{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,5]],"date-time":"2026-06-05T00:41:00Z","timestamp":1780620060588,"version":"3.54.1"},"reference-count":33,"publisher":"Frontiers Media SA","license":[{"start":{"date-parts":[[2023,4,10]],"date-time":"2023-04-10T00:00:00Z","timestamp":1681084800000},"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":"Purpose:<\/jats:bold> To investigate the relationship between the corneal material stiffness parameter stress-strain index (SSI) and axial length (AL) elongation with varying severities of myopia, based on a mathematical estimation model.<\/jats:p>Methods:<\/jats:bold> This single-center, cross-sectional study included data from healthy subjects and patients preparing for refractive surgery in the Qingdao Eye Hospital of Shandong First Medical University. Data were collected from July 2021 to April 2022. First, we performed and tested an estimated AL model (A<\/mml:mi>L<\/mml:mi>M<\/mml:mi>o<\/mml:mi>r<\/mml:mi>g<\/mml:mi>a<\/mml:mi>n<\/mml:mi><\/mml:mrow><\/mml:msub><\/mml:mrow><\/mml:math><\/jats:inline-formula>) based on the mathematical equation proposed by Morgan. Second, we proposed an axial increment model (\u0394<\/mml:mo>A<\/mml:mi>L<\/mml:mi><\/mml:mrow><\/mml:math><\/jats:inline-formula>) corresponding to spherical equivalent error (SER) based on A<\/mml:mi>L<\/mml:mi><\/mml:mrow>e<\/mml:mi>m<\/mml:mi>m<\/mml:mi>e<\/mml:mi>t<\/mml:mi>r<\/mml:mi>o<\/mml:mi>p<\/mml:mi>i<\/mml:mi>a<\/mml:mi><\/mml:mrow><\/mml:msub><\/mml:mrow><\/mml:math><\/jats:inline-formula> (A<\/mml:mi>L<\/mml:mi>M<\/mml:mi>o<\/mml:mi>r<\/mml:mi>g<\/mml:mi>a<\/mml:mi>n<\/mml:mi><\/mml:mrow><\/mml:msub><\/mml:mrow><\/mml:math><\/jats:inline-formula> at SER = 0) and subject\u2019s real AL. Finally, we evaluated the variations of \u0394<\/mml:mo>A<\/mml:mi>L<\/mml:mi><\/mml:mrow><\/mml:math><\/jats:inline-formula> with SSI changes based on the mathematical estimation model.<\/jats:p>Results:<\/jats:bold> We found that AL was closely associated with A<\/mml:mi>L<\/mml:mi>M<\/mml:mi>o<\/mml:mi>r<\/mml:mi>g<\/mml:mi>a<\/mml:mi>n<\/mml:mi><\/mml:mrow><\/mml:msub><\/mml:mrow><\/mml:math><\/jats:inline-formula> (r<\/jats:italic> = 0.91, t<\/jats:italic> = 33.8, p<\/jats:italic> &lt; 0.001) with good consistency and SER was negatively associated with \u0394<\/mml:mo>A<\/mml:mi>L<\/mml:mi><\/mml:mrow><\/mml:math><\/jats:inline-formula> (r<\/jats:italic> = \u22120.89, t<\/jats:italic> = \u221230.7, p<\/jats:italic> &lt; 0.001). The association of SSI with AL, A<\/mml:mi>L<\/mml:mi><\/mml:mrow>e<\/mml:mi>m<\/mml:mi>m<\/mml:mi>e<\/mml:mi>t<\/mml:mi>r<\/mml:mi>o<\/mml:mi>p<\/mml:mi>i<\/mml:mi>a<\/mml:mi><\/mml:mrow><\/mml:msub><\/mml:mrow><\/mml:math><\/jats:inline-formula>, and \u0394<\/mml:mo>A<\/mml:mi>L<\/mml:mi><\/mml:mrow><\/mml:math><\/jats:inline-formula> can be summarized using the following equations: A<\/mml:mi>L<\/mml:mi>=<\/mml:mo>27.7<\/mml:mn>\u2212<\/mml:mo>2.04<\/mml:mn>\u00d7<\/mml:mo>S<\/mml:mi>S<\/mml:mi>I<\/mml:mi><\/mml:mrow><\/mml:math><\/jats:inline-formula>, A<\/mml:mi>L<\/mml:mi><\/mml:mrow>e<\/mml:mi>m<\/mml:mi>m<\/mml:mi>e<\/mml:mi>t<\/mml:mi>r<\/mml:mi>o<\/mml:mi>p<\/mml:mi>i<\/mml:mi>a<\/mml:mi><\/mml:mrow><\/mml:msub>=<\/mml:mo>23.2<\/mml:mn>+<\/mml:mo>0.561<\/mml:mn>\u00d7<\/mml:mo>S<\/mml:mi>S<\/mml:mi>I<\/mml:mi><\/mml:mrow><\/mml:math><\/jats:inline-formula>, and \u0394<\/mml:mo>A<\/mml:mi>L<\/mml:mi>=<\/mml:mo>4.52<\/mml:mn>\u2212<\/mml:mo>2.6<\/mml:mn>\u00d7<\/mml:mo>S<\/mml:mi>S<\/mml:mi>I<\/mml:mi><\/mml:mrow><\/mml:math><\/jats:inline-formula>. In adjusted models, SSI was negatively associated with AL (Model 1: \u03b2<\/jats:italic> = \u22122.01, p<\/jats:italic> &lt; 0.001) and \u0394<\/mml:mo>A<\/mml:mi>L<\/mml:mi><\/mml:mrow><\/mml:math><\/jats:inline-formula> (Model 3: \u03b2<\/jats:italic> = \u22122.49, p<\/jats:italic> &lt; 0.001) but positively associated with A<\/mml:mi>L<\/mml:mi>e<\/mml:mi>m<\/mml:mi>m<\/mml:mi>e<\/mml:mi>t<\/mml:mi>r<\/mml:mi>o<\/mml:mi>p<\/mml:mi>i<\/mml:mi>a<\/mml:mi><\/mml:mrow><\/mml:msub><\/mml:mrow><\/mml:math><\/jats:inline-formula> (Model 2: \u03b2<\/jats:italic> = 0.48, p<\/jats:italic> &lt; 0.05). In addition, SSI was negatively associated with \u0394<\/mml:mo>A<\/mml:mi>L<\/mml:mi><\/mml:mrow><\/mml:math><\/jats:inline-formula> among subjects with AL \u2265 26\u00a0mm (\u03b2<\/jats:italic> = \u22121.36, p<\/jats:italic> = 0.02).<\/jats:p>Conclusion:<\/jats:bold> AL increased with decreasing SSI in myopia.<\/jats:p>","DOI":"10.3389\/fbioe.2023.1145032","type":"journal-article","created":{"date-parts":[[2023,4,10]],"date-time":"2023-04-10T04:30:06Z","timestamp":1681101006000},"update-policy":"https:\/\/doi.org\/10.3389\/crossmark-policy","source":"Crossref","is-referenced-by-count":7,"title":["Effect of corneal stiffness decrease on axial length elongation in myopia determined based on a mathematical estimation model"],"prefix":"10.3389","volume":"11","author":[{"given":"Qi","family":"Ren","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhe","family":"Chu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wei","family":"Cui","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lu","family":"Cheng","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wenjie","family":"Su","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hao","family":"Cheng","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jie","family":"Wu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1965","published-online":{"date-parts":[[2023,4,10]]},"reference":[{"key":"B1","doi-asserted-by":"publisher","first-page":"614","DOI":"10.1167\/iovs.09-3653","article-title":"Age-related changes in accommodative dynamics from preschool to adulthood","volume":"51","author":"Anderson","year":"2010","journal-title":"Invest. 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