Article

Geometric algorithms for static leaf sequencing problems in radiation therapy

Authors:

Chao WangAuthors Info & Claims

SCG '03: Proceedings of the nineteenth annual symposium on Computational geometry

Pages 88 - 97

https://doi.org/10.1145/777792.777805

Published: 08 June 2003 Publication History

Abstract

The static leaf sequencing (SLS) problem arises in radiation therapy for cancer treatments, aiming to accomplish the delivery of a radiation prescription to a target tumor in the minimum amount of delivery time. Geometrically, the SLS problem can be formulated as a 3-D partition problem for which the 2-D problem of partitioning a polygonal domain (possibly with holes) into a minimum set of monotone polygons is a special case. In this paper, we present new geometric algorithms for a basic case of the 3-D SLS problem (which is also of clinical value) and for the general 3-D SLS problem. Our basic 3-D SLS algorithm, based on new geometric observations, produces guaranteed optimal quality solutions using Steiner points in polynomial time; the previously best known basic 3-D SLS algorithm gives optimal outputs only for the case without any Steiner points, and its time bound involves a multiplicative factor of a factorial function of the input. Our general 3-D SLS algorithm is based on our basic 3-D SLS algorithm and a polynomial time algorithm for partitioning a polygonal domain (possibly with holes) into a minimum set of x-monotone polygons, and has a fast running time. Experiments and comparisons using real medical data and on a real radiotherapy machine have shown that our 3-D SLS algorithms and software produce treatment plans that use significantly shorter delivery time and give better treatment quality than the current most popular commercial treatment planning system and the most well-known SLS algorithm. Some of our techniques and geometric procedures (e.g., for the problem of partitioning a polygonal domain into a minimum set of x-monotone polygons) are interesting in their own right.

References

[1]

R.K. Ahuja, T.L. Magnanti, and J.B. Orlin. Network Flows: Theory, Algorithms, and Applications. Prentice Hall, Inc., 1993.]]

Digital Library

[2]

E.M. Arkin, R. Connelly, and J.S.B. Mitchell. On monotone paths among obstacles, with applications to planning assemblies. In Proc. 8th ACM Symposium on Computational Geometry, pages 334--343, 1989.]]

Digital Library

[3]

T.R. Bortfeld, A.L. Boyer, W. Schlegel, D.L. Kahler, and T.L. Waldron. Experimental verification of multileaf conformal radiotherapy. In A.R. Hounsell, J.M. Wilkinson, and P.C. Williams, editors, Proc. 11th Int. Conf. on the Use of Computers in Radiation Therapy, pages 180--181, 1994.]]

[4]

T.R. Bortfeld, A.L. Boyer, W. Schlegel, D.L. Kahler, and T.L. Waldron. Realization and verification of three-dimensional conformal radiotherapy with modulated fields. Int. J. Radiat. Oncol. Biol. Phys., 30:899--908, 1994.]]

[5]

T.R. Bortfeld, D.L. Kahler, T.J. Waldron, and A.L. Boyer. X-ray field compensation with multileaf collimators. Int. J. Radiat. Oncol. Biol. Phys., 28:723--730, 1994.]]

[6]

T.R. Bortfeld, J. Stein, K. Preiser, and K. Hartwig. Intensity modulation for optimized conformal therapy. In Proc. Symp. Principles and Practice of 3-D Radiation Treatment Planning, 1996.]]

[7]

A.L. Boyer. Use of MLC for intensity modulation. Med. Phys., 21:1007, 1994.]]

[8]

A.L. Boyer, T.R. Bortfeld, D.L. Kahler, and T.J. Waldron. MLC modulation of X-ray beams in discrete steps. In Proc. 11th Int. Conf. on the Use of Computers in Radiation Therapy, pages 178--179, 1994.]]

[9]

A.L. Boyer and C.X. Yu. Delivery of intensity-modulated radiation therapy using dynamic multileaf collimator. In Seminar in Radiat. Oncol., volume 9, 1999.]]

[10]

M. Carol. An automatic 3-D treatment planning and implementation system for optimized conformal therapy. In 34th Annual Meeting of the American Society for Therapeutic Radiology and Oncology (ASTRO), 1992.]]

[11]

W.-T. Chan and F.Y.L. Chin. Efficient algorithms for finding a maximum number of disjoint paths in grids. Journal of Algorithms, 34:337--369, 2000.]]

Digital Library

[12]

W.-T. Chan, F.Y.L. Chin, and H.-F. Ting. Escaping a grid by edge-disjoint paths. In Proc. 11th Annual ACM-SIAM Symposium on Discrete Algorithms, pages 726--734, 2000.]]

Digital Library

[13]

D.Z. Chen, X. Hu, and X. Wu. Maximum red/blue interval matching with applications. In Proc. 7th Annual International Computing and Combinatorics Conf., pages 150--158, 2001.]]

Digital Library

[14]

D.Z. Chen, X.S. Hu, S. Luan, X. Wu, and C.X. Yu. Optimal terrain construction problems and applications in intensity-modulated radiation therapy. In Lecture Notes in Computer Science, Springer-Verlag, Proc. 10th Annual European Symposium on Algorithms (ESA'02), volume 2461, pages 270--283, 2002.]]

Digital Library

[15]

D.J. Convery and S. Webb. Generation of discrete beam-intensity modulation by dynamic multileaf collimation under minimum leaf separation constraints. Phys. Med. Biol., 43:2521--2538, 1998.]]

[16]

J. Dai and Y. Zhu. Minimizing the number of segments in a delivery sequence for intensity modulated radiation therapy with multileaf collimator. Med. Phys., 28(10):2113--2120, 2001.]]

[17]

M.N. Du, C.X. Yu, J.W. Wong, M. Symons, D. Yan, R.C. Matter, and A. Martinez. A multi-leaf collimator prescription preparation system for conventional radiotherapy. Int. J. Radiat. Oncol. Biol. Phys., 30(3):707--714, 1994.]]

[18]

P.M. Evans, V.N. Hansen, and W. Swindell. The optimum intensities for multiple static collimator field compensation. Med. Phys., 24(7):1147--1156, 1997.]]

[19]

L.R. Ford and D.R. Fulkerson. Maximal flow through a network. Canad. J. Math., 8:399--4045, 1956.]]

[20]

G. Gademann, W. Schlegel, G. Becker, J. Romahn, K.H. Hover, O. Pastyr, G. van Kaick, and M. Wannenmacher. High precision photon radiotherapy of head and neck tumors by means of an integrated stereotactic and 3D planning system. Int. J. Radiation Oncology Biol. Phys., 19(S1):135, 1990.]]

[21]

J. Hershberger and S. Suri. Efficient breakout routing in printed circuit boards. In Algorithms and Data Structures, 5th International Workshop, Lecture Notes in Computer Science, volume 1272, pages 462--471, 1997.]]

Digital Library

[22]

T.W. Holmes, A.R. Bleier, M.P. Carol, B.H. Curran, A.A. Kania, R.J. Lalonde, L.S. Larson, and E.S. Sternick. The effect of MLC leakage on the calculation and delivery of intensity modulated radiation therapy. In Proc. 12th Int. Conf. on the Use of Computers in Radiation Therapy, pages 346--349, 1997.]]

[23]

J.E. Hopcroft and R.M. Karp. An n 5/2 algorithm for maximum matching in bipartite graphs. SIAM J. Comput., 2:225--231, 1973.]]

Digital Library

[24]

J.M. Keil. Decomposing a polygon into simpler components. SIAM J. Comput., 14(4):799--817, 1985.]]

Digital Library

[25]

J.M. Keil. Polygon decomposition. In J.-R. Sack and J. Urrutia, editors, Handbook on Computational Geometry. Elsevier Science Publishers, 1999.]]

[26]

H. Kobayashi, S. Sakuma, O. Kaii, and H. Yogo. Computer-assisted conformation radiotherapy with a variable thickness multi-leaf filter. Int. J. Radiation Oncology Biol. Phys., 16(6):1631--1635, 1989.]]

[27]

D.D. Leavitt, F.A. Gibbs, M.P. Heilbrun, J.H. Moeller, and G.A. Takach. Dynamic field shaping to optimize stereotaxic radiosurgery. Int. J. Radiat. Oncol. Biol. Phys., 21(5):1247--1255, 1991.]]

[28]

D.D. Leavitt, M. Martin, J.H. Moeller, and W.L. Lee. Dynamic wedge field techniques through computer-controlled collimator or motion and dose delivery. Med. Phys., 17(1):87--91, 1990.]]

[29]

C. Lee. Personal communication, Department of Radiation Oncology, University of Maryland School of Medicine. October 2002.]]

[30]

A. Lingas and V. Soltan. Minimum convex partition of a polygon with holes by cuts in given directions. Theory of Computing Systems, 31:507--538, 1998.]]

[31]

R. Liu and S. Ntafos. On decomposing polygons into uniformly monotone parts. Information Processing Letters, 27:85--89, 1988.]]

Digital Library

[32]

S. Naqvi. Personal communication, Department of Radiation Oncology, University of Maryland School of Medicine. October 2002.]]

[33]

L.A. Nedzi, H.M. Kooy, E. Alexander, G.K. Svensson, and J.S. Loeffler. Dynamic field shaping for stereotaxic radiosurgery: A modeling study. Int. J. Radiat. Oncol. Biol. Phys., 25(5):859--869, 1993.]]

[34]

L. Palios. Connecting the maximum number of nodes in the grid to the boundary with non intersecting line segments. J. Algorithms, 22:57--92, 1997.]]

Digital Library

[35]

W. Que. Comparison of algorithms for multileaf collimator field segmentation. Med. Phys., 26:2390--2396, 1999.]]

[36]

V.P. Roychowdhury and J. Bruck. On finding non-intersecting paths in the grids and its application in reconfiguring VLSI/WSI arrays. In Proc. 1st Annual ACM-SIAM Symposium on Discrete Algorithms, pages 454--464, 1990.]]

Digital Library

[37]

A. Schweikard, R.Z. Tombropoulos, and J.R. Adler. Robotic radiosurgery with beams of adaptable shapes. In Springer, editor, Proc. 1st Int. Conf. on Computer Vision, Virtual Reality and Robotics in Medicine, Lecture Notes in Computer Science, volume 905, pages 138--149, 1995.]]

Digital Library

[38]

V. Soltan and A. Gorpinevich. Minimum dissection of rectilinear polygon with arbitrary holes into rectangles. In Proc. 8th Annual ACM Symposium on Computational Geometry, pages 296--302, 1992.]]

Digital Library

[39]

S. Webb. The Physics of Conformal Radiotherapy --- Advances in Technology. Bristol, Institute of Physics Publishing, 1997.]]

[40]

S. Webb. Configuration options for intensity-modulated radiation therapy using multiple static fields shaped by a multileaf collimator. Phys. Med. Biol., 43:241--260, 1998.]]

[41]

X. Wu, D.Z. Chen, X.S. Hu, S. Luan, L. Zhang, and C.X. Yu. A new leaf-sequencing algorithm for intensity-modulated arc therapy. Medical Physics, 28(6):1252, 2001.]]

[42]

P. Xia and L.J. Verhey. MLC leaf sequencing algorithm for intensity modulated beams with multiple static segments. Medical Physics, 25:1424--1434, 1998.]]

[43]

C.X. Yu. Intensity-modulated arc therapy with dynamic multileaf collimation: An alternative to tomotherapy. Phys. Med. Biol., 40:1435--1449, 1995.]]

[44]

C.X. Yu. Design considerations of the sides of the multileaf collimator. Phys. Med. Biol., 43(5):1335--1342, 1998.]]

[45]

C.X. Yu. Personal communication, Department of Radiation Oncology, University of Maryland School of Medicine. October 2002.]]

[46]

C.X. Yu, D. Yan, M.N. Du, S. Zhou, and L.J. Verhey. Optimization of leaf positioning when shaping a radiation field with a multileaf collimator. Phys. Med. Biol., 40(2):305--308, 1995.]]

[47]

M.-F. Yu and W.W.-M. Dai. Single-layer fanout routing and routability analysis for ball grid arrays. In Proc. of IEEE/ACM International Conference on Computer Aided Design, pages 581--586, 1995.]]

Digital Library

Cited By

Wu XDou XBayouth JBuatti J(2013)An almost linear time algorithm for field splitting in radiation therapyComputational Geometry: Theory and Applications10.1016/j.comgeo.2012.11.00146:6(673-687)Online publication date: 1-Aug-2013
https://dl.acm.org/doi/10.1016/j.comgeo.2012.11.001
Liu YWu X(2010)Minimizing total variation for field splitting with feathering in intensity-modulated radiation therapyProceedings of the 4th international conference on Frontiers in algorithmics10.5555/1881195.1881204(65-76)Online publication date: 11-Aug-2010
https://dl.acm.org/doi/10.5555/1881195.1881204
Liu YWu X(2010)Minimizing Total Variation for Field Splitting with Feathering in Intensity-Modulated Radiation TherapyFrontiers in Algorithmics10.1007/978-3-642-14553-7_9(65-76)Online publication date: 2010
https://doi.org/10.1007/978-3-642-14553-7_9
Show More Cited By

Index Terms

Geometric algorithms for static leaf sequencing problems in radiation therapy
1. Applied computing
  1. Life and medical sciences
2. Theory of computation
  1. Randomness, geometry and discrete structures
    1. Computational geometry

Recommendations

Polygon simplification by minimizing convex corners
Abstract
Let P be a polygon with r > 0 reflex vertices and possibly with holes and islands (i.e., components of the polygon inside holes). A subsuming polygon of P is a polygon P ′ such that P ⊆ P ′, each connected component R of P is a subset ...
Mountain reduction, block matching, and applications in intensity-modulated radiation therapy
SCG '05: Proceedings of the twenty-first annual symposium on Computational geometry

In this paper, we present a new geometric algorithm for the 3-D static leaf sequencing (SLS) problem arising in intensity-modulated radiation therapy (IMRT), a modern cancer treatment technique. The treatment time and machine delivery error are two ...
Geometric algorithms for leaf sequencing problems in intensity modulated radiation therapy

Comments

Information & Contributors

Information

Published In

cover image ACM Conferences

SCG '03: Proceedings of the nineteenth annual symposium on Computational geometry

June 2003

398 pages

ISBN:1581136633

DOI:10.1145/777792

Conference Chair:
Steve Fortune
Bell Laboratories

Copyright © 2003 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

Sponsors

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 08 June 2003

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Author Tags

Qualifiers

Article

Conference

SoCG03

Sponsor:

SoCG03: Annual ACM Symposium on Computational Geometry

June 8 - 10, 2003

California, San Diego, USA

Acceptance Rates

SCG '03 Paper Acceptance Rate 42 of 118 submissions, 36%;

Overall Acceptance Rate 625 of 1,685 submissions, 37%

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

14
Total Citations
View Citations
232
Total Downloads

Downloads (Last 12 months)2
Downloads (Last 6 weeks)0

Reflects downloads up to 15 Oct 2024

Other Metrics

View Author Metrics

Citations

Cited By

Wu XDou XBayouth JBuatti J(2013)An almost linear time algorithm for field splitting in radiation therapyComputational Geometry: Theory and Applications10.1016/j.comgeo.2012.11.00146:6(673-687)Online publication date: 1-Aug-2013
https://dl.acm.org/doi/10.1016/j.comgeo.2012.11.001
Liu YWu X(2010)Minimizing total variation for field splitting with feathering in intensity-modulated radiation therapyProceedings of the 4th international conference on Frontiers in algorithmics10.5555/1881195.1881204(65-76)Online publication date: 11-Aug-2010
https://dl.acm.org/doi/10.5555/1881195.1881204
Liu YWu X(2010)Minimizing Total Variation for Field Splitting with Feathering in Intensity-Modulated Radiation TherapyFrontiers in Algorithmics10.1007/978-3-642-14553-7_9(65-76)Online publication date: 2010
https://doi.org/10.1007/978-3-642-14553-7_9
Wu X(2008)Efficient intensity map splitting algorithms for intensity-modulated radiation therapyInformation Processing Letters10.1016/j.ipl.2007.11.008106:5(188-194)Online publication date: 1-May-2008
https://dl.acm.org/doi/10.1016/j.ipl.2007.11.008
Chen DLuan SWang C(2008)Coupled Path Planning, Region Optimization, and Applications in Intensity-Modulated Radiation TherapyAlgorithms - ESA 200810.1007/978-3-540-87744-8_23(271-283)Online publication date: 2008
https://doi.org/10.1007/978-3-540-87744-8_23
Luan SWang CChen DHu XNaqvi SWu XYu C(2006)An improved MLC segmentation algorithm and software for step‐and‐shoot IMRT delivery without tongue‐and‐groove errorMedical Physics10.1118/1.218882333:5(1199-1212)Online publication date: 12-Apr-2006
https://doi.org/10.1118/1.2188823
Chen DWang C(2006)Field splitting problems in intensity-modulated radiation therapyProceedings of the 17th international conference on Algorithms and Computation10.1007/11940128_69(690-700)Online publication date: 18-Dec-2006
https://dl.acm.org/doi/10.1007/11940128_69
Wu X(2005)Efficient Algorithms for Intensity Map Splitting Problems in Radiation TherapyProceedings of the 11th Annual International Conference on Computing and Combinatorics - Volume 359510.5555/2958119.2958132(504-513)Online publication date: 16-Aug-2005
https://dl.acm.org/doi/10.5555/2958119.2958132
Wu XAbraham JHaddad HOmicini AWainwright R(2005)The intensity level reduction in radiation therapyProceedings of the 2005 ACM symposium on Applied computing10.1145/1066677.1066736(242-246)Online publication date: 13-Mar-2005
https://dl.acm.org/doi/10.1145/1066677.1066736
Chen DHu XWang CWu XMitchell JRote G(2005)Mountain reduction, block matching, and applications in intensity-modulated radiation therapyProceedings of the twenty-first annual symposium on Computational geometry10.1145/1064092.1064101(35-44)Online publication date: 6-Jun-2005
https://dl.acm.org/doi/10.1145/1064092.1064101
Show More Cited By

View Options

Get Access

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Full Access

Get this Publication

View options

PDF

View or Download as a PDF file.

eReader

View online with eReader.

Media

Figures

Other

Tables

View Table of Contents