{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,16]],"date-time":"2026-01-16T11:06:40Z","timestamp":1768561600209,"version":"3.49.0"},"reference-count":35,"publisher":"IOP Publishing","issue":"16","license":[{"start":{"date-parts":[[2025,8,6]],"date-time":"2025-08-06T00:00:00Z","timestamp":1754438400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2025,8,6]],"date-time":"2025-08-06T00:00:00Z","timestamp":1754438400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/iopscience.iop.org\/info\/page\/text-and-data-mining"}],"funder":[{"name":"NIH","award":["R01CA230278"],"award-info":[{"award-number":["R01CA230278"]}]}],"content-domain":{"domain":["iopscience.iop.org"],"crossmark-restriction":false},"short-container-title":["Phys. Med. Biol."],"published-print":{"date-parts":[[2025,8,17]]},"abstract":"Abstract<\/jats:title>\n \n Purpose<\/jats:italic>. In radiotherapy, dose distribution conformity and compactness are critical to patient outcomes. Advanced techniques like \n \n \n \n 4<\/mml:mn>\n \u03c0<\/mml:mi>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:inline-formula> radiotherapy leverage non-coplanar beams for superior dosimetry by exploring additional degrees of freedom. However, \n \n \n \n 4<\/mml:mn>\n \u03c0<\/mml:mi>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:inline-formula> planning is computationally intensive due to large dose-loading matrices for candidate beams. This work presents an ultra-high performance parallel (UHPP) framework to accelerate high-dimensional treatment planning. Methods<\/jats:italic>. For dose calculation, we developed: (1) a two-step total energy released per unit mass (TERMA) computation module calculating the TERMA array once per beam, enabling reuse across convolution directions; (2) a synchronized dose calculation module based on collapsed-cone convolution superposition (CCCS), arranging rays in dedicated sequences to preserve thread efficiency and minimize memory access; (3) a scattering-based coordinate transformation mapping dose from beamlet to patient Cartesian coordinates, eliminating aliasing without atomic operations. The framework includes CCCS exponential kernel calculation for varying LINAC spectra. For beam orientation optimization, we employed fast iterative shrinkage-thresholding algorithm with group sparsity regularization, accelerated using cuSPARSE library on GPUs. We benchmarked against Monte Carlo (MC) simulations for dose accuracy and compared computational performance to state-of-the-art (SOTA) methods. Plan quality was evaluated across four approaches: UHPP, SOTA, clinical VMAT plans, and MC calculations based on UHPP plans. Results<\/jats:italic>. Compared to MC simulations, UHPP achieved minimum 98% gamma passing rates under 1.5%\/1.5 mm criterion for water and slab phantoms, and average 97.35% and 92.18% under 3%\/3 mm criterion for pancreas and head-and-neck patients, respectively. UHPP delivered 8.86\u00d7 and 6.99\u00d7 speedups in dose calculation and plan optimization while maintaining comparable or superior plan quality. Both UHPP and SOTA consistently produced \n \n \n \n 4<\/mml:mn>\n \u03c0<\/mml:mi>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:inline-formula> plans outperforming clinical VMAT plans in organ-at-risk sparing and target coverage. Conclusion<\/jats:italic>. The UHPP framework delivers high dose accuracy and substantial computational speedup without sacrificing \n \n \n \n 4<\/mml:mn>\n \u03c0<\/mml:mi>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:inline-formula> planning\u2019s dosimetric advantages, supporting practical adoption of advanced \n \n \n \n 4<\/mml:mn>\n \u03c0<\/mml:mi>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:inline-formula> radiotherapy in clinical workflows.<\/jats:p>","DOI":"10.1088\/1361-6560\/adf2f2","type":"journal-article","created":{"date-parts":[[2025,7,22]],"date-time":"2025-07-22T22:54:31Z","timestamp":1753224871000},"page":"165004","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":1,"title":["An ultra-high performance parallel (UHPP) framework for complex 4\u03c0<\/i> radiotherapy planning"],"prefix":"10.1088","volume":"70","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7155-9552","authenticated-orcid":true,"given":"Qifan","family":"Xu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1835-3870","authenticated-orcid":true,"given":"Qihui","family":"Lyu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7616-1746","authenticated-orcid":true,"given":"Lu","family":"Jiang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shusen","family":"Jing","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3400-7684","authenticated-orcid":true,"given":"Dan","family":"Ruan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6696-5409","authenticated-orcid":true,"given":"Ke","family":"Sheng","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"266","published-online":{"date-parts":[[2025,8,6]]},"reference":[{"key":"pmbadf2f2bib1","doi-asserted-by":"publisher","first-page":"250","DOI":"10.1016\/S0168-9002(03)01368-8","article-title":"Geant4\u2014a simulation toolkit","volume":"506","author":"Agostinelli","year":"2003","journal-title":"Nucl. Instrum. Methods Phys. Res. A"},{"key":"pmbadf2f2bib2","doi-asserted-by":"publisher","first-page":"577","DOI":"10.1118\/1.596360","article-title":"Collapsed cone convolution of radiant energy for photon dose calculation in heterogeneous media","volume":"16","author":"Ahnesj\u00f6","year":"1989","journal-title":"Med. Phys."},{"key":"pmbadf2f2bib3","doi-asserted-by":"publisher","first-page":"270","DOI":"10.1109\/TNS.2006.869826","article-title":"Geant4 developments and applications","volume":"53","author":"Allison","year":"2006","journal-title":"IEEE Trans. Nucl. Sci."},{"key":"pmbadf2f2bib4","doi-asserted-by":"publisher","first-page":"186","DOI":"10.1016\/j.nima.2016.06.125","article-title":"Recent developments in Geant4","volume":"835","author":"Allison","year":"2016","journal-title":"Nucl. Instrum. Methods Phys. Res. A"},{"key":"pmbadf2f2bib5","doi-asserted-by":"publisher","first-page":"1326","DOI":"10.1002\/mp.16899","article-title":"Dosimetrically motivated beam-angle optimization for non-coplanar arc radiotherapy with and without dynamic collimator rotation","volume":"51","author":"Bertholet","year":"2024","journal-title":"Med. Phys."},{"key":"pmbadf2f2bib6","doi-asserted-by":"publisher","article-title":"Head-Neck Cetuximab","author":"Bosch","DOI":"10.7937\/K9\/TCIA.2015.7AKGJUPZ"},{"key":"pmbadf2f2bib7","doi-asserted-by":"publisher","first-page":"1150","DOI":"10.1118\/1.3551996","article-title":"Ultrafast convolution\/superposition using tabulated and exponential kernels on GPU","volume":"38","author":"Chen","year":"2011","journal-title":"Med. Phys."},{"key":"pmbadf2f2bib8","doi-asserted-by":"publisher","first-page":"407","DOI":"10.1016\/j.ijrobp.2013.02.002","article-title":"4\u03c0 noncoplanar stereotactic body radiation therapy for centrally located or larger lung tumors","volume":"86","author":"Dong","year":"2013a","journal-title":"Int. J. Radiat. Oncol. Biol. Phys."},{"key":"pmbadf2f2bib9","doi-asserted-by":"publisher","first-page":"1360","DOI":"10.1016\/j.ijrobp.2012.09.028","article-title":"4\u03c0 non-coplanar liver SBRT: a novel delivery technique","volume":"85","author":"Dong","year":"2013b","journal-title":"Int. J. Radiat. Oncol."},{"key":"pmbadf2f2bib10","doi-asserted-by":"publisher","DOI":"10.3389\/fphy.2021.718873","article-title":"Variance-reduction methods for Monte Carlo simulation of radiation transport","volume":"9","author":"Garc\u00eda-Pareja","year":"2021","journal-title":"Front. Phys."},{"key":"pmbadf2f2bib11","doi-asserted-by":"publisher","first-page":"1338","DOI":"10.1002\/mp.12788","article-title":"Integrated beam orientation and scanning-spot optimization in intensity-modulated proton therapy for brain and unilateral head and neck tumors","volume":"45","author":"Gu","year":"2018","journal-title":"Med. Phys."},{"key":"pmbadf2f2bib12","article-title":"Eigen v3","author":"Guennebaud","year":"2010"},{"key":"pmbadf2f2bib13","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6560\/ad75e1","article-title":"A dosimetrically motivated pathfinding approach for non-isocentric dynamic trajectory radiotherapy","volume":"69","author":"Guyer","year":"2024","journal-title":"Phys. Med. Biol."},{"key":"pmbadf2f2bib14","doi-asserted-by":"publisher","article-title":"Breath-hold CT and cone-beam CT images with expert manual organ-at-risk segmentations from radiation treatments of locally advanced pancreatic cancer","author":"Hong","DOI":"10.7937\/TCIA.ESHQ-4D90"},{"key":"pmbadf2f2bib15","doi-asserted-by":"publisher","first-page":"7439","DOI":"10.1002\/mp.15223","article-title":"Fully automated noncoplanar radiation therapy treatment planning","volume":"48","author":"Huang","year":"2021","journal-title":"Med. Phys."},{"key":"pmbadf2f2bib16","doi-asserted-by":"publisher","first-page":"6205","DOI":"10.1088\/0031-9155\/56\/19\/004","article-title":"Beam orientation optimization for intensity modulated radiation therapy using adaptive l(2,1)-minimization","volume":"56","author":"Jia","year":"2011","journal-title":"Phys. Med. Biol."},{"key":"pmbadf2f2bib17","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1177\/15330338211019511","article-title":"Noncoplanar versus coplanar intensity-modulated radiation therapy (IMRT) for protection of the lip and buccal mucosa","volume":"20","author":"Lao","year":"2021","journal-title":"Technol. Cancer Res. Treat."},{"key":"pmbadf2f2bib18","doi-asserted-by":"publisher","first-page":"7175","DOI":"10.1088\/0031-9155\/55\/23\/002","article-title":"A non-voxel-based broad-beam (NVBB) framework for IMRT treatment planning","volume":"55","author":"Lu","year":"2010","journal-title":"Phys. Med. Biol."},{"key":"pmbadf2f2bib19","doi-asserted-by":"publisher","first-page":"655","DOI":"10.1088\/0031-9155\/50\/4\/007","article-title":"Accurate convolution\/superposition for multi-resolution dose calculation using cumulative tabulated kernels","volume":"50","author":"Lu","year":"2005","journal-title":"Phys. Med. Biol."},{"key":"pmbadf2f2bib20","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6560\/ab63b8","article-title":"Many-isocenter optimization for robotic radiotherapy","volume":"65","author":"Lyu","year":"2020","journal-title":"Phys. Med. Biol."},{"key":"pmbadf2f2bib21","doi-asserted-by":"publisher","first-page":"2399","DOI":"10.1002\/mp.12915","article-title":"VMAT optimization with dynamic collimator rotation","volume":"45","author":"Lyu","year":"2018a","journal-title":"Med. Phys."},{"key":"pmbadf2f2bib22","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6560\/aac704","article-title":"A novel optimization framework for VMAT with dynamic gantry couch rotation","volume":"63","author":"Lyu","year":"2018b","journal-title":"Phys. Med. Biol."},{"key":"pmbadf2f2bib23","doi-asserted-by":"publisher","first-page":"188","DOI":"10.1118\/1.595774","article-title":"A convolution method of calculating dose for 15-MV x-rays","volume":"12","author":"Mackie","year":"1985","journal-title":"Med. Phys."},{"key":"pmbadf2f2bib24","doi-asserted-by":"publisher","first-page":"64","DOI":"10.1118\/1.595924","article-title":"Differential pencil beam dose computation model for photons","volume":"13","author":"Mohan","year":"1986","journal-title":"Med. Phys."},{"key":"pmbadf2f2bib25","doi-asserted-by":"publisher","first-page":"126","DOI":"10.1007\/978-3-319-14612-6_10","article-title":"Low rank priors for color image regularization","author":"M\u00f6llenhoff","year":"2015"},{"key":"pmbadf2f2bib26","doi-asserted-by":"publisher","first-page":"3719","DOI":"10.1002\/mp.13651","article-title":"Parallel beamlet dose calculation via beamlet contexts in a distributed multi\u2010GPU framework","volume":"46","author":"Neph","year":"2019","journal-title":"Med. Phys."},{"key":"pmbadf2f2bib27","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6560\/aaa94f","article-title":"Fraction-variant beam orientation optimization for non-coplanar IMRT","volume":"63","author":"O\u2019Connor","year":"2018","journal-title":"Phys. Med. Biol."},{"key":"pmbadf2f2bib28","article-title":"OpenMP application program interface version 3.0","author":"OpenMP Architecture Review Board"},{"key":"pmbadf2f2bib29","doi-asserted-by":"publisher","first-page":"3826","DOI":"10.1120\/jacmp.v13i4.3826","article-title":"Coplanar versus noncoplanar intensity-modulated radiation therapy (IMRT) and volumetric-modulated arc therapy (VMAT) treatment planning for fronto-temporal high-grade glioma","volume":"13","author":"Panet-Raymond","year":"2012","journal-title":"J. Appl. Clin. Med. Phys."},{"key":"pmbadf2f2bib30","doi-asserted-by":"publisher","first-page":"95","DOI":"10.1186\/s13014-019-1309-x","article-title":"Ablative radiation therapy for locally advanced pancreatic cancer: techniques and results","volume":"14","author":"Reyngold","year":"2019","journal-title":"Radiat. Oncol. Lond. Engl."},{"key":"pmbadf2f2bib31","doi-asserted-by":"publisher","DOI":"10.1016\/j.adro.2024.101570","article-title":"Quantification of dosimetry improvement with or without patient surface guidance","volume":"9","author":"Sheng","year":"2024","journal-title":"Adv. Radiat. Oncol."},{"key":"pmbadf2f2bib32","doi-asserted-by":"publisher","DOI":"10.1148\/ryai.230024","article-title":"TotalSegmentator: robust segmentation of 104 anatomic structures in CT images","volume":"5","author":"Wasserthal","year":"2023","journal-title":"Radiol. Artif. Intell."},{"key":"pmbadf2f2bib33","doi-asserted-by":"publisher","first-page":"4","DOI":"10.3390\/cancers14040939","article-title":"A prospective phase II study of automated non-coplanar VMAT for recurrent head and neck cancer: initial report of feasibility, safety, and patient-reported outcomes","volume":"14","author":"Woods","year":"2022","journal-title":"Cancers"},{"key":"pmbadf2f2bib34","doi-asserted-by":"publisher","first-page":"144","DOI":"10.1016\/j.ijrobp.2018.01.048","article-title":"A prospective 4\u03c0 radiation therapy clinical study in recurrent high-grade glioma patients","volume":"101","author":"Yu","year":"2018","journal-title":"Int. J. Radiat. Oncol."},{"key":"pmbadf2f2bib35","doi-asserted-by":"publisher","first-page":"6457","DOI":"10.1118\/1.4932631","article-title":"The development and verification of a highly accurate collision prediction model for automated noncoplanar plan delivery","volume":"42","author":"Yu","year":"2015","journal-title":"Med. Phys."}],"container-title":["Physics in Medicine & Biology"],"original-title":[],"link":[{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6560\/adf2f2","content-type":"text\/html","content-version":"am","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6560\/adf2f2\/pdf","content-type":"application\/pdf","content-version":"am","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6560\/adf2f2","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6560\/adf2f2\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6560\/adf2f2\/pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6560\/adf2f2\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6560\/adf2f2\/pdf","content-type":"application\/pdf","content-version":"am","intended-application":"similarity-checking"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6560\/adf2f2\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,8,6]],"date-time":"2025-08-06T09:32:24Z","timestamp":1754472744000},"score":1,"resource":{"primary":{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6560\/adf2f2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,8,6]]},"references-count":35,"journal-issue":{"issue":"16","published-online":{"date-parts":[[2025,8,6]]},"published-print":{"date-parts":[[2025,8,17]]}},"URL":"https:\/\/doi.org\/10.1088\/1361-6560\/adf2f2","relation":{},"ISSN":["0031-9155","1361-6560"],"issn-type":[{"value":"0031-9155","type":"print"},{"value":"1361-6560","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,8,6]]},"assertion":[{"value":"An ultra-high performance parallel (UHPP) framework for complex 4\u03c0 radiotherapy planning","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 2025 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":"2024-11-02","name":"date_received","label":"Date Received","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2025-07-22","name":"date_accepted","label":"Date Accepted","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2025-08-06","name":"date_epub","label":"Online publication date","group":{"name":"publication_dates","label":"Publication dates"}}]}}