Presbyopia, accommodation, and mature catenary

Abstract

The anterior surface of the catenary model reported by Coleman and Fish only matches the magnetic resonance imaging and ultrasonographic crystalline lens images over a 2-mm aperture. Because optical power is very sensitive to small changes in radius of curvature,1Bom M. Wolf E. Principles of Optics; Electromagnetic Theory of Propagation, Interference and Diffraction of Light. 4th ed. Pergamon, New York1970: 161-163Google Scholar a rigorous model must accurately match the entire crystalline lens surface and not just an aperture of 2 mm. This is clinically relevant, because the average pupil size is ≥ 2.5 mm.2Loewenfeld I.E. The Pupil Anatomy, Physiology, and Clinical Applications, 2nd ed.. Butterworth-Heinemann, Boston1999: 104-105Google Scholar The anterior surface of the lens is much more complex than a catenary or a parabola and requires at least a 5th order polynomial to properly represent the curvature of the anterior surface of the crystalline lens.3Burd H.J. Judge S.J. Flavell M.J. Mechanics of accommodation of the human eye.Vis Res. 1999; 39: 1591-1595Crossref PubMed Scopus (44) Google Scholar, 4Schachar R.A. Bax A.J. Mechanism of human accommodation as analyzed by nonlinear finite element analysis.Compr Ther. 2001; 27: 122-132Crossref PubMed Scopus (31) Google Scholar The anterior surface of the catenary model reported by Coleman and Fish only matches the magnetic resonance imaging and ultrasonographic crystalline lens images over a 2-mm aperture. Because optical power is very sensitive to small changes in radius of curvature,1Bom M. Wolf E. Principles of Optics; Electromagnetic Theory of Propagation, Interference and Diffraction of Light. 4th ed. Pergamon, New York1970: 161-163Google Scholar a rigorous model must accurately match the entire crystalline lens surface and not just an aperture of 2 mm. This is clinically relevant, because the average pupil size is ≥ 2.5 mm.2Loewenfeld I.E. The Pupil Anatomy, Physiology, and Clinical Applications, 2nd ed.. Butterworth-Heinemann, Boston1999: 104-105Google Scholar The anterior surface of the lens is much more complex than a catenary or a parabola and requires at least a 5th order polynomial to properly represent the curvature of the anterior surface of the crystalline lens.3Burd H.J. Judge S.J. Flavell M.J. Mechanics of accommodation of the human eye.Vis Res. 1999; 39: 1591-1595Crossref PubMed Scopus (44) Google Scholar, 4Schachar R.A. Bax A.J. Mechanism of human accommodation as analyzed by nonlinear finite element analysis.Compr Ther. 2001; 27: 122-132Crossref PubMed Scopus (31) Google Scholar Presbyopia, accommodation, and mature catenary: author replyOphthalmologyVol. 109Issue 8Preview Full-Text PDF