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Abhijit Sinha Roy, Rohit Shetty; Estimated corneal elastic moduli from inverse finite element analysis of corneal deformation in vivo. Invest. Ophthalmol. Vis. Sci. 2014;55(13):3701.
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© ARVO (1962-2015); The Authors (2016-present)
To develop a patient-specific inverse finite element (iFE) optimization method to estimate the corneal elastic moduli from corneal deformation measured in vivo
A subject with a normal cornea was subjected to an air-puff applanation with the Corvis-ST (Oculus Inc., Germany). Corvis-ST only captures images of a cross-section of the cornea. The subject was imaged with Pentacam (Oculus Inc., Germany) A 3-D structure of the cornea and sclera shell was constructed from tomographic measurements (Pentacam, Oculus Inc. Germany). The eye model was supported at four quadrants by structures to approximate the muscles and fat. The transient air-puff pressure was applied on the anterior surface of the cornea. The intraocular pressure was 15 mmHg. For optimization, the coordinates of the deforming anterior edge of the cornea was extracted from the images at different time points. The optimized function was defined as the difference between the displacement of the anterior edge of the cornea estimated by iFE and obtained after image processing of Corvis-ST images. All tissue structures were assumed to be hyperelastic, isotropic and incompressible. The reduced polynomial material model was used for the cornea-sclera shell and support structures, respectively (Abaqus v.6.12, Simulia Inc., USA).
The estimated material properties (coefficients of reduced polynomial model) were C10=75kPa, and C20=20MPa. Figure 1 shows a comparison of the deformation amplitude of the apex of the cornea measured by Corvis-ST (dots) and estimated by the inverse method (line). The level of agreement is excellent during the pressure increase period. However after around 0.02 sec, there is difference between the estimated and measured displacement. Figure 2 shows a comparison of the displacement of the anterior edge of the cornea measured by Corvis-ST (dots) and estimated by the inverse method at different time (line). At time 0.01 and 0.015, the profiles match very well but at 0.02 sec, differences are evident.
A novel method of inverse estimation of corneal material properties from in vivo measurements of corneal deformation was developed. The difference in the result after 0.02 sec was most likely due to approximation of the globe structure in the FE model. Future work will focus on incorporation of fiber directions in the cornea and improved estimation of the globe biomechanical response.
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