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An Automatic Approach for Satisfying Dose-Volume Constraints in Linear Fluence Map Optimization for IMPT

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DOI: 10.4236/jct.2014.52025    2,889 Downloads   4,144 Views   Citations


Prescriptions for radiation therapy are given in terms of dose-volume constraints (DVCs). Solving the fluence map optimization (FMO) problem while satisfying DVCs often requires a tedious trial-and-error for selecting appropriate dose control parameters on various organs. In this paper, we propose an iterative approach to satisfy DVCs using a multi-objective linear programming (LP) model for solving beamlet intensities. This algorithm, starting from arbitrary initial parameter values, gradually updates the values through an iterative solution process toward optimal solution. This method finds appropriate parameter values through the trade-off between OAR sparing and target coverage to improve the solution. We compared the plan quality and the satisfaction of the DVCs by the proposed algorithm with two nonlinear approaches: a nonlinear FMO model solved by using the L-BFGS algorithm and another approach solved by a commercial treatment planning system (Eclipse 8.9). We retrospectively selected from our institutional database five patients with lung cancer and one patient with prostate cancer for this study. Numerical results show that our approach successfully improved target coverage to meet the DVCs, while trying to keep corresponding OAR DVCs satisfied. The LBFGS algorithm for solving the nonlinear FMO model successfully satisfied the DVCs in three out of five test cases. However, there is no recourse in the nonlinear FMO model for correcting unsatisfied DVCs other than manually changing some parameter values through trial and error to derive a solution that more closely meets the DVC requirements. The LP-based heuristic algorithm outperformed the current treatment planning system in terms of DVC satisfaction. A major strength of the LP-based heuristic approach is that it is not sensitive to the starting condition.

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The authors declare no conflicts of interest.

Cite this paper

M. Zaghian, G. Lim, W. Liu and R. Mohan, "An Automatic Approach for Satisfying Dose-Volume Constraints in Linear Fluence Map Optimization for IMPT," Journal of Cancer Therapy, Vol. 5 No. 2, 2014, pp. 198-207. doi: 10.4236/jct.2014.52025.


[1] A. Lomax, “Intensity Modulation Methods for Proton Radiotherapy,” Physics in Medicine and Biology, Vol. 44, No. 1, 1999, pp. 185-205.
[2] W. Chen, G. Herman and Y. Censor, “Algorithms for Satisfying Dose Volume Constraints in Intensity-Modulated Radiation Therapy,” Proceedings of the Interdisciplinary Workshop on Mathematical Methods in Biomedical Imaging and Intensity-Modulated Radiation Therapy (IMRT), Pisa, October 2007.
[3] Y. Zhang and M. Merritt, “Dose-Volume-Based IMRT Fluence Optimization: A Fast Least-Squares Approach with Differentiability,” Linear Algebra and Its Applications, Vol. 428, No. 5, 2008, pp. 1365-1387.
[4] J. O. Deasy, “Multiple Local Minima in Radiotherapy Optimization Problems with Dose-Volume Constraints,” Medical Physics, Vol. 24, 1997, pp. 1157-1162.
[5] A. T. Tuncel, F. Preciado, R. L. Rardin, M. Langer and J. P. P. Richard, “Strong Valid Inequalities for Fluence Map Optimization Problem under Dose-Volume Restrictions,” Annals of Operations Research, Vol. 196, No. 1, 2012, pp. 819-840.
[6] M. Ehrgott, C. Güler, H. W. Hamacher and L. Shao, “Mathematical Optimization in Intensity Modulated Radiation Therapy,” 4OR, Vol. 6, No. 3, 2008, pp. 199-262.
[7] T. Bortfeld, J. Stein and K. Preiser, “Clinically Relevant Intensity Modulation Optimization Using Physical Criteria,” Proceedings of the XII ICCR, Salt Lake City, Utah, 27-30 May, 1997.
[8] Q. Wu and R. Mohan, “Algorithms and Functionality of an Intensity Modulated Radiotherapy Optimization System,” Medical Physics, Vol. 27, 2000, pp. 701-711. 598932
[9] 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.
[10] M. Langer, R. Brown, S. Morrill, R. Lane and O. Lee, “A Generic Genetic Algorithm for Generating Beam Weights,” Medical Physics, Vol. 23, 1996, pp. 965-972.
[11] L. Xing, J. G. Li, S. Donaldson, Q. T. Le, and A. L. Boyer, “Optimization of Importance Factors in Inverse Planning,” Physics in Medicine and Biology, Vol. 44, 1999, pp. 2525-2536.
[12] P.S. Cho, S. Lee, R. J. Marks II, 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, 1998, pp. 435-444. 1118/1.598218
[13] D. Michalski, Y. Xiao, Y. Censor, J. M. Galvin, “The Dose-Volume Constraint Satisfaction Problem for Inverse Treatment Planning with Field Segments,” Physics in Medicine and Biology, Vol. 49, No. 4, 2004, pp. 601-616.
[14] Q. Wu and R. Mohan, “Multiple Local Minima in IMRT Optimization Based on Dose-Volume Criteria,” Medical Physics, Vol. 29, 2002, pp. 1514-1528.
[15] 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 Therapy Treatment Planning,” Physics in Medicine and Biology, Vol. 48, No. 21, 2003, pp. 3521-3542.
[16] M. Langer and J. Leong, “Optimization of Beam Weights under Dose-Volume Restrictions,” International Journal of Radiation Oncology * Biology * Physics, Vol. 13, No. 8, 1987, pp. 1255-1260.
[17] H. E. Romeijn, R. K. Ahuja, J. F. Dempsey and A. Kumar, “A New Linear Programming Approach to Radiation Therapy Treatment Planning Problems,” Operations Research, Vol. 54, No. 2, 2006, pp. 201-216.
[18] H. Rocha, J. M. Dias, B. C. Ferreira and M. C. Lopes, “Discretization of Optimal Beamlet Intensities in IMRT: A Binary Integer Programming Approach,” Search ResultsMathematical and Computer Modelling, Vol. 428, No. 5, 2011, pp. 1345-1364.
[19] M. C. Ferris, R. R. Meyer and W. D’Souza, “Radiation Treatment Planning: Mixed Integer Programming Formulations and Approaches,” Handbook on Modelling for Discrete Optimization, 2006, pp. 317-340.
[20] E. K. Lee, T. Fox and I. Crocker, “Integer Programming Applied to Intensity-Modulated Radiation Therapy Treatment Planning,” Annals of Operations Research, Vol. 119, No. 1, 2003, pp. 165-181.
[21] Y. Lan, C. Li, H. Ren, Y. Zhang and Z. Min, “Fluence Map Optimization (FMO) with Dose-Volume Constraints in IMRT Using the Geometric Distance Sorting Method,” Physics in Medicine and Biology, Vol. 57, No. 20, 2012, pp. 6407-6428.
[22] F. Preciado-Walters, R. Rardin, M. 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.
[23] M. Langer, R. Brown, P. Kijewski and C. Ha, “The Reliability of Optimization under Dose-Volume Limits,” Mathematical Programming, Vol. 26, No. 3, 1993, pp. 529-538. 0360-3016(93)90972-X
[24] 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.
[25] D. 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.
[26] D. Dink, M. P. Langer, R. L. Rardin, J. F. Pekny, G. V. Reklaitis and B. Saka, “Intensity Modulated Radiation Therapy with Field Rotation—A Time-Varying Fractionation Study,” Health Care Management Science, Vol. 15, No. 2, 2012, pp. 138-154.
[27] S. M. Morrill, R. G. Lane, J. A. Wong, I. I. Rosen, “Dose-Volume Considerations with Linear Programming Optimization,” Medical Physics, Vol. 18, 1991, pp. 1201-1211. 1118/1.596592
[28] G. J. Lim, J. Choi and R. Mohan, “Iterative Solution Methods for Beam Angle and Fluence Map Optimization in Intensity Modulated Radiation Therapy Planning,” OR Spectrum, Vol. 30, No. 2, 2008, pp. 289-309.
[29] Y. Li, R. X. Zhu, N. Sahoo, A. Anand and X. Zhang, “Beyond Gaussians: A Study of Single-Spot Modeling for Scanning Proton Dose Calculation,” Physics in Medicine and Biology, Vol. 57, No. 4, 2012, pp. 983-997.
[30] G. J. Lim, M. C. Ferris, D. M. Shepard, S. J. Wright and M. A. Earl, “An Optimization Framework for Conformal Radiation Treatment Planning,” INFORMS Journal on Computing, Vol. 19, No. 3, 2007, pp. 366-380.
[31] D. C. Liu and J. Nocedal, “On the Limited Memory BFGS Method for Large Scale Optimization,” Mathematical Programming, Vol. 45, No. 1, 1989, pp. 503-528. 589116
[32] S. Bochkanov and V. Bystritsky, “ALGLIB,”

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