the staircase Monge property. Consequently, the resulting algorithm runs in almost linear time and generates an optimal quality field splitting.
This research was supported in part by 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 to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Aggarwal, A., Park, J.: Notes on Searching in Multidimensional Monotone Arrays. In: Proc. 29th Annual IEEE Symp. on Foundations of Computer Science, pp. 497–512. IEEE Computer Society Press, Los Alamitos (1988)
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. ACM Press, New York (2005)
Chen, D.Z., Wang, C.: Field Splitting Problems in Intensity-Modulated Radiation Therapy. In: Proc. of 17th International Symp. on Algorithms and Computation, pp. 690–700 (2006)
Deng, J., Pawlicki, T., Chen, Y., Li, J., Jiang, S.B., Ma, C.-M.: The MLC Tongue-and-Groove Effect on IMRT Dose Distribution. Physics in Medicine and Biology 46, 1039–1060 (2001)
Dogan, N., Leybovich, L.B., Sethi, A., Emami, B.: Automatic Feathering of Split Fields for Step-and-Shoot Intensity Modulated Radiation Therapy. Phys. Med. Biol. 48, 1133–1140 (2003)
Dou, X., Wu, X., Bayouth, J.E., Buatti, J.M.: The Matrix Orthogonal Decomposition Problem in Intensity-Modulated Radiation Therapy. In: Proc. 12th Annual International Computing and Combinatorics Conf., pp. 156–165 (2006)
Engel, K.: A New Algorithm for Optimal Multileaf Collimator Field Segmentation. Discrete Applied Mathematics 152(1-3), 35–51 (2005)
Gabow, H.N., Bentley, J., Tarjan, R.E.: Scaling and Related Techniques for Geometric Problems. In: Proc. 16th Annual ACM Symp. Theory of Computing, pp. 135–143. ACM Press, New York (1984)
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. 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., Ranka, S., Li, J., Palta, J.: A Comparison of Step-and-Shoot Leaf Sequencing Algorithms That Eliminate Tongue-and-Groove. Phys. Med. Biol. 49, 3137–3143 (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)
Klawe, M.M., Kleitman, D.J.: An Almost Linear Time Algorithm for Generalized Matrix Searching. Technical Report RJ 6275, IBM Research Division, Almaden Research Center (August 1988)
Luan, S., Wang, C., Chen, D.Z., Hu, X.S., Naqvi, S.A., Wu, X., Yu, C.X.: An Improved MLC Segmentation Algorithm and Software for Step-and-Shoot IMRT Delivery without Tongue-and-Groove Error. Med. Phys. 33(5), 1199–1212 (2006)
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: Proc. 11th Annual International Computing and Combinatorics Conf., pp. 504–513 (2005)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Chen, D.Z., Healy, M.A., Wang, C., Wu, X. (2007). A New Field Splitting Algorithm for Intensity-Modulated Radiation Therapy . In: Lin, G. (eds) Computing and Combinatorics. COCOON 2007. Lecture Notes in Computer Science, vol 4598. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73545-8_4
Download citation
DOI: https://doi.org/10.1007/978-3-540-73545-8_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-73544-1
Online ISBN: 978-3-540-73545-8
eBook Packages: Computer ScienceComputer Science (R0)