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M. A. Reilly, N. Ravi; A Simple Geometric Mechanics Model of Accommodation. Invest. Ophthalmol. Vis. Sci. 2009;50(13):6137.
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© ARVO (1962-2015); The Authors (2016-present)
To develop an exoteric model that qualitatively predicts the behavior of the lens during accommodation.
The relaxed state of the lens was defined as a spherical cap, torispherical dome, or oblate spheroid with symmetry about both the optical axis and equatorial plane. Each of these geometries has one parameter corresponding to the thickness and another to the equatorial radius. The equatorial radius parameter was increased to simulate accommodation. The remaining geometric parameters were then computed under the assumption of constant lens volume. In the case of the torispherical dome, the knuckle radius was held constant at 0.5 mm, though varying this value did not substantially change the results.
All of the test geometries behaved in accordance with the Helmholtz theory of accommodation (Fig. 1). The responses of the test geometries to increasing equatorial diameter were very similar, indicating that any incompressible lens-shaped object should deform in a qualitatively similar fashion.
The similarity of the responses between test geometries suggests that this modeling method is robust for qualitatively predicting changes in an incompressible lens during accommodation. These findings strongly support the Helmholtz theory of accommodation. However, since they treat the lens as an incompressible fluid, they do not account for the role of lens elasticity in accommodation. This model may be used to explore the role of lens geometry in the pathogenesis of presbyopia.
Fig. 1: Normalized change in thickness t, radius of curvature R, surface area S, and optical power P with fractional change in equatorial radius D.
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