Typical localised element-specific finite element anterior eye model

Joseph Towler; Alejandra Consejo; Dong Zhou; Vito Romano; Hannah Levis; Craig Boote; Ahmed Elsheikh; Brendan Geraghty; Ahmed Abass

doi:10.1016/j.heliyon.2023.e13944

Typical localised element-specific finite element anterior eye model

Heliyon. 2023 Mar 4;9(4):e13944. doi: 10.1016/j.heliyon.2023.e13944. eCollection 2023 Apr.

Authors

Joseph Towler¹, Alejandra Consejo², Dong Zhou³, Vito Romano^{1

4}, Hannah Levis¹, Craig Boote⁵, Ahmed Elsheikh^{6

7

3}, Brendan Geraghty¹, Ahmed Abass^{8

9}

Affiliations

¹ Institute of Life Course and Medical Sciences, University of Liverpool, Liverpool, UK.
² Applied Physics Department, University of Zaragoza, Zaragoza, Spain.
³ Department of Civil Engineering and Industrial Design, School of Engineering, University of Liverpool, Liverpool, UK.
⁴ Department of Medical and Surgical Specialities, Radiological Sciences, And Public Health, Ophthalmology Clinic, University of Brescia, Italy.
⁵ School of Optometry and Vision Sciences, Cardiff University, Cardiff, UK.
⁶ Beijing Advanced Innovation Centre for Biomedical Engineering, Beihang University, Beijing, China.
⁷ NIHR Biomedical Research Centre for Ophthalmology, Moorfields Eye Hospital NHS Foundation Trust and UCL Institute of Ophthalmology, London, UK.
⁸ Department of Mechanical, Materials and Aerospace Engineering, School of Engineering, University of Liverpool, Liverpool, UK.
⁹ Department of Production Engineering and Mechanical Design, Faculty of Engineering, Port Said University, Egypt.

Abstract

Purpose: The study presents an averaged anterior eye geometry model combined with a localised material model that is straightforward, appropriate and amenable for implementation in finite element (FE) modelling.

Methods: Both right and left eye profile data of 118 subjects (63 females and 55 males) aged 22-67 years (38.5 ± 7.6) were used to build an averaged geometry model. Parametric representation of the averaged geometry model was achieved through two polynomials dividing the eye into three smoothly connected volumes. This study utilised the collagen microstructure x-ray data of 6 ex-vivo healthy human eyes, 3 right eyes and 3 left eyes in pairs from 3 donors, 1 male and 2 females aged between 60 and 80 years, to build a localised element-specific material model for the eye.

Results: Fitting the cornea and the posterior sclera sections to a 5th-order Zernike polynomial resulted in 21 coefficients. The averaged anterior eye geometry model recorded a limbus tangent angle of 37° at a radius of 6.6 mm from the corneal apex. In terms of material models, the difference between the stresses generated in the inflation simulation up to 15 mmHg in the ring-segmented material model and localised element-specific material model were significantly different (p < 0.001) with the ring-segmented material model recording average Von-Mises stress 0.0168 ± 0.0046 MPa and the localised element-specific material model recording average Von-Mises stress 0.0144 ± 0.0025 MPa.

Conclusions: The study illustrates an averaged geometry model of the anterior human eye that is easy to generate through two parametric equations. This model is combined with a localised material model that can be used either parametrically through a Zernike fitted polynomial or non-parametrically as a function of the azimuth angle and the elevation angle of the eye globe. Both averaged geometry and localised material models were built in a way that makes them easy to implement in FE analysis without additional computation cost compared to the limbal discontinuity so-called idealised eye geometry model or ring-segmented material model.

Keywords: Average eye; Eye model; Ideal eye; Localised eye; Mathematical model.