{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T10:14:28Z","timestamp":1773828868853,"version":"3.50.1"},"reference-count":66,"publisher":"Public Library of Science (PLoS)","issue":"7","license":[{"start":{"date-parts":[[2025,7,1]],"date-time":"2025-07-01T00:00:00Z","timestamp":1751328000000},"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":"The ability to focus at near is achieved by dynamic changes in the shape of the lens of the eye. The Helmholtz hypothesis of accommodation proposes that, at distance gaze, all of the lenticular supporting zonules are at maximal tension. To bring a near object into focus, this tension is reduced by action of the ciliary muscle. The resultant release of tension allows the elastic lens capsule to mold the lens into a more rounded shape, increasing both its central thickness and central optical power (COP). Based upon Helmholtz\u2019s hypothesis, complete removal of these zonules should result in a rounded shaped lens of maximal COP. Schachar has offered an alternative mechanism of accommodation based upon the distinct actions of the three different groups of lenticular zonules. Schachar believes that for distant objects, all the zonules are under the minimum tension required to maintain lens stability; however, during lenticular accommodation, equatorial zonular tension increases while, simultaneously, the anterior and posterior zonular tension decreases. The selective increase in equatorial zonular tension results from the unique orientation of the different ciliary muscle fiber groups. With this increase in equatorial zonular tension, the peripheral lens surfaces flatten, central surfaces steepen and central lens thickness and COP increase. Schachar\u2019s hypothesis would anticipate that with zonular removal, the COP of the isolated lens would be minimal and diametrically opposite to the high lens COP expected with the Helmholtz hypothesis. In order to determine the COP of the isolated human lens, we obtained, through the kindness of the authors of an independent research study, the x-y coordinates of the central sagittal lens profiles of 10 freshly isolated human lenses (donors aged 20\u201330 years). These coordinate data were then mathematically utilized by fitting them into Chien, Forbes, Fourier, and elliptical equations. Additionally, the coordinate data was smoothed and fit to third-degree polynomials (S4W 3rd Poly). Independent of which of these equations was employed, within central optical zone diameters of \u2264<\/mml:mo><\/mml:mrow><\/mml:math><\/jats:alternatives><\/jats:inline-formula> 3\u2009mm, the COP was found to be minimal. Since the S4W 3rd Poly provided the best fit, it was used to represent lens surfaces in optically modeled eyes. In all modeled eyes, Zernike spherical aberration (SA) coefficients were positive. These findings are consistent with in vivo<\/jats:italic> measurements of SA obtained from human eyes while viewing distant visual objects. Having thus demonstrated that freshly removed human lenses, free of zonular tension, have their least COP, it is likely that this condition mimics the physiologic status of the human lens in the eye while attending to the most distant visual objects. In an independent, companion paper, we observed, using interferometric measurements of surface radius of curvatures of 12 fresh, isolated human lenses, obtained from donors aged 20\u201330 years, that the minimal COP was also associated with the unaccommodated state in vivo.<\/jats:italic><\/jats:p>","DOI":"10.1371\/journal.pone.0326954","type":"journal-article","created":{"date-parts":[[2025,7,1]],"date-time":"2025-07-01T17:52:58Z","timestamp":1751392378000},"page":"e0326954","update-policy":"https:\/\/doi.org\/10.1371\/journal.pone.corrections_policy","source":"Crossref","is-referenced-by-count":1,"title":["Central optical power of the isolated human lens without zonular tension"],"prefix":"10.1371","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2802-4031","authenticated-orcid":true,"given":"Ronald A.","family":"Schachar","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ira H.","family":"Schachar","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shubham","family":"Kumar","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Farhad","family":"Kamangar","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Boyd","family":"Hunter","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Barbara K.","family":"Pierscionek","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Pamela C.","family":"Cosman","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"340","published-online":{"date-parts":[[2025,7,1]]},"reference":[{"key":"pone.0326954.ref001","doi-asserted-by":"crossref","first-page":"108334","DOI":"10.1016\/j.exer.2020.108334","article-title":"Morphometric analysis of in vitro human crystalline lenses using digital shadow photogrammetry","volume":"202","author":"A Mohamed","year":"2021","journal-title":"Exp Eye Res"},{"issue":"11","key":"pone.0326954.ref002","doi-asserted-by":"crossref","first-page":"1041","DOI":"10.1016\/j.visres.2010.03.012","article-title":"Age-dependent Fourier model of the shape of the isolated ex vivo human crystalline lens","volume":"50","author":"R Urs","year":"2010","journal-title":"Vision Res"},{"issue":"6","key":"pone.0326954.ref003","doi-asserted-by":"crossref","first-page":"2541","DOI":"10.1167\/iovs.07-1385","article-title":"Optical power of the isolated human crystalline lens","volume":"49","author":"D Borja","year":"2008","journal-title":"Invest Ophthalmol Vis Sci"},{"key":"pone.0326954.ref004","first-page":"1","article-title":"Uber die Akkommodation des Auges","volume":"1","author":"H Helmholtz","year":"1855","journal-title":"Archiv f\u00fcr Ophthalmologie"},{"key":"pone.0326954.ref005","first-page":"429","article-title":"Die Ver\u00e4nderung der Linse bei Traktion der Zonula","volume":"34","author":"AE Stadfeldt","year":"1896","journal-title":"Klin Monatsbl Augenheilkd"},{"issue":"9","key":"pone.0326954.ref006","first-page":"1699","article-title":"Central surface curvatures of postmortem- extracted intact human crystalline lenses: implications for understanding the mechanism of accommodation","volume":"111","author":"RA Schachar","year":"2004","journal-title":"Ophthalmology"},{"key":"pone.0326954.ref007","first-page":"115","article-title":"Ophthalmic optics and refraction. vol. v.","volume-title":"System of Ophthalmology","author":"S Duke-Elder","year":"1970"},{"issue":"2","key":"pone.0326954.ref008","doi-asserted-by":"crossref","first-page":"567","DOI":"10.1016\/1350-9462(94)00019-C","article-title":"The development of lens sutures","volume":"14","author":"JR Kuszak","year":"1995","journal-title":"Prog Retin Eye Res"},{"issue":"1","key":"pone.0326954.ref009","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1111\/j.1444-0938.2003.tb03053.x","article-title":"The optical properties of the crystalline lens and their significance","volume":"86","author":"G Smith","year":"2003","journal-title":"Clin Exp Optom"},{"key":"pone.0326954.ref010","first-page":"58","article-title":"A. 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