Estimating the material properties of collagen fibril using optical behavior of the human cornea

Abstract

Purpose : To improve the accuracy of estimating collagen fibril properties by using optical behavior of the cornea with an inverse analysis method.

Methods : A three-dimensional anisotropic corneal model with regionally varying fibril distribution (Pandolfi, 2008) was generated in finite element software (ABAQUS 6.14). The model used two known average material parameters, depth-dependent matrix stiffness C₁₀ (Sloan, 2014) and fibril dispersion parameter κ (Pandolfi, 2008), and two unknown parameters for the model, fibril stiffness k₁ and fibril nonlinearity k₂ were estimated with an inverse algorithm developed based on design of experiment method. This iterative method estimates k₁ and k₂ by minimizing the average difference between the predicted and the theoretical corneal responses simulated under multiple intraocular pressure (IOP) levels ranging from 5-30mmHg. To test the accuracy, three different combinations of k₁ and k₂ were assumed: k₁ = 30kPa, k₂ = 800 (case 1); k₁ = 80kPa, k₂ = 800 (case 2); k₁ = 80kPa, k₂ = 1200 (case 3). We compared estimated k₁ and k₂ based on apical displacement and spherical aberration (SA). The iterative algorithm was considered converged with a threshold of 0.01mm for apical displacement and 0.1μm for SA. Accuracy of the estimation was judged by prediction error of apical displacement and SA, as well as refractive power as an independent corneal response.

Results : Estimation of k₁ and k₂ using apical displacement led to non-unique solutions for all three cases. Different combinations of k₁ and k₂ predicted similar apical displacement and SA within the thresholds. However, average estimation error of k₁ and k₂ relative to their assumed magnitudes for the three cases was 28.8% and 18.8%, which led to an average error of 0.25D in refractive power compared to the theoretical data. In contrast, the algorithm based on SA resulted in a unique solution of k₁ and k₂ and the error was reduced to 8.5% and 2.8%. In addition, the resulting corneal responses for the three cases all matched the theoretical data, with an average difference of 0.006mm in apical displacement, 0.006μm in SA and 0.13D in refractive power.

Conclusions : For this model with regionally varying fibril distribution, an inverse analysis based on optical responses of the cornea at multiple IOPs improved the accuracy in estimating corneal collagen fibril properties compared to the result based on apical displacement.

This is an abstract that was submitted for the 2017 ARVO Annual Meeting, held in Baltimore, MD, May 7-11, 2017.