Abstract
In this paper, we study an interesting matrix decomposition problem that seeks to decompose a “complicated” matrix into two “simpler” matrices while minimizing the sum of the horizontal complexity of the first sub-matrix and the vertical complexity of the second sub-matrix. The matrix decomposition problem is crucial for improving the “step-and-shoot” delivery efficiency in Intensity-Modulated Radiation Therapy, which aims to deliver a highly conformal radiation dose to a target tumor while sparing the surrounding normal tissues. Our algorithm is based on a non-trivial graph construction scheme, which enables us to formulate the decomposition problem as computing a minimum s-t cut in a 3-D geometric multi-pillar graph. Experiments on randomly generated intensity map matrices and on clinical data demonstrated the efficiency of our algorithm.
This research was supported in part by a faculty start-up fund from the University of Iowa, and in part by a fund from the American Cancer Society through an Institutional Research Grant to the Holden Comprehensive Cancer Center, the University of Iowa, Iowa City, IA, USA.
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References
Boland, N., Hamacher, H.W., Lenzen, F.: Minimizing Beam-on Time in Cancer Radiation Treatment Using Multileaf Collimators. Networks 43(4), 226–240 (2004)
Chen, Y., Hou, Q., Galvin, J.M.: A graph-searching method for MLC leaf sequencing under constraints. Med. Phys. 31, 1504–1511 (2004)
Chen, D.Z., Hu, X.S., Luan, S., Wang, C.: Mountain Reduction, Block Matching, and Medical Applications. In: Proc. of the 21st Annual Symposium on Computational Geometry (SoCG), Pisa, Italy, pp. 35–44 (2005)
Chen, D.Z., Hu, X.S., Luan, S., Wang, C., Wu, X.: Geometric Algorithms for Static Leaf Sequencing Problems in Radiation Therapy. International Journal of Computational Geometry and Applications 14(5), 311–339 (2004)
Dai, J., Zhu, Y.: Minimizing the Number of Segments in a Delivery Sequence for Intensity-Modulated Ratiation Therapy with Multileaf Collimator. Med. Phys. 28(10), 2113–2120 (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)
Engel, K.: A New Algorithm for Optimal Multileaf Collimator Field Segmentation (March 2003), http://www.trinity.edu/aholder/HealthApp/oncology/papers/paperlist.html
Hardemark, B., Rehbinder, H., Lof, J.: Rotating the MLC Between Segments Improves Performance in step-andshoot IMRT delivery. In: The AAPM 45th Meeting, Med. Phys., August 10-14, vol. 30 (2003)
Kalinowski, T.: Reducing the number of monitor units in multileaf collimator field segmentation. Physics in Medicine and Biology 50, 1147–1161 (2005)
Langer, M., Thai, V., Papiez, L.: Improved Leaf Sequencing Reduces Segments of Monitor Units Needed to Deliver IMRT Using Multileaf Collimators. Med. Phys. 28, 2450–2458 (2001)
Potter, L.D., Chang, S.X., Cullip, T.J., Siochi, A.C.: A Quality and Efficiency Analysis of the IMFAST TM Segmentation Algorithm in Head and Neck “Step & Shoot” IMRT Treatments. Med. Phys. 29(3), 275–283 (2002)
Que, W.: Comparison of Algorithms for Multileaf Collimator Field Segmentation. Med. Phys. 26, 2390–2396 (1999)
Svensson, R., Kallman, P., Brahme, A.: An Analytical Solution for the Dynamic Control of Multileaf Collimation. Phys. in Med. and Biol. 39, 37–61 (1994)
Webb, S.: The Physics of Conformal Radiotherapy Advances in Technology. Institute of Physics Publishing, Bristol (1997)
Webb, S.: Intensity-Modulated Radiation Therapy, Institute of Cancer Research and Royal Marsden NHS Trust (January 2001)
Wu, X., Chen, D.Z.: Optimal Net Surface Problems with Applications. In: Widmayer, P., Triguero, F., Morales, R., Hennessy, M., Eidenbenz, S., Conejo, R. (eds.) ICALP 2002. Wu, X., Chen, D.Z, vol. 2380, pp. 1029–1042. Springer, Heidelberg (2002)
Wu, Q., Arnfield, M., Tong, S., Wu, Y., Mohan, R.: Dynamic Splitting of Large Intensity-Modulated Fields. Phys. Med. Biol. 45, 1731–1740 (2000)
Xia, P., Verhey, L.J.: MLC Leaf Sequencing Algorithm for Intensity Modulated Beams with Multiple Static Segments. Med. Phys. 25, 1424–1434 (1998)
Boykov, Y., Jolly, M.-P.: Interactive Organ Segmentation Using Graph Cuts. In: Delp, S.L., DiGoia, A.M., Jaramaz, B. (eds.) MICCAI 2000. LNCS, vol. 1935, pp. 276–286. Springer, Heidelberg (2000)
Kim, J., Zabih, R.: A Segmentation Algorithm for Contrast-Enhanced Images. In: Proc. IEEE Int’l Conf. Computer Vision, pp. 502–509 (2003)
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Dou, X., Wu, X., Bayouth, J.E., Buatti, J.M. (2006). The Matrix Orthogonal Decomposition Problem in Intensity-Modulated Radiation Therapy. In: Chen, D.Z., Lee, D.T. (eds) Computing and Combinatorics. COCOON 2006. Lecture Notes in Computer Science, vol 4112. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11809678_18
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DOI: https://doi.org/10.1007/11809678_18
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