{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,31]],"date-time":"2026-07-31T23:10:26Z","timestamp":1785539426713,"version":"3.56.0"},"reference-count":36,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2021,5,20]],"date-time":"2021-05-20T00:00:00Z","timestamp":1621468800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Acta Ophthalmologica"],"published-print":{"date-parts":[[2022,2]]},"abstract":"<jats:title>ABSTRACT<\/jats:title><jats:sec><jats:title>Background<\/jats:title><jats:p>Spherical and astigmatic powers for phakic intraocular lenses are frequently calculated using fixed ratios of phakic lens refractive power to refractive spherical equivalent, and of phakic lens astigmatism to refractive cylinder. In this study, a Monte\u2010Carlo simulation based on biometric data was used to investigate how variations in biometrics affect these ratios, in order to improve the calculation of implantable lens parameters.<\/jats:p><\/jats:sec><jats:sec><jats:title>Methods<\/jats:title><jats:p>A data set of over sixteen thousand biometric measurements including axial length, phakic anterior chamber depth, and corneal equivalent and astigmatic power was used to construct a multidimensional probability density distribution. From this, we determined the axial position of the implanted lens and estimated the refractive spherical equivalent and refractive cylinder. A generic data model resampled the density distributions and interactions between variables, and the implantable lens power was determined using vergence propagation.<\/jats:p><\/jats:sec><jats:sec><jats:title>Results<\/jats:title><jats:p>50\u2009000 artificial data sets were used to calculate the phakic lens spherical equivalent and astigmatism required for emmetropization, and to determine the corresponding ratios for these two values. The spherical ratio ranged from 1.0640 to 1.3723 and the astigmatic ratio from 1.0501 to 1.4340. Both ratios are unaffected by the corneal spherical \/ astigmatic powers, or the refractive cylinder, but show strong correlation with the refractive spherical equivalent, mild correlation with the lens axial position, and moderate negative correlation with axial length. As a simplification, these ratios could be modelled using a bi\u2010variable linear regression based on the first two of these factors.<\/jats:p><\/jats:sec><jats:sec><jats:title>Conclusion<\/jats:title><jats:p>Fixed spherical and astigmatic ratios should not be used when selecting high refractive power phakic IOLs as their variation can result in refractive errors of up to \u00b10.3\u2009D for a 8\u2009D lens. Both ratios can be estimated with clinically acceptable precision using a linear regression based on the refractive spherical equivalent and the axial position.<\/jats:p><\/jats:sec>","DOI":"10.1111\/aos.14902","type":"journal-article","created":{"date-parts":[[2021,5,21]],"date-time":"2021-05-21T06:10:15Z","timestamp":1621577415000},"page":"58-67","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Ratio of torus and equivalent power to refractive cylinder and spherical equivalent in phakic lenses \u2013 a Monte\u2010Carlo simulation study"],"prefix":"10.1111","volume":"100","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9175-6177","authenticated-orcid":false,"given":"Achim","family":"Langenbucher","sequence":"first","affiliation":[{"name":"Department of Experimental Ophthalmology Saarland University Homburg Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jens","family":"Schrecker","sequence":"additional","affiliation":[{"name":"Department of Ophthalmology Rudolf\u2010Virchow\u2010Clinics Glauchau Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0661-6239","authenticated-orcid":false,"given":"Timo","family":"Eppig","sequence":"additional","affiliation":[{"name":"Department of Experimental Ophthalmology Saarland University Homburg Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6406-7795","authenticated-orcid":false,"given":"Simon","family":"Schr\u00f6der","sequence":"additional","affiliation":[{"name":"Department of Experimental Ophthalmology Saarland University Homburg Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Alan","family":"Cayless","sequence":"additional","affiliation":[{"name":"School of Physical Sciences The Open University Milton Keynes UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Michael","family":"Schwemm","sequence":"additional","affiliation":[{"name":"Department of Experimental Ophthalmology Saarland University Homburg Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6566-4324","authenticated-orcid":false,"given":"Zolt\u00e1n","family":"Nagy","sequence":"additional","affiliation":[{"name":"Department of Ophthalmology Semmelweis\u2010University Budapest Hungary"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8019-1481","authenticated-orcid":false,"given":"N\u00f3ra","family":"Szentm\u00e1ry","sequence":"additional","affiliation":[{"name":"Department of Ophthalmology Semmelweis\u2010University Budapest Hungary"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2021,5,20]]},"reference":[{"key":"e_1_2_7_2_1","first-page":"182","article-title":"Pair\u2010copula constructions of multiple dependence","volume":"44","author":"Aas K","year":"2009","journal-title":"IME"},{"key":"e_1_2_7_3_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcrs.2014.08.036"},{"key":"e_1_2_7_4_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00417-012-1957-0"},{"key":"e_1_2_7_5_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcrs.2013.06.029"},{"key":"e_1_2_7_6_1","volume-title":"Optics of the human eye","author":"Atchison DA","year":"2000"},{"key":"e_1_2_7_7_1","doi-asserted-by":"publisher","DOI":"10.2307\/2347111"},{"key":"e_1_2_7_8_1","doi-asserted-by":"crossref","unstructured":"Bouy\u00e9EV DurrlemanBEV NikeghbaliA RibouletG&RoncalliT(2000):Copulas for finance: A reading guide and some applications. Working Paper. Groupe de Recherche Op\u00e9rationnelle Cr\u00e9dit Lyonnais Paris.","DOI":"10.2139\/ssrn.1032533"},{"key":"e_1_2_7_9_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcrs.2018.02.022"},{"key":"e_1_2_7_10_1","doi-asserted-by":"publisher","DOI":"10.1055\/s-0031-1281598"},{"key":"e_1_2_7_11_1","doi-asserted-by":"publisher","DOI":"10.1055\/s-2008-1050218"},{"key":"e_1_2_7_12_1","doi-asserted-by":"publisher","DOI":"10.1016\/0002-9394(89)90264-X"},{"key":"e_1_2_7_13_1","doi-asserted-by":"publisher","DOI":"10.1097\/OPX.0b013e318221727d"},{"key":"e_1_2_7_14_1","volume-title":"Statistics: Textbooks and monographs","author":"Gibbons JD","year":"2011"},{"key":"e_1_2_7_15_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00347-016-0386-6"},{"key":"e_1_2_7_16_1","first-page":"8","article-title":"Monte Carlo simulation of expected outcomes with the AcrySof toric intraocular lens","volume":"27","author":"Hill W","year":"2008","journal-title":"BMC Ophthalmol"},{"key":"e_1_2_7_17_1","volume-title":"Nonparametric statistical methods","author":"Hollander M","year":"2013"},{"key":"e_1_2_7_18_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.optom.2018.02.002"},{"key":"e_1_2_7_19_1","volume-title":"Griffin book series","author":"Kendall M","year":"1970"},{"key":"e_1_2_7_20_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00417-019-04570-1"},{"key":"e_1_2_7_21_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00347-005-1274-7"},{"key":"e_1_2_7_22_1","doi-asserted-by":"publisher","DOI":"10.1097\/00055735-200402000-00002"},{"key":"e_1_2_7_23_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1475-1313.2004.00231.x"},{"key":"e_1_2_7_24_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1600-0420.2004.00264.x"},{"key":"e_1_2_7_25_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1475-1313.2007.00487.x"},{"key":"e_1_2_7_26_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1600-0420.2006.00721.x"},{"key":"e_1_2_7_27_1","doi-asserted-by":"publisher","DOI":"10.1055\/s-2008-1027502"},{"key":"e_1_2_7_28_1","first-page":"1","article-title":"Phakic intraocular lenses for the treatment of refractive errors: an evidence\u2010based analysis","volume":"9","author":"Medical Advisory Secretariat","year":"2009","journal-title":"Ont Health Technol Assess Ser"},{"key":"e_1_2_7_29_1","doi-asserted-by":"publisher","DOI":"10.1111\/aos.1264413"},{"key":"e_1_2_7_30_1","doi-asserted-by":"publisher","DOI":"10.3928\/1081597X-20130415-06"},{"key":"e_1_2_7_31_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcrs.2012.10.047"},{"key":"e_1_2_7_32_1","doi-asserted-by":"publisher","DOI":"10.3928\/1081597X-20160630-02"},{"key":"e_1_2_7_33_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00417-017-3775-x"},{"key":"e_1_2_7_34_1","unstructured":"SchwemmM Schr\u00f6derS EppigT&LangenbucherA(2017): [IOLCon \u2010 International internet platform for optimization of formula constants]. Proceedings 30. International Congress of DOC Nuremberg doi:https:\/\/doi.org\/10.3205\/17doc112"},{"key":"e_1_2_7_35_1","doi-asserted-by":"publisher","DOI":"10.1111\/cxo.12689"},{"key":"e_1_2_7_36_1","volume-title":"Simulation","author":"Sheldon MR","year":"2012"},{"key":"e_1_2_7_37_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10654-015-0010-0"}],"container-title":["Acta Ophthalmologica"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1111\/aos.14902","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1111\/aos.14902","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1111\/aos.14902","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,8,27]],"date-time":"2023-08-27T04:38:15Z","timestamp":1693111095000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1111\/aos.14902"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,5,20]]},"references-count":36,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2022,2]]}},"alternative-id":["10.1111\/aos.14902"],"URL":"https:\/\/doi.org\/10.1111\/aos.14902","archive":["Portico"],"relation":{},"ISSN":["1755-375X","1755-3768"],"issn-type":[{"value":"1755-375X","type":"print"},{"value":"1755-3768","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,5,20]]},"assertion":[{"value":"2020-06-12","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2021-04-18","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2021-05-20","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}