Finite element accommodation models using elasticity gradients from Brillouin microscopy

Abstract

Purpose : To develop elasticity models of the crystalline lens using Brillouin microscopy data and evaluate their performance in lens accommodation models.

Methods : Results from compression tests and Brillouin data on human crystalline lenses aged 14, 37, and 67, and Brillouin microscopy data on longitudinal modulus variation (Besner et al IOVS 2016) were used in a finite element model of lens compression to obtain parameters for elasticity profiles of crystalline lenses in the form E(r,θ) = E_n – E_s(r/r_s)^k, where E_n and E_s are elasticity (in Young's Modulus) at nucleus and surface, r_s is distance from center to surface at θ, and k is rate of change from nucleus to surface. Then, finite element models of crystalline lenses subjected to accommodation forces (for lenses aged 29 and 45 years) were developed to incorporate these gradient elasticity profiles. The models were evaluated for two separate boundary conditions: 1) with a fixed displacement corresponding to expected ciliary body expansion, 2) with a fixed force of 0.08 N. Deformation of nodes was used to calculate the deformed radii of curvature of anterior and posterior surfaces (as spherical fit) as well as the deformed thickness. Accommodation amplitude was calculated by computing lens power for deformed and undeformed conditions. Results were compared to lenses using elasticity profiles from earlier studies (Burd et al Vision Res 2002).

Results : Elasticity profiles obtained had average E value of 0.0048 MPa and E_n>E_s. For a fixed displacement, simulations using elasticity profiles derived from Brillouin microscopy data showed 42% and 32% less power change than elasticity profiles derived from other methods for two lenses. For a fixed force of 0.08 N, the difference between Brillouin and other gradient profiles increased, to 56% for 29-year-old model and 46% for 45-year-old model. Difference in diopter between 29 and 45 year models was smaller in Brillouin profiles than in other gradient profiles. Values of parameter k were found to affect the power change by 0.2-0.5 D for a fixed geometry.

Conclusions : Elasticity profiles found in Brillouin microscopy (where E_n>E_s) show less accommodation amplitude than those with E_s>E_n. Variations of rate of change in gradient (with fixed E_n, E_s) have a minor effect on accommodation amplitude. Conversion process from Brillouin frequency shift to Elastic Modulus might account for reduced accommodation amplitude.

This is an abstract that was submitted for the 2017 ARVO Annual Meeting, held in Baltimore, MD, May 7-11, 2017.