A numerical model for metabolism, metabolite transport and edema in the human cornea

Abstract

When metabolic function in tissues such as brain, intervertebral disc and cornea is modified by disease processes or surgical intervention, the tissue may respond by swelling, a condition with significant clinical implications. A swelling response to metabolic change also signifies a change in the biomechanical behavior of the tissue. The connection between the metabolic and biomechanical states of the tissue is a complex and open problem. In this work we propose a multiphasic theory applicable to the human cornea. The model has three principal elements. The first is a diffusion–reaction model for cellular metabolism with reactions modeling aerobic respiration and anaerobic fermentation. The second element describes how metabolism-based ion production in the corneal stroma and active ion transport in the corneal endothelium modify the tissue osmotic pressure. Finally, the coupling between osmotic pressure and mechanical expansion of the tissue is described. The proposed model is assessed by predicting oxygen depletion and corneal edema due to contact lens wear, and by comparing the results with direct clinical measurements. To illustrate the interactions between metabolism and biomechanics under more extreme metabolic conditions, the model is used to predict the hypoxia and consequent swelling response of the cornea resulting from the introduction of an impermeable lamellar inlay (implant). The results confirm the importance of maintaining unhindered transport of metabolic species in the human cornea.