{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,18]],"date-time":"2026-08-18T03:01:43Z","timestamp":1787022103764,"version":"build-2736575974"},"reference-count":32,"publisher":"Public Library of Science (PLoS)","issue":"5","license":[{"start":{"date-parts":[[2022,5,16]],"date-time":"2022-05-16T00:00:00Z","timestamp":1652659200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["www.plosone.org"],"crossmark-restriction":false},"short-container-title":["PLoS ONE"],"abstract":"\n Background<\/jats:title>\n The Chang-Waring chord is provided by many ophthalmic instruments, but proper interpretation of this chord for use in centring refractive procedures at the cornea is not fully understood. The purpose of this study is to develop a strategy for translating the Chang-Waring chord (position of pupil centre relative to the Purkinje reflex PI) into angle Alpha using raytracing techniques.<\/jats:p>\n <\/jats:sec>\n \n Methods<\/jats:title>\n \n The retrospective analysis was based on a large dataset of 8959 measurements of 8959 eyes from 1 clinical centre, using the Casia2 anterior segment tomographer. An optical model based on: corneal front and back surface radius Ra and Rp, asphericities Qa and Qp, corneal thickness CCT, anterior chamber depth ACD, and pupil centre position (X-Y position: Pup\n X<\/jats:sub>\n and Pup\n Y<\/jats:sub>\n ), was defined for each measurement. Using raytracing rays with an incident angle I\n X<\/jats:sub>\n and I\n Y<\/jats:sub>\n the CW chord (CW\n X<\/jats:sub>\n and CW\n Y<\/jats:sub>\n ) was calculated. Using these data, a multivariable linear model was built up in terms of a Monte-Carlo simulation for a simple translation of incident ray angle to CW chord.\n <\/jats:p>\n <\/jats:sec>\n \n Results<\/jats:title>\n \n Raytracing allows for calculation of the CW chord CW\n X<\/jats:sub>\n \/CW\n Y<\/jats:sub>\n from biometric measures and the incident ray angle I\n X<\/jats:sub>\n \/I\n Y<\/jats:sub>\n . In our dataset mean values of CW\n X<\/jats:sub>\n = 0.32\u00b10.30 mm and CW\n Y<\/jats:sub>\n = -0.10\u00b10.26 mm were derived for a mean incident ray angle (angle Alpha) of I\n X<\/jats:sub>\n = -5.02\u00b11.77\u00b0 and I\n Y<\/jats:sub>\n = 0.01\u00b11.47\u00b0. The raytracing results could be modelled with a linear multivariable model, and the effect sizes for the prediction model for CW\n X<\/jats:sub>\n are identified as Ra, Qa, Rp, CCT, ACD, Pup\n X<\/jats:sub>\n , Pup\n Y<\/jats:sub>\n , I\n X<\/jats:sub>\n , and for CW\n Y<\/jats:sub>\n they are Ra, Rp, Pup\n Y<\/jats:sub>\n , and I\n Y<\/jats:sub>\n .\n <\/jats:p>\n <\/jats:sec>\n \n Conclusion<\/jats:title>\n \n Today the CW chord can be directly measured with any biometer, topographer or tomographer. If biometric measures of Ra, Qa, Rp, CCT, ACD, Pup\n X<\/jats:sub>\n , Pup\n Y<\/jats:sub>\n are available in addition to the CW chord components CW\n X<\/jats:sub>\n and CW\n Y<\/jats:sub>\n , a prediction of angle Alpha is possible using a simple matrix operation.\n <\/jats:p>\n <\/jats:sec>","DOI":"10.1371\/journal.pone.0267028","type":"journal-article","created":{"date-parts":[[2022,5,16]],"date-time":"2022-05-16T13:25:14Z","timestamp":1652707514000},"page":"e0267028","update-policy":"https:\/\/doi.org\/10.1371\/journal.pone.corrections_policy","source":"Crossref","is-referenced-by-count":8,"title":["Translation model for CW chord to angle Alpha derived from a Monte-Carlo simulation based on raytracing"],"prefix":"10.1371","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9175-6177","authenticated-orcid":true,"given":"Achim","family":"Langenbucher","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"N\u00f3ra","family":"Szentm\u00e1ry","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Alan","family":"Cayless","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7741-1447","authenticated-orcid":true,"given":"Johannes","family":"Weisensee","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4145-2559","authenticated-orcid":true,"given":"Jascha","family":"Wendelstein","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Peter","family":"Hoffmann","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"340","published-online":{"date-parts":[[2022,5,16]]},"reference":[{"issue":"9","key":"pone.0267028.ref001","doi-asserted-by":"crossref","first-page":"1187","DOI":"10.1038\/eye.2011.150","article-title":"Predictive factor and kappa angle analysis for visual satisfactions in patients with multifocal IOL implantation","volume":"25","author":"G Prakash","year":"2011","journal-title":"Eye (Lond)"},{"issue":"2","key":"pone.0267028.ref002","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1016\/j.jcrs.2013.12.011","article-title":"Multifocal intraocular lenses: relative indications and contraindications for implantation","volume":"40","author":"ASCRS Cataract Clinical Committee","year":"2014","journal-title":"J Cataract Refract Surg"},{"key":"pone.0267028.ref003","doi-asserted-by":"crossref","first-page":"4","DOI":"10.1186\/s40662-015-0014-6","article-title":"Centration axis in refractive surgery","volume":"2","author":"S Arba Mosquera","year":"2015","journal-title":"Eye Vis (Lond)"},{"issue":"3","key":"pone.0267028.ref004","doi-asserted-by":"crossref","first-page":"164","DOI":"10.3928\/1081597X-20180103-02","article-title":"The sensitivity of clinical outcomes to centration on the light-constricted pupil for a shape-changing corneal inlay","volume":"34","author":"E Barrag\u00e1n-Garza","year":"2018","journal-title":"J Refract Surg"},{"issue":"5","key":"pone.0267028.ref005","doi-asserted-by":"crossref","first-page":"467","DOI":"10.3928\/1081-597X-20060501-08","article-title":"Centration analysis of ablation over the coaxial corneal light reflex for hyperopic LASIK","volume":"22","author":"CC Chan","year":"2006","journal-title":"J Refract Surg"},{"issue":"4","key":"pone.0267028.ref006","doi-asserted-by":"crossref","first-page":"317","DOI":"10.3349\/ymj.1998.39.4.317","article-title":"Comparison of corneal centering in photorefractive keratectomy","volume":"39","author":"EK Kim","year":"1998","journal-title":"Yonsei Med J"},{"issue":"4","key":"pone.0267028.ref007","doi-asserted-by":"crossref","first-page":"B103","DOI":"10.1364\/JOSAA.36.00B103","article-title":"Optical quality comparison between laser ablated myopic eyes with centration on coaxially sighted corneal light reflex and on entrance pupil center","volume":"36","author":"Y Liu","year":"2019","journal-title":"J Opt Soc Am A Opt Image Sci Vis"},{"issue":"3","key":"pone.0267028.ref008","doi-asserted-by":"crossref","first-page":"372","DOI":"10.1097\/j.jcrs.0000000000000066","article-title":"Angle alpha orientation and magnitude distribution in a cataract surgery population","volume":"46","author":"MA Mahr","year":"2020","journal-title":"J Cataract Refract Surg"},{"issue":"3","key":"pone.0267028.ref009","doi-asserted-by":"crossref","first-page":"151","DOI":"10.4103\/0974-620X.122268","article-title":"Angle Kappa and its importance in refractive surgery","volume":"6","author":"M Moshirfar","year":"2013","journal-title":"Oman J Ophthalmol"},{"issue":"10 Suppl","key":"pone.0267028.ref010","first-page":"944","article-title":"Comparison of myopic LASIK centered on the coaxially sighted corneal light reflex or line of sight","volume":"25","author":"S Okamoto","year":"2009","journal-title":"J Refract Surg"},{"issue":"4","key":"pone.0267028.ref011","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1097\/ICU.0b013e3283543c41","article-title":"Measurement of angle kappa and centration in refractive surgery","volume":"23","author":"CY Park","year":"2012","journal-title":"Curr Opin Ophthalmol"},{"issue":"8","key":"pone.0267028.ref012","doi-asserted-by":"crossref","first-page":"518","DOI":"10.3928\/1081597X-20130719-08","article-title":"Coaxially sighted corneal light reflex versus entrance pupil center centration of moderate to high hyperopic corneal ablations in eyes with small and large angle kappa","volume":"29","author":"DZ Reinstein","year":"2013","journal-title":"J Refract Surg"},{"key":"pone.0267028.ref013","first-page":"9873504","article-title":"Correlation analysis of refractive and visual quality after wavefront-optimized laser In situ keratomileusis for 50% and 100% angle kappa compensation","volume":"2020","author":"XY Ru","year":"2020","journal-title":"J Ophthalmol"},{"issue":"12","key":"pone.0267028.ref014","doi-asserted-by":"crossref","first-page":"3555","DOI":"10.1007\/s10792-020-01506-1","article-title":"Clinical outcomes of corneal refractive surgery comparing centration on the corneal vertex with the pupil center: a meta-analysis","volume":"40","author":"J Zhang","year":"2020","journal-title":"Int Ophthalmol"},{"issue":"4","key":"pone.0267028.ref015","first-page":"624","article-title":"Comparison of visual effects of FS-LASIK for myopia centered on the coaxially sighted corneal light reflex or the line of sight","volume":"10","author":"J Zhang","year":"2017","journal-title":"Int J Ophthalmol"},{"issue":"12","key":"pone.0267028.ref016","first-page":"2597","article-title":"Limbus versus pupil center for ocular alignment measurement with corneal reflexes","volume":"38","author":"JC Barry","year":"1997","journal-title":"Invest Ophthalmol Vis Sci"},{"issue":"3","key":"pone.0267028.ref017","doi-asserted-by":"crossref","first-page":"412","DOI":"10.1016\/j.jcrs.2015.09.030","article-title":"Comparison of refractive and visual outcomes with centration points 80% and 100% from pupil center toward the coaxially sighted corneal light reflex","volume":"42","author":"JS Chang","year":"2016","journal-title":"J Cataract Refract Surg"},{"key":"pone.0267028.ref018","doi-asserted-by":"crossref","first-page":"495","DOI":"10.2147\/OPTH.S282469","article-title":"Predictors of photic phenomena with a trifocal IOL","volume":"15","author":"A Espaillat","year":"2021","journal-title":"Clin Ophthalmol"},{"issue":"5","key":"pone.0267028.ref019","doi-asserted-by":"crossref","first-page":"456","DOI":"10.3928\/1081-597X-20070501-06","article-title":"Measurement of angle kappa with synoptophore and Orbscan II in a normal population","volume":"23","author":"H Basmak","year":"2007","journal-title":"J Refract Surg"},{"issue":"8","key":"pone.0267028.ref020","doi-asserted-by":"crossref","first-page":"1684","DOI":"10.1364\/JOSAA.14.001684","article-title":"Anatomically accurate, finite model eye for optical modeling","volume":"14","author":"HL Liou","year":"1997","journal-title":"J Opt Soc Am A Opt Image Sci Vis"},{"issue":"5","key":"pone.0267028.ref021","doi-asserted-by":"crossref","first-page":"863","DOI":"10.1016\/j.ajo.2014.06.028","article-title":"The subject-fixated coaxially sighted corneal light reflex: a clinical marker for centration of refractive treatments and devices","volume":"158","author":"DH Chang","year":"2014","journal-title":"Am J Ophthalmol"},{"issue":"8","key":"pone.0267028.ref022","doi-asserted-by":"crossref","first-page":"1198","DOI":"10.1016\/j.jcrs.2019.03.029","article-title":"Apparent chord mu and actual chord mu and their clinical value","volume":"45","author":"JT Holladay","year":"2019","journal-title":"J Cataract Refract Surg"},{"issue":"7","key":"pone.0267028.ref023","doi-asserted-by":"crossref","first-page":"998","DOI":"10.1111\/ceo.13800","article-title":"Understanding chord mu through a large population-based study","volume":"48","author":"JY Jiang","year":"2020","journal-title":"Clin Exp Ophthalmol"},{"key":"pone.0267028.ref024","doi-asserted-by":"crossref","first-page":"302","DOI":"10.1145\/800057.808695","article-title":"A new polynomial-time algorithm for linear programming","author":"N. Karmarkar","year":"1984","journal-title":"Proceedings of the sixteenth annual ACM symposium on Theory of computing\u2014STOC"},{"key":"pone.0267028.ref025","unstructured":"St. Pierre J. Quaternion Toolbox. (https:\/\/www.mathworks.com\/matlabcentral\/fileexchange\/1176-quaternion-toolbox), MATLAB Central File Exchange. Retrieved October 3, 2021."},{"key":"pone.0267028.ref026","volume-title":"Probability and Statistics","author":"NR Draper","year":"1998","edition":"3"},{"issue":"3","key":"pone.0267028.ref027","doi-asserted-by":"crossref","first-page":"513","DOI":"10.1016\/j.jcrs.2010.10.041","article-title":"Evaluation of 2 new optical biometry devices and comparison with the current gold standard biometer","volume":"37","author":"YA Chen","year":"2011","journal-title":"J Cataract Refract Surg"},{"issue":"1","key":"pone.0267028.ref028","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1097\/j.jcrs.0000000000000373","article-title":"Comparison of two swept-source optical coherence tomography-based biometry devices","volume":"47","author":"AD Fi\u0219u\u0219","year":"2020","journal-title":"J Cataract Refract Surg"},{"issue":"10","key":"pone.0267028.ref029","doi-asserted-by":"crossref","first-page":"1302","DOI":"10.1097\/j.jcrs.0000000000000633","article-title":"Repeatability of two swept-source optical coherence tomography biometers and one optical low coherence reflectometry biometer","volume":"47","author":"AD Fi\u0219u\u0219","year":"2021","journal-title":"J Cataract Refract Surg"},{"issue":"5","key":"pone.0267028.ref030","doi-asserted-by":"crossref","first-page":"530","DOI":"10.3928\/1081597X-20080501-12","article-title":"Pupil center shift relative to the coaxially sighted corneal light reflex under natural and pharmacologically dilated conditions","volume":"24","author":"U Erdem","year":"2008","journal-title":"J Refract Surg"},{"issue":"6","key":"pone.0267028.ref031","doi-asserted-by":"crossref","first-page":"634","DOI":"10.1111\/opo.12086","article-title":"Variations of pupil centration and their effects on video eye tracking","volume":"33","author":"U Wildenmann","year":"2013","journal-title":"Ophthalmic Physiol Opt"},{"issue":"7","key":"pone.0267028.ref032","first-page":"2508","article-title":"Pupil location under mesopic, photopic, and pharmacologically dilated conditions","volume":"43","author":"Y Yang","year":"2002","journal-title":"Invest Ophthalmol Vis Sci"}],"container-title":["PLOS ONE"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pone.0267028","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,5,16]],"date-time":"2022-05-16T13:25:40Z","timestamp":1652707540000},"score":1,"resource":{"primary":{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pone.0267028"}},"subtitle":[],"editor":[{"given":"Paul J","family":"Atzberger","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"editor"}]}],"short-title":[],"issued":{"date-parts":[[2022,5,16]]},"references-count":32,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2022,5,16]]}},"URL":"https:\/\/doi.org\/10.1371\/journal.pone.0267028","relation":{},"ISSN":["1932-6203"],"issn-type":[{"value":"1932-6203","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,5,16]]}}}