Collagen-proteoglycan structural interactions in corneal biomechanics [electronic resource] : fundamental mechanics and computational modeling

The cornea provides the protective outer covering of the eye. Its almost perfect transparency allows light to pass through it with little loss and its external curvature and refractive index are responsible for most of the bending of light rays needed to focus light on the retina. In the simplest terms, the cornea is a fiber-reinforced fluid shell that supports the intraocular pressure (IOP) applied on its inner surface. Recent developments in imaging the organization of collagen fibers throughout the cornea have provided a quantification of collagen distributions that shed light on how the collagen maintains the cornea's shape and provides elastic resiliency. In addition to the collagen, another defining feature of the cornea is its high water content. The tissue hydration level plays a vital role in transparency, with deviations from normal resulting in corneal opacity. The interfibrillar water supports the tissue fluid pressure which has both hydrostatic (IOP) and osmotic pressure components, and the osmotic pressure is actively modulated to control tissue hydration. In this thesis a comprehensive model for these elements of tissue behavior is introduced with the goal of providing a predictive model for the living human cornea. Common defects in corneal shape lead to refractive errors (e.g. astigmatism). But most sources of refractive error do not have their prime origin in the cornea (e.g. myopia, hyperopia and presbyopia). However, in case of corneal disease such as keratoconus, refractive disruption due to corneal reshaping can be extreme. The surgical accessibility of the cornea makes it a desirable target for surgical correction of many refractive conditions, and not only those arising in the cornea. As a result, surgeons have great interests in being able to accurately predict changes in corneal curvature resulting from a wide range of surgical procedures, in which tissue is cut, removed, modified, added to or redistributed or in which synthetic implants are introduced. The list of surgical approaches is remarkably long and ever-increasing; this is an area of active innovation. In this thesis, a first-principles approach to modeling the biomechanics of the cornea is presented and is demonstrated to extend current predictive capabilities for refractive procedures. The research described in this thesis is organized into three major areas. (1) The active hydration control mechanism in the living cornea and its interaction with the collagen architecture, (2) the force mechanisms that maintain the regular order of the collagen fibrils within the stroma which are necessary for corneal transparency and (3) the influence of metabolic species on osmotic pressure, and the relationship between corneal edema and metabolic processes under normal and pathological conditions. For the studies of collagen-swelling interaction, we propose a structural model of the \textit{in vivo} cornea, which accounts for tissue swelling behavior and the three-dimensional organization of stromal fibers. The cornea is modeled as an electrolyte gel in which the osmotic pressure is modulated by the active endothelial ionic transport. The stromal fiber elasticity is modeled based on three-dimensional collagen orientation probability distributions for every point in the stroma obtained by synthesizing x-ray diffraction data and second harmonic-generated imaging data. The model is implemented in a finite element framework and employed to study the effect of fiber inclination in stabilizing the corneal refractive surface with respect to changes in tissue hydration and IOP. The transparency of the human cornea depends on the pseudohexagonal arrangement of the collagen fibrils and on the maintenance of an optimal hydration -- the achievement of both depends on the presence of negatively charged glycosaminoglycans (GAGs). While the GAGs produce osmotic pressure by Donnan effect, the means by which they exert positional control of the fibril arrangement is less clear. In this thesis, a theoretical model based on equilibrium thermodynamics is proposed to describe restoring force mechanisms that may control and maintain the fibril arrangement. 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 neighboring fibrils, are described. A striking result is that the electrostatic restoring forces alone are able to reproduce the image-based distribution function of fibrils for the human cornea, and thus maintain the short-range order of the lattice-like fibril arrangement. The cornea contains cells, which require nutrient supply from the aqueous humor to maintain their metabolic activities. Disturbances in metabolite concentrations can cause corneal edema and result in loss of corneal transparency. In order to study the relationship between metabolic processes and corneal edema, we introduce a chemo-electro-mechanical model based on balance equations for the stromal fluid and metabolic species. The model describes interactions among metabolic species, charged GAGs and other mobile ions. The model is employed to predict corneal swelling with an intrastromal inlay for refractive correction of presbyopia. The results provide comprehensive explanations for clinical observations, and demonstrate the predictive capabilities of the proposed theory for refractive procedures.

Keywords: Mechanical Engineering.
Advisor: Pinsky Peter M. (Peter Michael)
Cai Wei
Kuhl Ellen