Ocular elasticity. Is engineering stiffness a more useful characterization parameter than ocular rigidity?

Abstract

Purpose: The purpose of this study is to present an analysis of the pressure-volume relation of the eye in basic engineering terms, so as to characterize the deformability of the ocular shell based on its intrinsic stiffness (Young modulus) and morphology, as opposed to the empirical measure of ocular rigidity.

Methods: Starting from the structural mechanics equations describing the stress of spherical thin-walled vessels, the differential equation governing the eye pressure-volume relation is derived. This analysis, which is more rigorous than previously published derivations, assumes that the ocular shell has a Poisson ratio of 0.5. This assumption is experimentally confirmed by ultrasonic measurements of changes in bovine corneal thickness with intraocular pressure.

Results: Even with a number of simplifying assumptions, this basic analysis yields a complex result, showing that the Young modulus of the ocular shell material increases rapidly with distension of the eye, and is approximately proportional to the fourth power of the ocular shell radius.

Conclusion: Due to the complexity of the phenomenon, engineering analysis does not lead to a simple picture of pressure-volume relation of the eye. However, it does explicitly separate the material properties of the ocular shell from morphologic contributions to pressure-volume relation of the eye. This approach allows pathologic changes in the pressure-volume relation of the eye to be related more easily to the fundamental structural mechanisms governing the nonlinear mechanical properties of ocular shell materials.