A mathematical model for the elastic and fluid mechanical behavior of the human eye

Abstract

A simplified mathematical model for the eye is proposed. This idealized model simulates the aquaous flow and intraocular pressure behavior of the human eye. Starting from elementary concepts in elasticity and fluid mechanics, one can derive differential equations governing the behavior of the mathematical model. When integrated, these equations yield algebraic relationships which are closely related to some of the widely used empirical formulae in ophthalmology, e.g., Friedenwald's (1948) formula for the scleral rigidity coefficient and Grant's (1950) equation for the facility of aqueous outflow. The eye's intraocular pressure variations are simply related to its aqueous and blood volume changes if one assumes that ocular tissue has essentially linear elastic properties. St. Helen's and McEwen's (1961) experiments indicate that a linear approximation is reasonably accurate if the standard Hookian stress strain law is modified to take into account the anelastic or time-dependent elastic behavior of the corneo-scleral membrane. The last part of the paper discusses transient phenomena in an externally disturbed eye, e.g., when a tonometer is applied. One important result is a theoretical equation to describe the mean curve that one records in a tonographic tracing. This paper represents the first attempt to formulate a mathematical model relating the over-all elastic and fluid mechanical behavior of the eye. It is hoped that the model will stimulate interst and prove useful to the medical profession in motivating future experiments and in suggesting improvements for existing empirical formulae.