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R. C. Anderson; Finite Element Modeling of Corneal Applanation: Effects of Mesh Density and Contact Algorithms. Invest. Ophthalmol. Vis. Sci. 2008;49(13):696.
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© ARVO (1962-2015); The Authors (2016-present)
To determine how the finite element modeling considerations of mesh refinement and hard or soft contact algorithms affect calculated corneal contact pressure during applanation.
Models of the cornea were created in ABAQUS 6.4 assuming spherical geometry and hyperelastic material behavior. Increasingly refined meshes of hexahedral elements were examined. Loading consisted of a 15 mmHg pressure applied to the internal corneal surface, and a 1.5 gmf force applied to a glass applanator. Contact was frictionless, subject to the surface normal behaviors of "hard" and "soft" contact, which assumed zero overclosure with infinite contact stiffness, and 10 µm overclosure with an exponentially increasing stiffness, respectively. Soft contact represented tear film thickness and epithelial cell layer compression.
As shown below, mesh density and contact algorithm had a marked effect on calculated contact pressure, with values differing as much as 7 mmHg. Contact pressure tended to increase with mesh refinement because contact area generally decreased. The soft contact algorithm significantly reduced calculated contact pressure, particularly for high mesh refinement.
A conventional convergence test indicated that all meshes were acceptable (< 0.5% error) when subject to inflation. While contact pressure did demonstrate convergence, trends were not monotonic and comparably weak. It can, however, be concluded that a coarse mesh will result in a significant underestimate of contact pressure. It is surmised that this result reflects the inclusion of unnecessarily large perimeter elements in the contact area calculation. Assuming soft contact interfacial behavior improved solutions, likely due to "blurring" of the overclosed perimeter nodes accepted in the contact solution. Such a soft contact interface is justifiable in principle as a result of tear film and epithelium overlying a mechanically dominant stroma. This study demonstrated that finite element simulations of Goldmann-like tonometric measurement are especially mesh dependent. Thus, careful mesh design is critical for simulating corneal applanation.
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