{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,10]],"date-time":"2026-07-10T15:16:38Z","timestamp":1783696598726,"version":"3.55.0"},"reference-count":28,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T00:00:00Z","timestamp":1777507200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T00:00:00Z","timestamp":1777507200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"name":"This project was funded by the State as part of France 2030, and is part of the project PREMYOM."}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Int J CARS"],"DOI":"10.1007\/s11548-026-03675-3","type":"journal-article","created":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T06:56:53Z","timestamp":1777532213000},"page":"1113-1120","update-policy":"https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A differentiable simulation of the eye for patient-specific strabismus surgery planning"],"prefix":"10.1007","volume":"21","author":[{"given":"Even","family":"Harsigny","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Pablo","family":"Alvarez","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Michel","family":"Duprez","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"St\u00e9phane","family":"Cotin","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,4,30]]},"reference":[{"key":"3675_CR1","doi-asserted-by":"publisher","DOI":"10.1186\/s12886-024-03712-2","author":"R Niu","year":"2024","unstructured":"Niu R, Lv P, Hao R, Zhang W (2024) Comprehensive analysis of strabismus reoperations: clinical insights and progression factors. BMC Ophthalmol. https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1186\/s12886-024-03712-2","journal-title":"BMC Ophthalmol"},{"issue":"2","key":"3675_CR2","doi-asserted-by":"publisher","first-page":"396","DOI":"10.1016\/j.ophtha.2011.07.044","volume":"119","author":"MS Zhang","year":"2012","unstructured":"Zhang MS, Hutchinson AK, Drack AV, Cleveland J, Lambert SR (2012) Improved ocular alignment with adjustable sutures in adults undergoing strabismus surgery. Ophthalmology 119(2):396\u2013402. https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1016\/j.ophtha.2011.07.044","journal-title":"Ophthalmology"},{"key":"3675_CR3","first-page":"97","volume":"107","author":"KW Wright","year":"2009","unstructured":"Wright KW (2009) Mini-tenotomy procedure to correct diplopia associated with small-angle strabismus. Trans Am Ophthalmol Soc 107:97\u2013102","journal-title":"Trans Am Ophthalmol Soc"},{"issue":"9","key":"3675_CR4","doi-asserted-by":"publisher","first-page":"1930","DOI":"10.1016\/j.ophtha.2012.02.035","volume":"119","author":"SR Hatt","year":"2012","unstructured":"Hatt SR, Leske DA, Liebermann L, Holmes JM (2012) Comparing outcome criteria performance in adult strabismus surgery. Ophthalmology 119(9):1930\u20131936. https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1016\/j.ophtha.2012.02.035","journal-title":"Ophthalmology"},{"key":"3675_CR5","doi-asserted-by":"publisher","unstructured":"Khurana R, Singh N, Srivastava RM, Agrawal S (2019) Planning strabismus surgery. In: Agrawal, S. (ed.) Strabismus: for every ophthalmologist, Springer, pp 115\u2013130 https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1007\/978-981-13-1126-0_7","DOI":"10.1007\/978-981-13-1126-0_7"},{"issue":"11","key":"3675_CR6","first-page":"801","volume":"14","author":"DA Robinson","year":"1975","unstructured":"Robinson DA (1975) A quantitative analysis of extraocular muscle cooperation and squint. Investig Ophthalmol Vis Sci 14(11):801\u2013825","journal-title":"Investig Ophthalmol Vis Sci"},{"issue":"5","key":"3675_CR7","doi-asserted-by":"publisher","first-page":"436","DOI":"10.1016\/0010-4809(84)90012-0","volume":"17","author":"JM Miller","year":"1984","unstructured":"Miller JM, Robinson DA (1984) A model of the mechanics of binocular alignment. Comput Biomed Res 17(5):436\u2013470. https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1016\/0010-4809(84)90012-0","journal-title":"Comput Biomed Res"},{"issue":"1","key":"3675_CR8","doi-asserted-by":"publisher","first-page":"9","DOI":"10.1196\/annals.1325.002","volume":"1039","author":"T Haslwanter","year":"2005","unstructured":"Haslwanter T, Buchberger M, Kaltofen T, Hoerantner R, Priglinger S (2005) See++: a biomechanical model of the oculomotor plant. Ann N Y Acad Sci 1039(1):9\u201314","journal-title":"Ann N Y Acad Sci"},{"issue":"2\u20133","key":"3675_CR9","doi-asserted-by":"publisher","first-page":"273","DOI":"10.1016\/j.pbiomolbio.2010.09.002","volume":"103","author":"Q Wei","year":"2010","unstructured":"Wei Q, Sueda S, Pai DK (2010) Physically-based modeling and simulation of extraocular muscles. Prog Biophys Mol Biol 103(2\u20133):273\u2013283. https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1016\/j.pbiomolbio.2010.09.002","journal-title":"Prog Biophys Mol Biol"},{"key":"3675_CR10","doi-asserted-by":"publisher","first-page":"208","DOI":"10.1016\/j.jbiomech.2018.02.006","volume":"71","author":"J Iskander","year":"2018","unstructured":"Iskander J, Hossny M, Nahavandi S, Porto L (2018) An ocular biomechanic model for dynamic simulation of different eye movements. J Biomech 71:208\u2013216. https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1016\/j.jbiomech.2018.02.006","journal-title":"J Biomech"},{"key":"3675_CR11","doi-asserted-by":"publisher","DOI":"10.1016\/j.compbiomed.2021.104493","volume":"134","author":"FHF Leite","year":"2021","unstructured":"Leite FHF, Almeida JDS, Cruz LB, Teixeira JAM, Junior GB, Silva AC, Paiva AC (2021) Surgical planning of horizontal strabismus using multiple output regression tree. Comput Biol Med 134:104493. https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1016\/j.compbiomed.2021.104493","journal-title":"Comput Biol Med"},{"issue":"5","key":"3675_CR12","doi-asserted-by":"publisher","first-page":"374","DOI":"10.21037\/atm-20-5442","volume":"9","author":"K Mao","year":"2021","unstructured":"Mao K, Yang Y, Guo C, Zhu Y, Chen C, Chen J, Liu L, Chen L, Mo Z, Lin B, Zhang X, Li S, Lin X, Lin H (2021) An artificial intelligence platform for the diagnosis and surgical planning of strabismus using corneal light-reflection photos. Annals Transl Med 9(5):374\u2013374. https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.21037\/atm-20-5442","journal-title":"Annals Transl Med"},{"issue":"12","key":"3675_CR13","doi-asserted-by":"publisher","first-page":"1483","DOI":"10.1055\/a-1699-2679","volume":"239","author":"N Hirnschall","year":"2022","unstructured":"Hirnschall N, Malek K, Kaltofen T, Priglinger S, Priglinger S, Harrer A, Findl O, Partik G (2022) Einfluss von biometrischen daten auf die planung der augenmuskeloperation. Klin Monbl Augenheilkd 239(12):1483\u20131488. https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1055\/a-1699-2679","journal-title":"Klin Monbl Augenheilkd"},{"issue":"6","key":"3675_CR14","doi-asserted-by":"publisher","first-page":"1319","DOI":"10.1007\/s00417-020-04690-z","volume":"258","author":"F Beisse","year":"2020","unstructured":"Beisse F, Koch M, Uhlmann L, Beisse C (2020) Consideration of eyeball length and prismatic side-effects of spectacle lenses in strabismus surgery: a randomised, double-blind interventional study. Graefe\u2019s Archive Clin Exp Ophthalmol 258(6):1319\u20131326. https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1007\/s00417-020-04690-z","journal-title":"Graefe\u2019s Archive Clin Exp Ophthalmol"},{"issue":"3","key":"3675_CR15","doi-asserted-by":"publisher","first-page":"1133","DOI":"10.1167\/iovs.06-0769","volume":"48","author":"R Hoerantner","year":"2007","unstructured":"Hoerantner R, Kaltofen T, Priglinger S, Fock C-M, Buchberger M, Haslwanter T (2007) Model-based improvements in the treatment of patients with strabismus and axial high myopia. Investig Ophthalmol Vis Sci 48(3):1133. https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1167\/iovs.06-0769","journal-title":"Investig Ophthalmol Vis Sci"},{"key":"3675_CR16","doi-asserted-by":"publisher","first-page":"70","DOI":"10.1016\/j.exer.2012.06.009","volume":"102","author":"RC Augusteyn","year":"2012","unstructured":"Augusteyn RC, Nankivil D, Mohamed A, Maceo B, Pierre F, Parel J-M (2012) Human ocular biometry. Exp Eye Res 102:70\u201375. https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1016\/j.exer.2012.06.009","journal-title":"Exp Eye Res"},{"issue":"1115\/1","key":"3675_CR17","first-page":"4023390","volume":"10","author":"M Millard","year":"2013","unstructured":"Millard M, Uchida T, Seth A, Delp SL (2013) Flexing computational muscle: modeling and simulation of musculotendon dynamics. J Biomech Eng Doi 10(1115\/1):4023390","journal-title":"J Biomech Eng Doi"},{"issue":"10","key":"3675_CR18","doi-asserted-by":"publisher","first-page":"3380","DOI":"10.1167\/iovs.04-0292","volume":"45","author":"DA Atchison","year":"2004","unstructured":"Atchison DA, Jones CE, Schmid KL, Pritchard N, Pope JM, Strugnell WE, Riley RA (2004) Eye shape in emmetropia and myopia. Investig Ophthalmol Vis Sci 45(10):3380. https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1167\/iovs.04-0292","journal-title":"Investig Ophthalmol Vis Sci"},{"key":"3675_CR19","doi-asserted-by":"publisher","unstructured":"Faure F, Duriez C, Delingette H, Allard J, Gilles B, Marchesseau S, Talbot H, Courtecuisse H, Bousquet G, Peterlik I, Cotin S (2012) In: Payan, Y (ed.) SOFA: a multi-model framework for interactive physical simulation, Springer, pp 283\u2013321 https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1007\/8415_2012_125","DOI":"10.1007\/8415_2012_125"},{"key":"3675_CR20","doi-asserted-by":"publisher","DOI":"10.1007\/s10792-024-03324-1","author":"RR Kassem","year":"2024","unstructured":"Kassem RR, Radwan RE, El-Mofty RMA-M, Elhilali HM (2024) Unilateral versus bilateral lateral rectus recession for correction of small to moderate angle exotropia. Int Ophthalmol. https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1007\/s10792-024-03324-1","journal-title":"Int Ophthalmol"},{"issue":"5","key":"3675_CR21","doi-asserted-by":"publisher","first-page":"335","DOI":"10.1097\/icu.0b013e32833bd953","volume":"21","author":"L Wang","year":"2010","unstructured":"Wang L, Nelson LB (2010) One muscle strabismus surgery. Curr Opin Ophthalmol 21(5):335\u2013340. https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1097\/icu.0b013e32833bd953","journal-title":"Curr Opin Ophthalmol"},{"key":"3675_CR22","doi-asserted-by":"publisher","first-page":"3669","DOI":"10.2147\/OPTH.S324517","volume":"15","author":"A Lekskul","year":"2021","unstructured":"Lekskul A, Wuthisiri W, Jarupanich N (2021) A prospective study of one-muscle surgery in 15\u201325 prism diopters horizontal comitant strabismus in adults. Clin Ophthalmol 15:3669\u20133678. https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.2147\/OPTH.S324517","journal-title":"Clin Ophthalmol"},{"issue":"1","key":"3675_CR23","doi-asserted-by":"publisher","first-page":"56","DOI":"10.1016\/j.jaapos.2003.08.006","volume":"8","author":"A Gezer","year":"2004","unstructured":"Gezer A, Sezen F, Nasri N, G\u00f6z\u00fcm N (2004) Factors influencing the outcome of strabismus surgery in patients with exotropia. J American Association Pediatr Ophthalmol Strabismus 8(1):56\u201360. https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1016\/j.jaapos.2003.08.006","journal-title":"J American Association Pediatr Ophthalmol Strabismus"},{"key":"3675_CR24","first-page":"365","volume":"78","author":"L Apt","year":"1980","unstructured":"Apt L (1980) An anatomical reevaluation of rectus muscle insertions. Trans Am Ophthalmol Soc 78:365","journal-title":"Trans Am Ophthalmol Soc"},{"issue":"7","key":"3675_CR25","first-page":"2179","volume":"43","author":"R Kono","year":"2002","unstructured":"Kono R, Clark RA, Demer JL (2002) Active pulleys: magnetic resonance imaging of rectus muscle paths in tertiary gazes. Investig Ophthalmol Vis Sci 43(7):2179\u20132188","journal-title":"Investig Ophthalmol Vis Sci"},{"issue":"5","key":"3675_CR26","doi-asserted-by":"publisher","first-page":"1098","DOI":"10.1007\/s10439-014-1181-7","volume":"43","author":"CA Myers","year":"2014","unstructured":"Myers CA, Laz PJ, Shelburne KB, Davidson BS (2014) A probabilistic approach to quantify the impact of uncertainty propagation in musculoskeletal simulations. Ann Biomed Eng 43(5):1098\u20131111. https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1007\/s10439-014-1181-7","journal-title":"Ann Biomed Eng"},{"issue":"3","key":"3675_CR27","doi-asserted-by":"publisher","first-page":"399","DOI":"10.1007\/s00417-008-0961-x","volume":"247","author":"S Schutte","year":"2008","unstructured":"Schutte S, Polling JR, Helm FCT, Simonsz HJ (2008) Human error in strabismus surgery: quantification with a sensitivity analysis. Graefe\u2019s Arch Clin Exp Ophthalmol 247(3):399\u2013409. https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1007\/s00417-008-0961-x","journal-title":"Graefe\u2019s Arch Clin Exp Ophthalmol"},{"issue":"1","key":"3675_CR28","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1080\/2576117X.2025.2499545","volume":"75","author":"IH Ludwig","year":"2025","unstructured":"Ludwig IH (2025) Novel approaches to surgical correction of strabismus based on current understanding of orbital pulley anatomy. J Binocul Vis Ocular Motil 75(1):19\u201335","journal-title":"J Binocul Vis Ocular Motil"}],"container-title":["International Journal of Computer Assisted Radiology and Surgery"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/link.springer.com\/content\/pdf\/10.1007\/s11548-026-03675-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/link.springer.com\/article\/10.1007\/s11548-026-03675-3","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/link.springer.com\/content\/pdf\/10.1007\/s11548-026-03675-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,7,10]],"date-time":"2026-07-10T14:55:46Z","timestamp":1783695346000},"score":1,"resource":{"primary":{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/link.springer.com\/10.1007\/s11548-026-03675-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,4,30]]},"references-count":28,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2026,5]]}},"alternative-id":["3675"],"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1007\/s11548-026-03675-3","relation":{},"ISSN":["1861-6429"],"issn-type":[{"value":"1861-6429","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,4,30]]},"assertion":[{"value":"20 February 2026","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 April 2026","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"30 April 2026","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors have no conflict of interest to declare that is relevant to the content of this article.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"This article does not contain any studies with human participants or animals performed by any of the authors.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical approval"}},{"value":"Not applicable. This article does not contain any studies with human participants performed by any of the authors.","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"Informed consent"}}]}}