Simulation of Dynamic Contour Tonometry on a Non–linear, Non–spherical Eye Model Using Finite Element Methods

Abstract

Abstract: : Purpose:To evaluate the influence of different corneal properties on the results obtained with Dynamic Contour Tonometry (DCT) we generated a numerical model of the eye that closer matches living human eyes. Methods: We enhanced the spherical eye model of Gullstrand using an ellipsoid approach. Both corneal surfaces were fitted using ellipse equations. To describe the mechanical behavior of the cornea we used the non–linear material model presented by Kanngiesser et al., ARVO 2004. We simulated Goldmann Applanation Tonometer (GAT) measurements to verify our eye model: We used a modified Newton iteration method, to determine the initial eye geometry needed to give the desired ellipsoid shape to the bulbus under IOP. Using a force driven tip with a planar surface we applanated the fully inflated cornea with increasing appositional forces. We applied the precise capillary force, as calculated by the formulas presented by Kanngiesser et al., ARVO 2003. We generated the model for the DCT tip using an incompressible pressure sensor element molded into a rubber–like material having the desired contoured shape. Using the eye model we simulated DCT measurements using different appositional forces. We changed the central corneal thickness (CCT), the corneal radius (CR) and the stiffness of the eye. We simulated measurements with DCT using a fixed force of 10mN and measurements with GAT using a constant applanation diameter of 3.06mm to determine the maximum possible error in a close to clinical use setup. Results:We used an ellipsoid model with an anterior surface asperity of Q=–0.18, a ratio between anterior and posterior radius of 0.81 and an asperity ratio of 1.1 as proposed by Dubbelman et al., Acta Ophthalmologica Scandinavica 2002. Simulations of GAT showed similar correlation with CCT and CR as reported in the literature on a cornea with mechanical properties described by Young’s modulus E=42.66*10⁶*ε²–2.66*10⁶*ε+0.24*10⁶[N/m²] and Poisson ratio =0.46. Simulations of measurement errors obtained with DCT agree well with measurements obtained by the in vitro study presented at by Kanngiesser et al., ARVO 2003. Changes in corneal properties influence DCT to a lesser degree than GAT. Conclusions: The new non–spherical finite element model confirms the results obtained by Kanngiesser et al., ARVO 2004. In contrast the results are stable over a larger range of corneal properties. The model is ready to predict the behaviour of DCT on abnormal corneas like on keratoconus, scars, extreme astigmatisms and other irregularities.

Keywords: intraocular pressure • shape and contour • refractive surgery