Numerical investigation of oxygen transport in the retinal artery with higher order accuracy by using seven and nine point finite difference technique: a comparative study

The model explains the special distribution of oxygen pressure, typically normal breathing pressure with time-dependent diffusion including depletion of oxygen by normal metabolism. The model considered here has four sections described as the inner retina, the outer retina, the fluid layer, and the choriocapillaris. The oxygen transportation is considered through these four layers with metabolism in each layer that consumes oxygen. For the numerical investigation of the diffusion model, the method of lines (MOL) with Runge–Kutta (RK4) method is implemented. For the spatial derivatives, the different 6th (seven-point) and 8th order (nine-point) finite difference schemes are used to achieve higher accuracy. Three various models are thoroughly focused in the study. The normal metabolism rate of oxygen through each layer is found in the first case while abnormal rate is predicted in the second case and in third case; the vision loss due to extensive stage of hypoxia is observed. The key finding of the study comes in terms of getting higher accuracy by seven-point and nine-point formula as compared to five-point formula. All the major results are tabulated and sketched diagrammatically. (paper)