A structural model for the in vivo human cornea including collagen-swelling interaction.

A structural model of the in vivo cornea, which accounts for tissue swelling behaviour, for the three-dimensional organization of stromal fibres and for collagen-swelling interaction, is proposed. Modelled as a binary electrolyte gel in thermodynamic equilibrium, the stromal electrostatic free energy is based on the mean-field approximation. To account for active endothelial ionic transport in the in vivo cornea, which modulates osmotic pressure and hydration, stromal mobile ions are shown to satisfy a modified Boltzmann distribution. The elasticity of the stromal collagen network is modelled based on three-dimensional collagen orientation probability distributions for every point in the stroma obtained by synthesizing X-ray diffraction data for azimuthal angle distributions and second harmonic-generated image processing for inclination angle distributions. The model is implemented in a finite-element framework and employed to predict free and confined swelling of stroma in an ionic bath. For the in vivo cornea, the model is used to predict corneal swelling due to increasing intraocular pressure (IOP) and is adapted to model swelling in Fuchs' corneal dystrophy. The biomechanical response of the in vivo cornea to a typical LASIK surgery for myopia is analysed, including tissue fluid pressure and swelling responses. The model provides a new interpretation of the corneal active hydration control (pump-leak) mechanism based on osmotic pressure modulation. The results also illustrate the structural necessity of fibre inclination in stabilizing the corneal refractive surface with respect to changes in tissue hydration and IOP.

Three-dimensional distribution of transverse collagen fibers in the anterior human corneal stroma.

PURPOSE: Recent investigations of human corneal structure and biomechanics have shown that stromal collagen fibers (lamellae) are organized into a complex, highly intertwined three-dimensional meshwork of transverse oriented fibers that increases stromal stiffness and controls corneal shape. The purpose of this study was to characterize the three-dimensional distribution of transverse collagen fibers along the major meridians of the cornea using an automated method to rapidly quantify the collagen fibers' angular orientation. METHODS: Three eyes from three donors were perfusion-fixed under pressure, excised, and cut into four quadrants. Quadrants were physically sectioned using a vibratome and scanned using nonlinear optical high-resolution macroscopy. Planes were analyzed numerically using software to identify collagen fiber angles relative to the corneal surface, stromal depth, and radial position within the anterior 250 µm of the stroma. RESULTS: The range of fiber angles and the fiber percentage having an angular displacement greater than ±3.5° relative to the corneal surface ("transverse fibers") was highest in the anterior stroma and decreased with depth. Numerical analysis showed no significant differences in fiber angles and transverse fibers between quadrants, meridians, and radial position. CONCLUSIONS: These results match our previous observation of a depth-dependent gradient in stromal collagen interconnectivity in the central cornea, and show that this gradient extends from the central cornea to the limbus. The lack of a preferred distribution of angled fibers with regard to corneal quadrant or radial position likely serves to evenly distribute loads and to avoid the formation of areas of stress concentration.

The role of 3-D collagen organization in stromal elasticity: a model based on X-ray diffraction data and second harmonic-generated images.

Examining the cross-section of the human cornea with second harmonic-generated (SHG) imaging shows that many lamellae do not lie parallel to the cornea's anterior surface but have inclined trajectories that take them through the corneal thickness with a depth-dependent distribution. A continuum mechanics-based model of stromal elasticity is developed based on orientation information extracted and synthesized from both X-ray scattering studies and SHG imaging. The model describes the effects of inclined lamella orientation by introducing a probability function that varies with depth through the stroma, which characterizes the range and distribution of lamellae at inclined angles. When combined with the preferred lamellar orientations found from X-ray scattering experiments, a fully 3-D representation of lamella orientation is achieved. Stromal elasticity is calculated by a weighted average of individual lamella properties based on the spatially varying 3-D orientation distribution. The model is calibrated with in vitro torsional shear experiments and in vivo indentation data and then validated with an in vitro inflation study. A quantitative explanation of the experimentally measured depth dependence of mechanical properties emerges from the model. The significance of the 3-D lamella orientation in the mechanics of the human cornea is demonstrated by investigating and contrasting the effects of previous modeling assumptions made on lamella orientation.

Depth-dependent transverse shear properties of the human corneal stroma.

PURPOSE: To measure the transverse shear modulus of the human corneal stroma and its profile through the depth by mechanical testing, and to assess the validity of the hypothesis that the shear modulus will be greater in the anterior third due to increased interweaving of lamellae. METHODS: Torsional rheometry was used to measure the transverse shear properties of 6 mm diameter buttons of matched human cadaver cornea pairs. One cornea from each pair was cut into thirds through the thickness with a femtosecond laser and each stromal third was tested individually. The remaining intact corneas were tested to measure full stroma shear modulus. The shear modulus from a 1% shear strain oscillatory test was measured at various levels of axial compression for all samples. RESULTS: After controlling for axial compression, the transverse shear moduli of isolated anterior layers were significantly higher than central and posterior layers. Mean modulus values at 0% axial strain were 7.71 ± 6.34 kPa in the anterior, 1.99 ± 0.45 kPa in the center, 1.31 ± 1.01 kPa in the posterior, and 9.48 ± 2.92 kPa for full thickness samples. A mean equilibrium compressive modulus of 38.7 ± 8.6 kPa at 0% axial strain was calculated from axial compression measured during the shear tests. CONCLUSIONS: Transverse shear moduli are two to three orders of magnitude lower than tensile moduli reported in the literature. The profile of shear moduli through the depth displayed a significant increase from posterior to anterior. This gradient supports the hypothesis and corresponds to the gradient of interwoven lamellae seen in imaging of stromal cross-sections.