Nonlinear Finite Element Model Analysis Of Human Accommodation Lens

The crystalline human lens is modeled by using the finite element software, ABAQUS/CAE Version 6.5-1 as an axisymmetric shell to study the optical power and displacement of anterior and posterior poles induced due to zonule traction. Several different element types were tested to obtain the optimum mesh. These elements were three and six-noded triangular hybrid and four-noded quadrilateral hybrid for modeling of the cortex and nucleus. Constant strain triangular and regular quadrilateral elements were examined for modeling the capsule. One dimensional two degree of freedom spring elements were used to model the anterior, posterior, and equatorial zonules. Five different lens profiles were selected to mathematically model the lens geometry, which included Lizak; Krueger A; Krueger B; Strenk A; and Strenk B. A displacement-based incremental loading history was applied to the equatorial zonule to conduct geometric nonlinear analysis. The converged solution was obtained by coupling Hilbert L-2 norm and equating external work done to internal system strain energy. The converged and optimum solution was compared with analytical solution reported in literature and was selected to conduct a comprehensive parametric study.

To study the effect of relative movement, due to zonule traction, between the capsule and the cortex, and cortex and nucleus, contact elements were introduced in the interface between each two regions. A parametric study was conducted to study the effects of force and geometry related variables on the lens's optical power based on the aforementioned lens profiles, including the variation of their central and capsular thicknesses within their physiologically possible range. The position of the zonules was also varied for each profile. The force related variables were stiffness of: capsule; cortex; nucleus and zonules.

The complete analysis of the parametric study including the comparison between this study and those reported in the literature is presented. The findings are also compared with physiology of the lens.