No abstract

The transparency of the human cornea depends on the regular lattice arrangement of the collagen fibrils and on the maintenance of an optimal hydration--the achievement of both depends on the presence of stromal proteoglycans (PGs) and their linear sidechains of negatively charged glycosaminoglycans (GAGs). Although the GAGs produce osmotic pressure by the Donnan effect, the means by which they exert positional control of the lattice is less clear. In this study, a theoretical model based on equilibrium thermodynamics is used to describe restoring force mechanisms that may control and maintain the fibril lattice and underlie corneal transparency. Electrostatic-based restoring forces that result from local charge density changes induced by fibril motion, and entropic elastic restoring forces that arise from duplexed GAG structures that bridge neighbouring fibrils, are described. The model allows for the possibility that fibrils have a GAG-dense coating that adds an additional fibril force mechanism preventing fibril aggregation. Swelling pressure predictions are used to validate the model with results showing excellent agreement with experimental data over a range of hydration from 30 to 200% of normal. The model suggests that the electrostatic restoring force is dominant, with the entropic forces from GAG duplexes being an order or more smaller. The effect of a random GAG organization, as observed in recent imaging, is considered in a dynamic model of the lattice that incorporates randomness in both the spatial distribution of GAG charge and the topology of the GAG duplexes. A striking result is that the electrostatic restoring forces alone are able to reproduce the image-based lattice distribution function for the human cornea, and thus dynamically maintain the short-range order of the lattice.

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 harmonicgenerated 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.

No abstract

In order to quantitatively predict Peierls stress, a semi-discrete variational Peierls-Nabarro model is improved by incorporating an additional gradient energy term into the energy functional. This gradient energy term is designed to effectively represent the influence of both the discreteness of atoms and the quick variations of the displacement profile in the dislocation core. Using face-centered-cubic metals as a model system for validation, we obtain a more accurate prediction of the displacement profile across the slip plane, and consequent precise Peierls stress, within few times the prediction from molecular dynamics calculations.