Modelling the mechanics of accommodation and presbyopia.

Finite element methods have been used to compute the expected relationship between changes in ciliary body diameter and the change in refractive power implied by the change in geometry of the human ocular lens, using values for the material properties and initial geometry taken from the literature (notably the slit lamp photography of Brown (1973) and the studies by Fisher (1969) of the lens material properties). The results show that if the non-linearity associated with the changing geometry is taken into account the lens does not respond to ciliary body stretch by an increase in power [as recently claimed by Schachar et al. (1993), but in the conventional way with a decrease in power. The models show a decrease in the amplitude of accommodation between the age of 29 and 45 years (using Brown's data, 1973), but using Brown's data for the 11-year-old eye leads to the paradoxical conclusion that accommodation amplitude in this eye would have been small. In the process of carrying out the modelling, we have examined the consistency of the published measurements and also the validity of the mathematical methods used in interpreting them, and this analysis suggests that further work is needed before one can be confident that the assumptions about geometry and material properties on which the modelling is based are sound.