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A thin-shell model of the cornea and its application to corneal surgery
H C Howland1, R H Rand, S R Lubkin
1Section of Neurobiology and Behavior, Cornell University, Ithaca, NY 14853.
Background:
We present a thin-shell, analytical model of the vertebrate cornea to study the changes in shape resulting from surgical operations (eg, radial keratotomy).
Methods:
A simple closed-form solution is derived for a thin linearly elastic spherical model of the cornea. We assume that the shell is symmetrical about a central axis and that the modulus of elasticity is the same in all directions. The surgery is modeled by allowing the modulus of elasticity (or equivalently the thickness) of the shell to depend upon position, measured as an angle from the axis of symmetry.
Results:
The analytical nature of the solution allows us to compute the principal curvatures of the cornea explicitly. For example, for representative parameters, the model predicts the average corneal curvature changes from about 43 diopters before keratotomy to about 38 D after keratotomy.
Conclusions:
The model is used to estimate Young's modulus from experimental data reported previously by Thomas et al (Invest Ophthalmol Vis Sci 1991;32:1000), as well as to investigate the effect of surgery on corneal flattening and the associated sensitivity to intraocular pressure changes.