{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,12]],"date-time":"2026-04-12T08:41:59Z","timestamp":1775983319454,"version":"3.50.1"},"reference-count":36,"publisher":"Wiley","issue":"11","license":[{"start":{"date-parts":[[2025,11,13]],"date-time":"2025-11-13T00:00:00Z","timestamp":1762992000000},"content-version":"vor","delay-in-days":12,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"},{"start":{"date-parts":[[2025,11,1]],"date-time":"2025-11-01T00:00:00Z","timestamp":1761955200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"content-domain":{"domain":["aapm.onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Medical Physics"],"published-print":{"date-parts":[[2025,11]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:sec>\n                    <jats:title>Background<\/jats:title>\n                    <jats:p>Intensity\u2010modulated radiation therapy (IMRT) utilizes inverse optimization to calculate beamlet intensities, achieving clinical dose objectives for tumors while minimizing dose to organs\u2010at\u2010risk (OARs). However, incorporating non\u2010convex dose\u2010volume constraints into IMRT planning is challenging due to their combinatorial nature and computational complexity.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Purpose<\/jats:title>\n                    <jats:p>This study explores a novel approach to IMRT fluence map optimization (FMO) by leveraging deep inverse optimization (DIO). Our method aims to approximate non\u2010convex constraints efficiently while preserving convexity, improving adherence to clinical dose objectives.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Methods<\/jats:title>\n                    <jats:p>We introduce a new relaxation technique that preserves convexity by incorporating second\u2010order cone constraints to approximate non\u2010convex conditions. A DIO framework is then employed to solve the second\u2010order cone programming problem, generating clinically feasible treatment plans. To balance tumor coverage and OAR sparing, we employ sequential optimization to integrate multiple objectives, ensuring effective dose distributions across patient datasets. The method was evaluated retrospectively on 30 locally advanced non\u2010small cell lung cancer (NSCLC) patients treated with 60\u00a0Gy in 30 fractions. Plan quality was assessed using dosimetric metrics, including D98%, D2%, and maximum dose for the planning target volume (PTV), as well as dose\u2010volume percentages, mean, and maximum doses for the lung, heart, esophagus, and spinal cord. Additionally, optimization convergence complexity and duty cycle were analyzed to assess planning and delivery efficiency.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Results<\/jats:title>\n                    <jats:p>\n                      Compared to traditional convex optimization, the proposed method maintains comparable PTV coverage while significantly improving dose homogeneity (narrower D98%\u2010to\u2010D2% range, reduced hotspots). It enhances OAR sparing, reducing lung V5Gy (\n                      <jats:italic>p<\/jats:italic>\n                      \u00a0=\u00a00.01), heart V30Gy (\n                      <jats:italic>p<\/jats:italic>\n                      \u00a0=\u00a00.04), and spinal cord maximum dose (\n                      <jats:italic>p<\/jats:italic>\n                      \u00a0&lt;\u00a00.01), while ensuring clinically acceptable dose distributions. Additionally, the optimization process demonstrates significantly faster convergence (\u223c5\u00a0vs. \u223c39 iterations).\n                    <\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Conclusion<\/jats:title>\n                    <jats:p>This study presents an effective and computationally efficient approach to IMRT treatment planning by approximating non\u2010convex dose\u2010volume constraints with second\u2010order cone programming and DIO. The method enhances plan quality by improving dose homogeneity and OAR sparing while significantly accelerating optimization convergence, offering a practical solution for advanced radiation therapy planning.<\/jats:p>\n                  <\/jats:sec>","DOI":"10.1002\/mp.70141","type":"journal-article","created":{"date-parts":[[2025,11,13]],"date-time":"2025-11-13T17:13:55Z","timestamp":1763054035000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Non\u2010convex IMRT treatment planning using deep inverse optimization"],"prefix":"10.1002","volume":"52","author":[{"given":"Yang","family":"Lei","sequence":"first","affiliation":[{"name":"Department of Radiation Oncology Icahn School of Medicine at Mount Sinai  New York New York USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiahan","family":"Zhang","sequence":"additional","affiliation":[{"name":"Department of Radiation Oncology Icahn School of Medicine at Mount Sinai  New York New York USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tian","family":"Liu","sequence":"additional","affiliation":[{"name":"Department of Radiation Oncology Icahn School of Medicine at Mount Sinai  New York New York USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2025,11,13]]},"reference":[{"key":"e_1_2_8_2_1","doi-asserted-by":"publisher","DOI":"10.1259\/bjr\/65676879"},{"key":"e_1_2_8_3_1","doi-asserted-by":"publisher","DOI":"10.1016\/S1053\u20104296(99)80052\u20106"},{"key":"e_1_2_8_4_1","doi-asserted-by":"publisher","DOI":"10.1016\/0167\u20108140(88)90167\u20103"},{"key":"e_1_2_8_5_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10479\u2010009\u20100659\u20104"},{"key":"e_1_2_8_6_1","doi-asserted-by":"publisher","DOI":"10.1016\/0360\u20103016(87)90203\u20103"},{"key":"e_1_2_8_7_1","doi-asserted-by":"publisher","DOI":"10.1118\/1.598932"},{"key":"e_1_2_8_8_1","doi-asserted-by":"publisher","DOI":"10.1088\/0031\u20109155\/44\/2\/014"},{"key":"e_1_2_8_9_1","doi-asserted-by":"publisher","DOI":"10.1118\/1.1598852"},{"key":"e_1_2_8_10_1","doi-asserted-by":"publisher","DOI":"10.1088\/0031\u20109155\/46\/10\/309"},{"key":"e_1_2_8_11_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijrobp.2007.08.019"},{"key":"e_1_2_8_12_1","doi-asserted-by":"publisher","DOI":"10.1118\/1.1528179"},{"key":"e_1_2_8_13_1","doi-asserted-by":"publisher","DOI":"10.1088\/0031\u20109155\/46\/10\/306"},{"key":"e_1_2_8_14_1","doi-asserted-by":"publisher","DOI":"10.1118\/1.4875700"},{"key":"e_1_2_8_15_1","doi-asserted-by":"publisher","DOI":"10.1287\/ijoc.2018.0841"},{"key":"e_1_2_8_16_1","doi-asserted-by":"publisher","DOI":"10.1016\/0360\u20103016(90)90145\u2010A"},{"key":"e_1_2_8_17_1","doi-asserted-by":"publisher","DOI":"10.1137\/S1052623499350013"},{"key":"e_1_2_8_18_1","doi-asserted-by":"publisher","DOI":"10.1118\/1.598202"},{"key":"e_1_2_8_19_1","doi-asserted-by":"publisher","DOI":"10.1002\/mp.13572"},{"key":"e_1_2_8_20_1","doi-asserted-by":"publisher","DOI":"10.1088\/1361\u20106560\/ade8ce"},{"key":"e_1_2_8_21_1","doi-asserted-by":"publisher","DOI":"10.1118\/1.598017"},{"key":"e_1_2_8_22_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02592208"},{"key":"e_1_2_8_23_1","doi-asserted-by":"publisher","DOI":"10.1137\/140978077"},{"key":"e_1_2_8_24_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11081\u2010018\u20109409\u20102"},{"key":"e_1_2_8_25_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.2517\u20106161.1996.tb02080.x"},{"key":"e_1_2_8_26_1","doi-asserted-by":"publisher","DOI":"10.48550\/arXiv.1304.6655"},{"key":"e_1_2_8_27_1","doi-asserted-by":"publisher","DOI":"10.1287\/ijoc.2021.1129"},{"key":"e_1_2_8_28_1","doi-asserted-by":"publisher","DOI":"10.1088\/1361\u20106560\/ace09e"},{"key":"e_1_2_8_29_1","doi-asserted-by":"publisher","DOI":"10.1137\/040606612"},{"key":"e_1_2_8_30_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10589\u2010017\u20109919\u20104"},{"key":"e_1_2_8_31_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0024\u20103795(98)10032\u20100"},{"key":"e_1_2_8_32_1","doi-asserted-by":"crossref","unstructured":"TanY DelongA TerekhovD.Deep Inverse Optimization. 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