Sensitivity analysis of corneal biomechanical and optical behavior to material and geometrical parameters.

Abstract

Purpose: To quantify the relative contribution of different material and geometrical parameters to apical displacement and optical aberrations using finite element method and a statistical approach.

Methods: A 3D anisotropic corneal model (Pandolfi, 2006) with collagen fibril distribution was generated in FEM software (ABAQUS). The sensitivity analyses were performed in two groups of parameters (1) geometrical parameters: central and peripheral corneal thickness, apical rise (H) and base diameter (2Ri), (2) radius of curvature (R) and material parameters: matrix stiffness (C₁₀), fiber dispersion (k) denoting the degree of anisotropy, fiber stiffness and nonlinearity. Ranges of the parameters were chosen from previously reported data. Outcome measures included apical displacement and changes in refractive power and spherical aberration (SA) calculated for 6 mm corneal diameter using an optical ray-tracing software at multiple intraocular pressures (IOP). Sixteen combinations of the parameters in each group were designed based on Taguchi style 16TC Factorial Array (Funkenbusch, 2004). The relative contribution of each factor to the variance in results was represented by percentage of total sum of squares (%TSS) and quantified through ANOM and ANOVA analyses.

Results: Among geometrical parameters, 2Ri influenced apical displacement most (85.6%TSS) while H was the most important factor influencing refractive power change (90.4%TSS). Change in SA was sensitive to both 2Ri and H (37.1 and 57%TSS). In the second group, k, R and C₁₀ were found to be significantly important (P<0.01) for apical displacement (80.9%TSS total at 20mmHg IOP). The significance of k was increased with higher IOP, demonstrating that fiber dispersion dominated corneal behavior. For optical behavior, k was the most contributing factor. Varying the degree of anisotropy due to fiber dispersion from highly oriented to fully isotropic induced positive SA up to 0.78µm and myopic refractive power up to 9.9D at 20mmHg IOP. In addition, the interactions of k with R or C₁₀ also had a significant impact.

Conclusions: Apical rise and base diameter were the two critical geometrical parameters while fiber dispersion was the most important material parameter contributing to corneal biomechanical and optical behavior. These parameters need to be well characterized in individualized cornea modeling in order to reliably predict surgical outcomes.