{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,6]],"date-time":"2026-05-06T19:07:52Z","timestamp":1778094472425,"version":"3.51.4"},"reference-count":39,"publisher":"Frontiers Media SA","license":[{"start":{"date-parts":[[2021,3,11]],"date-time":"2021-03-11T00:00:00Z","timestamp":1615420800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["frontiersin.org"],"crossmark-restriction":true},"short-container-title":["Front. Bioeng. Biotechnol."],"abstract":"<jats:sec><jats:title>Purpose<\/jats:title><jats:p>To introduce a new method to map the mechanical stiffness of healthy and keratoconic corneas.<\/jats:p><\/jats:sec><jats:sec><jats:title>Methods<\/jats:title><jats:p>Numerical modeling based on the finite element method was used to carry out inverse analysis of simulated healthy and keratoconic corneas to determine the regional variation of mechanical stiffness across the corneal surface based on established trends in collagen fibril distribution. The Stress\u2013Strain Index (SSI), developed and validated in an earlier study and presented as a parameter that can estimate the overall stress\u2013strain behavior of corneal tissue, was adopted in this research as a measure of corneal stiffness. The regional variation of SSI across the corneal surface was estimated using inverse analysis while referring to the common features of collagen fibrils\u2019 distribution obtained from earlier x-ray scattering studies. Additionally, for keratoconic corneas, a method relating keratoconic cone features and cornea\u2019s refractive power to the reduction in collagen fibril density inside the cone was implemented in the development of SSI maps. In addition to the simulated cases, the study also included two keratoconus cases, for which SSI maps were developed.<\/jats:p><\/jats:sec><jats:sec><jats:title>Results<\/jats:title><jats:p>SSI values varied slightly across corneal surface in the simulated healthy eyes. In contrast, both simulated and clinical keratoconic corneas demonstrated substantial reductions in SSI values inside the cone. These SSI reductions depended on the extent of the disease and increased with more considerable simulated losses in fibril density in the cone area. SSI values and their regional variation showed little change with changes in IOP, corneal thickness, and curvature.<\/jats:p><\/jats:sec><jats:sec><jats:title>Conclusion<\/jats:title><jats:p>SSI maps provide an estimation of the regional variation of biomechanical stiffness across the corneal surface. The maps could be particularly useful in keratoconic corneas, demonstrating the dependence of corneal biomechanical behavior on the tissue\u2019s microstructure and offering a tool to fundamentally understand the mechanics of keratoconus progression in individual patients.<\/jats:p><\/jats:sec>","DOI":"10.3389\/fbioe.2021.640434","type":"journal-article","created":{"date-parts":[[2021,3,11]],"date-time":"2021-03-11T06:09:26Z","timestamp":1615442966000},"update-policy":"https:\/\/doi.org\/10.3389\/crossmark-policy","source":"Crossref","is-referenced-by-count":30,"title":["Stress\u2013Strain Index Map: A New Way to Represent Corneal Material Stiffness"],"prefix":"10.3389","volume":"9","author":[{"given":"Haixia","family":"Zhang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ashkan","family":"Eliasy","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bernardo","family":"Lopes","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ahmed","family":"Abass","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Riccardo","family":"Vinciguerra","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Paolo","family":"Vinciguerra","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"suffix":"Jr.","given":"Renato","family":"Ambr\u00f3sio","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Cynthia J.","family":"Roberts","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ahmed","family":"Elsheikh","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1965","published-online":{"date-parts":[[2021,3,11]]},"reference":[{"key":"B1","doi-asserted-by":"publisher","first-page":"216","DOI":"10.1016\/j.actbio.2017.11.015","article-title":"The hierarchical response of human corneal collagen to load.","volume":"65","author":"Bell","year":"2018","journal-title":"Acta Biomater."},{"key":"B2","doi-asserted-by":"publisher","first-page":"771","DOI":"10.1007\/s003470050201","article-title":"Measuring intraocular pressure in keratoconus. Effect of the changed biomechanics.","volume":"94","author":"B\u00f6hm","year":"1997","journal-title":"Ophthalmol. Zeitschr. Deutsch. Ophthalmol. Gesellsch."},{"key":"B3","doi-asserted-by":"publisher","first-page":"2941","DOI":"10.1167\/iovs.03-0131","article-title":"Collagen fibrils appear more closely packed in the prepupillary cornea: optical and biomechanical implications.","volume":"44","author":"Boote","year":"2003","journal-title":"Investigat. Ophthalmol. Vis. Sci."},{"key":"B4","doi-asserted-by":"publisher","first-page":"901","DOI":"10.1167\/iovs.05-0893","article-title":"Mapping collagen organization in the human cornea: left and right eyes are structurally distinct.","volume":"47","author":"Boote","year":"2006","journal-title":"Investigat. Ophthalmol. Vis. Sci."},{"key":"B5","first-page":"644","article-title":"Collagen fibrils in the human corneal stroma: structure and aging.","volume":"39","author":"Daxer","year":"1998","journal-title":"Investigat. Ophthalmol. Vis. Sci."},{"key":"B6","doi-asserted-by":"publisher","first-page":"709","DOI":"10.1016\/j.exer.2006.03.015","article-title":"Biomechanics and wound healing in the cornea.","volume":"83","author":"Dupps","year":"2006","journal-title":"Exp. Eye Res."},{"key":"B7","doi-asserted-by":"publisher","DOI":"10.3389\/fbioe.2019.00105","article-title":"Determination of corneal biomechanical behavior in-vivo for healthy eyes using CorVis ST tonometry: stress-strain index.","volume":"7","author":"Eliasy","year":"2019","journal-title":"Front. Bioeng. Biotechnol."},{"key":"B8","doi-asserted-by":"publisher","DOI":"10.1098\/rsif.2020.0271","article-title":"Characterization of cone size and centre in keratoconic corneas.","volume":"17","author":"Eliasy","year":"2020","journal-title":"J. R. Soc. Interface"},{"key":"B9","doi-asserted-by":"publisher","first-page":"1707","DOI":"10.1016\/j.jcrs.2013.05.042","article-title":"Comprehensive anterior segment normal values generated by rotating Scheimpflug tomography.","volume":"39","author":"Gilani","year":"2013","journal-title":"J. Cataract. Refract. Surg."},{"key":"B10","doi-asserted-by":"publisher","first-page":"459","DOI":"10.1016\/j.ophtha.2013.09.013","article-title":"Discriminant value of custom ocular response analyzer waveform derivatives in keratoconus.","volume":"121","author":"Hallahan","year":"2014","journal-title":"Ophthalmology"},{"key":"B11","doi-asserted-by":"publisher","first-page":"423","DOI":"10.1016\/j.exer.2006.10.014","article-title":"A study of corneal thickness, shape and collagen organisation in keratoconus using videokeratography and X-ray scattering techniques.","volume":"84","author":"Hayes","year":"2007","journal-title":"Exp. Eye Res."},{"key":"B12","doi-asserted-by":"publisher","first-page":"5662","DOI":"10.1167\/iovs.14-14561","article-title":"Magic angle\u2013enhanced MRI of fibrous microstructures in sclera and cornea with and without intraocular pressure loading.","volume":"55","author":"Ho","year":"2014","journal-title":"Investigat. Ophthalmol. Vis. Sci."},{"key":"B13","doi-asserted-by":"publisher","first-page":"885","DOI":"10.1016\/j.ajo.2013.12.024","article-title":"Corneal biomechanics as a function of intraocular pressure and pachymetry by dynamic infrared signal and Scheimpflug imaging analysis in normal eyes.","volume":"157","author":"Huseynova","year":"2014","journal-title":"Am. J. Ophthalmol."},{"key":"B14","doi-asserted-by":"publisher","first-page":"240","DOI":"10.1111\/opo.12345","article-title":"Corneal biomechanics \u2013 a review.","volume":"37","author":"Kling","year":"2017","journal-title":"Ophthal. Physiol. Opt."},{"key":"B15","doi-asserted-by":"publisher","first-page":"1122","DOI":"10.1364\/BOE.382755","article-title":"Vectorial birefringence imaging by optical coherence microscopy for assessing fibrillar microstructures in the cornea and limbus.","volume":"11","author":"Li","year":"2020","journal-title":"Biomed. Optics Exp."},{"key":"B16","doi-asserted-by":"publisher","first-page":"156","DOI":"10.1016\/j.jcrs.2004.10.044","article-title":"Determining in vivo biomechanical properties of the cornea with an ocular response analyzer.","volume":"31","author":"Luce","year":"2005","journal-title":"J. Cataract. Refract Surg."},{"key":"B17","doi-asserted-by":"publisher","first-page":"851","DOI":"10.1016\/j.survophthal.2018.05.004","article-title":"Biomechanics and structure of the cornea: implications and association with corneal disorders.","volume":"63","author":"Ma","year":"2018","journal-title":"Surv. Ophthalmol."},{"key":"B18","doi-asserted-by":"publisher","first-page":"369","DOI":"10.1016\/j.preteyeres.2009.06.005","article-title":"The use of X-ray scattering techniques to quantify the orientation and distribution of collagen in the corneal stroma.","volume":"28","author":"Meek","year":"2009","journal-title":"Progr. Retin. Eye Res."},{"key":"B19","doi-asserted-by":"publisher","DOI":"10.4103\/0974-620X.159255","article-title":"Ocular response analyzer parameters in healthy, keratoconus suspect and manifest keratoconus eyes.","volume":"8","author":"Mohammadpour","year":"2015","journal-title":"Oman J. Ophthalmol."},{"key":"B20","doi-asserted-by":"publisher","first-page":"30","DOI":"10.1016\/j.preteyeres.2009.11.001","article-title":"Clinical in vivo confocal microscopy of the human cornea in health and disease.","volume":"29","author":"Niederer","year":"2010","journal-title":"Progr. Retin. Eye Res."},{"key":"B21","doi-asserted-by":"publisher","first-page":"1371","DOI":"10.1016\/j.jcrs.2007.04.021","article-title":"Corneal biomechanical properties in normal, post-laser in situ keratomileusis, and keratoconic eyes.","volume":"33","author":"Ortiz","year":"2007","journal-title":"J. Catar. Refract. Surg."},{"key":"B22","doi-asserted-by":"publisher","DOI":"10.1098\/rsta.2018.0079","article-title":"A microstructural model of cross-link interaction between collagen fibrils in the human cornea.","volume":"377","author":"Pandolfi","year":"2019","journal-title":"Philos. Transact. R. Soc. A"},{"key":"B23","doi-asserted-by":"publisher","first-page":"1481","DOI":"10.1107\/S0021889813022358","article-title":"A wide-angle X-ray fibre diffraction method for quantifying collagen orientation across large tissue areas: application to the human eyeball coat.","volume":"46","author":"Pijanka","year":"2013","journal-title":"J. Appl. Crystallogr."},{"key":"B24","doi-asserted-by":"crossref","first-page":"S589","DOI":"10.3928\/1081-597X-20020901-18","article-title":"Biomechanics of the cornea and wavefront-guided laser refractive surgery.","volume":"18","author":"Roberts","year":"2002","journal-title":"J. Refract. Surg."},{"key":"B25","doi-asserted-by":"publisher","DOI":"10.18502\/jovr.v15i3.7446","article-title":"In vivo corneal microstructural changes in herpetic stromal keratitis: a spectral domain optical coherence tomography analysis.","volume":"15","author":"Rodriguez-Garcia","year":"2020","journal-title":"J. Ophthal. Vis. Res."},{"key":"B26","doi-asserted-by":"publisher","first-page":"4490","DOI":"10.1167\/iovs.14-14450","article-title":"Biomechanical characterization of keratoconus corneas ex vivo with Brillouin microscopy.","volume":"55","author":"Scarcelli","year":"2014","journal-title":"Investigat. Ophthalmol. Vis. Sci."},{"key":"B27","doi-asserted-by":"publisher","first-page":"1418","DOI":"10.1167\/iovs.12-11387","article-title":"Brillouin microscopy of collagen crosslinking: noncontact depth-dependent analysis of corneal elastic modulus.","volume":"54","author":"Scarcelli","year":"2013","journal-title":"Investigat. Ophthalmol. Vis. Sci."},{"key":"B28","doi-asserted-by":"publisher","first-page":"185","DOI":"10.1167\/iovs.11-8281","article-title":"Brillouin optical microscopy for corneal biomechanics.","volume":"53","author":"Scarcelli","year":"2012","journal-title":"Invest. Ophthalmol. Vis. Sci."},{"key":"B29","doi-asserted-by":"publisher","first-page":"39","DOI":"10.1038\/nphoton.2007.250","article-title":"Confocal Brillouin microscopy for three-dimensional mechanical imaging.","volume":"2","author":"Scarcelli","year":"2008","journal-title":"Nat. Photon."},{"key":"B30","doi-asserted-by":"publisher","first-page":"257","DOI":"10.1016\/j.clae.2006.09.006","article-title":"The use of the Reichert ocular response analyser to establish the relationship between ocular hysteresis, corneal resistance factor and central corneal thickness in normal eyes.","volume":"29","author":"Shah","year":"2006","journal-title":"Contact Lens Anter. Eye"},{"key":"B31","doi-asserted-by":"publisher","first-page":"123","DOI":"10.1016\/j.clae.2009.02.005","article-title":"The use of the ocular response analyser to determine corneal hysteresis in eyes before and after excimer laser refractive surgery.","volume":"32","author":"Shah","year":"2009","journal-title":"Contact Lens Anter. Eye"},{"key":"B32","doi-asserted-by":"publisher","first-page":"836","DOI":"10.1016\/j.jbiomech.2009.11.021","article-title":"Biomechanical model of human cornea based on stromal microstructure.","volume":"43","author":"Studer","year":"2010","journal-title":"J. Biomechan."},{"key":"B33","doi-asserted-by":"publisher","first-page":"803","DOI":"10.3928\/1081597X-20160629-01","article-title":"Detection of keratoconus with a new biomechanical index.","volume":"32","author":"Vinciguerra","year":"","journal-title":"J. Refract. Surg."},{"key":"B34","doi-asserted-by":"publisher","first-page":"550","DOI":"10.3928\/1081597X-20160524-01","article-title":"Influence of pachymetry and intraocular pressure on dynamic corneal response parameters in healthy patients.","volume":"32","author":"Vinciguerra","year":"","journal-title":"J. Refract. Surg."},{"key":"B35","doi-asserted-by":"publisher","DOI":"10.1097\/ICU.0000000000000489","article-title":"Brillouin microscopy: assessing ocular tissue biomechanics.","volume":"29","author":"Yun","year":"2018","journal-title":"Curr. Opin. Ophthalmol."},{"key":"B36","doi-asserted-by":"publisher","DOI":"10.1098\/rsif.2020.0900","article-title":"Fibril density reduction in keratoconic corneas.","volume":"18","author":"Zhou","year":"","journal-title":"J. R. Soc. Interf."},{"key":"B37","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pone.0214770","article-title":"Analysis of X-ray scattering microstructure data for implementation in numerical simulations of ocular biomechanical behaviour.","volume":"14","author":"Zhou","year":"2019","journal-title":"PLoS One"},{"key":"B38","doi-asserted-by":"publisher","DOI":"10.1098\/rsif.2020.0900","article-title":"Fibril density reduction in keratoconic corneas.","volume":"18","author":"Zhou","year":"","journal-title":"R. Soc. Interf."},{"key":"B39","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1038\/s41467-019-12803-4","article-title":"Reverberant 3D optical coherence elastography maps the elasticity of individual corneal layers.","volume":"10","author":"Zvietcovich","year":"2019","journal-title":"Nat. Commun."}],"container-title":["Frontiers in Bioengineering and Biotechnology"],"original-title":[],"link":[{"URL":"https:\/\/www.frontiersin.org\/articles\/10.3389\/fbioe.2021.640434\/full","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,4,28]],"date-time":"2021-04-28T21:39:01Z","timestamp":1619645941000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.frontiersin.org\/articles\/10.3389\/fbioe.2021.640434\/full"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,3,11]]},"references-count":39,"alternative-id":["10.3389\/fbioe.2021.640434"],"URL":"https:\/\/doi.org\/10.3389\/fbioe.2021.640434","relation":{},"ISSN":["2296-4185"],"issn-type":[{"value":"2296-4185","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,3,11]]},"article-number":"640434"}}