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Steven J. Petsche, Peter M. Pinsky; The Role of Collagen Interweaving in Stromal Elasticity: A Model Based on the 3-D Collagen Architecture. Invest. Ophthalmol. Vis. Sci. 2012;53(14):6796.
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The architectural organization of lamellae as viewed in the plane perpendicular to the optical axis has been well characterized by x-ray diffraction experiments. Examining the cross-section of the cornea under polarized light or with second harmonic generated imaging shows that many lamellae do not lie parallel to the corneal anterior surface but have trajectories that take them pitching through the corneal thickness with a depth-dependent distribution. We use a numerical model of the corneal microstructure to investigate the mechanics of these interweaving lamellae and demonstrate that their depth-dependent distribution explains the experimentally measured depth-dependence of the tissue shear modulus.
A new micromechanically-based model of the cornea is developed by building the stromal elasticity from lamella contributions using an averaging approach. This is accomplished by assigning a three-dimensional orientation probability for lamellae at all points in the cornea. These distributions are generated from direct interpolation of x-ray diffraction data and measurements taken from a second harmonic generated image of a human corneal cross-section. The elasticity at each point in the stroma is calculated as a weighted average of lamella elasticity over all directions using the angular probability distribution.
Data from in vitro shear experiments was used to calibrate the model. The depth-dependence of the probability distribution was set to allow the model to capture the 6 to 1 ratio of anterior to posterior shear modulus values. Other model parameters were evaluated by fitting to data from an in vivo indentation study of a single subject using an inverse methodology. To validate the model, the fit parameters were used to model a corneal inflation experiment and the results showed good agreement with the experimental data.
The model allows lamellae to interweave outside of the tangent plane and this feature was essential for matching the in vitro and in vivo experiments. All examples showed the significant effect of interweaving lamellae on the mechanics of the cornea, which has been entirely neglected in previous models. The new model offers improved accuracy for simulating refractive surgery and for modeling corneal diseases, such as keratoconus, where lamellar organization is compromised.
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