Finite-element simulation of corneal applanation

Abstract

investigated the effect of corneal biomechanical properties on Goldmann applanation tonometry. Using a theoretical model, they showed that Young's modulus of the cornea (a measure of corneal rigidity) can have large effects on the measurement result. As Figure 1 shows, the Liu-Roberts model predicts deviations up to about 15 mm Hg from an assumed true intraocular pressure (IOP) of 20 mm Hg if the corneal Young's modulus varies between 0.1 and 0.9 MPa.The Liu-Roberts-model is based on an equation from Young, 2 which had been used in another important model of tonometry by Orssengo and Pye 3 :Here, d is the maximum deflection of the cornea, a is an empirical factor, 2 P is the pressure applied in the zone where the tonometer head is in contact with the cornea, A is the surface area of the contact zone, R is the corneal radius of curvature, is Poisson's ratio, E is the corneal Young's modulus, and t (constant) is corneal thickness.Equation (1) is based on the assumption that a uniform pressure P is applied in the contact zone. To analyze the consequences of this assumption, we have generated a finite element (FE) model of the geometric configuration described by Young (following a similar procedure described by Vito and Carnell 4 ). Based on the FE model and using the same material parameters as Liu and Roberts, 1 we obtained the result labeled as ''simulation 1'' in Figure 1. As the figure shows, we obtained a perfect coincidence with the results obtained by Liu and Roberts 1 based on equation (1). This means that our FE model correctly models the situation behind equation (1).Using the FE model, we plotted the deformed corneal surface in simulation 1. It turned out that the deformed corneal surface is curved in the contact zone À1.53 mm % r % 1.53 mm, although it should be flat there if this were a correct model of Goldmann applanation tonometry. Using FE terminology, one can say that equation (1) is based on a wrong '

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