Inverse radiation therapy planning — a multiple objective optimization approach
For some decades, radiation therapy has been proved successful in cancer treatment. It is the major task of clinical radiation treatment planning to realize, on the one hand, a high level dose of radiation in the cancer tissue in order to obtain maximum tumor control. On the other hand, it is obviou...
Saved in:
| Published in: | Discrete Applied Mathematics Vol. 118; no. 1; pp. 145 - 161 |
|---|---|
| Main Authors: | , |
| Format: | Journal Article Conference Proceeding |
| Language: | English |
| Published: |
Lausanne
Elsevier B.V
01.09.2002
Amsterdam Elsevier New York, NY |
| Subjects: | |
| ISSN: | 0166-218X, 1872-6771 |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Abstract | For some decades, radiation therapy has been proved successful in cancer treatment. It is the major task of clinical radiation treatment planning to realize, on the one hand, a high level dose of radiation in the cancer tissue in order to obtain maximum tumor control. On the other hand, it is obvious that it is absolutely necessary to keep the unavoidable radiation in the tissue outside the tumor, particularly in organs at risk, as low as possible. No doubt, these two objectives of treatment planning—high level dose in the tumor, low radiation outside the tumor—have a basically contradictory nature. Thus, there is need to compromise between overdosing the organs at risk and underdosing the target volume. Differing from the currently used time consuming interactive approach between dosimetrists and physicians, we consider the radiation therapy planning problem as a multiple objective linear programming problem and build a data base of relatively few efficient solutions representing the set of Pareto solutions. This data base can be easily scanned by physicians looking for an adequate treatment plan with the aid of an appropriate online tool. The paper includes a report on first numerical experiments and a list of further research topics which is hoped to stimulate interest of the OR community in a subject, where OR methods can make a difference for many individual's lives. |
|---|---|
| AbstractList | For some decades, radiation therapy has been proved successful in cancer treatment. It is the major task of clinical radiation treatment planning to realize, on the one hand, a high level dose of radiation in the cancer tissue in order to obtain maximum tumor control. On the other hand, it is obvious that it is absolutely necessary to keep the unavoidable radiation in the tissue outside the tumor, particularly in organs at risk, as low as possible. No doubt, these two objectives of treatment planning—high level dose in the tumor, low radiation outside the tumor—have a basically contradictory nature. Thus, there is need to compromise between overdosing the organs at risk and underdosing the target volume. Differing from the currently used time consuming interactive approach between dosimetrists and physicians, we consider the radiation therapy planning problem as a multiple objective linear programming problem and build a data base of relatively few efficient solutions representing the set of Pareto solutions. This data base can be easily scanned by physicians looking for an adequate treatment plan with the aid of an appropriate online tool. The paper includes a report on first numerical experiments and a list of further research topics which is hoped to stimulate interest of the OR community in a subject, where OR methods can make a difference for many individual's lives. |
| Author | Küfer, K.-H. Hamacher, H.W. |
| Author_xml | – sequence: 1 givenname: H.W. surname: Hamacher fullname: Hamacher, H.W. email: hamacher@mathematik.uni-kl.de – sequence: 2 givenname: K.-H. surname: Küfer fullname: Küfer, K.-H. email: kuefer@mathematik.uni-kl.de |
| BackLink | http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=13543028$$DView record in Pascal Francis |
| BookMark | eNqFkMtKAzEUhoNUsK0-gjAbQRejyWQuKS5EipdCQUSF7sKZzBmbMs2EZCzUlQ_hE_okTjvShZtucoH_-8_hG5CeqQ0ScsroJaMsvXppjzSMmJidU3ZBaZSycHZA-kxkUZhmGeuR_i5yRAbeLyilrP31yfPErNB5DBwUGhpdm6CZowO7DmwFxmjzHvx8fQcQLD-qRtsKgzpfoGr0qn3ZRi_1Z4eBta4GNT8mhyVUHk_-7iF5u797HT-G06eHyfh2GirOR03IUgqCcg6qUDlkmGFUMlakSuRZIXhcgspjISKa5SOFokSME46FSHIe57RM-JCcdb0WvIKqdGCU9tI6vQS3lownMaeRaHPXXU652nuHpVS62a7cONCVZFRuLMqtRblRJCmTW4ty1tLJP3o3YA9303HYKlhpdNIrjUZhoV1rTxa13tPwCzP7j4o |
| CODEN | DAMADU |
| CitedBy_id | crossref_primary_10_1088_1361_6560_aabd14 crossref_primary_10_1007_s10589_023_00531_x crossref_primary_10_1118_1_2900716 crossref_primary_10_1287_opre_1050_0261 crossref_primary_10_1016_j_media_2019_04_002 crossref_primary_10_1371_journal_pcbi_1008538 crossref_primary_10_1016_j_ejor_2018_08_019 crossref_primary_10_1002_mcda_1547 crossref_primary_10_1016_j_bspc_2021_102884 crossref_primary_10_1088_0031_9155_49_10_011 crossref_primary_10_1088_0031_9155_55_18_013 crossref_primary_10_1109_TRPMS_2018_2805876 crossref_primary_10_1016_j_ejor_2021_04_007 crossref_primary_10_1088_0031_9155_49_9_004 crossref_primary_10_1016_j_laa_2007_05_045 crossref_primary_10_1007_s11081_005_2065_3 crossref_primary_10_1088_0031_9155_51_24_005 crossref_primary_10_1088_0031_9155_52_24_009 crossref_primary_10_1088_0031_9155_52_6_009 crossref_primary_10_1007_s11590_013_0672_z crossref_primary_10_1007_s00186_008_0220_2 crossref_primary_10_1007_s10288_008_0083_7 crossref_primary_10_1111_itor_12241 crossref_primary_10_1007_s10479_009_0659_4 crossref_primary_10_1002_net_20324 crossref_primary_10_1002_mp_12338 crossref_primary_10_1142_S0217595916500068 crossref_primary_10_1080_10556780600604940 crossref_primary_10_1002_net_20007 crossref_primary_10_1137_070698750 crossref_primary_10_1016_j_laa_2007_05_039 crossref_primary_10_1007_s00291_007_0096_1 crossref_primary_10_1088_0031_9155_53_4_011 crossref_primary_10_1007_s11750_008_0064_1 crossref_primary_10_1007_s10479_010_0741_y crossref_primary_10_1016_j_laa_2003_09_013 crossref_primary_10_1002_zamm_201000191 crossref_primary_10_1080_10556788_2011_636506 crossref_primary_10_1007_s10479_010_0767_1 crossref_primary_10_1287_ijoc_1060_0179 crossref_primary_10_1007_s10601_010_9104_1 crossref_primary_10_1007_s10898_008_9286_x crossref_primary_10_1080_10170669_2011_580467 crossref_primary_10_1007_s10729_012_9190_2 crossref_primary_10_1186_s13014_018_1000_7 crossref_primary_10_1007_s10288_016_0336_9 crossref_primary_10_1007_s11081_005_2066_2 crossref_primary_10_2478_pjmpe_2020_0024 crossref_primary_10_1007_s10878_008_9159_8 crossref_primary_10_1016_j_radonc_2007_06_020 crossref_primary_10_1088_0031_9155_51_15_014 crossref_primary_10_1007_s11081_018_9409_2 crossref_primary_10_1287_opre_2014_1267 crossref_primary_10_1088_0031_9155_48_21_005 crossref_primary_10_1137_040606612 crossref_primary_10_1007_s00186_024_00849_0 crossref_primary_10_1023_A_1022951027498 crossref_primary_10_1007_s11590_019_01394_0 crossref_primary_10_1016_j_cor_2011_10_020 crossref_primary_10_1088_1361_6560_ad4a00 crossref_primary_10_1007_s00291_007_0106_3 crossref_primary_10_1137_060672029 crossref_primary_10_1287_opre_1090_0759 |
| Cites_doi | 10.1016/0022-247X(68)90201-1 10.1006/jcom.1998.0480 10.1118/1.597302 10.1016/S0939-3889(15)70758-0 10.1016/0360-3016(91)90171-Y 10.1088/0031-9155/38/6/001 10.1016/0360-3016(91)90172-Z 10.1016/0360-3016(90)90413-E 10.1016/0360-3016(93)90189-3 |
| ContentType | Journal Article Conference Proceeding |
| Copyright | 2002 Elsevier Science B.V. 2002 INIST-CNRS |
| Copyright_xml | – notice: 2002 Elsevier Science B.V. – notice: 2002 INIST-CNRS |
| DBID | 6I. AAFTH AAYXX CITATION IQODW |
| DOI | 10.1016/S0166-218X(01)00261-X |
| DatabaseName | ScienceDirect Open Access Titles Elsevier:ScienceDirect:Open Access CrossRef Pascal-Francis |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Mathematics |
| EISSN | 1872-6771 |
| EndPage | 161 |
| ExternalDocumentID | 13543028 10_1016_S0166_218X_01_00261_X S0166218X0100261X |
| GroupedDBID | -~X 6I. AAFTH ADEZE AFTJW AI. ALMA_UNASSIGNED_HOLDINGS FA8 FDB OAUVE VH1 WUQ AAYXX CITATION IQODW |
| ID | FETCH-LOGICAL-c339t-160a8033acdcba7e7e2f11d6c8b7d834facb488207b9ce8fee453ed85b34b0f53 |
| ISICitedReferencesCount | 96 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000174401100011&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 0166-218X |
| IngestDate | Sun Oct 22 16:07:08 EDT 2023 Sat Nov 29 03:57:20 EST 2025 Tue Nov 18 21:43:56 EST 2025 Sat Apr 29 22:44:06 EDT 2023 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 1 |
| Keywords | Intensity modulated radiation therapy Medical physics Multicriteria linear programming Goal programming |
| Language | English |
| License | http://www.elsevier.com/open-access/userlicense/1.0 https://www.elsevier.com/tdm/userlicense/1.0 https://www.elsevier.com/open-access/userlicense/1.0 CC BY 4.0 |
| LinkModel | OpenURL |
| MeetingName | Third ALIO-EURO Meeting on Applied Combinatorial Optimization |
| MergedId | FETCHMERGED-LOGICAL-c339t-160a8033acdcba7e7e2f11d6c8b7d834facb488207b9ce8fee453ed85b34b0f53 |
| OpenAccessLink | https://dx.doi.org/10.1016/S0166-218X(01)00261-X |
| PageCount | 17 |
| ParticipantIDs | pascalfrancis_primary_13543028 crossref_citationtrail_10_1016_S0166_218X_01_00261_X crossref_primary_10_1016_S0166_218X_01_00261_X elsevier_sciencedirect_doi_10_1016_S0166_218X_01_00261_X |
| PublicationCentury | 2000 |
| PublicationDate | 2002-09-01 |
| PublicationDateYYYYMMDD | 2002-09-01 |
| PublicationDate_xml | – month: 09 year: 2002 text: 2002-09-01 day: 01 |
| PublicationDecade | 2000 |
| PublicationPlace | Lausanne Amsterdam New York, NY |
| PublicationPlace_xml | – name: Amsterdam – name: Lausanne – name: New York, NY |
| PublicationTitle | Discrete Applied Mathematics |
| PublicationYear | 2002 |
| Publisher | Elsevier B.V Elsevier |
| Publisher_xml | – name: Elsevier B.V – name: Elsevier |
| References | Steuer (BIB19) 1985 Burkard, Leitner, Rudolf, Siegl, Tabbert (BIB6) 1995 Schön, Bertz, Görsch, Haberland, Ziegler, Stegmaier, Eisinger, Stabenow (BIB18) 1999 Brahme (BIB4) 1995 Francis, McGiniis, White (BIB10) 1992 Webb (BIB21) 1993 Burman, Kutcher, Emami, Goitein (BIB7) 1991; 21 T. Bortfeld, J. Stein, K. Preiser, Clinically relevant intensity modulation optimization using physical criteria, in: D.D. Leavitt, G. Starkschall (Eds.), Proceedings of the XIIth ICCR, Salt Lake City, 1997. Emami, Lyman, Brown, Coia, Goitein, Munzenrieder, Shank, Solin, Wesson (BIB9) 1991; 21 Becker, Wahrendorf (BIB1) 1997 Bortfeld (BIB2) 1995 Geoffrion (BIB11) 1968; 22 Gustafsson, Lind, Brahme (BIB12) 1994; 21 Küfer (BIB16) 1998; 14 Brenner (BIB5) 1993; 26 Höffner (BIB15) 1997 Drezner (BIB8) 1995 Hamacher (BIB13) 1995 Langer, Brown, Urie, Leong, Stracher, Shapiro (BIB17) 1990; 18 Webb, Nahum (BIB22) 1993; 38 Ulmer, Harder (BIB20) 1995; 5 http://www-phys.llnl.gov/peregrine. Langer (10.1016/S0166-218X(01)00261-X_BIB17) 1990; 18 Steuer (10.1016/S0166-218X(01)00261-X_BIB19) 1985 Burkard (10.1016/S0166-218X(01)00261-X_BIB6) 1995 Francis (10.1016/S0166-218X(01)00261-X_BIB10) 1992 Gustafsson (10.1016/S0166-218X(01)00261-X_BIB12) 1994; 21 Küfer (10.1016/S0166-218X(01)00261-X_BIB16) 1998; 14 10.1016/S0166-218X(01)00261-X_BIB3 Brenner (10.1016/S0166-218X(01)00261-X_BIB5) 1993; 26 Burman (10.1016/S0166-218X(01)00261-X_BIB7) 1991; 21 Webb (10.1016/S0166-218X(01)00261-X_BIB21) 1993 Ulmer (10.1016/S0166-218X(01)00261-X_BIB20) 1995; 5 Geoffrion (10.1016/S0166-218X(01)00261-X_BIB11) 1968; 22 Bortfeld (10.1016/S0166-218X(01)00261-X_BIB2) 1995 Höffner (10.1016/S0166-218X(01)00261-X_BIB15) 1997 10.1016/S0166-218X(01)00261-X_BIB14 Becker (10.1016/S0166-218X(01)00261-X_BIB1) 1997 Emami (10.1016/S0166-218X(01)00261-X_BIB9) 1991; 21 Hamacher (10.1016/S0166-218X(01)00261-X_BIB13) 1995 Schön (10.1016/S0166-218X(01)00261-X_BIB18) 1999 Brahme (10.1016/S0166-218X(01)00261-X_BIB4) 1995 Webb (10.1016/S0166-218X(01)00261-X_BIB22) 1993; 38 Drezner (10.1016/S0166-218X(01)00261-X_BIB8) 1995 |
| References_xml | – reference: http://www-phys.llnl.gov/peregrine. – year: 1999 ident: BIB18 publication-title: Entwicklung der Überlebensraten von Krebspatienten in Deutschland. Gesundheitsberichterstattung für Deutschland – volume: 14 start-page: 333 year: 1998 end-page: 377 ident: BIB16 article-title: On the asymptotic average number of efficient vertices in multiple objective linear programming publication-title: J. Complexity – volume: 22 start-page: 618 year: 1968 end-page: 630 ident: BIB11 article-title: Proper efficiency and the theory of vector maximization publication-title: J. Math. Anal. Appl. – year: 1997 ident: BIB1 publication-title: Krebsatlas der Bundesrepublik Deutschland 1981–1990, Atlas of Cancer Mortality in the Federal Republic of Germany – year: 1995 ident: BIB8 publication-title: Facility Location: a Survey of Applications and Methods – year: 1992 ident: BIB10 publication-title: Facility Layout and Location: an Analytical Approach – year: 1995 ident: BIB4 article-title: Treatment optimization using physical and radiobiological objective functions publication-title: Radiation Therapy Physics – volume: 18 start-page: 887 year: 1990 end-page: 893 ident: BIB17 article-title: Large scale optimization of beam weights under dose-volume restrictions publication-title: J. Radiat. Oncol. Biol. Phys. – volume: 38 start-page: 653 year: 1993 end-page: 666 ident: BIB22 article-title: A model for calculating tumour control probability in radiotherapy including the effects of inhomogeneous distribution of dose and clonogenic cell density publication-title: Phys. Med. Biol. – volume: 21 start-page: 343 year: 1994 end-page: 356 ident: BIB12 article-title: A generalized pencil beam algorithm for optimization of radiation therapy publication-title: Med. Phys. – year: 1985 ident: BIB19 publication-title: Multicriteria Optimization: Theory, Computation and Applications – year: 1995 ident: BIB13 publication-title: Mathematische Lösungsverfahren für Standortprobleme – reference: T. Bortfeld, J. Stein, K. Preiser, Clinically relevant intensity modulation optimization using physical criteria, in: D.D. Leavitt, G. Starkschall (Eds.), Proceedings of the XIIth ICCR, Salt Lake City, 1997. – volume: 5 start-page: 25 year: 1995 end-page: 30 ident: BIB20 article-title: A triple Gaussian pencil beam model for photon beam treatment planning publication-title: Z. Med. Phys. – volume: 21 start-page: 109 year: 1991 end-page: 122 ident: BIB9 article-title: Tolerance of normal tissue to therapeutic irradiation publication-title: Int. J. Radiat. Oncol. Biol. Phys. – volume: 21 start-page: 123 year: 1991 end-page: 135 ident: BIB7 article-title: Fitting of normal tissue tolerance data to an analytic function publication-title: Int. J. Radiat. Oncol. Biol. Phys. – year: 1993 ident: BIB21 publication-title: The Physics of Three-Dimensional Radiation Therapy – year: 1995 ident: BIB6 article-title: Discrete optimization models for treatment planning in radiation therapy publication-title: Science and Technology for Medicine Biomedical Engineering in Graz – volume: 26 start-page: 171 year: 1993 end-page: 179 ident: BIB5 article-title: Dose, volume, and tumor-control predictions in radiotherapy publication-title: Int. J. Radiat. Oncol. Biol. Phys. – year: 1997 ident: BIB15 publication-title: New Methods for Solving the Inverse Problem in Radiation Therapy Planning – year: 1995 ident: BIB2 article-title: Dosiskonformation in der Tumortherapie mit externer ionisierender Strahlung: Physikalische Möglichkeiten und Grenzen – year: 1999 ident: 10.1016/S0166-218X(01)00261-X_BIB18 – volume: 22 start-page: 618 year: 1968 ident: 10.1016/S0166-218X(01)00261-X_BIB11 article-title: Proper efficiency and the theory of vector maximization publication-title: J. Math. Anal. Appl. doi: 10.1016/0022-247X(68)90201-1 – volume: 14 start-page: 333 year: 1998 ident: 10.1016/S0166-218X(01)00261-X_BIB16 article-title: On the asymptotic average number of efficient vertices in multiple objective linear programming publication-title: J. Complexity doi: 10.1006/jcom.1998.0480 – year: 1995 ident: 10.1016/S0166-218X(01)00261-X_BIB13 – volume: 21 start-page: 343 issue: 3 year: 1994 ident: 10.1016/S0166-218X(01)00261-X_BIB12 article-title: A generalized pencil beam algorithm for optimization of radiation therapy publication-title: Med. Phys. doi: 10.1118/1.597302 – volume: 5 start-page: 25 year: 1995 ident: 10.1016/S0166-218X(01)00261-X_BIB20 article-title: A triple Gaussian pencil beam model for photon beam treatment planning publication-title: Z. Med. Phys. doi: 10.1016/S0939-3889(15)70758-0 – volume: 21 start-page: 109 year: 1991 ident: 10.1016/S0166-218X(01)00261-X_BIB9 article-title: Tolerance of normal tissue to therapeutic irradiation publication-title: Int. J. Radiat. Oncol. Biol. Phys. doi: 10.1016/0360-3016(91)90171-Y – volume: 38 start-page: 653 year: 1993 ident: 10.1016/S0166-218X(01)00261-X_BIB22 article-title: A model for calculating tumour control probability in radiotherapy including the effects of inhomogeneous distribution of dose and clonogenic cell density publication-title: Phys. Med. Biol. doi: 10.1088/0031-9155/38/6/001 – volume: 21 start-page: 123 year: 1991 ident: 10.1016/S0166-218X(01)00261-X_BIB7 article-title: Fitting of normal tissue tolerance data to an analytic function publication-title: Int. J. Radiat. Oncol. Biol. Phys. doi: 10.1016/0360-3016(91)90172-Z – year: 1995 ident: 10.1016/S0166-218X(01)00261-X_BIB4 article-title: Treatment optimization using physical and radiobiological objective functions – year: 1995 ident: 10.1016/S0166-218X(01)00261-X_BIB8 – volume: 18 start-page: 887 year: 1990 ident: 10.1016/S0166-218X(01)00261-X_BIB17 article-title: Large scale optimization of beam weights under dose-volume restrictions publication-title: J. Radiat. Oncol. Biol. Phys. doi: 10.1016/0360-3016(90)90413-E – year: 1992 ident: 10.1016/S0166-218X(01)00261-X_BIB10 – ident: 10.1016/S0166-218X(01)00261-X_BIB14 – year: 1985 ident: 10.1016/S0166-218X(01)00261-X_BIB19 – year: 1993 ident: 10.1016/S0166-218X(01)00261-X_BIB21 – year: 1997 ident: 10.1016/S0166-218X(01)00261-X_BIB1 – year: 1995 ident: 10.1016/S0166-218X(01)00261-X_BIB6 article-title: Discrete optimization models for treatment planning in radiation therapy – year: 1997 ident: 10.1016/S0166-218X(01)00261-X_BIB15 – volume: 26 start-page: 171 issue: 1 year: 1993 ident: 10.1016/S0166-218X(01)00261-X_BIB5 article-title: Dose, volume, and tumor-control predictions in radiotherapy publication-title: Int. J. Radiat. Oncol. Biol. Phys. doi: 10.1016/0360-3016(93)90189-3 – year: 1995 ident: 10.1016/S0166-218X(01)00261-X_BIB2 – ident: 10.1016/S0166-218X(01)00261-X_BIB3 |
| SSID | ssj0001218 ssj0000186 ssj0006644 |
| Score | 1.9695463 |
| Snippet | For some decades, radiation therapy has been proved successful in cancer treatment. It is the major task of clinical radiation treatment planning to realize,... |
| SourceID | pascalfrancis crossref elsevier |
| SourceType | Index Database Enrichment Source Publisher |
| StartPage | 145 |
| SubjectTerms | Exact sciences and technology Goal programming Intensity modulated radiation therapy Mathematics Medical physics Multicriteria linear programming Sciences and techniques of general use |
| Title | Inverse radiation therapy planning — a multiple objective optimization approach |
| URI | https://dx.doi.org/10.1016/S0166-218X(01)00261-X |
| Volume | 118 |
| WOSCitedRecordID | wos000174401100011&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVESC databaseName: Elsevier SD Freedom Collection Journals 2021 customDbUrl: eissn: 1872-6771 dateEnd: 20171231 omitProxy: false ssIdentifier: ssj0001218 issn: 0166-218X databaseCode: AIEXJ dateStart: 19950101 isFulltext: true titleUrlDefault: https://www.sciencedirect.com providerName: Elsevier |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1Bb9MwFLbKxmGIw4AhxtjkAwdQ5RLHTuxwm7pNhUE1iYFyixzHkYa2tGq7aYg_z0vsOBkDVRy4RG1aJ5bf5_een_2-h9BrWYalgsUxUSHVhJtCEmmiAr5KRfNC8agp5_Ptk5hOZZomZ4PBzzYX5uZSVJW8vU3m_1XUcA-EXafO_oO4_UPhBnwGocMVxA7X-4L_o_05ugBdAM7wUDkX88pzsy77EKk5NhZLM1zU_AQNDmw21o-6tnRTysimQvtDh7P8u9WPwxlomiuXwul5yT1EQJGPJ_aIxWQ09FGc03pXPhmf2F9OR2RyJ-YQ-kNVLhDmrHY_LhnHBLyF1JoVq0ulCEksbIUVr2w7bdtLfbTKk1piSWeHqSVpv6fibbThi38jOOJ1sYGkWU2StLNr7V7-b-bOH0KkLOIM3KsHaDNksYSV--bhh-P0Y499rKbW22rjdd32FLhp3JHG2z50qWHvuo69Cehb16m_OT2P52oJU7G0NVR6js35NtrpUj7xmQfTEzQw1VP06HMHnGdo6vCCPV6wwwtu8fIeK9yiBXu04D5acIuWHfT15Ph8PCGuHAfRjCUrQuNAyYAxpQudK2GECUtKi1jLXBSS8VLpHMxBGIg80UaWxsBEh8kf5YznQRmx52ijmlXmBcLc6KKEIQfjEXCTR0qUOqYFL6hQoYrCXcTb8cq046qvS6ZcZr1DiXGc1cOcBTRrhjlLd9HIN5tbspZ1DWQrjMx5nNaTzABt65oe3BFe90IHq5fr_rCHtrq59QptrBbXZh891Deri-XiwIHxF9pKomk |
| linkProvider | Elsevier |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=proceeding&rft.title=Discrete+applied+mathematics&rft.atitle=Inverse+radiation+therapy+planning%3A+a+multiple+objective+optimization+approach&rft.au=HAMACHER%2C+H.+W&rft.au=K%C3%9CFER%2C+K.-H&rft.date=2002-09-01&rft.pub=Elsevier&rft.issn=0166-218X&rft.eissn=1872-6771&rft.volume=118&rft.issue=1-2&rft.spage=145&rft.epage=161&rft_id=info:doi/10.1016%2FS0166-218X%2801%2900261-X&rft.externalDBID=n%2Fa&rft.externalDocID=13543028 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0166-218X&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0166-218X&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0166-218X&client=summon |