Numerical Modelling of Accommodation and Presbyopia

Dr Harvey Burd

A program of research has been underway in the Civil Engineering Research Group at Oxford on developing computational methods to study the accommodation performance of the human eye. The standard textbook description of the accommodation mechanism is based on the work of von Helmholtz, published in 1855. More recently however, alternative mechanisms have been proposed. One such proposal, which is sometimes referred to as the ‘Schachar theory of accommodation’ has been the subject of recent academic publications describing the use of numerical methods to model the human accommodation process. In our early work on the mechanics of accommodation (Burd et al. 1999) we found that the apparent tendency of a previously-published numerical model to demonstrate the correctness of the Schachar mechanism was, in fact, the unforeseen consequence of a numerical artefact. (Results from our own numerical modelling studies are all entirely consistent with the Helmholtz description of the accommodation process.)

The next step was to begin the development of a finite element model of the accommodation process that incorporates the influence of the mechanical and geometric changes that occur within the eye as a consequence of ageing. This led to the publication (Burd et al. 2002) of an axisymmetric finite element model of the accommodation apparatus for eyes of ages 11, 29 and 45 years. A final year undergraduate project student, Jac Cross, worked through all of the available literature to compile data on the relevant geometric, mechanical and optical parameters that were needed for this model. Typical results – for a 29 year lens – are shown below.

finiteelement2

Computed accommodated and unaccommodated lens shapes for 29-year lens (adapted from Burd 2002)

It became clear during these early modelling studies that the available data in the literature on lens shape and stiffness are insufficient to form models of the accommodation process that are able to provide a reliable assessment of the various factors that cause presbyopia. A key issue was the paucity of published data on the stiffness of the lens. Our early modelling studies were based on the spinning lens data of Fisher (1971) but, on a detailed inspection of these data, it became clear that they were subject to certain systematic errors. (The data were, of course, never intended for use in detailed numerical models of the lens!). We therefore decided to collect some new lens stiffness data of our own. This project formed the basis of Geoffrey Wilde’s doctoral thesis. The lens stiffness data were published in Experimental Eye Research in 2012.

Our early modelling work was based on the commercial finite element program ABAQUS. More recently, however, we have written our own finite element program - Oxfem_hyperelastic – to conduct these modelling studies. Oxfem-hyperelastic is based on conventional non-linear continuum mechanics procedures but with special features for ophthalmic modelling. For example, the program has built-in functions for the variation of capsule thickness with position. It also allows non-homogeneous stiffness models for the lens to be included in a straightforward way. Oxfem_hyperelastic can be used to model the mechanical performance of the lens during the accommodation process. We also used it as part of the data analysis process required by our spinning lens stiffness tests.

A finite element accommodation model – which incorporated our recent lens stiffness data - was presented to the ECSRS Congress in September 2011. Preliminary results from this model suggest that age-related stiffening of the lens is the principal factor causing presbyopia. There are other relevant factors, however, such as the changes in lens geometry, capsule thickness and stiffness and lens refractive index that occur during life.

Although it is now possible to assemble finite element models of the accommodation process that give plausible results, there remains a need for improved data on the geometric, mechanical and optical properties of the lens for future finite element studies of the accommodation process. This is something that we are continuing to work on.

Downloads

The ABAQUS input file used to conduct one of the analyses in Burd, Judge and Cross (2002) may be downloaded by clicking here. This file corresponds to the 29 year Mesh B analysis illustrated in Fig 4(b) of the paper.

Publications

  • Judge, S.J. and Burd, H.J. (2002) Modelling the Mechanics of Accommodation and Presbyopia. Ophthal. Physiol. Opt. 22, 397-300
  • Burd, H.J., Judge, S.J. and Cross, J.A. (2002) Numerical Modelling of the Accommodating Lens. Vision Research 42, 2235-2251
  • Burd, H.J., Judge, S.J. and Cross, J.A. (1999) Numerical modelling of ocular accommodation. (ARVO Abstract) Investigative Ophthalmology and Visual Science, 40(4), Abstract No. 4678
  • Burd, H.J., Judge, S.J. and Flavell, M.J. (1999) Mechanics of Accommodation of the Human Eye. Vision Research 39, 1591-1595