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J. F. Koretz, G. H. Handelman; A New Analytic Representation of Human Accommodation and Presbyopia. Invest. Ophthalmol. Vis. Sci. 2008;49(13):4025.
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To update the geometric (Koretz-Handelman) model of accommodation in the human eye by incorporating experimental data on changes in lens shape and thickness into the inverse biomechanical model. An older initial analytic model (Koretz and Handelman, 1982, 1983), which included a number of approximations to simplify this representation, was nevertheless extremely valuable in providing guidelines for development and testing of ideas about accommodation and presbyopia. This analytic model is being re-derived to (a) eliminate many of the original simplifications, which limited the model’s applicability; (b) represent the human focusing process more accurately; (c) enable extension of the model to include data from older, peri-presbyopic eyes; and (d) provide a platform for in silico testing of hypotheses about the development of presbyopia and strategies for treating age-related accommodative loss.
Because the changes in lens shape, thickness, and origentation relative to the cornea can be described very accurately, our strategy continues to be to work from a complete description of lens deformation during a small accommodative change to pattern of forces acting upon the lens that cause this deformation. I.e., the elements of the strain tensor element are derived, and are then used to enable the stress tensor elements to be completely defined, thereby allowing the tractions to be described. We have dropped most of our original simplifying assumptions, but continue to assume that lens material properties are anisotropic in the radial and polar directions, in agreement with lens fiber cell organization, and that for a small accommodative change, the meridional distance (arc length) for a generic point on or in the lens is unchanged.
Analytic expressions for the elements of the strain tensor have been derived and, using the relationship between stress and strain tensors for an anisotropic, rotationally symmetric object, the elements of the stress tensor, and thus the tractions, are also defined. It was not possible to use a polynomial representation of lens curvature, because the resultant derived equations are not subject to a closed form solution and thus must be solved numerically. However, it can be shown that, for the very broad range of possible lens curvatures, a caternary is an excellent substitute that enables the completion of the derivation.
The completion of this analytic representation provides a new approach for exploring issues related to the accommodative process and the development of presbyopia, and can provide experimentally testable hypotheses.
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