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E. Hermans, M. Dubbelman, G.L. van der Heijde; Estimating the External Force Acting on the Human Eye Lens During Accommodation Using Finite Elements Modelling . Invest. Ophthalmol. Vis. Sci. 2005;46(13):727.
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Purpose:To estimate the radial force distributed by the zonular fibres, which is needed for the accommodation process of a 29 year old human eye lens. No a priori knowledge is necessary about the elasticity of the zonular fibres and the ciliary muscle power. More information on this external force on its own allows a better understanding of presbyopia and is important for IOL design aspects. Methods:For the estimation of the external force acting on the eye lens a finite element model is used. The shape information is based on recent Scheimpflug images that are corrected for optical distortions (Dubbelman, 2005). From these Scheimpflug images, the accommodative change in radius, asphericity and thickness of the lens was measured in a group of 65 people (age 16 – 51). The average geometry changes during accommodation were estimated for a 29 year old person and the curvature at a fully accommodated (+8 dpt) and fully unaccommodated (0 dpt.) state as well as the thickness were derived. The material properties are obtained from in vitro studies in literature (Burd, 2002). The zonular fibres are divided in three groups; anterior, central and posterior. At these three regions a set of loads will be applied. Starting point for the linear elastic, axisymmetric finite element model is the fully accommodated state. Using the Helmholtz theory, zero force acting on the eye lens in this situation is assumed. Choosing the input to the finite element model as a set of three loads applied on the zonula points, the geometry (surface curvature, thickness) of the deformed lens is generated. Using least squares method, an estimation for the forces that are needed to match the shape of the deformed lens with that of the unaccommodated lens is obtained. Results: The estimated anterior and posterior radial loads are approximately 0.014 N. The central load is about 0.017 N. Conclusions: Although the experimental approach was quite different, the results of our model study are in good agreement with the in vitro studies of Fisher (1977). Fisher measured during his spinning lens experiment a radial force of around 0.015 N to keep the eye lens in an unaccommodated state. The estimated loads can be used to develop an extended model with the zonular fibres and ciliary muscle incorporated. To determine the cause of presbyopia, one could use the same method for the estimation of lenticular forces as a function of age. Furthermore, knowledge about the magnitude of the forces, acting on the human lens, is important for the design of an accommodative IOL.
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