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Mariana Garcia, Andrew Rau, Judd Day, Jorge Ochoa, Scott Lovald; Finite Element Analysis of Whole Globe Goldmann Applanation Tonometry: A Closer Look at Model Sensitivity and Mechanics. Invest. Ophthalmol. Vis. Sci. 2016;57(12):6458.
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© ARVO (1962-2015); The Authors (2016-present)
The literature is full of experimentally-determined correction factors, but there is still no theoretical explanation forthe variation in results for Goldmann applanation tonometry (GAT). This study evaluated corneal strain during GAT under varying levels of internal pressure.
An axisymmetric finite element (FE) model of the human globe was created in Abaqus 6.14 according to idealized geometric dimensions (Fig. 1). Cornea and sclera were modeled as isotropic nonlinear hyperelastic materials. GAT was simulated by displacing a 3.06 mm diameter flat plane into the corneal apex until applanation. The model was validated to published experimental force-displacement results. Internal pressures of 1-40 mmHg were applied as direct pressure boundary conditions on the internal surface of the aqueous and vitreous cavities. Results of interest included the tonometric force and corneal strain at applanation. To evaluate model sensitivity, three separate cornea and sclera <span style="line-height:20.8px">models </span>were built (minimum, medium, and maximum stiffness) within the range of experimentally-observed material behavior.
Force-displacement results for the base model fit well to previously published experimental data. Analyses showed a decrease in tonometer force for decreasing cavity pressure, though even the 1 mmHg internal pressure analysis displayed substantial stiffness due to the nonlinear bending stiffness of the material. Principal strain in the cornea ranged from approximately -4% to +4% for each analysis (Fig. 2), with the anterior corneal surface experiencing compressive hoop strain and tensile radial strain. As internal pressure increased, hoop strain peripheral to the tonometer increased and radial tension at the tonometer contact location decreased.
This study developed and validated a whole globe FE model for GAT. The high bending resistance in the models indicates that many previous studies of GAT FE may be considering corneal material properties with insufficient stiffness. The markedly different strain fields observed at varying pressures may provide further explanation for the inability of previous studies to accurately predict appropriate correction factors for GAT.
This is an abstract that was submitted for the 2016 ARVO Annual Meeting, held in Seattle, Wash., May 1-5, 2016.
FE model set-up to simulate GAT indentation.
Maximum principal strain (absolute value of tension and compression) for an applanated cornea at each internal pressure.
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