{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,15]],"date-time":"2026-10-15T16:56:54Z","timestamp":1792083414660,"version":"4.4.0"},"reference-count":18,"publisher":"Wiley","issue":"10","license":[{"start":{"date-parts":[[2026,9,30]],"date-time":"2026-09-30T00:00:00Z","timestamp":1790726400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"},{"start":{"date-parts":[[2026,9,30]],"date-time":"2026-09-30T00:00:00Z","timestamp":1790726400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62103366"],"award-info":[{"award-number":["62103366"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["aapm.onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Medical Physics"],"published-print":{"date-parts":[[2026,10]]},"abstract":"Abstract<\/jats:title>\n \n Background<\/jats:title>\n Conventional volumetric modulated arc therapy (VMAT) optimization relies on gradient\u2010based methods in which analytical gradients must be explicitly derived for each objective function and machine constraint. This dedicated mathematical derivation imposes substantial barriers to extending the optimization framework with new clinical objectives or delivery constraints, and the resulting CPU\u2010based implementations do not natively exploit modern GPU hardware.<\/jats:p>\n <\/jats:sec>\n \n Purpose<\/jats:title>\n To develop an end\u2010to\u2010end differentiable VMAT optimization framework using computation graphs that enable automatic differentiation\u2013based gradient computation for both fluence map optimization (FMO) and direct aperture optimization (DAO), while incorporating VMAT machine delivery constraints within a unified, GPU\u2010accelerated pipeline.<\/jats:p>\n <\/jats:sec>\n \n Methods<\/jats:title>\n A two\u2010stage pipeline\u2014fluence map optimization (FMO) followed by DAO\u2014was developed. FMO reformulates dose calculation as a differentiable computation graph, enabling gradient computation for arbitrary objective functions including non\u2010smooth Heaviside step terms. For DAO, a novel analytically derived computation graph maps MLC leaf positions to delivered fluence through closed\u2010form time\u2010averaged bixel exposure integration with finite\u2010width boundary corrections, ensuring exact differentiability. Machine delivery constraints\u2014including leaf collision, speed limits, and dose rate bounds\u2014are incorporated as differentiable penalty terms for joint end\u2010to\u2010end optimization. Twenty lung cancer cases from the GDP\u2010HMM AAPM Challenge dataset (60\u00a0Gy\/30 fractions) were optimized using objectives derived from clinical Eclipse reference plans and compared against MatRad and Eclipse.<\/jats:p>\n <\/jats:sec>\n \n Results<\/jats:title>\n \n The proposed method achieved PTV D98 of 58.88\u00a0\u00b1\u00a00.33\u00a0Gy, comparable to Eclipse (59.07\u00a0\u00b1\u00a00.55\u00a0Gy,\n p\u00a0=<\/jats:italic>\n \u00a00.26) and significantly higher than MatRad (57.27\u00a0\u00b1\u00a00.48\u00a0Gy,\n p\u00a0<<\/jats:italic>\n \u00a00.001). The Paddick conformity index was 0.81\u00a0\u00b1\u00a00.06, comparable to Eclipse (0.84\u00a0\u00b1\u00a00.22,\n p\u00a0=<\/jats:italic>\n \u00a00.48) and superior to MatRad (0.64\u00a0\u00b1\u00a00.11,\n p\u00a0<<\/jats:italic>\n \u00a00.001). OAR sparing closely matched Eclipse: heart mean dose 10.74\u00a0\u00b1\u00a04.89\u00a0Gy vs. 11.55\u00a0\u00b1\u00a04.76\u00a0Gy; lung mean dose 15.33\u00a0\u00b1\u00a03.50\u00a0Gy vs. 16.70\u00a0\u00b1\u00a03.29\u00a0Gy; LAD mean dose 9.55\u00a0\u00b1\u00a04.97\u00a0Gy vs. 9.05\u00a0\u00b1\u00a03.94\u00a0Gy (\n p\u00a0=<\/jats:italic>\n \u00a00.18). MatRad achieved lower heart doses at the cost of degraded PTV coverage and conformity. Optimization time was significantly shorter (59.28\u00a0\u00b1\u00a043.95 s vs. 390.30\u00a0\u00b1\u00a0184.90 s,\n p\u00a0<<\/jats:italic>\n \u00a00.001), while delivery times were equivalent (\n p\u00a0=<\/jats:italic>\n \u00a00.92).\n <\/jats:p>\n <\/jats:sec>\n \n Conclusions<\/jats:title>\n The proposed differentiable VMAT framework demonstrated superior goal\u2010directed optimization fidelity compared with MatRad\u2014more reliably translating objectives into intended dosimetric outcomes\u2014achieving plan quality approaching clinical Eclipse plans with faster optimization.<\/jats:p>\n <\/jats:sec>","DOI":"10.1002\/mp.70685","type":"journal-article","created":{"date-parts":[[2026,9,30]],"date-time":"2026-09-30T16:00:34Z","timestamp":1790784034000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["End\u2010to\u2010end differentiable volumetric modulated arc therapy optimization via computation graph\u2013driven automatic differentiation"],"prefix":"10.1002","volume":"53","author":[{"given":"Hongkai","family":"Wang","sequence":"first","affiliation":[{"name":"Department of Radiation Oncology National Cancer Center\/National Clinical Research Center for Cancer\/Cancer Hospital, Chinese Academy of Medical Sciences and Peking Union Medical College Beijing China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wenzheng","family":"Sun","sequence":"additional","affiliation":[{"name":"Department of Radiation Oncology The Second Affiliated Hospital, School of Medicine, Zhejiang University Hangzhou Zhejiang China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wenlong","family":"Xia","sequence":"additional","affiliation":[{"name":"Department of Radiation Oncology National Cancer Center\/National Clinical Research Center for Cancer\/Cancer Hospital, Chinese Academy of Medical Sciences and Peking Union Medical College Beijing China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Bin","family":"Liang","sequence":"additional","affiliation":[{"name":"Department of Radiation Oncology National Cancer Center\/National Clinical Research Center for Cancer\/Cancer Hospital, Chinese Academy of Medical Sciences and Peking Union Medical College Beijing China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2026,9,30]]},"reference":[{"key":"e_1_2_10_2_1","doi-asserted-by":"publisher","DOI":"10.1118\/1.2818738"},{"key":"e_1_2_10_3_1","doi-asserted-by":"publisher","DOI":"10.1259\/bjr\/22373346"},{"key":"e_1_2_10_4_1","doi-asserted-by":"publisher","DOI":"10.1088\/0031\u20109155\/54\/1\/N02"},{"key":"e_1_2_10_5_1","doi-asserted-by":"publisher","DOI":"10.1118\/1.4908224"},{"key":"e_1_2_10_6_1","doi-asserted-by":"publisher","DOI":"10.1118\/1.1477415"},{"key":"e_1_2_10_7_1","doi-asserted-by":"publisher","DOI":"10.1088\/0031\u20109155\/57\/14\/4569"},{"key":"e_1_2_10_8_1","doi-asserted-by":"publisher","DOI":"10.1186\/s13014\u2010022\u201002045\u2010y"},{"key":"e_1_2_10_9_1","doi-asserted-by":"publisher","DOI":"10.1088\/2057\u20101976\/adcaca"},{"key":"e_1_2_10_10_1","doi-asserted-by":"crossref","unstructured":"CisternasE MairaniA ZiegenheinP et\u00a0al.matRad\u2014a multi\u2010modality open source 3D treatment planning toolkit. 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