{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,6]],"date-time":"2026-10-06T01:25:00Z","timestamp":1791249900618,"version":"4.1.0"},"reference-count":77,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM Rev."],"published-print":{"date-parts":[[1999,1]]},"abstract":"<jats:p>In the field of radiation therapy, much of the research is aimed at developing new and innovative techniques for treating cancer patients with radiation. In recent years, new treatment machines have been developed that provide a much greater degree of computer control than was available with the machines of previous generations. One innovation has been the development of an approach called \"tomotherapy.' Tomotherapy can be defined as computer-controlled rotational radiotherapy delivered using an intensity-modulated fan beam of radiation.<\/jats:p>\n                  <jats:p>The successful implementation of the new delivery techniques requires the development of a suitable approach for optimizing each patient's treatment plan. One of the challenges is to quantify optimality in radiation therapy. We have tested a variety of objective functions and constraints in pursuit of a formulation that performs well for a wide variety of disease sites. An additional challenge stems from the sizable amount of data and the large number of variables that are involved in each optimization. This paper presents several approaches to optimizing treatment plans in radiation therapy, and the advantages and disadvantages of a number of formulations are explored.<\/jats:p>","DOI":"10.1137\/s0036144598342032","type":"journal-article","created":{"date-parts":[[2005,10,17]],"date-time":"2005-10-17T21:00:17Z","timestamp":1129582817000},"page":"721-744","source":"Crossref","is-referenced-by-count":189,"title":["Optimizing the Delivery of Radiation Therapy to Cancer Patients"],"prefix":"10.1137","volume":"41","author":[{"given":"David M.","family":"Shepard","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Michael C.","family":"Ferris","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Gustavo H.","family":"Olivera","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"T. Rockwell","family":"Mackie","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,8,2]]},"reference":[{"key":"R1","unstructured":"J. Balog, L. Angelos, T. R. Mackie, and P. Reckwerdt,\n                      Dose computation for a onedimensional multileaf collimator\n                      , in Proceedings of the XII International Conference on the Use of Computers in Radiation Therapy, Salt Lake City, D. D. Leavitt and G. Starkshall, eds., Medical Physics Publishing, St. Louis, MO, 1997, pp. 323\u2013326."},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1088\/0031-9155\/38\/2\/006"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1016\/0360-3016(94)90200-3"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1016\/S1053-4296(95)80007-7"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1016\/0167-8140(88)90167-3"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1016\/0360-3016(93)90362-Y"},{"key":"R7","doi-asserted-by":"crossref","unstructured":"A. Brahme,\n                      Treatment optimization: Using physical and radiobiological objective functions\n                      , in Radiation Therapy Physics, A. R. Smith, ed., Springer\u2010Verlag, Berlin, 1995, pp. 209\u2013246.","DOI":"10.1007\/978-3-662-03107-0_11"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1016\/0360-3016(95)02061-6"},{"key":"R9","unstructured":"A. Brooke, D. Kendrick, and A. Meeraus,\n                      GAMS: A User's Guide\n                      , The Scientific Press, South San Francisco, CA, 1988."},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1016\/0360-3016(91)90172-Z"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1159\/000099664"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1118\/1.598218"},{"key":"R13","unstructured":"V. Chv\u00e1tal,\n                      Linear Programming\n                      , W. H. Freeman, New York, 1983."},{"key":"R14","unstructured":"A. R. Conn, N. I. M. Gould, and Ph. L. Toint,\n                      LANCELOT: A Fortran package for Large\u2013 Scale Nonlinear Optimization (Release A)\n                      , Springer Ser. Comput. Math. 17, Springer\u2010Verlag, Heidelberg, Berlin, 1992."},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1148\/128.1.235"},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1016\/0360-3016(87)90082-4"},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.1016\/0360-3016(87)90361-0"},{"key":"R18","doi-asserted-by":"crossref","unstructured":"G. B. Dantzig,\n                      Linear Programming and Extensions\n                      , Princeton University Press, Princeton, NJ, 1963.","DOI":"10.7249\/R366"},{"key":"R19","doi-asserted-by":"crossref","unstructured":"J. O. Deasy,\n                      Multiple local minima in radiotherapy optimization problems with dose volume constraints\n                      , Medical Physics, 1997.","DOI":"10.1118\/1.598017"},{"key":"R20","doi-asserted-by":"publisher","DOI":"10.1118\/1.598256"},{"key":"R21","doi-asserted-by":"publisher","DOI":"10.1007\/BF02591747"},{"key":"R22","doi-asserted-by":"publisher","DOI":"10.1016\/0360-3016(92)90959-L"},{"key":"R23","unstructured":"G. Fang, B. Geiser, and T. R. Mackie,\n                      Software system for uw\/ge tomotherapy prototype\n                      , in Proceedings of the XII International Conference on the Use of Computers in Radiation Therapy, Salt Lake City, Medical Physics Publishing, St. Louis, MO, 1997, pp. 332\u2013334."},{"key":"R24","unstructured":"M. C. Ferris,\n                      MATLAB and GAMS: Interfacing Optimization and Visualization Software\n                      , Mathematical Programming Technical Report 98\u201019, Computer Sciences Department, University of Wisconsin, Madison, 1998."},{"key":"R25","doi-asserted-by":"publisher","DOI":"10.1088\/0031-9155\/43\/6\/020"},{"key":"R26","doi-asserted-by":"publisher","DOI":"10.1118\/1.597446"},{"key":"R27","unstructured":"P. E. Gill, W. Murray, and M. H. Wright,\n                      Practical Optimization\n                      , Academic Press, London, 1981."},{"key":"R28","doi-asserted-by":"publisher","DOI":"10.1016\/S1053-4296(99)80057-5"},{"key":"R29","doi-asserted-by":"publisher","DOI":"10.1118\/1.597507"},{"key":"R30","doi-asserted-by":"publisher","DOI":"10.1088\/0031-9155\/39\/1\/006"},{"key":"R31","doi-asserted-by":"publisher","DOI":"10.1118\/1.597291"},{"key":"R32","unstructured":"M. S. Hung, W. O. Rom, and A. D. Warren,\n                      OSL Handbook\n                      , Boyd and Fraser, Danvers, MA, 1995."},{"key":"R33","unstructured":"CPLEX Version\n                      6.0, ILOG CPLEX Division, Incline Village, NV; also available online from http:\/\/www.cplex.com\/."},{"key":"R34","doi-asserted-by":"publisher","DOI":"10.1118\/1.597056"},{"key":"R35","first-page":"1006","volume":"21","author":"Jackson A.","year":"1994","journal-title":"Med. Phys.","ISSN":"https:\/\/id.crossref.org\/issn\/0094-2405","issn-type":"print"},{"key":"R36","doi-asserted-by":"publisher","DOI":"10.1080\/09553009214552071"},{"key":"R37","doi-asserted-by":"publisher","DOI":"10.1016\/0360-3016(89)90972-3"},{"key":"R38","doi-asserted-by":"publisher","DOI":"10.1016\/0360-3016(91)90173-2"},{"key":"R39","doi-asserted-by":"publisher","DOI":"10.1118\/1.597857"},{"key":"R40","doi-asserted-by":"publisher","DOI":"10.1118\/1.596533"},{"key":"R41","doi-asserted-by":"publisher","DOI":"10.1016\/0360-3016(91)90030-8"},{"key":"R42","doi-asserted-by":"publisher","DOI":"10.1007\/BF01589116"},{"key":"R43","doi-asserted-by":"publisher","DOI":"10.1118\/1.597961"},{"key":"R44","doi-asserted-by":"publisher","DOI":"10.1016\/0360-3016(89)90462-8"},{"key":"R45","doi-asserted-by":"publisher","DOI":"10.1118\/1.596958"},{"key":"R46","doi-asserted-by":"publisher","DOI":"10.1002\/ima.1850060107"},{"key":"R47","doi-asserted-by":"publisher","DOI":"10.1118\/1.595774"},{"key":"R48","unstructured":"MATLAB,\n                      User's Guide\n                      , The MathWorks, Natick, MA, 1992."},{"key":"R49","doi-asserted-by":"publisher","DOI":"10.1016\/S1053-4296(95)80003-4"},{"key":"R50","doi-asserted-by":"publisher","DOI":"10.1118\/1.596781"},{"key":"R51","doi-asserted-by":"publisher","DOI":"10.1137\/0801008"},{"key":"R52","doi-asserted-by":"crossref","unstructured":"J. J. Mor\u00e9 and S. J. Wright,\n                      Optimization Software Guide\n                      , Frontiers Appl. Math. 14, SIAM, Philadelphia, 1993.","DOI":"10.1137\/1.9781611970951"},{"key":"R53","doi-asserted-by":"publisher","DOI":"10.1118\/1.596592"},{"key":"R54","doi-asserted-by":"publisher","DOI":"10.1016\/0360-3016(94)00350-T"},{"key":"R55","unstructured":"G. P. Murphy, W. L. Lawrence, and R. E. Lenhard, eds.\n                      American Cancer Society Textbook of Clinical Oncology\n                      , The American Cancer Society, Atlanta, GA, 1995."},{"key":"R56","doi-asserted-by":"crossref","unstructured":"B. A. Murtagh and M. A. Saunders,\n                      MINOS 5.0 User's Guide\n                      , Technical Report SOL 83.20, Stanford University, Stanford, CA, 1983.","DOI":"10.21236\/ADA138522"},{"key":"R57","unstructured":"K. G. Murty,\n                      Linear Programming\n                      , John Wiley, New York, 1983."},{"key":"R58","doi-asserted-by":"publisher","DOI":"10.1137\/0801023"},{"key":"R59","unstructured":"J. L. Nazareth,\n                      Computer Solution of Linear Programs\n                      , Oxford University Press, Oxford, UK, 1987."},{"key":"R60","doi-asserted-by":"publisher","DOI":"10.1016\/0360-3016(92)90548-V"},{"key":"R61","unstructured":"A. Niemierko,\n                      Treatment plan optimization\n                      , in 3\u2010D Radiation Treatment Planning and Conformal Therapy, J. A. Purdy and B. Emami, eds., Medical Physics Publishing, St. Louis, MO, 1993, pp. 49\u201355."},{"key":"R62","unstructured":"N. C. I. National Institutes of Health,\n                      Radiation Therapy and You\u2014A Guide to Self\u2010Help During Treatment\n                      , NIH Publication 97\u20102227, National Institutes of Health, Bethesda, MD, 1997."},{"key":"R63","doi-asserted-by":"publisher","DOI":"10.1088\/0031-9155\/43\/11\/008"},{"key":"R64","unstructured":"W. Orchard\u2010Hays,\n                      Advanced Linear Programming Computing Techniques\n                      , McGraw\u2013Hill, New York, 1968."},{"key":"R65","doi-asserted-by":"publisher","DOI":"10.1118\/1.597154"},{"key":"R66","unstructured":"C. A. Perez and L. W. Brady,\n                      Principles and Practice of Radiotherapy\n                      , 3rd ed., Lippincott\u2010Raven, Philadelphia, 1998."},{"key":"R67","unstructured":"P. J. Reckwerdt, T. R. Mackie, J. P. Balog, and T. R. McNutt,\n                      Three\u2010dimensional inverse treatment optimization for tomotherapy\n                      , in XII International Conference on the Use of Computers in Radiation Therapy, D. D. Leavitt and G. Starkshall, eds., Salt Lake City, UT, Medical Physics Publishing, St. Louis, MO, 1997, pp. 420\u2013422."},{"key":"R68","doi-asserted-by":"publisher","DOI":"10.1118\/1.596700"},{"key":"R69","unstructured":"K. J. Ruchala, G. H. Olivera, E. A. Schloesser, and T. R. Mackie,\n                      Megavoltage CT on a tomotherapy system\n                      , Phys. Med. Biol., to appear."},{"key":"R70","unstructured":"D. M. Shepard, L. Angelos, O. A. Sauer, and T. R. Mackie,\n                      A simple model for examining radiotherapy optimization\n                      , in Proceedings of the XII International Conference on the Use of Computers in Radiation Therapy, Salt Lake City, UT, Medical Physics Publishing, St. Louis, MO, 1997."},{"key":"R71","doi-asserted-by":"publisher","DOI":"10.1016\/S1053-4296(95)80004-2"},{"key":"R72","doi-asserted-by":"publisher","DOI":"10.1088\/0031-9155\/39\/11\/007"},{"key":"R73","doi-asserted-by":"crossref","unstructured":"S. Webb,\n                      The Physics of Conformal Radiotherapy\u2014Advances in Technology\n                      , Institute of Physics Publishing, Philadelphia, PA, 1997.","DOI":"10.1201\/9781420050806"},{"key":"R74","unstructured":"S. Webb,\n                      Inverse Planning for IMRT: The Role of Simulated Annealing\n                      , The Theory and Practice of Intensity Modulated Radiation Therapy, Advanced Medical Publishing, Madison, WI, 1997."},{"key":"R75","doi-asserted-by":"publisher","DOI":"10.1016\/0360-3016(94)90250-X"},{"key":"R76","doi-asserted-by":"crossref","unstructured":"S. J. Wright,\n                      Primal\u2010Dual Interior\u2010Point Methods\n                      , SIAM, Philadelphia, 1996.","DOI":"10.1137\/1.9781611971453"},{"key":"R77","doi-asserted-by":"publisher","DOI":"10.1118\/1.597909"}],"container-title":["SIAM Review"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S0036144598342032","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T14:54:42Z","timestamp":1787237682000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S0036144598342032"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1999,1]]},"references-count":77,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1999,1]]}},"alternative-id":["10.1137\/S0036144598342032"],"URL":"https:\/\/doi.org\/10.1137\/s0036144598342032","relation":{},"ISSN":["0036-1445","1095-7200"],"issn-type":[{"value":"0036-1445","type":"print"},{"value":"1095-7200","type":"electronic"}],"subject":[],"published":{"date-parts":[[1999,1]]}}}