Finite element model of the influence of zonules-capsule attachment position on accommodation amplitude

Abstract

Purpose : As the eye lens grows, the non-uniform expansion of the capsule causes the attachment points of zonules anchored to the sliding capsule to appear to shift in a central/anterior direction along the lens surface. We explored the effect this antero-central shift of zonular attachment position may have on lens accommodation using a finite element (FE) model.

Methods : A simplified model for lens accommodation was constructed using Solidworks 2017 and ported to ANSYS Workbench 18.1 for analysis. The model comprised the lens, zonules and ciliary body configured as a 45° sector of an axisymmetric system. The gradient properties of the lens was modelled as four layers with Young’s modulus (E) increasing to the centre. Bodies were assumed to be isotropic (Table 1) and are based on values in the literature^1-3.
The zonules was modelled using five quadrilateral elements each of 0.02 mm thickness. For the base model, the anterior-most and posterior-most zonules were connected at 3.43 mm from the lens axis on the front and back surfaces with the remaining three distributed approximately equally around the surface (Figure 1).
An outward radial load to stretch the zonules and lens body simulated disaccommodation. This was continued until a target ciliary position is reached. Lens thickness, diameter, surface curvatures and conic constants and surface and total lens powers were calculated for the unstretched and stretched states with the difference reported as the change due to disaccommodation.
Two experiments were conducted. The first varied the point of attachment of the anterior zonules by -0.2 to 0.2 mm from the base model. In the second, partial zonules transection were simulated to compare against ex vivo results.^3,4

Results : In the base model, the change in lens power due to stretching was 12.61 D. As the zonules position shifts centrally/anteriorly, the change in lens power increased from 12.29 D to 12.83 D. Posterior zonules transection reduced the power change to 10.14 D while anterior transection reduced the power change to 6.74 D, the latter result comparing reasonably against empirical results⁴.

Conclusions : The shift in position of zonules connection to the capsule with aging appears to provide a very slight ‘compensatory’ effect against reduction in accommodation due to presbyopia.

1. Hermans et al 2008 J Vis Res
2. Burd et al 2002 Vis Res
3. Mohammad Pour et al 2015 CEO
4. Bernal et al 2009 IOVS

This abstract was presented at the 2019 ARVO Annual Meeting, held in Vancouver, Canada, April 28 - May 2, 2019.