{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,23]],"date-time":"2026-02-23T09:38:11Z","timestamp":1771839491669,"version":"3.50.1"},"reference-count":39,"publisher":"IOP Publishing","issue":"4","license":[{"start":{"date-parts":[[2026,2,23]],"date-time":"2026-02-23T00:00:00Z","timestamp":1771804800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2026,2,23]],"date-time":"2026-02-23T00:00:00Z","timestamp":1771804800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/iopscience.iop.org\/info\/page\/text-and-data-mining"},{"start":{"date-parts":[[2026,2,23]],"date-time":"2026-02-23T00:00:00Z","timestamp":1771804800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/publishingsupport.iopscience.iop.org\/questions\/alternative-author-rights-policies\/"},{"start":{"date-parts":[[2026,2,23]],"date-time":"2026-02-23T00:00:00Z","timestamp":1771804800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/publishingsupport.iopscience.iop.org\/questions\/alternative-author-rights-policies\/"}],"funder":[{"DOI":"10.13039\/501100001691","name":"Japan Society for the Promotion of Science","doi-asserted-by":"crossref","award":["24K10822"],"award-info":[{"award-number":["24K10822"]}],"id":[{"id":"10.13039\/501100001691","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["iopscience.iop.org"],"crossmark-restriction":false},"short-container-title":["Phys. Med. Biol."],"published-print":{"date-parts":[[2026,2,28]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    <jats:italic>Objective.<\/jats:italic>\n                    The generalized equivalent uniform dose (gEUD) is a well-established metric for radiotherapy dose optimization, particularly for normal tissues. However, the lack of theoretical clarity in its application has often led to empirical use in clinical practice. This study aims to reformulate gEUD-based optimization in a theoretical framework using the gEUD curve concept, and to develop a robust optimization strategy tailored for stereotactic radiation therapy (SRT), with a specific focus on bone and spinal metastases.\n                    <jats:italic>Approach.<\/jats:italic>\n                    We interpreted the gEUD as a smooth function of its\n                    <jats:italic>a<\/jats:italic>\n                    -parameter, forming a continuous curve whose deformability decreases with increasing\n                    <jats:italic>a<\/jats:italic>\n                    . Based on this understanding, we proposed two methods: the multiple gEUD objective (MgEUDO) for optimizing the remaining volume at risk, and the selective gEUD objective (SgEUDO) for critical organs at risk. These methods were retrospectively evaluated in 22 patients who received five-fraction SRT (35 Gy total prescription).\n                    <jats:italic>Main results.<\/jats:italic>\n                    Using consistent gEUD-based optimization, all cases achieved clinically favorable dose distributions. Compared to conventional normal tissue objective constraints, the proposed strategy reduced mean dose to surrounding tissues by 10%, while improving tumor dose coverage by 0.6%. SgEUDO further achieved 39% and 37.5% mean dose reductions in the left and right kidneys, respectively.\n                    <jats:italic>Significance.<\/jats:italic>\n                    Our theoretical and practical refinement of gEUD optimization enables systematic control of dose distribution with reduced inter-planner variability. The combined MgEUDO and SgEUDO strategies provide a generalizable and clinically effective framework for high-precision radiotherapy.\n                  <\/jats:p>","DOI":"10.1088\/1361-6560\/ae443d","type":"journal-article","created":{"date-parts":[[2026,2,11]],"date-time":"2026-02-11T09:32:33Z","timestamp":1770802353000},"page":"045015","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Practical gEUD optimization technique for stereotactic radiation therapy based on a theoretical reinterpretation using the gEUD curve concept"],"prefix":"10.1088","volume":"71","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2284-7582","authenticated-orcid":true,"given":"Yusuke","family":"Anetai","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0142-6607","authenticated-orcid":false,"given":"Keita","family":"Kurosu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yusuke","family":"Tsuruta","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3205-3487","authenticated-orcid":true,"given":"Hideki","family":"Takegawa","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3963-4257","authenticated-orcid":false,"given":"Yuhei","family":"Koike","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1525-9264","authenticated-orcid":false,"given":"Kentaro","family":"Doi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ken","family":"Yoshida","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5721-3734","authenticated-orcid":false,"given":"Satoaki","family":"Nakamura","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6406-2097","authenticated-orcid":true,"given":"Mitsuhiro","family":"Nakamura","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"266","published-online":{"date-parts":[[2026,2,23]]},"reference":[{"key":"pmbae443dbib1","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6560\/adb099","type":"journal-article","article-title":"Deep learning-based quick MLC sequencing for MRI-guided online adaptive radiotherapy: a feasibility study for pancreatic cancer patients","volume":"70","author":"Ahunbay","year":"2025","journal-title":"Phys. Med. Biol."},{"key":"pmbae443dbib2","doi-asserted-by":"publisher","first-page":"1386","DOI":"10.1118\/1.3685447","type":"journal-article","article-title":"The use and QA of biologically related models for treatment planning: short report of the TG\u2010166 of the therapy physics committee of the AAPM","volume":"39","author":"Allen Li","year":"2012","journal-title":"Med. Phys."},{"key":"pmbae443dbib3","doi-asserted-by":"publisher","first-page":"185","DOI":"10.1016\/0925-2312(93)90006-O","type":"journal-article","article-title":"Backpropagation and stochastic gradient descent method","volume":"5","author":"Amari","year":"1993","journal-title":"Neurocomputing"},{"key":"pmbae443dbib4","doi-asserted-by":"publisher","DOI":"10.1002\/acm2.13745","type":"journal-article","article-title":"Assessment of using a gamma index analysis for patient\u2010specific quality assurance in Japan","volume":"23","author":"Anetai","year":"2022","journal-title":"J. Appl. Clin. Med. Phys."},{"key":"pmbae443dbib5","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6560\/acb989","type":"journal-article","article-title":"Effective optimization strategy for large optimization volume object, remaining volume at risk (RVR): \u03b1-value selection and usage from generalized equivalent uniform dose (gEUD) curve deviation perspective","volume":"68","author":"Anetai","year":"2023","journal-title":"Phys. Med. Biol."},{"key":"pmbae443dbib6","doi-asserted-by":"publisher","first-page":"52","DOI":"10.1016\/j.ejmp.2021.02.026","type":"journal-article","article-title":"Deep learning dose prediction for IMRT of esophageal cancer: the effect of data quality and quantity on model performance","volume":"83","author":"Barrag\u00e1n-Montero","year":"2021","journal-title":"Phys. Med."},{"key":"pmbae443dbib7","doi-asserted-by":"publisher","first-page":"3679","DOI":"10.1002\/mp.13597","type":"journal-article","article-title":"Three\u2010dimensional dose prediction for lung IMRT patients with deep neural networks: robust learning from heterogeneous beam configurations","volume":"46","author":"Barrag\u00e1n\u2010Montero","year":"2019","journal-title":"Med. Phys."},{"key":"pmbae443dbib8","doi-asserted-by":"publisher","first-page":"3579","DOI":"10.1088\/0031-9155\/47\/20\/302","type":"journal-article","article-title":"The generalized equivalent uniform dose function as a basis for intensity-modulated treatment planning","volume":"47","author":"Choi","year":"2002","journal-title":"Phys. Med. Biol."},{"key":"pmbae443dbib9","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1186\/s13014-017-0808-x","type":"journal-article","article-title":"RapidPlan head and neck model: the objectives and possible clinical benefit","volume":"12","author":"Fogliata","year":"2017","journal-title":"Radiat. Oncol."},{"key":"pmbae443dbib10","doi-asserted-by":"publisher","first-page":"106","DOI":"10.1002\/acm2.12224","type":"journal-article","article-title":"On the gEUD biological optimization objective for organs at risk in Photon Optimizer of Eclipse treatment planning system","volume":"19","author":"Fogliata","year":"2018","journal-title":"J. Appl. Clin. Med. Phys."},{"key":"pmbae443dbib11","doi-asserted-by":"publisher","first-page":"115","DOI":"10.1016\/j.ejmp.2007.07.001","type":"journal-article","article-title":"A free program for calculating EUD-based NTCP and TCP in external beam radiotherapy","volume":"23","author":"Gay","year":"2007","journal-title":"Phys. Med."},{"key":"pmbae443dbib12","doi-asserted-by":"publisher","first-page":"267","DOI":"10.1111\/1754-9485.13374","type":"journal-article","article-title":"Plan quality in radiotherapy treatment planning\u2013Review of the factors and challenges","volume":"66","author":"Hansen","year":"2022","journal-title":"J. Med. Imaging Radiat. Oncol."},{"key":"pmbae443dbib13","doi-asserted-by":"publisher","first-page":"2041","DOI":"10.1118\/1.2896070","type":"journal-article","article-title":"Investigation of intensity\u2010modulated radiotherapy optimization with gEUD\u2010based objectives by means of simulated annealing","volume":"35","author":"Hartmann","year":"2008","journal-title":"Med. Phys."},{"key":"pmbae443dbib14","doi-asserted-by":"publisher","first-page":"156","DOI":"10.1186\/s13014-022-02128-w","type":"journal-article","article-title":"Stereotactic body radiotherapy versus conventional radiotherapy for painful bone metastases: a systematic review and meta-analysis of randomised controlled trials","volume":"17","author":"Ito","year":"2022","journal-title":"Radiat. Oncol."},{"key":"pmbae443dbib15","doi-asserted-by":"publisher","first-page":"1442","DOI":"10.1093\/jjco\/hyaa128","type":"journal-article","article-title":"Stereotactic body radiotherapy for bone metastases in patients with colorectal cancer","volume":"50","author":"Ito","year":"2020","journal-title":"Japan. J. Clin. Oncol."},{"key":"pmbae443dbib16","doi-asserted-by":"publisher","DOI":"10.1259\/bjr.20190001","type":"journal-article","article-title":"Applications and limitations of machine learning in radiation oncology","volume":"92","author":"Jarrett","year":"2019","journal-title":"Br. J. Radiol."},{"key":"pmbae443dbib17","first-page":"113","author":"Ketkar","year":"2017","type":"book"},{"key":"pmbae443dbib18","article-title":"Adam: a method for stochastic optimization","author":"Kingma","year":"2014","type":"preprint"},{"key":"pmbae443dbib19","doi-asserted-by":"publisher","first-page":"199","DOI":"10.1016\/j.ejmp.2017.06.026","type":"journal-article","article-title":"Dosimetric comparison of RapidPlan and manually optimized plans in volumetric modulated arc therapy for prostate cancer","volume":"44","author":"Kubo","year":"2017","journal-title":"Phys. Med."},{"key":"pmbae443dbib20","first-page":"30106","type":"conference-proceedings","article-title":"Heavy-tailed class imbalance and why adam outperforms gradient descent on language models","volume":"vol 37","author":"Kunstner","year":"2024"},{"key":"pmbae443dbib21","doi-asserted-by":"publisher","first-page":"182","DOI":"10.1016\/j.ijrobp.2012.03.024","type":"journal-article","article-title":"Using generalized equivalent uniform dose atlases to combine and analyze prospective dosimetric and radiation pneumonitis data from 2 non-small cell lung cancer dose escalation protocols","volume":"85","author":"Liu","year":"2013","journal-title":"Int. J. Radiat. Oncol. Biol. Phys."},{"key":"pmbae443dbib22","doi-asserted-by":"publisher","DOI":"10.1016\/j.jrras.2023.100757","type":"journal-article","article-title":"A deep learning-based dose prediction method for evaluation of radiotherapy treatment planning","volume":"17","author":"Liu","year":"2024","journal-title":"J. Radiat. Res. Appl. Sci."},{"key":"pmbae443dbib23","doi-asserted-by":"publisher","first-page":"1754","DOI":"10.1109\/TPDS.2020.2975189","type":"journal-article","article-title":"Accelerating federated learning via momentum gradient descent","volume":"31","author":"Liu","year":"2020","journal-title":"IEEE Trans. Parallel Distrib. Syst."},{"key":"pmbae443dbib24","doi-asserted-by":"publisher","first-page":"402","DOI":"10.1109\/JAS.2020.1003396","type":"journal-article","article-title":"Efficient and high-quality recommendations via momentum-incorporated parallel stochastic gradient descent-based learning","volume":"8","author":"Luo","year":"2020","journal-title":"IEEE\/CAA J. Autom. Sin."},{"key":"pmbae443dbib25","doi-asserted-by":"publisher","first-page":"1711","DOI":"10.1088\/0031-9155\/49\/9\/009","type":"journal-article","article-title":"Incorporation of functional imaging data in the evaluation of dose distributions using the generalized concept of equivalent uniform dose","volume":"49","author":"Miften","year":"2004","journal-title":"Phys. Med. Biol."},{"key":"pmbae443dbib26","doi-asserted-by":"publisher","first-page":"1446","DOI":"10.1016\/j.ijrobp.2006.07.1383","type":"journal-article","article-title":"Update of human spinal cord reirradiation tolerance based on additional data from 38 patients","volume":"66","author":"Nieder","year":"2006","journal-title":"Int. J. Radiat. Oncol. Biol. Phys."},{"key":"pmbae443dbib27","doi-asserted-by":"publisher","first-page":"103","DOI":"10.1118\/1.598063","type":"journal-article","article-title":"Reporting and analyzing dose distributions: a concept of equivalent uniform dose","volume":"24","author":"Niemierko","year":"1997","journal-title":"Med. Phys."},{"key":"pmbae443dbib28","doi-asserted-by":"publisher","DOI":"10.1002\/acm2.14403","type":"journal-article","article-title":"Dosimetric impact of the respiratory motion of the liver dome in stereotactic body radiotherapy for spine metastasis: a planning study","volume":"25","author":"Okamoto","year":"2024","journal-title":"J. Appl. Clin. Med. Phys."},{"key":"pmbae443dbib29","doi-asserted-by":"publisher","first-page":"145","DOI":"10.1016\/S0893-6080(98)00116-6","type":"journal-article","article-title":"On the momentum term in gradient descent learning algorithms","volume":"12","author":"Qian","year":"1999","journal-title":"Neural Netw."},{"key":"pmbae443dbib30","article-title":"An overview of gradient descent optimization algorithms","author":"Ruder","year":"2016","type":"preprint"},{"key":"pmbae443dbib31","doi-asserted-by":"publisher","first-page":"e112","DOI":"10.1017\/S1460396923000389","type":"journal-article","article-title":"Potential advantages of gEUD optimisation as compared with conventional physical optimisation for stereotactic treatment planning","volume":"22","author":"Sait","year":"2023","journal-title":"J. Radiother Pract."},{"key":"pmbae443dbib32","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1186\/s13014-016-0684-9","type":"journal-article","article-title":"Applying a RapidPlan model trained on a technique and orientation to another: a feasibility and dosimetric evaluation","volume":"11","author":"Wu","year":"2016","journal-title":"Radiat. Oncol."},{"key":"pmbae443dbib33","doi-asserted-by":"publisher","first-page":"279","DOI":"10.1088\/0031-9155\/48\/3\/301","type":"journal-article","article-title":"Intensity-modulated radiotherapy optimization with gEUD-guided dose\u2013volume objectives","volume":"48","author":"Wu","year":"2003","journal-title":"Phys. Med. Biol."},{"key":"pmbae443dbib34","first-page":"1","type":"conference-proceedings","volume":"vol Series","author":"Yazan","year":"2017"},{"key":"pmbae443dbib35","first-page":"2359","type":"conference-proceedings","volume":"vol Series","author":"Zhang","year":"2018"},{"key":"pmbae443dbib36","first-page":"1","type":"conference-proceedings","volume":"vol Series","author":"Zhang","year":"2018"},{"key":"pmbae443dbib37","first-page":"21285","type":"conference-proceedings","article-title":"Towards theoretically understanding why sgd generalizes better than adam in deep learning","volume":"vol 33","author":"Zhou","year":"2020"},{"key":"pmbae443dbib38","doi-asserted-by":"publisher","first-page":"3231","DOI":"10.1088\/0031-9155\/53\/12\/011","type":"journal-article","article-title":"Controlling the dose distribution with gEUD-type constraints within the convex radiotherapy optimization framework","volume":"53","author":"Zinchenko","year":"2008","journal-title":"Phys. Med. Biol."},{"key":"pmbae443dbib39","type":"conference-proceedings","article-title":"Parallelized stochastic gradient descent","volume":"vol 23","author":"Zinkevich","year":"2010"}],"container-title":["Physics in Medicine &amp; Biology"],"original-title":[],"link":[{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6560\/ae443d","content-type":"text\/html","content-version":"am","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6560\/ae443d\/pdf","content-type":"application\/pdf","content-version":"am","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6560\/ae443d","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6560\/ae443d\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6560\/ae443d\/pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6560\/ae443d\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6560\/ae443d\/pdf","content-type":"application\/pdf","content-version":"am","intended-application":"similarity-checking"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6560\/ae443d\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,2,23]],"date-time":"2026-02-23T08:54:54Z","timestamp":1771836894000},"score":1,"resource":{"primary":{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6560\/ae443d"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,2,23]]},"references-count":39,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2026,2,23]]},"published-print":{"date-parts":[[2026,2,28]]}},"URL":"https:\/\/doi.org\/10.1088\/1361-6560\/ae443d","relation":{},"ISSN":["0031-9155","1361-6560"],"issn-type":[{"value":"0031-9155","type":"print"},{"value":"1361-6560","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,2,23]]},"assertion":[{"value":"Practical gEUD optimization technique for stereotactic radiation therapy based on a theoretical reinterpretation using the gEUD curve concept","name":"article_title","label":"Article Title"},{"value":"Physics in Medicine & Biology","name":"journal_title","label":"Journal Title"},{"value":"paper","name":"article_type","label":"Article Type"},{"value":"\u00a9 2026 The Author(s). Published on behalf of Institute of Physics and Engineering in Medicine by IOP Publishing Ltd","name":"copyright_information","label":"Copyright Information"},{"value":"2025-08-26","name":"date_received","label":"Date Received","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2026-02-10","name":"date_accepted","label":"Date Accepted","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2026-02-23","name":"date_epub","label":"Online publication date","group":{"name":"publication_dates","label":"Publication dates"}}]}}