IMRT Optimization with Both Fractionation and Cumulative Constraints

Author(s)
Delal Dink,
Mark Langer,
Seza Orcun,
Joseph Pekny,
Ronald Rardin,
Gintaras Reklaitis,
Behlul Saka

ABSTRACT

Radiation therapy plans are optimized as a single treatment plan, but delivered over 30 - 50 treatment sessions (known as fractions). This paper proposes a new mixed-integer linear programming model to simultaneously incorporate fractionation and cumulative constraints in Intensity Modulated Radiation Therapy (IMRT) planning optimization used in cancer treatment. The method is compared against a standard practice of posing only cumulative limits in the optimization. In a prostate case, incorporating both forms of limits into planning converted an undeliverable plan obtained by considering only the cumulative limits into a deliverable one within 3% of the value obtained by ignoring the fraction size limits. A two-phase boosting strategy is studied as well, where the first phase aims to radiate primary and secondary targets simultaneously, and the second phase aims to escalate the tumor dose. Using of the simultaneous strategy on both phases, the dose difference between the primary and secondary targets was enhanced, with better sparing of the rectum and bladder.

Radiation therapy plans are optimized as a single treatment plan, but delivered over 30 - 50 treatment sessions (known as fractions). This paper proposes a new mixed-integer linear programming model to simultaneously incorporate fractionation and cumulative constraints in Intensity Modulated Radiation Therapy (IMRT) planning optimization used in cancer treatment. The method is compared against a standard practice of posing only cumulative limits in the optimization. In a prostate case, incorporating both forms of limits into planning converted an undeliverable plan obtained by considering only the cumulative limits into a deliverable one within 3% of the value obtained by ignoring the fraction size limits. A two-phase boosting strategy is studied as well, where the first phase aims to radiate primary and secondary targets simultaneously, and the second phase aims to escalate the tumor dose. Using of the simultaneous strategy on both phases, the dose difference between the primary and secondary targets was enhanced, with better sparing of the rectum and bladder.

KEYWORDS

IMRT, Mixed-Integer Linear Programming, Optimization, Cumulative Dose Constraints, Fractionation, Two-Phase Planning, Uniform Fractionation

IMRT, Mixed-Integer Linear Programming, Optimization, Cumulative Dose Constraints, Fractionation, Two-Phase Planning, Uniform Fractionation

Cite this paper

nullD. Dink, M. Langer, S. Orcun, J. Pekny, R. Rardin, G. Reklaitis and B. Saka, "IMRT Optimization with Both Fractionation and Cumulative Constraints,"*American Journal of Operations Research*, Vol. 1 No. 3, 2011, pp. 160-171. doi: 10.4236/ajor.2011.13018.

nullD. Dink, M. Langer, S. Orcun, J. Pekny, R. Rardin, G. Reklaitis and B. Saka, "IMRT Optimization with Both Fractionation and Cumulative Constraints,"

References

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[2] A. I. Blanco and K. S. C. Chao, “Intensity-Modulated Radiation Therapy and Protection of Normal Tissue Function in Head and Neck Cancer,” In: C. A. Perez and L. W. Brady, Eds., Principles and Practice of Radiation Oncology Updates, Lippincott Williams & Wilkins Healthcare, New York, 2002, pp. 2-12.

[3] M. Langer, R. Brown, M. Urie, J. Leong, M. Stracher and J. Shapiro, “Large Scale Optimization of Beam Weights under Dose-Volume Restrictions,” International Journal of Radiation Oncology, Biology, Physics, Vol. 18, No. 4, 1990, pp. 887-893. doi:10.1016/0360-3016(90)90413-E

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[8] H. E. Romeijn, R. K. Ahuja, J. F. Dempsey, A. Kumar and J. G. Li, “A Novel Linear Programming Approach to Fluence Map Optimization for Intensity Modulated Radiation Treatment Planning,” Physics in Medicine and Biology, Vol. 48, No. 21, 2003, pp. 3521-3542. doi:10.1088/0031-9155/48/21/005

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[10] F. Preciado-Walters, R. L. Rardin, M. P. Langer and V. Thai, “A Coupled Column Generation, Mixed Integer Approach to Optimal Planning of Intensity Modulated Radiation Therapy for Cancer,” Mathematical Programming, Vol. 101, No. 2, 2004, pp. 319-338. doi:10.1007/s10107-004-0527-6

[11] A. Tuncel, “Methods and Algorithms for Radiation Therapy Optimization under Dose-Volume Restrictions,” Ph.D. Dissertation, Purdue University, West Lafayette, 2008.

[12] F. Preciado-Walters, M. P. Langer, R. L. Rardin and V. Thai, “Column Generation for IMRT Cancer Therapy Optimization with Implementable Segments,” Annals of Operations Research, Vol. 148, No. 1, 2006, pp. 65-79. doi:10.1007/s10479-006-0080-1

[13] H. E. Romeijn, R. K. Ahuja, J. F. Dempsey and A. Kumar, “A Column Generation Approach to Radiation Therapy Treatment Planning Using Aperture Modulation,” SIAM Journal on Optimization, Vol. 15, No. 3, 2005, pp. 838-862. doi:10.1137/040606612

[14] S. Webb, “Optimization by Simulated Annealing of Three- Dimensional Conformal Treatment Planning for Radiation Fields Defined by a Multileaf Collimator,” Physics in Medicine and Biology, Vol. 36, No. 9, 1991, pp. 1201- 1226. doi:10.1088/0031-9155/36/9/004

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[16] G. S. Mageras and R. Mohan, “Application of Fast Simulated Annealing to Optimization of Conformal Radiation Treatments,” Medical Physics, Vol. 20, No. 3, 1993, pp. 639-647. doi:10.1118/1.597012

[17] M. Langer, S. Morrill, R. Brown, O. Lee and R. Lane, “A Comparison of Mixed-Integer Programming and Fast Simulated Annealing for Optimizing Beam Weights in Radiation Therapy,” Medical Physics, Vol. 23, No. 6, 1996, pp. 957-964. doi:10.1118/1.597857

[18] M. Langer, S. Morrill, R. Brown, O. Lee and R. Lane, “A Genetic Algorithm for Generating Beam Weights,” Medical Physics, Vol. 23, No. 6, 1996, pp. 965-971. doi:10.1118/1.597858

[19] G. A. Ezzel, “Genetic and Geometric Optimization of Three-Dimensional Radiation Therapy Treatment Planning,” Medical Physics, Vol. 23, No. 3, 1996, pp. 293- 305. doi:10.1118/1.597660

[20] X. Wu, Y. Zhu, J. Dai and Z. Wang, “Selection and Determination of Beam Weights based on Genetic Algorithms for Conformal Radiotherapy Treatment Planning,” Physics in Medicine and Biology, Vol. 45, No. 9, 2000, pp. 2547-2558. doi:10.1088/0031-9155/45/9/308

[21] P. S. Cho, S. Lee, R. J. Marks, S. Oh, S. G. Sutlief and M. H. Phillips, “Optimization of Intensity Modulated Beams with Volume Constraints Using Two Methods: Cost Function Minimization and Projections onto Convex Sets,” Medical Physics, Vol. 25, No. 4, 1998, pp. 435- 443. doi:10.1118/1.598218

[22] D. H. Hristov and B. G. Fallone, “A Continuous Penalty Function Method for Inverse Treatment Planning,” Medical Physics, Vol. 25, No. 2, 1998, pp. 208-223. doi:10.1118/1.598183

[23] S. V. Spirou and C. S. Chui, “A Gradient Inverse Planning Algorithm with Dose-Volume Constraints,” Medical Physics, Vol. 25, No. 3, 1998, pp. 321-333. doi:10.1118/1.598202

[24] Q. Wu and R. Mohan, “Algorithms and Functionality of an Intensity Modulated Radiotherapy Optimization System,” Medical Physics, Vol. 27, No. 4, 2000, pp. 701- 711. doi:10.1118/1.598932

[25] P. Cheung, K. Sixel, G. Morton, D. A. Loblaw, R. Tirona, G. Pang, R. Choo, E. Szumacher, G. Deboer and J. P. Pignol, “Individualized Planning Target Volumes for Intrafraction Motion during Hypofractionated Intensity- Modulated Radiotherapy Boost for Prostate Cancer,” International Journal of Radiation Oncology, Biology, Phy- sics, Vol. 62, No. 2, 2005, pp. 418-425.

[26] M. Guerrero, X. A. Li, L. Ma, J. Linder, C. Deyoung and B. Erickson, “Simultaneous Integrated Intensity-Modulated Radiotherapy Boost for Locally Advanced Gynecological Cancer: Radiobiological and Dosimetric Considerations,” International Journal of Radiation Oncology, Biology, Physics, Vol. 62, No. 3, 2005, pp. 933-939. doi:10.1016/j.ijrobp.2004.11.040

[27] M. L. Cavey, J. E. Bayouth, M. Colman, E. J. Endres and G. Sanguineti, “IMRT to Escalate the Dose to the Prostate While Treating the Pelvic Nodes,” Strahlenther Onkol, Vol. 181, No. 7, 2005, pp. 431-441. doi:10.1007/s00066-005-1384-9

[28] X. A. Li, J. Z. Wang, P. A. Jursinic, C. A. Lawton and D. Wang, “Dosimetric Advantages of IMRT Simultaneous Integrated Boost for High-Risk Prostate Cancer,” International Journal of Radiation Oncology, Biology, Physics, Vol. 61, No. 4, 2005, pp. 1251-1257. doi:10.1016/j.ijrobp.2004.11.034

[29] R. A. Popple, P. B. Prellop, S. A. Spencer, J. F. De Los Santos, J. Duan, J. B. Fiveash and I. A. Brezovich, “Simultaneous Optimization of Sequential IMRT Plans,” Medical Physics, Vol. 32, No. 11, 2005, pp. 3257-3266. doi:10.1118/1.2064849

[30] S. M. Morrill, R. G. Lane, J. A. Wong and I. I. Rosen, “Dose-Volume Considerations with Linear Programming Optimization,” Medical Physics, Vol. 18, No. 6, 1991, pp. 1201-1210. doi:10.1118/1.596592

[31] D. Dink, “Approaches to 4-D Intensity Modulated Radiation Therapy Planning with Fraction Constraints,” Ph.D. Dissertation, Purdue University, West Lafayette, 2005.

[32] S. M. Morrill, I. I. Rosen, R. G. Lane and J. A. Belli, “The Influence of Dose Constraint Point Placement on Optimized Radiation Therapy Treatment Planning,” International Journal of Radiation Oncology, Biology, Phy- sics, Vol. 19, No. 1, 1990, pp. 129-1241.

[33] A. Niemierko and M. Goitein, “Random Sampling for Evaluating Treatment Plans,” Medical Physics, Vol. 17, No. 5, 1990, pp. 753-762. doi:10.1118/1.596473

[34] A. Niemierko and M. Goitein, “Letter to the Editor, Comments on ‘Sampling Techniques for the Evaluation of Treatment Plans’,” Medical Physics, Vol. 20, No. 1, 1993, pp. 1377-1380. doi:10.1118/1.597103

[35] X.-Q. Lu and L. M. Chin, “Sampling Techniques for the Evaluation of Treatment Plans,” Medical Physics, Vol. 20, No. 1, 1993, pp. 151-161. doi:10.1118/1.597096

[36] R. Acosta, W. Brick, A. Hanna, A. Holder, D. Lara, G. McQuilen, D. Nevin, P. Uhlig and B. Salter, “Radiotherapy Optimal Design: An Academic Radiotherapy Treatment Design System,” In: J. W. Chinneck, B. Kristjansson, and M. J. Saltman, Eds., Operations Research and Cyber-Infrastructure, Springer, New York, 2009, pp. 401- 425. doi:10.1007/978-0-387-88843-9_21

[37] Sherouse Systems Inc., 2011. http://www.gwsherouse.com

[1] Q. Wu, M. Manning, R. Schmidt-Ulrich and R. Mohan, “The Potential for Sparing of Parotids and Escalation of Biologically Effective Dose with Intensity-Modulated Radiation Treatments of Head and Neck Cancers: A Treatment Design Study,” International Journal of Radiation Oncology, Biology, Physics, Vol. 46, No. 1, 2000, pp. 195-205. doi:10.1016/S0360-3016(99)00304-1

[2] A. I. Blanco and K. S. C. Chao, “Intensity-Modulated Radiation Therapy and Protection of Normal Tissue Function in Head and Neck Cancer,” In: C. A. Perez and L. W. Brady, Eds., Principles and Practice of Radiation Oncology Updates, Lippincott Williams & Wilkins Healthcare, New York, 2002, pp. 2-12.

[3] M. Langer, R. Brown, M. Urie, J. Leong, M. Stracher and J. Shapiro, “Large Scale Optimization of Beam Weights under Dose-Volume Restrictions,” International Journal of Radiation Oncology, Biology, Physics, Vol. 18, No. 4, 1990, pp. 887-893. doi:10.1016/0360-3016(90)90413-E

[4] M. Langer, P. Kijewski, R. Brown and C. Ha, “The Effect on Minimum Tumor Dose of Restricting Target-Dose Inhomogeneity in Optimized Three-Dimensional Treatment of Lung Cancer,” Radiotherapy and Oncology, Vol. 21, No. 4, 1991, pp. 245-256. doi:10.1016/0167-8140(91)90049-M

[5] M. Langer, E. K. Lee, J. O. Deasy, R. L. Rardin and J. A. Deye, “Operations Research Applied to Radiotherapy, An NCI-NSF-Sponsored Workshop,” International Journal of Radiation Oncology, Biology, Physics, Vol. 57, No. 3, 2003, pp. 762-768. doi:10.1016/S0360-3016(03)00720-X

[6] E. K. Lee, T. Fox and I. Crocker, “Integer Programming Applied to Intensity-Modulated Radiation Treatment Planning,” Annals of Operations Research, Vol. 119, No. 1-4, 2003, pp. 165-181. doi:10.1023/A:1022938707934

[7] E. K. Lee, T. Fox and I. Crocker, “Simultaneous Beam Geometry and Intensity Map Optimization in Intensity-Modulated Radiation Therapy,” International Journal of Radiation Oncology, Biology, Physics, Vol. 64, No. 1, 2006, pp. 301-320. doi:10.1016/j.ijrobp.2005.08.023

[8] H. E. Romeijn, R. K. Ahuja, J. F. Dempsey, A. Kumar and J. G. Li, “A Novel Linear Programming Approach to Fluence Map Optimization for Intensity Modulated Radiation Treatment Planning,” Physics in Medicine and Biology, Vol. 48, No. 21, 2003, pp. 3521-3542. doi:10.1088/0031-9155/48/21/005

[9] H. E. Romeijn, R. K. Ahuja and J. F. Dempsey, “A New Linear Programming Approach to Radiation Therapy Treatment Planning Problems,” Operations Research, Vol. 54, No. 2, 2006, pp. 201-216. doi:10.1287/opre.1050.0261

[10] F. Preciado-Walters, R. L. Rardin, M. P. Langer and V. Thai, “A Coupled Column Generation, Mixed Integer Approach to Optimal Planning of Intensity Modulated Radiation Therapy for Cancer,” Mathematical Programming, Vol. 101, No. 2, 2004, pp. 319-338. doi:10.1007/s10107-004-0527-6

[11] A. Tuncel, “Methods and Algorithms for Radiation Therapy Optimization under Dose-Volume Restrictions,” Ph.D. Dissertation, Purdue University, West Lafayette, 2008.

[12] F. Preciado-Walters, M. P. Langer, R. L. Rardin and V. Thai, “Column Generation for IMRT Cancer Therapy Optimization with Implementable Segments,” Annals of Operations Research, Vol. 148, No. 1, 2006, pp. 65-79. doi:10.1007/s10479-006-0080-1

[13] H. E. Romeijn, R. K. Ahuja, J. F. Dempsey and A. Kumar, “A Column Generation Approach to Radiation Therapy Treatment Planning Using Aperture Modulation,” SIAM Journal on Optimization, Vol. 15, No. 3, 2005, pp. 838-862. doi:10.1137/040606612

[14] S. Webb, “Optimization by Simulated Annealing of Three- Dimensional Conformal Treatment Planning for Radiation Fields Defined by a Multileaf Collimator,” Physics in Medicine and Biology, Vol. 36, No. 9, 1991, pp. 1201- 1226. doi:10.1088/0031-9155/36/9/004

[15] S. M. Morril, R. G. Lane and I. I. Rosen, “Constrained Simulated Annealing for Optimized Radiation Therapy,” Computer Methods and Programs in Biomedicine, Vol. 33, No. 3, 1990, pp. 135-144. doi:10.1016/0169-2607(90)90035-8

[16] G. S. Mageras and R. Mohan, “Application of Fast Simulated Annealing to Optimization of Conformal Radiation Treatments,” Medical Physics, Vol. 20, No. 3, 1993, pp. 639-647. doi:10.1118/1.597012

[17] M. Langer, S. Morrill, R. Brown, O. Lee and R. Lane, “A Comparison of Mixed-Integer Programming and Fast Simulated Annealing for Optimizing Beam Weights in Radiation Therapy,” Medical Physics, Vol. 23, No. 6, 1996, pp. 957-964. doi:10.1118/1.597857

[18] M. Langer, S. Morrill, R. Brown, O. Lee and R. Lane, “A Genetic Algorithm for Generating Beam Weights,” Medical Physics, Vol. 23, No. 6, 1996, pp. 965-971. doi:10.1118/1.597858

[19] G. A. Ezzel, “Genetic and Geometric Optimization of Three-Dimensional Radiation Therapy Treatment Planning,” Medical Physics, Vol. 23, No. 3, 1996, pp. 293- 305. doi:10.1118/1.597660

[20] X. Wu, Y. Zhu, J. Dai and Z. Wang, “Selection and Determination of Beam Weights based on Genetic Algorithms for Conformal Radiotherapy Treatment Planning,” Physics in Medicine and Biology, Vol. 45, No. 9, 2000, pp. 2547-2558. doi:10.1088/0031-9155/45/9/308

[21] P. S. Cho, S. Lee, R. J. Marks, S. Oh, S. G. Sutlief and M. H. Phillips, “Optimization of Intensity Modulated Beams with Volume Constraints Using Two Methods: Cost Function Minimization and Projections onto Convex Sets,” Medical Physics, Vol. 25, No. 4, 1998, pp. 435- 443. doi:10.1118/1.598218

[22] D. H. Hristov and B. G. Fallone, “A Continuous Penalty Function Method for Inverse Treatment Planning,” Medical Physics, Vol. 25, No. 2, 1998, pp. 208-223. doi:10.1118/1.598183

[23] S. V. Spirou and C. S. Chui, “A Gradient Inverse Planning Algorithm with Dose-Volume Constraints,” Medical Physics, Vol. 25, No. 3, 1998, pp. 321-333. doi:10.1118/1.598202

[24] Q. Wu and R. Mohan, “Algorithms and Functionality of an Intensity Modulated Radiotherapy Optimization System,” Medical Physics, Vol. 27, No. 4, 2000, pp. 701- 711. doi:10.1118/1.598932

[25] P. Cheung, K. Sixel, G. Morton, D. A. Loblaw, R. Tirona, G. Pang, R. Choo, E. Szumacher, G. Deboer and J. P. Pignol, “Individualized Planning Target Volumes for Intrafraction Motion during Hypofractionated Intensity- Modulated Radiotherapy Boost for Prostate Cancer,” International Journal of Radiation Oncology, Biology, Phy- sics, Vol. 62, No. 2, 2005, pp. 418-425.

[26] M. Guerrero, X. A. Li, L. Ma, J. Linder, C. Deyoung and B. Erickson, “Simultaneous Integrated Intensity-Modulated Radiotherapy Boost for Locally Advanced Gynecological Cancer: Radiobiological and Dosimetric Considerations,” International Journal of Radiation Oncology, Biology, Physics, Vol. 62, No. 3, 2005, pp. 933-939. doi:10.1016/j.ijrobp.2004.11.040

[27] M. L. Cavey, J. E. Bayouth, M. Colman, E. J. Endres and G. Sanguineti, “IMRT to Escalate the Dose to the Prostate While Treating the Pelvic Nodes,” Strahlenther Onkol, Vol. 181, No. 7, 2005, pp. 431-441. doi:10.1007/s00066-005-1384-9

[28] X. A. Li, J. Z. Wang, P. A. Jursinic, C. A. Lawton and D. Wang, “Dosimetric Advantages of IMRT Simultaneous Integrated Boost for High-Risk Prostate Cancer,” International Journal of Radiation Oncology, Biology, Physics, Vol. 61, No. 4, 2005, pp. 1251-1257. doi:10.1016/j.ijrobp.2004.11.034

[29] R. A. Popple, P. B. Prellop, S. A. Spencer, J. F. De Los Santos, J. Duan, J. B. Fiveash and I. A. Brezovich, “Simultaneous Optimization of Sequential IMRT Plans,” Medical Physics, Vol. 32, No. 11, 2005, pp. 3257-3266. doi:10.1118/1.2064849

[30] S. M. Morrill, R. G. Lane, J. A. Wong and I. I. Rosen, “Dose-Volume Considerations with Linear Programming Optimization,” Medical Physics, Vol. 18, No. 6, 1991, pp. 1201-1210. doi:10.1118/1.596592

[31] D. Dink, “Approaches to 4-D Intensity Modulated Radiation Therapy Planning with Fraction Constraints,” Ph.D. Dissertation, Purdue University, West Lafayette, 2005.

[32] S. M. Morrill, I. I. Rosen, R. G. Lane and J. A. Belli, “The Influence of Dose Constraint Point Placement on Optimized Radiation Therapy Treatment Planning,” International Journal of Radiation Oncology, Biology, Phy- sics, Vol. 19, No. 1, 1990, pp. 129-1241.

[33] A. Niemierko and M. Goitein, “Random Sampling for Evaluating Treatment Plans,” Medical Physics, Vol. 17, No. 5, 1990, pp. 753-762. doi:10.1118/1.596473

[34] A. Niemierko and M. Goitein, “Letter to the Editor, Comments on ‘Sampling Techniques for the Evaluation of Treatment Plans’,” Medical Physics, Vol. 20, No. 1, 1993, pp. 1377-1380. doi:10.1118/1.597103

[35] X.-Q. Lu and L. M. Chin, “Sampling Techniques for the Evaluation of Treatment Plans,” Medical Physics, Vol. 20, No. 1, 1993, pp. 151-161. doi:10.1118/1.597096

[36] R. Acosta, W. Brick, A. Hanna, A. Holder, D. Lara, G. McQuilen, D. Nevin, P. Uhlig and B. Salter, “Radiotherapy Optimal Design: An Academic Radiotherapy Treatment Design System,” In: J. W. Chinneck, B. Kristjansson, and M. J. Saltman, Eds., Operations Research and Cyber-Infrastructure, Springer, New York, 2009, pp. 401- 425. doi:10.1007/978-0-387-88843-9_21

[37] Sherouse Systems Inc., 2011. http://www.gwsherouse.com