Designing radiotherapy plans with elastic constraints and interior point methods

Health Care Management Science

Volumn 6, Issue 1, 2003, Pages 5-16

  Holder, Allen ^a  

^a TRINITY UNIVERSITY   (United States)

Author keywords

Analytic center; Elastic constraints; Radiation oncology

Indexed keywords

ACCURACY; ANALYTIC METHOD; ANTINEOPLASTIC ACTIVITY; AUTOMATION; CANCER RESEARCH; CORRELATION COEFFICIENT; ELASTICITY; FEASIBILITY STUDY; GAMMA RADIATION; HEALTH CARE MANAGEMENT; HEALTH CARE QUALITY; HUMAN; MATHEMATICAL ANALYSIS; MATHEMATICAL COMPUTING; RADIATION BEAM; RADIATION DOSE; RADIATION RESPONSE; REVIEW; TECHNIQUE; TREATMENT PLANNING; ARTICLE; COMPUTER ASSISTED RADIOTHERAPY; INSTRUMENTATION; METHODOLOGY; NEOPLASM; ONCOLOGY; STATISTICAL ANALYSIS; STATISTICS; SYSTEM ANALYSIS; UNITED STATES;

DATA INTERPRETATION, STATISTICAL; HUMANS; MATHEMATICAL COMPUTING; NEOPLASMS; PROGRAMMING, LINEAR; RADIATION DOSAGE; RADIATION ONCOLOGY; RADIOTHERAPY PLANNING, COMPUTER-ASSISTED; UNITED STATES;

EID: 0037316769     PISSN: 13869620     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1021970819104     Document Type: Review

References (34)

1. M. Altschuler, Y. Censor and W. Powlis, Feasibility and optimization methods in teletherapy planning, in: Advances in Radiation Oncology Physics: Dosimetry, Treatment Planning and Brachytherapy, Medical Physics Monograph, Vol. 19 (American Institute of Physics, Woodbury, NY, 1992) pp. 1022-1057.
2. G.K. Bahr, J.G. Kereiakes, H. Horwitz, R. Finney, J. Galvin and K. Goode, The method of linear programming applied to radiation treatment planning, Radiology 91 (1968) 686-693.
3. A. Berkelaar, C. Roos and T. Terlaky, The optimal set and optimal partition approach to linear and quadratic programming, in: Recent Advances in Sensitivity Analysis and Parametric Programming, eds. T. Gal and H. Greenberg (Kluwer Academic Publishers, Boston, MA, 1997) ch. 6.
4. A. Berman and R. Plemmons, Nonnegative Matrices in the Mathematical Sciences (Academic Press, New York, NY, 1979).
5. R. Caron, H. Greenberg and A. Holder, Analytic centers and repelling inequalities, Technical Report CCM 142, Center for Computational Mathematics, University of Colorado at Denver, Denver, CO (1999).
6. Y. Censor, M. Altschuler and W. Powlis, A computational solution of the inverse problem in radiation-therapy treatment planning, Applied Mathematics and Computation 25 (1988) 57-87.
7. Y. Censor, M. Altschuler and W. Powlis, On the use of Cimmino's simultaneous projections method for computing a solution of the inverse problem in radiation therapy treatment planning, Inverse Problems 4 (1988) 607-623.
8. A. Cormack and E. Quinto, The mathematics and physics of radiation dose planning using X-rays, Contemporary Mathematics 113 (1990) 41-55.
9. I. Das and J. Dennis, A closer look at drawbacks of minimizing weighted sums of objectives for Pareto set generation in multicriteria optimization problems, Structural Optimization 41(1) (1997) 63-69.
10. M. Goitein and A. Niemierko, Biologically based models for scoring treatment plans, in: Scandanavian Symposium on Future Directions of Computer-Aided Radiotherapy (1988).
11. A. Goldman and A. Tucker, Theory of linear programming, in: Linear Inequalities and Related Systems, Vol. 38, eds. H. Kuhn and A. Tucker (Princeton University Press, Princeton, NJ, 1956) pp. 53-97.
12. H. Greenberg, Mathematical Programming Glossary (1997-1999). http://www.cudenver.edu/~hgreenbe/glossary/ glossary.html.
13. L. Hodes, Semiautomatic optimization of external beam radiation treatment planning, Radiology 110 (1974) 191-196.
14. L. Khachiyan, A polynomial algorithm in linear programming, Doklady Akademii Nauk SSSR 244 (1979) 1093-1096.
15. M. Langer and J. Leong, Optimization of beam weights under dose-volume restrictions, International Journal of Radiation Oncology, Biology, Physics 13 (1987) 1255-1260.
16. 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 18 (1990) 887-893.
17. J. Legras, B. Legras and J. Lambert, Software for linear and non-linear optimization in external radiotherapy, Computer Programs in Biomedicine 15 (1982) 233-242.
18. W. Lodwick, S. McCourt, F. Newman and S. Humphries, Optimization methods for radiation therapy plans, in: IMA Series in Applied Mathematics - Computational, Radiology and Imaging, Therapy and Diagnosis, eds. C. Borgers and F. Natterer (Springer, 1998).
19. S. McDonald and P. Rubin, Optimization of external beam radiation therapy, International Journal of Radiation Oncology, Biology, Physics 2 (1977) 307-317.
20. L. McLinden, An analogue of Moreau's proximation theorem, with applications to the nonlinear complementary problem, Pacific Journal of Mathematics 88(1) (1980) 101-161.
21. L. McLinden, The complementarity problem for maximal monotone multifunctions, in: Variational Inequalities and Complementarity Problems, eds. R. Cottle, R. Giannessi and J. Lions (Wiley, 1980) pp. 251-270.
22. S. Morrill, R. Lane, G. Jacobson and I. Rosen, Treatment planning optimization using constrained simulated annealing, Physics in Medicine and Biology 36(10) (1991) 1341-1361.
23. S. Morrill, I. Rosen, R. Lane and J. Belli, The influence of dose constraint point placement on optimized radiation therapy treatment planning, International Journal of Radiation Oncology, Biology, Physics 19 (1990) 129-141.
24. W. Powlis, M. Altschuler, Y. Censor and E. Buhle, Semi-automatic radiotherapy treatment plannnig with a mathematical model to satisfy treatment goals. International Journal of Radiation Oncology, Biology, Physics 16 (1989) 271-276.
25. C. Raphael, Mathematical modeling of objectives in radiation therapy treatment planning, Physics in Medicine and Biology 37 (6) (1992) 1293-1311.
26. C. Roos, T. Terlaky and J.-P. Vial, Theory and Algorithms for Linear Optimization, An Interior Point Approach (Wiley, New York, NY, 1997).
27. I. Rosen, R. Lane, S. Morrill and J. Belli, Treatment plan optimization using linear programming, Medical Physics 18(2) (1991) 141-152.
28. W. Sandham, Y. Yuan and T. Durrani, Conformal therapy using maximum entropy optimization, International Journal of Imaging Systems and Technology 1995 (1995) 80-90.
29. D. Shepard, M. Ferris, G. Olivera and T. Mackie, Optimizing the delivery of radiation therapy to cancer patients, SIAM Review 41(4) (1999) 721-744.
30. D. Sonderman and P. Abrahamson, Radiotherapy treatment design using mathematical programming models. Operations Research 33(4) (1985) 705-725.
31. H. Withers, J. Taylor and B. Maciejewski, Treatment volume and tissue tolerance, International Journal of Radiation Oncology, Biology, Physics 14 (1987) 751-759.
32. A. Wolbarst, Optimization of radiation therapy II: The critical-voxel model, International Journal of Radiation Oncology, Biology, Physics 10 (1984) 741-745.
33. S. Wright, Primal-Dual Interior-Point Methods (SIAM, Philadelphia, PA, 1997).
34. Y. Ye, Interior Point Algorithms Theory and Analysis (Wiley, New York, NY, 1997).