Mixed integer programming approaches to exact minimization of total treatment time in cancer radiotherapy using multileaf collimators

Computers and Operations Research

Volumn 36, Issue 3, 2009, Pages 795-810

  Wake, Giulia M G H ^a   Boland, Natashia ^b   Jennings, Les S ^a  

^a UNIVERSITY OF WESTERN AUSTRALIA   (Australia)

^b UNIVERSITY OF MELBOURNE   (Australia)

Author keywords

Intensity modulated radiation therapy; Mixed integer programming; Multileaf collimator; Step and shoot; Total treatment time minimization

Indexed keywords

DYNAMIC PROGRAMMING; MATHEMATICAL PROGRAMMING; OPTICAL INSTRUMENTS; PATIENT TREATMENT; PLASMA WAVES; RADIOTHERAPY;

INTENSITY MODULATED RADIATION THERAPY; MIXED INTEGER PROGRAMMING; MULTILEAF COLLIMATOR; STEP-AND-SHOOT; TOTAL TREATMENT TIME MINIMIZATION;

INTEGER PROGRAMMING;

EID: 53749099071     PISSN: 03050548     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cor.2007.10.027     Document Type: Article

References (27)

1. Lee E.K., Fox T., and Crocker I. Integer programming applied to intensity-modulated radiation therapy treatment planning. Annals of Operations Research 119 (2003) 165-181
2. Olafsson A., and Wright S.J. Linear programming formulations and algorithms for radiotherapy treatment planning. Optimization Methods and Software 21 (2006) 201-231
3. Galvin J.M., Chen X., and Smith R.M. Combining multileaf fields to modulate fluence distributions. International Journal of Radiation Oncology, Biology and Physics 27 (1993) 697-705
4. Bortfeld T.R., Kahler D.L., Waldron T.J., and Boyer A.L. X-ray field compensation with multileaf collimators. International Journal of Radiation Oncology, Biology and Physics 28 (1994) 723-730
5. Siochi R.A.C. Minimizing static intensity modulation delivery time using an intensity solid paradigm. International Journal of Radiation Oncology, Biology and Physics 43 (1999) 671-680
6. Beavis A.W., Ganney P.S., Whitton V.J., and Zing L. Optimization of the step-and-shoot leaf sequence for delivery of intensity modulated radiation therapy using a variable division scheme. Physics in Medicine and Biology 46 (2001) 2457-2465
7. Baatar D., Hamacher H.W., Ehrgott M., and Woeginger G.J. Decomposition of integer matrices and multileaf collimator sequencing. Discrete Applied Mathematics 152 (2005) 6-34
8. Collins M.J., Kempe D., Saia J., and Young M. Nonnegative integral subset representation of integer sets. Information Processing Letters 101 (2007) 129-133
9. Xia P., and Verhey L.J. Multileaf collimator leaf sequencing algorithm for intensity modulated beams with multiple static segments. Medical Physics 25 (1998) 1424-1434
10. Que W. Comparison of algorithms for multileaf collimator field segmentation. Medical Physics 26 (1999) 2390-2396
11. Dai J., and Zhu Y. Minimizing the number of segments in a delivery sequence for intensity-modulated radiation therapy with a multileaf collimator. Medical Physics 28 (2001) 2113-2120
12. Crooks S.M., McAven L.F., Robinson D.F., and Xing L. Minimizing delivery time and monitor units in static IMRT by leaf sequencing. Physics in Medicine and Biology 47 (2002) 3105-3116
13. Fu W., Dai J., Hu Y., Han D., and Song Y. Delivery time comparison for intensity-modulated radiation therapy with/without flattening filter: a planning study. Physics in Medicine and Biology 49 (2004) 1535-1547
14. Siochi R.A.C. Modifications to the imfast leaf sequencing optimization algorithm. Medical Physics 31 (2004) 3267-3278
15. Baatar D. Matrix decomposition with time and cardinality objectives: theory, algorithms and application to multileaf collimator sequencing. PhD thesis, The Technical University of Kaiserslautern, Kaiserslautern, Germany, August 2005.
16. Engel K. A new algorithm for optimal multileaf collimator field segmentation. Discrete Applied Mathematics 152 (2005) 35-51
17. Kalinowski T. Optimal multileaf collimator field segmentation. PhD thesis, University of Rostock, Rostock, Germany, September 2004.
18. Kalinowski T. Multileaf collimator field segmentation without tongue-and-groove effect. Technical Report, University of Rostock, Rostock, Germany, October 2004.
19. Kalinowski T. A duality based algorithm for multileaf collimator field segmentation with interleaf collision constraint. Discrete Applied Mathematics 152 (2005) 52-88
20. Nußbaum M. Min cardinality C1 decomposition of integer matrices. Master's thesis, TU Kaiserslautern, 2006.
21. Ehrgott M., Hamacher H.W., and Nußbaum M. Decomposition of matrices and static multileaf collimators: a survey. In: Alves C.J.S., Pardalos P.M., and Vicente L.N. (Eds). Optimization in medicine (2007), Springer, Berlin 27-48
22. Langer M., Thai V., and Papiez L. Tradeoffs between segments and monitor units are not required for static field IMRT delivery. Journal of Radiation Oncology, Biology and Physics 51 (2001) 75
23. Boland N., Hamacher H.W., and Lenzen F. Minimizing beam-on time in cancer radiation treatment using multileaf collimators. Networks 43 (2004) 226-240
24. Ahuja R.K., and Hamacher H.W. A network flow algorithm to minimize beam-on time for unconstrained multileaf collimator problems in cancer radiation therapy. Networks 45 (2005) 36-41
25. Langer M., Thai V., and Papiez L. Improved leaf sequencing reduces segments of monitor units needed to deliver IMRT using multileaf collimators. Medical Physics 28 (2001) 2450-2458
26. Baatar D, Boland N, Brand S, Stuckey PJ. Minimum cardinality matrix decomposition into consecutive-ones matrices: CP and IP approaches. In: Integration of AI and OR techniques in constraint programming for combinatorial optimization problems. Lecture Notes in Computer Science, vol. 4510. Berlin: Springer; 2007. p. 1-15.
27. Johnston R.E., and Sadinlija E. A new model for complete solutions to one-dimensional cutting stock problems. Europearn Journal of Operational Research 153 (2004) 176-183