Thesis: Geoffrey S. Wilde

Doctor of Philosophy, Brasenose College, University of Oxford, Hilary Term 2011

Measurement of Human Lens Stiffness for Modelling Presbyopia Treatments

Computational models of human accommodation hold the promise of an improved understanding of the mechanism and of the development of presbyopia. A detailed and reliable model could greatly assist the design of treatments to restore accommodation to presbyopic eyes. However, a large quantity of data is required for such an endeavour. Currently, the details of the age-related increase in the stiffness of the lens is a major source of uncertainty as the published data differ markedly depending on the form of testing employed.

A new version of the spinning lens test is presented, based on the method originated by Fisher, R. F. (1971) ‘The elastic constants of the human lens’, Journal of Physiology, 212(1):147–180. This test assesses the stiffness of the lens substance by photographically measuring the deformations induced by rotation of the lens about its axis of symmetry. The principal changes introduced in the present version are the removal of the capsule from the lens prior to testing, the synchronization of the photography with the orientation of the lens, and the use of a hyperelastic finite-element model of the test coupled with a numerical optimization procedure to quantify the heterogeneous stiffness of the lens. These alterations, together with further improvements, provide a substantially more accurate means of measuring the stiffness of the lens ‘substance’.

Measurements made with the new test on a series of human lenses are reported. Goodquality tests were obtained for 29 lenses aged from 12 to 58 years. The older lenses were found to be much stiffer than younger lenses. In younger lenses the cortex of the lens is found to be stiffer than the nucleus, but the nucleus stiffens more rapidly, surpassing the cortex byabout 44 years. These results differ substantially from those of the original spinning test.

The stiffness values calculated for the lens substance are used in a series of hyperelastic finite-element models of the accommodation mechanism. Models corresponding to subjects aged 29 and 45 years follow clinical measurements of the decline in accommodation amplitude between these ages. Adjusting the material parameters values indicates that it is the increase in stiffness which is largely responsible for the modelled fall in accommodation amplitude. The 45-year model is adapted to represent the effect of laser lentotomy, a proposed presbyopia treatment. Among the lentotomy options trialled, the best result is a modest 0.4D increase in the modelled accommodation amplitude.