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J. F. Koretz, G. H. Handelman; Accommodation in the Human Eye: The Influence of Lens Compressibility and Elasticity on the Focusing Mechanism. Invest. Ophthalmol. Vis. Sci. 2009;50(13):4292.
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Our new, analytic human accommodation model uses well-defined changes in lens shape with accommodation for a given age to characterize the magnitude and direction of the forces leading to those deformations. While this inverse biomechanical model has been derived using a few simple, generally accepted assumptions, its use in studying the mechanisms of accommodation and presbyopia will depend critically on lens material properties. Testing them for a given lens age can provide insight into their ability to affect the accommodative process.
The biomechanical approach taken in deriving the model is based on a rotationally symmetric anisotropic lens structure. The change in shape of a 20 yr old human lens from 0 to 2 D was used for all calculations. There are five elastic constants: E and E’, the Young’s moduli in the plane of symmetry and perpendicular to it respectively; v and v’, the Poisson ratios in the plane of symmetry and perpendicular to it; and G’, a function of E’ and v’ representing shear modulus perpendicular to the isotropy plane. Setting v and v’ equal to previously determined optimal values for a 10 year old eye (0.46 and 0.42 respectively), E and E’ were systematically varied between 0.0001 and 0.0020); integrating tractions in each direction over the anterior lens surface for each pair of values defines a surface. Then setting E and E’ equal to values determined by Fisher for 20 yr old human lenses (0.0009 and 0.0007 respectively), v and v’ were systematically varied between values of 0.30 and 0.50 (incompressible).
Using the Fisher values for E and E’, the resultant surfaces generated by varying v and v’ are generally smooth, increasing with increasing v and v’ to a sharply defined ridge that falls abruptly as the values approach those of an incompressible material. Altering the E and E’ values shifts the location of the discontinuity ridge, but does not eliminate it. Similarly, holding v and v’ constant and varying E and E’ leads to integrated traction surfaces that exhibit discontinuity ridges; the location of these ridges is dependent on the initial values of v and v’. Similar results are obtained for the posterior lens surface.
The magnitude and direction of the forces acting upon the lens surfaces depend critically on the selection of initial values for v and v’, and to a lesser extent on E and E’. In theory, both Helmholtzian and non-Helmholtzian representations of accommodation can be developed using this analytic model, with the former localized around the ridge regions of the Poisson ratio surfaces and the latter at Poisson ratio values close to incompressible.
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