Mathematical Modeling of Flow and Diffusion in the Lens of the Eye

Abstract

The present work is concerned with the development of a simple transient mathematical model for the oxygen diffusion-consumption in the eye lens. The model takes into account the transport of oxygen by diffusion and consumption of oxygen is assumed to follow the Michaelis- Menten’s kinetics. The partial differential equation governing the partial pressure of oxygen has been solved by using implicit Crank-Nicholson’s iteration scheme. The prime objective of the present study is to investigate the effect of model parameters: the Michaelis- Menten’s kinetic constant and maximum rate of consumption on the partial pressure of oxygen in the mammalian lens. The computational results of the model have been presented by graphs and effects of model parameters also have been shown through the graphs and discussed. The present mathematical analysis of oxygen diffusion in the lens may contribute to the knowledge of regulation of tissue oxygen in the lens and quantitative understanding achieved through the analysis may facilitate the design of new therapeutic procedures. This analysis may help in regulating the partial pressure of oxygen in the lens.