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Three-dimensional modeling of glucose and oxygen transport in the cornea with an intrastromal inlay

Session Details

Session Title: Intracorneal inlays for correction of presbyopia

Session Date/Time: Tuesday 08/10/2013 | 08:00-10:30

Paper Time: 09:18

Venue: Main Lecture Hall (Ground Floor)

First Author: : P.Pinsky USA

Co Author(s): :    A. Chayet              

Abstract Details

Purpose:

A range of corneal inlays is now commercially available in Europe. Despite efficacy, one concern of this technology is the impact that an implant will have on the health of the cornea due to disturbances in concentrations of metabolic species. Because it is very difficult to measure these effects experimentally, it is useful to create a computational model to simulate changes in the normal metabolic conditions of the tissue. In this work, a three-dimensional model is used to calculate glucose and oxygen transport in corneas with hydrogel-based intrastromal inlays. The steady-state model is applied to both the normal cornea and corneas with inlays implanted under LASIK?like flaps to evaluate changes in glucose concentration and oxygen tension. The model is also employed to evaluate the sensitivity of glucose concentration and oxygen tension to changes in parameters such as corneal thickness and depth of implantation.

Setting:

Project performed in a private university department.

Methods:

Modeling has been performed previously for transport of oxygen through contact lenses for which only a simple one-dimensional model is required due to the large size of the lens and the fact that the lens is external to the cornea (Chhabra et al., 2009). For a small inlay embedded in the cornea, a three dimensional model is required. The kinetics-based model developed here describes glucose breakdown by aerobic glycolysis requiring consumption of glucose and oxygen to produce carbon dioxide and water, and anaerobic glycolysis requiring consumption of glucose to produce lactic acid. The model has been implemented in a four-region (epithelium, stroma, endothelium, and inlay) representation of the cornea-inlay system using finite element multiphysics modeling software COMSOL (Version 4.3, 2012) to simulate steady-state oxygen, glucose and lactate ion transport in the normal cornea with and without an inlay. The normal cornea model solution is subtracted from the model solution for the cornea with inlay to produce a contour map of regions of depletion/excess concentration for each species.

Results:

Glucose, oxygen and lactate ion concentration profiles across the central corneal thickness (CCT) were obtained for a three-layer (epithelium, stroma, endothelium) normal cornea. As an example of a system that can be simulated using this technique, an axisymmetric model of the RVO Raindrop™ Near Vision Inlay under a conforming 150 um flap was analyzed with known values for oxygen permeability, glucose diffusivity, and lactate ion diffusivity. Depletion/excess concentration contours relative to the normal cornea were obtained for the three species. For glucose, the maximum depletion was 2.6% at the epithelium; the maximum concentration excess was 0.6% at the bottom of the inlay. For oxygen, the maximum depletion was 3.2% at the bottom of the inlay; the maximum concentration excess was 3.3% at the top of the inlay. The model was further employed to evaluate the sensitivity of changes in glucose, oxygen and lactate ion transport to variations in depth of placement (flap thickness) and CCT.

Conclusions:

The atmosphere supplies almost all of the oxygen needed for metabolism whereas the aqueous humor supplies all of the needed glucose. These two species are transported by diffusion across the cornea in opposite directions. Likewise anaerobic breakdown of glucose produces lactate ions which must also diffuse out of the cornea and into the aqueous chamber. When an implant is introduced into the cornea, the flux of all three species is potentially hindered by the implant which acts as an obstacle to flow, and which in turn can disturb local metabolic reactions. Furthermore, metabolic reactions are absent in the inlay. Unlike the metabolic analysis of a cornea-contact-lens system, which can be treated as a one-dimensional problem, the diffusional transport of metabolic species in the vicinity of an intrastromal implant is an intrinsically three-dimensional problem that may involve redirection of nutrients around and through the implant. In the case of the analyzed hydrogel-based RVO Raindrop inlay, the model predicted very small relative changes in glucose and oxygen concentrations. The study of parameter variations indicated that sensitivity to flap thickness (depth of placement) is similarly small, with thinner (100 um) and thicker (250 um) flaps producing maximum glucose depletion also below 5%. Simulations indicated that for a 150 um flap thickness, sensitivity to CCT was also very small with 450 um and 650 um CCT producing maximum glucose percent depletion again below 5%. In a normal cornea without an inlay, oxygen tension varies by a factor of about 6.5 whereas glucose concentration varies by a factor of about 1.4. Changes due to implantation of the corneal inlay considered in this study are therefore considered negligible.

Financial Interest:

... receives consulting fees, retainer, or contract payments from a company producing, developing or supplying the product or procedure presented, ... travel has been funded, fully or partially, by a company producing, developing or supplying the product or procedure presented, ... research is funded, fully or partially, by a company producing, developing or supplying the product or procedure presented